# Gibbs free energy

**Gibbs free energy** (also called Gibbs energy or free enthalpy, symbol G) is a thermodynamic state function defined as enthalpy minus the product of thermodynamic temperature and entropy, G = H − TS. It was formerly called free energy or free enthalpy, and it is named for [Josiah Willard Gibbs](https://www.edgepedia.org/josiah-willard-gibbs), the scientist who developed the measurement.<sup>[1](https://goldbook.iupac.org/terms/view/G02629/pdf)</sup><sup> • </sup><sup>[2](https://openstax.org/books/biology/pages/6-2-potential-kinetic-free-and-activation-energy)</sup> At constant temperature and pressure, the change in G determines whether a process is spontaneous, how far it is from equilibrium, and how much non-expansion work it can deliver.<sup>[3](https://openstax.org/books/chemistry-2e/pages/16-4-free-energy)</sup>

| Key fact | Detail |
|---|---|
| Definition | G = H − TS, enthalpy minus the product of thermodynamic temperature and entropy; formerly called free energy or free enthalpy<sup>[1](https://goldbook.iupac.org/terms/view/G02629/pdf)</sup> |
| Natural variables | Temperature and pressure, G(T, P); G is a Legendre transform of enthalpy<sup>[4](https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Free_Energy_1e_%28Snee%29/05%3A_Helmholtz_and_Gibbs_Energy/5.02%3A_Gibbs_Energy)</sup> |
| Spontaneity criterion | At constant T and P, ΔG < 0 for a spontaneous process and ΔG = 0 at equilibrium<sup>[3](https://openstax.org/books/chemistry-2e/pages/16-4-free-energy)</sup> |
| Work interpretation | At constant T and P, the maximum non-expansion (non-pV) work obtainable from the system is −ΔG<sup>[5](https://faculty.ksu.edu.sa/sites/default/files/Second%20%26%20third%20laws%20with%20exo%20%26%20answers%20-%20Physical%20Chemistry%209ed.pdf)</sup><sup> • </sup><sup>[16](https://chem.libretexts.org/Courses/University_of_Georgia/CHEM_3212%3A_Physical_Chemistry_II/08%3A_Gibbs_and_Helmholtz_Energies/8.03%3A_%CE%94A%2C_%CE%94G%2C_and_Maximum_Work)</sup><sup> • </sup><sup>[17](https://farside.ph.utexas.edu/teaching/sm1/Thermalhtml/node117.html)</sup> |
| Equilibrium link | ΔG° = −RT ln K, with R = 8.314 J/(K·mol)<sup>[6](https://openstax.org/books/organic-chemistry/pages/6-7-describing-a-reaction-equilibria-rates-and-energy-changes)</sup> |
| Chemical potential | μ_B = (∂G/∂n_B) at constant T, p, and other amounts; for a pure substance μ_B* = G_m*, the molar Gibbs energy<sup>[7](https://goldbook.iupac.org/terms/view/C01032/html)</sup> |

## Definition and spontaneity

The Gibbs energy combines the two tendencies that govern spontaneous change: a fall in enthalpy and a rise in entropy. For a change at constant temperature and pressure,

\[ \Delta G = \Delta H - T\Delta S \]

where ΔH is the enthalpy change, ΔS the entropy change of the system, and T the absolute temperature in kelvin.<sup>[2](https://openstax.org/books/biology/pages/6-2-potential-kinetic-free-and-activation-energy)</sup> This criterion is a rearrangement of the second law: the entropy change of the surroundings at constant pressure is −ΔH/T, so a negative ΔG corresponds to a positive total entropy change for system plus surroundings.<sup>[8](https://chirp1.chem.ubc.ca/part-1-thermodynamics/section-4-gibbs-free-energy/4-1-defining-gibbs-free-energy/)</sup>

The signs of ΔH and ΔS fix the temperature dependence of spontaneity:<sup>[9](https://openstax.org/books/chemistry-atoms-first-2e/pages/13-introduction)</sup>

- ΔH negative, ΔS positive: spontaneous at all temperatures.
- ΔH positive, ΔS negative: never spontaneous.
- ΔH positive, ΔS positive: spontaneous at high temperatures.
- ΔH negative, ΔS negative: spontaneous at low temperatures.

Only in the last two cases does the process pass through a temperature at which ΔG = 0, given by T = ΔH/ΔS when ΔH and ΔS are approximately temperature independent.<sup>[9](https://openstax.org/books/chemistry-atoms-first-2e/pages/13-introduction)</sup>

## Maximum non-expansion work

At constant temperature and pressure, the decrease in Gibbs energy equals the maximum non-expansion work the system can deliver, sometimes called useful work. Expansion work against the atmosphere is excluded because the process is held at constant pressure.<sup>[5](https://faculty.ksu.edu.sa/sites/default/files/Second%20%26%20third%20laws%20with%20exo%20%26%20answers%20-%20Physical%20Chemistry%209ed.pdf)</sup> The maximum is obtained only for a reversible transformation; in an irreversible process, less of the available energy goes into work and more into internal energy.<sup>[10](https://theory.physics.manchester.ac.uk/~judith/stat_therm/node10.html)</sup> This interpretation is why G is preferred over the Helmholtz energy in chemistry: laboratory and industrial chemistry usually happen at constant pressure rather than constant volume.<sup>[5](https://faculty.ksu.edu.sa/sites/default/files/Second%20%26%20third%20laws%20with%20exo%20%26%20answers%20-%20Physical%20Chemistry%209ed.pdf)</sup>

## Chemical potential and mixtures

For a mixture, the chemical potential of a substance B is the partial molar Gibbs energy,

\[ \mu_{\mathrm{B}} = \left( \frac{\partial G}{\partial n_{\mathrm{B}}} \right)_{T,\,p,\,n_{\mathrm{C} \neq \mathrm{B}}} \]

For a pure substance the chemical potential equals the molar Gibbs energy, μ_B* = G_m*.<sup>[7](https://goldbook.iupac.org/terms/view/C01032/html)</sup> The total Gibbs energy of a mixture is the sum of n_i μ_i over its components, and at constant temperature and pressure the chemical potentials obey the Gibbs-Duhem constraint, Σ_i n_i dμ_i = 0, so the potentials of the components cannot change independently.<sup>[11](https://chem.libretexts.org/Courses/Stanford_Online_High_School/ChemTEN_S1/06%3A_SPONTANEITY/6.02%3A_The_Gibbs-Duhem_Equation)</sup>

[Chemical potential](https://www.edgepedia.org/chemical-potential) also supplies the equilibrium condition for phases: material moves between phases until the chemical potential of each species is the same in every phase present. Counting the resulting constraints gives Gibbs' phase rule, F = 2 + C − P, for the degrees of freedom of a system with C components and P phases; for a single component at most three phases can coexist at equilibrium.<sup>[12](https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_%28Fleming%29/08%3A_Phase_Equilibrium/8.03%3A_Criterion_for_Phase_Equilibrium)</sup>

## Free energy and equilibrium

For a reaction under arbitrary conditions, the free energy change is related to the standard value through the reaction quotient Q:

\[ \Delta G = \Delta G^{\circ} + RT \ln Q \]

where R is the gas constant, 8.314 J/(K·mol).<sup>[3](https://openstax.org/books/chemistry-2e/pages/16-4-free-energy)</sup> As the reaction proceeds, Q moves toward the equilibrium constant K, at which point ΔG = 0 and the relation reduces to

\[ \Delta G^{\circ} = -RT \ln K \]

so the standard free energy change fixes the equilibrium position.<sup>[3](https://openstax.org/books/chemistry-2e/pages/16-4-free-energy)</sup> A large negative ΔG° corresponds to a large K; for example, a reaction with K_eq = 7.1 × 10⁷ has ΔG° = −44.8 kJ/mol at 298 K.<sup>[6](https://openstax.org/books/organic-chemistry/pages/6-7-describing-a-reaction-equilibria-rates-and-energy-changes)</sup> In electrochemistry the same quantity links to cell voltage through ΔG° = −nFE°_cell.<sup>[13](https://openstax.org/books/chemistry-atoms-first-2e/pages/16-4-potential-free-energy-and-equilibrium)</sup>

For biological reactions a modified standard state is used: ΔG°′ refers to a reaction at pH 7.0 with solute concentrations of 1.0 M, because cellular conditions differ considerably from the usual chemical standard state.<sup>[6](https://openstax.org/books/organic-chemistry/pages/6-7-describing-a-reaction-equilibria-rates-and-energy-changes)</sup>

## Structure of the potential

Gibbs energy is one of the family of thermodynamic potentials obtained by Legendre transforms of the internal energy U. A Legendre transform exchanges a natural variable for its conjugate derivative without losing information; transforming away both S and V yields G = U + PV − TS = H − TS, whose natural variables are temperature and pressure.<sup>[4](https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Free_Energy_1e_%28Snee%29/05%3A_Helmholtz_and_Gibbs_Energy/5.02%3A_Gibbs_Energy)</sup> The differential form is

\[ dG = V\,dp - S\,dT + \sum_i \mu_i\,dn_i \]

which shows why G is minimized at equilibrium for systems held at constant T and p, and why the Helmholtz energy F = U − TS, with natural variables T and V, is the corresponding potential for constant-volume systems.<sup>[11](https://chem.libretexts.org/Courses/Stanford_Online_High_School/ChemTEN_S1/06%3A_SPONTANEITY/6.02%3A_The_Gibbs-Duhem_Equation)</sup><sup> • </sup><sup>[14](https://notes.amittai.studio/statistical-mechanics/thermodynamics/thermodynamic-potentials-and-maxwell-relations)</sup> When a species' chemical potential is held fixed, a further Legendre transform defines a transformed Gibbs energy that is minimized at equilibrium under that constraint, a device used in biochemical thermodynamics.<sup>[15](https://www.nist.gov/publications/use-legendre-transforms-chemical-thermodynamics)</sup>

## References

1. [IUPAC Gold Book: Gibbs energy (function), G](https://goldbook.iupac.org/terms/view/G02629/pdf)
2. [OpenStax Biology 6.2: Potential, Kinetic, Free, and Activation Energy](https://openstax.org/books/biology/pages/6-2-potential-kinetic-free-and-activation-energy)
3. [OpenStax Chemistry 2e 16.4: Free Energy](https://openstax.org/books/chemistry-2e/pages/16-4-free-energy)
4. [Chemistry LibreTexts (Snee): 5.2 Gibbs Energy](https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Free_Energy_1e_%28Snee%29/05%3A_Helmholtz_and_Gibbs_Energy/5.02%3A_Gibbs_Energy)
5. [Physical Chemistry 9ed, Second and Third Laws (course text)](https://faculty.ksu.edu.sa/sites/default/files/Second%20%26%20third%20laws%20with%20exo%20%26%20answers%20-%20Physical%20Chemistry%209ed.pdf)
6. [OpenStax Organic Chemistry 6.7: Equilibria, Rates, and Energy Changes](https://openstax.org/books/organic-chemistry/pages/6-7-describing-a-reaction-equilibria-rates-and-energy-changes)
7. [IUPAC Gold Book: chemical potential (C01032)](https://goldbook.iupac.org/terms/view/C01032/html)
8. [UBC ChIRP: 4.1 Defining Gibbs free energy](https://chirp1.chem.ubc.ca/part-1-thermodynamics/section-4-gibbs-free-energy/4-1-defining-gibbs-free-energy/)
9. [OpenStax Chemistry: Atoms First 2e, Ch. 13 Introduction](https://openstax.org/books/chemistry-atoms-first-2e/pages/13-introduction)
10. [University of Manchester: Work during free and reversible expansions](https://theory.physics.manchester.ac.uk/~judith/stat_therm/node10.html)
11. [Chemistry LibreTexts: 6.2 The Gibbs-Duhem Equation](https://chem.libretexts.org/Courses/Stanford_Online_High_School/ChemTEN_S1/06%3A_SPONTANEITY/6.02%3A_The_Gibbs-Duhem_Equation)
12. [Chemistry LibreTexts (Fleming): 8.3 Criterion for Phase Equilibrium](https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_%28Fleming%29/08%3A_Phase_Equilibrium/8.03%3A_Criterion_for_Phase_Equilibrium)
13. [OpenStax Chemistry: Atoms First 2e 16.4: Potential, Free Energy, and Equilibrium](https://openstax.org/books/chemistry-atoms-first-2e/pages/16-4-potential-free-energy-and-equilibrium)
14. [Thermodynamic Potentials and Maxwell Relations (study notes)](https://notes.amittai.studio/statistical-mechanics/thermodynamics/thermodynamic-potentials-and-maxwell-relations)
15. [NIST: Use of Legendre Transforms in Chemical Thermodynamics](https://www.nist.gov/publications/use-legendre-transforms-chemical-thermodynamics)
16. [8.3: ΔA, ΔG, and Maximum Work](https://chem.libretexts.org/Courses/University_of_Georgia/CHEM_3212%3A_Physical_Chemistry_II/08%3A_Gibbs_and_Helmholtz_Energies/8.03%3A_%CE%94A%2C_%CE%94G%2C_and_Maximum_Work)
17. [Equilibrium of Constant-Temperature Constant-Pressure System](https://farside.ph.utexas.edu/teaching/sm1/Thermalhtml/node117.html)

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*Topic: Encyclopedia › Physical world and mathematics › Physics › Classical physics › Thermodynamics › Laws, states, and potentials › Thermodynamic potentials and free energy › Gibbs free energy › Chemical potential and the Gibbs function*

*Initially written Sep 17, 2026 · Reviewed: Sep 30, 2026; Oct 15, 2026 · Edited: Sep 30, 2026; Oct 15, 2026 · Last review: Oct 15, 2026*

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