Hess’ law requires modified mathematical rules for information entropy of interdependent chemical reactions

Abstract

In mathematical chemistry, a chemical reaction is represented as a transformation of one molecular ensemble into another one, and information entropy is used for quantitative describing changes in the molecular complexity. The information entropy of a chemical reaction is the difference between the values of the ensembles of products and reagents. As is known, the information entropy of molecular ensemble depends on the information entropies of individual molecules and, additionally, on the cooperative entropy, an emergent parameter that reflects uniting the molecules into the ensemble. Accounting this parameter determines the peculiarities of calculating the information entropy for interdependent chemical reactions. In the present study, we have derived a general formula that connects the information entropy of the complex chemical process with the parameters of its elementary stages and demonstrated its work on typical examples of successive, parallel, and conjugated chemical reactions. Notably, the view of the derived formula differs from the equations used when Hess’ law is applied to the thermodynamic parameters of interdependent reactions. The only case when the Hess’ law has the same analytical expression for both information-entropy and thermodynamic parameters is the isomegethic set of chemical reactions, viz. the system of the successive reactions, in which the size of the molecular ensemble remains constant.