chapter04 Material Equilibrium.ppt

PhysicalChemistry ChengXuan February2004 SpringSemester PhysicalChemistry PhysicalChemistry Reviewfromthelastclass MaterialEquilibrium BasicEquations MaterialEquilibrium PhysicalChemistry PhysicalChemistry Reviewfromthelastclass MaterialEquilibrium Relationsamongdifferentfunctions TheGibbsEquations MaterialEquilibrium PhysicalChemistry MaterialEquilibrium PhysicalChemistry dG SdT VdP dA SdT PdV dH TdS VdP dU TdS PdV MaxwellRelations MaterialEquilibrium PhysicalChemistry 4 39 Isobaricthermalexpansivity MaterialEquilibrium PhysicalChemistry Isothermalcompressibility 1 43 1 44 4 53 4 52 2 64 ApplicationofMaxwellRelations MaterialEquilibrium PhysicalChemistry Example1 Provethattheinternalenergyofidealgasisafunctionoftemperatureonly Answers Foridealgas MaterialEquilibrium PhysicalChemistry ApplicationofMaxwellRelations Example2 Calculate UwhenanidealgaschangesfromP1 V1 T1toP2 V2 T2 Hint applying Answers 4 59 Calculationof S Calculationofchangesinstatefunctions 4 60 4 50 4 49 PhysicalChemistry Chapter4MaterialEquilibrium MaterialEquilibrium Calculationofchangesinstatefunctions 4 60 Sfortheprocess P1 T1 P2 T2 is Sfortheprocess P1 T1 P2 T2 isindependentofthepathused Aconvenientpath Fig 4 5 issuggested PhysicalChemistry MaterialEquilibrium Calculationof Hand U 4 63 const P P1 const T T2 Hfortheprocess P1 T1 P2 T2 is Hfortheprocess P1 T1 P2 T2 isindependentofthepathused Aconvenientpath Fig 4 5 issuggested PhysicalChemistry MaterialEquilibrium Calculationof Gand A Aforanisothermalprocess T 0 Gforanisothermalprocess T 0 4 20 PhysicalChemistry 4 51 MaterialEquilibrium ChemicalPotentialsandMaterialEquilibrium 4 68 GibbsEquationsforNonequilibriumSystems Thetotaldifferentialof 4 67 Atanyinstantduringachemicalprocessinthesystem Forareversibleprocesswherenochangeincompositionoccurs Eq 4 36 reads dG SdT VdP 4 69 PhysicalChemistry MaterialEquilibrium Chemicalpotentialofsubstanceiintheone phasesystem 4 70 4 71 4 72 4 73 Substitutionof 4 70 in 4 68 dG SdT VdP PhysicalChemistry MaterialEquilibrium dU dG PdV VdP TdS SdT G H TS U PV TS TheequationfordUcorrespondingto 4 73 PhysicalChemistry MaterialEquilibrium 4 75 4 77 4 76 4 78 CollectionsofalltheexpressionfordU dH dAanddG Gibbsequations one phasesyst inmech andtherm equilib P Vworkonly closedsyst rev proc P Vworkonly Theaboveequationsconsidertheeffectofthecompositionchangesonstatefunctions U H A G PhysicalChemistry MaterialEquilibrium 4 75 4 77 4 76 4 78 Gibbsequations one phasesyst inmech andtherm equilib P Vworkonly Ifthesystemhasseveralphases G forphase Theentiresystem Theone phaseGibbsequation 4 78 writtenforphase PhysicalChemistry MaterialEquilibrium 4 79 4 80 Thechemicalpotentialforphase substitutetheaboveequationinto S theentropyofphase V thevolumeofphase thenumberofmolesofiinphase thechemicalpotentialofchemicalspeciesiinphase 4 81 syst inmech andtherm equilib P Vworkonly PhysicalChemistry MaterialEquilibrium MaterialEquilibrium from 4 82 from 4 84 TheAisaminimumforchemicalequilibriumatconstantTandV HencedA 0atdT 0 dV 0 4 81 4 83 TheGisaminimumforchemicalequilibriumatconstantTandP TheequilibriumconditiondG 0atdT 0 dP 0 materialequilib closedsyst P Vworkonly const T V materialequilib closedsyst P Vworkonly const T P PhysicalChemistry MaterialEquilibrium PhaseEquilibrium 4 85 Equation 4 84 alsoholdsnomatterhowtheclosedsystemreachesequilibrium from 4 81 AnyreversibleprocessinaclosedsystemwithP Vworkonly Anyclosedsystemsinmaterialequilibrium 4 85 Thedesiredgeneralconditionformaterialequilibrium PhysicalChemistry MaterialEquilibrium ChemicalPotentials Thechemicalpotentialofsubstanceiinone phasesystem iisastatefunction iisanintensiveproperty 4 72 G G T P n1 n2 i i T P n1 n2 TherateofchangeoftheGibbsenergyGofthephasewithrespecttothemolesofiaddedatconstantT P andothermolenumbers Foraseveral phasesystem molarGibblsfreeenergy PhysicalChemistry MaterialEquilibrium PhaseEquilibrium 4 85 Eq 4 85 becomes Consideraseveral phasesystemthatisinequilibrium supposethatdnimolesofsubstancejweretoflowfromphase tophase Fig 4 8 4 87 from FromFig 4 8 PhysicalChemistry MaterialEquilibrium ForaclosedsystemwithP Vworkonlyinthermalandmechanicalequilibrium thephaseequilibriumconditionis 4 88 Thechemicalpotentialofagivensubstanceisthesameineveryphaseofthesystem anirreversibleprocess 4 89 Forthespontaneousflowofdnjmolesofjfromphase tophase PhysicalChemistry MaterialEquilibrium 4 89 positive negative Substancejflowsspontaneouslyfromaphasewithhigherchemicalpotential itoaphasewithlowerchemicalpotential i Adifferenceinchemicalpotential iisthedrivingforcefortheflowofchemicalspeciesifromonephasetoanother PhysicalChemistry MaterialEquilibrium Letthereactionbe ReactionEquilibrium Let 4 94 WhereA1 A2 arethereactants Am Am 1 aretheproducts a b e f arethecoefficients Applythematerial equilibriumconditiontoreactionequilibrium 4 92 4 93 PhysicalChemistry MaterialEquilibrium 4 95 Duringachemicalreaction thechange ninthenumberofmolesofeachsubstanceisproportionaltoitsstoichiometriccoefficient wheretheproportionalityconstantisthesameforallspecies Thisproportionalityconstantiscalledtheextentofreaction Forafiniteextentofreaction Eq 4 95 Foraninfinitesimalextentofreactiond 4 97 4 96 4 94 Wherethestoichiometriccoefficients iarenegativeforreactantsandpositiveforproducts 2C6H6 15O2 12CO2 6H2O PhysicalChemistry MaterialEquilibrium 1moleofAhasbeendestroyedand1moleofBhasbeenformed changeinamountofApresent Theextentofreactionisameasureoftheprogressofthereaction Supposeaninfinitesimalamountd ofAturnsintoB thenwrite Forthereaction Theextentofreaction changeinamountofBpresent PhysicalChemistry Material