Question

The value of $\Delta G^\circ $ for the following equation at $300K$ temperature is $-xkJmol^{- 1}$ .
$A_{\left(g\right)}+B_{\left(g\right)}\rightleftharpoons\left(AB\right)_{\left(g\right)}$ .
If the $E_{a}$ of the backward reaction minus that of the forward reaction is equal to $2RT$ (in $Jmol^{- 1}$ ) and the pre-exponential factor for the forward reaction is $4$ times of that for the reverse reaction.
Find the value of $10x$ (nearest integer).
(Given, $ln \left(2\right)= \, 0.7,RT= \, 2500 \, J \, \left(mol\right)^{- 1} \, at \, 300 \, K$ and G is the Gibbs energy)

Answer 1

$A_{\left(g\right)}+B_{\left(g\right)}\rightleftharpoons\left(AB\right)_{\left(g\right)}$
$E_{ab}-E_{af}=2RT \, and\frac{A_{f}}{A_{b}}=4$
$K_{eq}=\left(\frac{K_{f}}{K_{b}}\right)=\frac{A_{f \, } e^{- E_{af} / RT}}{A_{b} e^{- E_{ab} / RT}}=4e^{2}$
$\Delta G^{o}=-RTln K=-2500\times ln⁡\left(4 \times e^{2}\right)=-8500J/mol$
$\therefore \, \, $ Absolute value of $\Delta G^{o}=-8500J/mol$