Gibbs free energy

The Gibbs free energy (G) is defined by G = H − TS, where H is enthalpy, T is absolute temperature and S is entropy. Since H and TS have units of energy, G is measured in joules (often per mole for molar quantities). The function is a state function: its change depends on the initial and final states rather than the path between them. The name “Gibbs energy” is often used to avoid implying that this quantity is energy conserved independently of the system.

For a process at constant temperature and pressure, ΔG = ΔH − TΔS. A negative ΔG indicates a spontaneous direction under those conditions, a positive ΔG indicates a nonspontaneous direction, and ΔG = 0 describes equilibrium. This criterion does not specify how quickly a process occurs: reaction rates and activation barriers are kinetic properties. A process with positive ΔG can proceed when coupled to another process so that the combined change in Gibbs energy is negative.

For a reaction away from standard-state conditions, the Gibbs energy change is related to the standard change by ΔG = ΔG° + RT ln Q, where R is the gas constant, T is absolute temperature and Q is the reaction quotient for the current mixture. At equilibrium Q equals the equilibrium constant K and ΔG is zero, giving ΔG° = −RT ln K. Thus the sign and magnitude of ΔG° relate to the equilibrium composition, while ΔG under actual conditions reflects the mixture at that moment.

In a reversible galvanic cell under standard conditions, the standard Gibbs energy change is related to the standard cell potential by ΔG° = −nFE°cell, where n is the amount of electrons transferred per reaction as a number of moles and F is the Faraday constant. A positive standard cell potential therefore corresponds to a negative standard Gibbs energy change for the cell reaction as written. Under nonstandard conditions, reaction composition also matters and is accounted for through the Nernst equation.