The Concept of an Activation Energy

What is an activation energy? This week we talked about reaction equilibria and rates, which are related by detailed balance.

What is an "activated population"? The population at the barrier top? What if we take another approach and say simply that the activated population is the population of "reacting reactants".

The following link is to a paper that takes this definition, assumes that a linear rate relationship exists, and derives the existence of a barrier. This is opposite to the normal direction, where one often starts with the assumption of a barrier.

Of course, it relies on detailed balance as a core assumption, just as any argument going the other way must also.

Levine, R. (1979). Free energy of activation. Definition, properties, and dependent variables with special reference to “linear” free energy relations. The Journal of Physical Chemistry, 83(1), 159–170. doi:doi: 10.1021/j100464a023

Here is a (very profound) quote:

"The mathematical definition is given a physical inter- pretation by the assumption that in a series of “similar” reactions, structural changes in the reactants change the reaction rate primarily via the change in the dG ” of the process. This interpretation is saved from being a circular one (“a series of similar reactions is one for which the Brdnsted relation is a useful measure”, “the Bransted slope is a useful measure for a series of similar reactions”) by the empirical observation that there are indeed many known examples of the utility of the concept."

In fact, I would assert that most of what we do involves arguing in circles (wherein the circuity is often given the lofty name of "internal logical consistency"), and that the only thing that ever saves us is the empirical observation that what we are doing is sometimes useful.