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Rate Constant and Tolman’s Theorem for a General Reaction

Rate Constant and Tolman’s Theorem for a General Reaction

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Question:
A theorem by Tolman states that the activation energy for a reaction is the difference between the average energy of those molecules that react and the average energy of all the molecules: Ea =< Er > − < E >.
a. Show for a general reaction of cross section σ(ϵr ) that the rate constant is

b. Recalling that Ea = kT2 ∂ lnk(T )/∂T prove Tolman’s theorem.

This is the problem 3.15 of the book "Chemical Kinetics and Reaction Dynamics, written by Paul L. Houston".

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