For a reversible process in a state of equilibrium, the change in Gibbs free energy ($\Delta G$) is zero. The mathematical relationship between the standard Gibbs free energy change ($\Delta G^\circ$) and the equilibrium constant ($K$) is given by the equation: $\Delta G^\circ = -RT \ln K$. When converting the natural logarithm ($\ln$) to the base-10 logarithm ($\log$), we multiply by $2.303$. Therefore, the equation becomes $\Delta G^\circ = -2.303 RT \log K \approx -2.30 RT \log K$.