The graph automorphism group of the dissociation microequilibrium of polyprotic acids

Abstract

The dissociation micro-states (DMSs) of an N-protic acid are described using set theory notation, which 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 the DME in terms of graph theory allows us to identify permutations between DMSs that preserve the vertex-edge connectivity of the graph. These permutations, along with their compositions, led to the identification of the direct product C₂ × S_N of the cyclic group C₂ and the symmetric group S_N as the graph automorphism group of the microdissociation of N-protic acids with N = 1, 2, …, 6. In this context, the microdissociations are associated with the C₂ group while the tautomerizations are related to the S_N group.