Langmuir-Hinshelwood使用条件

2010ChineseJournalofCatalysisVol.31No.8文章编号:0253-9837(2010)08-0972-07国际版DOI:10.1016/S1872-2067(10)60103-9研究论文:972~978Receiveddate:31May2010.*Correspondingauthor.Tel:[phone];Fax:[phone];E-mail:[e-mail]:SupportedbytheNationalBasicResearchProgramofChina(2005CB221405)andtheNationalNaturalScienceFoundationofChina(20773075).EnglisheditionavailableonlineatScienceDirect().Langmuir-Hinshelwood动力学的有效实验条件王德峥清华大学化学工程系北京市绿色反应工程与工艺重点实验室,北京100084摘要：使用Langmuir-Hinshelwood(L-H)动力学的学者大部分未注意到该动力学包含了所有吸附物种采用拟稳态假设的隐含条件,因而他们通常忽视了确认实验条件是否允许采用拟稳态假设.然而,对于大部分气固催化反应,拟稳态假设的成立需基于催化活性位浓度很小的前提.对于催化活性位浓度高的反应体系,其覆盖度较高的吸附物种不满足拟稳态假设.因此,在这种情况下通过实验测定的动力学常数没有物理意义,而仅为该实验条件下的数学回归参数.本文将活性位浓度小于最高反应气浓度的十分之一视为拟稳态假设成立的充分条件,通过估算发现许多催化剂并不满足该条件.关键词：朗格缪尔吸附等温线;Langmuir-Hinshelwood动力学;吸附物种;拟稳态假设;速控步骤;微观动力学中图分类号：O643文献标识码：AExperimentalConditionsforValidLangmuir-HinshelwoodKineticsWANGDezheng*BeijingKeyLaboratoryofGreenChemicalReactionEngineeringandTechnology,DepartmentofChemicalEngineering,TsinghuaUniversity,Beijing100084,ChinaAbstract:UsersofLangmuir-Hinshelwoodkineticsoftenneglectthatitinvokesthepseudo-steadystatehypothesis(PSSH)foralladsorbedspecies,andtheydonotcheckthatthePSSHisvalidlyused.However,withsolidcatalyzedreactions,thevalidityofthePSSHmustoftenbebasedontheconcentrationofactivesitesbeingverysmall.Withahighsiteconcentrationcatalyst,thePSSHwouldbeincorrectforadsor-bateswithsignificantcoverages,whichwouldmakethededucedkineticparameterslosetheirphysicalmeaningandbeonlytheparametersofcurvefitting.Itisestimatedthatmanycatalystsdonotmeetthecriterionfortheirsiteconcentrationtobelessthanone-tenththehighestreactantconcentration.Keywords:Langmuiradsorptionisotherm;Langmuir-Hinshelwoodkinetics;adsorbedspecies;pseudo-steadystatehypothesis;rate-determiningstep;microkineticsCongratulationstoChineseJournalofCatalysisonitsthirtiethanniversary!ThisisatimelyoccasiontorevisitachemicalkineticsassumptioninLangmuir-Hinshelwood(L-H)kinetics,namely,thatofsteadystatekinetics,andaskthequestionifpeoplehavebeennegligentinnotknowingthatanassumptionofsteadystatekineticswasusedandthus,hadnotcheckedthatitsusewasvalid.Anotherwaytoposethisquestionis:can,andifyes,whatexperimentalconditionsmake,L-Hkineticsbeonlycurvefitting?Sometextbooks[1,2]stateclearlythatL-Hkineticsisbasedonthepseudo-steadystatehypothesis(PSSH;alsoquasi-steadystateassumption),butmanyothertextbooksimplythattherewasnoPSSHandL-Hkineticsarenotcon-strainedbythePSSH.Hence,L-Hkineticsarefirstre-examinedtoshowwherethePSSHwasinvoked.Then,itisarguedthattherightfuluseofthePSSHisviolatedwithmanycatalysts.AconsequenceofthewrongfuluseofthePSSHisthatthefittedkineticparametersarevalidonlyfortheirspecificexperimentalconditions.ThismakesL-Hki-neticsacurvefittingexercise.1TheinvokingofthePSSHinL-Hkinetics1.1ValidL-HkineticsneedsthePSSHtobevalidatedAtextbookonenzymekinetics[3]wouldwarnreadersto王德峥:Langmuir-Hinshelwood动力学的有效实验条件973checkthattheydonotviolatethePSSHintheirkineticsexperiments,buttextbooksonheterogeneouscatalysisoftendonotgivethiswarning,nordopeopleinthisfieldperformthischeck.Threereasons,thatwillbeshownasgroundless,canbesuggestedforthisnegligence:(1)thebeliefthatthePSSHissurelysatisfiedbysolidcatalysts,(2)ignorancethatthePSSHwasinvoked,or(3)thebeliefthatthePSSHdoesnothavetobeinvokedwithflowreactors.Thefirstreasonwouldbeduetothe“magical”feelingonegetswhenacatalystworkswell,fromwhichapersoncanwrongfullyimbibethenotionthatadsorbedspeciesarehighlyreactive.But,sincethePSSHcanbevalidlyusedonlywithhighlyreactivespecies[2,4],thePSSHwouldbeinvalidlyusedifadsorbedspeciesarenothighlyreactive.Aqualitativereasoningthatadsorbedspeciesarenothighlyreactivecanbebasedontheobservationthatwithagoodcatalyst,mostadsorbedspeciesarelessreactivethanthereactants(thatarebeingadsorbed)becauseofthehighad-sorptionactivityofthecatalyst.Withmanycatalysts,gasadsorptionisfacileandnon-activatedwithhighstickingprobabilities[5].Thus,inmanymechanisms,asurfacere-actionisaratecontrollingstep(RCS)[1],andclearly,whenastepthatrequiresitsreactionisaRCS,thenthecorre-spondingsurfacespeciesisnot,relatively,highlyactive.Thus,thePSSHincatalysismustoftenbebasedontheac-tivesiteconcentrationbeingverysmall[6].Itwillbearguedlaterthatsincelargesurfaceareacatalystsareused,thiswillnotbesatisfiedandthePSSHisincorrectwhenadsorbedspeciesarepresentatsignificantcoverages.1.2AratecontrollingstepimpliesthePSSH1.2.1RatecontrollingstepandpartialequilibriumThesecondreason,ignorancethatthePSSHwasin-voked,isduetothewrongbeliefthattheRCSassumptionissufficientforL-HkineticswithouttheneedtoinvokethePSSH.ThiswillbeshowntobewrongwithScheme1.Scheme1.Threestepreactionmechanismwithreversiblesteps.Thedifferentialequationsforthelawofmassactionare*A1A*1AddCkCCkCt−=−+(1)****A1A*1A2A2PddCkCCkCkCkCt−−=−−+(2)****P2A2P3P3P*ddCkCkCkCkCCt−−=−−+(3)*P3P3P*ddCkCkCCt−=−(4)Ciistheconcentrationofthesubscriptedspecies.WhenthePSSHisinvokedforCA*andCP*,Eqs.(2)and(3)aresim-plifiedto***1A*1A2A2P0kCCkCkCkC