Behavior of Behavior of GasesGases

Airbags fill with NAirbags fill with N22 gas in an accident. gas in an accident.

Gas is generated by the decomposition of sodium azideGas is generated by the decomposition of sodium azideGas molecules save your life! Gas molecules save your life!

2 NaN2 NaN33 ---> 2 Na + 3 N ---> 2 Na + 3 N22

Example of Importance of GasesExample of Importance of Gases

Kinetic Molecular Theory (KMT)Kinetic Molecular Theory (KMT)

Particles in an Particles in an ideal gasideal gas……have no volume.have no volume.have elastic collisions. have elastic collisions. are in constant, random, straight-line motion.are in constant, random, straight-line motion.don’t attract or repel each other.don’t attract or repel each other.have an avg. KE directly related to Kelvin have an avg. KE directly related to Kelvin

temperature.temperature.

Real GasesReal Gases

Particles in a Particles in a REAL gasREAL gas…… have their own volumehave their own volume attract each otherattract each other

Gas behavior is Gas behavior is most idealmost ideal…… at low pressuresat low pressures at high temperaturesat high temperatures when very small in sizewhen very small in size when nonpolarwhen nonpolar

PLIGHTPLIGHT

Characteristics of GasesCharacteristics of GasesGases expand to fill any container uniformly.Gases expand to fill any container uniformly.

Are in random motion, have no attractionAre in random motion, have no attraction

Gases have very low densities.Gases have very low densities.Particles have no volume = lots of empty spaceParticles have no volume = lots of empty space

Characteristics of GasesCharacteristics of Gases There is a lot of “free” space in a gas.There is a lot of “free” space in a gas.

Gases can be compressed.Gases can be compressed.no volume = lots of empty spaceno volume = lots of empty space

Gases undergo diffusion & effusion.Gases undergo diffusion & effusion.Are always in random motionAre always in random motionSmaller and lighter gas particles do this fasterSmaller and lighter gas particles do this faster

Gas PressureGas Pressure

area

forcepressure

Which shoes create the most pressure?

What Causes Pressure?What Causes Pressure?http://www.chm.davidson.edu/vce/http://www.chm.davidson.edu/vce/

kineticmoleculartheory/Pressure.htmlkineticmoleculartheory/Pressure.html

Factors Affecting Gas PressureFactors Affecting Gas Pressure

Number of MolesNumber of Moles (Amount of gas) (Amount of gas)As # of particles increase, the number of As # of particles increase, the number of

collisions with the container wall increases.collisions with the container wall increases.

VolumeVolumeSmaller the volume, the greater the pressure Smaller the volume, the greater the pressure

exerted on the container.exerted on the container.

TemperatureTemperatureAs temp. increases, KE increases, this increases As temp. increases, KE increases, this increases

frequency of collisions making pressure frequency of collisions making pressure increase.increase.

Measuring Gas PressureMeasuring Gas PressureBarometerBarometer

measures atmospheric pressuremeasures atmospheric pressure (developed by Torricelli in 1643)(developed by Torricelli in 1643)

Mercury BarometerAneroid Barometer

Standard Pressure (Sea Level)Standard Pressure (Sea Level)

101.3 kPa (kilopascal)101.3 kPa (kilopascal)

1 atm 1 atm

760 mm Hg (also called torr)760 mm Hg (also called torr)

You may be asked to convert between units of pressure!You may be asked to convert between units of pressure!

Hg rises in tube until force ofHg rises in tube until force ofHg (down) balances the forceHg (down) balances the forceof atmosphere (pushing up). of atmosphere (pushing up).

(Just like a straw in soft drink)(Just like a straw in soft drink)

Column height measuresColumn height measurespressure of atmospherepressure of atmosphere

1 standard atmosphere (atm) 1 standard atmosphere (atm) = 760 mm Hg (or torr) = 760 mm Hg (or torr)

Measuring Gas PressureMeasuring Gas PressureManometerManometer

measures contained gas pressuremeasures contained gas pressure

U-tube Manometer

Working Working withwith

FormulasFormulas

The Gas LawsThe Gas Laws

TemperatureTemperature

ºC

K

-273 0 100

0 273 373

K = ºC + 273

Always use absolute temperature (Kelvin) Always use absolute temperature (Kelvin) when working with gases.when working with gases.

Gas properties can be modeled using math.Gas properties can be modeled using math.Model depends on:Model depends on:

V = volume of the gas (L)V = volume of the gas (L)

T = temperature (K)T = temperature (K)ALL temperatures MUST be in Kelvin!!! ALL temperatures MUST be in Kelvin!!!

n = amount (moles)n = amount (moles)

P = pressure (atmospheres or kPa)P = pressure (atmospheres or kPa)

Standard Temperature & PressureStandard Temperature & Pressure

0°C 1 atm

273 K 101.325 kPa

760 mmHg

-OR-

STP

Boyle’s LawBoyle’s Law

The pressure and volume of a The pressure and volume of a gas are inversely related gas are inversely related at constant mass & tempat constant mass & temp

P

V

PV = k

Robert Boyle Robert Boyle (1627-1691). Son (1627-1691). Son of Earl of Cork, of Earl of Cork, IrelandIreland..

Boyle’s Law

Since P x V is always a constant:

P1 x V1 = P2 x V2

Pressure and Volume Relationshiphttp://www.chm.davidson.edu/vce/kineticmoleculartheory/PV.html

If Mass and Temp are ConstantIf Mass and Temp are Constant

Boyle’s LawBoyle’s Law

Balloon in a Vacuum

kT

VV

T

Charles’ LawCharles’ Law

The volume and absolute The volume and absolute temperature (K) of a gas are temperature (K) of a gas are directly related directly related at constant mass & pressureat constant mass & pressure

Jacques Charles Jacques Charles (1746-1823). Isolated (1746-1823). Isolated boron and studied boron and studied gases. Balloonistgases. Balloonist..

Charles’ Law

Since V/T is always a constant:

V1 = V2

T1 T2

If Mass and Pressure are ConstantIf Mass and Pressure are Constant

Charles’ LawCharles’ Law

http://group.chem.iastate.edu/Greenbowe/sections/projectfolder/flashfiles/gaslaw/charles_law.html

http://www.pinnaclescience.com/demo.htm

Pour Liquid Nitrogen on Balloon!!

kT

PP

T

Gay-Lussac’s LawGay-Lussac’s Law The pressure and absolute The pressure and absolute

temperature (K) of a gas are temperature (K) of a gas are directly related directly related at constant mass & volumeat constant mass & volume

Gay – Lussac’s Law

Since P/T is always a constant:

P1 = P2

T1 T2

Pressure and Temperature RelationshipPressure and Temperature Relationship http://www.chm.davidson.edu/vce/http://www.chm.davidson.edu/vce/

kineticmoleculartheory/PT.htmlkineticmoleculartheory/PT.html

Review of 3 Gas Laws

Summary of Changing VariablesSummary of Changing Variableshttp://www.mhhe.com/physsci/chemistry/http://www.mhhe.com/physsci/chemistry/essentialchemistry/flash/gasesv6.swfessentialchemistry/flash/gasesv6.swf

P1V1

T1

=P2V2

T2

P1V1T2 = P2V2T1

The good news is that you don’t have to remember all three gas laws! The good news is that you don’t have to remember all three gas laws! We can combine them into a single equation.We can combine them into a single equation.If you should only need one of the other gas laws, you can cover up the item that is constant and you will get that gas law!

Combined Gas Law (on Ref Table)Combined Gas Law (on Ref Table)

ExampleExample

Set up Data TableSet up Data Table

PP1 1 = 0.800 atm V= 0.800 atm V11 = .180 L = .180 L T T11 = 302 K = 302 K

PP22 = 3.20 atm V = 3.20 atm V22= .090 L T= .090 L T2 2 = ??= ??

A sample of helium gas has a volume of 0.180 L, a pressure of 0.800 atm and a temperature of 29°C. What is the new temperature (°C) of the gas at a volume of .090 L and a pressure of 3.20 atm?

GIVEN:

V1 = 473 ml

T1 = 36°C = 309K

V2 = ?

T2 = 94°C = 367K

WORK:

P1V1T2 = P2V2T1

Gas Law ProblemsGas Law ProblemsA gas occupies 473 ml at 36°C. Find its A gas occupies 473 ml at 36°C. Find its

volume at 94°C. volume at 94°C. CHARLES’ LAW

T V

(473 ml )(367 K)=V2(309 K)

V2 = 562 ml

GIVEN:

V1 = 100. mL

P1 = 150. kPa

V2 = ?

P2 = 200. kPa

WORK:

P1V1T2 = P2V2T1

Gas Law ProblemsGas Law Problems

A gas occupies 100. mL at 150. kPa. Find A gas occupies 100. mL at 150. kPa. Find its volume at 200. kPa. its volume at 200. kPa.

BOYLE’S LAW

P V

(150.kPa)(100.mL)=(200.kPa)V2

V2 = 75.0 mL

GIVEN:

V1 = 7.84 ml

P1 = 71.8 kPa

T1 = 25°C = 298 K

V2 = ?

P2 = 101.325 kPa

T2 = 273 K

WORK:

P1V1T2 = P2V2T1

(71.8 kPa)(7.84 ml)(273 K)

=(101.325 kPa) V2 (298 K)

V2 = 5.09 ml

Gas Law ProblemsGas Law Problems A gas occupies 7.84 ml at 71.8 kPa & 25°C. A gas occupies 7.84 ml at 71.8 kPa & 25°C.

Find its volume at STP. Find its volume at STP.

P T VCOMBINED GAS LAW

GIVEN:

P1 = 765 torr

T1 = 23°C = 296K

P2 = 560. torr

T2 = ?

WORK:

P1V1T2 = P2V2T1

Gas Law ProblemsGas Law Problems

A gas’ pressure is 765 torr at 23°C. At A gas’ pressure is 765 torr at 23°C. At what temperature will the pressure be 560. what temperature will the pressure be 560. torr? torr?

GAY-LUSSAC’S LAW

P T

(765 torr)T2 = (560. torr)(309K)

T2 = 226 K = -47°C

Dalton’s Law of Partial PressuresDalton’s Law of Partial Pressures

PPtotal total == PP11+P+P22+….+….

Total pressure of a mixture of gases in a Total pressure of a mixture of gases in a container is the container is the sum sum of the individual of the individual pressures (pressures (partial pressurespartial pressures) of each gas, ) of each gas, as if each took up the total space alone.as if each took up the total space alone.

This is often useful when gases are This is often useful when gases are collected “over water”collected “over water”

Dalton’s Law of Dalton’s Law of Partial PressuresPartial Pressures

The total pressure of a mixture of The total pressure of a mixture of gases equals the sum of the partial gases equals the sum of the partial pressures of the individual gases.pressures of the individual gases.

Ptotal = P1 + P2 + ...

Patm = PH2 + PH2O

GIVEN:

PH2 = ?

Ptotal = 94.4 kPa

PH2O = 2.72 kPa

WORK:

Ptotal = PH2 + PH2O

94.4 kPa = PH2 + 2.72 kPa

PH2 = 91.7 kPa

Dalton’s LawDalton’s Law Hydrogen gas is collected over water at Hydrogen gas is collected over water at

22.5°C. Find the pressure of the dry gas if the 22.5°C. Find the pressure of the dry gas if the atmospheric pressure is 94.4 kPa.atmospheric pressure is 94.4 kPa.

Look up water-vapor pressure on for 22.5°C.

Sig Figs: Round to least number of decimal places.

The total pressure in the collection bottle is equal to atmospheric pressure and is a mixture of H2 and water vapor.

GIVEN:

Pgas = ?

Ptotal = 742.0 torr

PH2O = 42.2 torr

WORK:

Ptotal = Pgas + PH2O

742.0 torr = PH2 + 42.2 torr

Pgas = 699.8 torr

A gas is collected over water at a temp of 35.0°C when A gas is collected over water at a temp of 35.0°C when the barometric pressure is 742.0 torr. What is the partial the barometric pressure is 742.0 torr. What is the partial pressure of the dry gas? pressure of the dry gas?

DALTON’S LAW

Look up water-vapor pressure for 35.0°C.

Sig Figs: Round to least number of decimal places.

Dalton’s LawDalton’s Law

The total pressure in the collection bottle is equal to barometric pressure and is a mixture of the “gas” and water vapor.

Graham’s LawGraham’s Law

DiffusionDiffusionSpreading of gas molecules throughout a Spreading of gas molecules throughout a

container until evenly distributed.container until evenly distributed.

EffusionEffusionPassing of gas molecules through a tiny Passing of gas molecules through a tiny

opening in a containeropening in a container

Graham’s LawGraham’s Law

Speed of diffusion/effusionSpeed of diffusion/effusionKinetic energy is determined by the Kinetic energy is determined by the

temperature of the gas.temperature of the gas.

At the same temp & KE, At the same temp & KE, heavier molecules heavier molecules move more slowlymove more slowly..

kn

VV

n

Avogadro’s Principle Equal volumes of gases contain

equal numbers of moles at constant temp & pressure true for any gas

Equal volumes of gases at the same T and P have the Equal volumes of gases at the same T and P have the same number of same number of moleculesmolecules..