Test of the formal basis of Arrhenius law with heat capacities

The exponential factor of Arrhenius satisfactorily quantifies the energetic restriction of chemical reactions but is still awaiting a rigorous basis. By assuming that the Arrhenius equation should be grounded on statistical mechanics and is probabilistic in nature, two structures are compared for this equation, depending on whether reactant energies are envisioned as the mean values of specific energy distributions, or as particular levels in a global energy distribution. In the first version, the Arrhenius exponential factor would be a probability depending once on temperature while in the second one it is a ratio of probabilities, depending twice on temperature. These concurrent equations are tested using experimental data for the isomerization of 2-butene. This comparison reveals the fundamental structure of the Arrhenius law in isothermal systems and overlooked properties resulting from the introduction of reactant energies in the equation.