Collision Theory of Unimolecular Reactions

Steps (A), (B), and (C) constitute a reaction mechanism from which a rate law may be deduced for the overall reaction. Thus, if, in a generic sense, we replace I, by the reactant A, l 2 by A, and 21 by the product P, the rate of formation of A is 

according to this (Lindemann) mechanism, a unimolecular reaction is first-order at relatively high concentration (cM) and second-order at low concentration. There is a 

This mechanism also illustrates the concept of a rate-determining Step (rds) to designate a slow step (relatively low value of rate constant as opposed to a fast step), which then controls the overall rate for the purpose of constructing the rate law. 

At low cM, the rate-determining step is the second-order rate of activation by collision, since there is sufficient time between collisions that virtually every activated molecule reacts only the rate constant K appears in the rate law (equation 6.4-22). At high cM, the rate-determining step is the first-order disruption of A molecules, since both activation and deactivation are relatively rapid and at virtual equilibrium. Hence, we have the additional concept of a rapidly established equilibrium in which an elementary process and its reverse are assumed to be at equilibrium, enabling the introduction of an equilibrium constant to replace the ratio of two rate constants. 

In equation 6.4-21, although all three rate constants appear, the ratio may be considered to be a virtual equilibrium constant (but it is not usually represented as such). 

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