continuation to periodic table, measurement, dimensional analysis, gases and kinetic molecular...

8/14/2019 Continuation to Periodic Table, Measurement, Dimensional Analysis, Gases and Kinetic Molecular Theory of Gases

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IsotopesIsotopes

The different possibleThe different possible

versions of the sameversions of the sameelement havingelement having

different numbers of different numbers of neutron.neutron.



Natural AbundanceNatural Abundance

The relativeThe relative

abundance of anabundance of anisotope in nature asisotope in nature as

compared to thecompared to theother isotope of theother isotope of the

same element.same element.



Atomic Weight of Atomic Weight of ElementElement

This is defined as theThis is defined as the

average atomicaverage atomicmasses of differentmasses of different

isotopes of theisotopes of theelement.element.



Atomic Weight of Atomic Weight of ElementElement

The light metal lithiumThe light metal lithiumdiscovered by Arfvedson havediscovered by Arfvedson havetwo stable isotopes. Calculatetwo stable isotopes. Calculate

the atomic weight of lithiumthe atomic weight of lithiumgiven the percent abundance of given the percent abundance of Lithium-6 to be 7.5% and anLithium-6 to be 7.5% and an

atomic mass of 6.015122 amu.atomic mass of 6.015122 amu.On the other hand, Lithium-7On the other hand, Lithium-7has an isotopic abundance of has an isotopic abundance of

92.5% and an atomic mass of 92.5% and an atomic mass of



(7.5%)(6.015122) +(7.5%)(6.015122) +(92.5%)(7.016003)(92.5%)(7.016003)

=(0.45113415) +=(0.45113415) +

(6.489802775)(6.489802775)= 6.940936925= 6.940936925



Powers of ten

•are used for convenience withsmaller or larger units in the SI

system.



Unit…Unit…

ia group or troopa group or troopia component ora component or

thingthing

i

a part or piecea part or pieceia divisiona division

ia quantitya quantity

i f



Units of Units of

Measurement Measurement

There are two types of units:fundamental (or base)units;

derived units.

There are 7 base units in the

Système International(SI) system.

Derived units are obtained



Units of Measurement Units of Measurement

PHYSICALQUANTITY

Name of UnitAbbreviationMass

Length

Time

Electric current

Temperature

Luminousintensity

Kilogram

Meter

Second

Ampere

Kelvin

Candela

Mole

kg

m

s

a

K

cd

mol



Unit of velocity =

————————— unit of time

unit of distance

= m/s

meters

seconds=

they are obtained from the baseunits

Derived unitsDerived units




PHYSICALQUANTITY

Name of Unit

Area

Volume

Velocity

Acceleration

Current density

Luminance

Magnetic field

Square meter, m2

Cubic meter, m3

Meter/second, m/s

Meter/second

squared, m/s

2

Ampere/square meter,A/m2

Candela/square




TemperatureTemperature

•Celsius ScaleUsed in science.

Water freezes at 0oC and boils at 100oC.To convert: K = oC + 273.15.

•Kelvin ScaleAlso used in science.Same temperature increment as Celsiusscale.Lowest temperature possible is zeroKelvin.





•Fahrenheit ScaleNot generally used in science.

Water freezes at 32oF and boils at212oF.To convert:

( )32-F95C ° ( ) 32C

59F +




Volume

q The units forvolume are givenby (units of

length)3.i.e., SI unit for

volume is 1 m3.

qWe usually use 1mL = 1 cm3.

qOther volume

units:




DensityUsed to characterize substances.

Defined as mass divided by

volume.

Units: g/cm3.

Originally based on mass (thedensity was defined as the mass of 1.00 g of pure water).



All scientific measures are subjectAll scientific measures are subjectto error.to error.

These errors are reflected in the These errors are reflected in the

number of figures reported for thenumber of figures reported for themeasurement.measurement.

These errors are also reflected in These errors are also reflected in

the observation that twothe observation that two

successive measures of the samesuccessive measures of the same

quantity are different.quantity are different.

Points to Ponder?



Precision and AccuracyMeasurements that are close to the

“correct” value are accurate.

Measurements which are close toeach other are precise.

Measurements can be:

accurate and precise;precise but inaccurate;

neither accurate nor precise.

Uncertainty in Measurement Uncertainty in Measurement



Comparison of Precision andAccuracy





The number of digits reported in ameasurement reflect the accuracy of themeasurement and the precision of themeasuring device.

All the figures known with certainty plusone extra figure are called significantfigures.

In any calculation, the results arereported to the fewest significant figures(for multiplication and division) or fewest

decimal places (addition and




Significant Figures

Non-zero numbers are alwayssignificant.

Zeros between non-zero numbers are

always significant.

Zeros before the first non-zero digit arenot significant. (Example: 0.0003 has

one significant figure.)Zeros at the end of the number after a

decimal place are significant.

Zeros at the end of a number before a



Method of calculation utilizing aknowledge of units.

Given units can be multiplied or

divided to give the desired units.Conversion factors are used to

manipulate units:

Desired unit = given unit × (conversion factor)

The conversion factors are simple

Dimensional AnalysisDimensional Analysis



Conversion factor Conversion factor

unitgiven

unitdesiredfactorConversion =

1000cm3

1L

1000cm3

1LOR





Example to convert length in metersto length in inches:

(length in m)×(conversion factor form→cm)×(conversion factor for cm→

inches).




In dimensional analysis alwaysask three questions:

What data are we given?

What quantity do we need?

What conversion factors areavailable to take us from whatwe are given to what we need?



Question?Question?

We measure length inWe measure length in metersmeters using ausing a

meter stick or a rulermeter stick or a ruler..

We measure time in seconds using aWe measure time in seconds using a

clock or a timerclock or a timer..

We measure temperature inWe measure temperature in °C, °F or K °C, °F or K using ausing a thermometerthermometer..

We measure volume inWe measure volume in litersliters using ausing a

graduated cylinder or containergraduated cylinder or container..

We measure speed inWe measure speed in m/sm/s using ausing a

speedometer (or combination of #1speedometer (or combination of #1& #2& #2)..

We can measure mass, length, time,temperature, volume, etc. Wemeasure mass in grams using a

balance or a weighing scale.How can you measure length?

How can you measure time?

How can you measure temperature?

How can you measure volume?

How can you measure speed?



We count atoms,

molecules, substances,particles, and pieces inMOLES.

How can you measure, or

count atoms, molecules,substances and/or

particles?



MolesMoles

Defined as the numberDefined as the numberof carbon atoms inof carbon atoms in

exactly 12 grams of exactly 12 grams of carbon-12.carbon-12.

1 mole is 6.02 x 101 mole is 6.02 x 102323

particles.particles.

6.02 x 106.02 x 102323

is calledis called’



Representative particlesRepresentative particles

The smallest pieces of a The smallest pieces of asubstance.substance.

For a molecular compoundFor a molecular compoundit is ait is a moleculemolecule..

For an ionic compound it isFor an ionic compound it is

aa formula unitformula unit..

For an element it is anFor an element it is an

atomatom..



Types of questionsTypes of questions

How many oxygen atoms in theHow many oxygen atoms in thefollowing?following?

CaCOCaCO33

AlAl22(SO(SO44))33

How many ions in the following?How many ions in the following?

CaClCaCl22NaOHNaOH

AlAl22(SO(SO44))33



Types of questionsTypes of questions

How many molecules of COHow many molecules of CO22 are theare thein 4.56 moles of COin 4.56 moles of CO22 ??

How many moles of water is 5.87 xHow many moles of water is 5.87 x

10102222 water molecules?water molecules?

How many atoms of carbon areHow many atoms of carbon are

there in 1.23 moles of Cthere in 1.23 moles of C66HH1212OO66 ??

How many moles is 7.78 x 10How many moles is 7.78 x 102424

formula units of MgClformula units of MgCl22??



Measuring MolesMeasuring Moles

remember relative atomic mass?remember relative atomic mass?the amu was one twelfth thethe amu was one twelfth the

mass of a carbon-12 atom.mass of a carbon-12 atom.

since the mole is the number of since the mole is the number of

atoms in 12 grams of carbon-12,atoms in 12 grams of carbon-12,

the decimal number on thethe decimal number on theperiodic table is also the mass of periodic table is also the mass of

1 mole of those atoms in grams.1 mole of those atoms in grams.



Gram Atomic MassGram Atomic Mass

The mass of 1 mole of an The mass of 1 mole of an

element in grams.element in grams.

12.01 grams of carbon has the12.01 grams of carbon has the

same number of pieces as 1.01same number of pieces as 1.01grams of hydrogen and 55.85grams of hydrogen and 55.85

grams of iron.grams of iron.

We can write this asWe can write this as

12.01 g C = 1 mole12.01 g C = 1 mole

We can count things by weighingWe can count things by weighing

l



ExamplesExamples

How much would 2.34 moles of How much would 2.34 moles of carbon weigh?carbon weigh?

How many moles of magnesiumHow many moles of magnesium

in 24.31 g of Mg?in 24.31 g of Mg?

How many atoms of lithium inHow many atoms of lithium in

1.00 g of Li?1.00 g of Li?How much would 3.45 x 10How much would 3.45 x 102222

atoms of U weigh?atoms of U weigh?

f d ?



Mass of compounds?Mass of compounds?

in 1 mole of Hin 1 mole of H22O molecules thereO molecules thereare two moles of H atoms and 1are two moles of H atoms and 1

mole of O atomsmole of O atoms

To find the mass of one mole of a To find the mass of one mole of acompoundcompound

determine the moles of thedetermine the moles of the

elements they haveelements they have

find out how much they wouldfind out how much they would

weighweigh

add them u

G M l l M



Gram Molecular MassGram Molecular Mass

What is the mass of one mole of What is the mass of one mole of

CHCH44??

1 mole of C = 12.01 g1 mole of C = 12.01 g

4 mole of H x 1.01 g = 4.04g4 mole of H x 1.01 g = 4.04g1 mole CH1 mole CH44 = 12.01 + 4.04 = 16.05g= 12.01 + 4.04 = 16.05g

The The Gram Molecular massGram Molecular mass of CHof CH44 isis16.0516.05

The mass of one mole of a molecular The mass of one mole of a molecular

compound.compound.

lG F l M



Gram Formula MassGram Formula Mass

The mass of one mole of an ionic The mass of one mole of an ionic

compound.compound.

Calculated the same way.Calculated the same way.

Example, what is the GFM of Example, what is the GFM of FeFe22OO33??

2 moles of Fe x 55.85 g = 111.702 moles of Fe x 55.85 g = 111.70gg

3 moles of O x 16.00 g = 48.003 moles of O x 16.00 g = 48.00

lM l M



Molar MassMolar Mass

The generic term for the mass of one The generic term for the mass of one

mole.mole.

The same as gram molecular mass, The same as gram molecular mass,

gram formula mass, and gramgram formula mass, and gram

atomic mass.atomic mass.

The number of grams of 1 mole of The number of grams of 1 mole of

atoms, ions, or molecules.atoms, ions, or molecules.Using molar mass, we can makeUsing molar mass, we can make

conversion factors and;conversion factors and;

We can chan e rams of aWe can chan e rams of a

F lF l



For exampleFor example

How many moles is 5.69 g of How many moles is 5.69 g of

NaOH?NaOH?

F lF l





NaOH?NaOH?

F lF l





NaOH?NaOH?

NaOHmol? NaOHg ?

NaOHmol ?

NaOHg69.5 =

q need to change grams to moles

F lF l





NaOH?NaOH?q

need to change grams to molesq for NaOH:

q1mole Na = 22.99g

q1 mol O = 16.00 g

q1 mole of H = 1.01 g

F lF l





NaOH?NaOH?

40.00g

mol1

qneed to change grams to moles

qfor NaOH:q1 mole NaOH = 40.00 g

F lF l





NaOH?NaOH?

?40.00

mol1g69.5 =

g

q

need to change grams to molesqfor NaOH:

q1 mole NaOH = 40.00 g

F lF l





NaOH?NaOH?

NaOHmol0.142 =40.00mol1g69.5

g

E lE l



ExamplesExamples

How many moles is 4.56 g of How many moles is 4.56 g of COCO22??

How many grams is 9.87 molesHow many grams is 9.87 moles

of Hof H22O?O?

How many molecules in 6.8 g of How many molecules in 6.8 g of

CHCH44??

49 molecules of C49 molecules of C66HH1212OO66 weighsweighs

how much?how much?



Gases and the MoleGases and the Mole

St d d T t dSt d d T t d



Standard Temperature andStandard Temperature andPressurePressure

0ºC and 1 atm0ºC and 1 atmabbreviated STPabbreviated STP

At STP 1 mole of gas occupiesAt STP 1 mole of gas occupies22.42L22.42L (called the molar(called the molar

volume)volume)

Note: Avogadro’s Hypothesis - at theNote: Avogadro’s Hypothesis - at the

same temperature and pressuresame temperature and pressure

equal volumes of gas have the sameequal volumes of gas have the same

E lExamples



ExamplesExamples

What is the volume of 4.59 moleWhat is the volume of 4.59 moleof COof CO22 gas at STP?gas at STP?

How many moles is 5.67 L of OHow many moles is 5.67 L of O22

at STP?at STP?

What is the volume of 8.8g of What is the volume of 8.8g of

CHCH44 gas at STP?gas at STP?

Densit of a gasDensity of a gas



Density of a gasDensity of a gas

D = m /VD = m /V

for a gas the units will be g / Lfor a gas the units will be g / L

We can determine the density of We can determine the density of

any gas at STP if we know itsany gas at STP if we know itsformula.formula.

To find the density we need the To find the density we need the

mass and the volume.mass and the volume. If you assume you have 1 moleIf you assume you have 1 mole

then the mass is the molar mass.then the mass is the molar mass.

ExamplesExamples



ExamplesExamples

Find the density of COFind the density of CO22 at STP.at STP.Find the density of CHFind the density of CH

44 atat

STP.STP.



What I expected you to haveWhat I expected you to have



What I expected you to haveWhat I expected you to havelearned:learned:

change moles to gramschange moles to grams

moles to atomsmoles to atoms

moles to formula unitsmoles to formula units

moles to moleculesmoles to molecules

moles to litersmoles to liters

molecules to atomsmolecules to atomsformula units to atomsformula units to atoms

formula units to ionsformula units to ions



Moles

Mass



Moles

MassPT



Moles

MassVolume PT



Moles

MassVolume PT22.4 L



Moles

MassVolume

RepresentativeParticles

PT22.4 L



Moles

MassVolume


6.02 x 1023

PT

Atoms

22.4 L



Moles

MassVolume


6.02 x 1023

PT

Atoms Ions

22.4 L

Percent CompositionPercent Composition



Percent CompositionPercent Composition

Like all percentsLike all percents Part x 100 %Part x 100 %

wholewhole

Find the mass of eachFind the mass of each

component,component,

divide by the total mass.divide by the total mass.

ExampleExample



ExampleExample

Calculate the percentCalculate the percentcomposition of a compoundcomposition of a compound

that is 29.0 g of Ag withthat is 29.0 g of Ag with

4.30 g of S.4.30 g of S.87n1387n13



ExamplesExamples



ExamplesExamples

Calculate the percentCalculate the percentcomposittion of Ccomposittion of C22HH44??86n1486n14

Aluminum carbonate.Aluminum carbonate.



Empirical FormulaEmpirical Formula

From percentage to formulaFrom percentage to formula

The Empirical FormulaThe Empirical Formula



The Empirical FormulaThe Empirical Formula

The lowest whole number ratio of The lowest whole number ratio of

elements in a compound.elements in a compound. The molecular formula the actual The molecular formula the actual

ratio of elements in a compound.ratio of elements in a compound. The two can be the same. The two can be the same.

CHCH22 empirical formulaempirical formula

CC22HH44 molecular formulamolecular formula

CC33HH66 molecular formulamolecular formula

H O both

Calculating EmpiricalCalculating Empirical




Just find the lowest whole number Just find the lowest whole number

ratioratio

CC66HH1212OO66 ---> ?---> ?

CHCH44NNIt is not just the ratio of atoms, it isIt is not just the ratio of atoms, it is

also the ratio of moles of atoms.also the ratio of moles of atoms.

In 1 mole of COIn 1 mole of CO22 there is 1 mole of there is 1 mole of

carbon and 2 moles of oxygen.carbon and 2 moles of oxygen.

In one molecule of COIn one molecule of CO22 there is 1there is 1





Means we can get ratio fromMeans we can get ratio frompercent composition.percent composition.

Assume you have a 100 g.Assume you have a 100 g.

The percentages become The percentages become

grams.grams.

Can turn grams to moles.Can turn grams to moles.

Find lowest whole numberFind lowest whole number

How do we do it?How do we do it?



How do we do it?How do we do it?

Calculate the empirical formula of aCalculate the empirical formula of acompound composed of 38.67 % C,compound composed of 38.67 % C,

16.22 % H, and 45.11 %N.16.22 % H, and 45.11 %N.

Assume 100 g soAssume 100 g so38.67 g C x 1mol C = 3.22038.67 g C x 1mol C = 3.220

mole Cmole C 12.01 g C12.01 g C

16.22 g H x 1mol H = 16.0916.22 g H x 1mol H = 16.09mole Hmole H 1.01 g H1.01 g H

45.11 g N x 1mol N = 3.219 mole45.11 g N x 1mol N = 3.219 mole

NN 14.01 g N14.01 g N

ExampleExample



ExampleExample

The ratio is 3.220 mol C = 1 mol C The ratio is 3.220 mol C = 1 mol C3.219 mol N 13.219 mol N 1

mol Nmol N

The ratio is 16.09 mol H = 5 mol H The ratio is 16.09 mol H = 5 mol H

3.219 mol N 13.219 mol N 1

mol Nmol N

1 C : 1 N 5 H : 1 N1 C : 1 N 5 H : 1 N

CC11HH55NN11

ExampleExample



ExampleExample

i

A compound is 43.64 % PA compound is 43.64 % Pand 56.36 % O. What is theand 56.36 % O. What is the

empirical formula?empirical formula?

iCaffeine is 49.48% C, 5.15%Caffeine is 49.48% C, 5.15%

H, 28.87% N and 16.49% O.H, 28.87% N and 16.49% O.

What is its empirical formula?What is its empirical formula?

Empirical to molecularEmpirical to molecular



Empirical to molecularEmpirical to molecular

Since the empirical formula is theSince the empirical formula is the

lowest ratio, the actual moleculelowest ratio, the actual molecule

would weigh more.would weigh more.

By a whole number multiple.By a whole number multiple.Divide the actual molar mass byDivide the actual molar mass by

the the mass of one mole of thethe the mass of one mole of the

empirical formula.empirical formula.

Caffeine has a molar mass of 194Caffeine has a molar mass of 194

g what is its molecular mass?g what is its molecular mass?



ExampleExample



ExampleExample

What is its molecularWhat is its molecularformula?formula?

E.F. = CHE.F. = CH22ClCl

E.W. = 49.5E.W. = 49.5∴∴M.F. =M.F. = C2H4Cl2



The effect of adding gas.The effect of adding gas.



The effect of adding gas.The effect of adding gas.

When we blow up a balloonWhen we blow up a balloonwe are adding gaswe are adding gas

molecules.molecules.

((we can see an increase inwe can see an increase insize of the balloonsize of the balloon))Doubling the the number of

gas particles doubles thepressure.

(given the same volume at

Pressure and the number of Pressure and the number of



molecules are directly relatedmolecules are directly related

½More molecules meansMore molecules meansmore collisions.more collisions.

½

Fewer molecules meansFewer molecules meansfewer collisions.fewer collisions.

½Gases naturally move fromGases naturally move from

areas of high pressure to lowareas of high pressure to lowpressure because there ispressure because there isempty space to move in.empty space to move in.



1 atm

If you double the number of If you double the number of moleculesmolecules



You double the pressure. You double the pressure.2 atm

If you double the number of molecules



4 atm Assuming theAssuming thepressure outsidepressure outside

is 1 atm.is 1 atm.

As you removeAs you removemolecules from amolecules from a

containercontainer

Patm = 1 atm



As you removeAs you remove

molecules from amolecules from a

container thecontainer the

pressurepressuredecreasesdecreases

2 atm2 atm



Molecules naturally move fromMolecules naturally move from

high to low pressurehigh to low pressure

1 atmAs you removemolecules from acontainer the

pressuredecreases until thepressure inside

equals thepressure outside

containercontainer



containercontainer

½In a smaller container,In a smaller container,molecules have less room tomolecules have less room to

move.move.

½ They hit the sides of the They hit the sides of the

container more often.container more often.

½As volume decreasesAs volume decreases

pressure increases.pressure increases.



1 atm

4 Liters

As theAs the

pressure onpressure ona gasa gas

increasesincreases



pp

½Raising the temperature of aRaising the temperature of agas increases the pressure if gas increases the pressure if

the volume is held constant.the volume is held constant.

½ The molecules hit the walls The molecules hit the walls

harder.harder.

½ The only way to increase the The only way to increase the

temperature at constanttemperature at constant

ressure is to increase theressure is to increase the

300 K



1L ; 1 atm

If you start with 1 liter of gas at 1atm pressure and 300 K and heat itto 600 K one of 2 things happens



For this course we

are going toassume the gases

behave ideally.



vacuum



hole



Effusion



The term used to

describe the passageof gas through a tiny

orifice into anevacuated chamber



Ideal Gases don’t existIdeal Gases don’t exist



½Gas molecules do takeGas molecules do take

up spaceup space

½ There are attractive There are attractive

forces between them,forces between them,

otherwise there would beotherwise there would beno liquidsno liquids

Ideal Gases



½ There are no gases forwhich this is true. Does notreally exist

½Makes the math easier andis a close approximation.

½Particles have no volume.

½No attractive forces.

Ideal GasesIdeal Gases



Real gases

behave likeideal gases athigh temperatureand low

GasesGases



½When the moleculesWhen the molecules

do not take up as bigdo not take up as biga percentage of thea percentage of the

spacespace

½We can ignore theirWe can ignore their

volume.volume.

½When the moleculesare far apart

½ This is at low

pressure

gasesgases



½When molecules are movingWhen molecules are moving

fast.fast.

½Collisions are harder and faster.Collisions are harder and faster.

½Gas molecules are not next toGas molecules are not next to

each other very long.each other very long.



PressuresPressures



½ The total pressure inside a The total pressure inside a

container is equal to thecontainer is equal to the

partial pressure due to eachpartial pressure due to each

gas.gas.

½ The partial pressure of a The partial pressure of a

gas is the contribution bygas is the contribution by

that gas.that gas.

ExamplesExamples



What is the total pressure in aWhat is the total pressure in a

balloon filled with air if theballoon filled with air if the

pressure of the oxygen is 170 mmpressure of the oxygen is 170 mm

Hg and the pressure of nitrogen isHg and the pressure of nitrogen is620 mm Hg?620 mm Hg?

In a second balloon the totalIn a second balloon the totalpressure is 790 mm Hg. What ispressure is 790 mm Hg. What is

the pressure of oxygen if thethe pressure of oxygen if the

Boyle’s LawBoyle’s Law



½At a constant temperature,At a constant temperature,

pressure and volume arepressure and volume are

inversely related.inversely related.

½As one goes up the otherAs one goes up the other

goes downgoes down

½P x V =P x V = kk ((k is some constantk is some constant))

½Easier to use PEasier to use P11 x Vx V11 = P= P22 xx

Boyle’s LawBoyle’s Law



ExamplesExamples



A balloon is filled with 25 L of A balloon is filled with 25 L of air at 1.0 atm pressure. If theair at 1.0 atm pressure. If the

pressure is change to 1.5 atmpressure is change to 1.5 atm

what is the new volume?what is the new volume?16.6716.67

A balloon is filled with 73 L of A balloon is filled with 73 L of

air at 1.3 atm pressure. Whatair at 1.3 atm pressure. Whatpressure is needed to changepressure is needed to change

to volume to 43 L?to volume to 43 L?2.22.2

Charles’ LawCharles’ Law



½ The volume of a gas is directly The volume of a gas is directly

proportional to theproportional to the KelvinKelvin

temperature if the pressure istemperature if the pressure is

held constant.held constant.

½V =V = kk xx T T ((k is some constantk is some constant))

½V/T=V/T= kk

½Easier to useEasier to use VV11/T/T11= V= V22/T/T22

Charles’ LawCharles’ Law



T

ExamplesExamples



What is the temperature of What is the temperature of a gas that is expanded froma gas that is expanded from

2.5 L at 25ºC to 4.1 L at2.5 L at 25ºC to 4.1 L at

constant pressure.constant pressure.216216

What is the final volume of What is the final volume of

a gas that starts at 8.3 La gas that starts at 8.3 L

and 17ºC and is heated toand 17ºC and is heated to

Gay Lussac’s LawGay Lussac’s Law



½ The temperature and the The temperature and thepressure of a gas arepressure of a gas are

directly related at constantdirectly related at constantvolume.volume.

½P =P = kk xx T T ((k is somek is some

constantconstant))

½ ==

Gay Lussac’s LawGay Lussac’s Law



T

ExamplesExamples



What is the pressure inside aWhat is the pressure inside a

0.250 L can of deodorant that0.250 L can of deodorant that

starts at 25ºC and 1.2 atm if starts at 25ºC and 1.2 atm if

the temperature is raised tothe temperature is raised to

100ºC?100ºC?1.51.5

At what temperature will theAt what temperature will the

can above have a pressure of can above have a pressure of

Combined Gas LawCombined Gas Law



½Deals with the situationDeals with the situationwhere only the number of where only the number of

molecules stays constant.molecules stays constant.

½(P(P11 x Vx V11)/T)/T11 = (P= (P22 x Vx V22)/T)/T22

½

PP11VV11 T T22 = P= P22VV22 T T11

ExamplesExamples



A 15 L cylinder of gas at 4.8A 15 L cylinder of gas at 4.8

atm pressure and 25ºC isatm pressure and 25ºC is

heated to 75ºC andheated to 75ºC and

compressed to 17 atm. Whatcompressed to 17 atm. Whatis the new volume?is the new volume?4.954.95

If 6.2 L of gas at 723 mm HgIf 6.2 L of gas at 723 mm Hgat 21ºC is compressed to 2.2at 21ºC is compressed to 2.2

L at 4117 mm Hg, what is theL at 4117 mm Hg, what is the

The combined gas law contains The combined gas law contains

ll th th l !all the other gas laws!



all the other gas laws!all the other gas laws!

If the temperature remainsIf the temperature remainsconstant.constant.

P1 V1

T1

x = P2 V2

T2

x

Boyle’s Law

The combined gas law contains The combined gas law contains

all the other gas la s!all the other gas laws!



all the other gas laws!all the other gas laws!

If the pressure remainsIf the pressure remainsconstant.constant.

P1 V1

T1

x = P2 V2

T2

x

Charles’ Law

The combined gas law containsll th th l !



P1 V1

T1

x = P2 V2

T2

x

Gay-Lussac Law

all the other gas laws!

If the volume remains constant.

Volume and molesVolume and moles



½Avogadro’s Hypothesis - atAvogadro’s Hypothesis - at

the same temperature andthe same temperature and

pressure equal volumes of pressure equal volumes of

gas have the same numbergas have the same numberof particles.of particles.

½V is proportional to numberV is proportional to number

of molecules at constant Tof molecules at constant Tand P.and P.

½V is ro ortional to molesV is proportional to moles

The Ideal Gas LawThe Ideal Gas Law



½PP xx V = nV = n xx RR xx T T

½ This time R does not depend This time R does not depend

on anything, it is reallyon anything, it is really

constantconstant

½

R = 0.0821 (L atm)/(mol K)R = 0.0821 (L atm)/(mol K)½R = 8.3145 J/(mol K)R = 8.3145 J/(mol K)

½

The Ideal Gas LawThe Ideal Gas Law



½We now have a new way toWe now have a new way tocount the number of moles of count the number of moles of

a gas. By measuringa gas. By measuring TT,, PP, and, and

VV. We aren’t. We aren’t restrictedrestricted totoSTPSTP..

½n = PV/RTn = PV/RT

ExamplesExamples



How many moles of air areHow many moles of air arethere in a 2.0 L bottle at 19 ºCthere in a 2.0 L bottle at 19 ºC

and 747 mm Hg?and 747 mm Hg?0.080.08

What is the pressure exertedWhat is the pressure exerted

by 1.8 g of Hby 1.8 g of H22 gas exert in a 4.3gas exert in a 4.3L balloon at 27 ºC?L balloon at 27 ºC?3918mm5.2atm3918mm5.2atm

Points to Ponder?



½ The molar mass of a gas can be The molar mass of a gas can be

determined by the density of determined by the density of

the gas.the gas.

½Density = mass/Volume = m/VDensity = mass/Volume = m/V

½Molar mass = mass/moles =Molar mass = mass/moles =

m/nm/n

Points to Ponder?



½Molar Mass =Molar Mass = mm(PV/RT)(PV/RT)

½Molar mass =Molar mass = m RTm RTV PV P

½

Molar mass =Molar mass = D RTD RTPP

At STPAt STP



½

At STP determining the amountAt STP determining the amountof gas required or produced isof gas required or produced is

easy.easy.

½For example, how many liters of For example, how many liters of

OO22 at STP areat STP are required torequired to

produce 20.3 g of Hproduce 20.3 g of H22O?O?14.22L14.22L



Kinetic Molecular Theory of Gases

Th l f th i di id lTh l f th i di id l

PostulatesPostulates



½ The volume of the individual gas The volume of the individual gas

particles can beparticles can be assumed to beassumed to benegligiblenegligible½ The particles are in The particles are in constantconstant

motionmotion½ The particles are The particles are assumed toassumed to

exertexert nono forcesforces on each otheron each other

½ The The average kinetic energyaverage kinetic energy of of the gas isthe gas is assumed to be directlyassumed to be directlyproportional to the temperatureproportional to the temperature

of the gasof the gas

From the theory



PV n ∝ T

23 (KE)av

g

From the theory



PV

n∝

T

From the experiment



PV

n = RT

combining



(KE)av

g

RT32

ExampleExample



It was found out that 1.0 LIt was found out that 1.0 Lof carbon dioxide (COof carbon dioxide (CO22) took) took

3 minutes to effuse through3 minutes to effuse through

a porous filter. How longa porous filter. How long

will it take 1.0 L of methanewill it take 1.0 L of methane

(CH(CH44) to effuse under the) to effuse under thesame conditions?same conditions?

Can we predict the distanceCan we predict the distancetraveled by NHtraveled by NH and HCl?and HCl?



traveled by NHtraveled by NH33 and HCl?and HCl?

Graham Law

A



1

2

M

M

2gasof effusionof rate

1gasof effusionof rate=

At constant temperature,the relative rates of effusion of two gases are

given by the inverse ratioof the square roots of

their masses

1

2

M

M2gasof effusionof rate1gasof effusionof rate =



= 0.55 L /min

2

4

CO

CH

4

2

MM

CHrateCOrate =

2

4

CO

CH

4 MM

MM

CHrate

L/min.0.33 =

44

16

CHrate

L/min.0.33

4

=4416

CHrate

L/min.0.33

4

=

= 1.8 min

continuation to periodic table, measurement, dimensional analysis, gases and kinetic molecular...

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