Achieving Chemical Equilibrium: The Role of Imposed Conditions in the Ammonia Formation Reaction

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 G T,P (ξ) and A T,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 ° = –Δ G ° Δ G ° 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.