Geometric description of chemical reactions

TL;DR

This paper applies Geometrothermodynamics to model chemical reactions as geodesics on a thermodynamic manifold, providing a geometric perspective on reaction equilibrium states for systems with varying species.

Contribution

It introduces a geometric framework for describing chemical reactions as geodesics in a thermodynamic space, extending previous models to reactions with multiple species.

Findings

Reactions with two species are represented as geodesics in ideal and van der Waals gases.

The initial state of a reaction determines the starting point of the geodesic.

The final equilibrium state corresponds to a coordinate singularity in the thermodynamic metric.

Abstract

We use the formalism of Geometrothermodynamics to describe chemical reactions in the context of equilibrium thermodynamics. Any chemical reaction in a closed system is shown to be described by a geodesic in a $2-$dimensional manifold that can be interpreted as the equilibrium space of the reaction. We first show this in the particular cases of a reaction with only two species corresponding to either two ideal gases or two van der Waals gases. We then consider the case of a reaction with an arbitrary number of species. The initial equilibrium state of the geodesic is determined by the initial conditions of the reaction. The final equilibrium state, which follows from a thermodynamic analysis of the reaction, is shown to correspond to a coordinate singularity of the thermodynamic metric which describes the equilibrium manifold.