spontaneity

Meaning: A spontaneous process is thermodynamically favorable: it proceeds forward from the given conditions without continuous outside work. At constant T and P, ΔG < 0 is spontaneous, ΔG = 0 is equilibrium, and ΔG > 0 means the forward reaction is nonspontaneous (the reverse is spontaneous). If ΔH < 0 and ΔS > 0, ΔG < 0 at every temperature. If ΔH > 0 and ΔS < 0, ΔG > 0 at every temperature. The other two combinations depend on temperature.

Equation: ΔG = ΔH − TΔS, where ΔG is the Gibbs free energy change (J/mol), ΔH is the enthalpy change (J/mol), T is the absolute temperature (K), and ΔS is the entropy change of the system (J/(mol·K)).

On the MCAT: You are given the signs of ΔH and ΔS and asked whether a reaction is spontaneous at high or low temperature, or you find the crossover temperature T = ΔH/ΔS. If Q < Keq, ΔG < 0 and the reaction shifts forward. A galvanic cell has E°cell > 0. In biochemistry, coupling an unfavorable step to ATP hydrolysis can make the overall process spontaneous.

Common confusion: Spontaneous does not mean fast. Rate depends on activation energy, and a catalyst lowers that barrier without changing ΔG. Diamond turning to graphite is spontaneous but extremely slow.