Gibbs Free Energy and Spontaneity

Spontaneity Without Looking at the Surroundings

Judging spontaneity by $\Delta S_{universe}$ is correct but inconvenient, it demands information about the surroundings. At constant temperature and pressure, that requirement can be folded into a single property of the system:

$$\Delta G = \Delta H - T\Delta S$$

The criterion becomes wonderfully simple. $\Delta G < 0$ means spontaneous, $\Delta G > 0$ means non-spontaneous (the reverse is spontaneous), and $\Delta G = 0$ means the system is at equilibrium.

Because the entropy term is multiplied by $T$, the two contributions compete, and which one wins can depend on temperature:

The two mixed cases have a crossover temperature where $\Delta G$ passes through zero:

$$T = \frac{\Delta H}{\Delta S}$$

Below it one term dominates, above it the other. Ice melting is the everyday example: $\Delta H > 0$ and $\Delta S > 0$, with a crossover at exactly 273 K.

Gibbs energy also connects to equilibrium. $\Delta G^\circ = -RT\ln K$ links the standard free-energy change to the equilibrium constant, so a strongly negative $\Delta G^\circ$ means a large $K$ and a reaction that runs nearly to completion. But note the word standard: $\Delta G^\circ$ describes one specific reference condition, while $\Delta G$ varies as the mixture's composition changes, reaching zero at equilibrium.

Common pitfall: reading $\Delta G < 0$ as "fast". Gibbs energy says only that a reaction can proceed, never how quickly. Diamond converting to graphite has $\Delta G < 0$ at room temperature and takes geological time, spontaneity is thermodynamics, rate is kinetics.