Gibbs Free Energy
The Gibbs free energy is the thermodynamic potential G = H − TS = U + pV − TS. At constant temperature and pressure, a process is spontaneous only if ΔG < 0, equilibrium corresponds to a minimum of G, and −ΔG equals the maximum work available other than expansion work, such as electrical work in a battery or fuel cell (ΔG = −nFE).
Curious
Will ice melt? Will salt dissolve? Will a reaction go? At constant temperature and pressure, the answer depends on a balance between enthalpy (energy released or absorbed; see Enthalpy) and entropy (spreading out of energy; see Entropy), weighted by temperature. Gibbs free energy packages both: ΔG = ΔH − TΔS. Negative ΔG means the process is spontaneous.
Spontaneous does not mean fast. Diamond turning into graphite at room conditions has negative ΔG, but it is so slow that diamonds last for billions of years. Thermodynamics says what can happen; kinetics says how fast.
Exploring
| ΔH | ΔS | Spontaneous? |
|---|---|---|
| Negative | Positive | At all temperatures |
| Positive | Negative | Never (reverse is spontaneous) |
| Negative | Negative | Below T = ΔH/ΔS |
| Positive | Positive | Above T = ΔH/ΔS (e.g. melting) |
Deep Dive
Chemical potential. dG = −S dT + V dp + ΣμidNi, so the chemical potential μi = (∂G/∂Ni)T,p is the Gibbs energy per particle of species i. At equilibrium, the chemical potential of each species is equal in all phases, which gives the conditions for phase coexistence and the Clausius–Clapeyron relation (see Latent Heat), and ΔG° = −RT ln K gives the equilibrium constant of a reaction (see Josiah Willard Gibbs).
Electrochemistry and biology. The Nernst equation, E = E° − (RT/nF) ln Q, follows directly from ΔG = −nFE (see Walther Nernst). Living cells couple unfavourable reactions to favourable ones, notably ATP hydrolysis, whose ΔG under cellular conditions is roughly −50 to −60 kJ/mol, more negative than its standard value of about −30.5 kJ/mol.
Phase stability. The phase with the lowest G at given T and p is the stable one; metastable phases (supercooled water, diamond) persist because transformation requires overcoming a free-energy barrier, as described by nucleation theory. Phase diagrams are maps of which phase minimises G.
Concept Relationship Map
Requires: enthalpy, entropy, Helmholtz free energy
Enables: chemical equilibrium, phase diagrams, electrochemistry
Commonly confused with: reaction rate (kinetics)
Sources
- Gibbs, J.W. (1876, 1878). Transactions of the Connecticut Academy, 3, 108–248, 343–524.
- Atkins, P., de Paula, J. (2014). Atkins' Physical Chemistry (10th ed.). Oxford University Press.
- Callen, H.B. (1985). Thermodynamics and an Introduction to Thermostatistics (2nd ed.). Wiley.