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Is this best answered through quantum theory, Boltzmann statistics, or what?

For example, in a reaction energy diagram, only some of the reactants go over to the side of the products, and then get stuck there. So the progression of the reaction can be thought of in probabilities - what are the chances that something will go to products, and what are the chances the products will revert back. So you'd use the Arrhenius equation here. Could you dig deeper and find a quantum mechanical reason for this?

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  • $\begingroup$ You might want to check the Eyring equation. That equation is derived from general principles, while the Arhenius equation (powerful though it may be) is empirical. $\endgroup$
    – Eljee
    Dec 9 '14 at 14:47
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Actually, a huge amount of the probablistic nature of chemistry is simply the Law of Large Numbers (LLN). A mole of any substance is approximately $6\times10^{23}$ molecules, which is 600 sextillion molecules! The LLN kicks in at quantities much smaller than the sextillion level. Put simply, there are so many interactions occurring in any macro-level reaction that these are inevitably going to converge to the theoretical mean by the LLN.

Now your question adds in the issue of activation energy, but I still think it fits this model, because activation energy tends to produce a sharp difference: too low, and little reaction happens; but high enough, and we mostly go to completion. Once activation energy is high enough, the LLN applies.

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If you want to address only chemical reactions, than best answer is the statistical mechanics, which exercises Maxwell-Boltzmann statistics, exactly as you suggested.

In any reasonable chemical experiments, you are dealing with enormously large ensembles, Avogadro number is $6 \times 10^{23}$ and extremely long times (compared to all motions accessible to molecules).

Therefore, you can follow quasi-equilibrium reasoning, leading to transition state theory.

Sometimes, this is not enough and you want to go further and include coupling between the motions, which leads you to Reaction Dynamics (no wiki article yet, but this is an excellent book). This approach was needed to describe the crossed molecular beam experiment (Nobel prize 1986).

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