Gibbs Free Energy Calculator (ΔG = ΔH − TΔS)

Gibbs Free Energy Guide

What do I need to know about ΔG = ΔH − TΔS Explained?

Gibbs free energy combines enthalpy (ΔH) and entropy (ΔS) into a single spontaneity criterion. ΔG < 0: spontaneous (thermodynamically favourable). ΔG = 0: at equilibrium. ΔG > 0: non-spontaneous (reverse reaction is spontaneous). ΔH < 0 (exothermic) and ΔS > 0: always spontaneous (ΔG always negative). ΔH > 0 (endothermic) and ΔS < 0: never spontaneous (ΔG always positive). ΔH < 0 and ΔS < 0: spontaneous at low temperature (enthalpy drives). ΔH > 0 and ΔS > 0: spontaneous at high temperature (entropy drives). This is why some reactions that don't occur at room temperature — like the thermal decomposition of calcium carbonate to make lime — become spontaneous only above a specific temperature, the point at which the TΔS term grows large enough to overcome a positive ΔH.

What should I know about The Crossover Temperature?

When ΔH and ΔS have the same sign, there is a crossover temperature: T_crossover = ΔH / ΔS. Above T_crossover: TΔS > ΔH → entropy term dominates. Below T_crossover: ΔH > TΔS → enthalpy term dominates. Example: decomposition of limestone CaCO₃ → CaO + CO₂. ΔH = +178 kJ/mol (endothermic). ΔS = +165 J/mol·K (positive — produces gas from solid). T_crossover = 178,000/165 = 1,079 K = 806°C. Below 806°C: not spontaneous. Above 806°C: spontaneous. This is why lime kilns operate at 900°C.

What's the key thing to understand about ΔG and Equilibrium Constant?

Standard Gibbs energy and K are directly related: ΔG° = −RT ln(K). R = 8.314 J/mol·K. At 25°C (298K): ΔG° = −2.479 × ln(K) kJ/mol. ΔG° = −5.708 × log₁₀(K) kJ/mol. K > 1 (products favoured): ΔG° < 0. K < 1 (reactants favoured): ΔG° > 0. K = 1: ΔG° = 0. For water formation: H₂ + ½O₂ → H₂O. ΔG° = −237 kJ/mol. K = e^(237,000/8.314/298) ≈ 10^41 — essentially irreversible under standard conditions.

What do I need to know about Entropy Changes in Reactions?

Standard molar entropy values allow ΔS calculation: ΔS°reaction = Σ S°products − Σ S°reactants. Rules of thumb for entropy changes: gas produced: large positive ΔS. Gas consumed: large negative ΔS. Dissolution of solids in water: usually positive ΔS (more disorder). Precipitation: negative ΔS. Increase in moles of gas: positive ΔS per extra mole (~130-200 J/mol·K). Temperature always increases entropy. The second law of thermodynamics: the entropy of the universe always increases in any spontane