Criteria for Equilibrium

Equilibrium, viewed through the lens of Gibbs free energy, is not a state in which nothing is happening — it is the specific point at which the system's free energy has reached its lowest possible value under the prevailing conditions, and can decrease no further in either direction.

As a reaction proceeds from pure reactants toward products, its Gibbs free energy generally falls, since the reaction is spontaneous ($\Delta G < 0$) in the forward direction. It does not, however, fall indefinitely all the way to pure products; instead, $G$ typically passes through a minimum at some intermediate mixture of reactants and products, then begins to rise again if the reaction is pushed further toward completion. The equilibrium composition of the reaction mixture is exactly the composition at that minimum-$G$ point — any further change in composition, in either direction (more product formation, or reactants re-forming from product), would actually increase $G$, and since a spontaneous process must have $\Delta G < 0$, neither further change occurs spontaneously. At this minimum, the instantaneous free-energy change is zero:

Substituting this condition into $\Delta G = \Delta H - T\Delta S$ gives a further useful relation that holds specifically at equilibrium:

$\Delta H = T\Delta S \quad \text{i.e.} \quad T_{eq} = \frac{\Delta H}{\Delta S}$ …