化工热力学第八章课件

8

化学反应平衡熟悉化学平衡判据。掌握掌握化学反应的计量关系，能以反应进度表达平衡组成和平衡常数。理解化学平衡常数的概念及有关计算。掌握简单系统化学平衡计算。了解复杂系统的化学平衡计算。学习本章的目的8.1化学反应进度∣υi∣为化学计量系数stoichiometriccoefficientυi为化学计量数stoichiometricnumber反应物的υi取负值，生成物的υi取正值考虑下列化学反应

nN2=-1,nH2=-3,nNH3=2反应进行时，各物质量的变化dni与ni的比值都相等。dni与ni的普遍关系为e为反应进度例8.1一系统发生下列反应各物质的初始含量为1molCH4,2molH2O,1molCO和5molH2。求ni和yi对e的函数关系式。解如果系统中有N个组分，同时有r个独立反应发生υi,j为第j个反应中i组分的化学计量数定义例8.2系统发生下列反应

CH4+H2O→CO+3H2(

1

)CH4+2H2O→CO2+4H2(

2

)反应开始时只有2molCH4

和3molH2O,将各yi

表示成ε1和ε2的函数。

ijCH4H2OCOCO2H2υj1-1-110322-1-201428.2化学反应平衡常数及计算8.2.1ChemicalReactionEquilibriumCriteria

WehaveseenthatGTofaclosedsystematT,Preachesaminimumatanequilibriumstate:8.2.2标准自由焓变化与平衡常数Forthetimebeing,considerasinglephasesysteminwhichchemicalreactionsarepossible.ThechangesinGibbsenergyresultingfromshiftsintemperature,pressureandcompositionaredescribedbythefundamentalequation:Atconstanttemperatureandpressure,thisreducesto: andtheonlymeansthesystemhastolowertheGibbsenergyistoalterthenumberofmolesofindividualcomponents.ForasinglechemicalreactionSubstitutingfordniinthefundamentalequationyields:Atequilibrium

standardconditionspurecomponentiatthereactiontemperatureinauser-definedphaseatauser-definedpressure(often100kPa)

Theequilibriumconstant,K,forthereactionisdefinedas:TheconventionalmeansofrepresentingtheequilibriumconstantusesDGo,thestandardGibbsenergychangethereaction.

Usingthisnotation,ourequilibriumconstantassumesthefamiliarform:

Whencalculatinganequilibriumconstant(orinterpretingaliteraturevalue),payattentiontostandardstateconditions.EachGiomustrepresentthepurecomponentatthetemperatureofinterestThestateofthecomponentandthepressurearearbitrary,buttheymustcorrespondwithfiousedtocalculatetheactivityofthecomponentinthemixture.8.2.3平衡常数的计算

KiscalculatedfromthestandardGibbsenergiesofthepurecomponentsandthestoichiometriccoefficientsofthereaction.8.2.4温度对平衡常数的影响IfweassumethatDHoisindependentoftemperature8-25KvsTemperatureEquation8-25predictsthatlnKversus1/Tislinear.ThisisbasedontheassumptionthatDHoisaweakFunctionoftemperatureovertherangeofinterest.Thisistrueforanumberofreactions,includingthosedepictedbyFigure8-2.Arigorousdevelopmentof temperaturedependence ofKmaybefoundinthetext8.3平衡常数与平衡组成间的关系8.3.1气相反应各组分的标准态都取系统温度、100kPa的理想气体，理想气体的逸度等于压力fio=Po，标准态压力Po为100kPa。ν=∑νi，Po为100kPa的标准态压力，采用和P相同的单位。

如果反应体系为理想混合物,为纯组分i在反应T和P时的逸度。如果反应混合物为理想气体8.3.2液相与固相反应各组分的标准态都取系统温度、100kPa时纯组分i的液体或固体fio化学反应的标准态fiol相平衡的标准态

若低压下，P≤2MP，一般情况∴对于理想液体

例10-3试计算在700K和30.39MPa下合成氨反应的平衡组成。已知反应物为75%H2和25%N2（均为摩尔分数）.(1)(2）(3)解：（1）写出反应式，确定出（2）写出K的表达式，假定为理想溶液(A)就可以求出平衡时的组成。已知：700K时，K=0.0091，P=30.39MPa平衡常数已知，计算出,再据间的关系由普维法计算：(3)用ε表示和计算出下面我们求由（8-2）式知：的关系式若n=2mol，则n01=1/2moln02=3/2mol

n=2-ε（4）将有关量代入（A）式，得解一元二次方程得：将其整理，得式中A=4.9255故平衡组成平衡时的转化率

8.4复杂反应物系中的化学平衡8.4.1平衡常数法Example8.4Afeedstockofpuren-butaneiscrackedat750Kand1.2bartoproduceolefins.Onlytworeactionshavefavorableequilibriumconversionsattheseconditions;(1)(2)lfthesereactionsreachequilibrium,whatistheproductcomposition?Theequilibriumconstantsat750Karefoundtobe:K1=3.856andK2=268.4EquationsrelatingtheproductcompositiontothereactioncoordinatesareTheequilibriumrelationsare:Combinetheseequilibriumequationswiththemole-fractionequations:DivideEq.(B)byEq.(A)andsolveforε2:(A)

(B)

(C)

(D)CombineEqs.(A)and(C).Aftersomereduction,solutionforε1gives:(E)

SubstitutionofnumericalvaluesinEqs.(D),(E),and(C)yields:

Theproduct-gascompositionisthen

Themethodofequilibriumconstantsdoesnotlenditselftostandardizationsoastoallowageneralprogramtobewrittenforcomputersolution.8.4.2总自由焓极值法ThetotalGibbsenergyofasingle-phasesystemshowsthat:Theproblemistofindtheset{ni}whichminimizesGtforspecifiedTandP,subjecttotheconstrainsofthematerialbalances.ThestandardsolutiontothisproblemisbasedonthemethodofLagrange’sundeterminedmultipliers.Theprocedureforgas-phasereactionisdescribedasfollows.(1)Thefirststepistoformulatetheconstrainingequations,i.e.,thematerialbalances.Althoughreactingmolecularspeciesarenotconservedinaclosedsystem,thetotalnumberofatomsofeachelementisconstant.Letsubscriptkidentityaparticularatom.ThendefineAkasthetotalnumberofatomicmassesofthekthelementinthesystem,asdeterminedbytheinitialconstitutionofthesystem.Further,letaikbethenumberofatomsofthekthelementpresentineachmoleculeofchemicalspeciesi.Thematerialbalanceoneachelementkmaythenbewritten:whereωisthetotalnumberofelementscomprisingthesystem.(2)Next,weintroducetheLagrangemultipliersλk,oneforeachelement,bymultiplyingeachelementbalancebyitsλk:

Theseequationsaresummedoverk,giving:(3)ThenanewfunctionFisformedbyadditionofthislastsumtoGt.Thus,

ThisnewfunctionisidenticalwithGt,becausethesummationtermiszero.However,thepartialderivativesofFandGtwithrespecttoniaredifferent,becausethefunctionFincorporatestheconstraintsofthematerialbalances.(4)TheminimumvalueF(andGt)occurswhenallofthepartialderivatives(∂F/∂ni)T,P,nj,arezero.Wethereforedifferentiatetheprecedingequation,andsettheresultingderivativeequaltozero:

Sincethefirsttermontherightisthedefinitionofthechemicalpotential,thisequationcanbewritten:(8.34)

Forgas-phasereactionsandstandardstatesasthepureidealgasesat100kPa:IfGioisarbitrarilysetequaltozeroforallelementsintheirstandardstates,thenforcompoundsGoi=∆Gofi,thestandardGibbs-energychangeofformationforspeciesi.CombinationwithEq.(8.34)gives:Example8.5Calculatetheequilibriumcompositionsat1,000Kand100kPaofagas-phasesystemcontainingthespeciesCH4,H2O,CO,CO2,andH2.Intheinitialunreactedstatetherearepresent2molofCH4and3molofH2O.Valuesof∆Gofiat1,000Kare:

ElementkCarbonOxygenHydrogenAk=no.ofatomicmassesofkinthesystemAC=2AO=3AH=14Speciesiaik=no.ofatomsofkpermoleculeofiCH4