A Physical Basis for Kinetic Compensation

Kinetic compensation is a strong, positive correlation between the Arrhenius activation energy E and the frequency factor A for a reaction between the same reactants under similar experimental conditions or similar reactants under the same conditions, even though these parameters are supposed to be independent. The kinetic compensation effect (KCE) is demonstrated by a linear relationship between ln[A] and E/R in the eponymous Constable plot and has been the subject of more than 50 000 publications over the past 100 years, with no consensus opinion about the cause of this effect. In this paper, it is suggested that the linear relationship between ln[A] and E is the result of a real or spurious path dependence of the reaction history between the initial state of the pure reactant(s) and the final state of the pure product(s) having standard enthalpy and entropy differences, ΔH° and ΔS°, respectively. The single-step rate law approximation of a reversible reaction leads to T₀ = H°/ΔS° as the dynamic thermal (thermodynamic) equilibrium temperature and 1/T₀ = (ln[A̅/k₀])/(E̅/R) as the slope of a Constable/KCE plot or the crossover temperature of Arrhenius lines in an isokinetic relationship (IKR), where A̅ and E̅ are mean values for the ensemble of compensating {E_i, A_i} pairs and k₀ is a constant that accounts for the path dependence of the reaction history and reconciles the KCE with the IKR. This proposed physical basis for the KCE and IKR is supported by qualitative agreement between ΔH° and ΔS° calculated from the statistics of compensating {E_i, A_i} pairs in the literature, and the difference in the standard enthalpies and entropies of formation of the products and reactants for thermal decomposition of organic peroxides, calcium carbonate, and poly(methyl methacrylate).