1. Tardigrade
  2. Question
  3. Chemistry
  4. Consider the following reversible reaction, A(g) + B(g) leftharpoons AB(g). The activation energy of the backward reaction exceeds that of the forward reaction by 2RT (in J mol−1). If the pre-exponential factor of the forward reaction is 4 times that of the reverse reaction, the absolute value of ΔGƟ (in J mol−1) for the reaction at 300 K is . (Given; ln(2) = 0.7, RT = 2500 J mol−1 at 300 K and G is the Gibbs energy)

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Q. Consider the following reversible reaction,
$A\left(g\right) + B\left(g\right) {\rightleftharpoons} AB\left(g\right).$
The activation energy of the backward reaction exceeds that of the forward reaction by $2RT$ (in $J \,mol^{−1}$). If the pre-exponential factor of the forward reaction is $4$ times that of the reverse reaction, the absolute value of $ΔG^Ɵ$ (in J mol$^{−1}$) for the reaction at $300\, K$ is ____.
(Given; $ln(2) = 0.7, RT = 2500\, J mol^{−1}$ at $300\, K$ and $G$ is the Gibbs energy)

JEE AdvancedJEE Advanced 2018

Solution:

$A_{(g)}+B_{(g)} \rightleftharpoons A B_{(g)}$
$E_{a b}-E_{a f}=2 R T $
$\Rightarrow \Delta H=-2 R T$ and $\frac{A_{f}}{A_{b}}=$
$K_{e q}=\left(\frac{K_{f}}{K_{b}}\right)=\frac{A_{f} e^{-E_{ af } R T}}{A_{b} e^{-E_{ ab } / R T}}=4\left(e^{2}\right)$
$\Delta G^{\circ}=-R T \ln K=-2500 \times \ln \left(4 \times e^{2}\right)$
$=-8500\, J / mol$