The activation energy of the backward reaction exceed, that of the forward reaction by 2RT $(i n J m o l^{- 1})$ . If the Pre- Exponential factor of the forward reaction is 4 times that of the reverse reaction. The absolute value of $Δ G^{0} (i n J m o l^{- 1})$ for the reaction at 300 k is_______
(given : ln(2)=0.7 RT = $2500 J m o l^{- 1}$ at 300k and G is the Gibb’s energy)

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answer is 8500.

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Detailed Solution

$\begin{array}{l} \Rightarrow E_{b} = E_{f} + 2 R T \\ (E_{f} - E_{b}) = - 2 R T \to (1) \\ A_{f} = 4 A b \\ K_{f} = A_{F} \cdot e^{- E f / R T} \\ K_{b} = A b \cdot e^{- E b / R T} \end{array}$
$\begin{array}{l} K_{e q m} = \frac{K_{f}}{K} \\ K_{e q m} = \frac{4 A b e^{- E f / R T}}{A b \cdot e^{- E b / R T}} \\ K_{e q m} = \frac{K_{f}}{K_{b}} = 4 e^{- (\frac{E_{f} - E_{b}}{R T})} \\ K_{eqm} = 4 r^{+ 2} \\ Δ G = - R T \ln K e q m \\ Δ G^{0} = - 2500 \ln (4 . e^{+ 2}) \\ Δ G^{0} = - 2500 \ln (2 + \ln 4) \\ Δ G^{0} = - 2500 \ln (3.4) \\ Δ G^{0} = - 8500 J / mol \end{array}$