Gibbs Free Energy and Spontaneity

Applying the Second Law directly requires tracking the entropy change of both the system and its surroundings — inconvenient for everyday laboratory chemistry, where what is really wanted is a single criterion, calculable purely from properties of the system itself, that predicts whether a reaction will proceed spontaneously.

Gibbs free energy, $G$, supplies exactly this. It is defined as

For a process occurring at constant temperature and pressure — the overwhelming majority of chemical reactions run in the laboratory — the change in Gibbs free energy works out to be

where $\Delta H$ and $\Delta S$ here refer only to the system. This single equation is derived directly from the Second Law by substituting $\Delta S_{surroundings} = -\Delta H_{system}/T$ (the heat released by the system, $-\Delta H$, is exactly the heat absorbed by the surroundings at constant $T$ and $P$) into $\Delta S_{total} = \Delta S_{system} + \Delta S_{surroundings} \geq 0$, then multiplying through by $-T$ (which reverses the inequality).

The result is the single most useful spontaneity criterion in chemical thermodynamics: