Gibbs Free Energy Change (ΔG = ΔH − TΔS)

Josiah Willard Gibbs worked out this balance in "On the Equilibrium of Heterogeneous Substances", published in 1876–78 in the Transactions of the Connecticut Academy of Arts and Sciences — a journal so obscure that European chemists only learned of it after Maxwell began championing the work and Ostwald translated it into German in 1892. The idea is a tug of war: enthalpy pulls a reaction toward lower energy, entropy pulls it toward greater disorder, and temperature decides who wins. ΔG negative means the process can run on its own; ΔG positive means it needs driving; ΔG zero is equilibrium.

Limestone decomposition, CaCO₃ → CaO + CO₂, is the textbook illustration: ΔH = +178.3 kJ/mol (strongly endothermic) and ΔS = +160.5 J/(mol·K) (a gas is released). At 25 °C, ΔG = 178.3 − 298.15 × 0.1605 = +130.4 kJ/mol, so nothing happens. Solve ΔG = 0 for T and you get 178300/160.5 = 1111 K, or about 838 °C — which is why lime kilns are fired to roughly that temperature and no lower. The classic unit trap lives right here: ΔH is tabulated in kJ/mol while ΔS is tabulated in J/(mol·K), and forgetting the factor of 1000 makes the entropy term vanish. Enter ΔS in J/(mol·K) and this calculator handles the rest.