成果下半学期eng-yxwhk

Chapter

-5thPhaseequilibriumandphaseThesimpleapplicationsofthethermodynamicstochemicallysignificantsystemsaretothediscussionofthephasetransitionsofpuresubstancesandponentaswell ponent systemofpuresubstances ponentwell ponentsystemsinthis1Bothgeometricmethodandthermodynamicmethodaretwocommonwaystoresearchthemulti-phaseequilibriumsystemsof ponentand geometrymethod:ThestateandruleofthephasesystemsarestudiedbyusingageometricPhasediagramisageometricmapatwhichthephaseequilibriumruleofasubstanceisexpressed.Eachphaseofasubstanceisthemoststable(equilibriumstate)init.Thermodynamicmethod:Theruleofthephasesystemsareexploredbyusingthermodynamic2Thephase,Aphaseofsubstanceisaformofmatterthatisuniformthroughoutinchemicalcompositionandphysicalstate.whichthecompositionisuniformonamicroscopic3Adispersion,inwhichregionsofonecomponentareembeddedinamatrixofasecondcomponent31).Thephase,ThenumberofphasesinasystemisdenotedAgas,oragaseousmixture,isasingleAcrystalisasingleTwototallymiscibleliquidsoralloyformasingle φIceisasinglephaseeventhoughitmightbechippedintosmallfragments.4Anysamplecutsfromthesample,howeversmall,isrepresentativeofthecompositionofthewhole.4Thephase,Aslurryoficeandwaterisatwo-phaseloyoftwometalsisatwo-phasesystemifthemetalsareimmiscible.Adispersionofclaysinwaterisuniformonmacroscopicscalebutnotonamicroscopic

φAsmallsamplecomesentirelyfromoneoftheminimal5ofpureAandwouldnotberepresentativeofthe56Thephase,6Gasphase:φLiquidphase:fromtheextentofmiscible,φ=1,2,Solidphase:ingeneral,eachsolidisaindependentphase.forthesolidsolution:φ=1loyoftwometalsifthemetalsareimmiscible(φ=2),blackphosphorusandwhitephosphorus(φ=2).One-phasesystem:onlyaphaseinaMulti-phasesystem:twoormorephasesinaComponents,Aconstituentisachemicalspeciesthatispresentinasystem,andthenumberofconstituentisdenotedasS.Acomponentisachemicallyindependentconstituentofa7Thenumberofcomponents,C,inasystemistheminimumnumberofindependentspeciesnecessarytodefinethecompositionofallthephasespresentinthesystem.7Components,NoconfiningrelationsbothconcentrationandchemicalreactionsWhennoreactiontakesplace,thenumberofcomponentsequaltothenumberof8Thepurewaterisa ponentsystem,C=1,becauseweneedonlythespeciesH2Otospecifyitscomposition.Similarly,amixtureofethanolandwaterisa system,C=2:weneedthespeciesH2OandC2H5OHtospecifyitscomposition.899Components,Withchemicalreactions,andwithoutconcentrationconfiningrelationinthesamephaseWhenareactioncanoccurinthesystem,weneedtodecidetheminimumnumberofspeciesthatcanbeusedtospecifythecompositionofallthephases.Ingeneral:C=S-Risthenumberofindependentchemical2).Components,Withchemicalreactions, paniedwithconcentrationconfiningrelationshipinthesamephaseWhenconcentrationconfiningrelationshipexistsinthesamephase,weneedtodecidetheminimumnumberofspeciesthatcanbeusedtospecifythecompositionofallthephases.Ingeneral:C=S-R–R’isthenumberofconcentrationconfiningFreedomdegree,Freedomdegree,f:Itisthenumberoftheindependentintensityvariables(temperature,pressureandconcentrationofeachphase)thatcanchangefreelyinthephaseequilibriumPhaseruleisageneralrelationbetweenthefreedomdegree,f,thenumberofcomponents,C,andthethenumberofphasesatequilibriumφ,forasystemofanycomposition,whichillustratesabasicruleoftransitionofthephaseequilibrium.ponentphaseThemaintopicsofsection5.2arethephaseruleand ponentphaseequilibrium.5.2.1.Derivesthephaserule,whichlsushowmanyintensivevariablesareneededtospecifythethermodynamicstateofasystem.5.2.2.Discussesthefeatures ponentphase5.2.3.DerivestheClapeyronequation,whichgivesthe ponentphasediagram(dpdT).5.2.4.ThetypeofphasePhaseAllphasediagramscanbediscussedintermsofarelationship,thephaserule,derivedbyJ.W.Gibbs.InapVTsystemoftheequilibriumstate,thenumberofphasesisφ,andthenumberofspeciesisSineachphase.Now,wecalculatethenumberoftheindependentintensivevariables,f,Thetotalnumberofintensivevariables: ST,p,x,x ST,p

,

,

,...,x

(S1S1S ST,p,x,x SThevariablesarenotallindependent,havingrelationsbetweenThenumberofrelationsbetweenthevariablesintheequilibriumsystem: TT...Tmechanics pp... phase

(φ-1)independentequationstoeachvariable,(S+2)variables,thenumberof=(φ-1)chemicalequilibrium: equilibriumreaction,wehaveii Anrestrictionsrelationofindependentconcentrationof electroneutralityconditions:Degreeoffreedomofanequilibriumsystem,f:itisthenumberoftheindependentintensivevariables(temperature,pressureandconcentrationofeachphase)todefinetheequilibriumstateofamulti-phase, ponentsystem.Thenumberofindependentintensivevariables,f,isequaltothetotalnumberofintensivevariablessubtractthetotalnumberofrelationsTherefore,wehave:f(S1)[(1)(S2)RR'(SRR')thenumberofindependentcomponents,C,whichexpressestheleastindependentspecies:C=S-R-R’Gibbsphaserule:f=C-φ+WhenthereareothervariablesbesidesT,p,x1,x2,…,xS-1,commonformatofGibbsphaserule:f=C-φ+n,n≥ Example1,whatisthenumberofcomponentanddegreefreedominthefollowingAmixinggasesconsistofArandS=2，R=0,R’=0,C=S=2,f=C-φ+2=2-1+2=3(anythreevariablesT,p,xArorEquilibriumofosmosisbetweenNaClaqueoussolutionandpurewaterbysemipermeableS=2,R=0,R’=0,C=S-R-R’=[2-0-0]=2,f=C-φ+3=2-2+3=3(T,p,xNaClorT,p,AmixinggasesconsistofN2,H2and①thesystemexistsinitiallyN2andH2,

n nH H2therefore,N2(g)+3H2(g)f=C-φ+2=2-1+2=3((anythreevariablesT,p,xNH3,xN2,or②thesystemexistsinitiallyNH3(g)therefore:N2(g)/3H2(g)=1/3,Then:S=3,R=1,R’=1,C=S-R-R’=3-1-1=1,f=C-φ+2=1- (anytwovariablesT,porT,NH4Cl(s) posed,attheequilibriumNH4Cl(s)=NH3(g)+HCl①systemcontainsinitiallyS=3,R=1,R’=1,(NH3(g):HCl(g)Then:f=C-φ+2=1- (Tor②systemcontainsinitially S=3,R=1,R’=0,C=S-R-R’=2,Then:f=C-φ+2=2- (anytwovariablesT,p,or 3CaCO3(s) posed,attheequilibriumCaCO3(s)=CaO(s)+CO2S=3,R=1,R’=0,C=S-R-R’=2,f=2-3+2=1(anyvariableinT,p(6).ThesystemofliquidwatercontainingH2O,(H2O)2,…,f=C-φ+2=1-1+2=2(anytwovariablesin p,(7)BothKClandNaNO3dissolveinthewaterhavingH2O,Na+,K+,Cl-,NO3-inthesystem,S=5,R=0,R’=2,([Na+]=[Cl-];[K+]=[NO3-C=S-R-R’=5-0-f=C-φ+2=3-(8).298K,100kPa,theequilibriumsystemofNaCl(s)anditssaturatedaqueoussolutionS=2,R=0,R’=0,C=S-R-R’=[2-0-0]=2,f=C-φ+2=2-2+0=BothKClandAgNO3dissolveinthewater,andbuiltanKCl+AgNO3=KNO3+AgCl①formmolecularlever:havingKCl,AgNO3,KNO3, H2Ointhesystem,S=5,R=1,R’=0,C=S-R-R’=[5-1-0]=4,②fromioniclever,havingH2O,AgCl(s),K+,Cl-,Ag+,NO3-,inthesystem,S=6,R=2,R’=0,(AgCl(s)=K++NO3-)C=S-R-R’=6-2-C=4,φ=2,f=C-φ+2=4-LetAlCl3dissolveinwater,andhydrolyze AlCl3+3H2O=Al(OH)3(s)+S=4,R=1,R’=0,C=S-R-R’=[4-1-0]=3,f=C-φ+2=3-2+2= Al3++3H2O=Al(OH)3(s)+3H+Al(OH)3=Al3++3OH-fromioniclever,havingAl3+,H2O,Al(OH)3(s),H+,OH-S=5,R=2,R’=0,C=5-2-0=3,φ=2,f=C-φ+2=3-2+2=3说明求组分数时可根据不同出发点自不同途径得到相同将某固态金属MNO2加热，平衡体MNO2MNO3M2ON2，NO，NO2，O2a).前三个化合物不互溶；b).前三个化合物完全互溶；求：C，φf解：先确定此体系中的独立反应数，一般来说独立反应数RR化学物种数原子种类数R=7-3=4，R’=0，S=7，C=S-R-R’=7-4-aφ=4，则：fCφ2=3-4+2bφ=2，则：fCφ2=3-2+2将NH4HCO3(s)放入真空容器中，恒温至400K分解，求：KfNH4HCO3(s)=NH3(g)+H2O(g)+CO2(g)NH3(g):H2O(g)=1:1,C=S-R-R’=4-1-φ=2f*=C-φ+1=1-例2Na2CO3与水可形成三种水合物，Na2CO3·Na2CO3·7H2O(s)，Na2CO3·问这些水合物能否与Na2CO3水溶液及冰同时平衡共在pΘ下，与水溶液及冰共存的含水盐最多可有C=S-R-R’=5-3-0=2;f＝0时的相数是平衡时体系能共存的最多02max2,max4因此三种水合物(三相)不能同时与Na2CO3水溶液及冰平衡共(2).在pΘf*C-φ102-φ1，则φ现已有多只能有一种。ponentphase ponentphasediagramshowstheregionoftemperatureandpressureinwhicheachofthephasesofasubstanceisstable.SincetheequilibriumconditionatfixedTandpistheminimizationoftheGibb’senergyG,ThemoststablephaseofapuresubstanceatagivenTandpisthephasewiththelowestvalueofGm=. ponentphase. eralfeatures ponentphasePhaserulegivesthecommoncharactersofphasediagramsofponentsystem.ToapVTsystem,fromthephaserule,f=C–φ+2=3-Becausef≥0,φ≥1,thenwe 3≥φ≥φ＝1,f＝2,doublevariablesystem,mapisaplaneinplotofp-Tφ＝2,f＝1,one-variablesystem,mapisalineinplotofp-Tφ＝3,f＝0,non-variablesystem,mapisapointinplotofp-TBasiccaobThephase

Thephasediagramshowstheregionsofpressureandtemperatureatwhichitsvariousphasesarethermodynamicallystable.phaseboundaries:Thelinesseparatingtheregionsarecalled.TheselinesshowthevaluesofpandTatwhichtwophasescoexistinequilibrium.Theliquid-vapourphaseboundary(Thelineo-a);Theliquid-solidphaseboundary(Thelineo-c); trsHm

T

(Thelineo-ThetriplepointThephasetransition:A

TheschematicTdependenceofthechemicalpotentialofthesolid,liquid,andgasphasesofasubstanceanotherphase,occursTheschematicTdependenceofthechemicalpotentialofthesolid,liquid,andgasphasesofasubstancetemperatureforagivene.g.at1atm,iceisthestablephasebelow0℃,butabove0℃liquidwateristhestablephase.Ttrs:Atransitiontemperature,representsthetemperatureatwhichthetwochemicalpotentialsareequalandthetwophasesareinequilibriumatthespecificpressure.Notethatthenormaltransitiontemperatureofp=1.0atm.orVapourpressureofaliquidorsolidisthepressureexertedbythevapourinequilibriumwiththecondensedphase,whichincreaseswithtemperatureinaclosedvessel.Theliquid-vapourphaseboundaryshowshowthevapourpressureoftheliquidvarieswithtemperature.Thesolid-vapourphaseboundaryshowshowthesublimationvapourpressureofthesolidvarieswithc

BoilingWhenaliquidisheatedinanopenvessel,theliquidvaporizesfromitssurface.AtTatwhichitsvapourpwouldbeequaltotheexternalvaporizationcanoccur

oftheliquid.Theoffreevaporizationtheliquidiscalled Thenormalboilingpoint,p=1 Thestandardboilingpoint,p=1CriticalBoilingdoesnotoccurwhenaliquidisheatedinaclosedvessel.

AliquidinequilibriumwithitsWhenaliquidisheatedinasealedcontainer,thedensityofthevapourphaseincreasesandthatoftheliquiddecreasesTherecomesastage,atwhichthetwodensitiesareequalandtheinterfacebetweenthefluidsdisappears.Thisdisappearanceoccursatthecriticaltemperature.Thecriticaltemperatureofwateris374℃andthevapourpressureisthen218atm.CriticalcaobThephase

ofthevapourisequaltothatoftheremainingliquidandthe whichthesurfacedisappearsisthecriticaltemperature,Tc,oftheAtandaboveTc,asingleuniformphaseiscalledasupercriticalfluid.AboveTc,theliquidphaseofthesubstancedoesnotexist.MeltingandfreezingThemeltingor temperature:thetemperature which,underaspecifiedtheliquidandsolidphasesofasubstancecoexistinequilibriumiscalled.Thenormalmeltingor point:Thetemperaturewhen pressureis1atmiscalledthenormalmeltingorfreezingpoint. freezingpoint:themeltingThephase

freezingpointwhenthepressureis1bar.ThetripleThereisasetofconditions whichthreedifferentphasesofa substanceallsimultaneouslycoexistinequilibrium.Itisrepresentedbythetriplepoint,apointatwhichthethreephaseboundariesmeet.temperatureatthetriplepoint denotedT3.Thetriplepointof puresubstanceisoutsideourcontrol:itoccursatasingledefinitepressureandtemperaturecharacteristicofthesubstance.Thephase

Thetriplepoint waterlies273.16Kand6.Threetypicalphase(a)Waterhasthreekindsofexistentstate,whichcanbuildanequilibriumatfixedTandp,ly:icewater,watervapour,vapourattriplepoint:icewaterFollowingdataistherelationbetweenpressureandtemperatureintheequilibriumstate,phasediagramsmaybedrewfromtheseexperimentaldata.TemperatureandpressureofwaterbeingequilibriumatnormalTwophase Threephaset/

ofwaterorice/Pa

watericewatericeice

PlotofpagainstTisdrewbytheabove1.Water-lowC

f＝3－onephaseφ=1,f=twophaseφ=2,f=Oa,vapour(condensation)watericeObsublime凝华iceOe,vapour(condensation)linethemetastableThemetastablephase:ThermodynamicallyunstablephasespersistbecausethetransitioniskineticallyWater-low(3)Triplepoint:φ=3，f PointO:T3=(3’).Normalfreezingpoint(IcePointO’:Tf=273.15K，101325Pa: (4)SlopeoflineOadpdT:Whythetemperatureinnormalfreezingpointis0.01Klowerthanthatintriplepoint?Tworeasons:(1)freezingpointdecreasesindilutewhichcausesadecreaseof0.00242K; causesadecreaseof0.00747 dT

,1.Water-lowC(5).CriticalPointC:Thenegativeslopeupto2kbarmeansthatthemeltingtemperaturefallsasthepressureisraised,indicatingthatthevolumedecreasesonmeltingliquidisdenserthantheWater-lowcp/p/105d

DrawcoolingC fromYiscooledtott

aO

gasgas liquid

liquid M’liquidsolidXt/Water-lowpp/105X

Describefollowingcourse:Atransitionfromatod

O

isobariccoolingto

pressiontoAnswer:Abovechangefromgas(a)toliquid(b)undergoingphase1.Water1.Water-highphasediagramforwaterAthighpressures,differentstructuralformsoficecomeintostability.SomeofthesephaseswhicharecallediceII,III,V,VI,andVIImeltathightemperatures(iceIVisunstable).Notethatfivemoretriplepointsoccurinthediagramotherthantheonewherevapour,liquid,andiceIcoexis