Relationship between ΔG0 and Keq

In a reversible chemical equilibrium, the system stays in perfect equilibrium with its surroundings at every instant, and the reaction can proceed in both the forward and reverse directions SIMULTANEOUSLY, so that a dynamic equilibrium is set up. For both directions to keep proceeding with a decrease in free energy (as spontaneity would seem to demand) is only possible if, right AT equilibrium, the system's free energy sits at a genuine MINIMUM.

For a general equilibrium reaction $A+B\rightleftharpoons C+D$, the free energy change in any (non-equilibrium) state, $\Delta G$, is related to the standard free energy change, $\Delta G^0$, by:

where $Q$ is the reaction quotient -- the ratio of product concentrations to reactant concentrations under whatever (non-equilibrium) conditions currently apply.

When the system reaches equilibrium, there is no further free energy change ($\Delta G=0$), and $Q$ becomes equal to the equilibrium constant $K_{eq}$. Equation (7.39) then reduces to:

known as the Van't Hoff equation, more commonly written using base-10 logarithms as:

We also know from (7.36) that $\Delta G^0=\Delta H^0-T\Delta S^0$, so all three quantities are linked: $\Delta G^0=\Delta H^0-T\Delta S^0=-RT\ln K_{eq}$. …