Gibbs Free Energy of Reaction

Gibbs free energy: ΔG = ΔH − T·ΔS

The Gibbs free energy change tells you whether a reaction will run on its own at constant pressure and temperature: ΔG = ΔH − T·ΔS. Here ΔH is the enthalpy change (kJ/mol), T the absolute temperature (K), and ΔS the entropy change (J/mol·K). The spontaneity criterion is straightforward: ΔG < 0 means spontaneous, ΔG = 0 means equilibrium, ΔG > 0 means non-spontaneous. Because temperature multiplies the entropy term, the sign can flip as T changes. Ice melts above 273 K precisely because T·ΔS grows large enough to overtake ΔH. The equilibrium constant ties in through ΔG° = −RT·ln K, and in electrochemistry you get ΔG = −nFE (F = Faraday constant). Example: ΔH = −100 kJ/mol, T = 298 K, ΔS = 50 J/mol·K → ΔG = −100 − 298·0.050 = −114.9 kJ/mol, so the reaction is spontaneous.

Applications: electrochemistry, biochemistry, refrigeration

ΔG lets you screen chemical reactions before ever touching a flask. It also drives electrochemistry: galvanic cells release a ΔG < 0 as voltage, while electrolysis pushes a ΔG > 0 reaction by feeding in external power. In biochemistry it explains why ATP → ADP hydrolysis, releasing roughly −30.5 kJ/mol, powers the cell. And it sits behind refrigeration cycles, where work is spent forcing things against the natural direction of ΔG.

FAQ

Can an endothermic reaction be spontaneous? Yes, as long as ΔS is positive and T is high enough that T·ΔS > ΔH. Ammonium nitrate dissolving in water is the classic case.

What does ΔG = 0 mean? The reaction has reached equilibrium. Forward and reverse rates match, so the net composition stops changing.

Why use absolute temperature? Entropy lives on an absolute (Kelvin) scale, so plugging in °C would hand you wrong signs near 0 °C.

How does ΔG relate to the equilibrium constant K? Through ΔG° = −RT·ln K. When K > 1 you get ΔG° < 0 (products favored); when K < 1 you get ΔG° > 0 (reactants favored).