When is a reaction spontaneous using Gibbs free energy

The Gibbs free energy equation ΔG = ΔH – TΔS links three thermodynamic quantities. ΔH is the enthalpy change, representing heat absorbed or released at constant pressure. ΔS is the entropy change, measuring the disorder introduced by the reaction. Temperature T (in kelvin) scales the entropy term, so the sign of ΔG can flip as T varies.

Temperature dependence of spontaneity

When ΔH and ΔS have the same sign, temperature determines the outcome. If both are negative, the reaction is favored at low temperatures because the enthalpy term dominates. If both are positive, high temperatures make the TΔS term large enough to overcome a positive ΔH, driving spontaneity.

Four sign combinations and their typical behavior:

• ΔH < 0, ΔS > 0 → spontaneous at all temperatures
• ΔH < 0, ΔS < 0 → spontaneous only at low T
• ΔH > 0, ΔS > 0 → spontaneous only at high T
• ΔH > 0, ΔS < 0 → never spontaneous

Procedure to test spontaneity for a given reaction:

1. 1Calculate ΔH and ΔS from standard formation data
2. 2Convert ΔS to kJ·mol⁻¹·K⁻¹ if needed
3. 3Choose the temperature of interest (in K)
4. 4Compute ΔG = ΔH – TΔS
5. 5If ΔG < 0, the reaction is spontaneous

Sample thermodynamic data for the synthesis of ammonia (N₂+3H₂→2NH₃):

Worked example: At 500 K, determine if the ammonia synthesis is spontaneous. First convert ΔS: ‑198 J·mol⁻¹·K⁻¹ = ‑0.198 kJ·mol⁻¹·K⁻¹. Then compute ΔG = ‑92.4 kJ – (500 K × ‑0.198 kJ·mol⁻¹·K⁻¹) = ‑92.4 kJ + 99.0 kJ = +6.6 kJ. Because ΔG is positive, the reaction is non‑spontaneous at 500 K, illustrating how a high temperature can reverse spontaneity when ΔS is negative.