级物理化学4、参考已双语chapter2plex reactions

plex2.1Elementaryreactions2.2Reversiblereactions2.3Parallelreactions2.4ConsecutivereactionsMai�Bac plex2.5Steady-stateapproximation2.6Rate-determiningstepandPre-2.7Activationenergyfor 2.8SpeculationofreactionMai�BacElementary

ReactionorderReactionmechanismMai�BacAnAnelementaryreactionreferstoasingle-stepreactioninvolvingasmallnumberofmoleculesorions.Forexamples：Cl2M2ClClH2HClHHCl2HClCl2ClMCl2MAnAnoverallreactionisareactioncombinedwithaseriesofelementaryreactionsForexamples：H2 Mai�BacThemolecularityofanelementaryreactionisthenumberofmoleculescomingtogethertoreactinanelementaryreaction.Elementary UnimolecularAUnimolecularABP2ABP

BimolecularreactionTrimolecularreactionMai�BacLawLawofMassForanelementaryreaction,therateisproportionaltotheconcentrationofofthereactantmoleculesmeettogetherCl2M2ClClH2HClHCl2HCl Mai Mai �Bac

ratek2[Cl][H2ReactionForanoverallreaction,thecombinationofaseriesofelementary-reactionstepsisthereactionmechanism.Mai�BacReversible(Opposing k-A

BConsecutive ABMai�BacMorecommonsituationisthattheforwardandthebackreactionsmaynotbeelementaryreactions,andmaybefirst-,second-orthird-orderreactionsFor A+ B+Mai�BacReversibleFirst-OrderReactions:DifferentialAt

k-

d[A]k1[A]k-t=tt=te

[A]0–[A]0–

[B]0+[B]0+

k1/k-1[B]=[A]e+[A]ek1/k-Differentiald[A](k1k-1)([A][A]e)Mai�BacReversibleFirst-OrderReactions:Integrated∫∫

=－(k1+k-0=(k+k)10→[A]0[A]e,[A]→[A][A]e,k→k1+k-Mai�Back1k-1。在平衡态产生一个微扰使反=1/(k1+k-间的方法求k1k-1，再通过平衡关Mai�BacMai�BacRelaxationTimefor1st-orderReversiblek krIntegratedrate

ln[A]0[A]e

k[A]e[A][A]e=([A]0[A]e)exp[(kf+kr)Assumee0，eexp{(kf+kr)t}=expR=1/(kf+Mai�BacRelaxationTimefor2nd-orderReversible A+B

C+Assume:eeCCe DDed[A]k[A][B]k dk([A])([B])k([C])([D] kfee=krCe={kf(ee)+kr(CeDe)}(kfkr)Mai�BacRelaxationTimefor2nd-orderReversibled{k([A][B])k([C][D]

RkfR

[D]eexp{[kf(ee)+kr(CeDe)]Mai�BacRelaxationTimeforSomeTypicalReversible fA f

+22A 2

4kf[A]e+krk B+k

k+k(BC rkA+ kr

kf(ee)+kA+kr

C+

kf(ee)+kr(CeMai�Bac率常数之比等于平衡常数K=[B]e/[A]e=kf/kbMai�BacTheparallelreactionistheoccurrenceofdifferentreactionsfromthesamereactant(s).Itisusuallyseeninorganicchemistry.Thedesiredproductisthemainproductandtheothersareby-products.TheTheoverallconversionrateisthesumofallwhichmaybethesame-orderreactionsormaybeMai�BacTwoParallelFirst-orderReactions:DifferentialC－－d[A]=(k+k)12d[B]=k d[C]=k Mai�BacTwoParallelFirst-orderReactions:IntegratedAssumeatt=0，[A]=[A]0,[B]0=[C]0=0,[A]=[A]0e-[B]

k1+

[B]/[C]=[B]/[C]=[C] (1–e-k1+Mai�BacA

—d[A]=(k+k+k)[A]n=

k3 k3D

（1）kapp=k1+k2+k3=E1-（3）[B]/[C]=k1/k2=exp(﹣ Mai�BacA+

k1,

G+G+

Bothreactionsarefirst-orderwithrespecttobothAandk2,If[C]0=[D]0=0，givetheexpressionfor[C]/[D]withTandk2,Answer：[C]/[D]=k1/k2=exp[(E2-TherearetwotypicalroutestoincreasetheselectivitytoToincreaseE2-E1byusingasuitableIfE2>E1，todecreasetheT,selectivitywillincrease,buttheratewilldecrease.IfE1>E2，toincreasetheT，boththeselectivityratewillMai�BacTheproductofareactionmayactasareactantofanotherreaction.Manyreactionsproceedasthis,i.e.,throughtheformationofanintermediate.Forexample:239UNpThetreatmentoftheconsecutivereactionsisrathercomplex.Hereweonlyconsidertwoconsecutiveirreversiblefirst-orderreactions.Mai�Bac A→B→—d[A]=k d[B]=k[A]﹣ d[C]=k Assumeatt=0，[A]=[A]0,[B]0=[C]0[A]0=[A]+[B]+ d[A]/dt+d[B]/dt+d[C]/dt=OnlytwoequationsareMai�Bac[A]=[A]0[A]=[A]0e-SubstitutethisintoEq.(2),wed[B]=k[A]e-

[B]k1[A]o(e[B]k1[A]o(ek1tek2tk2Using[C]=[A]0-[A]-[C][C][A]ok2ek1tk2ek2tMai�BacCharacteristicsofConsecutiveReactions：c～tThe[B]risestoa umatacertaint,while[A]isafirst-orderdecaywithtandthatofCrisesfrom0towardMai�Bac[B]k1[A]o(ek1tek2tk2 umshouldoccur d[B]d[B]

(kektkekt)12 122 k22 Mai �B Mai �Bac tlnk2lnk211

ke

kek2t

k1[A]o ek2tmax k lnk2ln

k2

[B]/[A]0onlydependsonk/kok2Foragivenvalueofk1,ask2increases,boththetimeatwhich[B]isa umandtheyieldofBdecrease.Mai�BacThereisaconsiderableincreaseinmathematicalcomplexityassoonasthereactionmechanismhasmorethanacoupleofsteps.Areactionschemeinvolvingmanystepsisnearlyalwaysunsolvable ytically.Awidelyusedalternativeapproachistomakeanapproximation.☺Thesteady-stateapproximation稳态近似)isoneofthemostimportantapproachesinchemicalkinetics.Mai�BacTheBasisoftheSteady-State A→B→Atk2>>k1，theconcentrationofBissmallandthechangeofitsconcentrationisnegligible.d[B]/dtd[B]=k[A]﹣k[B]≈0 —d[A]

=k1

Mai�BacWhentoUseSteady-StateThebasicrequirementfortheSSapproximationWhenWhenactiveintermediatessuchasatoms,radicalsandexcitedmoleculesappearinasequenceofreactions,theSSapproximationcanbeapplied.Mai�BacHowtoUseSteady-StateFirstidentifytheactiveintermediates,andwriteexpressionsfortheirnetratesofformation.Thensettheratesequaltozero.d[Xd[Xi=formationrateofX－consumingrateofX≈iiTheSSapproximationiswidelyusedinchainreactions,enzyme-catalyzedreactionsandphotochemicalMai�BacInasequenceofconsecutivereactions,ifonestepproceedssoslowtocontroltheoverallreactionrate,thisstepiscalledtherate-determiningsteprdsExample:2NO2+F2→Ratelawfrom1d[NO2

AssumedreactionNO+ NOF+

Slow 2 NO+ NO

r=Mai�Bac

A+

Ifk2<<k1,I→Pistherate-determiningFurtherifk-1>>k2,A+B→Iwillarriveataequilibrium.Wethuscanconsiderapre-equilibrium.K rd[P]k[I]kK[A][B] kappk2Kk2k1/k-Acomplicated esveryMai�BacHowHowtodevisetheratelawfromacomplexmechanismandtomakediscussionstosimplifythecomplicatedratelawExample:2O3→

Usingsteady-stateapproximationfor3 3

O2+

d[O]

O+O3→

[O]sskk

[O3r1d[O2

1k[O] [O][O]2k[O][O

12k[O][O]k[O][O

kk[O

k2[O][O3] Mai�BacDiscussionwithaComplicatedRater k1k2[O3(1)As[O3]issolowthatk-1[O2]>>k2[O3]isrk1k2[O3k[O[O]2[O322kapp=k1k2/k-1=(2)As[O3]issohighthatk-1[O2]<<k2[O3]isr=Mai�BacActivationEnergiesofElementaryandComposite芍芍Activationenergyofelementary芍Evaluationofactivationenergyfrombonding芍芍ActivationenergyofcompositeMai�BacTolman用统计平均的概念对基元反应的活化能 aMai�BacA+ C+Ea﹣Ea’=Mai�BacEvaluationofActivationEnergyfromBondpositionofamoleculetotwoCl2+M→2Cl+Ea≈H=DCl-

H=DCl-Combinationofradicalstoamolecule，2Cl+M→Cl2+MEa≈ThereactionofaradicalwithaA+BC→A…B…C→AB+Forexothermicdirection：Ea=DBCForendothermicdirection：Ea’=EaHMai�BacEvaluationofActivationEnergyfromBondReactionsbetweentwomoleculesA-B+C-D→A-C+B-DForexothermicdirection：Ea=(DA-B+DC-D)×30%Forendothermicdirection：Ea’=EaH(H<0)Theaboverulesareonlyapplicabletosimplegas-phasereactionsandcannotbeusedforthereactionsinsolutions.However,theyareusefulforsimpleandrapidestimation.Mai�Bac22IH2HIH已知键能DHI297kJmol-1DH=435kJmol-1试估算该反应正逆方向的活正方向的热效应： =- )=138kJmol-1>0,吸 其活化能Ea0.05DHI14.9kJmol-1Ea=Ea’+△rHm=152.9kJmol-Mai�BacForacompositereactionwhichisacombinationofseveralelementarysteps,theapparentratecoefficient(kapp)maybeamathematicalcombinationoftherateconstantsoftheelementaryreactions.Here,theactivationenergy(Ea)isalsotheapparentactivationenergy.Wecanevaluatetheapparentactivationenergyfromthoseoftheelementaryreactions,whichmaybesimplyestimatedfrombondenergies.Mai�Bacikobs=∏ki

Ea=RT2 =

ConsiderthefollowingmechanismforA+B→A+B k

AssumeaPre-equilibrium21 =k2[D]=(k2k1/k-21D2

kobs=kkk-Ea=E2+E1﹣E-Mai�Backobs=ERT

RT2(1

)RT

1(

dk2

k

1)k2 2)k3 3)

k1Ea1k2Ea2k3Ea3kikki

ForparallelA

d[A]CC

kk)[A]n

kobs=k1+k2+Mai�BacHowtoProposeaReaction Mai�BacHowtoProposeaReactionMai�BacFora ExperimentalRatelaw,rkJmolCH3andC2H5radicalshavebeenMai�BacToproposeaC2H62CH Ea351.5kJCH3C2H6CH4C2H

Ea33.5kJC2H5C2H4HC2H6C2H5H HC2H5C2H

Ea167kJmolEa29.3kJEa0kJMai�BacTodeviseratelawfromtheproposedd[CH kk

1/r 1 4

E1 )274kJmol- 7.Judge:BecausetheratelawandtheEaareconsistentwiththeexperimentalfacts,theproposedmechanismisareasonableone.Mai�Bac规则Ir=k∏例液相反应Cr3+3Ce4+Cr6+由实验得到：rk[Ce4+]2[Cr3+[Ce3+]-推测机理：Ce4++Cr3+ Ce3++

Ce4++Cr4+→Ce3++

+

→ +由机理得到：rk2K[Ce4+]2[Cr3+[Ce3+]-1Mai�Bac规则II就总反应计量数与反应级数之间的关系而言II-1若反应级数>3,由于4分子反应不大可能，因而速控步前Mai�Bac 反应A+B→P,如速率方程中,A出现分数级有两种:(1)A离解产生中间物直接参加速控步;(2)B规则IV若反应无简单级数，速率方程的分母为几项Mai�Bac Mai�BacForth