A portrait of J. Willard Gibbs

J. Willard Gibbs (1839-1903) proposed a single state function to determine spontaneity:

G = H – TS

where H is the enthalpy of the system, S is the entropy of the system, and G is Gibbs free energy.

The change in Gibbs free energy, ΔG, is the maximum amount of free energy available to do useful work. For an isothermal process, it can be expressed as:

ΔG = ΔH – TΔS          or at standard conditions:            ΔG⁰ = ΔH⁰ – TΔS⁰

This single term, Gibbs free energy (G), allows us to avoid calculating the entropy of the surroundings. It is really just a simplification of our previous method of estimating spontaneity:

ΔS_universe = ΔS_sys + ΔS_surr

ΔSuniverse = ΔSsys + (− ΔHsys/T)

Multiply both sides of the equation by –T:

–TΔS_universe = ΔH_sys – TΔS_sys

Therefore ΔG = –TΔS_universe

As a result of this relationship, the sign of Gibbs free energy provides information on the spontaneity of a given reaction:

If ΔG > 0, the reaction is nonspontaneous in the direction written.

If ΔG = 0, the reaction is in a state of equilibrium.

If ΔG < 0, the reaction is spontaneous in the direction written.

The significance of the sign of a change in Gibbs free energy parallels the relationship of terms from the equilibrium chapter: the reaction quotient, Q, and the equilibrium constant, K.

If Q > K, the reaction is nonspontaneous in the direction written.

If Q = K, the reaction is in a state of equilibrium.

If Q < K, the reaction is spontaneous in the direction written.