Gibbs free energy (G) combines enthalpy and entropy into a single value that tells us whether a reaction is spontaneous.
The Gibbs Equation
\( \Delta G = \Delta H - T\Delta S \)
where T is temperature in Kelvin
Interpreting ΔG
- ΔG < 0 — reaction is spontaneous (thermodynamically feasible)
- ΔG > 0 — reaction is non-spontaneous
- ΔG = 0 — system is at equilibrium
Note: "spontaneous" does NOT mean fast! It only means thermodynamically favourable. The reaction may still be very slow if Ea is high.
The Four Scenarios
| ΔH | ΔS | ΔG | Spontaneous? |
|---|---|---|---|
| − (exo) | + (increase) | Always − | Always |
| + (endo) | − (decrease) | Always + | Never |
| − (exo) | − (decrease) | Depends on T | At low T |
| + (endo) | + (increase) | Depends on T | At high T |
Finding the Crossover Temperature
When ΔG = 0 (equilibrium), we can find the temperature at which spontaneity switches:
\( T = \frac{\Delta H}{\Delta S} \)
Both ΔH and ΔS must be in the same units (e.g. both in J or both in kJ).
Think About It
Water freezes spontaneously below 0 °C but not above. How does the Gibbs equation explain this?
Freezing: H₂O(l) → H₂O(s). ΔH is negative (exothermic), ΔS is negative (decrease in disorder). ΔG = ΔH − TΔS. At low T, the ΔH term dominates → ΔG < 0 (spontaneous). At high T, the TΔS term dominates → ΔG > 0 (non-spontaneous). The crossover is 273 K.