lindemann-theory-of-unimolecular-reactions .pdf

LindemannTheoryofUnimolecularReactions GauravTiwari Itiseasytounderstandabimolecularreactiononthebasisofcollisiontheory.  Whentwomolecule WhentwomoleculesA sA andB collide,theirrelati collide,theirrelativekinetic vekinetic energyexceedsthethreshol energyexceedsthethresholdenergy denergy withtheresultthatthecollisionresult withtheresultthatthecollisionresultsinthebreaki sinthebreakingofcomesandtheformati ngofcomesandtheformationofnewbonds. onofnewbonds.

 Buthowcanoneaccountforaunimolecularreaction?Ifweassumethatinareactionoftype

    themolecule Aacquiresthe acquirestheneces necessaryacti saryactivatio vationenergyforcollidin nenergyforcollidingwithanothermole gwithanothermolecule, cule,then then thereactionshouldobeysecond‐orderkineticsandnotthefirst‐orderkineticswhichisactually observedinseveralunimoleculargaseousreactions.Asatisfactorytheoryofthesereactionswas proposedby in1922.  Accordingtohim,aunimolecularreaction     proceedsviathefollowingmechanism: Infirststepthemoleculereactswithitselftoproduceaconjugatepair. 2 ≡ A  A     ∗ Here,let,therateconstantbeingforforwardreaction&forbackward. Andfor∗   assume assumetherateco therateconstant nstant .   ∗istheenergized   moleculewhichhasacquiredsufficientvibrationalenergytoenableit Here  toisomerizeordecompose.Inotherwords,thevibrationalenergyof  exceedsthethresholdenergy fortheoverallreaction   .Itmustbeborneinmindthat     ∗issimplyamoleculeinahigh vibrationalenergylevelandnotanactivatedcomplex.Inthefirststep,theenergizedmolecule ∗is producedbycollisionwithanothermolecule .Whatactuallyhapp .Whatactuallyhappensisthatthe ensisthatthekinetic kineticenergyof energyof thesecondmoleculeistransferredintothevibrationalenergyofthefirst.Infact,thesecondmolecule neednottobeofthesamespecies neednottobeofthesamespecies;itcouldbeaproduct ;itcouldbeaproductmolecul moleculeoraforeign eoraforeignmolecul moleculepresen epresentin tin    .Therate thesystemwhich,however thesystemwhich,however,doesno ,doesnotappear tappearintheoverallstoichiometricr intheoverallstoichiometricreaction eaction  ∗ constantfortheenergizationstepis.Aftertheproductionof    ,itcaneitherbede‐energizedback  inthereversestepbycollisionin to  reversestepbycollisioninwhichcase whichcaseitsvibrationalenergyistransferred itsvibrationalenergyistransferredandaddedto andaddedto  orbedecom thekineticenergyofmolecule  orbe decomposed posedor orisome isomerized rizedto toproduc productsinthesecondstep, tsinthesecondstep,   ∗  inwhichcasetheexcessvibrationalenergyisusedtobreaktheappropriatechemical bonds. 

∗andthe In the Linde Lindema mann nn mech mechan anisism, m, a time time∗ lag lag exis existsts betw betwee eenn the the ener energigiza zati tion on of  →  decompositionorisomerizationof toproducts.Duringthetimelag, ∗canbede‐energizedback to.

MathematicalTreatment  Accordingtothesteadystateapproximations.s.a.,wheneverareactivei.e.Shortlivedspeciesis producedasanintermediateinachemicalreaction,itsrateofformationisequaltoitsrateof decomposition.Here,theenergizedspecies∗isshortlived. Itsrateofformation     anditsrateofdecomposition         ∗    ∗ . Thus  ∗           ∗    ∗ 0.....1          Sothat       ∗    ........2  Therateofthereactionisgivenby        ∗....3 SubstitutingEq.2inEq.3,          

   Or,    ....4 TheratelawgivenbyEquation4hasnodefiniteorder.Wecan,howeverconsidertwolimiting cases,dependinguponwhichofthetwotermsinthedenominatorofEquation4isgreater. Case1:If     ≫  ,thenthe terminthedenominatorcanbeneglectedgiving: .......5 whichis whichistheratereac theratereactionforafirstorderreacti tionforafirstorderreaction.Ina on.Inagaseo gaseousreacti usreaction,thisisthehighpressu on,thisisthehighpressure re limitbecauseatveryhighpressures.Aisverylargesothat      . Case2:If ,thenthe terminthedenominatorofEquation4canbeneglected giving       ......6 whichistherateequationofasecondorderreaction.Thisis whichistherateequationofasecondorderreaction.Thisisthelowpressurelimit. thelowpressurelimit.

Theexperimentalrateisdefinedas    .....7 whereisunimolecularrateconstant. ComparingEqs.4&7wehave therateconstantofUnimolecularreaction:                  or    

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