Rate Constant and Tolman’s Theorem for a General Reaction

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: E_a =< E_r > − < E >.
a. Show for a general reaction of cross section that the rate constant is

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

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

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