Q.Find out the value of equilibrium constant for the following reaction at 298K, $2NH_3(g) + CO_2(g) \rightleftharpoons NH_2CONH_2(aq) + H_2O(l)$. Standard Gibbs energy change, $\Delta G_r^0$ at the given temperature is $-13.6$ kJ mol$^{-1}$.

At true chemical equilibrium, a reversible reaction proceeds in both directions simultaneously, which is only possible if the system's free energy sits at a genuine MINIMUM there. For a general equilibrium $A+B\rightleftharpoons C+D$, the free energy at any (non-equilibrium) point relates to the standard free energy by $\Delta G=\Delta G^0+RT\ln Q$ ($Q$ = reaction quotient). At equilibrium, $\Delta G=0$ and $Q\rightarrow K_{eq}$, collapsing this to the Van't Hoff equation:

$\Delta G^0=-RT\ln K_{eq}=-2.303RT\log K_{eq}$ …