Entropy in Multiple Equilibria, Systems with Two Different Sites

Abstract

The influence of entropy in multiple chemical equilibria is investigated for systems with two different types of sites for Langmuir’s condition, which means that the binding enthalpy of the species is the same for each type of sites and independent of those that are already bonded and that this holds for both types of sites independently. The analysis makes use of the particle distribution theory which holds for each type of sites separately. We provide physical insight by discussing an Xm{AB}Xn system with m = 0, 1, …, M and n = 0, 1, …, N in detail. The procedure and results are exemplified for an Xm{AB}Xn system with M = 3 and N = 2. A satisfactory consequence of the results is that the eleven equilibrium constants needed to describe such a system can be expressed as a function of two constants only. This is generally valid for any Xm{AB}Xn system where the [(M + 1)(N + 1) − 1] equilibrium constants can be expressed as a function of 2 constants only. This has also implication for quantum-theoretical studies in the sense that it is sufficient to model only two reactions instead of many in order to describe the system. We have observed that it is sufficient to have two different sites in a multiple equilibrium in order to observe a characteristic of isotherms that cannot be described by Langmuir’s equation. This is a result that may be useful for explaining experimental data which otherwise have not been explained satisfactory so far. Instead of inventing adsorption models it might often make sense of describing the system in terms of multiple equilibria.

Keywords

• Chemical equilibria, entropy, particle distribution, Langmuir, equilibrium constants