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Recall
Recall: KMT Assumptions 1. Gasesaremadeofmanyspherical
particlesthatareinconstant,randommotion
– theyhavekineticenergy
2. Gasparticlesexertneitherattractivenorrepulsiveforcesononeanother
3. Gasparticleshaveinsignificantvolume.– Thereissomuchspacebetweenparticles
thatmostofthevolumeisemptyspace
4. Collisionsareperfectlyelastic.– Whentheycollide,nokineticenergyislost.
5. AverageKEisdependentonthetemperature.
– Theyaredirectlyproportional
TheIdealGasLaw
Ideal Gas Law PV=nRT
• P=Pressure• V=Volume• n=Amount(mol)• T=Temperature(K)• R=universalgasconstant
– USEREFERENCESHEET–theygiveyou3differentvaluesdependingonyourunits
Ideal Gas Law
PV=nRT• Describesahypotheticalgas(idealgas)• FollowstheKMTassumptions
Ideal Gas Law PV=nRT
• From your reference sheet: R = 0.08206 L x atm/ mol x K R = 8.314 J/ mol x K R = 62.36 L x torr/ mol x K
• The units MUST match in order to cancel out
• Wrong units = wrong answer
Ideal Gas Law PV=nRT
• You can derive R using conditions at STP
• R = PV/nT • = (1 atm) (22.4 L) / (1 mol) (273 K)
“Ideal”Gases
Ideal Gases • We are going to assume the gases
behave “ideally”and that they obey the Gas Laws under all T and P conditions
• An ideal gas does not really exist, but it makes the math easier and is a close approximation.
• Real gases = behave like ideal gases at high T and low P
Example • A cylinder of argon gas contains 50.0 L of
Ar at 1860 kPa and 400. K. What mass of argon is in the cylinder?
SampleQuestion• WhichofthefollowinggraphsrepresentsaplotofP(y-axis)versusV(x-axis)foranidealgasatconstantTandn?a. ab. bc. cd. de. e
SampleQuestion• Fouridentical1.0-LflaskscontainthegasesHe,Cl2,CH4,andNH3– Eachgasisat0°Cand1atmpressure– Whichgassamplehasthegreatestnumberof
molecules?a. Heb. Cl2c. CH4
d. NH3
e. Allthesame
SampleQuestion• Whichofthefollowinggraphsrepresentsaplotofn(y-axis)versusT(x-axis)foranidealgasatconstantPandV?a. ab. bc. cd. de. e
a)
e) d)
b) c)
SampleQuestion• WhichofthefollowinggraphsrepresentsaplotofV(y-axis)versusT(Kelvin,x-axis)foranidealgasatconstantPandn?a. ab. bc. cd. de. e
a)
e) d)
b) c)
SampleQuestion• WhichofthefollowinggraphsrepresentsaplotofV(y-axis)versusT(Celsius,x-axis)foranidealgasatconstantPandn?a. ab. bc. cd. de. e
a)
e) d)
b) c)
SampleQuestion• WhichofthefollowinggraphsrepresentsaplotofV(y-axis)versusn(x-axis)foranidealgasatconstantPandT?a. ab. bc. cd. de. e
a)
e) d)
b) c)
SampleQuestion• WhichofthefollowinggraphsrepresentsaplotofPV(y-axis)versusV(x-axis)for1.0molofanidealgasatconstantT?a. ab. bc. cd. de. e
a)
e) d)
b) c)
SampleQuestion• WhichofthefollowinggraphsrepresentsaplotofPV(y-axis)versusn(x-axis)foranidealgasatconstantT?a. ab. bc. cd. de. e
a)
e) d)
b) c)
GasStoichiometry
Gas Stoichiometry • Asampleofmethanegashavingavolumeof2.80Lat25°Cand1.65atmwasmixedwithasampleofoxygengashavingavolumeof35.0Lat31°Cand1.25atm.Themixturewasthenignitedtoformcarbondioxideandwater.CalculatethevolumeofCO2formedatapressureof2.50atmandatemperatureof125°C
Gas Stoichiometry • Asampleofmethanegashavingavolumeof2.80Lat25°Cand1.65atmwasmixedwithasampleofoxygengashavingavolumeof35.0Lat31°Cand1.25atm.Themixturewasthenignitedtoformcarbondioxideandwater.CalculatethevolumeofCO2formedatapressureof2.50atmandatemperatureof125°C
• First:• Writeyourbalancedchemicalequation
CH4(g)+2O2(g)àCO2(g)+2H2O(g)
Gas Stoichiometry • Asampleofmethanegashavingavolumeof2.80Lat25°Cand1.65atmwasmixedwithasampleofoxygengashavingavolumeof35.0Lat31°Cand1.25atm.Themixturewasthenignitedtoformcarbondioxideandwater.CalculatethevolumeofCO2formedatapressureof2.50atmandatemperatureof125°C
• Second:Writeyourknowns• PCH4=1.65atm PO2=1.25atm PCO2=2.50atm• VCH4=2.80L VO2=35.0L VCO2=?• TCH4=298K TO2=304K TCO2=398K
Gas Stoichiometry • Asampleofmethanegashavingavolumeof2.80Lat25°Cand1.65atmwasmixedwithasampleofoxygengashavingavolumeof35.0Lat31°Cand1.25atm.Themixturewasthenignitedtoformcarbondioxideandwater.CalculatethevolumeofCO2formedatapressureof2.50atmandatemperatureof125°C
• Third:• UsePV=nRTtofindthemolesofeachofyourreactants• nCH4=• 0.189mol• nO2=• 1.75mol
Gas Stoichiometry • Asampleofmethanegashavingavolumeof2.80Lat25°Cand1.65atmwasmixedwithasampleofoxygengashavingavolumeof35.0Lat31°Cand1.25atm.Themixturewasthenignitedtoformcarbondioxideandwater.CalculatethevolumeofCO2formedatapressureof2.50atmandatemperatureof125°C
• Fourth:• Determineyourlimitingreactant• nCH4=0.189mol nO2=1.75mol
CH4(g)+2O2(g)àCO2(g)+2H2O(g)
Gas Stoichiometry • Asampleofmethanegashavingavolumeof2.80Lat25°Cand1.65atmwasmixedwithasampleofoxygengashavingavolumeof35.0Lat31°Cand1.25atm.Themixturewasthenignitedtoformcarbondioxideandwater.CalculatethevolumeofCO2formedatapressureof2.50atmandatemperatureof125°C
• Fifth:• UseyourLRtocalculateyourmolesofproduct
Gas Stoichiometry • Asampleofmethanegashavingavolumeof2.80Lat25°Cand1.65atmwasmixedwithasampleofoxygengashavingavolumeof35.0Lat31°Cand1.25atm.Themixturewasthenignitedtoformcarbondioxideandwater.CalculatethevolumeofCO2formedatapressureof2.50atmandatemperatureof125°C
• Sixth:• Sincewe’renotatSTP,usePV=nRTtocalculateV
DensityandMolarMass
Recall • PV=nRT• Sincen=m/M
– m=mass(g)– M=molarmass(g/mol)
• WecansaythatPV=mRT/M• Sinced=m/V• WecansaythatP=dRT/M• RearranginggivesM=dRT/P
Example • Thedensityofagaswasmeasuredat1.50atmand27oCandfoundtobe1.95g/L.Calculatethemolarmassofthegas.
• First:Writeyourknowns• d=1.95g/L• R=0.08206L.atm/mol.K• T=27oC+273=300.K• P=1.50atm
Example • Thedensityofagaswasmeasuredat1.50atmand27oCandfoundtobe1.95g/L.Calculatethemolarmassofthegas.
• Second:Writeyourformulaandplug-in• M=dRT/P• =(1.95g/L)(0.08206L.atm/mol.K)(300.K)/(1.50atm)• M=32.0g/mol
SampleQuestion• Whathappenstothedensityofagascontainedinarigidsteelcontainerasyouheatthegas?a. Densityofthegasincreasesb. Densityofthegasdecreasesc. Densityofthegasdoesnotchange
SampleQuestion• Whathappenstothedensityofagascontainedinacontainerfittedwithamovablepistonasyouheatthegas?a. Densityofthegasincreasesb. Densityofthegasdecreasesc. Densityofthegasdoesnotchange
SampleQuestion• Youareholdingtwoballoons,eachofwhichisfilledwiththesamemassofgas– Oneballooncontainshydrogengas(H2)– Otherballooncontainsheliumgas(He)– Whichofthefollowingstatementsiscorrect?
a. Balloonfilledwithhydrogenistwiceaslargeastheballoonfilledwithhelium
b. Balloonfilledwithheliumistwiceaslargeastheballoonfilledwithhydrogen
c. Balloonshaveequalvolumes
SampleQuestion• Whichofthefollowingisareasonableestimateofthevolumeofaballoonfilledwith35gofheliumonaspringdayinChicago,Illinois?a. 1Lb. 10Lc. 50Ld. 200Le. 1000L
SampleQuestion• Considerasampleofneongasinacontainerfittedwithamovablepiston(assumethepistonismasslessandfrictionless)– Temperatureofthegasisincreasedfrom20.0°Cto40.0°C
– Densityofneon:a. Increaseslessthan10%b. Decreaseslessthan10%c. Increasesmorethan10%d. Decreasesmorethan10%e. Doesnotchange
SampleQuestion• Fouridentical1.0-LflaskscontainthegasesHe,Cl2,CH4,andNH3,eachat0°Cand1atmpressure– Whichgashasthehighestdensity?
a. Heb. Cl2c. CH4
d. NH3
e. Allarethesame
Dalton’sLawofPartialPressures
Dalton’s Law of Partial Pressures • Howcanyoufindthepartialpressures?• Assumingthateachgasbehavesideally,usePV=nRT– Ex/PA=nART/V– Ex/PB=nBRT/V
• Fromhere,wecaninferthat– PT=PA+PB+PC+...– PT=(nA+nB+nC+…)RT/V– PT=nT(RT/V)
Figure5.12-SchematicDiagramofDalton’sLawofPartialPressures
47Copyright©CengageLearning.Allrightsreserved
Dalton’s Law of Partial Pressures • IfwearelookingatnTasthetotalnumberofmoles,wecanalsolookatthemolefraction(X)
IfXA=nA/nTThenPA=PTXA
(Theseareonyourformulasheet.Beabletointerpretandusethem)
Example • Thepartialpressureofoxygenwasobservedtobe156torrinairwithatotalatmosphericpressureof743torr.CalculatethemolefractionofO2present.
• Whatdoweknow?• PO2=156torr• PT=643torr• XO2=?• Let’susePA=PTXA
Example • Thepartialpressureofoxygenwasobservedtobe156torrinairwithatotalatmosphericpressureof743torr.CalculatethemolefractionofO2present.
• PO2=PTXO2• SoXO2=PO2/PT• XO2=156torr/743torr• XO2=0.210• (Themolefractionhasnounits)
Try This: • Amixtureofgasescontains4.46molNe,0.74molAr,and2.15molXe.Calculatethepartialpressuresofeachofthesegasesifthetotalpressureis2.00atm.
• Hint:• What’sthemolefractionofeach?
Dalton’s Law of Partial Pressures • Collectingagasoverwater:
– Amixtureofgasesresultswheneveragasiscollectedbydisplacementofwater
– Vaporpressureofwater• Pressureofwatervaporthatremainsconstant
– Occursasthenumberofwatermoleculesinthevaporstateremainsconstantwhentherateofescapeequalstherateofreturn
• Dependsontemperature
Figure5.13-ProductionofOxygenbyThermalDecompositionofKClO3
Example • Asampleofsolidpotassiumchlorate(KClO3)washeatedinatesttubeanddecomposedbythefollowingreaction:2KClO3(s)à2KCl(s)+3O2(g)– Oxygenproducedwascollectedbydisplacementofwaterat22°Catatotalpressureof754torr
– Volumeofthegascollectedwas0.650L,andthevaporpressureofwaterat22°Cis21torr
– CalculatethepartialpressureofO2inthegascollectedandthemassofKClO3inthesamplethatwasdecomposed
Example • 2KClO3(s)à2KCl(s)+3O2(g)
– Oxygenproducedwascollectedbydisplacementofwaterat22°Catatotalpressureof754torr
– Volumeofthegascollectedwas0.650L,andthevaporpressureofwaterat22°Cis21torr
– CalculatethepartialpressureofO2inthegascollectedandthemassofKClO3inthesamplethatwasdecomposed
• First,writewhatweknow• Pgas=754torr Pwatervapor=21torr• Vgas=0.650L Vwatervapor=?• Tgas=22oC=295K Twatervapor=22oC=295K
Example • 2KClO3(s)à2KCl(s)+3O2(g)
– Oxygenproducedwascollectedbydisplacementofwaterat22°Catatotalpressureof754torr
– Volumeofthegascollectedwas0.650L,andthevaporpressureofwaterat22°Cis21torr
– CalculatethepartialpressureofO2inthegascollectedandthemassofKClO3inthesamplethatwasdecomposed
• Second,findPO2• PT=PO2+PH2O• SoPO2=PT–PH2O• PO2=754torr–21torr=733torr
Example • 2KClO3(s)à2KCl(s)+3O2(g)
– Oxygenproducedwascollectedbydisplacementofwaterat22°Catatotalpressureof754torr
– Volumeofthegascollectedwas0.650L,andthevaporpressureofwaterat22°Cis21torr
– CalculatethepartialpressureofO2inthegascollectedandthemassofKClO3inthesamplethatwasdecomposed
• Third,findmolesofO2• nO2=PO2V/RT• nO2=(0.964atm)(0.650L)/(0.08206L.atm/K.mol)(295K)
• =0.0259molO2
Example • 2KClO3(s)à2KCl(s)+3O2(g)
– Oxygenproducedwascollectedbydisplacementofwaterat22°Catatotalpressureof754torr
– Volumeofthegascollectedwas0.650L,andthevaporpressureofwaterat22°Cis21torr
– CalculatethepartialpressureofO2inthegascollectedandthemassofKClO3inthesamplethatwasdecomposed
• Finally,useyourbalancedequation(moleratio)tocalculatethemassofKClO3
• molO2àmolKClO3àgKClO3
SampleQuestion• ConsideraflaskatSTPcontainingequalmassesofHegas,O2gas,andH2gas– Forwhichgasisthepartialpressurethegreatest?
a. Heb. O2
c. H2
d. Allarethesame
MaxwellSpeedDistribution
MaxwellSpeedDistribution• AccordingtotheKMT,theKelvintemperatureindicatestheaveragekineticenergyofgasparticles
• Inrealgases,themotionofthemoleculesistotallyrandomandunpredictable
• Atagiveninstant,howmanymoleculesaremovingataparticularspeed?
MaxwellSpeedDistribution• Maxwell-BoltzmannDistributionsshowusthedistributionofspeedsforagasatagiventemperature
• Fromthesecurves,wecandeterminethemostprobablespeedandtheaveragespeedofmolecules.
MaxwellSpeedDistribution• Thepeakofthecurveshowsusthespeedofthelargestnumberofmolecules
• Thereforethepeakshowsusthemostprobablespeed
64
65
MaxwellSpeedDistribution• Astemperatureincreases,thepeakshiftsright,indicatingthatthemostprobablespeedisgettinghigher(aswe’dexpect)
• Thecurvealsoflattensoutasmoreandmoremoleculesmoveathigherspeeds
MaxwellSpeedDistribution• Ifwecomparedifferentgasesatthesametemperature,weoftenseeadifferencebecauselighteratomstendtomovefaster
MaxwellSpeedDistribution• Don’tforget:averagekineticenergyisdependentontemperature!
SampleQuestion• ApistoncontainingafixednumberofmolesofN2isheated,andthevolumeofthegasincreasestokeepthepressureconstant– Bestexplanationofwhatishappeningatthe
molecularlevelisthat:a. N2moleculeshavegottenlargerandtakeupmorevolumeb. N2moleculesaremovingfasterandcollidingwiththesides
ofthecontainerwithmoreforcec. N2moleculeshavegottensmaller,aremovingfaster,and
arecollidingwiththesidesofthecontainerwithmoreforce
SampleQuestion• Considerthree1.0-LflasksatSTP
– FlaskAcontainsHegas,flaskBcontainsO2gas,andflaskCcontainsH2gas
– Inwhichflaskdothegasparticleshavethelowestaveragekineticenergy?a. FlaskA
b. FlaskBc. FlaskCd. Allarethesame
SampleQuestion• Considerthree1.0-LflasksatSTP
– FlaskAcontainsHegas,flaskBcontainsO2gas,andflaskCcontainsH2gas
– Inwhichflaskdothegasparticleshavethehighestaveragevelocity?a. FlaskA
b. FlaskBc. FlaskCd. Allarethesame
SampleQuestion• Fouridentical1.0-LflaskscontainthegasesHe,Cl2,CH4,andNH3,eachat0°Cand1atmpressure– Forwhichgasdothemoleculeshavethehighestaveragevelocity?a. Heb. Cl2c. CH4
d. NH3
e. Allarethesame