Spontaneity and Equilibrium II: Multireaction Systems

Abstract

The thermodynamic criteria for spontaneity and equilibrium in multireaction systems are developed and discussed. When N reactions are occurring simultaneously, it is shown that G and A will depend upon N independent reaction coordinates, ξα (α = 1,2, ..., N), in addition to T and p for G or T and V for A. The general criteria for spontaneity and equilibrium are the same as those for a single-reaction system, dG ≤ 0 (T and p constant) or dA ≤ 0 (T and V constant). However, dG and dA are now the sum of N terms. It is shown that this sum has the form dG = dA = ∑α=1N Δrμα dξα, where Δrμα is the reaction chemical potential for reaction α, (∂G/∂ξα)T,p,ξj. Consequently, the result that dG < 0 at a particular composition provides no information about which of the N reactions are proceeding spontaneously and which are nonspontaneous. At most compositions, there exist an infinite number of both spontaneous and nonspontaneous pathways for the system. Equilibrium in a multireaction system exists at a single compositi...