Question

The value of $\Delta G^{\circ }$ for the following equation at $300K$ temperature is $-xkJmo{l}^{-1}$ .
$A_{\left(g\right)}+B_{\left(g\right)}\rightleftharpoons {\left(AB\right)}_{\left(g\right)}$ .
If the $E_a$ of the backward reaction minus that of the forward reaction is equal to $2RT$ (in $Jmo{l}^{-1}$ ) 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, $ln\left(2\right)=0.7,RT=2500J{\left(mol\right)}^{-1}at300K$ and G is the Gibbs energy)

Answer 1

Answer: 85

$A_{\left(g\right)}+B_{\left(g\right)}\rightleftharpoons {\left(AB\right)}_{\left(g\right)}$
$E_{ab}-E_{af}=2RTand\frac{A_f}{A_b}=4$
$K_{eq}=\left(\frac{K_f}{K_b}\right)=\frac{A_f{e}^{-E_{af}/RT}}{A_b{e}^{-E_{ab}/RT}}=4e^2$
$\Delta G^o=-RTlnK=-2500\times ln\left(4\times e^2\right)=-8500J/mol$
$\therefore$ Absolute value of $\Delta G^o=-8500J/mol$