Apparent Activation Energies in Complex Reaction Mechanisms: A Simple Relationship via Degrees of Rate Control

The apparent activation energy of chemical reactions has played a central role in the field of chemical kinetics and has served as an important tool for analyzing and understanding reaction rates, mechanistic details of complex reaction mechanisms, elementary-step energetics, catalytic activity, and reaction selectivity. We derive here a general expression that shows that the apparent activation energy equals a weighted average of the standard-state enthalpies (relative to reactants) of all of the species (intermediates, transition states, and products) in the reaction mechanism, each weighted by its generalized degree of rate control (DRC). Since the DRC is zero for most of these species, even in very complex mechanisms, the weighted average includes only a few terms. This simplicity provides deep insights into the connection between the reaction-energy diagram and the apparent activation energy. We prove both this and the quantitative validity of this equation by analysis of numerous reaction mechanisms. We also show the failures or weaknesses of previous equations for the apparent activation energy.