Gibbs Free Energy
Predict whether a reaction is spontaneous from its enthalpy change ΔH, entropy change ΔS and temperature T. Also finds the crossover temperature and the equilibrium constant K.
What is Gibbs Free Energy?
Two tendencies drive chemical change: releasing heat (negative ΔH) and increasing disorder (positive ΔS). The Gibbs free energy combines both into one number at a given temperature.
If ΔG < 0 the reaction is spontaneous: it can proceed without outside help. “Spontaneous” says nothing about speed — diamond turning into graphite is spontaneous but takes billions of years. ΔG also equals the maximum non-expansion work, such as the electrical work from a battery or fuel cell.
Live Graph
ΔG vs TThe Four Cases
| ΔH | ΔS | Spontaneous… | Example |
|---|---|---|---|
| − | + | at all temperatures | combustion |
| − | − | at low T | water freezing |
| + | + | at high T | ice melting |
| + | − | never | O₂ → O₃ |
Key Relations
ΔH is usually given in kJ/mol but ΔS in J/(mol·K). Convert before subtracting — the most common mistake in Gibbs problems.
When ΔH and ΔS have the same sign, the reaction switches between spontaneous and non-spontaneous at T*. For phase changes T* is the melting or boiling point.
A strongly negative ΔG° means K >> 1: products dominate at equilibrium. Using standard values (ΔH°, ΔS°) gives the standard-state K.
Sources & Verification
- S. S. Zumdahl & S. A. Zumdahl, Chemistry, 10th ed., Cengage, 2018 — Ch. 17 (Spontaneity, Entropy, and Free Energy).
- P. Atkins & J. de Paula, Atkins’ Physical Chemistry, 11th ed., Oxford University Press, 2018 — Focus 3 (The Second and Third Laws) and Focus 6 (Chemical Equilibrium).