Chapter 13: Reaction Equilibria in Condensed Solutions

Activity quantifies the decrease in a component's partial molar Gibbs free energy when dissolved, a change correlated with the observed decrease in its equilibrium vapor pressure. The fundamental criterion for equilibrium demands that the Gibbs free energy change for a reaction is zero. This chapter reinforces the relationship between the standard Gibbs free energy change (often represented as Delta G standard) and the equilibrium constant (K), confirming that K is the value of the activity quotient (Q) at the equilibrium point. The influence of solution behavior on gas-solid equilibrium is demonstrated using the reduction of silica, illustrating how the activity of the solid reactant in a solution directly impacts the unique equilibrium partial pressure of the gaseous product, such as oxygen. The discussion then rigorously defines and contrasts three essential thermodynamic reference points: the Raoultian standard state (the pure stable component), the Henrian standard state (a hypothetical ideal solute state derived by extrapolating Henry's law behavior to a mole fraction of one), and the highly practical one weight percent (1 wt%) standard state. Crucial conversion relationships utilizing the Henry’s law constant (gamma standard B) are provided to transition between these standard states for analyzing dilute solutions. Furthermore, the chapter introduces Phase Stability Diagrams, also known as predominance diagrams, as key graphical tools for mapping equilibrium regions in complex multicomponent, multiphase systems, exemplified by the Si–C–O system, utilizing variables like the logarithm of carbon activity or the logarithm of oxygen partial pressure. Complex binary systems are analyzed, including those forming stoichiometric compounds (Daltonides) and nonstoichiometric compounds (Berthollides), with a detailed thermodynamic treatment of the variable composition wustite phase in the Fe–O system that integrates the Gibbs–Duhem equation to determine activity variation across phase fields. Finally, the chapter addresses the solubility of gases in metals, explaining that molecular gases dissolve as atomic species (e.g., oxygen in silver), governed by Henry’s law and quantified by Sieverts’ law—which states that the concentration of the dissolved atom is proportional to the square root of the gas partial pressure—and discussing its applications, such as calculating the solubility limit of oxygen in silver and the resulting phenomenon of spitting during solidification.