AP Chem Week 7 Ch 5 Part B 2018flemingapchem.weebly.com/uploads/2/4/6/5/24658308/ap...rigid steel...

Recall

KMT Assumptions 1.   Gasesaremadeofmanyspherical

particlesthatareinconstant,randommotion

–  theyhavekineticenergy2.   Gasparticlesexertneitherattractivenor

repulsiveforcesononeanother3.   Gasparticleshaveinsignificantvolume.

–  Thereissomuchspacebetweenparticlesthatmostofthevolumeisemptyspace

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

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. How many moles of argon are 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.  CH4d.  NH3e.  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


•  First:Writeyourknowns•  PCH4=1.65atm PO2=1.25atm PCO2=2.50atm•  VCH4=2.80L VO2=35.0L VCO2=?•  TCH4=298K TO2=304K TCO2=398K


•  Second:•  Writeyourbalancedchemicalequation

CH4(g)+2O2(g)àCO2(g)+2H2O(g)


•  Third:•  UsePV=nRTtofindthemolesofeachofyourreactants•  nCH4=•  0.189mol•  nO2=•  1.75mol


•  Fourth:•  Determineyourlimitingreactant•  nCH4=0.189mol nO2=1.75mol

CH4(g)+2O2(g)àCO2(g)+2H2O(g)


•  Fifth:•  UseyourLRtocalculateyourmoles


•  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.  CH4d.  NH3e.  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

48Copyright©CengageLearning.Allrightsreserved

Dalton’s Law of Partial Pressures •  IfwearelookingatnTasthetotalnumberofmoles,wecanalsolookatthemolefraction(X)

IfXA=nA/nTThenPA=PTXA

(Theseareonyourformulasheet.Beabletointerpretatusethem)

Example •  Thepartialpressureofoxygenwasobservedtobe156torrinairwithatotalatmosphericpressureof743torr.CalculatethemolefractionofO2present.

•  Recall•  PA=PTXA

Example •  Thepartialpressureofoxygenwasobservedtobe156torrinairwithatotalatmosphericpressureof743torr.CalculatethemolefractionofO2present.

•  PA=PTXA•  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





•  Second,findPO2•  PT=PO2+PH2O•  SoPO2=PT–PH2O•  PO2=754torr–21torr=733torr





•  Third,findmolesofO2•  nO2=PO2V/RT•  nO2=(0.964atm)(0.650L)/(0.08206L.atm/K.mol)(295K)

•  =0.0259molO2





•  Finally,useyourbalancedequation(moleratio)tocalculatethemassofKClO3

•  molO2àmolKClO3àgKClO3

SampleQuestion•  ConsideraflaskatSTPcontainingequalmassesofHegas,O2gas,andH2gas– Forwhichgasisthepartialpressurethegreatest?

a.  Heb.  O2c.  H2d.  Allarethesame

MaxwellSpeedDistribution

MaxwellSpeedDistribution•  AccordingtotheKMT,theKelvintemperatureindicatestheaveragekineticenergyofgasparticles

•  Inrealgases,themotionofthemoleculesistotallyrandomandunpredictable

•  Atagiveninstant,howmanymoleculesaremovingataparticularspeed?

MaxwellSpeedDistribution•  Maxwell-BoltzmannDistributionsshowusthedistributionofspeedsforagasatagiventemperature

•  Fromthesecurves,wecandeterminethemostprobablespeedandtheaveragespeedofmolecules.

MaxwellSpeedDistribution•  Thepeakofthecurveshowsusthespeedofthelargestnumberofmolecules

•  Thereforethepeakshowsusthemostprobablespeed

MaxwellSpeedDistribution•  Astemperatureincreases,thepeakshiftsright,indicatingthatthemostprobablespeedisgettinghigher(aswe’dexpect)

•  Thecurvealsoflattensoutasmoreandmoremoleculesmoveathigherspeeds

MaxwellSpeedDistribution•  Ifwecomparedifferentgasesatthesametemperature,weoftenseeadifferencebecauselighteratomstendtomovefaster

SampleQuestion•  ApistoncontainingafixednumberofmolesofN2isheated,andthevolumeofthegasincreasestokeepthepressureconstant–  Bestexplanationofwhatishappeningatthe

molecularlevelisthat:a.  N2moleculeshavegottenlargerandtakeupmorevolumeb.  N2moleculesaremovingfasterandcollidingwiththesides

ofthecontainerwithmoreforcec.  N2moleculeshavegottensmaller,aremovingfaster,and

arecollidingwiththesidesofthecontainerwithmoreforce

SampleQuestion•  Considerthree1.0-LflasksatSTP

– FlaskAcontainsHegas,flaskBcontainsO2gas,andflaskCcontainsH2gas

–  Inwhichflaskdothegasparticleshavethelowestaveragekineticenergy?a.  FlaskAb.  FlaskBc.  FlaskCd.  Allarethesame

SampleQuestion•  Considerthree1.0-LflasksatSTP

– FlaskAcontainsHegas,flaskBcontainsO2gas,andflaskCcontainsH2gas

–  Inwhichflaskdothegasparticleshavethehighestaveragevelocity?a.  FlaskAb.  FlaskBc.  FlaskCd.  Allarethesame

SampleQuestion•  Fouridentical1.0-LflaskscontainthegasesHe,Cl2,CH4,andNH3,eachat0°Cand1atmpressure– Forwhichgasdothemoleculeshavethehighestaveragevelocity?a.  Heb.  Cl2c.  CH4d.  NH3e.  Allarethesame

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