Gibbs energy and equilibrium

Working out ∆S of the surroundings every time is awkward. Gibbs energy, G, combines enthalpy and entropy in one quantity about the system alone: G = H – TS. At constant temperature and pressure:

∆G = ∆H – T∆S.

• If ∆G < 0, the process is spontaneous.
• If ∆G = 0, the system is at equilibrium.
• If ∆G > 0, it is not spontaneous (the reverse process is).

The signs of ∆H and ∆S decide how temperature matters:

Gibbs energy is linked to the equilibrium constant:

∆rG⊖ = –RT ln K = –2.303 RT log K.

A large K (mostly products at equilibrium) means a negative ∆G⊖. So K can be found from ∆G⊖ (log K = –∆G⊖ / 2.303RT), and ∆G⊖ from a measured K. For example, a reaction with K = 100 at 298 K has ∆G⊖ = –2.303 × 8.314 × 298 × log 100 = –11.4 kJ mol⁻¹.

∆G also has a practical meaning: it is the maximum useful work a system can do (other than expansion work). A reaction with a large positive ∆G⊖ hardly goes at all on its own.