Will a reaction go?
Some reactions release heat and happen on their own, but others absorb heat and still proceed, like ice melting in a warm room. The deciding quantity is the Gibbs free energy, G = H − TS, introduced by Josiah Willard Gibbs in the 1870s. At constant temperature and pressure, a reaction is spontaneous in the forward direction when its change ΔG is negative.
The formulas
- ΔG = ΔH − T × ΔS
- Equilibrium constant K = exp(−ΔG° ÷ RT)
- Crossover temperature T = ΔH ÷ ΔS, where ΔG changes sign
ΔH is usually given in kJ/mol and ΔS in J/(mol·K), so divide ΔS by 1,000 before combining. T must be in kelvin; R = 8.314 J/(mol·K).
Worked example: ammonia synthesis
N₂ + 3 H₂ → 2 NH₃ has ΔH° = −92.2 kJ/mol and ΔS° = −198.7 J/(mol·K). At 25 °C:
- T = 298.15 K, so TΔS = 298.15 × (−0.1987) = −59.24 kJ/mol.
- ΔG° = −92.2 − (−59.24) = −32.96 kJ/mol: spontaneous.
- K = exp(32,960 ÷ (8.314 × 298.15)) ≈ 5.9 × 10⁵.
- Crossover temperature = −92.2 ÷ −0.1987 = 464 K, or 190.9 °C: above it, ΔG° turns positive.
Yet the Haber-Bosch process runs at 400 to 500 °C, where K is small, because at 25 °C the reaction is far too slow. High pressure and recycling make up for the lower equilibrium yield.
The four cases
| ΔH | ΔS | ΔG | Spontaneous |
|---|---|---|---|
| Negative | Positive | Always negative | At all temperatures |
| Positive | Negative | Always positive | Never |
| Negative | Negative | Negative when cold | Below ΔH/ΔS |
| Positive | Positive | Negative when hot | Above ΔH/ΔS |
Ice melting is the last case: ΔH and ΔS are both positive, so it is spontaneous above 0 °C.
ΔG versus ΔG°
The calculator works with standard values (1 bar, 1 mol/L). Under real conditions, ΔG = ΔG° + RT ln Q, where Q is the reaction quotient; the reaction proceeds until Q reaches K and ΔG becomes zero.
Spontaneous does not mean fast
Thermodynamics says where a reaction can go; kinetics says how fast. Diamond turning into graphite has a negative ΔG at room temperature, but the activation energy is so high that diamonds last for billions of years. Catalysts speed up reactions without changing ΔG.
Where the data come from
Standard enthalpies and entropies of formation are tabulated, for example in the CRC Handbook and the NIST Chemistry WebBook. Compute ΔH° and ΔS° of the reaction as products minus reactants, each multiplied by its coefficient.