Free Energy Change and the Equilibrium Constant

Free energy is a state function, so G for a reaction depends only on the free energy of the initial state (the reactants) and the free energy of the final state (the products):

> G = G(products) - G(reactants)

Consider the reaction aA + bB <=> cC + dD, where a is the number of moles of component A, b is the number of moles of component B, etc.

Using the equation for the chemical potential, and collecting the standard state terms into a single , yields

> G = + RT ln {([C]c[D]d)/([A]a[B]b)}

Simplifying (and remembering that each product and reactant must be raised to the appropriate power) yields the following general equation for determining G under any set of conditions, where is the free energy change for the standard state (1M):

> G = + RT ln{[Products]/[Reactants]}

At equilibrium, the equilibrium constant K for the reaction is given by

K = {([C]c[D]d)/([A]a[B]b)}

Recall that G = 0 at equilibrium, so substituting yields

> 0 = + RT ln K,

> - = RT lnK, or

Whenever a system is displaced from equilibrium, it will spontaneously proceed in the direction necessary to reestablish the equilibrium state. Negative G is the driving force for such a reaction.

See also: Internal Energy (E), Enthalpy, Interplay of Enthalpy and Entropy