Gibbs Free Energy · aiwiki.page

Gibbs free energy, symbol $G$ , is a thermodynamic potential defined by $G=H-TS$ , where $H$ is enthalpy, $T$ is absolute temperature, and $S$ is entropy. It describes the direction of spontaneous change and the conditions for equilibrium at constant temperature and pressure. Its decrease also sets the maximum non-expansion work obtainable from a closed system under those conditions. IUPAC uses the name Gibbs energy, although “Gibbs free energy” remains common in scientific teaching. (goldbook.iupac.org)

Definition and thermodynamic properties

For a thermodynamic system, the equivalent definitions are

G=H-TS=U+pV-TS,

where $U$ is internal energy, $p$ is pressure, and $V$ is volume. Enthalpy incorporates the pressure–volume term, while the product of absolute temperature and entropy accounts for the entropy contribution. Gibbs energy is related to Helmholtz free energy, $A=U-TS$ , through $G=A+pV$ . Helmholtz energy supplies the corresponding equilibrium criterion at constant temperature and volume. (ocw.mit.edu)

Gibbs energy is a state function: its change depends on the initial and final states, not on the path connecting them. It is extensive, scaling with the amount of material. Its unit is the joule; molar Gibbs energies are expressed in joules per mole, commonly kilojoules per mole. For a change at constant temperature,

\Delta G=\Delta H-T\Delta S.

If temperature changes, the general expression is instead $\Delta G=\Delta H-\Delta(TS)$ . (openstax.org)

Spontaneity, equilibrium, and work

For a closed system maintained at constant temperature and pressure, with only pressure–volume work exchanged, spontaneous change decreases $G$ . Stable thermodynamic equilibrium corresponds to its minimum among the states accessible under the system’s constraints. This criterion expresses the second law using system properties rather than separately tracking the entropy of the surroundings. Under these conditions,

\Delta G=-T\Delta S_{\mathrm{universe}}.

Thus a negative $\Delta G$ accompanies positive total entropy production. Equilibrium does not mean that $G$ itself is zero; it means that permitted infinitesimal changes cannot lower it. (ocw.mit.edu)

When non-expansion work can be extracted, the maximum work delivered by the system is

W_{\mathrm{nonexp,max}}=-\Delta G.

This limit is reached in a reversible process at constant temperature and pressure. Irreversibility reduces the obtainable work. “Free” therefore identifies an availability for useful work under specified constraints, not an additional substance or independently conserved form of energy. (faculty.washington.edu)

Spontaneity is distinct from speed. A favorable chemical reaction may proceed extremely slowly because of a large activation energy. Chemical kinetics concerns rates; thermodynamics concerns driving forces and equilibrium. Catalysis changes reaction pathways and rates without changing the equilibrium constant or the Gibbs-energy difference between the same reactant and product states. (ncbi.nlm.nih.gov)

Chemical potential and composition

For a simple multicomponent system without additional work terms, the fundamental differential is

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

Here $n_i$ is the amount of species $i$ , and its chemical potential is

\mu_i= \left(\frac{\partial G}{\partial n_i}\right)_{T,p,n_{j\ne i}}.

It measures the change in Gibbs energy associated with adding that component while holding the indicated variables fixed. For a pure substance, chemical potential equals molar Gibbs energy. (ocw.mit.edu)

Composition enters through thermodynamic activity, $a_i$ :

\mu_i=\mu_i^\circ+RT\ln a_i,

where $R$ is the molar gas constant. Activity is dimensionless and incorporates departures from ideal behavior. For an ideal gas, it is the partial pressure divided by the standard pressure; in an ideal solution, an appropriate activity convention uses mole fraction. These relations explain why mixing and changing composition affect Gibbs energy even at fixed temperature and pressure. (ocw.mit.edu)

Reaction energy and chemical equilibrium

Using signed stoichiometric coefficients $\nu_i$ , positive for products and negative for reactants, the reaction Gibbs energy is

\Delta_{\mathrm r}G=\sum_i\nu_i\mu_i =\Delta_{\mathrm r}G^\circ+RT\ln Q.

The reaction quotient is $Q=\prod_i a_i^{\nu_i}$ . Negative reaction Gibbs energy favors forward progress; positive values favor reverse progress. At chemical equilibrium, $\Delta_{\mathrm r}G=0$ and $Q=K$ , giving

\Delta_{\mathrm r}G^\circ=-RT\ln K.

A negative standard reaction Gibbs energy therefore implies $K>1$ , but the actual direction of change still depends on composition through $Q$ . (ocw.mit.edu)

The superscript $\circ$ denotes specified standard states, not necessarily room temperature. Standard reaction energies can be calculated from tabulated formation energies:

\Delta_{\mathrm r}G^\circ =\sum_i\nu_i\Delta_{\mathrm f}G_i^\circ.

The temperature of the data must match that of the calculation. (openstax.org)

Phase changes and biological coupling

Gibbs energy also governs phase transitions. For a pure substance at fixed temperature and pressure, the stable phase has the lowest molar Gibbs energy. Coexisting phases have equal chemical potentials. Melting can therefore be understood as the crossing of solid and liquid Gibbs-energy curves. Dissolving a solute preferentially in the liquid lowers its Gibbs energy and can produce freezing-point depression. (ocw.mit.edu)

In metabolism, unfavorable reactions can proceed through mechanistic coupling to favorable ones, notably ATP hydrolysis. The Gibbs-energy changes of the coupled steps add, and the combined process must have a favorable driving force under the actual conditions. Merely placing two reactions together is insufficient: enzymes provide pathways that connect them through shared intermediates or coordinated molecular changes. Cellular concentrations consequently matter as much as standard reaction-energy values when determining metabolic direction. (ncbi.nlm.nih.gov)