= Thermochemical equilibrium
{title2=$\Delta_rG=0,\quad Q=K$}
At fixed <temperature> and <pressure>, an interior reacting equilibrium minimizes <Gibbs free energy> under the constraints imposed by <stoichiometry>. Each independent reversible reaction then has zero actual <Gibbs energy of reaction>,
$$
\Delta_rG=\sum_i\nu_i\mu_i=0.
$$
This is not a requirement that the <standard Gibbs energy of reaction> vanish.
Using dimensionless <thermodynamic activities> $a_i$, define the <reaction quotient> $Q=\prod_i a_i^{\nu_i}$. The relation
$$
\Delta_rG=\Delta_rG^\circ+RT\ln Q
$$
therefore gives
$$
Q_{\rm eq}=K=\exp\!\left(-\frac{\Delta_rG^\circ}{RT}\right).
$$
The <equilibrium constant> $K$ is dimensionless because each activity is measured relative to its declared <standard state>. In general $K\ne1$ even though the actual equilibrium <Gibbs energy of reaction> is zero. <Chemistry 2e by Paul Flowers and others/16.4 Free Energy>[Free Energy and Equilibrium, actual versus standard reaction free energy and Q=K]{ref}
These equations determine an equilibrium composition within the model. They do not supply the <reaction rate> or guarantee rapid equilibration; that requires the <chemical kinetics>.
Back to article page
