Classical thermodynamics, heat transfer Definition

Chemical equilibrium

Builds on Chemical potential Gibbs free energy Thermodynamic equilibrium

Definition

Consider a closed system at fixed temperature $T$ and pressure $p$ containing species $A_1, \dots, A_k$ that can take part in a reaction $\sum_{i=1}^k \nu_i A_i = 0$ . Here $\nu_i$ is the stoichiometric coefficient of $A_i$ , positive for products and negative for reactants. The amounts change as $dn_i = \nu_i\, d\xi$ , where $\xi$ is the extent of reaction. Let $\mu_i$ be the chemical potential of $A_i$ and $G$ the Gibbs free energy of the system. The system is in chemical equilibrium if $G$ , as a function of $\xi$ at fixed $T$ and $p$ , is at its minimum. When this minimum lies in the interior of the allowed range of $\xi$ , the condition is $\left(\frac{\partial G}{\partial \xi}\right)_{T, p} = \sum_{i=1}^k \nu_i \mu_i = 0.$

Remarks

For $\mathrm{N_2} + 3\,\mathrm{H_2} \rightleftharpoons 2\,\mathrm{NH_3}$ , the coefficients are $\nu = (-1, -3, 2)$ , and equilibrium means $2\mu_{\mathrm{NH_3}} = \mu_{\mathrm{N_2}} + 3\mu_{\mathrm{H_2}}$ . A non-example: a mixture of hydrogen and oxygen at room temperature does not change in practice. But $2\mu_{\mathrm{H_2O}} - 2\mu_{\mathrm{H_2}} - \mu_{\mathrm{O_2}}$ is strongly negative, so $G$ is not minimal. The mixture is only kinetically stable, not in chemical equilibrium. With several independent reactions there is one such condition for each reaction. The quantity $\sum_i \nu_i \mu_i$ is the reaction Gibbs energy $\Delta_r G$ ; its negative is called the affinity. Chemical equilibrium is part of thermodynamic equilibrium, together with thermal and mechanical equilibrium.

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Tag	`N7GF31958G`
URI	`m2://N7GF31958G`
Kind	definition
Writing	W0 stub
MSC	80A50, 80A10, 92E20
Defines	Chemical equilibrium
Uses	Chemical potential, Gibbs free energy, Thermodynamic equilibrium
Changed	3 November 2026

Chemical equilibrium

Definition

Remarks

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