Uniqueness of chemical equilibria in ideal mixtures of ideal gases

We prove the uniqueness of chemical equilibrium for an ideal mixture of ideal gases in a closed, spatially homogeneous volume. Uniqueness, a fundamental issue of chemical physics, is incompletely justified in textbooks and much of the scientific literature. We first reproduce a little known proof by Zel’dovich and show in a more direct fashion than originally presented that a unique equilibrium exists for isothermal reactions. Zel’dovich’s approach is then extended to the adiabatic case, and a more complete exposition than that of Aris is provided. The example of an isothermal, isochoric O-O2-O3 system provides an illustration of uniqueness. The discussion should be useful for students and instructors of graduate level thermal physics, as well as for researchers in macroscale reaction dynamics. © 2008 American Association of Physics Teachers. DOI: 10.1119/1.2919742