物理化学英文6相平衡-Phase-Equilibrium课件

PhysicalChemistryPhysicalChemistryDefinitionofPhysicalChemistryPhysicalchemistry

standsinthesamerelationtothesubdivisionsofchemistryinwhichphilosophystandstowardallthesciences.Itsmainobjectistounifythoughtwithinthescienceofchemistry;therefore,itmightwellbenamed,the“philosophyofchemistry”-S.L.Bigelow,1912DefinitionofPhysicalChemistPhaseTransformationsPureSubstancesPhaseTransformationsPureSubsPhaseChangeChaptersPhaseChangeChaptersPhaseDiagramsolidliquidgaspTcriticalpointtriplepoint1atmTbPhaseDiagramsolidliquidgaspTcVaporPressurethepressureofthevaporinequilibriumwiththeliquid.dependsonthetemperature.theonlypressure(foragiventemperature)atwhichliquidandvaporcoexist.liquidvaporpVaporPressurethepressureofPhaseEquilibriumTemperaturemgasliquidsolidTfTbPhaseEquilibriumTemperaturemgPressureEffectsonPhaseEquil.TmgasliquidsolidTfTbTfTbPressureEffectsonPhaseEquiClapeyronEquationdms=dml,ifphaseequilibriumismaintainedtherefore,Vsdp-SsdT=Vldp-SldT

dp/dT=DSfus/DVfussolid(p,T)«liquid(p,T)solid(p+dp,T+dT)«liquid(p+dp,T+dT)dmsdmlClapeyronEquationdms=dml,ifClausius-ClapeyronEquationClausius-ClapeyronEquationNitricAcidVaporPressurelnp1/Tm=-4565KDHvap=mR=37.95kJNitricAcidVaporPressurelnpVaporPressureinGasMixturesliquid(p*)=gas(p*)liquid(p*+DP

)=gas(p)VaporPressureinGasMixturesInertGasEffectLetp*=vaporpressureofpuresubstanceLetp=vaporpressurewithinertgaspresentLetDP=increaseintotalpressureInertGasEffectLetp*=vaporPhaseEquilibriumBinarymixturesPhaseEquilibriumBinarymixturliq«vapEq.inBinaryMixturesBoththeliquidandthevaporphasearebinarymixturesofAandB.xA,xBarethemolefractionsintheliquid.yA,yBarethemolefractionsinthevapor.pA,pBarethepartialpressuresinthevapor.liq«vapEq.inBinaryMixturEthylAcetateinAceticAnhydridexethylacetatep/torrEthylAcetateinAceticAnhydrThevaporpressureofasubstancevarieslinearlywithitsmolefractioninsolution.\

pA=xApA*

Raoult’sLawbecomesexactasxA

®1.Raoult’sLawbecomesincreasinglyvalidasthecomponentsofthemixturebecomemorestructurallysimilar.Raoult’sLawThevaporpressureofasubstan-PentaneinMethylAcetatep/torrxpentanen-PentaneinMethylAcetatep/IdealSolutionModelwheremA*isthechemicalpotentialofthepureliquidIdealSolutionModelwheremA*IdealHeatofMixingIdealHeatofMixingMolecularBasisforIdealSol’ns.InpureliquidA,thereareonlyA-Ainteractions.InpureliquidB,thereareonlyB-B

interactions.InsolutionsofAandB,thereareA-B

interactionsaswell.DHmixing=0saysthatallthreeinteractionsareofequalstrength.

MolecularBasisforIdealSol’EthylAcetate-AceticAnhydridep/torrxethylacetatepaceticandydridepethylacetateptotalEthylAcetate-AceticAnhydrin-PentaneandMethylAcetatexpentanep/torrpmethylacetateppentaneptotaln-PentaneandMethylAcetatexpColligativePropertiesDefinition:colligativepropertiesdependonlyontheconcentrationofsoluteparticles,notontheiridentity.Assumptions:thesoluteisnon-volatile,i.e.thevaporphaseispuresolvent.thesoluteisinsolubleinthesolidsolvent,i.e.solidphasesarepuresubstances.ColligativePropertiesDefinitiBoilingPointElevationBoilingPointElevationMolalityandMoleFraction=k(mB/

mB0)MolalityandMoleFraction=kFreezingPointDepressionFreezingPointDepressionSolubilitySolubilityOsmoticPressurepp+PpuresolventsolutionOsmoticPressurepp+PpuresolutiMolalityandMoleFractionMolalityandMoleFractionn-PentaneinMethylAcetateHenry’sLawRaoult’sLawKp*xpentanep/torrn-PentaneinMethylAcetateHenThevaporpressureofasubstancevarieslinearlywithitsmolefractioninsolution.

pA=xAKA

whereKAistheHenry’sLawconstantHenry’sLawbecomesexactasxA

®0.KAisthehypotheticalvaporpressureofpureA,assumingthatitbehavedinitspureformasitdoesatinfinitedilution.Henry’sLawThevaporpressureofasubstaDilute-IdealSolutionModelwheremA+isthehypotheticalchemicalpotentialoftheliquidasxBapproachesunity.Dilute-IdealSolutionModelwheMolalityScaleMolalityScaleSolventActivityTheexactchemicalpotentialisgivenby

mA=mA*+RTln(pA/pA*)Thesolvent

activityisdefinedaA=pA/pA*Therefore,mA=mA*+RTlnaAisexact.

TheactivitycoefficientgAisdefined

aA=

gAxAAsxA

®1,aA

®xA

andgA

®1SolventActivityTheexactchemSoluteActivityTheexactchemicalpotentialisgivenby

mB=mB++RTln(pB/KB)Thesolute

activityisdefinedaB=pB/KB

Therefore,mB=mB++RTlnaBisexact.

TheactivitycoefficientgBisdefined

aB=

gBxBAsxB

®0,aB

®xB

andgB

®1SoluteActivityTheexactchemiMolalityScaleActivityTheexactchemicalpotentialisalsogivenbymB=mB0+RTln(pB/kKB)Themolalityscale

activityisdefinedby

aB=pB/kKB

Therefore,mB=mB0+RTlnaBisexact.

TheactivitycoefficientgBisdefined

aB=

gB(mB/

m0)AsxB

®0,aB

®mB/

m0

andgB

®1MolalityScaleActivityTheexa

Benzene-AceticAcidxaceticacidp/torr

Benzene-AceticAcidxaceticac

Benzene-AceticAcid

RaoultActivitiesxaceticacidActivity

Benzene-AceticAcid

RaoultABenzene-AceticAcid

BenzeneActivitiesxaceticacidActivityBenzene-AceticAcid

BenzeneA

Benzene-AceticAcid

ActivityCoefficientsxaceticacidActivityCoefficients

Benzene-AceticAcid

ActivityExcessDGofMixingExcessDGofMixingPhaseEquilibriumPhaseDiagramsPhaseEquilibriumPhaseDiagramDefinitionsF:thenumberofdegreesoffreedom,i.e.thenumberofindependentvariables

neededtodescribethestateofthesystem.C:thenumberofindependentsubstancesinthesystem.P:thenumberof

phases

inthesystem,whereaphaseisaformofmatterthatisuniformthroughoutincompositionandstate.DefinitionsF:thenumberofdeThePhaseRuleEach

phaseneedsC-1compositionvariablesplusTandptodescribeitsstate.Therefore,thetotalnumberofstatevariablesisP(C-1)+2Foreachsubstance,thereareP-1equil.constraintsoftheform(ThereforeF=P(C-1)+2-C(P-1)

orF=C-P+2ThePhaseRuleEachphaseneedsPhaseDiagramsolidliquidgaspTcriticalpointtriplepoint1atmTbPhaseDiagramsolidliquidgaspTcCoolingCurve:PureSubstancetimeTTfarrestliquidcoolingsolidcoolingliquidfreezingCoolingCurve:PureSubstancetBoilingPt./CompositionDiagramliquidxATb

vaporTA*TB*yAxATbfortheliquidwithcompositionxAcompositionofthevaporthatboilsoffatTb

boilingpt.ofpureAboilingpt.ofpureBBoilingPt./CompositionDiagraLeverRuleLetzbethetotalmolefractionofA,bothphasescombined.Letnandnbethemolesinphasesand.nz=nx+nyA

=nz+nzAn(z-x)=n(y-z)nl=nl

zAphasephasellTyAxALeverRuleLetzbethetotalliquidvaporTb

TA*TB*xAAzeotropesazeotropiccompositionazeotropicboilingpt.liquidvaporTbTA*TB*xAAzeoIdealBoilingPt./CompositionIdealBoilingPt./CompositionImmiscibleLiquidsxAT

uppercriticaltemperatureTxxcompositionofphaseatTcompositionofphaseatT2liquidphases1liquidphaseImmiscibleLiquidsxATuppeBoilingofImmiscibleLiquidsxAT

2liquidphases1liquidphasevaporphasel+vl+vzABoilingofImmiscibleLiquidsxBoilingofImmiscibleLiquidsxAT

2liquidphasesvaporphasel+vl+vzAllBoilingofImmiscibleLiquidsxMeltingofSolidMixturesxAT

2solidphasesliquidphases+ls+lzAEutecticpointMeltingofSolidMixturesxATIntermediateCompoundxAT

solidB+solidABliquidphases+ls+lBABAsolidAB+solidAs+lliquidphases+lIntermediateCompoundxATsSpinelxAT

SolidSol’n.liquidphaseBA2solidphasesandliquid+solid

SolidSol’n.liquid+solid

SpinelxATSolidliquidphasImmiscibleMelts:Ex8.17molefractionCF4

®T­

solidB+solidATwophaseliquidCH4CF4liquidphases+ls+lsolidB+liquid9186848994ImmiscibleMelts:Ex8.17moleIncongruentMeltingxAT

solidB+solidABliquidphaseB(s)+lBABAsolidAB+solidAA(s)+lAB(s)+lIncongruentMeltingxATsolTriangularCoordinatesEachvertexcorrespondstoapuresubstance.Thesideoppositeavertexcorrespondstoamixtureoftheothertwosubstances.ThemolefractionofAisproportionaltothedistancefromtheoppositeside.ABCxA=0.65xB=0.15xC=0.20TriangularCoordinatesEachverTriangularPhaseDiagramsfixedTandPABCP=1P=2compositionofB-richphasecompositionofC-richphasetielineTriangularPhaseDiagramsfixed“SaltingOut”H2OCH3OHK2CO3P=1liquidP=2K2CO3(s)+sol’nP=2K2CO3(s)+sol’nP=2immiscibleliquidsP=3K2CO3(s)and2immiscibleliquids“SaltingOut”H2OCH3OHK2CO3P=1DoubleSolubilityDiagramH2OP=2NH4Cl(s)&sat’d.sol’n.(NH4)2SO4NH4ClP=1sol’nP=2(NH4)2SO4(s)&sat’d.sol’n.P=3bothsolids&sat’d.sol’n.DoubleSolubilityDiagramH2OP=物理化学英文6相平衡-Phase-Equilibrium课件PhysicalChemistryPhysicalChemistryDefinitionofPhysicalChemistryPhysicalchemistry

standsinthesamerelationtothesubdivisionsofchemistryinwhichphilosophystandstowardallthesciences.Itsmainobjectistounifythoughtwithinthescienceofchemistry;therefore,itmightwellbenamed,the“philosophyofchemistry”-S.L.Bigelow,1912DefinitionofPhysicalChemistPhaseTransformationsPureSubstancesPhaseTransformationsPureSubsPhaseChangeChaptersPhaseChangeChaptersPhaseDiagramsolidliquidgaspTcriticalpointtriplepoint1atmTbPhaseDiagramsolidliquidgaspTcVaporPressurethepressureofthevaporinequilibriumwiththeliquid.dependsonthetemperature.theonlypressure(foragiventemperature)atwhichliquidandvaporcoexist.liquidvaporpVaporPressurethepressureofPhaseEquilibriumTemperaturemgasliquidsolidTfTbPhaseEquilibriumTemperaturemgPressureEffectsonPhaseEquil.TmgasliquidsolidTfTbTfTbPressureEffectsonPhaseEquiClapeyronEquationdms=dml,ifphaseequilibriumismaintainedtherefore,Vsdp-SsdT=Vldp-SldT

dp/dT=DSfus/DVfussolid(p,T)«liquid(p,T)solid(p+dp,T+dT)«liquid(p+dp,T+dT)dmsdmlClapeyronEquationdms=dml,ifClausius-ClapeyronEquationClausius-ClapeyronEquationNitricAcidVaporPressurelnp1/Tm=-4565KDHvap=mR=37.95kJNitricAcidVaporPressurelnpVaporPressureinGasMixturesliquid(p*)=gas(p*)liquid(p*+DP

)=gas(p)VaporPressureinGasMixturesInertGasEffectLetp*=vaporpressureofpuresubstanceLetp=vaporpressurewithinertgaspresentLetDP=increaseintotalpressureInertGasEffectLetp*=vaporPhaseEquilibriumBinarymixturesPhaseEquilibriumBinarymixturliq«vapEq.inBinaryMixturesBoththeliquidandthevaporphasearebinarymixturesofAandB.xA,xBarethemolefractionsintheliquid.yA,yBarethemolefractionsinthevapor.pA,pBarethepartialpressuresinthevapor.liq«vapEq.inBinaryMixturEthylAcetateinAceticAnhydridexethylacetatep/torrEthylAcetateinAceticAnhydrThevaporpressureofasubstancevarieslinearlywithitsmolefractioninsolution.\

pA=xApA*

Raoult’sLawbecomesexactasxA

®1.Raoult’sLawbecomesincreasinglyvalidasthecomponentsofthemixturebecomemorestructurallysimilar.Raoult’sLawThevaporpressureofasubstan-PentaneinMethylAcetatep/torrxpentanen-PentaneinMethylAcetatep/IdealSolutionModelwheremA*isthechemicalpotentialofthepureliquidIdealSolutionModelwheremA*IdealHeatofMixingIdealHeatofMixingMolecularBasisforIdealSol’ns.InpureliquidA,thereareonlyA-Ainteractions.InpureliquidB,thereareonlyB-B

interactions.InsolutionsofAandB,thereareA-B

interactionsaswell.DHmixing=0saysthatallthreeinteractionsareofequalstrength.

MolecularBasisforIdealSol’EthylAcetate-AceticAnhydridep/torrxethylacetatepaceticandydridepethylacetateptotalEthylAcetate-AceticAnhydrin-PentaneandMethylAcetatexpentanep/torrpmethylacetateppentaneptotaln-PentaneandMethylAcetatexpColligativePropertiesDefinition:colligativepropertiesdependonlyontheconcentrationofsoluteparticles,notontheiridentity.Assumptions:thesoluteisnon-volatile,i.e.thevaporphaseispuresolvent.thesoluteisinsolubleinthesolidsolvent,i.e.solidphasesarepuresubstances.ColligativePropertiesDefinitiBoilingPointElevationBoilingPointElevationMolalityandMoleFraction=k(mB/

mB0)MolalityandMoleFraction=kFreezingPointDepressionFreezingPointDepressionSolubilitySolubilityOsmoticPressurepp+PpuresolventsolutionOsmoticPressurepp+PpuresolutiMolalityandMoleFractionMolalityandMoleFractionn-PentaneinMethylAcetateHenry’sLawRaoult’sLawKp*xpentanep/torrn-PentaneinMethylAcetateHenThevaporpressureofasubstancevarieslinearlywithitsmolefractioninsolution.

pA=xAKA

whereKAistheHenry’sLawconstantHenry’sLawbecomesexactasxA

®0.KAisthehypotheticalvaporpressureofpureA,assumingthatitbehavedinitspureformasitdoesatinfinitedilution.Henry’sLawThevaporpressureofasubstaDilute-IdealSolutionModelwheremA+isthehypotheticalchemicalpotentialoftheliquidasxBapproachesunity.Dilute-IdealSolutionModelwheMolalityScaleMolalityScaleSolventActivityTheexactchemicalpotentialisgivenby

mA=mA*+RTln(pA/pA*)Thesolvent

activityisdefinedaA=pA/pA*Therefore,mA=mA*+RTlnaAisexact.

TheactivitycoefficientgAisdefined

aA=

gAxAAsxA

®1,aA

®xA

andgA

®1SolventActivityTheexactchemSoluteActivityTheexactchemicalpotentialisgivenby

mB=mB++RTln(pB/KB)Thesolute

activityisdefinedaB=pB/KB

Therefore,mB=mB++RTlnaBisexact.

TheactivitycoefficientgBisdefined

aB=

gBxBAsxB

®0,aB

®xB

andgB

®1SoluteActivityTheexactchemiMolalityScaleActivityTheexactchemicalpotentialisalsogivenbymB=mB0+RTln(pB/kKB)Themolalityscale

activityisdefinedby

aB=pB/kKB

Therefore,mB=mB0+RTlnaBisexact.

TheactivitycoefficientgBisdefined

aB=

gB(mB/

m0)AsxB

®0,aB

®mB/

m0

andgB

®1MolalityScaleActivityTheexa

Benzene-AceticAcidxaceticacidp/torr

Benzene-AceticAcidxaceticac

Benzene-AceticAcid

RaoultActivitiesxaceticacidActivity

Benzene-AceticAcid

RaoultABenzene-AceticAcid

BenzeneActivitiesxaceticacidActivityBenzene-AceticAcid

BenzeneA

Benzene-AceticAcid

ActivityCoefficientsxaceticacidActivityCoefficients

Benzene-AceticAcid

ActivityExcessDGofMixingExcessDGofMixingPhaseEquilibriumPhaseDiagramsPhaseEquilibriumPhaseDiagramDefinitionsF:thenumberofdegreesoffreedom,i.e.thenumberofindependentvariables

neededtodescribethestateofthesystem.C:thenumberofindependentsubstancesinthesystem.P:thenumberof

phases

inthesystem,whereaphaseisaformofmatterthatisuniformthroughoutincompositionandstate.DefinitionsF:thenumberofdeThePhaseRuleEach

phaseneedsC-1compositionvariablesplusTandptodescribeitsstate.Therefore,thetotalnumberofstatevariablesisP(C-1)+2Foreachsubstance,thereareP-1equil.constraintsoftheform(ThereforeF=P(C-1)+2-C(P-1)

orF=C-P+2ThePhaseRuleEachphaseneedsPhaseDiagramsolidliquidgaspTcriticalpointtriplepoint1atmTbPhaseDiagramsolidliquidgaspTcCoolingCurve:PureSubstancetimeTTfarrestliquidcoolingsolidcoolingliquidfreezingCoolingCurve:PureSubstancetBoilingPt./CompositionDiagramliquidxATb

vaporTA*TB*yAxATbfortheliquidwithcompositionxAcompositionofthevaporthatboilsoffatTb

boilingpt.ofpureAboilingpt.ofpureBBoilingPt./CompositionDiagraLeverRuleLetzbethetotalmolefractionofA,bothphasescombined.Letnandnbethemolesinphasesand.nz=nx+nyA

=nz+nzAn(z-x)=n(y-z)nl=nl

zAphasephasellTyAxALeverRuleLetzbethetotalliquidvaporTb

TA*TB*xAAzeotropesazeotropiccompositionazeotropicboilingpt.liquidvaporTbTA*TB*xAAzeoIdealBoilingPt./CompositionIdealBoilingPt./CompositionImmiscibleLiquidsxAT

uppercriticaltemperatureTxxcompositionofphaseatTcompositionofp