**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 σ(ϵ**

_{r}) that the rate constant is

**b. Recalling that E _{a} = kT^{2} ∂ 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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