On the Mathematics of the Law of Mass Action

TL;DR

This paper aims to formalize and mathematically solidify the foundations of the law of mass action, providing precise definitions and exploring its broader mathematical significance beyond chemistry.

Contribution

It offers a rigorous mathematical consolidation of the law of mass action using dynamical theory of binomials over complex numbers, clarifying its theoretical basis.

Findings

Provides a formal mathematical framework for the law of mass action.

Clarifies which aspects of the law are proved and which are conjectured.

Highlights the intrinsic mathematical interest of the law beyond chemistry.

Abstract

In 1864,Waage and Guldberg formulated the "law of mass action." Since that time, chemists, chemical engineers, physicists and mathematicians have amassed a great deal of knowledge on the topic. In our view, sufficient understanding has been acquired to warrant a formal mathematical consolidation. A major goal of this consolidation is to solidify the mathematical foundations of mass action chemistry -- to provide precise definitions, elucidate what can now be proved, and indicate what is only conjectured. In addition, we believe that the law of mass action is of intrinsic mathematical interest and should be made available in a form that might transcend its application to chemistry alone. We present the law of mass action in the context of a dynamical theory of sets of binomials over the complex numbers.