# GIBBS-HELMHOLTZ EQUATIONS

The name Gibbs-Helmholtz is usually associated with the equation:

(1) where H is enthalpy, G is Gibbs free energy and T temperature, with the implied assumption that the differentiation is to be carried out at constant composition. However, this is just one of a very large number of equations of similar form, which, at various times have been called Gibbs-Helmholtz equations. The equation given is, however, most appropriately called the Gibbs-Helmholtz equation since it was first recognized by both Gibbs and Helmholtz (independently).

The greatest utility of this equation lies in the presence of the temperature derivative of the Gibbs free energy. For example, the equilibrium constant in a chemical reaction is determined by the standard Free Energy change for the reaction. Thus, a knowledge of the temperature derivative of the free energy provides information relating the temperature derivative of the equilibrium constant. The equilibrium constant, K, may be written as:

(2) where Δg° is the standard Gibbs free energy change for the reaction at temperature T and is the universal gas constant.

Applying the Gibbs-Helmholtz equation to each component in the reaction gives:

(3) and hence

(4) 