| Under conditions of constant temperature T and pressure P, chemical equilibrium occurs in a closed system (fixed mass) when the Gibbs free energy G of the reaction mixture is minimized. However, when chemical reactions occur under other conditions, other thermodynamic functions are minimized or maximized. For processes at constant T and volume V, the Helmholtz energy A seeks a minimum. These points are illustrated for the ammonia formation reaction in the ideal gas approximation, through a numerical exercise in which both G and A are evaluated as functions of the extent of reaction ξ, under conditions of constant (T,P) and constant (T,V), for the same starting thermodynamic state. The equilibrium positions are different, but at both minima—in GT,P(ξ) and AT,V(ξ)—the value of the reaction quotient Q equals the equilibrium constant K°(T). In the familiar thermodynamics equation defining K°,
RT ln K° = –ΔG°
ΔG° has its origin in the fact that the chemical potential for a pure substance is its molar Gibbs energy, rather than from considerations about the conditions under which equilibrium occurs.
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