When every reactant and product is in its defined standard state, a reaction has a standard Gibbs free energy change, written $\Delta G_{\mathrm{rxn}}^\circ$.

At a specified temperature,

$$\boxed{\Delta G_{\mathrm{rxn}}^\circ =\Delta H_{\mathrm{rxn}}^\circ-T\Delta S_{\mathrm{rxn}}^\circ}.$$

All terms must use compatible units. If enthalpy is in $\mathrm{kJ/mol}$ and entropy in $\mathrm{J,mol^{-1},K^{-1}}$, convert one before subtracting $T\Delta S$.

Example from enthalpy and entropy data

Suppose at $298,\mathrm K$ a reaction has

$$\Delta H^\circ=-92.2,\mathrm{kJ/mol},$$

$$\Delta S^\circ=-198,\mathrm{J,mol^{-1},K^{-1}} =-0.198,\mathrm{kJ,mol^{-1},K^{-1}}.$$

Then

$$\begin{aligned} \Delta G^\circ &=-92.2-(298)(-0.198)\ &\approx-33.2,\mathrm{kJ/mol}. \end{aligned}$$

The negative value means the standard-state reaction direction is thermodynamically favorable at this temperature.

Standard Gibbs energies of formation

A standard Gibbs energy of formation, $\Delta G_f^\circ$, is the standard Gibbs free energy change for forming one mole of a substance from its constituent elements in their reference forms. As with standard formation enthalpies, an element in its reference form is assigned

$$\Delta G_f^\circ=0.$$

Reaction values can therefore be calculated directly from tabulated formation data:

$$\boxed{\Delta G_{\mathrm{rxn}}^\circ =\sum_{\mathrm{products}}\nu_i\Delta G_{f,i}^\circ -\sum_{\mathrm{reactants}}\nu_i\Delta G_{f,i}^\circ}.$$

For methane combustion,

$$\mathrm{CH_4(g)+2O_2(g)\rightarrow CO_2(g)+2H_2O(l)},$$

use approximate values

$$\Delta G_f^\circ(\mathrm{CH_4})=-50.8,\mathrm{kJ/mol},$$ $$\Delta G_f^\circ(\mathrm{CO_2})=-394.4,\mathrm{kJ/mol},$$ $$\Delta G_f^\circ(\mathrm{H_2O(l)})=-237.1,\mathrm{kJ/mol},$$

with $\Delta G_f^\circ(\mathrm{O_2})=0$. Then

$$\begin{aligned} \Delta G_{\mathrm{rxn}}^\circ &=[-394.4+2(-237.1)]-[-50.8]\ &\approx-817.8,\mathrm{kJ/mol}. \end{aligned}$$

The two methods are consistent: $\Delta H^\circ-T\Delta S^\circ$ builds the free-energy change from enthalpy and entropy, while $\Delta G_f^\circ$ tables package that thermodynamic information into a common reference.

A standard free-energy change describes a reaction whose species are in their standard states. It is not automatically the free-energy change in an arbitrary reaction mixture; composition modifies the driving force away from standard state.