Chapter 11: Reactions Involving Gases

The system's equilibrium state can be analyzed practically by defining it through the partial pressures of all resulting product and remaining reactant species, provided the total pressure is sufficiently low. The fundamental condition for equilibrium in any constant-temperature, constant-pressure system is the minimization of the Gibbs free energy of the system. This total change in Gibbs free energy is derived from two components: the energy change due to the chemical transformation (the appearance of products and disappearance of reactants) and the energy change resulting from the mixing of the gases. At equilibrium, the chemical potential (or partial molar Gibbs free energy) of the reactants must equal that of the products. This critical thermodynamic relationship is quantitatively defined by the equilibrium constant, K P. K P is calculated as the quotient of the equilibrium partial pressures of the products divided by those of the reactants, with each pressure raised to the power of its stoichiometric coefficient. The standard Gibbs free energy change (Delta G standard) for the reaction, based on all species being in their standard state (pure gas at one atmosphere pressure and temperature T), is linked directly to K P through the relation Delta G standard equals minus R T multiplied by the natural logarithm of K P. Because Delta G standard depends only on temperature, K P is also independent of the total system pressure. The van’t Hoff equation describes how temperature influences K P, showing that this effect is governed by the magnitude and sign of the standard enthalpy change (Delta H standard). Specifically, a graphical plot of the natural logarithm of K P versus the inverse of the absolute temperature yields a slope related to minus Delta H standard divided by R. Consequently, endothermic reactions (where Delta H standard is positive) show an increase in K P as temperature increases, while exothermic reactions (where Delta H standard is negative) show a decrease in K P as temperature rises. These thermal and pressure effects are consistent with Le Chatelier’s principle, which dictates that increasing pressure shifts equilibrium toward the side with fewer moles of gas. Although K P is constant at fixed temperature, the equilibrium constant expressed in terms of mole fractions (K x) remains independent of total pressure only if the chemical reaction does not alter the total number of moles in the system. Ultimately, the equilibrium state is defined as a thermodynamic compromise between the system's drive toward lower enthalpy and its tendency toward greater randomness (entropy). This principle is utilized practically for establishing precise, low oxygen partial pressures using H 2​ O–H 2​ or CO 2​ –CO gas mixtures.