Understanding Chemical Equilibrium: The Role of Gas Phases and Mixing Contributions in the Minimum of Free Energy Plots

Abstract

The use of free energy plots to understand the concept of thermodynamic equilibrium has been shown to be of great pedagogical value in materials science. Although chemical equilibrium is also amenable to this kind of analysis, it is not part of the agenda of materials science textbooks. Something similar is found in chemistry branches, where free energy plots in the context of chemical equilibrium are occasionally addressed, in qualitative fashion, and with a main focus on gas phase reactions. With the aim of providing a more complete perspective on the topic, free energy plots in several reactive systems that include condensed and gas phase components are analyzed. Free energy functions of the reactive systems are assembled using expressions of chemical potentials as building blocks, a useful approach to articulate several layers of concepts (fugacity coefficients, activity coefficients, solution thermodynamics) developed in earlier stages of thermodynamic courses. The examples presented highlight the influence of two factors on chemical equilibrium: mixing contributions and the presence of gas phases. A single gas phase reaction is first addressed to show a case where mixing contributions have direct impact on the minimum of free energy curves. The second example is a reaction involving a gas and two solid phases, formally similar to those represented in Ellingham charts, where despite the presence of a gas phase, mixing does not occur. A third example illustrates the case of a reaction between solid phases to generate a third solid, where neither mixing nor gas phases are present. The examples highlight the role played by entropic contributions in the minimum of free energy curves, providing a deeper understanding of chemical equilibrium in systems of interest to chemistry and material science.