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Chemical Thermodynamics-II , Semester 3, As per syllabus of the University of Mumbai

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AQEELAABDULQURESHI

Unit I:Physical Chemistry 1.1 Chemical Thermodynamics-II 1.Free Energy Functions: Helmholtz Free Energy, Gibb's Free Energy, Variation of Gibb's free energy with Pressure and Temperature. 2. Gibbs-Helmholtz equation 3. Thermodynamics of Open System: Partial Molal Properties, Chemical Potential and its variation with Pressure and Temperature, Gibb's Duhem equation. 4. Concept of Fugacity and Activity 5. van't Hoff reaction isotherm and van't Hoff reaction isochore.

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3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road CHEMICAL THERMODYNAMICS Semester : III PAPER 1 , UNIT - i
Chemical Thermodynamics • Chemical Thermodynamics deals with the application of the laws of thermodynamics to chemical system • FREE ENERGY FUNCTIONS • The concept of free energy gives the amount of available energy to perform useful work • The free energy change is used –  to predict the spontaneous nature of a chemical process  to study physical and chemical equilibria 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road
FREE ENERGY FUNCTIONS • HELMHOLTZ FREE ENERGY (A) • Introduced by German Physicist Hermann von Helmholtz (1821-1894) to define equilibrium at constant temeperature • Symbol ‘A’ is taken from German word ‘Arbeit’ which means work • Work function is defined as A = E – T S 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road
HELMHOLTZ FREE ENERGY (A) • Work function is defined as A = E – T S • ‘A’ is an extensive property • ‘’E’ and ‘S’ are state functions, independent of history , mechanism, path etc so A is also a state function • For an isothermal change from state 1 to state 2 • A1 = E1 – T S1 and A2 = E2 – T S2 • A2 - A1 = E2 – T S2 - E1 + T S1 • Δ A = Δ E – T ΔS 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road
HELMHOLTZ FREE ENERGY (A) 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road maxmax rev revrev rev rev rev WAorWA workmaximumtoequalisassociated work,reversiblyoutcarriedisprocessSince WA (3)and(2)equationComparing qEWi.eWqE micsthermodynaoflawfirstbyBut (2)---qEA (1)eqninngSubstituti qST T q S etemperaturconstantatprocessreversibleaFor (1)----STEA       )3( Thus decrease in Helmholtz free energy gives the maximum work that can be done by the system
GIBBS FREE ENERGY (G) • Introduced by American Physicist J. W. Gibbs (1839-1903) , it relates to net work done by the system • Gibbs free energy is defined as G = H– T S • ‘G’ is an extensive property • ‘G’ is also a state function • For an isothermal change from state 1 to state 2 • G1 = H1 – T S1 and G2 = H2 – T S2 • G2 - G1 = H2 – T S2 - H1 + T S1 • Δ G = Δ H – T ΔS 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road
gibbs FREE ENERGY (g) 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road VPWG (3)and(2)equationComparing qEWi.eWqE micsthermodynaoflawfirstbyBut VPqEG qVPEG VPEHBut qHG (1)eqninngSubstituti qST T q S etemperaturconstantatprocessreversibleaFor (1)----STHG rev revrev rev rev rev rev rev         )3( )2(
gibbs FREE ENERGY (g) 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road netexpmaxexpmax exp maxmax maxrev rev WWWWWG VPWbygivenispressureconstant againstgasofexpansiontoduedoneworkBut VPWG-ORVPWG WW workmaximumtoequalisassociated work,reversiblyoutcarriedisprocessSince VPWG      )( Thus decrease in Gibbs free energy gives the net work that can be done by the system
Relation between Gibb’s free energy and Helmholtz free energy • Gibbs free energy change ∆G is given by, ∆G = ∆H – T∆S -- (1) • Helmholtz free energy is given by , ∆A =∆E – T∆S -- (2) • But enthalpy change for a chemical reaction at constant pressure is given by, ∆H = ∆E + P∆V --(3) • Substituting (3) in equation (1) we get, • ∆G = ∆E + P∆V – T∆S ie. ∆G = ∆E – T∆S + P∆V • Since , ∆A = ∆E – T∆S • from equation (2), we get ∆G = ∆A + P∆V 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road
Significance of Gibb’s free energy 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road • The sign of ∆G helps to decide the nature of process  ∆G < 0 process is spontaneous  ∆G > 0 process is non-spontaneous  ∆G = 0 process has reached equilibrium
Variation of Gibb’s free energy with temperature and pressure 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road • Gibb’s free energy is defined as G = H – TS - - (1) • By definition H = E + PV • Therefore G = E + PV – TS •For infinitesimal change, equation (1) can be written as, dG = dE + PdV + VdP – SdT - TdS -- (2) • From the first law of thermodynamics, dE = dq + dW • If work is of expansion type, then dw = - PdV • . . . dE = dq - PdV or dq= dE + PdV ---- (3)
Variation of Gibb’s free energy with temperature and pressure 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road • According to definition of entropy • dS= dqrev / T or dqrev = T.dS where, dS is infinitesimal entropy change for a reversible process substituting (3) • TdS = dE + PdV --- (4) • Substituting in eqn (2) • dG = dE + PdV + VdP – SdT - TdS -- (2) • dG = TdS + VdP – SdT - TdS dG = VdP – S.dT ----- (5)
Variation of Gibb’s free energy with temperature and pressure 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road The rate of change of Gibb’s free energy with temperature at constant pressure is equal to decrease in entropy of the system. The rate of change of Gibb’s free energy with respect to pressure at constant temperature is equal to increase in volume occupied by the system. V dP dG i.eVdPdG 0dT,etemperaturconstantAt S dT dG i.eSdT-dG 0dP,pressureconstantAt SdTVdPdG T P                 
GIBB’S HELMHOLTZ EQUATION 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road dTSSSSdTGd(G dT)(-S-dT-SdGdG dTS-dGanddTS-dG dTamountsmallbychangedisetemperaturwhen energyfreeinchangesthebedGanddGLet SdT-dG 0dP,pressureconstantAt SdTVdPdG asbe writtencanpressureandetemperatur henergy witfreesGibb’ofVariation 122112 1212 2211 21 )()()      
GIBB’S HELMHOLTZ EQUATION 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road (1)---S dT Gd dTS-Gd dTSSSSdTGd(G 122112      )()()
GIBB’S HELMHOLTZ EQUATION 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road change.energyfreeof tcoefficieneTemperaturasknwonis dT Gd termThe equationHelmholtzGibbsasknownisequationAbove dT Gd THG (1)equationinS-ofvaluengSubstituti S)T(-HGi.e ST-HG bygivenisenergyfreein changeetemperaturcosnstantAt P P                  
GIBB’S HELMHOLTZ EQUATION 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road         (1)--- dT Gd T 1 T G TG dT d dT Gd T 1 T GTG dT d dT Gd T 1 T1 dT d GTG dT d pressure.constantatetemperaturto respectwith T G atingdifferentibyobtainedis equationHelmholtzGibbsofformAnother P P P                                  2 2 1
GIBB’S HELMHOLTZ EQUATION 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road )2( 2 2                                P 22 P 22 P dT Gd T 1 T H T G dT Gd T T T H T G TbyequationaboveDividing dT Gd THG isequationHelmholtzGibbs
partial molal quantity 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road     equationHelmholtzGibbs offormanotherisequationaboveThe T H TG dT d T H T G T G TG dT d (2)and(1)equationComparing 2 22         2
partial molal quantity 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road ) ...., i n......, 3 n, 2 n, 1 n,P,T(fX t.constituenvariousofamount andpressuree,temperaturondependwillx''thenstudy forselectedsystemofpropertyextensiveanyisx''If ly.respectivei....3,2,1tsconstituen ofmolesofno.thebe i n 3 n, 2 n 1 nLet tconstituenithofconsistingsystemopenanConsider 
partial molal quantity 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road i ....nn,P,nT,i 2 .....nn,P,nT, 1 .....nn,P,nT, i ....nn,P,nT,i 2 .....nn,P,nT, 1 .....nn,P,nT,.,....n,nT,n.,....n,nP,n dn n x dn n x dn n x dx Pressure,andeTemperaturconstantAt dn n x dn n x dn n x dP P x dT T x dx asbe writtencandx''systemtheinchangesmallaFor 1)-i(31i31i32 1)-i(31i31 i32i21i21 in......,2n,1n,P,T(fX                                                                        ....... ....... 21 2 1 )
partial molal quantity 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road system.ofncompositiothe affectnotdoesmoleaddedthethatsystemofquantitylargeasuchtoadded ispressureandetemperaturconstantatcomponentparticularofmole onewhen...systemofvolume,enthalpyenergy,freeassuchpropertyin changethegivesitthatisquantitymolarpartialofcesignificanphysicalThe dnxdnxdnxdx property.theofsymboltheoverbar by writingdrepresenteisItquantity.molalpartialasknownis n x termThe dn n x dn n x dn n x dx ii21 i ....nn,P,nT,i 2 .....nn,P,nT, 1 .....nn,P,nT, 1)-i(31i31i32                                     ...... .... 21 21
partial molal volume 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road dnV........dnVdnVdV dn n V dn n V dn n V dV ,belvolume wilin changesmallpressureandetemperaturconstantAt volume.molalpartialasknownis n V uantityq thethenpropertyextensivetheisvolumeIf ii2211 i ...n,nnP,T,2 2 ...n,nnP,T,2 1 ...n,nP,T,1 i31 i31i2                                    ...... ...
CHEMICAL POTENTIAL 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road dn........dndndG''by drepresenteisandpotentialchemicalasknownalsoistI .G)(energyfreemolalpartialasknownis n G uantityq dn n G dn n G dn n G dG ,bellenergy wifreein changesmallpressureandetemperaturconstantAt )n.....n,n,n,P,T(fGei. propertyextensiveanissystemaofenergyreeF ii21 i ...n,nnP,T,2 2 ...n,nnP,T,2 1 ...n,nP,T,1 i321 i31 i31i2                                      21 ...... ...
gibbs duhemequation 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road dn........dndndG''by drepresenteisandpotentialchemicalasknownalsoistI .G)(energyfreemolalpartialasknownis n G uantityq dn n G dn n G dn n G dG ,bellenergy wifreein changesmallpressureandetemperaturconstantAt )n.....n,n,n,P,T(fGei. propertyextensiveanissystemaofenergyreeF ii21 i ...n,nnP,T,2 2 ...n,nnP,T,2 1 ...n,nP,T,1 i321 i31 i31i2                                      21 ...... ...
gibbs duhem equation 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road ) )1( ) ) ( )2( 21 21 21 2211 21 21 ii21 ii21 ii21 iiii2211 ii21NP,T, ii21 dn....dnd(ndGdG dGbyreplacedbecaneqnaboveinbracketfirsttheeqnFrom dn....dnd(n dn....dndn(dG dndn....dndndndndG give,will(2)eqnofationdifferentiComplete n)compositiodefiniteN n........nn(G) bewill(1)eqnof nintegratiothencompositiodefinitehassystemtheIf (1)---dn........dndndG             
gibbs duhem equation 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road 21 21 21 21 21 0 0 0 )       d n n d dndn dndn isequationDuhemGibbsmixture binaryaForon.distillatiassuchequilibrialiquid -GasofstudytheinusefulisequationDuhemGibbs dn asbe writtenalsocanequationaboveThe equation.DuhemGibbsasknownisequationaboveThe dn....dndn dn....dnd(ndGdG 1 2 21 21 ii ii21 ii21       
gibbs duhem equation 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road energy.freetoequalispotential chemicalsubstancepureanyofmole1forThus G,1nwhen 2)eqnN(G)bewill equationDuhemGibbsthensubstancepurei.e tconstituen1onlyofconsistssystemaIf vedthenvedifi.etconstituen 2ndofpotentialchemicaltheaffectstconstituen1st ofpotentialchemicalthatindicatesequationAbove d n n d NP,T, 1 2         ( .21 21
3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road V dP dG i.eVdPdG 0dT,etemperaturconstantAt S dT dG i.eSdT-dG 0dP,pressureconstantAt SdTVdPdG T P                  Effect of temperature and Pressure on chemical potential
3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road iTi iTi i T dn dV dn dG Pd d dn dV dP dG nd d n'w.r.tequationaboveatingDifferenti V dP dG                     ' Effect ofPressureon chemical potential i i V Pd d  
3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road iPi iPi i P dn dS dn dG Td d dn dS dT dG nd d n'w.r.tequationaboveatingDifferenti S dT dG                     ' Effect of temperature on chemicalpotential i i S Td d  
3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road CONCEPT OF FUGACITY AND ACTIVITY   1 2 12 ln ln 2 1 P P RTG PRTGG dP P RT dGequation,abovegIntegratin dP P RT dG P RT V,RTPV,gasidealanFor VdPdGetemperaturconstantAt SdT-VdPdGbygivenis pressureandetemperaturhenergy witfreeofvariationThe P P P P G G 2 1 2 1        
3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road CONCEPT OF FUGACITY AND ACTIVITY (2)---BlnfRTG bygivenisfugacityandenergyfreebetweenrelationThe 'f'symbolthebydrepresenteisItsubstance.theof tendencyescapingthemeasuretousedisfugacitytermThe tendency.escapingas knownispropertyThisstate.anotherintopasstotendencyhas stategivenainsubstanceeverythatsuggestedHefugacity. andactivityasknownparametersmicthermodynanewtwo introducedLewisN.G.gasesrealforncalculatioenergyfree explaintoorderIngases.idealforonlyvalidisEquation P P RTG   )1( )1(ln 1 2
3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road CONCEPT OF FUGACITY AND ACTIVITY )4(ln lnln ln 0 0 0 0     f f RTG-G fRTfRTG-G (2)equationfrom(3)equationgSubtractin (3)---BfRTG statestandardinfugacityandenergyfreethebefandGLet condition.standardunderdonewasGoftsmeasuremenallHence .calculatedbecannotBknown,notisGofvalueabsoluteSince constantaisBwhere(2)---BlnfRTG 0 0 0 0
3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road CONCEPT OF FUGACITY AND ACTIVITY (6)-- a a RTG aRTGaRTGGG aRTGGandaRTGG bewillstatestwothefor(5)equationthethena andaareactivitieswhenenergiesfreeareGandGIf GG1,aIf aRTGG state.standardtheinsubstance sametheoffugacitytheatostategiventheinsubstance theoffugacityofratiotheasdefinedisactivityThus a'.'bydrepresenteisandactivityasknownis f f ratioThe 00 12 0 2 0 1 2 121 0 0 1 2 12 21 0 ln )ln()ln( lnln )5(ln     
3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road CONCEPT OF FUGACITY AND ACTIVITY aRT asbe writtencanaRTGGi.e(5)equation Gand1nsubstance,ofmole1For activity.byreplacedareionconcentrat wheneverobtainedareresultexactmoreHencesolvent. withsolutesofreactionsandattractionmutualthe ionconsideratintotakeactivitiesthesolutionsofcaseIn possible.becomenscalculatioexactpressureofplace inusedareactivitieswhenThus,pressure.ofplacethe takesactivitythatfoundisit(6)and(1)equationFrom (6)-- a a RTGand(1)-- P P RTG 0 ln ln lnln 0 1 2 1 2      
3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road VAN’ T HOFF’S REACTION ISOTHERM substance.indicatedofpotentialchemicalareswhere bereactiontheinparttaking substancesvariousofenergyfreemolalpartialtheLet quantitymolalpartialoftermsinexressedbemustsystem ofpropertymicthermodynachange,canncompositio osemixture whaisionconsideratundersystemtheSince .....mMLl....BbaA reactiongeneraltheConsider ,M,L,B,A ' .........     reactants.andproductofpressurespartialandG,G betweenrelationthegivesisothermreactionHofftVan' 0 
3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road VAN’ T HOFF’S REACTION ISOTHERM statestandard insubstanceaofpotentialchemicaliswhere aRT realtionfollowingusignactivityoftermsinexpressedbe canstateanyinsubstanceaofpotetntialchemicalThe bamlG GGGenergyfreeinChange baG mlG bewillreactantsandproductofenergyFree 0 0 BAML reactantproduct BAreactant MLproduct      )2(ln )1(.....)(.....)( ..... .....      
3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road VAN’ T HOFF’S REACTION ISOTHERM state.standardtheirinarereactiontheininvolved substancestheallnchange wheenergyfreeisGwhere aa aa RTGG aa aa RTbamlG aRTbaRTa aRTmaRTlG belenergy wilfreeinchangethen(2)equation fromderivedexpressioningcorrespondbyreplaced are(1)equationinofvaluestheIf 0 b B a A m M l L0 b B a A m M l L BAML BBAA MMLL MLBA           )3( .... .... ln .... .... ln..)](..)[( .....])ln()ln([ ...])ln()ln([ ..,,, 0000 00 00    
3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road VAN’ T HOFF’S REACTION ISOTHERM state.standardforequationHofftVan'is(5)Equation (5)---KpRTG GmequilibriuatprocesschemicalaFor isotherm.rxnHofftVan'asknwonare(4)and(3)Equation (4)---KpRTGG Kp aa aa system gaseousofcaseinandconstantmequilibriuasknownis reactants&productofactivitiesofratioinvolvingtermThe --- aa aa RTGG 0 0 b B a A m M l L b B a A m M l L0 ln 0 ln .... .... )3( .... .... ln         
3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road VAN’ T HOFF’S REACTION isochore T KpT R T G T KpRT T G pressureconstantatetemperaturw.r.t(1)eqnatingDifferenti (1)---KpRTG isstatestandardforisothermHofftVan' --- aa aa RTGG P 0 P 0 0 b B a A m M l L0                               .ln )ln( ln )3( .... .... ln equation.HelmholtzGibbsandisothermHofftvan'using obtainedbecanrelationThee.temperaturandconstant mequilibriubetweenrelationthegivesequationHofftVan'
3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road VAN’ T HOFF’S REACTION isochore KpRT T Kp RT T G T TbyequationabovegMultiplyin KpR T Kp RT T G Kp T Kp TR T G T T Kp T Kp TR T G T KpT R T G P 0 P 0 P 0 P 0 P 0 ln ln ln ln .ln ln .ln ln .ln 2                                                                                   
3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road VAN’ T HOFF’S REACTION isochore )3( )2( ln ln ln ln 2 2                                                      00 P 0 P 0 00 0 P 0 0 P 0 HG T G T T G THG isstatestandardforequationHelmholtzGibbs G T Kp RT T G T KpRTG(1)equationFrom KpRT T Kp RT T G T
3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road VAN’ T HOFF’S REACTION isochore (5)-- RT H T Kp T Kp RTHhencenegligibleis HandHbetweendifferencereactionchemicalaFor state.stdtheirinaresubstancestheallhenpressure w constantatreactionofenthalpyisHequationabovenI T Kp RTH G T Kp RTHG (3)and(2)equationEquating 0 0 0 000 2 2 2 2 ln ln )4( ln ln                 
3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road VAN’ T HOFF’S REACTION isochore                                     21 12 1 2 21 12 2 2 303.2 ln 11 lnln 1 ln . 1 ln ln 2 1 2 2 1 2 TT TT R H Kp Kp TTR H KpKp TR H Kp T TR H Kp :equationHofftVan'ofnIntegratio equation.HofftVan'asknowniseqnAbove (5)-- RT H T Kp T T Kp Kp T T Kp Kp 1 1
3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road VAN’ T HOFF’S REACTION isochore T lnRTn T Kc T Kp etemperaturw.r.tequtionaboveatingDifferenti lnRTnlnKclnKp equationaboveoflogTaking .(RT)KcKp equationfollowingusingbyobtainedbecanvolume constantatreactionofheatinvolving(5)eqnofformotherThe (5)-- RT H T Kp n                lnln ln 2
3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road VAN’ T HOFF’S REACTION isochore )7( ln ln ln ln )6( lnln lnln 2 2 2 2                                      RT nRT-H T Kc T n RT H T Kc RT H T n T Kc (5)-- RT H T Kp (5)eqnand(6)equationEquating T n T Kc T Kp T lnRTn T Kc T Kp
3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road VAN’ T HOFF’S REACTION isochore IsochoreHofftVan'or equationHofftVan'asknownisequationaboveThe RT E T Kc (7)equationinngSubstituti EnRT-H nRTEH equation followingthebyvolumeconstantatreactionofheat torelatedispressureconstantatreactionofheatThe RT nRT-H T Kc 2 2 ln )7( ln           
Reference Books : • Advanced Physical chemistry – Gurdeep Raj • Thermodynamics – A core course – 2nd edn by R.C. Srivastava • An introduction to chemical thermodynamics – 6th edn Rastogi & Misra • Advanced physical chemistry - D. N. Bajpai (S. Chand ) 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road Recommended Reading :
3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road

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Chemical Thermodynamics-II , Semester 3, As per syllabus of the University of Mumbai

  • 1. 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road CHEMICAL THERMODYNAMICS Semester : III PAPER 1 , UNIT - i
  • 2. Chemical Thermodynamics • Chemical Thermodynamics deals with the application of the laws of thermodynamics to chemical system • FREE ENERGY FUNCTIONS • The concept of free energy gives the amount of available energy to perform useful work • The free energy change is used –  to predict the spontaneous nature of a chemical process  to study physical and chemical equilibria 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road
  • 3. FREE ENERGY FUNCTIONS • HELMHOLTZ FREE ENERGY (A) • Introduced by German Physicist Hermann von Helmholtz (1821-1894) to define equilibrium at constant temeperature • Symbol ‘A’ is taken from German word ‘Arbeit’ which means work • Work function is defined as A = E – T S 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road
  • 4. HELMHOLTZ FREE ENERGY (A) • Work function is defined as A = E – T S • ‘A’ is an extensive property • ‘’E’ and ‘S’ are state functions, independent of history , mechanism, path etc so A is also a state function • For an isothermal change from state 1 to state 2 • A1 = E1 – T S1 and A2 = E2 – T S2 • A2 - A1 = E2 – T S2 - E1 + T S1 • Δ A = Δ E – T ΔS 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road
  • 5. HELMHOLTZ FREE ENERGY (A) 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road maxmax rev revrev rev rev rev WAorWA workmaximumtoequalisassociated work,reversiblyoutcarriedisprocessSince WA (3)and(2)equationComparing qEWi.eWqE micsthermodynaoflawfirstbyBut (2)---qEA (1)eqninngSubstituti qST T q S etemperaturconstantatprocessreversibleaFor (1)----STEA       )3( Thus decrease in Helmholtz free energy gives the maximum work that can be done by the system
  • 6. GIBBS FREE ENERGY (G) • Introduced by American Physicist J. W. Gibbs (1839-1903) , it relates to net work done by the system • Gibbs free energy is defined as G = H– T S • ‘G’ is an extensive property • ‘G’ is also a state function • For an isothermal change from state 1 to state 2 • G1 = H1 – T S1 and G2 = H2 – T S2 • G2 - G1 = H2 – T S2 - H1 + T S1 • Δ G = Δ H – T ΔS 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road
  • 7. gibbs FREE ENERGY (g) 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road VPWG (3)and(2)equationComparing qEWi.eWqE micsthermodynaoflawfirstbyBut VPqEG qVPEG VPEHBut qHG (1)eqninngSubstituti qST T q S etemperaturconstantatprocessreversibleaFor (1)----STHG rev revrev rev rev rev rev rev         )3( )2(
  • 8. gibbs FREE ENERGY (g) 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road netexpmaxexpmax exp maxmax maxrev rev WWWWWG VPWbygivenispressureconstant againstgasofexpansiontoduedoneworkBut VPWG-ORVPWG WW workmaximumtoequalisassociated work,reversiblyoutcarriedisprocessSince VPWG      )( Thus decrease in Gibbs free energy gives the net work that can be done by the system
  • 9. Relation between Gibb’s free energy and Helmholtz free energy • Gibbs free energy change ∆G is given by, ∆G = ∆H – T∆S -- (1) • Helmholtz free energy is given by , ∆A =∆E – T∆S -- (2) • But enthalpy change for a chemical reaction at constant pressure is given by, ∆H = ∆E + P∆V --(3) • Substituting (3) in equation (1) we get, • ∆G = ∆E + P∆V – T∆S ie. ∆G = ∆E – T∆S + P∆V • Since , ∆A = ∆E – T∆S • from equation (2), we get ∆G = ∆A + P∆V 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road
  • 10. Significance of Gibb’s free energy 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road • The sign of ∆G helps to decide the nature of process  ∆G < 0 process is spontaneous  ∆G > 0 process is non-spontaneous  ∆G = 0 process has reached equilibrium
  • 11. Variation of Gibb’s free energy with temperature and pressure 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road • Gibb’s free energy is defined as G = H – TS - - (1) • By definition H = E + PV • Therefore G = E + PV – TS •For infinitesimal change, equation (1) can be written as, dG = dE + PdV + VdP – SdT - TdS -- (2) • From the first law of thermodynamics, dE = dq + dW • If work is of expansion type, then dw = - PdV • . . . dE = dq - PdV or dq= dE + PdV ---- (3)
  • 12. Variation of Gibb’s free energy with temperature and pressure 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road • According to definition of entropy • dS= dqrev / T or dqrev = T.dS where, dS is infinitesimal entropy change for a reversible process substituting (3) • TdS = dE + PdV --- (4) • Substituting in eqn (2) • dG = dE + PdV + VdP – SdT - TdS -- (2) • dG = TdS + VdP – SdT - TdS dG = VdP – S.dT ----- (5)
  • 13. Variation of Gibb’s free energy with temperature and pressure 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road The rate of change of Gibb’s free energy with temperature at constant pressure is equal to decrease in entropy of the system. The rate of change of Gibb’s free energy with respect to pressure at constant temperature is equal to increase in volume occupied by the system. V dP dG i.eVdPdG 0dT,etemperaturconstantAt S dT dG i.eSdT-dG 0dP,pressureconstantAt SdTVdPdG T P                 
  • 14. GIBB’S HELMHOLTZ EQUATION 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road dTSSSSdTGd(G dT)(-S-dT-SdGdG dTS-dGanddTS-dG dTamountsmallbychangedisetemperaturwhen energyfreeinchangesthebedGanddGLet SdT-dG 0dP,pressureconstantAt SdTVdPdG asbe writtencanpressureandetemperatur henergy witfreesGibb’ofVariation 122112 1212 2211 21 )()()      
  • 15. GIBB’S HELMHOLTZ EQUATION 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road (1)---S dT Gd dTS-Gd dTSSSSdTGd(G 122112      )()()
  • 16. GIBB’S HELMHOLTZ EQUATION 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road change.energyfreeof tcoefficieneTemperaturasknwonis dT Gd termThe equationHelmholtzGibbsasknownisequationAbove dT Gd THG (1)equationinS-ofvaluengSubstituti S)T(-HGi.e ST-HG bygivenisenergyfreein changeetemperaturcosnstantAt P P                  
  • 17. GIBB’S HELMHOLTZ EQUATION 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road         (1)--- dT Gd T 1 T G TG dT d dT Gd T 1 T GTG dT d dT Gd T 1 T1 dT d GTG dT d pressure.constantatetemperaturto respectwith T G atingdifferentibyobtainedis equationHelmholtzGibbsofformAnother P P P                                  2 2 1
  • 18. GIBB’S HELMHOLTZ EQUATION 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road )2( 2 2                                P 22 P 22 P dT Gd T 1 T H T G dT Gd T T T H T G TbyequationaboveDividing dT Gd THG isequationHelmholtzGibbs
  • 19. partial molal quantity 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road     equationHelmholtzGibbs offormanotherisequationaboveThe T H TG dT d T H T G T G TG dT d (2)and(1)equationComparing 2 22         2
  • 20. partial molal quantity 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road ) ...., i n......, 3 n, 2 n, 1 n,P,T(fX t.constituenvariousofamount andpressuree,temperaturondependwillx''thenstudy forselectedsystemofpropertyextensiveanyisx''If ly.respectivei....3,2,1tsconstituen ofmolesofno.thebe i n 3 n, 2 n 1 nLet tconstituenithofconsistingsystemopenanConsider 
  • 21. partial molal quantity 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road i ....nn,P,nT,i 2 .....nn,P,nT, 1 .....nn,P,nT, i ....nn,P,nT,i 2 .....nn,P,nT, 1 .....nn,P,nT,.,....n,nT,n.,....n,nP,n dn n x dn n x dn n x dx Pressure,andeTemperaturconstantAt dn n x dn n x dn n x dP P x dT T x dx asbe writtencandx''systemtheinchangesmallaFor 1)-i(31i31i32 1)-i(31i31 i32i21i21 in......,2n,1n,P,T(fX                                                                        ....... ....... 21 2 1 )
  • 22. partial molal quantity 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road system.ofncompositiothe affectnotdoesmoleaddedthethatsystemofquantitylargeasuchtoadded ispressureandetemperaturconstantatcomponentparticularofmole onewhen...systemofvolume,enthalpyenergy,freeassuchpropertyin changethegivesitthatisquantitymolarpartialofcesignificanphysicalThe dnxdnxdnxdx property.theofsymboltheoverbar by writingdrepresenteisItquantity.molalpartialasknownis n x termThe dn n x dn n x dn n x dx ii21 i ....nn,P,nT,i 2 .....nn,P,nT, 1 .....nn,P,nT, 1)-i(31i31i32                                     ...... .... 21 21
  • 23. partial molal volume 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road dnV........dnVdnVdV dn n V dn n V dn n V dV ,belvolume wilin changesmallpressureandetemperaturconstantAt volume.molalpartialasknownis n V uantityq thethenpropertyextensivetheisvolumeIf ii2211 i ...n,nnP,T,2 2 ...n,nnP,T,2 1 ...n,nP,T,1 i31 i31i2                                    ...... ...
  • 24. CHEMICAL POTENTIAL 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road dn........dndndG''by drepresenteisandpotentialchemicalasknownalsoistI .G)(energyfreemolalpartialasknownis n G uantityq dn n G dn n G dn n G dG ,bellenergy wifreein changesmallpressureandetemperaturconstantAt )n.....n,n,n,P,T(fGei. propertyextensiveanissystemaofenergyreeF ii21 i ...n,nnP,T,2 2 ...n,nnP,T,2 1 ...n,nP,T,1 i321 i31 i31i2                                      21 ...... ...
  • 25. gibbs duhemequation 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road dn........dndndG''by drepresenteisandpotentialchemicalasknownalsoistI .G)(energyfreemolalpartialasknownis n G uantityq dn n G dn n G dn n G dG ,bellenergy wifreein changesmallpressureandetemperaturconstantAt )n.....n,n,n,P,T(fGei. propertyextensiveanissystemaofenergyreeF ii21 i ...n,nnP,T,2 2 ...n,nnP,T,2 1 ...n,nP,T,1 i321 i31 i31i2                                      21 ...... ...
  • 26. gibbs duhem equation 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road ) )1( ) ) ( )2( 21 21 21 2211 21 21 ii21 ii21 ii21 iiii2211 ii21NP,T, ii21 dn....dnd(ndGdG dGbyreplacedbecaneqnaboveinbracketfirsttheeqnFrom dn....dnd(n dn....dndn(dG dndn....dndndndndG give,will(2)eqnofationdifferentiComplete n)compositiodefiniteN n........nn(G) bewill(1)eqnof nintegratiothencompositiodefinitehassystemtheIf (1)---dn........dndndG             
  • 27. gibbs duhem equation 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road 21 21 21 21 21 0 0 0 )       d n n d dndn dndn isequationDuhemGibbsmixture binaryaForon.distillatiassuchequilibrialiquid -GasofstudytheinusefulisequationDuhemGibbs dn asbe writtenalsocanequationaboveThe equation.DuhemGibbsasknownisequationaboveThe dn....dndn dn....dnd(ndGdG 1 2 21 21 ii ii21 ii21       
  • 28. gibbs duhem equation 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road energy.freetoequalispotential chemicalsubstancepureanyofmole1forThus G,1nwhen 2)eqnN(G)bewill equationDuhemGibbsthensubstancepurei.e tconstituen1onlyofconsistssystemaIf vedthenvedifi.etconstituen 2ndofpotentialchemicaltheaffectstconstituen1st ofpotentialchemicalthatindicatesequationAbove d n n d NP,T, 1 2         ( .21 21
  • 29. 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road V dP dG i.eVdPdG 0dT,etemperaturconstantAt S dT dG i.eSdT-dG 0dP,pressureconstantAt SdTVdPdG T P                  Effect of temperature and Pressure on chemical potential
  • 30. 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road iTi iTi i T dn dV dn dG Pd d dn dV dP dG nd d n'w.r.tequationaboveatingDifferenti V dP dG                     ' Effect ofPressureon chemical potential i i V Pd d  
  • 31. 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road iPi iPi i P dn dS dn dG Td d dn dS dT dG nd d n'w.r.tequationaboveatingDifferenti S dT dG                     ' Effect of temperature on chemicalpotential i i S Td d  
  • 32. 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road CONCEPT OF FUGACITY AND ACTIVITY   1 2 12 ln ln 2 1 P P RTG PRTGG dP P RT dGequation,abovegIntegratin dP P RT dG P RT V,RTPV,gasidealanFor VdPdGetemperaturconstantAt SdT-VdPdGbygivenis pressureandetemperaturhenergy witfreeofvariationThe P P P P G G 2 1 2 1        
  • 33. 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road CONCEPT OF FUGACITY AND ACTIVITY (2)---BlnfRTG bygivenisfugacityandenergyfreebetweenrelationThe 'f'symbolthebydrepresenteisItsubstance.theof tendencyescapingthemeasuretousedisfugacitytermThe tendency.escapingas knownispropertyThisstate.anotherintopasstotendencyhas stategivenainsubstanceeverythatsuggestedHefugacity. andactivityasknownparametersmicthermodynanewtwo introducedLewisN.G.gasesrealforncalculatioenergyfree explaintoorderIngases.idealforonlyvalidisEquation P P RTG   )1( )1(ln 1 2
  • 34. 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road CONCEPT OF FUGACITY AND ACTIVITY )4(ln lnln ln 0 0 0 0     f f RTG-G fRTfRTG-G (2)equationfrom(3)equationgSubtractin (3)---BfRTG statestandardinfugacityandenergyfreethebefandGLet condition.standardunderdonewasGoftsmeasuremenallHence .calculatedbecannotBknown,notisGofvalueabsoluteSince constantaisBwhere(2)---BlnfRTG 0 0 0 0
  • 35. 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road CONCEPT OF FUGACITY AND ACTIVITY (6)-- a a RTG aRTGaRTGGG aRTGGandaRTGG bewillstatestwothefor(5)equationthethena andaareactivitieswhenenergiesfreeareGandGIf GG1,aIf aRTGG state.standardtheinsubstance sametheoffugacitytheatostategiventheinsubstance theoffugacityofratiotheasdefinedisactivityThus a'.'bydrepresenteisandactivityasknownis f f ratioThe 00 12 0 2 0 1 2 121 0 0 1 2 12 21 0 ln )ln()ln( lnln )5(ln     
  • 36. 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road CONCEPT OF FUGACITY AND ACTIVITY aRT asbe writtencanaRTGGi.e(5)equation Gand1nsubstance,ofmole1For activity.byreplacedareionconcentrat wheneverobtainedareresultexactmoreHencesolvent. withsolutesofreactionsandattractionmutualthe ionconsideratintotakeactivitiesthesolutionsofcaseIn possible.becomenscalculatioexactpressureofplace inusedareactivitieswhenThus,pressure.ofplacethe takesactivitythatfoundisit(6)and(1)equationFrom (6)-- a a RTGand(1)-- P P RTG 0 ln ln lnln 0 1 2 1 2      
  • 37. 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road VAN’ T HOFF’S REACTION ISOTHERM substance.indicatedofpotentialchemicalareswhere bereactiontheinparttaking substancesvariousofenergyfreemolalpartialtheLet quantitymolalpartialoftermsinexressedbemustsystem ofpropertymicthermodynachange,canncompositio osemixture whaisionconsideratundersystemtheSince .....mMLl....BbaA reactiongeneraltheConsider ,M,L,B,A ' .........     reactants.andproductofpressurespartialandG,G betweenrelationthegivesisothermreactionHofftVan' 0 
  • 38. 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road VAN’ T HOFF’S REACTION ISOTHERM statestandard insubstanceaofpotentialchemicaliswhere aRT realtionfollowingusignactivityoftermsinexpressedbe canstateanyinsubstanceaofpotetntialchemicalThe bamlG GGGenergyfreeinChange baG mlG bewillreactantsandproductofenergyFree 0 0 BAML reactantproduct BAreactant MLproduct      )2(ln )1(.....)(.....)( ..... .....      
  • 39. 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road VAN’ T HOFF’S REACTION ISOTHERM state.standardtheirinarereactiontheininvolved substancestheallnchange wheenergyfreeisGwhere aa aa RTGG aa aa RTbamlG aRTbaRTa aRTmaRTlG belenergy wilfreeinchangethen(2)equation fromderivedexpressioningcorrespondbyreplaced are(1)equationinofvaluestheIf 0 b B a A m M l L0 b B a A m M l L BAML BBAA MMLL MLBA           )3( .... .... ln .... .... ln..)](..)[( .....])ln()ln([ ...])ln()ln([ ..,,, 0000 00 00    
  • 40. 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road VAN’ T HOFF’S REACTION ISOTHERM state.standardforequationHofftVan'is(5)Equation (5)---KpRTG GmequilibriuatprocesschemicalaFor isotherm.rxnHofftVan'asknwonare(4)and(3)Equation (4)---KpRTGG Kp aa aa system gaseousofcaseinandconstantmequilibriuasknownis reactants&productofactivitiesofratioinvolvingtermThe --- aa aa RTGG 0 0 b B a A m M l L b B a A m M l L0 ln 0 ln .... .... )3( .... .... ln         
  • 41. 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road VAN’ T HOFF’S REACTION isochore T KpT R T G T KpRT T G pressureconstantatetemperaturw.r.t(1)eqnatingDifferenti (1)---KpRTG isstatestandardforisothermHofftVan' --- aa aa RTGG P 0 P 0 0 b B a A m M l L0                               .ln )ln( ln )3( .... .... ln equation.HelmholtzGibbsandisothermHofftvan'using obtainedbecanrelationThee.temperaturandconstant mequilibriubetweenrelationthegivesequationHofftVan'
  • 42. 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road VAN’ T HOFF’S REACTION isochore KpRT T Kp RT T G T TbyequationabovegMultiplyin KpR T Kp RT T G Kp T Kp TR T G T T Kp T Kp TR T G T KpT R T G P 0 P 0 P 0 P 0 P 0 ln ln ln ln .ln ln .ln ln .ln 2                                                                                   
  • 43. 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road VAN’ T HOFF’S REACTION isochore )3( )2( ln ln ln ln 2 2                                                      00 P 0 P 0 00 0 P 0 0 P 0 HG T G T T G THG isstatestandardforequationHelmholtzGibbs G T Kp RT T G T KpRTG(1)equationFrom KpRT T Kp RT T G T
  • 44. 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road VAN’ T HOFF’S REACTION isochore (5)-- RT H T Kp T Kp RTHhencenegligibleis HandHbetweendifferencereactionchemicalaFor state.stdtheirinaresubstancestheallhenpressure w constantatreactionofenthalpyisHequationabovenI T Kp RTH G T Kp RTHG (3)and(2)equationEquating 0 0 0 000 2 2 2 2 ln ln )4( ln ln                 
  • 45. 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road VAN’ T HOFF’S REACTION isochore                                     21 12 1 2 21 12 2 2 303.2 ln 11 lnln 1 ln . 1 ln ln 2 1 2 2 1 2 TT TT R H Kp Kp TTR H KpKp TR H Kp T TR H Kp :equationHofftVan'ofnIntegratio equation.HofftVan'asknowniseqnAbove (5)-- RT H T Kp T T Kp Kp T T Kp Kp 1 1
  • 46. 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road VAN’ T HOFF’S REACTION isochore T lnRTn T Kc T Kp etemperaturw.r.tequtionaboveatingDifferenti lnRTnlnKclnKp equationaboveoflogTaking .(RT)KcKp equationfollowingusingbyobtainedbecanvolume constantatreactionofheatinvolving(5)eqnofformotherThe (5)-- RT H T Kp n                lnln ln 2
  • 47. 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road VAN’ T HOFF’S REACTION isochore )7( ln ln ln ln )6( lnln lnln 2 2 2 2                                      RT nRT-H T Kc T n RT H T Kc RT H T n T Kc (5)-- RT H T Kp (5)eqnand(6)equationEquating T n T Kc T Kp T lnRTn T Kc T Kp
  • 48. 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road VAN’ T HOFF’S REACTION isochore IsochoreHofftVan'or equationHofftVan'asknownisequationaboveThe RT E T Kc (7)equationinngSubstituti EnRT-H nRTEH equation followingthebyvolumeconstantatreactionofheat torelatedispressureconstantatreactionofheatThe RT nRT-H T Kc 2 2 ln )7( ln           
  • 49. Reference Books : • Advanced Physical chemistry – Gurdeep Raj • Thermodynamics – A core course – 2nd edn by R.C. Srivastava • An introduction to chemical thermodynamics – 6th edn Rastogi & Misra • Advanced physical chemistry - D. N. Bajpai (S. Chand ) 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road Recommended Reading :
  • 50. 3oth November 2020 Dr. Aqeela Sattar Qureshi , Royal College , Mira Road