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 [xi], 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 G[subscript T,P]([xi]) and A[subscript T,V]([xi])--the value of the reaction quotient Q equals the equilibrium constant K[degree](T). In the familiar thermodynamics equation defining K[degree], RT ln K[degree] = -[delta]G[degree] [delta]G[degree] 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. (Contains 2 figures and 5 notes.)