Gibb's free energy

Meaning: Gibbs free energy (G = H − TS) is the energy available to do useful work at constant temperature and pressure. The sign of ΔG predicts spontaneity: ΔG < 0 is spontaneous as written, ΔG > 0 is nonspontaneous, and ΔG = 0 is equilibrium. It balances the enthalpy drive toward lower energy against the entropy drive toward disorder.

Equation: ΔG = ΔH − TΔS, where ΔG and ΔH are in J/mol, T is in K, and ΔS is in J/(mol·K). Related forms are ΔG = ΔG° + RT ln Q and ΔG° = −RT ln Keq, with R = 8.314 J/(mol·K).

On the MCAT: Expect a ΔH and ΔS sign table. ΔH < 0 with ΔS > 0 is spontaneous at all temperatures. ΔH > 0 with ΔS < 0 is nonspontaneous at all temperatures. The mixed cases change sign at a crossover temperature where ΔG = 0. If Q < Keq, then ΔG < 0 and the forward reaction proceeds. Passages also couple an unfavorable reaction to ATP hydrolysis. Convert ΔH from kJ to J to match ΔS before calculating.

Common confusion: Spontaneous does not mean fast. Rate depends on activation energy, not ΔG. Also, ΔG° applies only to standard conditions, so a reaction with ΔG° > 0 can still go forward if Q is small enough to make ΔG negative.