The correct relationship between standard free energy change in a reaction and the corresponding equilibrium constant K is

A mathematical expression of the thermodynamic view of equilibrium can be described by :

$∆\mathrm{G}=∆{\mathrm{G}}^{\mathrm{o}}+\mathrm{RTlnK}$

At equilibrium, $∆\mathrm{G}=0$

$\therefore ∆{\mathrm{G}}^{\mathrm{o}}=-\mathrm{RTlnK}$

$∆{\mathrm{G}}^{\mathrm{o}}=-2.303\mathrm{RTlogK}$
Where $∆{\mathrm{G}}^{\mathrm{o}}$ is standard Gibbs energy change.