Is the Eyring Plot Misleading? A Case for Arrhenius Analysis of Activation Parameters

Abstract

A common view in physical chemistry literature is that the Eyring representation, in which a linear fit of $\ln(k/T)$ versus $1/T$ is attempted, is more fundamental than the Arrhenius representation, $\ln(k)$ versus $1/T$. This perception is typically motivated by its derivation from statistical mechanics and quantum mechanics, and by the interpretation of the intercept in terms of the activation entropy $\Delta S^\ddagger$, whereas the Arrhenius equation and its prefactor are often regarded as purely phenomenological. However, harmonic approximation models yield exact linearity in Arrhenius plots but not in Eyring plots, although for real experimental data both generally appear equally linear within typical experimental accuracy. Furthermore, the impression that the Eyring formulation is inherently quantum mechanical arises from the presence of the Planck constant in the prefactor, whereas this term results from normalization conventions in the partition function. This also highlights an interpretational issue in $\Delta G^\ddagger$, which is based on partition functions of different dimensionality between reactant and transition state. This dimensional mismatch can be reformulated in an alternative representation that improves interpretability and reduces to an Arrhenius-type expression in which the prefactor is directly related to an entropy of activation. In this framework, both activation enthalpy and entropy obtained from an Arrhenius fit are arguably more physically relevant than the corresponding Eyring fit values.