2.6HeterogeneousCatalysis&Adsorption2.6.1HeterogeneouscatalysisForasolidcatalyzedreaction

thereactionmechanismmaybeA+BR(2.60)A+BAB+R+RcatalystadsorptionreactiondesorptiondiffusiondiffusionsurfacereactionactivesiteadsorbedmoleculesTheelementarystepsofsurfacereactionareassumedasadsorptionA+A(2.61a)adsorptionB+B(2.61b)reaction

A+BR+(2.61c)desorptionRR+(2.61d)2.6.2Adsorptionanddesorptionphysicaladsorptionbyintermolecularforces,multilayer

atlowertemperaturechemicaladsorptionbychemicalbond,monolayer

athightemperatureloweractivationenergyheatofadsorptionO(heatreaction)1.Idealadsorption

Basicassumptions:(1)thesurfaceishomogeneousforadsorption;(2)theintermolecularforcesbetweenadsorbedmoleculesarenegligible;(3)itisamonolayeradsorption.LangmuiradsorptionmodelAtthesurface,wherekaandkdareadsorptionanddesorptionrateconstant,respectively.adsorptionrate:

ra=ka

pA(1A)(2.62)desorptionrate:

rd=kdA

(2.63)whereAisthefractionofcoverageofA.A+A

kakdThenetadsorptionrateis

r=ka

pA(1A)

kdA

Atdynamicequilibrium,r=0,sothatka

pA(1A)=

kdAThefractionofcoverageis(2.64)where

KA=ka

/kd

isreferredtoasadsorptionequilibriumconstant.Langmuiradsorptionisotherm

kaand

kd

areusuallyexpressedas

ka

=ka0exp(Ea/RT)

kd

=kd0exp(Ed/RT)whereEaandEdareactivationenergyofadsorptionanddesorption,respectively.(2.66)whereq=Ed

Ea,heatofadsorption.Fortheadsorptionofmkindsofmolecules,thefractionofcoverageof

i

isthefractionofvacancyis(2.72)(2.73)whichwillbederivedlater.Ifanadsorbedmoleculeisdissociatedintoatoms,rateofadsorption:

ra=ka

pA(1A)2

rateofdesorption:

rd=

kdA2

fractionofcoverage:

A2+22A

kakd(2.74)Langmuirdissociativeadsorptionisotherm2.RealadsorptionThesurfaceisinhomogeneousforadsorption,

EaandEd

dependon.Theintermolecularforcesbetweenadsorbedmoleculesaresignificant.Itmaybeassumedthat

Ea=Ea0+A

(2.75)

Ed=Ed0

A

(2.76)wheresuperscript0referstozerocoverage,andareconstants.Theheatofadsorptionis

q=q0

(+)A(2.77)whereq0=Ed0

Ea0.Idealsurface:

ra=ka

pA(1A)(2.62)

rd=kdA

(2.63)Non-idealsurface:rateofadsorption:

ra=ka0

pAexp(A/RT)rateofdesorption:

rd=kd0exp(A/RT)A+A

kakdNon-idealsurface:

ra=ka0

pAexp(A/RT)rd=kd0exp(A/RT)Atadsorptionequilibrium,(2.78)whereK0=ka0/kd0.

The

adsorptionisothermisvalidformediumcoverage.Otherassumptionsotherisotherms.2.7HeterogeneousCatalyticKinetics2.7.1Importantapproximations

Steady-stateapproximation:foraseriesofreactionsteps,theconcentrationofintermediateisnotafunctionoftime,sothattheratesofallstepsareequal.

Ratedeterminingstepistheonewiththeslowestrateamongthesteps,whichdeterminestheoverallrate,andotherstepsareinequilibriumstate.2.7.2RateequationofheterogeneouscatalysisExample:A+BR(2.60)adsorptionA+A(2.61a)adsorptionB+B(2.61b)reaction

A+BR+

(2.61c)desorptionRR+(2.61d)with(1)forreactioncontrolling

Theoverallrateofreactionequalstherateofreaction,

r=k1AB

k2RV(2.82)Otherstepsreachequilibrium,sothatA:

kaA

pAV

kdAA=0B:

kaB

pBV

kdBB=0

R:

kaR

pRV

kdRR=0k1k2

A+BR+

(2.61c)Fractionofcoverage:

A=KA

pAV

(2.83)

B=KB

pBV(2.84)

R=KR

pRV(2.85)Kadsorptionequilibriumconstant,p

partialpressure.Since

A+B

+R+V=1(2.73)ThefractionofcoverageofcomponentiisNote:

includesalladsorbedcomponentswhethertheyreactornot.(2.72)Theoverallreactionrate

equationiswhere

k=k1KAKB

,apparentrateconstant;(2.87)apparentchemicalequilibriumconstant.If<<1,reactioninhomogeneousphase.(2)foradsorptionofAcontrolling

TheoverallrateofreactionequalstherateofadsorptionofA,

r=kaA

pAV

kdAA

(2.88)Otherstepsreachequilibrium,e.g.,reaction

(2.89)whereKsistheequilibriumconstantofsurfacereaction,BandRareexpressedbyEqs.(2.84)and(2.85).From A+B+R+V

=1,weobtainsotheoverallreactionrateequationis(2.92)(3)fordesorptionofRcontrolling

TheoverallrateofreactionequalstherateofdesorptionofR,

r=

kdRR

kaRpRV

(2.93)Theoverallreactionrateequationis(2.94)wherek’=kdRKsKAKB

.Rateequationsarealloftheform

kinetictermapparentrateconstantdrivingforcedisplacementfromequilibriumresistancetermadsorptiontermForidealsurface,theyarehyperbolictype.rateofreaction=(kineticterm)(drivingforce)resistancetermStepsforidealsurfaces:(1)assumethereactionmechanism;(2)theoverallrateequalstherateof

controllingstep,r=f(pi,i,V,…);(3)otherstepsinequilibriumleadto

i;(4)findV;(5)withiandV,r

=f(pA,pB,…)

Ifthereisnoratecontrollingstepornon-controllingstepisirreversible,thesteady-stateapproximation

isused.

Example2.7Idealadsorption

Cyclohexaneisproducedfrombenzeneandhydrogenwithanickelcatalyst,C6H6+3H2C6H12

Thereactionmechanismisassumedas(1)H2+222H2

(2)C6H6+1C6H61(3)C6H61+H2

C6H71+2(4)C6H71+H2C6H81+2

…………(8)C6H111+H2

C6H12+1+2

ratecontrollingstepweakadsorptionSolution:

Fortheirreversiblereaction,

r=

ks1B2H

(A)ForthedissociativeadsorptionofH2,(C)Fortheadsorptionofbenzene,(B)overallrateequation.Example2.8RealadsorptionThecatalyticreactionforsyntheticammoniaisN2+3H22NH3Thereactionmechanismisassumedas(1)N2+2

2N(2)H2+22H(3)N+HNH+(4)NH+HNH2+(5)NH2+HNH3+(6)NH3NH3+2N+3H22NH3+2

adsorptioncontrolSolution:

Theoverallrateofreactionisr=kapN

exp(N/RT)

kd

exp(N/RT)whereinwhichistheequilibriumpartialpressureofN2,whichmaybeobtainedfrom2N+3H22NH3+2

k1k2(B)fromEq.(2.78)Whenitreachesequilibrium,wehavewherepAandpHarethepartialpressureofNH3andH2.Theequilibriumconstantis(C)(=1/2)2N+3H22NH3+2

k1k2(B)Therateequationofreactioniswhichisapowerfunction.Exercises:Chap.2:14,15,16,17

(D)Fordifferentreactionmechanism,differentrateequationmaybeobtained,andshouldbeverifiedexperimentally.Thesimplestformofempiricalequationsisthepowerfunction,Inprinciple,theformofempiricalrateequationshouldbeassimpleaspossible.Theparametersaredeterminedexperimentally.2.8DeterminationofKineticParameters

e.g.,rateconstant,orderofreaction,

equilibriumconstantsofreaction,adsorptionanddesorption,

activationenergy,etc.2.8.1IntegralmethodIntegratetherateequationdeterminetheparametersfromexperimente.g.,

(2.95)Theintegrationis(2.96)(1)plotleastsquaredmethodTheexperimentaldata(cA

t)areuseddirectly,buttheorder

isassumed.(2.96)(1)(1)k0tlinearization

2.8.2DifferentialmethodLinearization:lnrA=

lncA+ln

kThedata(cA

t)arechangedto

rA,buttheorder

isobtainedfromplotorcalculationdirectly.(2.95)e.g.,0lncAlnrAab2.8.3Datafitting1.Linearregression

Whenthedataappearsastraightline,

y=ax+