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Chapter 17

“Free Energy and

Thermodynamics”

FirstLawofThermodynamics

•  FirstLawofThermodynamics:EnergycannotbeCreatedorDestroyed–  thetotalenergyoftheuniversecannotchange–  thoughyoucantransferitfromoneplacetoanother

•  ΔEuniverse=0=ΔEsystem+ΔEsurroundings

FirstLawofThermodynamics

•  Conserva>onofEnergy•  Foranexothermicreac>on,“lost”heatfromthesystem

goesintothesurroundings•  twowaysenergy“lost”fromasystem,

–  convertedtoheat,q–  usedtodowork,w

•  Energyconserva>onrequiresthattheenergychangeinthesystemequaltheheatreleased+workdone–  ΔE=q+w–  ΔE=ΔH+PΔV

•  ΔEisastatefunc,on–  internalenergychangeindependentofhowdone

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EnergyTax

•  Youcan’tbreakeven!•  TorechargeabaLerywith100kJofusefulenergywillrequiremorethan100kJ

•  Everyenergytransi>onresultsina“loss”ofenergy–  conversionofenergytoheatwhichis“lost”byhea>ngupthesurroundings

HeatTax

ThermodynamicsandSpontaneity

•  Thermodynamicspredictswhetheraprocesswillproceedunderthegivencondi>ons– spontaneousprocess

•  nonspontaneousprocessesrequireenergyinputtogo•  Spontaneityisdeterminedbycomparingthefreeenergyofthesystembeforethereac>onwiththefreeenergyofthesystemaPerreac>on.

•  Spontaneity≠fastorslow

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ComparingPoten>alEnergy

Thedirec>onofspontaneitycanbedeterminedbycomparingthepoten>alenergyofthesystematthestartandtheend.

Thermodynamicsvs.Kine>cs

FactorsAffec>ngWhetheraReac>onIsSpontaneous

•  Thetwofactorsthatdeterminethethermodynamicfavorabilityaretheenthalpyandtheentropy.

•  Theenthalpyisacomparisonofthebondenergyofthereactantstotheproducts.– bondenergy=amountneededtobreakabond.

– ΔH•  Theentropyfactorsrelatestotherandomness/orderlinessofasystem– ΔS

•  Theenthalpyfactorisgenerallymoreimportantthantheentropyfactor

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Enthalpy

•  Relatedtotheinternalenergy•  ΔHgenerallykJ/mol•  Strongerbonds=morestablemolecules•  Ifproductsmorestablethanreactants,energyreleased

–  exothermic–  ΔH=nega>ve

•  Ifreactantsmorestablethanproducts,energyabsorbed–  endothermic–  ΔH=posi>ve

•  Theenthalpyisfavorableforexothermicreac>onsandunfavorableforendothermicreac>ons.

•  Hess’LawΔH°rxn=Σ(ΔH°prod)‐Σ(ΔH°react)

Entropy

•  Entropyisathermodynamicfunc>onthatincreasesasthenumberofenerge>callyequivalentwaysofarrangingthecomponentsincreases,S•  SgenerallyJ/mol

•  S=klnW–  k=BoltzmannConstant=1.38x10‐23J/K– Wisthenumberofenerge>callyequivalentways,unitless

•  Randomsystemsrequirelessenergythanorderedsystems

W

•  Energe>callyEquivalentStatesfortheExpansionofaGas

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MacrostatesMicrostates

•  Thesemicrostatesallhavethesamemacrostate

•  Sothereare6differentpar>clearrangementsthatresultinthesamemacrostate

MacrostatesandProbability

•  ThereisonlyonepossiblearrangementthatgivesStateAandonethatgivesStateB

•  Thereare6possiblearrangementsthatgiveStateC

•  ThereforeStateChashigherentropythaneitherStateAorStateB

•  Themacrostatewiththehighestentropyalsohasthegreatestdispersalofenergy

ChangesinEntropy,ΔS

•  Entropychangeisfavorablewhentheresultisamorerandomsystem.–  ΔSisposi>ve

•  Somechangesthatincreasetheentropyare:–  reac>onswhoseproductsareinamoredisorderedstate.•  (solid>liquid>gas)

–  reac>onswhichhavelargernumbersofproductmoleculesthanreactantmolecules.

–  increaseintemperature– solidsdissocia>ngintoionsupondissolving

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IncreaseinEntropy

The2ndLawofThermodynamics

•  Thetotalentropychangeoftheuniversemustbeposi>veforaprocesstobespontaneous–  forreversibleprocessΔSuniv=0,–  forirreversible(spontaneous)processΔSuniv>0

•  ΔSuniverse=ΔSsystem+Δssurroundings•  Iftheentropyofthesystemdecreases,thentheentropyofthesurroundingsmustincreasebyalargeramount–  whenΔSsystemisnega>ve,ΔSsurroundingsisposi>ve

•  TheincreaseinΔSsurroundingsoPencomesfromtheheatreleasedinanexothermicreac>on

EntropyChangeinStateChange

•  Whenmaterialschangestate,thenumberofmacrostatesitcanhavechangesaswell–  forentropy:solid<liquid<gas– becausethedegreesoffreedomofmo>onincreasessolid→liquid→gas

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EntropyChangeandStateChange

HeatFlow,Entropy,andthe2ndLaw

•  Heatmustflowfromwatertoiceinorderfortheentropyoftheuniversetoincrease

TemperatureDependenceofΔSsurroundings

•  Whenasystemprocessisexothermic,itaddsheattothesurroundings,increasingtheentropyofthesurroundings

•  Whenasystemprocessisendothermic,ittakesheatfromthesurroundings,decreasingtheentropyofthesurroundings

•  Theamounttheentropyofthesurroundingschangesdependsonthetemperatureitisatoriginally

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GibbsFreeEnergy,ΔG

•  Maximumamountofenergyfromthesystemavailabletodoworkonthesurroundings

G=H–T∙SΔGsys=ΔHsys–TΔSsys ΔGsys=–TΔSuniverse

ΔGreacGon=ΣnΔGprod–ΣnΔGreact•  WhenΔG<0,thereisadecreaseinfreeenergyofthesystemthatisreleasedintothesurroundings;thereforeaprocesswillbespontaneouswhenΔGisnegaGve

Example

•  Thereac>onC3H8(g)+5O2(g)→3CO2(g)+4H2O(g)hasΔHrxn=‐2044kJat25°C.Calculatetheentropychangeofthesurroundings

FreeEnergyChangeandSpontaneity

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GibbsFreeEnergy,ΔG

•  ProcesswillbespontaneouswhenΔGisnega>ve•  ΔGwillbenega>vewhen

–  ΔHisnega>veandΔSisposi>ve•  exothermicandmorerandom

–  ΔHisnega>veandlargeandΔSisnega>vebutsmall

–  ΔHisposi>vebutsmallandΔSisposi>veandlarge• orhightemperature

•  ΔGwillbeposi>vewhenΔHis+andΔSis−– neverspontaneousatanytemperature

•  WhenΔG=0thereac>onisatequilibrium

ΔG,ΔH,andΔS

Example

•  Thereac>onCCl4(g)→C(s,graphite)+2Cl2(g)hasΔH=+95.7kJandΔS=+142.2J/Kat25°C.CalculateΔGanddetermineifitisspontaneous.

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The3rdLawofThermodynamicsAbsoluteEntropy

•  Theabsoluteentropyofasubstanceistheamountofenergyithasduetodispersionofenergythroughitspar>cles

•  The3rdLawstatesthatforaperfectcrystalatabsolutezero,theabsoluteentropy=0J/mol∙K–  therefore,everysubstancethatis

notaperfectcrystalatabsolutezerohassomeenergyfromentropy

–  therefore,theabsoluteentropyofsubstancesisalways+

StandardEntropies

•  S°•  Extensive•  Entropiesfor1moleat298Kforapar>cularstate,apar>cularallotrope,par>cularmolecularcomplexity,apar>cularmolarmass,andapar>culardegreeofdissolu>on

Rela>veStandardEntropiesStates

•  Thegasstatehasalargerentropythantheliquidstateatapar>culartemperature

•  Theliquidstatehasalargerentropythanthesolidstateatapar>culartemperature

Substance S°, (J/mol·K)

H2O (g) 70.0 H2O (l) 188.8

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Rela>veStandardEntropiesMolarMass

•  Thelargerthemolarmass,thelargertheentropy

•  Availableenergystatesmorecloselyspaced,allowingmoredispersalofenergythroughthestates

Rela>veStandardEntropiesAllotropes

•  Thelessconstrainedthestructureofanallotropeis,thelargeritsentropy

Rela>veStandardEntropiesMolecularComplexity

•  Larger,morecomplexmoleculesgenerallyhavelargerentropy

•  Moreavailableenergystates,allowingmoredispersalofenergythroughthestates

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Rela>veStandardEntropiesDissolu>on

•  Dissolvedsolidsgenerallyhavelargerentropy

•  Distribu>ngpar>clesthroughoutthemixture

Substance S°, (J/mol·K)

KClO3(s) 143.1 KClO3(aq) 265.7

Example

•  CalculateΔS°forthereac>on4NH3(g)+5O2(g)→4NO(g)+6H2O(l)

Calcula>ngΔG°

•  At25°C:ΔGo

reac>on=ΣnGof(products)‐ΣnGo

f(reactants)

•  Attemperaturesotherthan25°C:– assumingthechangeinΔHo

reac>onandΔSoreac>onisnegligible

ΔG°reacGon=ΔH°reacGon–TΔS°reacGon

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Example

•  CalculateΔG°at25°Cforthereac>onCH4(g)+8O2(g)→CO2(g)+2H2O(g)+4O3(g)

ΔGRela>onships

•  Ifareac>oncanbeexpressedasaseriesofreac>ons,thesumoftheΔGvaluesoftheindividualreac>onistheΔGofthetotalreac>on–  ΔGisastatefunc>on

•  Ifareac>onisreversed,thesignofitsΔGvaluereverses

•  Iftheamountsofmaterialsismul>pliedbyafactor,thevalueoftheΔGismul>pliedbythesamefactor–  thevalueofΔGofareac>onisextensive

FreeEnergyandReversibleReac>ons

•  Thechangeinfreeenergyisatheore>callimitastotheamountofworkthatcanbedone

•  Ifthereac>onachievesitstheore>callimit,itisareversiblereac>on

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RealReac>ons

•  Inarealreac>on,someofthefreeenergyis“lost”asheat–  ifnotmost

•  Therefore,realreac>onsareirreversible