Chemical thermodynamics answers a deceptively simple question: does a given reaction proceed spontaneously, and in what direction? The answer hinges on a single quantity, the Gibbs free energy change ΔG.
Definition
At constant temperature T and pressure P:
ΔG = ΔH − T·ΔS
with: - ΔH: enthalpy change (J), i.e. heat exchanged. - ΔS: entropy change (J/K), a measure of microstate disorder. - T: absolute temperature (K).
Spontaneity criterion
The second law of thermodynamics applied to a system at constant T, P gives:
- ΔG < 0: the transformation is spontaneous (proceeds in the written direction).
- ΔG > 0: the transformation is not spontaneous (the reverse is).
- ΔG = 0: the system is at equilibrium.
ΔG < 0 does not mean "fast": only thermodynamically allowed. Kinetics can prevent progress (diamond is unstable vs graphite at 25 °C but does not transform within twenty human lifetimes).
Reading the two contributions
ΔH < 0: exothermic reaction, energetically favorable. ΔH > 0: endothermic reaction, energetically unfavorable.
ΔS > 0: disorder produced, favorable. ΔS < 0: ordering, unfavorable.
Four possibilities:
| ΔH | ΔS | Behavior |
|---|---|---|
| < 0 | > 0 | Spontaneous at all T |
| > 0 | < 0 | Never spontaneous |
| < 0 | < 0 | Spontaneous at low T |
| > 0 | > 0 | Spontaneous at high T |
This is how we rationalize why ice melting (ΔH > 0, ΔS > 0) is spontaneous above 0 °C but not below: below, T·ΔS no longer compensates ΔH.
Link to the equilibrium constant
At chemical equilibrium, ΔG = 0 and the composition is set by the thermodynamic constant K:
ΔG° = −R·T·ln(K)
with ΔG° the standard free energy and R the ideal gas constant. Consequences:
- K >> 1 ⟺ ΔG° << 0 ⟺ products favored.
- K << 1 ⟺ ΔG° >> 0 ⟺ reactants favored.
Out of equilibrium, ΔG relates to the reaction quotient Q:
ΔG = ΔG° + R·T·ln(Q)
Coupling reactions
A non-spontaneous reaction (ΔG > 0) can be driven by coupling it to a strongly exergonic one. This is the ATP principle in biochemistry: ATP hydrolysis (ΔG° ≈ −30 kJ/mol) powers endergonic reactions essential to life (peptide synthesis, active transport).
Bottom line
ΔG is the only valid spontaneity criterion at constant T, P. It combines enthalpy and entropy, and explains why some reactions are impossible at 25 °C but feasible at 1000 °C, or why life can locally reduce entropy by increasing that of its surroundings (the universe always heads toward more disorder).