级物理化学-4、参考已双语chapter3rate theory for elementary reactions

TheoriesofReactionTheoriesofReactionMaiBackChapter3RateTheoriesforElementary3.1Collisiontheory3.2Thresholdenergyandprobability阈能3.3Potential-energysurfaces势能3.4Transition-state 过渡3.5Comparisonoftransition-statetheory&collision过渡态理论与碰撞理论3.6Thermodynamicaspectsoftransition-state过渡态理论的热力3.7Unimolecularreactions单分MaiBackCommonFeaturesoftheRateMaiBackGas-PhaseBimolecularCollisionBasicassumptions基本CollisiondensityCollisionfrequencyFractionofeffectivecollision有效Expressionofrate碰撞理论计算速率常数MaiBackBasicAssumptionsofSimpleCollisionTheoryThemoleculesarehardForareactiontooccur,thetwomoleculesmustNoteverycollisionwillleadtoreaction.Reactionoccursonlyiftherelativekineticenergyalongthelineofcentersofthecollidingmoleculesexceedsathresholdenergyc(阈能TheMaxwell-BoltzmanndistributionofenergyismaintainedduringthereactionMaiBackHowtoExpresstheRatefromCollisionConsiderabimolecularreaction:A+B→BasedontheSCTtheory,theratecanbeexpressed ZAB:collisiondensity(frequency)单位时间单位体积内A与B的碰撞次(m-3s-q:fractionofeffectivecollision有效碰撞分rd[A]rd[A] LKeypoint:HowtoobtainZABandMaiBackCollisionDensity,Basedonkinetictheoryof ZAB=<u>NA:Collisioncross-section 碰撞截 d <u>:relativemean8RT1/u=M

M+ +NA，NB:molecularMaiBackCollisionDensity,ZABand8RT1/2 uN N 1/ 2L28RT UnitofZAB:m-3s-Thecollisiondensityforlike 1uN

1

AA

A2 L MAMaiBackFractionofEffectiveCollisions—TheEnergyAccordingtocollisiontheory,onlythecollisionswithsufficientenergy(>c)leadtoreactions.Thefollowingequationcanbededucedforthefractionofreactioncollision:qqexp(c )exp(EcAssumeEc=160kJmol-1,q=1.38×10-MaiBackRateConstantfromCollisionForA+B→ rd[A]Fromcollision rd[A] 8RT1/

q

c8RT1/ r 2 exp(cEexp( cEexp( c k(T)k(T)28RT1/

kunit： MaiBackThresholdEnergyandProbabilityRelationshipbetweenthresholdenergy&activationenergyProbabilityfactor(stericfactor)碰撞理论的MaiBackThreshold反应阈能为碰撞理论 反应临界能。两个c(Ec)，这种碰撞才有可能化学反应，这个临界值c(Ec)就是反应阈能。EEc值与温度无关，但尚无法从非动力学的得，只能从实验活化能Ea计算MaiBackRelationbetweenThreshold&ActivationFromcollision 8RT1/ k(T) 2 lnklnC1lnT

c Cisaconstantindependentofdlnk 1 RT2 UsingthedefinitionofArrheniusactivationERT2dlnkE1EE1EE1 2MaiBackPre-exponentialFactorfromCollisionArrheniusequation：kAexp( Collision

8RTk(T)

1/

cAB EE1 Bycomparingthetwokexpressions,AA28RTe1/2 MaiBackComparisonofPre-exponentialEa/kJmol-

A/mol-1dm3s-2NO22ClOH2+C2H4K+Br2

Mai

Back

ProbabilityInmanycases,theexperimentalAvaluesareorderofmagnitudesmallerthanthosecalculatedfromthecollisiontheory.Usually,astericfactor,P,isintroducedto modatethedisagreementbetweenexperimentandtheory.P=Aexper./Atheo.or8RT1/ k(T)PLdAB2

exp( cGenerallyPislocatedin10-1～10-MaiBackExamplesofProbabilityEa/kJmol- A/mol-1dm3s- 2NO222ClO3H2+C2H46K+Br2MaiBackReasonsforProbability ，则反应仍不 MaiBack碰撞理优点：碰撞理论为我们描述了一幅虽然粗糙但十 MaiBackPotentialEnergyIntroductiontotransition-statetheoryPotentialenergyoftwo-atoms Potentialenergysurfaces:Potentialenergyofthree-atomsMaiBackIntroductiontoTransition-StateTransition-stateTheory(TST)wasproposedbyEyringetal.in1935onthebasisofstatisticalthermodynamicsandquantum被称为活化络合物(activatedcomplex)，所用该理论，只要知道分子(含活化络对反应速率理论(absoluteratetheory)。MaiBackPotentialenergyoftwo-atomssystem:MorsePotentialThepotentialenergyisthefunctionoftherelativepositionsofatomsinasystemForatwo-atommolecule,Morsepotentialcurveisusuallyused:Ep(r)De[exp{2a(rr0)}2exp{a(rr0:分子中双原子分子间的平衡核De:势能曲线的a:与分子结构有关的MaiBackPotentialenergyoftwo-atomssystem:MorsePotentialAtr>r0,attractiveforceAtr<r0,repulsionMaiBackPotentialEnergyConsiderareactionwiththreeA+BC→AB+ThepotentialenergyofthesystemshouldbethefunctionofthreevariablesconcerningtherelativepositionsofthethreeEPEP(rAB,rBC,rCA)orEPEP(rAB,rBC,ABCThiswillneedfour-dimensiongraphtodescribethechangeofthepotentialMaiBackPotentialEnergyA+BC→AB+Assume(collinearEP=Thepotentialenergyofthesystemcanbedescribedwitha3-Dgraphcalledpotentialenergy ThepotentialenergysurfacestheH+H2→MaiBackPotentialEnergyABCAB 图中R点是反应物BC分A----- A 的基态,随着B-C解离,势能沿着RT线升高A----- A 随着A-B的接近,势能沿着TP线下降到P点是生成物子时的势能；OEP一侧,是原子间的相斥能也很高。MaiBackSaddle位置T点称为saddlepoint马鞍点)。MaiBackContourDiagramforPotentialEnergyMaiBackSectionalPlaneofthePotentialEnergySurfacestheReaction 被成为reactioncoordinate(反应坐标)MaiBackReaction沿沿reactioncoordinate(反应坐标)从反应物A+BC经T生成物AB+C，必须越过势能垒EbMaiBackBasicassumptions基本Vibrationmodesofthree-atom三原Expressionofrateconstantbythe过渡态理论计算速率常MaiBackBasicTransitionstate过渡态MaiBackBasicEquilibriumMaiBack(c)和(d)为弯曲振动，分别发生在相互垂直的两MaiBackMaiBackHowtoExpressReactionRatesbytheConsiderthefollowingA+ [ABC]≠→AB+[ABC]≠isthetransitionstateortheactivatedOnevibrationmode(frequency,≠)alongthereactioncoordinateleadstotheformationofproducts.Sothereactionrateshouldbeproportionaltothis≠andtheconcentrationofthetransitionstate.r=

Accordingtotheequilibrium K r=r=≠[ABC]≠=MaiBackFrom r=≠[ABC]≠=≠K≠[A]CForbimolecular r=k[A]k ≠Fromthestatisticalthermodynamics,K≠canbeexpressed

K

qABC

E0 q qjisthepartition E0=E0≠-E0A-kLqABC exp(E0 MaiBackAvibrationoftheactivatedcomplexisresponsibleforthereaction,andthecorrespondingpartitionfunction(qv)canbe = = V1

h) kLqABC exp(E0 kL L exp( 0kT'hqAMaiBackForan-molecularkLn1 q'exp(E0 qj jqjarethepartitionfunctionsofreactantThisequationiscalledEyring∏qjmaybeobtainedfromspectroscopicmeasurements,q≠’maybecalculatedfrompotentialenergysurfacesquantumE0=Eb+L0≠–L∑0j=Eb+∑½Lh0≠–∑½So,theoretically,kcanbecalculated MaiBackTheoriesofReactionTheoriesofReactionMaiBackChapter3RateTheoriesforElementary3.1Collisiontheory3.2Thresholdenergyandprobability3.3Potential-energysurfaces3.4Transition-state 3.5Comparisonoftransition-statetheory&collision过渡态理论与碰撞理论3.6Thermodynamicaspectsoftransition-state过渡态理论的热力3.7Unimolecularreactions单分MaiBackComparisonofTransition-StateTheory&CollisionDiatomicreactionsOtherreactionskLn1 q'exp(E0 qj j

8RT1/ k(T)

exp( cMaiBackStructurelessParticles(Diatomic) Forreactionsbetweenstructurelessparticles A+B [AB]≠→PkLkBTqAB'exp(E0 ForAandB,onlytranslationaltermscontributedtotheirpartitionqA=qA,t/V=qB=qB,t/V= 2π(m+m)kT3/282[mm m qq

'

BeingthesamethatfromBeingthesamethatfromSCT,correspondstokLπ(r+r)2(8kBT)1/2exp(E0 MaiBackReactionsofOtherAssumefrepresentsapartitionfunction(perunitvolume)ofmotionmode(freedom),thetranslational,rotationalandvibrationalpartitionfunctioncanbesimplyexpressedasfollows:qt=ft qr=fr(non-linear);fr3N- 3N- (non-linear); IfassumeE0≈Ea,thepre-exponentialandprobabilityfactorsUsingTSTtoevaluateP= UsingTSTtoevaluateP= q Asestimation,ft≈109dm-1,fr≈10,fv≈1,kBT/h≈1013s-MaiBackReactionsofOther1.atomicA+atomic diatomiccomplex→k f3f A≈ = =1012dm3mol-1s- f3f f 2.atomicA+linear linear(N+1)complex→k f3f2f3(N+1)- fA≈ =L =1010dm3mol-1s- f3f3f2f3N- f P=fv2/fr2≈10-3.atomicA+linear non-linear(N+1)complex→3f3f3(N+1)- k frA≈ =L =1011dm3mol-1s-1 f3f3f2f3N- f P=fv/fr≈10-MaiBackReactionsofOtherlinearA(N1)+linear linearcomplex(N1+N2)→rA≈r

ft3f2

kT= kT

=108dm3mol-1s-P=

f3f2f3N1-5f3f2f3N2- f3f ≈ non-linearA(N1)+non-linear non-linearcomplex(N1+N2)→ft3f2

fA≈

=L

=107dm3mol-1s- f3f3f3N1-6f3f3f3N2- P=fv5/fr5≈10-MaiBackForreactionsbetweensimpleatoms(hardspheres),TSTisthesamewithSCT.Forreactionsbetweencomplexmolecules,TSTisbetterthanSCT,andTSTcanpredictthePfactorofSCT.FromtheAvalue,theconformationoftheactivatedcomplexmaybepredicted.MaiBackGivetheprobabilityfactorsforthefollowinggas-phasereactionspartitionfunction,andevaluatetheirA+B→(A-B)kT f3f fA≈

=L

P f3f f A+BC→(A-B-C)A≈

ft3fr2

f

f3

2 =L f

P≈fv2/f2

hr hrBA+BC→( C) =Lk =Lk P≈f/f≈10- f3f3f2 f MaiBackAB+CD→(A-B-C-D)f3f2f fA≈

=L

P=f4/f4≈10-t t v t r v f3f2ff3f2 t t v t r v平动配分函数ft=108,一维转动配分函数fr=10。推算反应的频率因解析kT f3f fA≈

=10-22k f3f f MaiBackThermodynamicAspectsofTransition-StateComparsionof△r≠Hm＄and△r≠Sm＄withEaandMaiBackThermodynamicAspectsofFornon-idealsystem,particularlythereactionsinsolutions,thecalculationofthepartitionfunction moreover,insightsintothestructureoftheactivatedcomplexcannotbeobtainedalso.Theconcepts:anequilibriumbetweenthereactantsandtheactivatedcomplexAgeneral,empiricalapproach:theactivationprocessisexpressedintermsofthermodynamicfunctions.MaiBackThermodynamicAspectsofFrom k q kL 0 jThisequationcontains'anequilibrium q exp( 0 discardonemodeofkkkBThCMaiBackThermodynamicAspectsofDefineaGibbsenergyofactivation,correspondingto RTlnK c/ForA+BC→[ABC]≠→AB+ K / (c)21K(cc/ [A] Ingeneral K(c)1nK c/ G (c)1nK (c)1nexp m c/c MaiBackThermodynamicAspectsofkT kT G kB K (c )1nexp m G H TS kT S H kB (c )1nexp mexp m Gibbsenergyof 此式即过 entropyof H enthalpyof 分别为由反应物形成活化络合物过程中的标准活化自由MaiBack

andkkBT(c)1nK Forcondensed-phaseEarEarmln

lnc/

lnTln Forgas-phase c/ (nisanumberofreactantmolecules (pV) dlnK c/ m a armERT (pV) MaiBack

andk k (c)1nexp( m)exp( mhkA

Forgas-phase

A A en(c )1n mkhRForliquid-phasereactions:E AA e(c)1nexp( mkhRMaiBack

andk en(c

在数量级上与碰撞理论中的 相对应，于是exp( m) 以双分子反应为例，ekBT/h在300K时的值为1013.23s-1。如≠S$0,A将有超常的大值，反之，则A将小于1013.23s-1。 单分子反应外，一般由反应物生成活化络合物时，分子减少的，因而△r≠Sm$0,这导致PMaiBack

and应当注意：此处的≠S$

$不同。两者间

△

﹣(1-n)Rln(cR’T/p式中R8.314Jmol-1K-1R0.08206atmLmol-1K-MaiBack过渡态理论的 MaiBack过渡态理论的引进“过渡系数”或 系数”kLn1 q'exp(E0 j表示在 势垒的体系中实际能达到产物区的体系所占的分率定性地讲，它由(1)隧道效应；(2)势能面的非标准形状；(3)有去活化；(4)和另一个势能面相交等四个因素中的某个项KaKCkk/

A MaiBackUnimolecularLindemann(