Ch.13ChemicalEquilibria

Introduction

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Introduction•  Imaginetwopopulationsthatweregeographicallyseparated.Theyarenothomogeneouspopulations.Whatwouuldhappeniftheboundarydisappears?

Introduction•  Anoverpopulatedregionmaytrytomovetotheunderpopulatedregion

•  Theremaybebothimmigrationandemigration

Introduction•  Consideringdifferencesinresourceandhabitatavailability,whatdoyouexpecttohappenovertime?

•  Thinkintermsofpopulationsizesandtherateofgeneflow

Recall

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ReactionRates•  ReactionRateàThechangeinconcentrationofareactantorproductperunitoftime

ReactionRates•  Rxnratesgenerallyincreasewithincreasing[reactant],anddecreasewithdecreasing[reactant]

H2(g)+I2(g)ßà2HI(g)•  Thisisareversiblereaction•  AsH2andI2react,theirconcentrationsdecrease,whichinturndecreasestherateoftheforwardrxn

•  As[HI]increases,thereverserxnoccursatafasterrate

•  Eventually,therateofthereverserxnequalstherateoftheforwardrxn(dynamicequilibriumisreached)

ChemicalEquilibrium

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ChemicalEquilibrium•  ßàindicatesthatareactionoccursinboththeforwardandreversedirectionsandcanreachchemicalequilibrium

ChemicalEquilibrium•  K(nottobeconfusedwithKork)istheequilibriumconstant

•  Itdescribestherelativeconcentrationsofthereactantsandproductsofareactionatequilibrium

•  AlargeKindicatesthatthereactionliesfartotherightatequilibrium(therewillbeahighconcentrationofproducts,andlowconcentrationofreactants)

•  AsmallKvalueindicatesthatthereactionliesfartotheleftatequilibrium(high[reactants],low[products])

ChemicalEquilibrium•  Inshort,thevalueofKisameasureofhowfarareactionproceeds

•  ThelargerthevalueofK,themorethereactionproceedstowardtheproducts

DynamicEquilibrium•  DynamicEquilibrium=theconditioninwhichtherateoftheforwardreactionequalstherateofthereversereaction

•  BOTHtheforwardandreverserxnsarestilloccurring

•  Thisdoesnotmeanthat[reactants]=[products]•  Ex/Areactioncanreachequilibriumwhenonlyasmallamountofreactantshaveformedproducts

•  Theforwardandbackreactionscontinue,butatequalrates,sotheconcentrationsremainconstant

H2(g)+I2(g)⇔2HI(g)attime0,thereareonlyreactantsinthemixture,soonlytheforwardreactioncantakeplace

[H2]=8,[I2]=8,[HI]=0

attime16,therearebothreactantsandproductsinthemixture,soboththeforwardreactionandreversereactioncantakeplace

[H2]=6,[I2]=6,[HI]=4

H2(g)+I2(g)⇔2HI(g)attime32,therearenowmoreproductsthanreactantsinthemixture−theforwardreactionhassloweddownasthereactantsrunout,andthereversereactionaccelerated

[H2]=4,[I2]=4,[HI]=8

attime48,theamountsofproductsandreactantsinthemixturehaven’tchanged–theforwardandreversereactionsareproceedingatthesamerate–ithasreachedequilibrium

H2(g)+I2(g)⇔2HI(g)Co

ncen

tration→

Time→ EquilibriumEstablished

Sincethe[HI]atequilibriumislargerthanthe[H2]or[I2],wesaythepositionofequilibriumfavorsproducts

Asthereactionproceeds,the[H2]and[I2]decreaseandthe[HI]increases

Sincethereactantconcentrationsaredecreasing,theforwardreactionrateslowsdown

Andsincetheproductconcentrationisincreasing,thereversereactionratespeedsup

Onceequilibriumisestablished,theconcentrationsnolongerchangeAtequilibrium,theforwardreactionrateisthesameasthereversereactionrate

TheEquilibriumConstant(K)

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TheEquilibriumConstant(K)

•  Molarconcentrationsofproductsoverreactants•  Raisedtotherespectivestoichiometriccoefficients•  Thisratioisalwaysaconstantwhenthereactantsandproductsareatequilibrium

•  Thisistheequilibriumexpression

TheEquilibriumConstant(K)

•  Therelationshipbetweenthebalancedchemicalequationandtheexpressionoftheequilibriumconstantisknownasthelawofmassaction

•  Inotherwords,thelawofmassactionsaysthattherateofachemicalreactionisdirectlyproportionaltotheproductoftheconcentrationsofthereactants

TheEquilibriumConstant(K)

•  Becarefulnottoconfusethiswithourreactionratediscussions

•  YoucancalculateKàitiswrittenwithoutunits•  Note:thetemperatureisoftenstatedsinceKdependsontemperature,thoughitoftenwillnotplayaroleinanycalculations

TheEquilibriumConstant(K)•  WhatwouldtheexpressionforKbeforthereaction2N2O5(g)ßà4NO2(g)+O2(g)

•  WhatwouldtheexpressionforKbeforthereactionCH3OH(g)ßàCO(g)+2H2(g)

CalculatingK•  ThefollowingequilibriumconcentrationswereobservedfortheHaberprocessforthesynthesisofammoniaat127°C:[NH3]=3.1x10-2mol/L,[N2]=8.5x10-1mol/L,and[H2]=3.1x10-3mol/L

a.  Writethebalancedchemicalequationb.  Writetheequilibriumexpressionc.  CalculatethevalueofKat127°C

EquilibriumPositionversusEquilibriumConstant

Equilibriumposition

• Referstoeachsetofequilibriumconcentrations

• Therecanbeinfinitenumberofpositionsforareaction

• Dependsoninitialconcentrations

Equilibriumconstant

• Oneconstantforaparticularsystemataparticulartemperature

• Remainsunchanged• Dependsontheratioofconcentrations

TheSignificanceofK

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TheSignificanceofK•  Note:Kdoesnotprovideuswithanyinformationaboutthereactionrate

TheSignificanceofK•  AlargeK(K>>1)indicatesthattheforwardreactionisfavored– Theequilibriumliesfartotheright– Youwillhaveahigherconc’ofproductsatequilibrium

•  AsmallK(K<<1)indicatesthatthereversereactionisfavored– Theequilibriumliesfartotheleft– Youwillhaveahigherconc’ofreactantsatequilibrium

•  IfK≈1,neitherreactionisfavored.– Theforwardreactionwillproceedabouthalfway

ALargeEquilibriumConstant

ASmallEquilibriumConstant

Example•  GivenA(g)ßàB(g),atwhichtemperatureistheequilibriumconstantlargest?(Aisred)

Example•  TheequilibriumconstantforthereactionA(g)ßàB(g)is10.Areactionmixtureinitiallycontains[A]=1.1Mand[B]=0.0M.Whichstatementistrueatequilibrium?

a.  Therxnmixcontains[A]=1.0Mand[B]=0.1Mb.  Therxnmixcontains[A]=0.1Mand[B]=1.0Mc.  TherxnmixcontainsequalconcentrationsofA

andB

RelationshipsBetweentheEquilibriumConstantandtheChemicalEquation

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Relationshipsb/tKandtheChemEq.1.  Ifyoureversetheequation,inverttheequilibrium

constant2.  Ifyoumultiplythecoefficientsintheequationbya

factor,raisetheequilibriumconstanttothesamefactor

3.  Ifyouaddtwoormoreindividualchemicalequationstoobtainanoverallchemicalequation,multiplythecorrespondingequilibriumconstantsbyeachothertoobtaintheoverallequilibriumconstant

Relationshipsb/tKandtheChemEq.1.  Ifyoureversetheequation,inverttheequilibrium

constant•  A+2Bßà3C

K=•  3CßàA+2B

K=

Relationshipsb/tKandtheChemEq.2.  Ifyoumultiplythecoefficientsintheequationbya

factor,raisetheequilibriumconstanttothesamefactor

•  A+2Bßà3C

K=•  nA+2nBßà3nC

K=

Relationshipsb/tKandtheChemEq.3.  Ifyouadd2+individualchemicalequationstoobtain

anoverallchemicalequation,multiplythecorrespondingequilibriumconstantsbyeachothertoobtaintheoverallequilibriumconstant

Aßà2B

2Bßà3C-------------------Aßà3C

Relationshipsb/tKandtheChemEq.•  Ex/ThereactionA(g)ßà2B(g)hasK=0.010.•  WhatistheequilibriumconstantforthereactionB(g)ßà½A(g)?

a.  1b.  10c.  100d.  0.0010

SampleQuestion•  Whichofthefollowingstatementsisfalseregardingchemicalequilibrium?a.  Asystemthatisdisturbedfromanequilibrium

conditionrespondsinamannertorestoreequilibriumb.  Thevalueoftheequilibriumconstantforagiven

reactionmixtureatconstanttemperatureisthesameregardlessofthedirectionfromwhichequilibriumisattained

c.  Whentwoopposingprocessesareproceedingatidenticalrates,thesystemisatequilibrium

d.  Asystemmovesspontaneouslytowardastateofequilibrium

e.  Allofthesestatementsaretrue

SampleQuestion•  EquilibriumconstantforA+2Bßà3Cis2.1×10–6– Determinetheequilibriumconstantfor2A+4Bßà6Ca. 4.2×10–6b. 4.4×10–12c.  2.3×1011d. 1.8×10–11e. Noneofthese

à àÜá àà2A + 4B 6C

PressureandtheEquilibriumConstant

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PressureandtheEquilibriumConstant•  SofarwehavebeentalkingaboutKC,whichistheequilibriumconstantwithrespecttomolarconcentration

•  Forgaseousreactions,thepartialpressureofaparticulargasisproportionaltoitsconcentration

•  Therefore,wecanalsoexpresstheequilibriumconstantintermsofthepartialpressuresofreactantsandproducts

PressureandtheEquilibriumConstant•  KP=Equilibriumconstantwithrespecttopartialpressuresinatmospheres

2SO3(g)ßà2SO2(g)+O2(g)

KC=

KP=

PressureandtheEquilibriumConstant•  KPisnotnecessarilyequaltoKC.•  TheconcentrationofanidealgasAisthenumberofmolesofA(nA)dividedbyitsvolume(V)inliters.

[A]=nA/V•  Fromtheidealgaslaw,wecanrelatethisquantitytothepartialpressureofA:

PAV=nARTPA=(nA/V)RT

PA=[A]RTor[A]=PA/RT•  Throughsomemathematicalarrangements,wecaneventuallyfindthatKP=KC(RT)Δn

PressureandtheEquilibriumConstantKP=KC(RT)Δn

•  Noticethatifthenumberofmolesdoesnotchange,thenΔn=0,andKP=KC

•  NotethatΔn=sumofcoefficientsofgaseousproductsminusthesumofthecoefficientsofthegaseousreactants

Example•  Given2NO(g)+O2(g)ßà2NO2(g)andKP=2.2x1012at25°C,findKC.

•  UseKP=KC(RT)Δn

SampleQuestion•  ForwhichofthefollowingreactionsdoesK=Kpatthesametemperature?a.  N2(g)+3H2(g)ßà2NH3(g)b.  CaCO3(s)ßàCaO(s)+CO2(g)c.  CO(g)+H2O(g)ßàCO2(g)+H2(g)d.  3Fe(s)+H2O(g)ßàFe3O4(s)+4H2(g)

HeterogeneousEquilibria

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HeterogeneousEquilibria•  ShouldallstatesofmatteraffectourK?•  Puresolids(s)andliquids(l)haveaconstantconcentration(aslongassomeisalreadypresent– Thenumberofatomsperunitvolumedoesnotchange

•  Puresolidsandliquidsarethereforeexcludedfromourequilibriumexpression

•  Ex/2CO(g)ßàCO2(g)+C(s)

•  Ex/CO2(g)+H2O(l)ßàH+(aq)+HCO3

-(aq)

HeterogeneousEquilibria•  WhatwouldtheequilibriumexpressionbeforCaCO3(s)ßàCaO(s)+CO2(g)?