chapter 12 gases and gas laws - corona-norco unified ... · • gas particles can flow ......
TRANSCRIPT
1
Temperature
Temperature
bull is a measure of how hot or cold an object is compared to another object
bull indicates that heat flows from the object with a higher temperature to the object with a lower temperature
bull is measured using a thermometer
2
Temperature Scales
Temperature Scales
bull Kelvin
bull Celsius
bull Fahrenheit
3
A What is the temperature of freezing water
1) 0degF 2) 0degC 3) 0 K
B What is the temperature of boiling water
1) 100degF 2) 32degF 3) 373 K
C How many Celsius units are between the boiling and freezing points of water
1) 100 2) 180 3) 273
Learning Check
Temperature conversions
Celsius to Kelvin K = deg C + 273
Kelvin to Celsius deg C = K - 273
Celsius to Fahrenheit F = 95 ( deg C) + 32
Fahrenheit to Celsius C = 59 (deg F - 32)
Kelvin to Fahrenheit deg F = 95 (K - 273) + 32
Fahrenheit to Kelvin K = 59 (deg F - 32) + 273
5
Temperatures
TABLE 25
Characteristic of
Gases
The Nature of Gasesbull Gases expand to fill their containers
bull Gases are fluid ndash they flow
bull Gases have low densityndash 11000 the density of the equivalent liquid or
solid
bull Gases are compressible
bull Gases effuse and diffuse
Gases Are Fluids
bull Gases are considered fluids
bull The word fluid means ldquoany substance that can flowrdquo
bull Gas particles can flow because they are relatively far apart and therefore are able to move past each other easily
Gases Have Low Densitybull Gases have much lower densities than liquids
and solids do - WHY ndash Because of the relatively large distances between
gas particles most of the volume occupied by a gas is empty space
bull The low density of gases also means that gas particles travel relatively long distances before colliding with each other
Gases are Highly Compressiblebull Suppose you completely fill a syringe with liquid and
try to push the plunger in when the opening is plugged ndash You cannot make the space the liquid takes up become
smaller
bull The space occupied by the gas particles is very small compared with the total volume of the gas
bull Applying a small pressure will move the gas particles closer together and will decrease the volume
Gases Completely Fill a Container
bull A solid has a certain shape and volume
bull A liquid has a certain volume but takes the shape of the lower part of its container
bull In contrast a gas completely fills its container
bull Gas particles are constantly moving at high speeds and are far apart enough that they do not attracteach other as much as particles of solids and liquids do
bull Therefore a gas expands to fill the entire volume available
Gas Pressure
Gas Pressurebull Earthrsquos atmosphere commonly known as air is a mixture
of gases mainly nitrogen and oxygen
bull As gas molecules are pulled toward the surface of Earth they collide with each other and with the surface of Earth more often Collisions of gas molecules are what cause air pressure
Measuring Pressure
Pressure = Area
Force Newton (N)
m2 cm2
Units of Pressure
1 atm = 760 torr = 1013 kPa = 760 mmHg
Standard Temperature Pressure (STP)
1 atm 0degC 224 L 1 mole
100 atm 760 mmHg = 760 x 10^2 mmHg
1 Covert 100 atm to mmHg
1 atm
300atm 1013 kPa = 304 kPa
2 Covert 300 atm to kPa
1 atm
3 What is 1000 KPa in atm
1000 kPa
1013 kPa = 09872 atm
1 atm
bull Measures atmospheric pressure
bull The atmosphere exerts pressure on the surface of mercury in the dish
bull This pressure goes through the fluid and up the column of mercury
bull The mercury settles at a point where the pressure exerted downward by its weight equals the pressure exerted by the atmosphere
Measuring Pressure Using Barometer
Gas Theory
Kinetic Molecular Theorybull Particles of matter are ALWAYS in motionbull Volume of individual particles is zerobull Collisions of particles with container walls cause pressure
exerted by gasbull Particles exert no forces on each otherbull Average kinetic energy is proportional to Kelvin
temperature of a gas
bull Ideal gas- imaginary perfect bull gas fitting the theory
Checking for understanding
List 5 characteristics of gases
1
2
3
4
5
List 5 characteristics of gases according to the KMT
1
2
3
4
5
Gas Laws
Measurable Properties of Gases
Gases are described by their measurable properties
bull P = pressure exerted by the gas
bull V = total volume occupied by the gas
bull T = temperature of the gas
bull n = number of moles of the gas
atm
Units
L
K
mol
Gas Laws ndash ABCGG LAWS
bull Abull Bbull Cbull G
bull G
vogadrorsquos
oylesrsquos
harlesrsquos
ay- Lussacrsquos
n is proportional to V constant T
P is inversely proportional to V constant T
V is proportional to T constant P
P is proportional to T constant V
rahamrsquos Rate of effusion is inversely proportional to square root of gasrsquos molar mass
Pressure-Volume Relationship Boylersquos Law
bull Pressure and Volume are inversely proportional at constant temperature
bull Pressure = Volume (when one increases the other one decreases)
bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the variable
you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atmwhile the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Real World Application BOYLErsquoS LAW
bull Syringes and turkey basters are operated by Boyles Law pulling back on the plunger increases the volume inside the syringe which decreases the pressure which then corrects when liquid is drawn into the syringe thereby shrinking the volume again
bull Spray cans like spray paint and air freshener are governed by Boyles Law intense pressure inside the can pushes outward on the liquid inside the can trying to escape and forces the liquid out when the cap makes an opening
bull You breathe because of Boyles Law
bull Balloons work because of Boyles Law
bull A car (combustion) engine works when the sudden increase in pressure from the combustion of the fuel expands the cylinder and pushes on the piston causing the crankshaft to turn
Temeperature-Volume Relationship Charlersquos Law
bull Volume and temperature are proportional at constant pressure
bull (when gases are heated they expand)
bull temperature = volume (K)
bull temperature = Volume (K)
= kV
T
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constant
V1= 665 mL V2= mL
T1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 K
V1
T1
=V2
T2
V1
T1
=V2T2 =
(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
=V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293 K T2= degC
V1
T1
=V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Real World Application CHARLErsquoS LAW
bull A balloon blown up inside a warm building will shrink when it is carried to a colder area like the outdoors
bull Humans lung capacity is reduced in colder weather runners and other athletes may find it harder to perform in cold weather for this reason
bull Charles Law along with a couple other gas laws is responsible for the rising of bread and other baked goods in the oven tiny pockets of air from yeast or other ingredients are heated and expand causing the dough to inflate which ultimately results in a lighter finished baked good
bull Car (combustion) engines work by this principle the heat from the combustion of the fuel causes the cylinder to expand which pushes the piston and turns the crankshaft
Temperature-Pressure Relationships Gay-Lussacrsquos Lawbull Pressure and temperature are proportional
at constant volume
bull pressure = temperature (K)
bull pressure = temperature (K)
= kP
T
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation1 An aerosol can containing gas at 101 kPaand 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
= 110 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
= 490K or 220degC
P2= 203 kPa
T1
Real World Application GAY-LUSSACrsquoS LAW
bull Bullets and cannons are based on these principles gas super-heated by the burning of gun powder is trapped behind the bullet and expands until the bullet leaves the barrel
bull Someone opening an oven may feel a quick flow of hot air the air inside the oven is heated therefore pressurized The same is true when heating food in closed containers often a container will open to release the pressure If it does not opening the container will quickly release all the pent-up pressure which can be very dangerous because the gases inside the hot container may be super-heated This is why it is always best to open hot containers away from your body and face
Volume-Molar Relationships Avogadrorsquos Law
bull Volume and number of moles (n) areproportional at constant temperature and pressure
bull volume = number of moles
bull volume = number of moles
bull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Real World Application AVOGADROrsquoS LAW
bull Avogadros Law along with other gas laws explains why bread and other baked goods rise Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol The carbon dioxide forms bubbles and as the yeast continues to leaven the dough the increase in the number of particles of carbon dioxide increase the volume of the bubbles thereby puffing up the dough
bull Avogadros Law explains projectiles like cannons and guns the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel
bull A balloon inflates because of Avogadros Law the person blowing into the balloon is inputing a lot of gas particles so the balloon increases in volume
bull We breathe because of Avogadros Law among others the lungs expand so more gas particles can enter the lungs from the outside air (inhaling) Then the lungs contract so the waste gas particles are expelled (exhaling)
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
2
Temperature Scales
Temperature Scales
bull Kelvin
bull Celsius
bull Fahrenheit
3
A What is the temperature of freezing water
1) 0degF 2) 0degC 3) 0 K
B What is the temperature of boiling water
1) 100degF 2) 32degF 3) 373 K
C How many Celsius units are between the boiling and freezing points of water
1) 100 2) 180 3) 273
Learning Check
Temperature conversions
Celsius to Kelvin K = deg C + 273
Kelvin to Celsius deg C = K - 273
Celsius to Fahrenheit F = 95 ( deg C) + 32
Fahrenheit to Celsius C = 59 (deg F - 32)
Kelvin to Fahrenheit deg F = 95 (K - 273) + 32
Fahrenheit to Kelvin K = 59 (deg F - 32) + 273
5
Temperatures
TABLE 25
Characteristic of
Gases
The Nature of Gasesbull Gases expand to fill their containers
bull Gases are fluid ndash they flow
bull Gases have low densityndash 11000 the density of the equivalent liquid or
solid
bull Gases are compressible
bull Gases effuse and diffuse
Gases Are Fluids
bull Gases are considered fluids
bull The word fluid means ldquoany substance that can flowrdquo
bull Gas particles can flow because they are relatively far apart and therefore are able to move past each other easily
Gases Have Low Densitybull Gases have much lower densities than liquids
and solids do - WHY ndash Because of the relatively large distances between
gas particles most of the volume occupied by a gas is empty space
bull The low density of gases also means that gas particles travel relatively long distances before colliding with each other
Gases are Highly Compressiblebull Suppose you completely fill a syringe with liquid and
try to push the plunger in when the opening is plugged ndash You cannot make the space the liquid takes up become
smaller
bull The space occupied by the gas particles is very small compared with the total volume of the gas
bull Applying a small pressure will move the gas particles closer together and will decrease the volume
Gases Completely Fill a Container
bull A solid has a certain shape and volume
bull A liquid has a certain volume but takes the shape of the lower part of its container
bull In contrast a gas completely fills its container
bull Gas particles are constantly moving at high speeds and are far apart enough that they do not attracteach other as much as particles of solids and liquids do
bull Therefore a gas expands to fill the entire volume available
Gas Pressure
Gas Pressurebull Earthrsquos atmosphere commonly known as air is a mixture
of gases mainly nitrogen and oxygen
bull As gas molecules are pulled toward the surface of Earth they collide with each other and with the surface of Earth more often Collisions of gas molecules are what cause air pressure
Measuring Pressure
Pressure = Area
Force Newton (N)
m2 cm2
Units of Pressure
1 atm = 760 torr = 1013 kPa = 760 mmHg
Standard Temperature Pressure (STP)
1 atm 0degC 224 L 1 mole
100 atm 760 mmHg = 760 x 10^2 mmHg
1 Covert 100 atm to mmHg
1 atm
300atm 1013 kPa = 304 kPa
2 Covert 300 atm to kPa
1 atm
3 What is 1000 KPa in atm
1000 kPa
1013 kPa = 09872 atm
1 atm
bull Measures atmospheric pressure
bull The atmosphere exerts pressure on the surface of mercury in the dish
bull This pressure goes through the fluid and up the column of mercury
bull The mercury settles at a point where the pressure exerted downward by its weight equals the pressure exerted by the atmosphere
Measuring Pressure Using Barometer
Gas Theory
Kinetic Molecular Theorybull Particles of matter are ALWAYS in motionbull Volume of individual particles is zerobull Collisions of particles with container walls cause pressure
exerted by gasbull Particles exert no forces on each otherbull Average kinetic energy is proportional to Kelvin
temperature of a gas
bull Ideal gas- imaginary perfect bull gas fitting the theory
Checking for understanding
List 5 characteristics of gases
1
2
3
4
5
List 5 characteristics of gases according to the KMT
1
2
3
4
5
Gas Laws
Measurable Properties of Gases
Gases are described by their measurable properties
bull P = pressure exerted by the gas
bull V = total volume occupied by the gas
bull T = temperature of the gas
bull n = number of moles of the gas
atm
Units
L
K
mol
Gas Laws ndash ABCGG LAWS
bull Abull Bbull Cbull G
bull G
vogadrorsquos
oylesrsquos
harlesrsquos
ay- Lussacrsquos
n is proportional to V constant T
P is inversely proportional to V constant T
V is proportional to T constant P
P is proportional to T constant V
rahamrsquos Rate of effusion is inversely proportional to square root of gasrsquos molar mass
Pressure-Volume Relationship Boylersquos Law
bull Pressure and Volume are inversely proportional at constant temperature
bull Pressure = Volume (when one increases the other one decreases)
bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the variable
you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atmwhile the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Real World Application BOYLErsquoS LAW
bull Syringes and turkey basters are operated by Boyles Law pulling back on the plunger increases the volume inside the syringe which decreases the pressure which then corrects when liquid is drawn into the syringe thereby shrinking the volume again
bull Spray cans like spray paint and air freshener are governed by Boyles Law intense pressure inside the can pushes outward on the liquid inside the can trying to escape and forces the liquid out when the cap makes an opening
bull You breathe because of Boyles Law
bull Balloons work because of Boyles Law
bull A car (combustion) engine works when the sudden increase in pressure from the combustion of the fuel expands the cylinder and pushes on the piston causing the crankshaft to turn
Temeperature-Volume Relationship Charlersquos Law
bull Volume and temperature are proportional at constant pressure
bull (when gases are heated they expand)
bull temperature = volume (K)
bull temperature = Volume (K)
= kV
T
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constant
V1= 665 mL V2= mL
T1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 K
V1
T1
=V2
T2
V1
T1
=V2T2 =
(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
=V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293 K T2= degC
V1
T1
=V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Real World Application CHARLErsquoS LAW
bull A balloon blown up inside a warm building will shrink when it is carried to a colder area like the outdoors
bull Humans lung capacity is reduced in colder weather runners and other athletes may find it harder to perform in cold weather for this reason
bull Charles Law along with a couple other gas laws is responsible for the rising of bread and other baked goods in the oven tiny pockets of air from yeast or other ingredients are heated and expand causing the dough to inflate which ultimately results in a lighter finished baked good
bull Car (combustion) engines work by this principle the heat from the combustion of the fuel causes the cylinder to expand which pushes the piston and turns the crankshaft
Temperature-Pressure Relationships Gay-Lussacrsquos Lawbull Pressure and temperature are proportional
at constant volume
bull pressure = temperature (K)
bull pressure = temperature (K)
= kP
T
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation1 An aerosol can containing gas at 101 kPaand 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
= 110 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
= 490K or 220degC
P2= 203 kPa
T1
Real World Application GAY-LUSSACrsquoS LAW
bull Bullets and cannons are based on these principles gas super-heated by the burning of gun powder is trapped behind the bullet and expands until the bullet leaves the barrel
bull Someone opening an oven may feel a quick flow of hot air the air inside the oven is heated therefore pressurized The same is true when heating food in closed containers often a container will open to release the pressure If it does not opening the container will quickly release all the pent-up pressure which can be very dangerous because the gases inside the hot container may be super-heated This is why it is always best to open hot containers away from your body and face
Volume-Molar Relationships Avogadrorsquos Law
bull Volume and number of moles (n) areproportional at constant temperature and pressure
bull volume = number of moles
bull volume = number of moles
bull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Real World Application AVOGADROrsquoS LAW
bull Avogadros Law along with other gas laws explains why bread and other baked goods rise Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol The carbon dioxide forms bubbles and as the yeast continues to leaven the dough the increase in the number of particles of carbon dioxide increase the volume of the bubbles thereby puffing up the dough
bull Avogadros Law explains projectiles like cannons and guns the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel
bull A balloon inflates because of Avogadros Law the person blowing into the balloon is inputing a lot of gas particles so the balloon increases in volume
bull We breathe because of Avogadros Law among others the lungs expand so more gas particles can enter the lungs from the outside air (inhaling) Then the lungs contract so the waste gas particles are expelled (exhaling)
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
3
A What is the temperature of freezing water
1) 0degF 2) 0degC 3) 0 K
B What is the temperature of boiling water
1) 100degF 2) 32degF 3) 373 K
C How many Celsius units are between the boiling and freezing points of water
1) 100 2) 180 3) 273
Learning Check
Temperature conversions
Celsius to Kelvin K = deg C + 273
Kelvin to Celsius deg C = K - 273
Celsius to Fahrenheit F = 95 ( deg C) + 32
Fahrenheit to Celsius C = 59 (deg F - 32)
Kelvin to Fahrenheit deg F = 95 (K - 273) + 32
Fahrenheit to Kelvin K = 59 (deg F - 32) + 273
5
Temperatures
TABLE 25
Characteristic of
Gases
The Nature of Gasesbull Gases expand to fill their containers
bull Gases are fluid ndash they flow
bull Gases have low densityndash 11000 the density of the equivalent liquid or
solid
bull Gases are compressible
bull Gases effuse and diffuse
Gases Are Fluids
bull Gases are considered fluids
bull The word fluid means ldquoany substance that can flowrdquo
bull Gas particles can flow because they are relatively far apart and therefore are able to move past each other easily
Gases Have Low Densitybull Gases have much lower densities than liquids
and solids do - WHY ndash Because of the relatively large distances between
gas particles most of the volume occupied by a gas is empty space
bull The low density of gases also means that gas particles travel relatively long distances before colliding with each other
Gases are Highly Compressiblebull Suppose you completely fill a syringe with liquid and
try to push the plunger in when the opening is plugged ndash You cannot make the space the liquid takes up become
smaller
bull The space occupied by the gas particles is very small compared with the total volume of the gas
bull Applying a small pressure will move the gas particles closer together and will decrease the volume
Gases Completely Fill a Container
bull A solid has a certain shape and volume
bull A liquid has a certain volume but takes the shape of the lower part of its container
bull In contrast a gas completely fills its container
bull Gas particles are constantly moving at high speeds and are far apart enough that they do not attracteach other as much as particles of solids and liquids do
bull Therefore a gas expands to fill the entire volume available
Gas Pressure
Gas Pressurebull Earthrsquos atmosphere commonly known as air is a mixture
of gases mainly nitrogen and oxygen
bull As gas molecules are pulled toward the surface of Earth they collide with each other and with the surface of Earth more often Collisions of gas molecules are what cause air pressure
Measuring Pressure
Pressure = Area
Force Newton (N)
m2 cm2
Units of Pressure
1 atm = 760 torr = 1013 kPa = 760 mmHg
Standard Temperature Pressure (STP)
1 atm 0degC 224 L 1 mole
100 atm 760 mmHg = 760 x 10^2 mmHg
1 Covert 100 atm to mmHg
1 atm
300atm 1013 kPa = 304 kPa
2 Covert 300 atm to kPa
1 atm
3 What is 1000 KPa in atm
1000 kPa
1013 kPa = 09872 atm
1 atm
bull Measures atmospheric pressure
bull The atmosphere exerts pressure on the surface of mercury in the dish
bull This pressure goes through the fluid and up the column of mercury
bull The mercury settles at a point where the pressure exerted downward by its weight equals the pressure exerted by the atmosphere
Measuring Pressure Using Barometer
Gas Theory
Kinetic Molecular Theorybull Particles of matter are ALWAYS in motionbull Volume of individual particles is zerobull Collisions of particles with container walls cause pressure
exerted by gasbull Particles exert no forces on each otherbull Average kinetic energy is proportional to Kelvin
temperature of a gas
bull Ideal gas- imaginary perfect bull gas fitting the theory
Checking for understanding
List 5 characteristics of gases
1
2
3
4
5
List 5 characteristics of gases according to the KMT
1
2
3
4
5
Gas Laws
Measurable Properties of Gases
Gases are described by their measurable properties
bull P = pressure exerted by the gas
bull V = total volume occupied by the gas
bull T = temperature of the gas
bull n = number of moles of the gas
atm
Units
L
K
mol
Gas Laws ndash ABCGG LAWS
bull Abull Bbull Cbull G
bull G
vogadrorsquos
oylesrsquos
harlesrsquos
ay- Lussacrsquos
n is proportional to V constant T
P is inversely proportional to V constant T
V is proportional to T constant P
P is proportional to T constant V
rahamrsquos Rate of effusion is inversely proportional to square root of gasrsquos molar mass
Pressure-Volume Relationship Boylersquos Law
bull Pressure and Volume are inversely proportional at constant temperature
bull Pressure = Volume (when one increases the other one decreases)
bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the variable
you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atmwhile the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Real World Application BOYLErsquoS LAW
bull Syringes and turkey basters are operated by Boyles Law pulling back on the plunger increases the volume inside the syringe which decreases the pressure which then corrects when liquid is drawn into the syringe thereby shrinking the volume again
bull Spray cans like spray paint and air freshener are governed by Boyles Law intense pressure inside the can pushes outward on the liquid inside the can trying to escape and forces the liquid out when the cap makes an opening
bull You breathe because of Boyles Law
bull Balloons work because of Boyles Law
bull A car (combustion) engine works when the sudden increase in pressure from the combustion of the fuel expands the cylinder and pushes on the piston causing the crankshaft to turn
Temeperature-Volume Relationship Charlersquos Law
bull Volume and temperature are proportional at constant pressure
bull (when gases are heated they expand)
bull temperature = volume (K)
bull temperature = Volume (K)
= kV
T
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constant
V1= 665 mL V2= mL
T1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 K
V1
T1
=V2
T2
V1
T1
=V2T2 =
(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
=V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293 K T2= degC
V1
T1
=V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Real World Application CHARLErsquoS LAW
bull A balloon blown up inside a warm building will shrink when it is carried to a colder area like the outdoors
bull Humans lung capacity is reduced in colder weather runners and other athletes may find it harder to perform in cold weather for this reason
bull Charles Law along with a couple other gas laws is responsible for the rising of bread and other baked goods in the oven tiny pockets of air from yeast or other ingredients are heated and expand causing the dough to inflate which ultimately results in a lighter finished baked good
bull Car (combustion) engines work by this principle the heat from the combustion of the fuel causes the cylinder to expand which pushes the piston and turns the crankshaft
Temperature-Pressure Relationships Gay-Lussacrsquos Lawbull Pressure and temperature are proportional
at constant volume
bull pressure = temperature (K)
bull pressure = temperature (K)
= kP
T
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation1 An aerosol can containing gas at 101 kPaand 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
= 110 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
= 490K or 220degC
P2= 203 kPa
T1
Real World Application GAY-LUSSACrsquoS LAW
bull Bullets and cannons are based on these principles gas super-heated by the burning of gun powder is trapped behind the bullet and expands until the bullet leaves the barrel
bull Someone opening an oven may feel a quick flow of hot air the air inside the oven is heated therefore pressurized The same is true when heating food in closed containers often a container will open to release the pressure If it does not opening the container will quickly release all the pent-up pressure which can be very dangerous because the gases inside the hot container may be super-heated This is why it is always best to open hot containers away from your body and face
Volume-Molar Relationships Avogadrorsquos Law
bull Volume and number of moles (n) areproportional at constant temperature and pressure
bull volume = number of moles
bull volume = number of moles
bull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Real World Application AVOGADROrsquoS LAW
bull Avogadros Law along with other gas laws explains why bread and other baked goods rise Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol The carbon dioxide forms bubbles and as the yeast continues to leaven the dough the increase in the number of particles of carbon dioxide increase the volume of the bubbles thereby puffing up the dough
bull Avogadros Law explains projectiles like cannons and guns the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel
bull A balloon inflates because of Avogadros Law the person blowing into the balloon is inputing a lot of gas particles so the balloon increases in volume
bull We breathe because of Avogadros Law among others the lungs expand so more gas particles can enter the lungs from the outside air (inhaling) Then the lungs contract so the waste gas particles are expelled (exhaling)
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Temperature conversions
Celsius to Kelvin K = deg C + 273
Kelvin to Celsius deg C = K - 273
Celsius to Fahrenheit F = 95 ( deg C) + 32
Fahrenheit to Celsius C = 59 (deg F - 32)
Kelvin to Fahrenheit deg F = 95 (K - 273) + 32
Fahrenheit to Kelvin K = 59 (deg F - 32) + 273
5
Temperatures
TABLE 25
Characteristic of
Gases
The Nature of Gasesbull Gases expand to fill their containers
bull Gases are fluid ndash they flow
bull Gases have low densityndash 11000 the density of the equivalent liquid or
solid
bull Gases are compressible
bull Gases effuse and diffuse
Gases Are Fluids
bull Gases are considered fluids
bull The word fluid means ldquoany substance that can flowrdquo
bull Gas particles can flow because they are relatively far apart and therefore are able to move past each other easily
Gases Have Low Densitybull Gases have much lower densities than liquids
and solids do - WHY ndash Because of the relatively large distances between
gas particles most of the volume occupied by a gas is empty space
bull The low density of gases also means that gas particles travel relatively long distances before colliding with each other
Gases are Highly Compressiblebull Suppose you completely fill a syringe with liquid and
try to push the plunger in when the opening is plugged ndash You cannot make the space the liquid takes up become
smaller
bull The space occupied by the gas particles is very small compared with the total volume of the gas
bull Applying a small pressure will move the gas particles closer together and will decrease the volume
Gases Completely Fill a Container
bull A solid has a certain shape and volume
bull A liquid has a certain volume but takes the shape of the lower part of its container
bull In contrast a gas completely fills its container
bull Gas particles are constantly moving at high speeds and are far apart enough that they do not attracteach other as much as particles of solids and liquids do
bull Therefore a gas expands to fill the entire volume available
Gas Pressure
Gas Pressurebull Earthrsquos atmosphere commonly known as air is a mixture
of gases mainly nitrogen and oxygen
bull As gas molecules are pulled toward the surface of Earth they collide with each other and with the surface of Earth more often Collisions of gas molecules are what cause air pressure
Measuring Pressure
Pressure = Area
Force Newton (N)
m2 cm2
Units of Pressure
1 atm = 760 torr = 1013 kPa = 760 mmHg
Standard Temperature Pressure (STP)
1 atm 0degC 224 L 1 mole
100 atm 760 mmHg = 760 x 10^2 mmHg
1 Covert 100 atm to mmHg
1 atm
300atm 1013 kPa = 304 kPa
2 Covert 300 atm to kPa
1 atm
3 What is 1000 KPa in atm
1000 kPa
1013 kPa = 09872 atm
1 atm
bull Measures atmospheric pressure
bull The atmosphere exerts pressure on the surface of mercury in the dish
bull This pressure goes through the fluid and up the column of mercury
bull The mercury settles at a point where the pressure exerted downward by its weight equals the pressure exerted by the atmosphere
Measuring Pressure Using Barometer
Gas Theory
Kinetic Molecular Theorybull Particles of matter are ALWAYS in motionbull Volume of individual particles is zerobull Collisions of particles with container walls cause pressure
exerted by gasbull Particles exert no forces on each otherbull Average kinetic energy is proportional to Kelvin
temperature of a gas
bull Ideal gas- imaginary perfect bull gas fitting the theory
Checking for understanding
List 5 characteristics of gases
1
2
3
4
5
List 5 characteristics of gases according to the KMT
1
2
3
4
5
Gas Laws
Measurable Properties of Gases
Gases are described by their measurable properties
bull P = pressure exerted by the gas
bull V = total volume occupied by the gas
bull T = temperature of the gas
bull n = number of moles of the gas
atm
Units
L
K
mol
Gas Laws ndash ABCGG LAWS
bull Abull Bbull Cbull G
bull G
vogadrorsquos
oylesrsquos
harlesrsquos
ay- Lussacrsquos
n is proportional to V constant T
P is inversely proportional to V constant T
V is proportional to T constant P
P is proportional to T constant V
rahamrsquos Rate of effusion is inversely proportional to square root of gasrsquos molar mass
Pressure-Volume Relationship Boylersquos Law
bull Pressure and Volume are inversely proportional at constant temperature
bull Pressure = Volume (when one increases the other one decreases)
bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the variable
you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atmwhile the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Real World Application BOYLErsquoS LAW
bull Syringes and turkey basters are operated by Boyles Law pulling back on the plunger increases the volume inside the syringe which decreases the pressure which then corrects when liquid is drawn into the syringe thereby shrinking the volume again
bull Spray cans like spray paint and air freshener are governed by Boyles Law intense pressure inside the can pushes outward on the liquid inside the can trying to escape and forces the liquid out when the cap makes an opening
bull You breathe because of Boyles Law
bull Balloons work because of Boyles Law
bull A car (combustion) engine works when the sudden increase in pressure from the combustion of the fuel expands the cylinder and pushes on the piston causing the crankshaft to turn
Temeperature-Volume Relationship Charlersquos Law
bull Volume and temperature are proportional at constant pressure
bull (when gases are heated they expand)
bull temperature = volume (K)
bull temperature = Volume (K)
= kV
T
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constant
V1= 665 mL V2= mL
T1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 K
V1
T1
=V2
T2
V1
T1
=V2T2 =
(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
=V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293 K T2= degC
V1
T1
=V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Real World Application CHARLErsquoS LAW
bull A balloon blown up inside a warm building will shrink when it is carried to a colder area like the outdoors
bull Humans lung capacity is reduced in colder weather runners and other athletes may find it harder to perform in cold weather for this reason
bull Charles Law along with a couple other gas laws is responsible for the rising of bread and other baked goods in the oven tiny pockets of air from yeast or other ingredients are heated and expand causing the dough to inflate which ultimately results in a lighter finished baked good
bull Car (combustion) engines work by this principle the heat from the combustion of the fuel causes the cylinder to expand which pushes the piston and turns the crankshaft
Temperature-Pressure Relationships Gay-Lussacrsquos Lawbull Pressure and temperature are proportional
at constant volume
bull pressure = temperature (K)
bull pressure = temperature (K)
= kP
T
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation1 An aerosol can containing gas at 101 kPaand 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
= 110 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
= 490K or 220degC
P2= 203 kPa
T1
Real World Application GAY-LUSSACrsquoS LAW
bull Bullets and cannons are based on these principles gas super-heated by the burning of gun powder is trapped behind the bullet and expands until the bullet leaves the barrel
bull Someone opening an oven may feel a quick flow of hot air the air inside the oven is heated therefore pressurized The same is true when heating food in closed containers often a container will open to release the pressure If it does not opening the container will quickly release all the pent-up pressure which can be very dangerous because the gases inside the hot container may be super-heated This is why it is always best to open hot containers away from your body and face
Volume-Molar Relationships Avogadrorsquos Law
bull Volume and number of moles (n) areproportional at constant temperature and pressure
bull volume = number of moles
bull volume = number of moles
bull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Real World Application AVOGADROrsquoS LAW
bull Avogadros Law along with other gas laws explains why bread and other baked goods rise Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol The carbon dioxide forms bubbles and as the yeast continues to leaven the dough the increase in the number of particles of carbon dioxide increase the volume of the bubbles thereby puffing up the dough
bull Avogadros Law explains projectiles like cannons and guns the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel
bull A balloon inflates because of Avogadros Law the person blowing into the balloon is inputing a lot of gas particles so the balloon increases in volume
bull We breathe because of Avogadros Law among others the lungs expand so more gas particles can enter the lungs from the outside air (inhaling) Then the lungs contract so the waste gas particles are expelled (exhaling)
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
5
Temperatures
TABLE 25
Characteristic of
Gases
The Nature of Gasesbull Gases expand to fill their containers
bull Gases are fluid ndash they flow
bull Gases have low densityndash 11000 the density of the equivalent liquid or
solid
bull Gases are compressible
bull Gases effuse and diffuse
Gases Are Fluids
bull Gases are considered fluids
bull The word fluid means ldquoany substance that can flowrdquo
bull Gas particles can flow because they are relatively far apart and therefore are able to move past each other easily
Gases Have Low Densitybull Gases have much lower densities than liquids
and solids do - WHY ndash Because of the relatively large distances between
gas particles most of the volume occupied by a gas is empty space
bull The low density of gases also means that gas particles travel relatively long distances before colliding with each other
Gases are Highly Compressiblebull Suppose you completely fill a syringe with liquid and
try to push the plunger in when the opening is plugged ndash You cannot make the space the liquid takes up become
smaller
bull The space occupied by the gas particles is very small compared with the total volume of the gas
bull Applying a small pressure will move the gas particles closer together and will decrease the volume
Gases Completely Fill a Container
bull A solid has a certain shape and volume
bull A liquid has a certain volume but takes the shape of the lower part of its container
bull In contrast a gas completely fills its container
bull Gas particles are constantly moving at high speeds and are far apart enough that they do not attracteach other as much as particles of solids and liquids do
bull Therefore a gas expands to fill the entire volume available
Gas Pressure
Gas Pressurebull Earthrsquos atmosphere commonly known as air is a mixture
of gases mainly nitrogen and oxygen
bull As gas molecules are pulled toward the surface of Earth they collide with each other and with the surface of Earth more often Collisions of gas molecules are what cause air pressure
Measuring Pressure
Pressure = Area
Force Newton (N)
m2 cm2
Units of Pressure
1 atm = 760 torr = 1013 kPa = 760 mmHg
Standard Temperature Pressure (STP)
1 atm 0degC 224 L 1 mole
100 atm 760 mmHg = 760 x 10^2 mmHg
1 Covert 100 atm to mmHg
1 atm
300atm 1013 kPa = 304 kPa
2 Covert 300 atm to kPa
1 atm
3 What is 1000 KPa in atm
1000 kPa
1013 kPa = 09872 atm
1 atm
bull Measures atmospheric pressure
bull The atmosphere exerts pressure on the surface of mercury in the dish
bull This pressure goes through the fluid and up the column of mercury
bull The mercury settles at a point where the pressure exerted downward by its weight equals the pressure exerted by the atmosphere
Measuring Pressure Using Barometer
Gas Theory
Kinetic Molecular Theorybull Particles of matter are ALWAYS in motionbull Volume of individual particles is zerobull Collisions of particles with container walls cause pressure
exerted by gasbull Particles exert no forces on each otherbull Average kinetic energy is proportional to Kelvin
temperature of a gas
bull Ideal gas- imaginary perfect bull gas fitting the theory
Checking for understanding
List 5 characteristics of gases
1
2
3
4
5
List 5 characteristics of gases according to the KMT
1
2
3
4
5
Gas Laws
Measurable Properties of Gases
Gases are described by their measurable properties
bull P = pressure exerted by the gas
bull V = total volume occupied by the gas
bull T = temperature of the gas
bull n = number of moles of the gas
atm
Units
L
K
mol
Gas Laws ndash ABCGG LAWS
bull Abull Bbull Cbull G
bull G
vogadrorsquos
oylesrsquos
harlesrsquos
ay- Lussacrsquos
n is proportional to V constant T
P is inversely proportional to V constant T
V is proportional to T constant P
P is proportional to T constant V
rahamrsquos Rate of effusion is inversely proportional to square root of gasrsquos molar mass
Pressure-Volume Relationship Boylersquos Law
bull Pressure and Volume are inversely proportional at constant temperature
bull Pressure = Volume (when one increases the other one decreases)
bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the variable
you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atmwhile the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Real World Application BOYLErsquoS LAW
bull Syringes and turkey basters are operated by Boyles Law pulling back on the plunger increases the volume inside the syringe which decreases the pressure which then corrects when liquid is drawn into the syringe thereby shrinking the volume again
bull Spray cans like spray paint and air freshener are governed by Boyles Law intense pressure inside the can pushes outward on the liquid inside the can trying to escape and forces the liquid out when the cap makes an opening
bull You breathe because of Boyles Law
bull Balloons work because of Boyles Law
bull A car (combustion) engine works when the sudden increase in pressure from the combustion of the fuel expands the cylinder and pushes on the piston causing the crankshaft to turn
Temeperature-Volume Relationship Charlersquos Law
bull Volume and temperature are proportional at constant pressure
bull (when gases are heated they expand)
bull temperature = volume (K)
bull temperature = Volume (K)
= kV
T
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constant
V1= 665 mL V2= mL
T1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 K
V1
T1
=V2
T2
V1
T1
=V2T2 =
(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
=V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293 K T2= degC
V1
T1
=V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Real World Application CHARLErsquoS LAW
bull A balloon blown up inside a warm building will shrink when it is carried to a colder area like the outdoors
bull Humans lung capacity is reduced in colder weather runners and other athletes may find it harder to perform in cold weather for this reason
bull Charles Law along with a couple other gas laws is responsible for the rising of bread and other baked goods in the oven tiny pockets of air from yeast or other ingredients are heated and expand causing the dough to inflate which ultimately results in a lighter finished baked good
bull Car (combustion) engines work by this principle the heat from the combustion of the fuel causes the cylinder to expand which pushes the piston and turns the crankshaft
Temperature-Pressure Relationships Gay-Lussacrsquos Lawbull Pressure and temperature are proportional
at constant volume
bull pressure = temperature (K)
bull pressure = temperature (K)
= kP
T
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation1 An aerosol can containing gas at 101 kPaand 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
= 110 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
= 490K or 220degC
P2= 203 kPa
T1
Real World Application GAY-LUSSACrsquoS LAW
bull Bullets and cannons are based on these principles gas super-heated by the burning of gun powder is trapped behind the bullet and expands until the bullet leaves the barrel
bull Someone opening an oven may feel a quick flow of hot air the air inside the oven is heated therefore pressurized The same is true when heating food in closed containers often a container will open to release the pressure If it does not opening the container will quickly release all the pent-up pressure which can be very dangerous because the gases inside the hot container may be super-heated This is why it is always best to open hot containers away from your body and face
Volume-Molar Relationships Avogadrorsquos Law
bull Volume and number of moles (n) areproportional at constant temperature and pressure
bull volume = number of moles
bull volume = number of moles
bull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Real World Application AVOGADROrsquoS LAW
bull Avogadros Law along with other gas laws explains why bread and other baked goods rise Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol The carbon dioxide forms bubbles and as the yeast continues to leaven the dough the increase in the number of particles of carbon dioxide increase the volume of the bubbles thereby puffing up the dough
bull Avogadros Law explains projectiles like cannons and guns the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel
bull A balloon inflates because of Avogadros Law the person blowing into the balloon is inputing a lot of gas particles so the balloon increases in volume
bull We breathe because of Avogadros Law among others the lungs expand so more gas particles can enter the lungs from the outside air (inhaling) Then the lungs contract so the waste gas particles are expelled (exhaling)
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Characteristic of
Gases
The Nature of Gasesbull Gases expand to fill their containers
bull Gases are fluid ndash they flow
bull Gases have low densityndash 11000 the density of the equivalent liquid or
solid
bull Gases are compressible
bull Gases effuse and diffuse
Gases Are Fluids
bull Gases are considered fluids
bull The word fluid means ldquoany substance that can flowrdquo
bull Gas particles can flow because they are relatively far apart and therefore are able to move past each other easily
Gases Have Low Densitybull Gases have much lower densities than liquids
and solids do - WHY ndash Because of the relatively large distances between
gas particles most of the volume occupied by a gas is empty space
bull The low density of gases also means that gas particles travel relatively long distances before colliding with each other
Gases are Highly Compressiblebull Suppose you completely fill a syringe with liquid and
try to push the plunger in when the opening is plugged ndash You cannot make the space the liquid takes up become
smaller
bull The space occupied by the gas particles is very small compared with the total volume of the gas
bull Applying a small pressure will move the gas particles closer together and will decrease the volume
Gases Completely Fill a Container
bull A solid has a certain shape and volume
bull A liquid has a certain volume but takes the shape of the lower part of its container
bull In contrast a gas completely fills its container
bull Gas particles are constantly moving at high speeds and are far apart enough that they do not attracteach other as much as particles of solids and liquids do
bull Therefore a gas expands to fill the entire volume available
Gas Pressure
Gas Pressurebull Earthrsquos atmosphere commonly known as air is a mixture
of gases mainly nitrogen and oxygen
bull As gas molecules are pulled toward the surface of Earth they collide with each other and with the surface of Earth more often Collisions of gas molecules are what cause air pressure
Measuring Pressure
Pressure = Area
Force Newton (N)
m2 cm2
Units of Pressure
1 atm = 760 torr = 1013 kPa = 760 mmHg
Standard Temperature Pressure (STP)
1 atm 0degC 224 L 1 mole
100 atm 760 mmHg = 760 x 10^2 mmHg
1 Covert 100 atm to mmHg
1 atm
300atm 1013 kPa = 304 kPa
2 Covert 300 atm to kPa
1 atm
3 What is 1000 KPa in atm
1000 kPa
1013 kPa = 09872 atm
1 atm
bull Measures atmospheric pressure
bull The atmosphere exerts pressure on the surface of mercury in the dish
bull This pressure goes through the fluid and up the column of mercury
bull The mercury settles at a point where the pressure exerted downward by its weight equals the pressure exerted by the atmosphere
Measuring Pressure Using Barometer
Gas Theory
Kinetic Molecular Theorybull Particles of matter are ALWAYS in motionbull Volume of individual particles is zerobull Collisions of particles with container walls cause pressure
exerted by gasbull Particles exert no forces on each otherbull Average kinetic energy is proportional to Kelvin
temperature of a gas
bull Ideal gas- imaginary perfect bull gas fitting the theory
Checking for understanding
List 5 characteristics of gases
1
2
3
4
5
List 5 characteristics of gases according to the KMT
1
2
3
4
5
Gas Laws
Measurable Properties of Gases
Gases are described by their measurable properties
bull P = pressure exerted by the gas
bull V = total volume occupied by the gas
bull T = temperature of the gas
bull n = number of moles of the gas
atm
Units
L
K
mol
Gas Laws ndash ABCGG LAWS
bull Abull Bbull Cbull G
bull G
vogadrorsquos
oylesrsquos
harlesrsquos
ay- Lussacrsquos
n is proportional to V constant T
P is inversely proportional to V constant T
V is proportional to T constant P
P is proportional to T constant V
rahamrsquos Rate of effusion is inversely proportional to square root of gasrsquos molar mass
Pressure-Volume Relationship Boylersquos Law
bull Pressure and Volume are inversely proportional at constant temperature
bull Pressure = Volume (when one increases the other one decreases)
bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the variable
you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atmwhile the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Real World Application BOYLErsquoS LAW
bull Syringes and turkey basters are operated by Boyles Law pulling back on the plunger increases the volume inside the syringe which decreases the pressure which then corrects when liquid is drawn into the syringe thereby shrinking the volume again
bull Spray cans like spray paint and air freshener are governed by Boyles Law intense pressure inside the can pushes outward on the liquid inside the can trying to escape and forces the liquid out when the cap makes an opening
bull You breathe because of Boyles Law
bull Balloons work because of Boyles Law
bull A car (combustion) engine works when the sudden increase in pressure from the combustion of the fuel expands the cylinder and pushes on the piston causing the crankshaft to turn
Temeperature-Volume Relationship Charlersquos Law
bull Volume and temperature are proportional at constant pressure
bull (when gases are heated they expand)
bull temperature = volume (K)
bull temperature = Volume (K)
= kV
T
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constant
V1= 665 mL V2= mL
T1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 K
V1
T1
=V2
T2
V1
T1
=V2T2 =
(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
=V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293 K T2= degC
V1
T1
=V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Real World Application CHARLErsquoS LAW
bull A balloon blown up inside a warm building will shrink when it is carried to a colder area like the outdoors
bull Humans lung capacity is reduced in colder weather runners and other athletes may find it harder to perform in cold weather for this reason
bull Charles Law along with a couple other gas laws is responsible for the rising of bread and other baked goods in the oven tiny pockets of air from yeast or other ingredients are heated and expand causing the dough to inflate which ultimately results in a lighter finished baked good
bull Car (combustion) engines work by this principle the heat from the combustion of the fuel causes the cylinder to expand which pushes the piston and turns the crankshaft
Temperature-Pressure Relationships Gay-Lussacrsquos Lawbull Pressure and temperature are proportional
at constant volume
bull pressure = temperature (K)
bull pressure = temperature (K)
= kP
T
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation1 An aerosol can containing gas at 101 kPaand 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
= 110 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
= 490K or 220degC
P2= 203 kPa
T1
Real World Application GAY-LUSSACrsquoS LAW
bull Bullets and cannons are based on these principles gas super-heated by the burning of gun powder is trapped behind the bullet and expands until the bullet leaves the barrel
bull Someone opening an oven may feel a quick flow of hot air the air inside the oven is heated therefore pressurized The same is true when heating food in closed containers often a container will open to release the pressure If it does not opening the container will quickly release all the pent-up pressure which can be very dangerous because the gases inside the hot container may be super-heated This is why it is always best to open hot containers away from your body and face
Volume-Molar Relationships Avogadrorsquos Law
bull Volume and number of moles (n) areproportional at constant temperature and pressure
bull volume = number of moles
bull volume = number of moles
bull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Real World Application AVOGADROrsquoS LAW
bull Avogadros Law along with other gas laws explains why bread and other baked goods rise Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol The carbon dioxide forms bubbles and as the yeast continues to leaven the dough the increase in the number of particles of carbon dioxide increase the volume of the bubbles thereby puffing up the dough
bull Avogadros Law explains projectiles like cannons and guns the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel
bull A balloon inflates because of Avogadros Law the person blowing into the balloon is inputing a lot of gas particles so the balloon increases in volume
bull We breathe because of Avogadros Law among others the lungs expand so more gas particles can enter the lungs from the outside air (inhaling) Then the lungs contract so the waste gas particles are expelled (exhaling)
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
The Nature of Gasesbull Gases expand to fill their containers
bull Gases are fluid ndash they flow
bull Gases have low densityndash 11000 the density of the equivalent liquid or
solid
bull Gases are compressible
bull Gases effuse and diffuse
Gases Are Fluids
bull Gases are considered fluids
bull The word fluid means ldquoany substance that can flowrdquo
bull Gas particles can flow because they are relatively far apart and therefore are able to move past each other easily
Gases Have Low Densitybull Gases have much lower densities than liquids
and solids do - WHY ndash Because of the relatively large distances between
gas particles most of the volume occupied by a gas is empty space
bull The low density of gases also means that gas particles travel relatively long distances before colliding with each other
Gases are Highly Compressiblebull Suppose you completely fill a syringe with liquid and
try to push the plunger in when the opening is plugged ndash You cannot make the space the liquid takes up become
smaller
bull The space occupied by the gas particles is very small compared with the total volume of the gas
bull Applying a small pressure will move the gas particles closer together and will decrease the volume
Gases Completely Fill a Container
bull A solid has a certain shape and volume
bull A liquid has a certain volume but takes the shape of the lower part of its container
bull In contrast a gas completely fills its container
bull Gas particles are constantly moving at high speeds and are far apart enough that they do not attracteach other as much as particles of solids and liquids do
bull Therefore a gas expands to fill the entire volume available
Gas Pressure
Gas Pressurebull Earthrsquos atmosphere commonly known as air is a mixture
of gases mainly nitrogen and oxygen
bull As gas molecules are pulled toward the surface of Earth they collide with each other and with the surface of Earth more often Collisions of gas molecules are what cause air pressure
Measuring Pressure
Pressure = Area
Force Newton (N)
m2 cm2
Units of Pressure
1 atm = 760 torr = 1013 kPa = 760 mmHg
Standard Temperature Pressure (STP)
1 atm 0degC 224 L 1 mole
100 atm 760 mmHg = 760 x 10^2 mmHg
1 Covert 100 atm to mmHg
1 atm
300atm 1013 kPa = 304 kPa
2 Covert 300 atm to kPa
1 atm
3 What is 1000 KPa in atm
1000 kPa
1013 kPa = 09872 atm
1 atm
bull Measures atmospheric pressure
bull The atmosphere exerts pressure on the surface of mercury in the dish
bull This pressure goes through the fluid and up the column of mercury
bull The mercury settles at a point where the pressure exerted downward by its weight equals the pressure exerted by the atmosphere
Measuring Pressure Using Barometer
Gas Theory
Kinetic Molecular Theorybull Particles of matter are ALWAYS in motionbull Volume of individual particles is zerobull Collisions of particles with container walls cause pressure
exerted by gasbull Particles exert no forces on each otherbull Average kinetic energy is proportional to Kelvin
temperature of a gas
bull Ideal gas- imaginary perfect bull gas fitting the theory
Checking for understanding
List 5 characteristics of gases
1
2
3
4
5
List 5 characteristics of gases according to the KMT
1
2
3
4
5
Gas Laws
Measurable Properties of Gases
Gases are described by their measurable properties
bull P = pressure exerted by the gas
bull V = total volume occupied by the gas
bull T = temperature of the gas
bull n = number of moles of the gas
atm
Units
L
K
mol
Gas Laws ndash ABCGG LAWS
bull Abull Bbull Cbull G
bull G
vogadrorsquos
oylesrsquos
harlesrsquos
ay- Lussacrsquos
n is proportional to V constant T
P is inversely proportional to V constant T
V is proportional to T constant P
P is proportional to T constant V
rahamrsquos Rate of effusion is inversely proportional to square root of gasrsquos molar mass
Pressure-Volume Relationship Boylersquos Law
bull Pressure and Volume are inversely proportional at constant temperature
bull Pressure = Volume (when one increases the other one decreases)
bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the variable
you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atmwhile the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Real World Application BOYLErsquoS LAW
bull Syringes and turkey basters are operated by Boyles Law pulling back on the plunger increases the volume inside the syringe which decreases the pressure which then corrects when liquid is drawn into the syringe thereby shrinking the volume again
bull Spray cans like spray paint and air freshener are governed by Boyles Law intense pressure inside the can pushes outward on the liquid inside the can trying to escape and forces the liquid out when the cap makes an opening
bull You breathe because of Boyles Law
bull Balloons work because of Boyles Law
bull A car (combustion) engine works when the sudden increase in pressure from the combustion of the fuel expands the cylinder and pushes on the piston causing the crankshaft to turn
Temeperature-Volume Relationship Charlersquos Law
bull Volume and temperature are proportional at constant pressure
bull (when gases are heated they expand)
bull temperature = volume (K)
bull temperature = Volume (K)
= kV
T
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constant
V1= 665 mL V2= mL
T1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 K
V1
T1
=V2
T2
V1
T1
=V2T2 =
(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
=V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293 K T2= degC
V1
T1
=V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Real World Application CHARLErsquoS LAW
bull A balloon blown up inside a warm building will shrink when it is carried to a colder area like the outdoors
bull Humans lung capacity is reduced in colder weather runners and other athletes may find it harder to perform in cold weather for this reason
bull Charles Law along with a couple other gas laws is responsible for the rising of bread and other baked goods in the oven tiny pockets of air from yeast or other ingredients are heated and expand causing the dough to inflate which ultimately results in a lighter finished baked good
bull Car (combustion) engines work by this principle the heat from the combustion of the fuel causes the cylinder to expand which pushes the piston and turns the crankshaft
Temperature-Pressure Relationships Gay-Lussacrsquos Lawbull Pressure and temperature are proportional
at constant volume
bull pressure = temperature (K)
bull pressure = temperature (K)
= kP
T
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation1 An aerosol can containing gas at 101 kPaand 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
= 110 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
= 490K or 220degC
P2= 203 kPa
T1
Real World Application GAY-LUSSACrsquoS LAW
bull Bullets and cannons are based on these principles gas super-heated by the burning of gun powder is trapped behind the bullet and expands until the bullet leaves the barrel
bull Someone opening an oven may feel a quick flow of hot air the air inside the oven is heated therefore pressurized The same is true when heating food in closed containers often a container will open to release the pressure If it does not opening the container will quickly release all the pent-up pressure which can be very dangerous because the gases inside the hot container may be super-heated This is why it is always best to open hot containers away from your body and face
Volume-Molar Relationships Avogadrorsquos Law
bull Volume and number of moles (n) areproportional at constant temperature and pressure
bull volume = number of moles
bull volume = number of moles
bull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Real World Application AVOGADROrsquoS LAW
bull Avogadros Law along with other gas laws explains why bread and other baked goods rise Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol The carbon dioxide forms bubbles and as the yeast continues to leaven the dough the increase in the number of particles of carbon dioxide increase the volume of the bubbles thereby puffing up the dough
bull Avogadros Law explains projectiles like cannons and guns the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel
bull A balloon inflates because of Avogadros Law the person blowing into the balloon is inputing a lot of gas particles so the balloon increases in volume
bull We breathe because of Avogadros Law among others the lungs expand so more gas particles can enter the lungs from the outside air (inhaling) Then the lungs contract so the waste gas particles are expelled (exhaling)
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Gases Are Fluids
bull Gases are considered fluids
bull The word fluid means ldquoany substance that can flowrdquo
bull Gas particles can flow because they are relatively far apart and therefore are able to move past each other easily
Gases Have Low Densitybull Gases have much lower densities than liquids
and solids do - WHY ndash Because of the relatively large distances between
gas particles most of the volume occupied by a gas is empty space
bull The low density of gases also means that gas particles travel relatively long distances before colliding with each other
Gases are Highly Compressiblebull Suppose you completely fill a syringe with liquid and
try to push the plunger in when the opening is plugged ndash You cannot make the space the liquid takes up become
smaller
bull The space occupied by the gas particles is very small compared with the total volume of the gas
bull Applying a small pressure will move the gas particles closer together and will decrease the volume
Gases Completely Fill a Container
bull A solid has a certain shape and volume
bull A liquid has a certain volume but takes the shape of the lower part of its container
bull In contrast a gas completely fills its container
bull Gas particles are constantly moving at high speeds and are far apart enough that they do not attracteach other as much as particles of solids and liquids do
bull Therefore a gas expands to fill the entire volume available
Gas Pressure
Gas Pressurebull Earthrsquos atmosphere commonly known as air is a mixture
of gases mainly nitrogen and oxygen
bull As gas molecules are pulled toward the surface of Earth they collide with each other and with the surface of Earth more often Collisions of gas molecules are what cause air pressure
Measuring Pressure
Pressure = Area
Force Newton (N)
m2 cm2
Units of Pressure
1 atm = 760 torr = 1013 kPa = 760 mmHg
Standard Temperature Pressure (STP)
1 atm 0degC 224 L 1 mole
100 atm 760 mmHg = 760 x 10^2 mmHg
1 Covert 100 atm to mmHg
1 atm
300atm 1013 kPa = 304 kPa
2 Covert 300 atm to kPa
1 atm
3 What is 1000 KPa in atm
1000 kPa
1013 kPa = 09872 atm
1 atm
bull Measures atmospheric pressure
bull The atmosphere exerts pressure on the surface of mercury in the dish
bull This pressure goes through the fluid and up the column of mercury
bull The mercury settles at a point where the pressure exerted downward by its weight equals the pressure exerted by the atmosphere
Measuring Pressure Using Barometer
Gas Theory
Kinetic Molecular Theorybull Particles of matter are ALWAYS in motionbull Volume of individual particles is zerobull Collisions of particles with container walls cause pressure
exerted by gasbull Particles exert no forces on each otherbull Average kinetic energy is proportional to Kelvin
temperature of a gas
bull Ideal gas- imaginary perfect bull gas fitting the theory
Checking for understanding
List 5 characteristics of gases
1
2
3
4
5
List 5 characteristics of gases according to the KMT
1
2
3
4
5
Gas Laws
Measurable Properties of Gases
Gases are described by their measurable properties
bull P = pressure exerted by the gas
bull V = total volume occupied by the gas
bull T = temperature of the gas
bull n = number of moles of the gas
atm
Units
L
K
mol
Gas Laws ndash ABCGG LAWS
bull Abull Bbull Cbull G
bull G
vogadrorsquos
oylesrsquos
harlesrsquos
ay- Lussacrsquos
n is proportional to V constant T
P is inversely proportional to V constant T
V is proportional to T constant P
P is proportional to T constant V
rahamrsquos Rate of effusion is inversely proportional to square root of gasrsquos molar mass
Pressure-Volume Relationship Boylersquos Law
bull Pressure and Volume are inversely proportional at constant temperature
bull Pressure = Volume (when one increases the other one decreases)
bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the variable
you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atmwhile the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Real World Application BOYLErsquoS LAW
bull Syringes and turkey basters are operated by Boyles Law pulling back on the plunger increases the volume inside the syringe which decreases the pressure which then corrects when liquid is drawn into the syringe thereby shrinking the volume again
bull Spray cans like spray paint and air freshener are governed by Boyles Law intense pressure inside the can pushes outward on the liquid inside the can trying to escape and forces the liquid out when the cap makes an opening
bull You breathe because of Boyles Law
bull Balloons work because of Boyles Law
bull A car (combustion) engine works when the sudden increase in pressure from the combustion of the fuel expands the cylinder and pushes on the piston causing the crankshaft to turn
Temeperature-Volume Relationship Charlersquos Law
bull Volume and temperature are proportional at constant pressure
bull (when gases are heated they expand)
bull temperature = volume (K)
bull temperature = Volume (K)
= kV
T
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constant
V1= 665 mL V2= mL
T1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 K
V1
T1
=V2
T2
V1
T1
=V2T2 =
(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
=V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293 K T2= degC
V1
T1
=V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Real World Application CHARLErsquoS LAW
bull A balloon blown up inside a warm building will shrink when it is carried to a colder area like the outdoors
bull Humans lung capacity is reduced in colder weather runners and other athletes may find it harder to perform in cold weather for this reason
bull Charles Law along with a couple other gas laws is responsible for the rising of bread and other baked goods in the oven tiny pockets of air from yeast or other ingredients are heated and expand causing the dough to inflate which ultimately results in a lighter finished baked good
bull Car (combustion) engines work by this principle the heat from the combustion of the fuel causes the cylinder to expand which pushes the piston and turns the crankshaft
Temperature-Pressure Relationships Gay-Lussacrsquos Lawbull Pressure and temperature are proportional
at constant volume
bull pressure = temperature (K)
bull pressure = temperature (K)
= kP
T
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation1 An aerosol can containing gas at 101 kPaand 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
= 110 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
= 490K or 220degC
P2= 203 kPa
T1
Real World Application GAY-LUSSACrsquoS LAW
bull Bullets and cannons are based on these principles gas super-heated by the burning of gun powder is trapped behind the bullet and expands until the bullet leaves the barrel
bull Someone opening an oven may feel a quick flow of hot air the air inside the oven is heated therefore pressurized The same is true when heating food in closed containers often a container will open to release the pressure If it does not opening the container will quickly release all the pent-up pressure which can be very dangerous because the gases inside the hot container may be super-heated This is why it is always best to open hot containers away from your body and face
Volume-Molar Relationships Avogadrorsquos Law
bull Volume and number of moles (n) areproportional at constant temperature and pressure
bull volume = number of moles
bull volume = number of moles
bull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Real World Application AVOGADROrsquoS LAW
bull Avogadros Law along with other gas laws explains why bread and other baked goods rise Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol The carbon dioxide forms bubbles and as the yeast continues to leaven the dough the increase in the number of particles of carbon dioxide increase the volume of the bubbles thereby puffing up the dough
bull Avogadros Law explains projectiles like cannons and guns the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel
bull A balloon inflates because of Avogadros Law the person blowing into the balloon is inputing a lot of gas particles so the balloon increases in volume
bull We breathe because of Avogadros Law among others the lungs expand so more gas particles can enter the lungs from the outside air (inhaling) Then the lungs contract so the waste gas particles are expelled (exhaling)
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Gases Have Low Densitybull Gases have much lower densities than liquids
and solids do - WHY ndash Because of the relatively large distances between
gas particles most of the volume occupied by a gas is empty space
bull The low density of gases also means that gas particles travel relatively long distances before colliding with each other
Gases are Highly Compressiblebull Suppose you completely fill a syringe with liquid and
try to push the plunger in when the opening is plugged ndash You cannot make the space the liquid takes up become
smaller
bull The space occupied by the gas particles is very small compared with the total volume of the gas
bull Applying a small pressure will move the gas particles closer together and will decrease the volume
Gases Completely Fill a Container
bull A solid has a certain shape and volume
bull A liquid has a certain volume but takes the shape of the lower part of its container
bull In contrast a gas completely fills its container
bull Gas particles are constantly moving at high speeds and are far apart enough that they do not attracteach other as much as particles of solids and liquids do
bull Therefore a gas expands to fill the entire volume available
Gas Pressure
Gas Pressurebull Earthrsquos atmosphere commonly known as air is a mixture
of gases mainly nitrogen and oxygen
bull As gas molecules are pulled toward the surface of Earth they collide with each other and with the surface of Earth more often Collisions of gas molecules are what cause air pressure
Measuring Pressure
Pressure = Area
Force Newton (N)
m2 cm2
Units of Pressure
1 atm = 760 torr = 1013 kPa = 760 mmHg
Standard Temperature Pressure (STP)
1 atm 0degC 224 L 1 mole
100 atm 760 mmHg = 760 x 10^2 mmHg
1 Covert 100 atm to mmHg
1 atm
300atm 1013 kPa = 304 kPa
2 Covert 300 atm to kPa
1 atm
3 What is 1000 KPa in atm
1000 kPa
1013 kPa = 09872 atm
1 atm
bull Measures atmospheric pressure
bull The atmosphere exerts pressure on the surface of mercury in the dish
bull This pressure goes through the fluid and up the column of mercury
bull The mercury settles at a point where the pressure exerted downward by its weight equals the pressure exerted by the atmosphere
Measuring Pressure Using Barometer
Gas Theory
Kinetic Molecular Theorybull Particles of matter are ALWAYS in motionbull Volume of individual particles is zerobull Collisions of particles with container walls cause pressure
exerted by gasbull Particles exert no forces on each otherbull Average kinetic energy is proportional to Kelvin
temperature of a gas
bull Ideal gas- imaginary perfect bull gas fitting the theory
Checking for understanding
List 5 characteristics of gases
1
2
3
4
5
List 5 characteristics of gases according to the KMT
1
2
3
4
5
Gas Laws
Measurable Properties of Gases
Gases are described by their measurable properties
bull P = pressure exerted by the gas
bull V = total volume occupied by the gas
bull T = temperature of the gas
bull n = number of moles of the gas
atm
Units
L
K
mol
Gas Laws ndash ABCGG LAWS
bull Abull Bbull Cbull G
bull G
vogadrorsquos
oylesrsquos
harlesrsquos
ay- Lussacrsquos
n is proportional to V constant T
P is inversely proportional to V constant T
V is proportional to T constant P
P is proportional to T constant V
rahamrsquos Rate of effusion is inversely proportional to square root of gasrsquos molar mass
Pressure-Volume Relationship Boylersquos Law
bull Pressure and Volume are inversely proportional at constant temperature
bull Pressure = Volume (when one increases the other one decreases)
bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the variable
you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atmwhile the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Real World Application BOYLErsquoS LAW
bull Syringes and turkey basters are operated by Boyles Law pulling back on the plunger increases the volume inside the syringe which decreases the pressure which then corrects when liquid is drawn into the syringe thereby shrinking the volume again
bull Spray cans like spray paint and air freshener are governed by Boyles Law intense pressure inside the can pushes outward on the liquid inside the can trying to escape and forces the liquid out when the cap makes an opening
bull You breathe because of Boyles Law
bull Balloons work because of Boyles Law
bull A car (combustion) engine works when the sudden increase in pressure from the combustion of the fuel expands the cylinder and pushes on the piston causing the crankshaft to turn
Temeperature-Volume Relationship Charlersquos Law
bull Volume and temperature are proportional at constant pressure
bull (when gases are heated they expand)
bull temperature = volume (K)
bull temperature = Volume (K)
= kV
T
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constant
V1= 665 mL V2= mL
T1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 K
V1
T1
=V2
T2
V1
T1
=V2T2 =
(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
=V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293 K T2= degC
V1
T1
=V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Real World Application CHARLErsquoS LAW
bull A balloon blown up inside a warm building will shrink when it is carried to a colder area like the outdoors
bull Humans lung capacity is reduced in colder weather runners and other athletes may find it harder to perform in cold weather for this reason
bull Charles Law along with a couple other gas laws is responsible for the rising of bread and other baked goods in the oven tiny pockets of air from yeast or other ingredients are heated and expand causing the dough to inflate which ultimately results in a lighter finished baked good
bull Car (combustion) engines work by this principle the heat from the combustion of the fuel causes the cylinder to expand which pushes the piston and turns the crankshaft
Temperature-Pressure Relationships Gay-Lussacrsquos Lawbull Pressure and temperature are proportional
at constant volume
bull pressure = temperature (K)
bull pressure = temperature (K)
= kP
T
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation1 An aerosol can containing gas at 101 kPaand 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
= 110 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
= 490K or 220degC
P2= 203 kPa
T1
Real World Application GAY-LUSSACrsquoS LAW
bull Bullets and cannons are based on these principles gas super-heated by the burning of gun powder is trapped behind the bullet and expands until the bullet leaves the barrel
bull Someone opening an oven may feel a quick flow of hot air the air inside the oven is heated therefore pressurized The same is true when heating food in closed containers often a container will open to release the pressure If it does not opening the container will quickly release all the pent-up pressure which can be very dangerous because the gases inside the hot container may be super-heated This is why it is always best to open hot containers away from your body and face
Volume-Molar Relationships Avogadrorsquos Law
bull Volume and number of moles (n) areproportional at constant temperature and pressure
bull volume = number of moles
bull volume = number of moles
bull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Real World Application AVOGADROrsquoS LAW
bull Avogadros Law along with other gas laws explains why bread and other baked goods rise Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol The carbon dioxide forms bubbles and as the yeast continues to leaven the dough the increase in the number of particles of carbon dioxide increase the volume of the bubbles thereby puffing up the dough
bull Avogadros Law explains projectiles like cannons and guns the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel
bull A balloon inflates because of Avogadros Law the person blowing into the balloon is inputing a lot of gas particles so the balloon increases in volume
bull We breathe because of Avogadros Law among others the lungs expand so more gas particles can enter the lungs from the outside air (inhaling) Then the lungs contract so the waste gas particles are expelled (exhaling)
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Gases are Highly Compressiblebull Suppose you completely fill a syringe with liquid and
try to push the plunger in when the opening is plugged ndash You cannot make the space the liquid takes up become
smaller
bull The space occupied by the gas particles is very small compared with the total volume of the gas
bull Applying a small pressure will move the gas particles closer together and will decrease the volume
Gases Completely Fill a Container
bull A solid has a certain shape and volume
bull A liquid has a certain volume but takes the shape of the lower part of its container
bull In contrast a gas completely fills its container
bull Gas particles are constantly moving at high speeds and are far apart enough that they do not attracteach other as much as particles of solids and liquids do
bull Therefore a gas expands to fill the entire volume available
Gas Pressure
Gas Pressurebull Earthrsquos atmosphere commonly known as air is a mixture
of gases mainly nitrogen and oxygen
bull As gas molecules are pulled toward the surface of Earth they collide with each other and with the surface of Earth more often Collisions of gas molecules are what cause air pressure
Measuring Pressure
Pressure = Area
Force Newton (N)
m2 cm2
Units of Pressure
1 atm = 760 torr = 1013 kPa = 760 mmHg
Standard Temperature Pressure (STP)
1 atm 0degC 224 L 1 mole
100 atm 760 mmHg = 760 x 10^2 mmHg
1 Covert 100 atm to mmHg
1 atm
300atm 1013 kPa = 304 kPa
2 Covert 300 atm to kPa
1 atm
3 What is 1000 KPa in atm
1000 kPa
1013 kPa = 09872 atm
1 atm
bull Measures atmospheric pressure
bull The atmosphere exerts pressure on the surface of mercury in the dish
bull This pressure goes through the fluid and up the column of mercury
bull The mercury settles at a point where the pressure exerted downward by its weight equals the pressure exerted by the atmosphere
Measuring Pressure Using Barometer
Gas Theory
Kinetic Molecular Theorybull Particles of matter are ALWAYS in motionbull Volume of individual particles is zerobull Collisions of particles with container walls cause pressure
exerted by gasbull Particles exert no forces on each otherbull Average kinetic energy is proportional to Kelvin
temperature of a gas
bull Ideal gas- imaginary perfect bull gas fitting the theory
Checking for understanding
List 5 characteristics of gases
1
2
3
4
5
List 5 characteristics of gases according to the KMT
1
2
3
4
5
Gas Laws
Measurable Properties of Gases
Gases are described by their measurable properties
bull P = pressure exerted by the gas
bull V = total volume occupied by the gas
bull T = temperature of the gas
bull n = number of moles of the gas
atm
Units
L
K
mol
Gas Laws ndash ABCGG LAWS
bull Abull Bbull Cbull G
bull G
vogadrorsquos
oylesrsquos
harlesrsquos
ay- Lussacrsquos
n is proportional to V constant T
P is inversely proportional to V constant T
V is proportional to T constant P
P is proportional to T constant V
rahamrsquos Rate of effusion is inversely proportional to square root of gasrsquos molar mass
Pressure-Volume Relationship Boylersquos Law
bull Pressure and Volume are inversely proportional at constant temperature
bull Pressure = Volume (when one increases the other one decreases)
bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the variable
you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atmwhile the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Real World Application BOYLErsquoS LAW
bull Syringes and turkey basters are operated by Boyles Law pulling back on the plunger increases the volume inside the syringe which decreases the pressure which then corrects when liquid is drawn into the syringe thereby shrinking the volume again
bull Spray cans like spray paint and air freshener are governed by Boyles Law intense pressure inside the can pushes outward on the liquid inside the can trying to escape and forces the liquid out when the cap makes an opening
bull You breathe because of Boyles Law
bull Balloons work because of Boyles Law
bull A car (combustion) engine works when the sudden increase in pressure from the combustion of the fuel expands the cylinder and pushes on the piston causing the crankshaft to turn
Temeperature-Volume Relationship Charlersquos Law
bull Volume and temperature are proportional at constant pressure
bull (when gases are heated they expand)
bull temperature = volume (K)
bull temperature = Volume (K)
= kV
T
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constant
V1= 665 mL V2= mL
T1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 K
V1
T1
=V2
T2
V1
T1
=V2T2 =
(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
=V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293 K T2= degC
V1
T1
=V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Real World Application CHARLErsquoS LAW
bull A balloon blown up inside a warm building will shrink when it is carried to a colder area like the outdoors
bull Humans lung capacity is reduced in colder weather runners and other athletes may find it harder to perform in cold weather for this reason
bull Charles Law along with a couple other gas laws is responsible for the rising of bread and other baked goods in the oven tiny pockets of air from yeast or other ingredients are heated and expand causing the dough to inflate which ultimately results in a lighter finished baked good
bull Car (combustion) engines work by this principle the heat from the combustion of the fuel causes the cylinder to expand which pushes the piston and turns the crankshaft
Temperature-Pressure Relationships Gay-Lussacrsquos Lawbull Pressure and temperature are proportional
at constant volume
bull pressure = temperature (K)
bull pressure = temperature (K)
= kP
T
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation1 An aerosol can containing gas at 101 kPaand 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
= 110 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
= 490K or 220degC
P2= 203 kPa
T1
Real World Application GAY-LUSSACrsquoS LAW
bull Bullets and cannons are based on these principles gas super-heated by the burning of gun powder is trapped behind the bullet and expands until the bullet leaves the barrel
bull Someone opening an oven may feel a quick flow of hot air the air inside the oven is heated therefore pressurized The same is true when heating food in closed containers often a container will open to release the pressure If it does not opening the container will quickly release all the pent-up pressure which can be very dangerous because the gases inside the hot container may be super-heated This is why it is always best to open hot containers away from your body and face
Volume-Molar Relationships Avogadrorsquos Law
bull Volume and number of moles (n) areproportional at constant temperature and pressure
bull volume = number of moles
bull volume = number of moles
bull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Real World Application AVOGADROrsquoS LAW
bull Avogadros Law along with other gas laws explains why bread and other baked goods rise Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol The carbon dioxide forms bubbles and as the yeast continues to leaven the dough the increase in the number of particles of carbon dioxide increase the volume of the bubbles thereby puffing up the dough
bull Avogadros Law explains projectiles like cannons and guns the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel
bull A balloon inflates because of Avogadros Law the person blowing into the balloon is inputing a lot of gas particles so the balloon increases in volume
bull We breathe because of Avogadros Law among others the lungs expand so more gas particles can enter the lungs from the outside air (inhaling) Then the lungs contract so the waste gas particles are expelled (exhaling)
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Gases Completely Fill a Container
bull A solid has a certain shape and volume
bull A liquid has a certain volume but takes the shape of the lower part of its container
bull In contrast a gas completely fills its container
bull Gas particles are constantly moving at high speeds and are far apart enough that they do not attracteach other as much as particles of solids and liquids do
bull Therefore a gas expands to fill the entire volume available
Gas Pressure
Gas Pressurebull Earthrsquos atmosphere commonly known as air is a mixture
of gases mainly nitrogen and oxygen
bull As gas molecules are pulled toward the surface of Earth they collide with each other and with the surface of Earth more often Collisions of gas molecules are what cause air pressure
Measuring Pressure
Pressure = Area
Force Newton (N)
m2 cm2
Units of Pressure
1 atm = 760 torr = 1013 kPa = 760 mmHg
Standard Temperature Pressure (STP)
1 atm 0degC 224 L 1 mole
100 atm 760 mmHg = 760 x 10^2 mmHg
1 Covert 100 atm to mmHg
1 atm
300atm 1013 kPa = 304 kPa
2 Covert 300 atm to kPa
1 atm
3 What is 1000 KPa in atm
1000 kPa
1013 kPa = 09872 atm
1 atm
bull Measures atmospheric pressure
bull The atmosphere exerts pressure on the surface of mercury in the dish
bull This pressure goes through the fluid and up the column of mercury
bull The mercury settles at a point where the pressure exerted downward by its weight equals the pressure exerted by the atmosphere
Measuring Pressure Using Barometer
Gas Theory
Kinetic Molecular Theorybull Particles of matter are ALWAYS in motionbull Volume of individual particles is zerobull Collisions of particles with container walls cause pressure
exerted by gasbull Particles exert no forces on each otherbull Average kinetic energy is proportional to Kelvin
temperature of a gas
bull Ideal gas- imaginary perfect bull gas fitting the theory
Checking for understanding
List 5 characteristics of gases
1
2
3
4
5
List 5 characteristics of gases according to the KMT
1
2
3
4
5
Gas Laws
Measurable Properties of Gases
Gases are described by their measurable properties
bull P = pressure exerted by the gas
bull V = total volume occupied by the gas
bull T = temperature of the gas
bull n = number of moles of the gas
atm
Units
L
K
mol
Gas Laws ndash ABCGG LAWS
bull Abull Bbull Cbull G
bull G
vogadrorsquos
oylesrsquos
harlesrsquos
ay- Lussacrsquos
n is proportional to V constant T
P is inversely proportional to V constant T
V is proportional to T constant P
P is proportional to T constant V
rahamrsquos Rate of effusion is inversely proportional to square root of gasrsquos molar mass
Pressure-Volume Relationship Boylersquos Law
bull Pressure and Volume are inversely proportional at constant temperature
bull Pressure = Volume (when one increases the other one decreases)
bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the variable
you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atmwhile the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Real World Application BOYLErsquoS LAW
bull Syringes and turkey basters are operated by Boyles Law pulling back on the plunger increases the volume inside the syringe which decreases the pressure which then corrects when liquid is drawn into the syringe thereby shrinking the volume again
bull Spray cans like spray paint and air freshener are governed by Boyles Law intense pressure inside the can pushes outward on the liquid inside the can trying to escape and forces the liquid out when the cap makes an opening
bull You breathe because of Boyles Law
bull Balloons work because of Boyles Law
bull A car (combustion) engine works when the sudden increase in pressure from the combustion of the fuel expands the cylinder and pushes on the piston causing the crankshaft to turn
Temeperature-Volume Relationship Charlersquos Law
bull Volume and temperature are proportional at constant pressure
bull (when gases are heated they expand)
bull temperature = volume (K)
bull temperature = Volume (K)
= kV
T
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constant
V1= 665 mL V2= mL
T1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 K
V1
T1
=V2
T2
V1
T1
=V2T2 =
(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
=V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293 K T2= degC
V1
T1
=V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Real World Application CHARLErsquoS LAW
bull A balloon blown up inside a warm building will shrink when it is carried to a colder area like the outdoors
bull Humans lung capacity is reduced in colder weather runners and other athletes may find it harder to perform in cold weather for this reason
bull Charles Law along with a couple other gas laws is responsible for the rising of bread and other baked goods in the oven tiny pockets of air from yeast or other ingredients are heated and expand causing the dough to inflate which ultimately results in a lighter finished baked good
bull Car (combustion) engines work by this principle the heat from the combustion of the fuel causes the cylinder to expand which pushes the piston and turns the crankshaft
Temperature-Pressure Relationships Gay-Lussacrsquos Lawbull Pressure and temperature are proportional
at constant volume
bull pressure = temperature (K)
bull pressure = temperature (K)
= kP
T
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation1 An aerosol can containing gas at 101 kPaand 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
= 110 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
= 490K or 220degC
P2= 203 kPa
T1
Real World Application GAY-LUSSACrsquoS LAW
bull Bullets and cannons are based on these principles gas super-heated by the burning of gun powder is trapped behind the bullet and expands until the bullet leaves the barrel
bull Someone opening an oven may feel a quick flow of hot air the air inside the oven is heated therefore pressurized The same is true when heating food in closed containers often a container will open to release the pressure If it does not opening the container will quickly release all the pent-up pressure which can be very dangerous because the gases inside the hot container may be super-heated This is why it is always best to open hot containers away from your body and face
Volume-Molar Relationships Avogadrorsquos Law
bull Volume and number of moles (n) areproportional at constant temperature and pressure
bull volume = number of moles
bull volume = number of moles
bull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Real World Application AVOGADROrsquoS LAW
bull Avogadros Law along with other gas laws explains why bread and other baked goods rise Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol The carbon dioxide forms bubbles and as the yeast continues to leaven the dough the increase in the number of particles of carbon dioxide increase the volume of the bubbles thereby puffing up the dough
bull Avogadros Law explains projectiles like cannons and guns the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel
bull A balloon inflates because of Avogadros Law the person blowing into the balloon is inputing a lot of gas particles so the balloon increases in volume
bull We breathe because of Avogadros Law among others the lungs expand so more gas particles can enter the lungs from the outside air (inhaling) Then the lungs contract so the waste gas particles are expelled (exhaling)
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Gas Pressure
Gas Pressurebull Earthrsquos atmosphere commonly known as air is a mixture
of gases mainly nitrogen and oxygen
bull As gas molecules are pulled toward the surface of Earth they collide with each other and with the surface of Earth more often Collisions of gas molecules are what cause air pressure
Measuring Pressure
Pressure = Area
Force Newton (N)
m2 cm2
Units of Pressure
1 atm = 760 torr = 1013 kPa = 760 mmHg
Standard Temperature Pressure (STP)
1 atm 0degC 224 L 1 mole
100 atm 760 mmHg = 760 x 10^2 mmHg
1 Covert 100 atm to mmHg
1 atm
300atm 1013 kPa = 304 kPa
2 Covert 300 atm to kPa
1 atm
3 What is 1000 KPa in atm
1000 kPa
1013 kPa = 09872 atm
1 atm
bull Measures atmospheric pressure
bull The atmosphere exerts pressure on the surface of mercury in the dish
bull This pressure goes through the fluid and up the column of mercury
bull The mercury settles at a point where the pressure exerted downward by its weight equals the pressure exerted by the atmosphere
Measuring Pressure Using Barometer
Gas Theory
Kinetic Molecular Theorybull Particles of matter are ALWAYS in motionbull Volume of individual particles is zerobull Collisions of particles with container walls cause pressure
exerted by gasbull Particles exert no forces on each otherbull Average kinetic energy is proportional to Kelvin
temperature of a gas
bull Ideal gas- imaginary perfect bull gas fitting the theory
Checking for understanding
List 5 characteristics of gases
1
2
3
4
5
List 5 characteristics of gases according to the KMT
1
2
3
4
5
Gas Laws
Measurable Properties of Gases
Gases are described by their measurable properties
bull P = pressure exerted by the gas
bull V = total volume occupied by the gas
bull T = temperature of the gas
bull n = number of moles of the gas
atm
Units
L
K
mol
Gas Laws ndash ABCGG LAWS
bull Abull Bbull Cbull G
bull G
vogadrorsquos
oylesrsquos
harlesrsquos
ay- Lussacrsquos
n is proportional to V constant T
P is inversely proportional to V constant T
V is proportional to T constant P
P is proportional to T constant V
rahamrsquos Rate of effusion is inversely proportional to square root of gasrsquos molar mass
Pressure-Volume Relationship Boylersquos Law
bull Pressure and Volume are inversely proportional at constant temperature
bull Pressure = Volume (when one increases the other one decreases)
bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the variable
you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atmwhile the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Real World Application BOYLErsquoS LAW
bull Syringes and turkey basters are operated by Boyles Law pulling back on the plunger increases the volume inside the syringe which decreases the pressure which then corrects when liquid is drawn into the syringe thereby shrinking the volume again
bull Spray cans like spray paint and air freshener are governed by Boyles Law intense pressure inside the can pushes outward on the liquid inside the can trying to escape and forces the liquid out when the cap makes an opening
bull You breathe because of Boyles Law
bull Balloons work because of Boyles Law
bull A car (combustion) engine works when the sudden increase in pressure from the combustion of the fuel expands the cylinder and pushes on the piston causing the crankshaft to turn
Temeperature-Volume Relationship Charlersquos Law
bull Volume and temperature are proportional at constant pressure
bull (when gases are heated they expand)
bull temperature = volume (K)
bull temperature = Volume (K)
= kV
T
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constant
V1= 665 mL V2= mL
T1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 K
V1
T1
=V2
T2
V1
T1
=V2T2 =
(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
=V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293 K T2= degC
V1
T1
=V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Real World Application CHARLErsquoS LAW
bull A balloon blown up inside a warm building will shrink when it is carried to a colder area like the outdoors
bull Humans lung capacity is reduced in colder weather runners and other athletes may find it harder to perform in cold weather for this reason
bull Charles Law along with a couple other gas laws is responsible for the rising of bread and other baked goods in the oven tiny pockets of air from yeast or other ingredients are heated and expand causing the dough to inflate which ultimately results in a lighter finished baked good
bull Car (combustion) engines work by this principle the heat from the combustion of the fuel causes the cylinder to expand which pushes the piston and turns the crankshaft
Temperature-Pressure Relationships Gay-Lussacrsquos Lawbull Pressure and temperature are proportional
at constant volume
bull pressure = temperature (K)
bull pressure = temperature (K)
= kP
T
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation1 An aerosol can containing gas at 101 kPaand 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
= 110 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
= 490K or 220degC
P2= 203 kPa
T1
Real World Application GAY-LUSSACrsquoS LAW
bull Bullets and cannons are based on these principles gas super-heated by the burning of gun powder is trapped behind the bullet and expands until the bullet leaves the barrel
bull Someone opening an oven may feel a quick flow of hot air the air inside the oven is heated therefore pressurized The same is true when heating food in closed containers often a container will open to release the pressure If it does not opening the container will quickly release all the pent-up pressure which can be very dangerous because the gases inside the hot container may be super-heated This is why it is always best to open hot containers away from your body and face
Volume-Molar Relationships Avogadrorsquos Law
bull Volume and number of moles (n) areproportional at constant temperature and pressure
bull volume = number of moles
bull volume = number of moles
bull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Real World Application AVOGADROrsquoS LAW
bull Avogadros Law along with other gas laws explains why bread and other baked goods rise Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol The carbon dioxide forms bubbles and as the yeast continues to leaven the dough the increase in the number of particles of carbon dioxide increase the volume of the bubbles thereby puffing up the dough
bull Avogadros Law explains projectiles like cannons and guns the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel
bull A balloon inflates because of Avogadros Law the person blowing into the balloon is inputing a lot of gas particles so the balloon increases in volume
bull We breathe because of Avogadros Law among others the lungs expand so more gas particles can enter the lungs from the outside air (inhaling) Then the lungs contract so the waste gas particles are expelled (exhaling)
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Gas Pressurebull Earthrsquos atmosphere commonly known as air is a mixture
of gases mainly nitrogen and oxygen
bull As gas molecules are pulled toward the surface of Earth they collide with each other and with the surface of Earth more often Collisions of gas molecules are what cause air pressure
Measuring Pressure
Pressure = Area
Force Newton (N)
m2 cm2
Units of Pressure
1 atm = 760 torr = 1013 kPa = 760 mmHg
Standard Temperature Pressure (STP)
1 atm 0degC 224 L 1 mole
100 atm 760 mmHg = 760 x 10^2 mmHg
1 Covert 100 atm to mmHg
1 atm
300atm 1013 kPa = 304 kPa
2 Covert 300 atm to kPa
1 atm
3 What is 1000 KPa in atm
1000 kPa
1013 kPa = 09872 atm
1 atm
bull Measures atmospheric pressure
bull The atmosphere exerts pressure on the surface of mercury in the dish
bull This pressure goes through the fluid and up the column of mercury
bull The mercury settles at a point where the pressure exerted downward by its weight equals the pressure exerted by the atmosphere
Measuring Pressure Using Barometer
Gas Theory
Kinetic Molecular Theorybull Particles of matter are ALWAYS in motionbull Volume of individual particles is zerobull Collisions of particles with container walls cause pressure
exerted by gasbull Particles exert no forces on each otherbull Average kinetic energy is proportional to Kelvin
temperature of a gas
bull Ideal gas- imaginary perfect bull gas fitting the theory
Checking for understanding
List 5 characteristics of gases
1
2
3
4
5
List 5 characteristics of gases according to the KMT
1
2
3
4
5
Gas Laws
Measurable Properties of Gases
Gases are described by their measurable properties
bull P = pressure exerted by the gas
bull V = total volume occupied by the gas
bull T = temperature of the gas
bull n = number of moles of the gas
atm
Units
L
K
mol
Gas Laws ndash ABCGG LAWS
bull Abull Bbull Cbull G
bull G
vogadrorsquos
oylesrsquos
harlesrsquos
ay- Lussacrsquos
n is proportional to V constant T
P is inversely proportional to V constant T
V is proportional to T constant P
P is proportional to T constant V
rahamrsquos Rate of effusion is inversely proportional to square root of gasrsquos molar mass
Pressure-Volume Relationship Boylersquos Law
bull Pressure and Volume are inversely proportional at constant temperature
bull Pressure = Volume (when one increases the other one decreases)
bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the variable
you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atmwhile the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Real World Application BOYLErsquoS LAW
bull Syringes and turkey basters are operated by Boyles Law pulling back on the plunger increases the volume inside the syringe which decreases the pressure which then corrects when liquid is drawn into the syringe thereby shrinking the volume again
bull Spray cans like spray paint and air freshener are governed by Boyles Law intense pressure inside the can pushes outward on the liquid inside the can trying to escape and forces the liquid out when the cap makes an opening
bull You breathe because of Boyles Law
bull Balloons work because of Boyles Law
bull A car (combustion) engine works when the sudden increase in pressure from the combustion of the fuel expands the cylinder and pushes on the piston causing the crankshaft to turn
Temeperature-Volume Relationship Charlersquos Law
bull Volume and temperature are proportional at constant pressure
bull (when gases are heated they expand)
bull temperature = volume (K)
bull temperature = Volume (K)
= kV
T
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constant
V1= 665 mL V2= mL
T1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 K
V1
T1
=V2
T2
V1
T1
=V2T2 =
(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
=V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293 K T2= degC
V1
T1
=V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Real World Application CHARLErsquoS LAW
bull A balloon blown up inside a warm building will shrink when it is carried to a colder area like the outdoors
bull Humans lung capacity is reduced in colder weather runners and other athletes may find it harder to perform in cold weather for this reason
bull Charles Law along with a couple other gas laws is responsible for the rising of bread and other baked goods in the oven tiny pockets of air from yeast or other ingredients are heated and expand causing the dough to inflate which ultimately results in a lighter finished baked good
bull Car (combustion) engines work by this principle the heat from the combustion of the fuel causes the cylinder to expand which pushes the piston and turns the crankshaft
Temperature-Pressure Relationships Gay-Lussacrsquos Lawbull Pressure and temperature are proportional
at constant volume
bull pressure = temperature (K)
bull pressure = temperature (K)
= kP
T
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation1 An aerosol can containing gas at 101 kPaand 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
= 110 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
= 490K or 220degC
P2= 203 kPa
T1
Real World Application GAY-LUSSACrsquoS LAW
bull Bullets and cannons are based on these principles gas super-heated by the burning of gun powder is trapped behind the bullet and expands until the bullet leaves the barrel
bull Someone opening an oven may feel a quick flow of hot air the air inside the oven is heated therefore pressurized The same is true when heating food in closed containers often a container will open to release the pressure If it does not opening the container will quickly release all the pent-up pressure which can be very dangerous because the gases inside the hot container may be super-heated This is why it is always best to open hot containers away from your body and face
Volume-Molar Relationships Avogadrorsquos Law
bull Volume and number of moles (n) areproportional at constant temperature and pressure
bull volume = number of moles
bull volume = number of moles
bull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Real World Application AVOGADROrsquoS LAW
bull Avogadros Law along with other gas laws explains why bread and other baked goods rise Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol The carbon dioxide forms bubbles and as the yeast continues to leaven the dough the increase in the number of particles of carbon dioxide increase the volume of the bubbles thereby puffing up the dough
bull Avogadros Law explains projectiles like cannons and guns the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel
bull A balloon inflates because of Avogadros Law the person blowing into the balloon is inputing a lot of gas particles so the balloon increases in volume
bull We breathe because of Avogadros Law among others the lungs expand so more gas particles can enter the lungs from the outside air (inhaling) Then the lungs contract so the waste gas particles are expelled (exhaling)
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Measuring Pressure
Pressure = Area
Force Newton (N)
m2 cm2
Units of Pressure
1 atm = 760 torr = 1013 kPa = 760 mmHg
Standard Temperature Pressure (STP)
1 atm 0degC 224 L 1 mole
100 atm 760 mmHg = 760 x 10^2 mmHg
1 Covert 100 atm to mmHg
1 atm
300atm 1013 kPa = 304 kPa
2 Covert 300 atm to kPa
1 atm
3 What is 1000 KPa in atm
1000 kPa
1013 kPa = 09872 atm
1 atm
bull Measures atmospheric pressure
bull The atmosphere exerts pressure on the surface of mercury in the dish
bull This pressure goes through the fluid and up the column of mercury
bull The mercury settles at a point where the pressure exerted downward by its weight equals the pressure exerted by the atmosphere
Measuring Pressure Using Barometer
Gas Theory
Kinetic Molecular Theorybull Particles of matter are ALWAYS in motionbull Volume of individual particles is zerobull Collisions of particles with container walls cause pressure
exerted by gasbull Particles exert no forces on each otherbull Average kinetic energy is proportional to Kelvin
temperature of a gas
bull Ideal gas- imaginary perfect bull gas fitting the theory
Checking for understanding
List 5 characteristics of gases
1
2
3
4
5
List 5 characteristics of gases according to the KMT
1
2
3
4
5
Gas Laws
Measurable Properties of Gases
Gases are described by their measurable properties
bull P = pressure exerted by the gas
bull V = total volume occupied by the gas
bull T = temperature of the gas
bull n = number of moles of the gas
atm
Units
L
K
mol
Gas Laws ndash ABCGG LAWS
bull Abull Bbull Cbull G
bull G
vogadrorsquos
oylesrsquos
harlesrsquos
ay- Lussacrsquos
n is proportional to V constant T
P is inversely proportional to V constant T
V is proportional to T constant P
P is proportional to T constant V
rahamrsquos Rate of effusion is inversely proportional to square root of gasrsquos molar mass
Pressure-Volume Relationship Boylersquos Law
bull Pressure and Volume are inversely proportional at constant temperature
bull Pressure = Volume (when one increases the other one decreases)
bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the variable
you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atmwhile the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Real World Application BOYLErsquoS LAW
bull Syringes and turkey basters are operated by Boyles Law pulling back on the plunger increases the volume inside the syringe which decreases the pressure which then corrects when liquid is drawn into the syringe thereby shrinking the volume again
bull Spray cans like spray paint and air freshener are governed by Boyles Law intense pressure inside the can pushes outward on the liquid inside the can trying to escape and forces the liquid out when the cap makes an opening
bull You breathe because of Boyles Law
bull Balloons work because of Boyles Law
bull A car (combustion) engine works when the sudden increase in pressure from the combustion of the fuel expands the cylinder and pushes on the piston causing the crankshaft to turn
Temeperature-Volume Relationship Charlersquos Law
bull Volume and temperature are proportional at constant pressure
bull (when gases are heated they expand)
bull temperature = volume (K)
bull temperature = Volume (K)
= kV
T
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constant
V1= 665 mL V2= mL
T1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 K
V1
T1
=V2
T2
V1
T1
=V2T2 =
(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
=V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293 K T2= degC
V1
T1
=V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Real World Application CHARLErsquoS LAW
bull A balloon blown up inside a warm building will shrink when it is carried to a colder area like the outdoors
bull Humans lung capacity is reduced in colder weather runners and other athletes may find it harder to perform in cold weather for this reason
bull Charles Law along with a couple other gas laws is responsible for the rising of bread and other baked goods in the oven tiny pockets of air from yeast or other ingredients are heated and expand causing the dough to inflate which ultimately results in a lighter finished baked good
bull Car (combustion) engines work by this principle the heat from the combustion of the fuel causes the cylinder to expand which pushes the piston and turns the crankshaft
Temperature-Pressure Relationships Gay-Lussacrsquos Lawbull Pressure and temperature are proportional
at constant volume
bull pressure = temperature (K)
bull pressure = temperature (K)
= kP
T
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation1 An aerosol can containing gas at 101 kPaand 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
= 110 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
= 490K or 220degC
P2= 203 kPa
T1
Real World Application GAY-LUSSACrsquoS LAW
bull Bullets and cannons are based on these principles gas super-heated by the burning of gun powder is trapped behind the bullet and expands until the bullet leaves the barrel
bull Someone opening an oven may feel a quick flow of hot air the air inside the oven is heated therefore pressurized The same is true when heating food in closed containers often a container will open to release the pressure If it does not opening the container will quickly release all the pent-up pressure which can be very dangerous because the gases inside the hot container may be super-heated This is why it is always best to open hot containers away from your body and face
Volume-Molar Relationships Avogadrorsquos Law
bull Volume and number of moles (n) areproportional at constant temperature and pressure
bull volume = number of moles
bull volume = number of moles
bull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Real World Application AVOGADROrsquoS LAW
bull Avogadros Law along with other gas laws explains why bread and other baked goods rise Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol The carbon dioxide forms bubbles and as the yeast continues to leaven the dough the increase in the number of particles of carbon dioxide increase the volume of the bubbles thereby puffing up the dough
bull Avogadros Law explains projectiles like cannons and guns the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel
bull A balloon inflates because of Avogadros Law the person blowing into the balloon is inputing a lot of gas particles so the balloon increases in volume
bull We breathe because of Avogadros Law among others the lungs expand so more gas particles can enter the lungs from the outside air (inhaling) Then the lungs contract so the waste gas particles are expelled (exhaling)
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
100 atm 760 mmHg = 760 x 10^2 mmHg
1 Covert 100 atm to mmHg
1 atm
300atm 1013 kPa = 304 kPa
2 Covert 300 atm to kPa
1 atm
3 What is 1000 KPa in atm
1000 kPa
1013 kPa = 09872 atm
1 atm
bull Measures atmospheric pressure
bull The atmosphere exerts pressure on the surface of mercury in the dish
bull This pressure goes through the fluid and up the column of mercury
bull The mercury settles at a point where the pressure exerted downward by its weight equals the pressure exerted by the atmosphere
Measuring Pressure Using Barometer
Gas Theory
Kinetic Molecular Theorybull Particles of matter are ALWAYS in motionbull Volume of individual particles is zerobull Collisions of particles with container walls cause pressure
exerted by gasbull Particles exert no forces on each otherbull Average kinetic energy is proportional to Kelvin
temperature of a gas
bull Ideal gas- imaginary perfect bull gas fitting the theory
Checking for understanding
List 5 characteristics of gases
1
2
3
4
5
List 5 characteristics of gases according to the KMT
1
2
3
4
5
Gas Laws
Measurable Properties of Gases
Gases are described by their measurable properties
bull P = pressure exerted by the gas
bull V = total volume occupied by the gas
bull T = temperature of the gas
bull n = number of moles of the gas
atm
Units
L
K
mol
Gas Laws ndash ABCGG LAWS
bull Abull Bbull Cbull G
bull G
vogadrorsquos
oylesrsquos
harlesrsquos
ay- Lussacrsquos
n is proportional to V constant T
P is inversely proportional to V constant T
V is proportional to T constant P
P is proportional to T constant V
rahamrsquos Rate of effusion is inversely proportional to square root of gasrsquos molar mass
Pressure-Volume Relationship Boylersquos Law
bull Pressure and Volume are inversely proportional at constant temperature
bull Pressure = Volume (when one increases the other one decreases)
bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the variable
you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atmwhile the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Real World Application BOYLErsquoS LAW
bull Syringes and turkey basters are operated by Boyles Law pulling back on the plunger increases the volume inside the syringe which decreases the pressure which then corrects when liquid is drawn into the syringe thereby shrinking the volume again
bull Spray cans like spray paint and air freshener are governed by Boyles Law intense pressure inside the can pushes outward on the liquid inside the can trying to escape and forces the liquid out when the cap makes an opening
bull You breathe because of Boyles Law
bull Balloons work because of Boyles Law
bull A car (combustion) engine works when the sudden increase in pressure from the combustion of the fuel expands the cylinder and pushes on the piston causing the crankshaft to turn
Temeperature-Volume Relationship Charlersquos Law
bull Volume and temperature are proportional at constant pressure
bull (when gases are heated they expand)
bull temperature = volume (K)
bull temperature = Volume (K)
= kV
T
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constant
V1= 665 mL V2= mL
T1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 K
V1
T1
=V2
T2
V1
T1
=V2T2 =
(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
=V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293 K T2= degC
V1
T1
=V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Real World Application CHARLErsquoS LAW
bull A balloon blown up inside a warm building will shrink when it is carried to a colder area like the outdoors
bull Humans lung capacity is reduced in colder weather runners and other athletes may find it harder to perform in cold weather for this reason
bull Charles Law along with a couple other gas laws is responsible for the rising of bread and other baked goods in the oven tiny pockets of air from yeast or other ingredients are heated and expand causing the dough to inflate which ultimately results in a lighter finished baked good
bull Car (combustion) engines work by this principle the heat from the combustion of the fuel causes the cylinder to expand which pushes the piston and turns the crankshaft
Temperature-Pressure Relationships Gay-Lussacrsquos Lawbull Pressure and temperature are proportional
at constant volume
bull pressure = temperature (K)
bull pressure = temperature (K)
= kP
T
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation1 An aerosol can containing gas at 101 kPaand 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
= 110 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
= 490K or 220degC
P2= 203 kPa
T1
Real World Application GAY-LUSSACrsquoS LAW
bull Bullets and cannons are based on these principles gas super-heated by the burning of gun powder is trapped behind the bullet and expands until the bullet leaves the barrel
bull Someone opening an oven may feel a quick flow of hot air the air inside the oven is heated therefore pressurized The same is true when heating food in closed containers often a container will open to release the pressure If it does not opening the container will quickly release all the pent-up pressure which can be very dangerous because the gases inside the hot container may be super-heated This is why it is always best to open hot containers away from your body and face
Volume-Molar Relationships Avogadrorsquos Law
bull Volume and number of moles (n) areproportional at constant temperature and pressure
bull volume = number of moles
bull volume = number of moles
bull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Real World Application AVOGADROrsquoS LAW
bull Avogadros Law along with other gas laws explains why bread and other baked goods rise Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol The carbon dioxide forms bubbles and as the yeast continues to leaven the dough the increase in the number of particles of carbon dioxide increase the volume of the bubbles thereby puffing up the dough
bull Avogadros Law explains projectiles like cannons and guns the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel
bull A balloon inflates because of Avogadros Law the person blowing into the balloon is inputing a lot of gas particles so the balloon increases in volume
bull We breathe because of Avogadros Law among others the lungs expand so more gas particles can enter the lungs from the outside air (inhaling) Then the lungs contract so the waste gas particles are expelled (exhaling)
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
bull Measures atmospheric pressure
bull The atmosphere exerts pressure on the surface of mercury in the dish
bull This pressure goes through the fluid and up the column of mercury
bull The mercury settles at a point where the pressure exerted downward by its weight equals the pressure exerted by the atmosphere
Measuring Pressure Using Barometer
Gas Theory
Kinetic Molecular Theorybull Particles of matter are ALWAYS in motionbull Volume of individual particles is zerobull Collisions of particles with container walls cause pressure
exerted by gasbull Particles exert no forces on each otherbull Average kinetic energy is proportional to Kelvin
temperature of a gas
bull Ideal gas- imaginary perfect bull gas fitting the theory
Checking for understanding
List 5 characteristics of gases
1
2
3
4
5
List 5 characteristics of gases according to the KMT
1
2
3
4
5
Gas Laws
Measurable Properties of Gases
Gases are described by their measurable properties
bull P = pressure exerted by the gas
bull V = total volume occupied by the gas
bull T = temperature of the gas
bull n = number of moles of the gas
atm
Units
L
K
mol
Gas Laws ndash ABCGG LAWS
bull Abull Bbull Cbull G
bull G
vogadrorsquos
oylesrsquos
harlesrsquos
ay- Lussacrsquos
n is proportional to V constant T
P is inversely proportional to V constant T
V is proportional to T constant P
P is proportional to T constant V
rahamrsquos Rate of effusion is inversely proportional to square root of gasrsquos molar mass
Pressure-Volume Relationship Boylersquos Law
bull Pressure and Volume are inversely proportional at constant temperature
bull Pressure = Volume (when one increases the other one decreases)
bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the variable
you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atmwhile the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Real World Application BOYLErsquoS LAW
bull Syringes and turkey basters are operated by Boyles Law pulling back on the plunger increases the volume inside the syringe which decreases the pressure which then corrects when liquid is drawn into the syringe thereby shrinking the volume again
bull Spray cans like spray paint and air freshener are governed by Boyles Law intense pressure inside the can pushes outward on the liquid inside the can trying to escape and forces the liquid out when the cap makes an opening
bull You breathe because of Boyles Law
bull Balloons work because of Boyles Law
bull A car (combustion) engine works when the sudden increase in pressure from the combustion of the fuel expands the cylinder and pushes on the piston causing the crankshaft to turn
Temeperature-Volume Relationship Charlersquos Law
bull Volume and temperature are proportional at constant pressure
bull (when gases are heated they expand)
bull temperature = volume (K)
bull temperature = Volume (K)
= kV
T
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constant
V1= 665 mL V2= mL
T1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 K
V1
T1
=V2
T2
V1
T1
=V2T2 =
(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
=V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293 K T2= degC
V1
T1
=V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Real World Application CHARLErsquoS LAW
bull A balloon blown up inside a warm building will shrink when it is carried to a colder area like the outdoors
bull Humans lung capacity is reduced in colder weather runners and other athletes may find it harder to perform in cold weather for this reason
bull Charles Law along with a couple other gas laws is responsible for the rising of bread and other baked goods in the oven tiny pockets of air from yeast or other ingredients are heated and expand causing the dough to inflate which ultimately results in a lighter finished baked good
bull Car (combustion) engines work by this principle the heat from the combustion of the fuel causes the cylinder to expand which pushes the piston and turns the crankshaft
Temperature-Pressure Relationships Gay-Lussacrsquos Lawbull Pressure and temperature are proportional
at constant volume
bull pressure = temperature (K)
bull pressure = temperature (K)
= kP
T
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation1 An aerosol can containing gas at 101 kPaand 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
= 110 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
= 490K or 220degC
P2= 203 kPa
T1
Real World Application GAY-LUSSACrsquoS LAW
bull Bullets and cannons are based on these principles gas super-heated by the burning of gun powder is trapped behind the bullet and expands until the bullet leaves the barrel
bull Someone opening an oven may feel a quick flow of hot air the air inside the oven is heated therefore pressurized The same is true when heating food in closed containers often a container will open to release the pressure If it does not opening the container will quickly release all the pent-up pressure which can be very dangerous because the gases inside the hot container may be super-heated This is why it is always best to open hot containers away from your body and face
Volume-Molar Relationships Avogadrorsquos Law
bull Volume and number of moles (n) areproportional at constant temperature and pressure
bull volume = number of moles
bull volume = number of moles
bull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Real World Application AVOGADROrsquoS LAW
bull Avogadros Law along with other gas laws explains why bread and other baked goods rise Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol The carbon dioxide forms bubbles and as the yeast continues to leaven the dough the increase in the number of particles of carbon dioxide increase the volume of the bubbles thereby puffing up the dough
bull Avogadros Law explains projectiles like cannons and guns the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel
bull A balloon inflates because of Avogadros Law the person blowing into the balloon is inputing a lot of gas particles so the balloon increases in volume
bull We breathe because of Avogadros Law among others the lungs expand so more gas particles can enter the lungs from the outside air (inhaling) Then the lungs contract so the waste gas particles are expelled (exhaling)
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Gas Theory
Kinetic Molecular Theorybull Particles of matter are ALWAYS in motionbull Volume of individual particles is zerobull Collisions of particles with container walls cause pressure
exerted by gasbull Particles exert no forces on each otherbull Average kinetic energy is proportional to Kelvin
temperature of a gas
bull Ideal gas- imaginary perfect bull gas fitting the theory
Checking for understanding
List 5 characteristics of gases
1
2
3
4
5
List 5 characteristics of gases according to the KMT
1
2
3
4
5
Gas Laws
Measurable Properties of Gases
Gases are described by their measurable properties
bull P = pressure exerted by the gas
bull V = total volume occupied by the gas
bull T = temperature of the gas
bull n = number of moles of the gas
atm
Units
L
K
mol
Gas Laws ndash ABCGG LAWS
bull Abull Bbull Cbull G
bull G
vogadrorsquos
oylesrsquos
harlesrsquos
ay- Lussacrsquos
n is proportional to V constant T
P is inversely proportional to V constant T
V is proportional to T constant P
P is proportional to T constant V
rahamrsquos Rate of effusion is inversely proportional to square root of gasrsquos molar mass
Pressure-Volume Relationship Boylersquos Law
bull Pressure and Volume are inversely proportional at constant temperature
bull Pressure = Volume (when one increases the other one decreases)
bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the variable
you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atmwhile the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Real World Application BOYLErsquoS LAW
bull Syringes and turkey basters are operated by Boyles Law pulling back on the plunger increases the volume inside the syringe which decreases the pressure which then corrects when liquid is drawn into the syringe thereby shrinking the volume again
bull Spray cans like spray paint and air freshener are governed by Boyles Law intense pressure inside the can pushes outward on the liquid inside the can trying to escape and forces the liquid out when the cap makes an opening
bull You breathe because of Boyles Law
bull Balloons work because of Boyles Law
bull A car (combustion) engine works when the sudden increase in pressure from the combustion of the fuel expands the cylinder and pushes on the piston causing the crankshaft to turn
Temeperature-Volume Relationship Charlersquos Law
bull Volume and temperature are proportional at constant pressure
bull (when gases are heated they expand)
bull temperature = volume (K)
bull temperature = Volume (K)
= kV
T
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constant
V1= 665 mL V2= mL
T1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 K
V1
T1
=V2
T2
V1
T1
=V2T2 =
(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
=V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293 K T2= degC
V1
T1
=V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Real World Application CHARLErsquoS LAW
bull A balloon blown up inside a warm building will shrink when it is carried to a colder area like the outdoors
bull Humans lung capacity is reduced in colder weather runners and other athletes may find it harder to perform in cold weather for this reason
bull Charles Law along with a couple other gas laws is responsible for the rising of bread and other baked goods in the oven tiny pockets of air from yeast or other ingredients are heated and expand causing the dough to inflate which ultimately results in a lighter finished baked good
bull Car (combustion) engines work by this principle the heat from the combustion of the fuel causes the cylinder to expand which pushes the piston and turns the crankshaft
Temperature-Pressure Relationships Gay-Lussacrsquos Lawbull Pressure and temperature are proportional
at constant volume
bull pressure = temperature (K)
bull pressure = temperature (K)
= kP
T
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation1 An aerosol can containing gas at 101 kPaand 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
= 110 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
= 490K or 220degC
P2= 203 kPa
T1
Real World Application GAY-LUSSACrsquoS LAW
bull Bullets and cannons are based on these principles gas super-heated by the burning of gun powder is trapped behind the bullet and expands until the bullet leaves the barrel
bull Someone opening an oven may feel a quick flow of hot air the air inside the oven is heated therefore pressurized The same is true when heating food in closed containers often a container will open to release the pressure If it does not opening the container will quickly release all the pent-up pressure which can be very dangerous because the gases inside the hot container may be super-heated This is why it is always best to open hot containers away from your body and face
Volume-Molar Relationships Avogadrorsquos Law
bull Volume and number of moles (n) areproportional at constant temperature and pressure
bull volume = number of moles
bull volume = number of moles
bull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Real World Application AVOGADROrsquoS LAW
bull Avogadros Law along with other gas laws explains why bread and other baked goods rise Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol The carbon dioxide forms bubbles and as the yeast continues to leaven the dough the increase in the number of particles of carbon dioxide increase the volume of the bubbles thereby puffing up the dough
bull Avogadros Law explains projectiles like cannons and guns the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel
bull A balloon inflates because of Avogadros Law the person blowing into the balloon is inputing a lot of gas particles so the balloon increases in volume
bull We breathe because of Avogadros Law among others the lungs expand so more gas particles can enter the lungs from the outside air (inhaling) Then the lungs contract so the waste gas particles are expelled (exhaling)
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Kinetic Molecular Theorybull Particles of matter are ALWAYS in motionbull Volume of individual particles is zerobull Collisions of particles with container walls cause pressure
exerted by gasbull Particles exert no forces on each otherbull Average kinetic energy is proportional to Kelvin
temperature of a gas
bull Ideal gas- imaginary perfect bull gas fitting the theory
Checking for understanding
List 5 characteristics of gases
1
2
3
4
5
List 5 characteristics of gases according to the KMT
1
2
3
4
5
Gas Laws
Measurable Properties of Gases
Gases are described by their measurable properties
bull P = pressure exerted by the gas
bull V = total volume occupied by the gas
bull T = temperature of the gas
bull n = number of moles of the gas
atm
Units
L
K
mol
Gas Laws ndash ABCGG LAWS
bull Abull Bbull Cbull G
bull G
vogadrorsquos
oylesrsquos
harlesrsquos
ay- Lussacrsquos
n is proportional to V constant T
P is inversely proportional to V constant T
V is proportional to T constant P
P is proportional to T constant V
rahamrsquos Rate of effusion is inversely proportional to square root of gasrsquos molar mass
Pressure-Volume Relationship Boylersquos Law
bull Pressure and Volume are inversely proportional at constant temperature
bull Pressure = Volume (when one increases the other one decreases)
bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the variable
you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atmwhile the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Real World Application BOYLErsquoS LAW
bull Syringes and turkey basters are operated by Boyles Law pulling back on the plunger increases the volume inside the syringe which decreases the pressure which then corrects when liquid is drawn into the syringe thereby shrinking the volume again
bull Spray cans like spray paint and air freshener are governed by Boyles Law intense pressure inside the can pushes outward on the liquid inside the can trying to escape and forces the liquid out when the cap makes an opening
bull You breathe because of Boyles Law
bull Balloons work because of Boyles Law
bull A car (combustion) engine works when the sudden increase in pressure from the combustion of the fuel expands the cylinder and pushes on the piston causing the crankshaft to turn
Temeperature-Volume Relationship Charlersquos Law
bull Volume and temperature are proportional at constant pressure
bull (when gases are heated they expand)
bull temperature = volume (K)
bull temperature = Volume (K)
= kV
T
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constant
V1= 665 mL V2= mL
T1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 K
V1
T1
=V2
T2
V1
T1
=V2T2 =
(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
=V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293 K T2= degC
V1
T1
=V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Real World Application CHARLErsquoS LAW
bull A balloon blown up inside a warm building will shrink when it is carried to a colder area like the outdoors
bull Humans lung capacity is reduced in colder weather runners and other athletes may find it harder to perform in cold weather for this reason
bull Charles Law along with a couple other gas laws is responsible for the rising of bread and other baked goods in the oven tiny pockets of air from yeast or other ingredients are heated and expand causing the dough to inflate which ultimately results in a lighter finished baked good
bull Car (combustion) engines work by this principle the heat from the combustion of the fuel causes the cylinder to expand which pushes the piston and turns the crankshaft
Temperature-Pressure Relationships Gay-Lussacrsquos Lawbull Pressure and temperature are proportional
at constant volume
bull pressure = temperature (K)
bull pressure = temperature (K)
= kP
T
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation1 An aerosol can containing gas at 101 kPaand 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
= 110 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
= 490K or 220degC
P2= 203 kPa
T1
Real World Application GAY-LUSSACrsquoS LAW
bull Bullets and cannons are based on these principles gas super-heated by the burning of gun powder is trapped behind the bullet and expands until the bullet leaves the barrel
bull Someone opening an oven may feel a quick flow of hot air the air inside the oven is heated therefore pressurized The same is true when heating food in closed containers often a container will open to release the pressure If it does not opening the container will quickly release all the pent-up pressure which can be very dangerous because the gases inside the hot container may be super-heated This is why it is always best to open hot containers away from your body and face
Volume-Molar Relationships Avogadrorsquos Law
bull Volume and number of moles (n) areproportional at constant temperature and pressure
bull volume = number of moles
bull volume = number of moles
bull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Real World Application AVOGADROrsquoS LAW
bull Avogadros Law along with other gas laws explains why bread and other baked goods rise Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol The carbon dioxide forms bubbles and as the yeast continues to leaven the dough the increase in the number of particles of carbon dioxide increase the volume of the bubbles thereby puffing up the dough
bull Avogadros Law explains projectiles like cannons and guns the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel
bull A balloon inflates because of Avogadros Law the person blowing into the balloon is inputing a lot of gas particles so the balloon increases in volume
bull We breathe because of Avogadros Law among others the lungs expand so more gas particles can enter the lungs from the outside air (inhaling) Then the lungs contract so the waste gas particles are expelled (exhaling)
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Checking for understanding
List 5 characteristics of gases
1
2
3
4
5
List 5 characteristics of gases according to the KMT
1
2
3
4
5
Gas Laws
Measurable Properties of Gases
Gases are described by their measurable properties
bull P = pressure exerted by the gas
bull V = total volume occupied by the gas
bull T = temperature of the gas
bull n = number of moles of the gas
atm
Units
L
K
mol
Gas Laws ndash ABCGG LAWS
bull Abull Bbull Cbull G
bull G
vogadrorsquos
oylesrsquos
harlesrsquos
ay- Lussacrsquos
n is proportional to V constant T
P is inversely proportional to V constant T
V is proportional to T constant P
P is proportional to T constant V
rahamrsquos Rate of effusion is inversely proportional to square root of gasrsquos molar mass
Pressure-Volume Relationship Boylersquos Law
bull Pressure and Volume are inversely proportional at constant temperature
bull Pressure = Volume (when one increases the other one decreases)
bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the variable
you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atmwhile the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Real World Application BOYLErsquoS LAW
bull Syringes and turkey basters are operated by Boyles Law pulling back on the plunger increases the volume inside the syringe which decreases the pressure which then corrects when liquid is drawn into the syringe thereby shrinking the volume again
bull Spray cans like spray paint and air freshener are governed by Boyles Law intense pressure inside the can pushes outward on the liquid inside the can trying to escape and forces the liquid out when the cap makes an opening
bull You breathe because of Boyles Law
bull Balloons work because of Boyles Law
bull A car (combustion) engine works when the sudden increase in pressure from the combustion of the fuel expands the cylinder and pushes on the piston causing the crankshaft to turn
Temeperature-Volume Relationship Charlersquos Law
bull Volume and temperature are proportional at constant pressure
bull (when gases are heated they expand)
bull temperature = volume (K)
bull temperature = Volume (K)
= kV
T
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constant
V1= 665 mL V2= mL
T1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 K
V1
T1
=V2
T2
V1
T1
=V2T2 =
(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
=V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293 K T2= degC
V1
T1
=V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Real World Application CHARLErsquoS LAW
bull A balloon blown up inside a warm building will shrink when it is carried to a colder area like the outdoors
bull Humans lung capacity is reduced in colder weather runners and other athletes may find it harder to perform in cold weather for this reason
bull Charles Law along with a couple other gas laws is responsible for the rising of bread and other baked goods in the oven tiny pockets of air from yeast or other ingredients are heated and expand causing the dough to inflate which ultimately results in a lighter finished baked good
bull Car (combustion) engines work by this principle the heat from the combustion of the fuel causes the cylinder to expand which pushes the piston and turns the crankshaft
Temperature-Pressure Relationships Gay-Lussacrsquos Lawbull Pressure and temperature are proportional
at constant volume
bull pressure = temperature (K)
bull pressure = temperature (K)
= kP
T
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation1 An aerosol can containing gas at 101 kPaand 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
= 110 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
= 490K or 220degC
P2= 203 kPa
T1
Real World Application GAY-LUSSACrsquoS LAW
bull Bullets and cannons are based on these principles gas super-heated by the burning of gun powder is trapped behind the bullet and expands until the bullet leaves the barrel
bull Someone opening an oven may feel a quick flow of hot air the air inside the oven is heated therefore pressurized The same is true when heating food in closed containers often a container will open to release the pressure If it does not opening the container will quickly release all the pent-up pressure which can be very dangerous because the gases inside the hot container may be super-heated This is why it is always best to open hot containers away from your body and face
Volume-Molar Relationships Avogadrorsquos Law
bull Volume and number of moles (n) areproportional at constant temperature and pressure
bull volume = number of moles
bull volume = number of moles
bull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Real World Application AVOGADROrsquoS LAW
bull Avogadros Law along with other gas laws explains why bread and other baked goods rise Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol The carbon dioxide forms bubbles and as the yeast continues to leaven the dough the increase in the number of particles of carbon dioxide increase the volume of the bubbles thereby puffing up the dough
bull Avogadros Law explains projectiles like cannons and guns the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel
bull A balloon inflates because of Avogadros Law the person blowing into the balloon is inputing a lot of gas particles so the balloon increases in volume
bull We breathe because of Avogadros Law among others the lungs expand so more gas particles can enter the lungs from the outside air (inhaling) Then the lungs contract so the waste gas particles are expelled (exhaling)
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Gas Laws
Measurable Properties of Gases
Gases are described by their measurable properties
bull P = pressure exerted by the gas
bull V = total volume occupied by the gas
bull T = temperature of the gas
bull n = number of moles of the gas
atm
Units
L
K
mol
Gas Laws ndash ABCGG LAWS
bull Abull Bbull Cbull G
bull G
vogadrorsquos
oylesrsquos
harlesrsquos
ay- Lussacrsquos
n is proportional to V constant T
P is inversely proportional to V constant T
V is proportional to T constant P
P is proportional to T constant V
rahamrsquos Rate of effusion is inversely proportional to square root of gasrsquos molar mass
Pressure-Volume Relationship Boylersquos Law
bull Pressure and Volume are inversely proportional at constant temperature
bull Pressure = Volume (when one increases the other one decreases)
bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the variable
you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atmwhile the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Real World Application BOYLErsquoS LAW
bull Syringes and turkey basters are operated by Boyles Law pulling back on the plunger increases the volume inside the syringe which decreases the pressure which then corrects when liquid is drawn into the syringe thereby shrinking the volume again
bull Spray cans like spray paint and air freshener are governed by Boyles Law intense pressure inside the can pushes outward on the liquid inside the can trying to escape and forces the liquid out when the cap makes an opening
bull You breathe because of Boyles Law
bull Balloons work because of Boyles Law
bull A car (combustion) engine works when the sudden increase in pressure from the combustion of the fuel expands the cylinder and pushes on the piston causing the crankshaft to turn
Temeperature-Volume Relationship Charlersquos Law
bull Volume and temperature are proportional at constant pressure
bull (when gases are heated they expand)
bull temperature = volume (K)
bull temperature = Volume (K)
= kV
T
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constant
V1= 665 mL V2= mL
T1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 K
V1
T1
=V2
T2
V1
T1
=V2T2 =
(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
=V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293 K T2= degC
V1
T1
=V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Real World Application CHARLErsquoS LAW
bull A balloon blown up inside a warm building will shrink when it is carried to a colder area like the outdoors
bull Humans lung capacity is reduced in colder weather runners and other athletes may find it harder to perform in cold weather for this reason
bull Charles Law along with a couple other gas laws is responsible for the rising of bread and other baked goods in the oven tiny pockets of air from yeast or other ingredients are heated and expand causing the dough to inflate which ultimately results in a lighter finished baked good
bull Car (combustion) engines work by this principle the heat from the combustion of the fuel causes the cylinder to expand which pushes the piston and turns the crankshaft
Temperature-Pressure Relationships Gay-Lussacrsquos Lawbull Pressure and temperature are proportional
at constant volume
bull pressure = temperature (K)
bull pressure = temperature (K)
= kP
T
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation1 An aerosol can containing gas at 101 kPaand 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
= 110 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
= 490K or 220degC
P2= 203 kPa
T1
Real World Application GAY-LUSSACrsquoS LAW
bull Bullets and cannons are based on these principles gas super-heated by the burning of gun powder is trapped behind the bullet and expands until the bullet leaves the barrel
bull Someone opening an oven may feel a quick flow of hot air the air inside the oven is heated therefore pressurized The same is true when heating food in closed containers often a container will open to release the pressure If it does not opening the container will quickly release all the pent-up pressure which can be very dangerous because the gases inside the hot container may be super-heated This is why it is always best to open hot containers away from your body and face
Volume-Molar Relationships Avogadrorsquos Law
bull Volume and number of moles (n) areproportional at constant temperature and pressure
bull volume = number of moles
bull volume = number of moles
bull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Real World Application AVOGADROrsquoS LAW
bull Avogadros Law along with other gas laws explains why bread and other baked goods rise Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol The carbon dioxide forms bubbles and as the yeast continues to leaven the dough the increase in the number of particles of carbon dioxide increase the volume of the bubbles thereby puffing up the dough
bull Avogadros Law explains projectiles like cannons and guns the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel
bull A balloon inflates because of Avogadros Law the person blowing into the balloon is inputing a lot of gas particles so the balloon increases in volume
bull We breathe because of Avogadros Law among others the lungs expand so more gas particles can enter the lungs from the outside air (inhaling) Then the lungs contract so the waste gas particles are expelled (exhaling)
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Measurable Properties of Gases
Gases are described by their measurable properties
bull P = pressure exerted by the gas
bull V = total volume occupied by the gas
bull T = temperature of the gas
bull n = number of moles of the gas
atm
Units
L
K
mol
Gas Laws ndash ABCGG LAWS
bull Abull Bbull Cbull G
bull G
vogadrorsquos
oylesrsquos
harlesrsquos
ay- Lussacrsquos
n is proportional to V constant T
P is inversely proportional to V constant T
V is proportional to T constant P
P is proportional to T constant V
rahamrsquos Rate of effusion is inversely proportional to square root of gasrsquos molar mass
Pressure-Volume Relationship Boylersquos Law
bull Pressure and Volume are inversely proportional at constant temperature
bull Pressure = Volume (when one increases the other one decreases)
bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the variable
you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atmwhile the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Real World Application BOYLErsquoS LAW
bull Syringes and turkey basters are operated by Boyles Law pulling back on the plunger increases the volume inside the syringe which decreases the pressure which then corrects when liquid is drawn into the syringe thereby shrinking the volume again
bull Spray cans like spray paint and air freshener are governed by Boyles Law intense pressure inside the can pushes outward on the liquid inside the can trying to escape and forces the liquid out when the cap makes an opening
bull You breathe because of Boyles Law
bull Balloons work because of Boyles Law
bull A car (combustion) engine works when the sudden increase in pressure from the combustion of the fuel expands the cylinder and pushes on the piston causing the crankshaft to turn
Temeperature-Volume Relationship Charlersquos Law
bull Volume and temperature are proportional at constant pressure
bull (when gases are heated they expand)
bull temperature = volume (K)
bull temperature = Volume (K)
= kV
T
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constant
V1= 665 mL V2= mL
T1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 K
V1
T1
=V2
T2
V1
T1
=V2T2 =
(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
=V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293 K T2= degC
V1
T1
=V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Real World Application CHARLErsquoS LAW
bull A balloon blown up inside a warm building will shrink when it is carried to a colder area like the outdoors
bull Humans lung capacity is reduced in colder weather runners and other athletes may find it harder to perform in cold weather for this reason
bull Charles Law along with a couple other gas laws is responsible for the rising of bread and other baked goods in the oven tiny pockets of air from yeast or other ingredients are heated and expand causing the dough to inflate which ultimately results in a lighter finished baked good
bull Car (combustion) engines work by this principle the heat from the combustion of the fuel causes the cylinder to expand which pushes the piston and turns the crankshaft
Temperature-Pressure Relationships Gay-Lussacrsquos Lawbull Pressure and temperature are proportional
at constant volume
bull pressure = temperature (K)
bull pressure = temperature (K)
= kP
T
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation1 An aerosol can containing gas at 101 kPaand 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
= 110 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
= 490K or 220degC
P2= 203 kPa
T1
Real World Application GAY-LUSSACrsquoS LAW
bull Bullets and cannons are based on these principles gas super-heated by the burning of gun powder is trapped behind the bullet and expands until the bullet leaves the barrel
bull Someone opening an oven may feel a quick flow of hot air the air inside the oven is heated therefore pressurized The same is true when heating food in closed containers often a container will open to release the pressure If it does not opening the container will quickly release all the pent-up pressure which can be very dangerous because the gases inside the hot container may be super-heated This is why it is always best to open hot containers away from your body and face
Volume-Molar Relationships Avogadrorsquos Law
bull Volume and number of moles (n) areproportional at constant temperature and pressure
bull volume = number of moles
bull volume = number of moles
bull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Real World Application AVOGADROrsquoS LAW
bull Avogadros Law along with other gas laws explains why bread and other baked goods rise Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol The carbon dioxide forms bubbles and as the yeast continues to leaven the dough the increase in the number of particles of carbon dioxide increase the volume of the bubbles thereby puffing up the dough
bull Avogadros Law explains projectiles like cannons and guns the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel
bull A balloon inflates because of Avogadros Law the person blowing into the balloon is inputing a lot of gas particles so the balloon increases in volume
bull We breathe because of Avogadros Law among others the lungs expand so more gas particles can enter the lungs from the outside air (inhaling) Then the lungs contract so the waste gas particles are expelled (exhaling)
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Gas Laws ndash ABCGG LAWS
bull Abull Bbull Cbull G
bull G
vogadrorsquos
oylesrsquos
harlesrsquos
ay- Lussacrsquos
n is proportional to V constant T
P is inversely proportional to V constant T
V is proportional to T constant P
P is proportional to T constant V
rahamrsquos Rate of effusion is inversely proportional to square root of gasrsquos molar mass
Pressure-Volume Relationship Boylersquos Law
bull Pressure and Volume are inversely proportional at constant temperature
bull Pressure = Volume (when one increases the other one decreases)
bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the variable
you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atmwhile the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Real World Application BOYLErsquoS LAW
bull Syringes and turkey basters are operated by Boyles Law pulling back on the plunger increases the volume inside the syringe which decreases the pressure which then corrects when liquid is drawn into the syringe thereby shrinking the volume again
bull Spray cans like spray paint and air freshener are governed by Boyles Law intense pressure inside the can pushes outward on the liquid inside the can trying to escape and forces the liquid out when the cap makes an opening
bull You breathe because of Boyles Law
bull Balloons work because of Boyles Law
bull A car (combustion) engine works when the sudden increase in pressure from the combustion of the fuel expands the cylinder and pushes on the piston causing the crankshaft to turn
Temeperature-Volume Relationship Charlersquos Law
bull Volume and temperature are proportional at constant pressure
bull (when gases are heated they expand)
bull temperature = volume (K)
bull temperature = Volume (K)
= kV
T
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constant
V1= 665 mL V2= mL
T1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 K
V1
T1
=V2
T2
V1
T1
=V2T2 =
(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
=V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293 K T2= degC
V1
T1
=V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Real World Application CHARLErsquoS LAW
bull A balloon blown up inside a warm building will shrink when it is carried to a colder area like the outdoors
bull Humans lung capacity is reduced in colder weather runners and other athletes may find it harder to perform in cold weather for this reason
bull Charles Law along with a couple other gas laws is responsible for the rising of bread and other baked goods in the oven tiny pockets of air from yeast or other ingredients are heated and expand causing the dough to inflate which ultimately results in a lighter finished baked good
bull Car (combustion) engines work by this principle the heat from the combustion of the fuel causes the cylinder to expand which pushes the piston and turns the crankshaft
Temperature-Pressure Relationships Gay-Lussacrsquos Lawbull Pressure and temperature are proportional
at constant volume
bull pressure = temperature (K)
bull pressure = temperature (K)
= kP
T
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation1 An aerosol can containing gas at 101 kPaand 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
= 110 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
= 490K or 220degC
P2= 203 kPa
T1
Real World Application GAY-LUSSACrsquoS LAW
bull Bullets and cannons are based on these principles gas super-heated by the burning of gun powder is trapped behind the bullet and expands until the bullet leaves the barrel
bull Someone opening an oven may feel a quick flow of hot air the air inside the oven is heated therefore pressurized The same is true when heating food in closed containers often a container will open to release the pressure If it does not opening the container will quickly release all the pent-up pressure which can be very dangerous because the gases inside the hot container may be super-heated This is why it is always best to open hot containers away from your body and face
Volume-Molar Relationships Avogadrorsquos Law
bull Volume and number of moles (n) areproportional at constant temperature and pressure
bull volume = number of moles
bull volume = number of moles
bull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Real World Application AVOGADROrsquoS LAW
bull Avogadros Law along with other gas laws explains why bread and other baked goods rise Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol The carbon dioxide forms bubbles and as the yeast continues to leaven the dough the increase in the number of particles of carbon dioxide increase the volume of the bubbles thereby puffing up the dough
bull Avogadros Law explains projectiles like cannons and guns the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel
bull A balloon inflates because of Avogadros Law the person blowing into the balloon is inputing a lot of gas particles so the balloon increases in volume
bull We breathe because of Avogadros Law among others the lungs expand so more gas particles can enter the lungs from the outside air (inhaling) Then the lungs contract so the waste gas particles are expelled (exhaling)
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Pressure-Volume Relationship Boylersquos Law
bull Pressure and Volume are inversely proportional at constant temperature
bull Pressure = Volume (when one increases the other one decreases)
bull Volume = Pressure
PV = k
P1V 1= P2V2
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the variable
you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atmwhile the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Real World Application BOYLErsquoS LAW
bull Syringes and turkey basters are operated by Boyles Law pulling back on the plunger increases the volume inside the syringe which decreases the pressure which then corrects when liquid is drawn into the syringe thereby shrinking the volume again
bull Spray cans like spray paint and air freshener are governed by Boyles Law intense pressure inside the can pushes outward on the liquid inside the can trying to escape and forces the liquid out when the cap makes an opening
bull You breathe because of Boyles Law
bull Balloons work because of Boyles Law
bull A car (combustion) engine works when the sudden increase in pressure from the combustion of the fuel expands the cylinder and pushes on the piston causing the crankshaft to turn
Temeperature-Volume Relationship Charlersquos Law
bull Volume and temperature are proportional at constant pressure
bull (when gases are heated they expand)
bull temperature = volume (K)
bull temperature = Volume (K)
= kV
T
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constant
V1= 665 mL V2= mL
T1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 K
V1
T1
=V2
T2
V1
T1
=V2T2 =
(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
=V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293 K T2= degC
V1
T1
=V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Real World Application CHARLErsquoS LAW
bull A balloon blown up inside a warm building will shrink when it is carried to a colder area like the outdoors
bull Humans lung capacity is reduced in colder weather runners and other athletes may find it harder to perform in cold weather for this reason
bull Charles Law along with a couple other gas laws is responsible for the rising of bread and other baked goods in the oven tiny pockets of air from yeast or other ingredients are heated and expand causing the dough to inflate which ultimately results in a lighter finished baked good
bull Car (combustion) engines work by this principle the heat from the combustion of the fuel causes the cylinder to expand which pushes the piston and turns the crankshaft
Temperature-Pressure Relationships Gay-Lussacrsquos Lawbull Pressure and temperature are proportional
at constant volume
bull pressure = temperature (K)
bull pressure = temperature (K)
= kP
T
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation1 An aerosol can containing gas at 101 kPaand 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
= 110 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
= 490K or 220degC
P2= 203 kPa
T1
Real World Application GAY-LUSSACrsquoS LAW
bull Bullets and cannons are based on these principles gas super-heated by the burning of gun powder is trapped behind the bullet and expands until the bullet leaves the barrel
bull Someone opening an oven may feel a quick flow of hot air the air inside the oven is heated therefore pressurized The same is true when heating food in closed containers often a container will open to release the pressure If it does not opening the container will quickly release all the pent-up pressure which can be very dangerous because the gases inside the hot container may be super-heated This is why it is always best to open hot containers away from your body and face
Volume-Molar Relationships Avogadrorsquos Law
bull Volume and number of moles (n) areproportional at constant temperature and pressure
bull volume = number of moles
bull volume = number of moles
bull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Real World Application AVOGADROrsquoS LAW
bull Avogadros Law along with other gas laws explains why bread and other baked goods rise Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol The carbon dioxide forms bubbles and as the yeast continues to leaven the dough the increase in the number of particles of carbon dioxide increase the volume of the bubbles thereby puffing up the dough
bull Avogadros Law explains projectiles like cannons and guns the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel
bull A balloon inflates because of Avogadros Law the person blowing into the balloon is inputing a lot of gas particles so the balloon increases in volume
bull We breathe because of Avogadros Law among others the lungs expand so more gas particles can enter the lungs from the outside air (inhaling) Then the lungs contract so the waste gas particles are expelled (exhaling)
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
For ALL calculations
1 Circle the numbers underline what you are looking for
2 Make a list of number you circled using variables
3 Write down the formula4 Derive the formula to isolate the variable
you are looking for5 Plug in the numbers6 Answer according to significant figures
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atmwhile the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Real World Application BOYLErsquoS LAW
bull Syringes and turkey basters are operated by Boyles Law pulling back on the plunger increases the volume inside the syringe which decreases the pressure which then corrects when liquid is drawn into the syringe thereby shrinking the volume again
bull Spray cans like spray paint and air freshener are governed by Boyles Law intense pressure inside the can pushes outward on the liquid inside the can trying to escape and forces the liquid out when the cap makes an opening
bull You breathe because of Boyles Law
bull Balloons work because of Boyles Law
bull A car (combustion) engine works when the sudden increase in pressure from the combustion of the fuel expands the cylinder and pushes on the piston causing the crankshaft to turn
Temeperature-Volume Relationship Charlersquos Law
bull Volume and temperature are proportional at constant pressure
bull (when gases are heated they expand)
bull temperature = volume (K)
bull temperature = Volume (K)
= kV
T
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constant
V1= 665 mL V2= mL
T1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 K
V1
T1
=V2
T2
V1
T1
=V2T2 =
(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
=V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293 K T2= degC
V1
T1
=V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Real World Application CHARLErsquoS LAW
bull A balloon blown up inside a warm building will shrink when it is carried to a colder area like the outdoors
bull Humans lung capacity is reduced in colder weather runners and other athletes may find it harder to perform in cold weather for this reason
bull Charles Law along with a couple other gas laws is responsible for the rising of bread and other baked goods in the oven tiny pockets of air from yeast or other ingredients are heated and expand causing the dough to inflate which ultimately results in a lighter finished baked good
bull Car (combustion) engines work by this principle the heat from the combustion of the fuel causes the cylinder to expand which pushes the piston and turns the crankshaft
Temperature-Pressure Relationships Gay-Lussacrsquos Lawbull Pressure and temperature are proportional
at constant volume
bull pressure = temperature (K)
bull pressure = temperature (K)
= kP
T
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation1 An aerosol can containing gas at 101 kPaand 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
= 110 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
= 490K or 220degC
P2= 203 kPa
T1
Real World Application GAY-LUSSACrsquoS LAW
bull Bullets and cannons are based on these principles gas super-heated by the burning of gun powder is trapped behind the bullet and expands until the bullet leaves the barrel
bull Someone opening an oven may feel a quick flow of hot air the air inside the oven is heated therefore pressurized The same is true when heating food in closed containers often a container will open to release the pressure If it does not opening the container will quickly release all the pent-up pressure which can be very dangerous because the gases inside the hot container may be super-heated This is why it is always best to open hot containers away from your body and face
Volume-Molar Relationships Avogadrorsquos Law
bull Volume and number of moles (n) areproportional at constant temperature and pressure
bull volume = number of moles
bull volume = number of moles
bull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Real World Application AVOGADROrsquoS LAW
bull Avogadros Law along with other gas laws explains why bread and other baked goods rise Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol The carbon dioxide forms bubbles and as the yeast continues to leaven the dough the increase in the number of particles of carbon dioxide increase the volume of the bubbles thereby puffing up the dough
bull Avogadros Law explains projectiles like cannons and guns the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel
bull A balloon inflates because of Avogadros Law the person blowing into the balloon is inputing a lot of gas particles so the balloon increases in volume
bull We breathe because of Avogadros Law among others the lungs expand so more gas particles can enter the lungs from the outside air (inhaling) Then the lungs contract so the waste gas particles are expelled (exhaling)
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Boylersquos Law CalculationA given sample of gas occupies 523mL at 100 atm The pressure is increased to 197 atmwhile the temperature stays the same What is the new volume of the gas
P1V 1= P2V2
P1= 100 atm P2= 197 atm
V1= 523 mL V2= mL
V2=P1V1
P2
= (100 atm) (523 mL)
(197 atm)
= 265 mL
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Real World Application BOYLErsquoS LAW
bull Syringes and turkey basters are operated by Boyles Law pulling back on the plunger increases the volume inside the syringe which decreases the pressure which then corrects when liquid is drawn into the syringe thereby shrinking the volume again
bull Spray cans like spray paint and air freshener are governed by Boyles Law intense pressure inside the can pushes outward on the liquid inside the can trying to escape and forces the liquid out when the cap makes an opening
bull You breathe because of Boyles Law
bull Balloons work because of Boyles Law
bull A car (combustion) engine works when the sudden increase in pressure from the combustion of the fuel expands the cylinder and pushes on the piston causing the crankshaft to turn
Temeperature-Volume Relationship Charlersquos Law
bull Volume and temperature are proportional at constant pressure
bull (when gases are heated they expand)
bull temperature = volume (K)
bull temperature = Volume (K)
= kV
T
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constant
V1= 665 mL V2= mL
T1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 K
V1
T1
=V2
T2
V1
T1
=V2T2 =
(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
=V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293 K T2= degC
V1
T1
=V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Real World Application CHARLErsquoS LAW
bull A balloon blown up inside a warm building will shrink when it is carried to a colder area like the outdoors
bull Humans lung capacity is reduced in colder weather runners and other athletes may find it harder to perform in cold weather for this reason
bull Charles Law along with a couple other gas laws is responsible for the rising of bread and other baked goods in the oven tiny pockets of air from yeast or other ingredients are heated and expand causing the dough to inflate which ultimately results in a lighter finished baked good
bull Car (combustion) engines work by this principle the heat from the combustion of the fuel causes the cylinder to expand which pushes the piston and turns the crankshaft
Temperature-Pressure Relationships Gay-Lussacrsquos Lawbull Pressure and temperature are proportional
at constant volume
bull pressure = temperature (K)
bull pressure = temperature (K)
= kP
T
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation1 An aerosol can containing gas at 101 kPaand 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
= 110 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
= 490K or 220degC
P2= 203 kPa
T1
Real World Application GAY-LUSSACrsquoS LAW
bull Bullets and cannons are based on these principles gas super-heated by the burning of gun powder is trapped behind the bullet and expands until the bullet leaves the barrel
bull Someone opening an oven may feel a quick flow of hot air the air inside the oven is heated therefore pressurized The same is true when heating food in closed containers often a container will open to release the pressure If it does not opening the container will quickly release all the pent-up pressure which can be very dangerous because the gases inside the hot container may be super-heated This is why it is always best to open hot containers away from your body and face
Volume-Molar Relationships Avogadrorsquos Law
bull Volume and number of moles (n) areproportional at constant temperature and pressure
bull volume = number of moles
bull volume = number of moles
bull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Real World Application AVOGADROrsquoS LAW
bull Avogadros Law along with other gas laws explains why bread and other baked goods rise Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol The carbon dioxide forms bubbles and as the yeast continues to leaven the dough the increase in the number of particles of carbon dioxide increase the volume of the bubbles thereby puffing up the dough
bull Avogadros Law explains projectiles like cannons and guns the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel
bull A balloon inflates because of Avogadros Law the person blowing into the balloon is inputing a lot of gas particles so the balloon increases in volume
bull We breathe because of Avogadros Law among others the lungs expand so more gas particles can enter the lungs from the outside air (inhaling) Then the lungs contract so the waste gas particles are expelled (exhaling)
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
1 A sample of oxygen gas has a volume of 1500mL at a pressure of 0947 atm What will the volume of the gas be at a pressure of 100 atm if the temperature remains constant
P1V 1= P2V2
P1= 0947 atm P2= 100 atmV1= 1500 mL V2= mL
V2=P1V1
P2
=(0947atm) (1500 mL)
(100atm)
= 142mL
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Real World Application BOYLErsquoS LAW
bull Syringes and turkey basters are operated by Boyles Law pulling back on the plunger increases the volume inside the syringe which decreases the pressure which then corrects when liquid is drawn into the syringe thereby shrinking the volume again
bull Spray cans like spray paint and air freshener are governed by Boyles Law intense pressure inside the can pushes outward on the liquid inside the can trying to escape and forces the liquid out when the cap makes an opening
bull You breathe because of Boyles Law
bull Balloons work because of Boyles Law
bull A car (combustion) engine works when the sudden increase in pressure from the combustion of the fuel expands the cylinder and pushes on the piston causing the crankshaft to turn
Temeperature-Volume Relationship Charlersquos Law
bull Volume and temperature are proportional at constant pressure
bull (when gases are heated they expand)
bull temperature = volume (K)
bull temperature = Volume (K)
= kV
T
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constant
V1= 665 mL V2= mL
T1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 K
V1
T1
=V2
T2
V1
T1
=V2T2 =
(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
=V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293 K T2= degC
V1
T1
=V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Real World Application CHARLErsquoS LAW
bull A balloon blown up inside a warm building will shrink when it is carried to a colder area like the outdoors
bull Humans lung capacity is reduced in colder weather runners and other athletes may find it harder to perform in cold weather for this reason
bull Charles Law along with a couple other gas laws is responsible for the rising of bread and other baked goods in the oven tiny pockets of air from yeast or other ingredients are heated and expand causing the dough to inflate which ultimately results in a lighter finished baked good
bull Car (combustion) engines work by this principle the heat from the combustion of the fuel causes the cylinder to expand which pushes the piston and turns the crankshaft
Temperature-Pressure Relationships Gay-Lussacrsquos Lawbull Pressure and temperature are proportional
at constant volume
bull pressure = temperature (K)
bull pressure = temperature (K)
= kP
T
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation1 An aerosol can containing gas at 101 kPaand 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
= 110 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
= 490K or 220degC
P2= 203 kPa
T1
Real World Application GAY-LUSSACrsquoS LAW
bull Bullets and cannons are based on these principles gas super-heated by the burning of gun powder is trapped behind the bullet and expands until the bullet leaves the barrel
bull Someone opening an oven may feel a quick flow of hot air the air inside the oven is heated therefore pressurized The same is true when heating food in closed containers often a container will open to release the pressure If it does not opening the container will quickly release all the pent-up pressure which can be very dangerous because the gases inside the hot container may be super-heated This is why it is always best to open hot containers away from your body and face
Volume-Molar Relationships Avogadrorsquos Law
bull Volume and number of moles (n) areproportional at constant temperature and pressure
bull volume = number of moles
bull volume = number of moles
bull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Real World Application AVOGADROrsquoS LAW
bull Avogadros Law along with other gas laws explains why bread and other baked goods rise Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol The carbon dioxide forms bubbles and as the yeast continues to leaven the dough the increase in the number of particles of carbon dioxide increase the volume of the bubbles thereby puffing up the dough
bull Avogadros Law explains projectiles like cannons and guns the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel
bull A balloon inflates because of Avogadros Law the person blowing into the balloon is inputing a lot of gas particles so the balloon increases in volume
bull We breathe because of Avogadros Law among others the lungs expand so more gas particles can enter the lungs from the outside air (inhaling) Then the lungs contract so the waste gas particles are expelled (exhaling)
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
2 If 25 L of a gas at 1100 kPa is expanded to 40 L at constant temperature what will be the new value of pressure
P1V 1= P2V2
P1=1100 kPa P2= kPa
V1= 25 L V2= 40 L
P2=P1V1
V2
=(1100 kPa) ( 25 L)
(40 L)
= 69 kPa
Real World Application BOYLErsquoS LAW
bull Syringes and turkey basters are operated by Boyles Law pulling back on the plunger increases the volume inside the syringe which decreases the pressure which then corrects when liquid is drawn into the syringe thereby shrinking the volume again
bull Spray cans like spray paint and air freshener are governed by Boyles Law intense pressure inside the can pushes outward on the liquid inside the can trying to escape and forces the liquid out when the cap makes an opening
bull You breathe because of Boyles Law
bull Balloons work because of Boyles Law
bull A car (combustion) engine works when the sudden increase in pressure from the combustion of the fuel expands the cylinder and pushes on the piston causing the crankshaft to turn
Temeperature-Volume Relationship Charlersquos Law
bull Volume and temperature are proportional at constant pressure
bull (when gases are heated they expand)
bull temperature = volume (K)
bull temperature = Volume (K)
= kV
T
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constant
V1= 665 mL V2= mL
T1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 K
V1
T1
=V2
T2
V1
T1
=V2T2 =
(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
=V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293 K T2= degC
V1
T1
=V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Real World Application CHARLErsquoS LAW
bull A balloon blown up inside a warm building will shrink when it is carried to a colder area like the outdoors
bull Humans lung capacity is reduced in colder weather runners and other athletes may find it harder to perform in cold weather for this reason
bull Charles Law along with a couple other gas laws is responsible for the rising of bread and other baked goods in the oven tiny pockets of air from yeast or other ingredients are heated and expand causing the dough to inflate which ultimately results in a lighter finished baked good
bull Car (combustion) engines work by this principle the heat from the combustion of the fuel causes the cylinder to expand which pushes the piston and turns the crankshaft
Temperature-Pressure Relationships Gay-Lussacrsquos Lawbull Pressure and temperature are proportional
at constant volume
bull pressure = temperature (K)
bull pressure = temperature (K)
= kP
T
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation1 An aerosol can containing gas at 101 kPaand 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
= 110 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
= 490K or 220degC
P2= 203 kPa
T1
Real World Application GAY-LUSSACrsquoS LAW
bull Bullets and cannons are based on these principles gas super-heated by the burning of gun powder is trapped behind the bullet and expands until the bullet leaves the barrel
bull Someone opening an oven may feel a quick flow of hot air the air inside the oven is heated therefore pressurized The same is true when heating food in closed containers often a container will open to release the pressure If it does not opening the container will quickly release all the pent-up pressure which can be very dangerous because the gases inside the hot container may be super-heated This is why it is always best to open hot containers away from your body and face
Volume-Molar Relationships Avogadrorsquos Law
bull Volume and number of moles (n) areproportional at constant temperature and pressure
bull volume = number of moles
bull volume = number of moles
bull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Real World Application AVOGADROrsquoS LAW
bull Avogadros Law along with other gas laws explains why bread and other baked goods rise Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol The carbon dioxide forms bubbles and as the yeast continues to leaven the dough the increase in the number of particles of carbon dioxide increase the volume of the bubbles thereby puffing up the dough
bull Avogadros Law explains projectiles like cannons and guns the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel
bull A balloon inflates because of Avogadros Law the person blowing into the balloon is inputing a lot of gas particles so the balloon increases in volume
bull We breathe because of Avogadros Law among others the lungs expand so more gas particles can enter the lungs from the outside air (inhaling) Then the lungs contract so the waste gas particles are expelled (exhaling)
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Real World Application BOYLErsquoS LAW
bull Syringes and turkey basters are operated by Boyles Law pulling back on the plunger increases the volume inside the syringe which decreases the pressure which then corrects when liquid is drawn into the syringe thereby shrinking the volume again
bull Spray cans like spray paint and air freshener are governed by Boyles Law intense pressure inside the can pushes outward on the liquid inside the can trying to escape and forces the liquid out when the cap makes an opening
bull You breathe because of Boyles Law
bull Balloons work because of Boyles Law
bull A car (combustion) engine works when the sudden increase in pressure from the combustion of the fuel expands the cylinder and pushes on the piston causing the crankshaft to turn
Temeperature-Volume Relationship Charlersquos Law
bull Volume and temperature are proportional at constant pressure
bull (when gases are heated they expand)
bull temperature = volume (K)
bull temperature = Volume (K)
= kV
T
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constant
V1= 665 mL V2= mL
T1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 K
V1
T1
=V2
T2
V1
T1
=V2T2 =
(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
=V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293 K T2= degC
V1
T1
=V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Real World Application CHARLErsquoS LAW
bull A balloon blown up inside a warm building will shrink when it is carried to a colder area like the outdoors
bull Humans lung capacity is reduced in colder weather runners and other athletes may find it harder to perform in cold weather for this reason
bull Charles Law along with a couple other gas laws is responsible for the rising of bread and other baked goods in the oven tiny pockets of air from yeast or other ingredients are heated and expand causing the dough to inflate which ultimately results in a lighter finished baked good
bull Car (combustion) engines work by this principle the heat from the combustion of the fuel causes the cylinder to expand which pushes the piston and turns the crankshaft
Temperature-Pressure Relationships Gay-Lussacrsquos Lawbull Pressure and temperature are proportional
at constant volume
bull pressure = temperature (K)
bull pressure = temperature (K)
= kP
T
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation1 An aerosol can containing gas at 101 kPaand 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
= 110 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
= 490K or 220degC
P2= 203 kPa
T1
Real World Application GAY-LUSSACrsquoS LAW
bull Bullets and cannons are based on these principles gas super-heated by the burning of gun powder is trapped behind the bullet and expands until the bullet leaves the barrel
bull Someone opening an oven may feel a quick flow of hot air the air inside the oven is heated therefore pressurized The same is true when heating food in closed containers often a container will open to release the pressure If it does not opening the container will quickly release all the pent-up pressure which can be very dangerous because the gases inside the hot container may be super-heated This is why it is always best to open hot containers away from your body and face
Volume-Molar Relationships Avogadrorsquos Law
bull Volume and number of moles (n) areproportional at constant temperature and pressure
bull volume = number of moles
bull volume = number of moles
bull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Real World Application AVOGADROrsquoS LAW
bull Avogadros Law along with other gas laws explains why bread and other baked goods rise Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol The carbon dioxide forms bubbles and as the yeast continues to leaven the dough the increase in the number of particles of carbon dioxide increase the volume of the bubbles thereby puffing up the dough
bull Avogadros Law explains projectiles like cannons and guns the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel
bull A balloon inflates because of Avogadros Law the person blowing into the balloon is inputing a lot of gas particles so the balloon increases in volume
bull We breathe because of Avogadros Law among others the lungs expand so more gas particles can enter the lungs from the outside air (inhaling) Then the lungs contract so the waste gas particles are expelled (exhaling)
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Temeperature-Volume Relationship Charlersquos Law
bull Volume and temperature are proportional at constant pressure
bull (when gases are heated they expand)
bull temperature = volume (K)
bull temperature = Volume (K)
= kV
T
V1
T1
=V2
T2
KE of the gases volume temperature
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constant
V1= 665 mL V2= mL
T1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 K
V1
T1
=V2
T2
V1
T1
=V2T2 =
(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
=V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293 K T2= degC
V1
T1
=V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Real World Application CHARLErsquoS LAW
bull A balloon blown up inside a warm building will shrink when it is carried to a colder area like the outdoors
bull Humans lung capacity is reduced in colder weather runners and other athletes may find it harder to perform in cold weather for this reason
bull Charles Law along with a couple other gas laws is responsible for the rising of bread and other baked goods in the oven tiny pockets of air from yeast or other ingredients are heated and expand causing the dough to inflate which ultimately results in a lighter finished baked good
bull Car (combustion) engines work by this principle the heat from the combustion of the fuel causes the cylinder to expand which pushes the piston and turns the crankshaft
Temperature-Pressure Relationships Gay-Lussacrsquos Lawbull Pressure and temperature are proportional
at constant volume
bull pressure = temperature (K)
bull pressure = temperature (K)
= kP
T
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation1 An aerosol can containing gas at 101 kPaand 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
= 110 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
= 490K or 220degC
P2= 203 kPa
T1
Real World Application GAY-LUSSACrsquoS LAW
bull Bullets and cannons are based on these principles gas super-heated by the burning of gun powder is trapped behind the bullet and expands until the bullet leaves the barrel
bull Someone opening an oven may feel a quick flow of hot air the air inside the oven is heated therefore pressurized The same is true when heating food in closed containers often a container will open to release the pressure If it does not opening the container will quickly release all the pent-up pressure which can be very dangerous because the gases inside the hot container may be super-heated This is why it is always best to open hot containers away from your body and face
Volume-Molar Relationships Avogadrorsquos Law
bull Volume and number of moles (n) areproportional at constant temperature and pressure
bull volume = number of moles
bull volume = number of moles
bull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Real World Application AVOGADROrsquoS LAW
bull Avogadros Law along with other gas laws explains why bread and other baked goods rise Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol The carbon dioxide forms bubbles and as the yeast continues to leaven the dough the increase in the number of particles of carbon dioxide increase the volume of the bubbles thereby puffing up the dough
bull Avogadros Law explains projectiles like cannons and guns the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel
bull A balloon inflates because of Avogadros Law the person blowing into the balloon is inputing a lot of gas particles so the balloon increases in volume
bull We breathe because of Avogadros Law among others the lungs expand so more gas particles can enter the lungs from the outside air (inhaling) Then the lungs contract so the waste gas particles are expelled (exhaling)
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Charless Law Calculation A balloon is inflated to 665 mL volume at 27degC It is immersed in a dry-ice bath at minus785degC What is its volume assuming the pressure remains constant
V1= 665 mL V2= mL
T1= 27degC + 273 K
= 300 K
T2= -785degC + 273 K
= 1945 K
V1
T1
=V2
T2
V1
T1
=V2T2 =
(665 mL)( 1945 K)
(300 K)
= 43 x 10^2 mL
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
=V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293 K T2= degC
V1
T1
=V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Real World Application CHARLErsquoS LAW
bull A balloon blown up inside a warm building will shrink when it is carried to a colder area like the outdoors
bull Humans lung capacity is reduced in colder weather runners and other athletes may find it harder to perform in cold weather for this reason
bull Charles Law along with a couple other gas laws is responsible for the rising of bread and other baked goods in the oven tiny pockets of air from yeast or other ingredients are heated and expand causing the dough to inflate which ultimately results in a lighter finished baked good
bull Car (combustion) engines work by this principle the heat from the combustion of the fuel causes the cylinder to expand which pushes the piston and turns the crankshaft
Temperature-Pressure Relationships Gay-Lussacrsquos Lawbull Pressure and temperature are proportional
at constant volume
bull pressure = temperature (K)
bull pressure = temperature (K)
= kP
T
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation1 An aerosol can containing gas at 101 kPaand 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
= 110 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
= 490K or 220degC
P2= 203 kPa
T1
Real World Application GAY-LUSSACrsquoS LAW
bull Bullets and cannons are based on these principles gas super-heated by the burning of gun powder is trapped behind the bullet and expands until the bullet leaves the barrel
bull Someone opening an oven may feel a quick flow of hot air the air inside the oven is heated therefore pressurized The same is true when heating food in closed containers often a container will open to release the pressure If it does not opening the container will quickly release all the pent-up pressure which can be very dangerous because the gases inside the hot container may be super-heated This is why it is always best to open hot containers away from your body and face
Volume-Molar Relationships Avogadrorsquos Law
bull Volume and number of moles (n) areproportional at constant temperature and pressure
bull volume = number of moles
bull volume = number of moles
bull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Real World Application AVOGADROrsquoS LAW
bull Avogadros Law along with other gas laws explains why bread and other baked goods rise Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol The carbon dioxide forms bubbles and as the yeast continues to leaven the dough the increase in the number of particles of carbon dioxide increase the volume of the bubbles thereby puffing up the dough
bull Avogadros Law explains projectiles like cannons and guns the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel
bull A balloon inflates because of Avogadros Law the person blowing into the balloon is inputing a lot of gas particles so the balloon increases in volume
bull We breathe because of Avogadros Law among others the lungs expand so more gas particles can enter the lungs from the outside air (inhaling) Then the lungs contract so the waste gas particles are expelled (exhaling)
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
1 Helium gas in a balloon occupies 25 L at 3000K The balloon is dipped into liquid nitrogen that is at a temperature of 800K What will be volume of the helium in the balloon at the lower temperature be
V1= 25 L
T1= 300 K T2= 800 K
V1
T1
=V2
T2
V1
T1
=V2 =(25 L)( 800 K)
(300 K)
= 067 L
V2= mL
T2
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293 K T2= degC
V1
T1
=V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Real World Application CHARLErsquoS LAW
bull A balloon blown up inside a warm building will shrink when it is carried to a colder area like the outdoors
bull Humans lung capacity is reduced in colder weather runners and other athletes may find it harder to perform in cold weather for this reason
bull Charles Law along with a couple other gas laws is responsible for the rising of bread and other baked goods in the oven tiny pockets of air from yeast or other ingredients are heated and expand causing the dough to inflate which ultimately results in a lighter finished baked good
bull Car (combustion) engines work by this principle the heat from the combustion of the fuel causes the cylinder to expand which pushes the piston and turns the crankshaft
Temperature-Pressure Relationships Gay-Lussacrsquos Lawbull Pressure and temperature are proportional
at constant volume
bull pressure = temperature (K)
bull pressure = temperature (K)
= kP
T
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation1 An aerosol can containing gas at 101 kPaand 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
= 110 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
= 490K or 220degC
P2= 203 kPa
T1
Real World Application GAY-LUSSACrsquoS LAW
bull Bullets and cannons are based on these principles gas super-heated by the burning of gun powder is trapped behind the bullet and expands until the bullet leaves the barrel
bull Someone opening an oven may feel a quick flow of hot air the air inside the oven is heated therefore pressurized The same is true when heating food in closed containers often a container will open to release the pressure If it does not opening the container will quickly release all the pent-up pressure which can be very dangerous because the gases inside the hot container may be super-heated This is why it is always best to open hot containers away from your body and face
Volume-Molar Relationships Avogadrorsquos Law
bull Volume and number of moles (n) areproportional at constant temperature and pressure
bull volume = number of moles
bull volume = number of moles
bull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Real World Application AVOGADROrsquoS LAW
bull Avogadros Law along with other gas laws explains why bread and other baked goods rise Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol The carbon dioxide forms bubbles and as the yeast continues to leaven the dough the increase in the number of particles of carbon dioxide increase the volume of the bubbles thereby puffing up the dough
bull Avogadros Law explains projectiles like cannons and guns the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel
bull A balloon inflates because of Avogadros Law the person blowing into the balloon is inputing a lot of gas particles so the balloon increases in volume
bull We breathe because of Avogadros Law among others the lungs expand so more gas particles can enter the lungs from the outside air (inhaling) Then the lungs contract so the waste gas particles are expelled (exhaling)
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
2 A helium filled balloon has a volume of 275 L at 200 degC The volume of the balloon changes to 246 L when placed outside on a cold day What is the temperature outside in degC
V1= 275 L
T1= 20 degC + 273 K = 293 K T2= degC
V1
T1
=V2
T2
V1
V2=T2 =(246 L)( 293 K )
(275 L)
= 26210 K = -1089 degC = -109 degC
V2= 246 L
T1
Real World Application CHARLErsquoS LAW
bull A balloon blown up inside a warm building will shrink when it is carried to a colder area like the outdoors
bull Humans lung capacity is reduced in colder weather runners and other athletes may find it harder to perform in cold weather for this reason
bull Charles Law along with a couple other gas laws is responsible for the rising of bread and other baked goods in the oven tiny pockets of air from yeast or other ingredients are heated and expand causing the dough to inflate which ultimately results in a lighter finished baked good
bull Car (combustion) engines work by this principle the heat from the combustion of the fuel causes the cylinder to expand which pushes the piston and turns the crankshaft
Temperature-Pressure Relationships Gay-Lussacrsquos Lawbull Pressure and temperature are proportional
at constant volume
bull pressure = temperature (K)
bull pressure = temperature (K)
= kP
T
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation1 An aerosol can containing gas at 101 kPaand 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
= 110 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
= 490K or 220degC
P2= 203 kPa
T1
Real World Application GAY-LUSSACrsquoS LAW
bull Bullets and cannons are based on these principles gas super-heated by the burning of gun powder is trapped behind the bullet and expands until the bullet leaves the barrel
bull Someone opening an oven may feel a quick flow of hot air the air inside the oven is heated therefore pressurized The same is true when heating food in closed containers often a container will open to release the pressure If it does not opening the container will quickly release all the pent-up pressure which can be very dangerous because the gases inside the hot container may be super-heated This is why it is always best to open hot containers away from your body and face
Volume-Molar Relationships Avogadrorsquos Law
bull Volume and number of moles (n) areproportional at constant temperature and pressure
bull volume = number of moles
bull volume = number of moles
bull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Real World Application AVOGADROrsquoS LAW
bull Avogadros Law along with other gas laws explains why bread and other baked goods rise Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol The carbon dioxide forms bubbles and as the yeast continues to leaven the dough the increase in the number of particles of carbon dioxide increase the volume of the bubbles thereby puffing up the dough
bull Avogadros Law explains projectiles like cannons and guns the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel
bull A balloon inflates because of Avogadros Law the person blowing into the balloon is inputing a lot of gas particles so the balloon increases in volume
bull We breathe because of Avogadros Law among others the lungs expand so more gas particles can enter the lungs from the outside air (inhaling) Then the lungs contract so the waste gas particles are expelled (exhaling)
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Real World Application CHARLErsquoS LAW
bull A balloon blown up inside a warm building will shrink when it is carried to a colder area like the outdoors
bull Humans lung capacity is reduced in colder weather runners and other athletes may find it harder to perform in cold weather for this reason
bull Charles Law along with a couple other gas laws is responsible for the rising of bread and other baked goods in the oven tiny pockets of air from yeast or other ingredients are heated and expand causing the dough to inflate which ultimately results in a lighter finished baked good
bull Car (combustion) engines work by this principle the heat from the combustion of the fuel causes the cylinder to expand which pushes the piston and turns the crankshaft
Temperature-Pressure Relationships Gay-Lussacrsquos Lawbull Pressure and temperature are proportional
at constant volume
bull pressure = temperature (K)
bull pressure = temperature (K)
= kP
T
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation1 An aerosol can containing gas at 101 kPaand 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
= 110 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
= 490K or 220degC
P2= 203 kPa
T1
Real World Application GAY-LUSSACrsquoS LAW
bull Bullets and cannons are based on these principles gas super-heated by the burning of gun powder is trapped behind the bullet and expands until the bullet leaves the barrel
bull Someone opening an oven may feel a quick flow of hot air the air inside the oven is heated therefore pressurized The same is true when heating food in closed containers often a container will open to release the pressure If it does not opening the container will quickly release all the pent-up pressure which can be very dangerous because the gases inside the hot container may be super-heated This is why it is always best to open hot containers away from your body and face
Volume-Molar Relationships Avogadrorsquos Law
bull Volume and number of moles (n) areproportional at constant temperature and pressure
bull volume = number of moles
bull volume = number of moles
bull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Real World Application AVOGADROrsquoS LAW
bull Avogadros Law along with other gas laws explains why bread and other baked goods rise Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol The carbon dioxide forms bubbles and as the yeast continues to leaven the dough the increase in the number of particles of carbon dioxide increase the volume of the bubbles thereby puffing up the dough
bull Avogadros Law explains projectiles like cannons and guns the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel
bull A balloon inflates because of Avogadros Law the person blowing into the balloon is inputing a lot of gas particles so the balloon increases in volume
bull We breathe because of Avogadros Law among others the lungs expand so more gas particles can enter the lungs from the outside air (inhaling) Then the lungs contract so the waste gas particles are expelled (exhaling)
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Temperature-Pressure Relationships Gay-Lussacrsquos Lawbull Pressure and temperature are proportional
at constant volume
bull pressure = temperature (K)
bull pressure = temperature (K)
= kP
T
P1
T1
=P2
T2
Gay-Lussacrsquos Law Calculation1 An aerosol can containing gas at 101 kPaand 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
= 110 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
= 490K or 220degC
P2= 203 kPa
T1
Real World Application GAY-LUSSACrsquoS LAW
bull Bullets and cannons are based on these principles gas super-heated by the burning of gun powder is trapped behind the bullet and expands until the bullet leaves the barrel
bull Someone opening an oven may feel a quick flow of hot air the air inside the oven is heated therefore pressurized The same is true when heating food in closed containers often a container will open to release the pressure If it does not opening the container will quickly release all the pent-up pressure which can be very dangerous because the gases inside the hot container may be super-heated This is why it is always best to open hot containers away from your body and face
Volume-Molar Relationships Avogadrorsquos Law
bull Volume and number of moles (n) areproportional at constant temperature and pressure
bull volume = number of moles
bull volume = number of moles
bull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Real World Application AVOGADROrsquoS LAW
bull Avogadros Law along with other gas laws explains why bread and other baked goods rise Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol The carbon dioxide forms bubbles and as the yeast continues to leaven the dough the increase in the number of particles of carbon dioxide increase the volume of the bubbles thereby puffing up the dough
bull Avogadros Law explains projectiles like cannons and guns the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel
bull A balloon inflates because of Avogadros Law the person blowing into the balloon is inputing a lot of gas particles so the balloon increases in volume
bull We breathe because of Avogadros Law among others the lungs expand so more gas particles can enter the lungs from the outside air (inhaling) Then the lungs contract so the waste gas particles are expelled (exhaling)
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Gay-Lussacrsquos Law Calculation1 An aerosol can containing gas at 101 kPaand 22degC is heated to 55degC Calculate the pressure in the heated can
P1= 101 kPa
T1= 22 degC + 273 K = 295 K T2= 55 degC + 273K = 328 K
P1
T1
=P2
T2
T1
P1=P2 =(101 kPa)( 328 K )
(295 K)
= 110 kPa
P2= kPa
T2
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
= 490K or 220degC
P2= 203 kPa
T1
Real World Application GAY-LUSSACrsquoS LAW
bull Bullets and cannons are based on these principles gas super-heated by the burning of gun powder is trapped behind the bullet and expands until the bullet leaves the barrel
bull Someone opening an oven may feel a quick flow of hot air the air inside the oven is heated therefore pressurized The same is true when heating food in closed containers often a container will open to release the pressure If it does not opening the container will quickly release all the pent-up pressure which can be very dangerous because the gases inside the hot container may be super-heated This is why it is always best to open hot containers away from your body and face
Volume-Molar Relationships Avogadrorsquos Law
bull Volume and number of moles (n) areproportional at constant temperature and pressure
bull volume = number of moles
bull volume = number of moles
bull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Real World Application AVOGADROrsquoS LAW
bull Avogadros Law along with other gas laws explains why bread and other baked goods rise Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol The carbon dioxide forms bubbles and as the yeast continues to leaven the dough the increase in the number of particles of carbon dioxide increase the volume of the bubbles thereby puffing up the dough
bull Avogadros Law explains projectiles like cannons and guns the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel
bull A balloon inflates because of Avogadros Law the person blowing into the balloon is inputing a lot of gas particles so the balloon increases in volume
bull We breathe because of Avogadros Law among others the lungs expand so more gas particles can enter the lungs from the outside air (inhaling) Then the lungs contract so the waste gas particles are expelled (exhaling)
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
2 A sample of helium gas is at 122 kPa and 22degC Assuming constant volume What will the temperature be when the pressure is 203 kPa
P1= 122 kPa
T1= 22 degC + 273 K = 295 K T2= K
P1
T1
=P2
T2
P1
P2=T2 =(203 kPa)(295K)
(122 kPa)
= 490K or 220degC
P2= 203 kPa
T1
Real World Application GAY-LUSSACrsquoS LAW
bull Bullets and cannons are based on these principles gas super-heated by the burning of gun powder is trapped behind the bullet and expands until the bullet leaves the barrel
bull Someone opening an oven may feel a quick flow of hot air the air inside the oven is heated therefore pressurized The same is true when heating food in closed containers often a container will open to release the pressure If it does not opening the container will quickly release all the pent-up pressure which can be very dangerous because the gases inside the hot container may be super-heated This is why it is always best to open hot containers away from your body and face
Volume-Molar Relationships Avogadrorsquos Law
bull Volume and number of moles (n) areproportional at constant temperature and pressure
bull volume = number of moles
bull volume = number of moles
bull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Real World Application AVOGADROrsquoS LAW
bull Avogadros Law along with other gas laws explains why bread and other baked goods rise Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol The carbon dioxide forms bubbles and as the yeast continues to leaven the dough the increase in the number of particles of carbon dioxide increase the volume of the bubbles thereby puffing up the dough
bull Avogadros Law explains projectiles like cannons and guns the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel
bull A balloon inflates because of Avogadros Law the person blowing into the balloon is inputing a lot of gas particles so the balloon increases in volume
bull We breathe because of Avogadros Law among others the lungs expand so more gas particles can enter the lungs from the outside air (inhaling) Then the lungs contract so the waste gas particles are expelled (exhaling)
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Real World Application GAY-LUSSACrsquoS LAW
bull Bullets and cannons are based on these principles gas super-heated by the burning of gun powder is trapped behind the bullet and expands until the bullet leaves the barrel
bull Someone opening an oven may feel a quick flow of hot air the air inside the oven is heated therefore pressurized The same is true when heating food in closed containers often a container will open to release the pressure If it does not opening the container will quickly release all the pent-up pressure which can be very dangerous because the gases inside the hot container may be super-heated This is why it is always best to open hot containers away from your body and face
Volume-Molar Relationships Avogadrorsquos Law
bull Volume and number of moles (n) areproportional at constant temperature and pressure
bull volume = number of moles
bull volume = number of moles
bull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Real World Application AVOGADROrsquoS LAW
bull Avogadros Law along with other gas laws explains why bread and other baked goods rise Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol The carbon dioxide forms bubbles and as the yeast continues to leaven the dough the increase in the number of particles of carbon dioxide increase the volume of the bubbles thereby puffing up the dough
bull Avogadros Law explains projectiles like cannons and guns the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel
bull A balloon inflates because of Avogadros Law the person blowing into the balloon is inputing a lot of gas particles so the balloon increases in volume
bull We breathe because of Avogadros Law among others the lungs expand so more gas particles can enter the lungs from the outside air (inhaling) Then the lungs contract so the waste gas particles are expelled (exhaling)
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Volume-Molar Relationships Avogadrorsquos Law
bull Volume and number of moles (n) areproportional at constant temperature and pressure
bull volume = number of moles
bull volume = number of moles
bull 224 L for 1 mole of a gas STP
= kVn
V1
n1
=V2
n2
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Real World Application AVOGADROrsquoS LAW
bull Avogadros Law along with other gas laws explains why bread and other baked goods rise Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol The carbon dioxide forms bubbles and as the yeast continues to leaven the dough the increase in the number of particles of carbon dioxide increase the volume of the bubbles thereby puffing up the dough
bull Avogadros Law explains projectiles like cannons and guns the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel
bull A balloon inflates because of Avogadros Law the person blowing into the balloon is inputing a lot of gas particles so the balloon increases in volume
bull We breathe because of Avogadros Law among others the lungs expand so more gas particles can enter the lungs from the outside air (inhaling) Then the lungs contract so the waste gas particles are expelled (exhaling)
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Avogadrorsquos Lawbull What volume of CO2 contains the same
number of molecules as 200mL of O2 at the same conditions
20 mL
Real World Application AVOGADROrsquoS LAW
bull Avogadros Law along with other gas laws explains why bread and other baked goods rise Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol The carbon dioxide forms bubbles and as the yeast continues to leaven the dough the increase in the number of particles of carbon dioxide increase the volume of the bubbles thereby puffing up the dough
bull Avogadros Law explains projectiles like cannons and guns the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel
bull A balloon inflates because of Avogadros Law the person blowing into the balloon is inputing a lot of gas particles so the balloon increases in volume
bull We breathe because of Avogadros Law among others the lungs expand so more gas particles can enter the lungs from the outside air (inhaling) Then the lungs contract so the waste gas particles are expelled (exhaling)
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Real World Application AVOGADROrsquoS LAW
bull Avogadros Law along with other gas laws explains why bread and other baked goods rise Yeast or other leavening agents in the dough break down the long carbohydrates from the flour or sugar and convert them into carbon dioxide gas and ethanol The carbon dioxide forms bubbles and as the yeast continues to leaven the dough the increase in the number of particles of carbon dioxide increase the volume of the bubbles thereby puffing up the dough
bull Avogadros Law explains projectiles like cannons and guns the rapid reaction of the gunpowder very suddenly creates a large amount of gas particles--mostly carbon dioxide and nitrogen gases--which increase the volume of the space behind the cannon or bullet until the projectile has enough speed to leave the barrel
bull A balloon inflates because of Avogadros Law the person blowing into the balloon is inputing a lot of gas particles so the balloon increases in volume
bull We breathe because of Avogadros Law among others the lungs expand so more gas particles can enter the lungs from the outside air (inhaling) Then the lungs contract so the waste gas particles are expelled (exhaling)
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
The CombinedGas Law
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Combining the gas laws
Jacques CharlesRobert Boyle
P1V1 = P2V2V1
T1
=V2
T2
These are all subsets of a
more encompassing law
the combined gas law
P1
T1
=P2
T2
P1V1 P2V2
T1 T2
=
Joseph Louis Gay-Lussac
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Gas Laws
Combined Gas Law 2
22
1
11
T
VP
T
VP
The ratio of the product
of pressure and volume and
the temperature of a gas is equal to a constant
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Boylersquos Law
Charlersquos Law
Gay-Lussacrsquos Law
Avogadrorsquos Law
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Ideal Gas
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Molecular Composition of Gasesbull No gas perfectly obeys all four of these laws under
all conditions
bull These assumptions work well for most gases and most conditions
bull One way to model a gasrsquos behavior is to assume that the gas is an ideal gas that perfectly follows these laws
bull An ideal gas unlike a real gas
bull does not condense to a liquid at low temperatures
bull does not have forces of attraction or repulsion between the particles and is
bull Is composed of particles that have no volume
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Ideal Gas Law
PV = nRTbull P = pressure in atmbull V = volume in litersbull n = molesbull R = proportionality constant
ndash= 00821 L atm molmiddotKbull T = temperature in Kelvins
The ideal gas law expresses the relationship between pressure volume and temperature of a fixed amount of gas
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Ideal Gas Law CalculationHow many moles of gas are contained in
224 L liter at 100 atm and 283K
P = 100 atm
V = 224 L
n = Moles
R = 00821 Latmmol K
T = 283 K
PV = nRT
RT
PVn =
(00821 Latmmol K) ( 283 K)
(100 atm)(224L)=
=964 moles
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Calculate the pressure exerted by 43 mol of nitrogen in a 65L of cylinder at 50degC
P = atm V = 65 L
n = 43 mol R = 00821 Latmmol K
T = 5degC + 273K = 278 K
PV = nRTnRT
VP =
(43 mol)(00821 Latmmol K) ( 278 K)
(65 L)=
=15 atm
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
What will be the volume of 111 mol of nitrogen where the temperature is -57degC and pressure is 250 atm
P = 250 atm V = L
n = 111 mol R = 00821 Latmmol K
T = -57degC + 273K = 216 K
PV = nRTnRT
PV =
(111 mol)(00821 Latmmol K) ( 216 K)
(250 atm)=
=79 L
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Real World Application IDEAL GAS LAW
bull The Ideal Gas Law provides important information regarding reactions like the combination of gases stoichiometry like the gas produced in a reaction physical processes like the mixing of gases and thermodynamic processes like the movement of matter toward disorder
bull The Ideal Gas Law is used in engineering to determine the capacity of storage containers It is also helpful in determining the efficiency and standard operation of equipment
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Checking for understanding
1 Explain how is ideal gas different from a normal gas
2 Write the formula for ideal gas
3 What variables can be determined by using the formula
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Gas Behavior ndash DiffusionEffusion
bull Diffusion is the movement of particles from regions of higher density to regions of lower density
bull Effusion is the passage of gas particles through a small opening
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
bull Both effusion and difusssion depend on
the molar mass of the particle which determines the speed
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Effusion
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
bullDiffusiondescribes the mixing
of gases The rate of
diffusion is the rate
of gas mixing
bullMolecules move
from areas of high
concentration to low
concentration
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Effusion a gas escapes through a tiny hole in its container
-Think of a nail in your car tirehellip
Diffusion
and effusion
are
explained
by the next
gas law
Grahamrsquos
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Next slides not used 2015
bull Grahams law calculations
bull Daltonrsquos law
bull Ideal gas law
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Comparing distance traveled
You can compare the distanced traveled by 2 gases in the same amount of time using this equation also
Distance traveled by A = MassB
Distance traveled by B MassA
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Grahamrsquos Lawbull The molecular speeds vA and vB of gases A and
B can be compared according to Grahamrsquos law of diffusion shown below
bull Grahamrsquos law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of the gasrsquos molar mass
bull Particles of low molar mass travel faster than heavier particles
A
B
B
A
M
M
r
r
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Grahamrsquos Law Calculation
bull At the same temperature which molecule travels faster O2 or H2
2
2
2
2
H
O
O
H
M
M
r
r
2
2
H
O
g 202
g 3200 = 398
Hydrogen travels 398 times faster than oxygen
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Grahamrsquos Law CalculationOxygen molecules have a rate of about 480 ms at room
temperature At the same temperature what is the rate of molecules of sulfur hexafluoride SF6
32g
146
r
480ms
6S
g
F
rO2 = 480 ms
rSF6= ms
MO2 = 32g
MSF6= 146g
2
6
6
2
O
S
S
O
M
M
r
r F
F
= 220 ms
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Daltonrsquos Lawbull The pressure of each gas in a mixture is called
the partial pressurebull The total pressure of a mixture of gases is the
sum of the partial pressures of the gases This principle is known as Daltonrsquos law of partial pressure
bull Ptotal = PA + PB + PC
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Daltonrsquos Law Calculation
bull What is the total pressure in a balloon filled with air (O2 amp N2) if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg
bullPtotal = POxygen + Pnitrogen
bullPtotal = PA + PB + PChellip
= 170 mmHg + 620 mmHg
= 790 mmHg
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Real World Application DALTONrsquoS LAW
bull Daltons Law is especially important in atmospheric studies The atmosphere is made up principally of nitrogen oxygen carbon dioxide and water vapors the total atmospheric pressure is the sum of the partial pressures of each gas The different partial pressures account for a lot of the weather we experience
bull Daltons Law plays a large role in medicine and other breathing areas Different proportions of gas have different therapeutic effects so it is important to know the partial pressures of each gas in a gas line or gas tank for example
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Checking for understanding
State the law
Explain the law in your own words
Write the formula(s)
Grahamrsquos Law
Daltonrsquos Law
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Grahamrsquos Law
bull The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules
bull Derived from Kinetic energy = 12 mv2
bull m = the molar mass and v = the
velocity
RateA MassB
RateB MassA
=
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
bull Sample compare rates of effusion of
Helium with Nitrogen ndash
bull With effusion and diffusion the type of
particle is important
ndash Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass
bull Helium effuses and diffuses faster than
nitrogen ndash thus helium escapes from a
balloon quicker than many other gases
Grahamrsquos Law
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves
Big Points to Remember
bull All gases at the same temperature have the same average kinetic energy
bull But they do not have the same average velocity (or speed)
bull Speed depends on Molar Mass
bull The heavier the gas the slower it moves
bull The lighter the gas the faster it moves