Enthalpy alone cannot say whether a reaction is feasible: some endothermic reactions happen on their own. The Gibbs equation weighs the enthalpy change against the entropy change at a given temperature, and tells you the temperature where a reaction switches on or off.
The Gibbs free energy change combines enthalpy and entropy: ΔG° = ΔH° − TΔS°, with T in kelvin. ΔH is in kJ mol−1 but ΔS is in J K−1 mol−1, so divide ΔS by 1000 first. A reaction is feasible when ΔG ≤ 0. When ΔH and ΔS have the same sign, temperature decides: the switch-over happens where ΔG = 0, at T = ΔH / ΔS. For CaCO3 → CaO + CO2 (ΔH +178 kJ mol−1, ΔS +161 J K−1 mol−1), T = 178 / 0.161 = 1106 K. A feasible reaction may still be very slow if its activation energy is high.
Work through the decomposition of calcium carbonate at two temperatures. Convert ΔS to kJ before you multiply by T.
| Step | At 298 K | At 1200 K |
|---|---|---|
| ΔH° | +178 kJ mol−1 | +178 kJ mol−1 |
| ΔS° in kJ | +161 ÷ 1000 = +0.161 | +0.161 |
| TΔS° | 298 × 0.161 = 48.0 | 1200 × 0.161 = 193.2 |
| ΔG° = ΔH° − TΔS° | +130 kJ mol−1: not feasible | −15.2 kJ mol−1: feasible |
Slide the temperature in the simulator for the decomposition of calcium carbonate. Nothing happens at room temperature; above a threshold ΔG turns negative and CO2 is given off, exactly as the Gibbs equation predicts.
| ΔH | ΔS | ΔG = ΔH − TΔS | Feasible? |
|---|---|---|---|
| − | + | always negative | at all temperatures |
| + | − | always positive | never |
| − | − | negative at low T | below T = ΔH/ΔS (Haber: below 462 K) |
| + | + | negative at high T | above T = ΔH/ΔS (CaCO3: above 1106 K) |
The classic slip is forgetting to divide ΔS by 1000: 178 − 298 × 161 gives a nonsense −47 800 kJ mol−1. Temperature must be in kelvin. ΔG ≤ 0 means feasible, not fast. When ΔH and ΔS have the same sign, always state whether the reaction is feasible above or below the calculated temperature.
Four quick checks. Each correct answer earns XP and records this skill on your profile.
Which is the Gibbs equation?
What sign of ΔG shows that a reaction is feasible?
A reaction has ΔH negative and ΔS positive. When is it feasible?
ΔS = +161 J K−1 mol−1. What value goes into ΔG = ΔH − TΔS when ΔH is in kJ mol−1?
Unlocks once the four checks above are done. Worth more XP, written to A Level Paper 4 standard.
For CaCO3 → CaO + CO2, ΔH = +178 kJ mol−1 and ΔS = +161 J K−1 mol−1. What is the minimum temperature for the reaction to be feasible?
For N2 + 3H2 → 2NH3, ΔH = −92 kJ mol−1 and ΔS = −199 J K−1 mol−1. What is ΔG at 298 K?
Above what temperature does the Haber reaction (ΔH −92 kJ mol−1, ΔS −199 J K−1 mol−1) stop being feasible?
Diamond → graphite has a negative ΔG at room temperature, yet diamonds do not change. Why?
This skill is now recorded on your profile. Keep the chain going.