Free Energy and the Equilibrium Constant

Although it is useful to have a ready means of determining ΔG^o for a reaction from tabulated values, we usually want to know about the direction of spontaneous change for systems that are not at standard conditions.  For any chemical process, the general relationship between the free-energy change under standard conditions, ΔG^o, and the free-energy change under any other conditions, ΔG, is given by the following equation.

ΔG = ΔG^o + RT ln Q

In this equation, R is the ideal-gas constant, 8.314 J/mol · K; T is the absolute temperature; and Q is the reaction quotient that corresponds to the chemical reaction and particular reaction mixture of interest.

In the discussion about spontaneity, we saw that that ΔG = 0 when a system is at equilibrium.  Also recall that the reaction quotient Q equals the equilibrium constant K when the system is at equilibrium.  Thus, at equilibrium (when ΔG = 0 and Q = K), the equation above can be rewritten as:

ΔG = ΔG^o + RT ln Q

  0  = ΔG^o + RT ln K

 ΔG^o = - RT ln K

The relationship between  ΔG^o and K can be summarized as follows:

ΔG^o negative:   K > 1

ΔG^o zero:          K > 1

ΔG^o positive:    K < 1