The Graph automorphism group of the dissociation microequilibrium of polyprotic acids

TL;DR

This paper models the micro-dissociation states of polyprotic acids using graph theory, revealing that their automorphism group is the direct product of a cyclic and a symmetric group, which helps understand their symmetry properties.

Contribution

It introduces a novel graph-theoretic framework to analyze the dissociation microstates of polyprotic acids and identifies their automorphism group as a specific mathematical product.

Findings

The automorphism group is C2 × SN.

Graph representation simplifies DME analysis.

Provides a group-theoretic perspective on acid dissociation.

Abstract

The dissociation micro-states (DMS) of an $N$-protic acid are described using set theory notation. This facilitates the mathematical description of the dissociation micro-equilibrium (DME). In particular, the DME constants are easily obtained in terms of the dissociation equilibrium constants and the molar fractions of the DMSs. Representing of the DMEs in terms of graph theory allows to identify permutations between DMSs that preserve the vertex-edge connectivity of the graph. These permutations, along with their composition, allow us to identify the direct product of the cyclic group $C_2$, and the symmetric group $S_N$, $C_2\times S_N$, as the graph automorphism group of the micro-dissociation of $N$-protic acids.