Recurrence relations for the equilibrium means of distributions arising in chemical reactions

Abstract EN

In this paper we derive recurrence relations that describe how the equilibrium mean of the number molecules of a reactant varies with each of the parameters defining the initial state for four basic reversible chemical reactions.

In essence, the relations provide a rationale for updating the equilibrium mean following the addition (or removal) of a molecule of one of the types involved in the reaction, there being a relation for each type.

With a new parameterization introduced for each reaction, the relations provide a convenient means of evaluating the means, variances and other important moments without any need to work out the underlying distributions.

As an application, the relations are used to numerically assess-approximate expressions for the means and variances.