Consider the following reversible reaction, $$A\left( g \right) + B\left( g \right) \to AB\left( g \right).$$ The activation energy of the backward reaction exceeds that of the forward reaction by $2RT$(in $J\,mo{l^{ - 1}}$). If the pre-exponential factor of the forward reaction is $4$ times that of the reverse reaction, the absolute value of $\Delta {G^ \circ }$(in $J\,mo{l^{ - 1}}$) for the reaction at $300K$ is $\underline{\hspace{2cm}}$. (Given; $$\ln \left( 2 \right) = 0.7,RT = 2500$$ $J\,mo{l^{ - 1}}$ at $300K$ and $G$ is the Gibbs energy)