Gibbs Energy (Free Enthalpy)

Subtract from the reaction enthalpy ΔH the product of absolute temperature T and reaction entropy ΔS: ΔG = ΔH − T·ΔS. Watch for consistent units: ΔH is usually in kJ/mol, but ΔS in J/(mol·K), so convert ΔS to kJ/(mol·K) by dividing by 1000. Example: ΔH = −100 kJ/mol, ΔS = +200 J/(mol·K) = +0.2 kJ/(mol·K), T = 500 K. Then ΔG = −100 − 500·0.2 = −200 kJ/mol. A negative ΔG shows that the reaction proceeds voluntarily, that is spontaneously, under these conditions. Always insert T in kelvin.

A reaction proceeds spontaneously at constant temperature and pressure when the Gibbs free energy decreases, that is when ΔG is negative. If ΔG is positive, the reaction is not spontaneous in this direction but proceeds in reverse. At ΔG = 0 there is equilibrium. Whether ΔG becomes negative is decided by the interplay of enthalpy and entropy. Exothermic reactions with negative ΔH and an entropy increase with positive ΔS are spontaneous at any temperature. If only one of the contributions is favourable, spontaneity depends on the temperature, because the term T·ΔS grows with rising temperature and can outweigh the enthalpy contribution.

An endothermic reaction has a positive ΔH and is therefore energetically unfavourable. It can still proceed spontaneously if the entropy increases strongly, that is ΔS is positive, and the temperature is high enough for the term T·ΔS to exceed ΔH. Then ΔG = ΔH − T·ΔS becomes negative. From this condition follows a threshold temperature T = ΔH/ΔS above which the reaction becomes spontaneous. An example is the melting of ice: it is endothermic but proceeds spontaneously above 0 °C, because the entropy of the liquid is greater than that of the solid and T·ΔS then dominates.

ΔH is the reaction enthalpy and describes the heat exchanged at constant pressure; negative means exothermic, positive endothermic. ΔS is the reaction entropy and measures the change in disorder or the number of possible states; positive means more disorder, for example when gas forms. ΔG is the Gibbs free energy and combines both through ΔG = ΔH − T·ΔS into a single criterion for spontaneity. While ΔH and ΔS each describe only one aspect, only ΔG decides whether a reaction actually proceeds at a given temperature. The temperature weights the entropy contribution. All three quantities are state functions and depend only on start and end.

Through the relation ΔG° = −R·T·ln K the standard Gibbs energy links thermodynamics with the equilibrium position. A strongly negative ΔG° means a large K, so the equilibrium lies far on the product side. A positive ΔG° leads to a small K and the reactants dominate. At ΔG° = 0, K equals one. Under non-standard conditions the more general ΔG = ΔG° + R·T·ln Q holds; at equilibrium ΔG = 0 and Q becomes K. This link makes it possible to predict the equilibrium constant of a reaction from thermodynamic table values without measuring it directly.