The Simple Idea

Gibbs free energy $G$ answers one question: "Can this reaction drive itself at constant temperature and pressure?"

Think of $\Delta G$ as the "maximum useful work" a reaction can do (beyond PV work). When $\Delta G < 0$, the system has "free energy" to drive the reaction forward spontaneously.

Why $G = H - TS$?

$H$ is the total energy content. But some energy is "locked up" in entropy — it is the thermal energy that must be there to maintain the level of disorder ($TS$). You cannot use this entropy-locked energy for work.

Useful energy = Total energy $-$ Entropy tax $G = H - TS$

The Driving Forces

1. Enthalpy drive ($\Delta H < 0$): System wants to go downhill in energy (like a ball rolling down a hill)
2. Entropy drive ($T\Delta S > 0$): System wants to maximize disorder (like a gas expanding to fill space)

When BOTH drives push the same direction → always spontaneous. When they oppose → the temperature determines which wins.

At Equilibrium

$\Delta G = 0$: no net driving force. The system has reached the lowest free energy state available. Forward and reverse rates are equal.

Intuition Check

• Large $K$ (products favored) ↔ $\Delta G^\circ \ll 0$ (reaction drives strongly to products)
• Small $K$ (reactants favored) ↔ $\Delta G^\circ \gg 0$ (system prefers reactants)
• $K = 1$ ↔ $\Delta G^\circ = 0$ (no preference at equilibrium)