Convex Geometry and Stoichiometry

TL;DR

This paper explores how convex geometry provides new insights into chemical stoichiometry, including equation balancing, reaction mechanisms, and lattice point enumeration, offering a unified geometric perspective.

Contribution

It introduces convex geometric interpretations for various stoichiometric concepts and addresses the inverse problem of deducing reaction mechanisms from linear constraints.

Findings

Convex geometric methods clarify chemical equation balancing.

Lattice point enumeration relates to reaction mechanism analysis.

Inverse problem of mechanism deduction is formulated and explored.

Abstract

We demonstrate the benefits of a convex geometric perspective for questions on chemical stoichiometry. We show that the balancing of chemical equations, the use of "mixtures" to explain multiple stoichiometry, and the half-reaction for balancing redox actions all yield nice convex geometric interpretations. We also relate some natural questions on reaction mechanisms with the enumeration of lattice points in polytopes. Lastly, it is known that a given reaction mechanism imposes linear constraints on observed stoichiometries. We consider the inverse question of deducing reaction mechanism consistent with a given set of linear stoichiometric restrictions.