JEE Chemistry Practice Question

Consider the following reversible reaction, \[ \mathrm{A}(\mathrm{g})+\mathrm{B}(\mathrm{g}) \rightleftharpoons \mathrm{AB}(\mathrm{g}) \] The activation energy of the backward reaction exceeds that of the forward reaction by $2 R T$ (in $\mathrm{J} \mathrm{mol}^{-1}$ ). If the pre-exponential factor of the forward reaction is 4 times that of the reverse reaction, what is the absolute value of $\Delta G^{\theta}$ (in $\mathrm{J} \mathrm{mol}^{-1}$ ) for the reaction at $300 \mathrm{~K}$? (Given; $\ln (2)=0.7, R T=2500 \mathrm{~J} \mathrm{~mol}^{-1}$ at $300 \mathrm{~K}$ and $G$ is the Gibbs energy)