Simply conceiving the Arrhenius law and absolute kinetic constants using the geometric distribution

TL;DR

This paper demonstrates that the Arrhenius law and kinetic constants can be derived directly from simple statistical principles, specifically the geometric distribution, offering a more straightforward understanding of reaction kinetics.

Contribution

It introduces a novel, rigorous approach linking the Arrhenius law to the geometric distribution, simplifying the conceptual basis of kinetic constants from complex physical mechanisms.

Findings

Arrhenius law naturally emerges from geometric distribution

Reaction event timing follows exponential distribution

Kinetic constants are governed by randomness and exponential processes

Abstract

Although first-order rate constants are basic ingredients of physical chemistry, biochemistry and systems modeling, their innermost nature is derived from complex physical chemistry mechanisms. The present study suggests that equivalent conclusions can be more straightly obtained from simple statistics. The different facets of kinetic constants are first classified and clarified with respect to time and energy and the equivalences between traditional flux rate and modern probabilistic modeling are summarized. Then, a naive but rigorous approach is proposed to concretely perceive how the Arrhenius law naturally emerges from the geometric distribution. It appears that (1) the distribution in time of chemical events as well as (2) their mean frequency, are both dictated by randomness only and as such, are accurately described by time-based and spatial exponential processes respectively.