For a reversible reaction A ⇌ B , the ∆ H forward reaction = 20 kJ mol – 1 . The activation energy of the uncatalyzed forward reaction is 300 kJ mol – 1 . When the reaction is catalysed keeping the re

Question

For a reversible reaction A ⇌ B , the ∆ H forward reaction = 20 kJ mol – 1 . The activation energy of the uncatalyzed forward reaction is 300 kJ mol – 1 . When the reaction is catalysed keeping the reactant concentration same, the rate of the catalysed forward reaction at 27 ∘ C is found to be same as that of the uncatalyzed reaction at 327 ∘ C . The activation energy of the catalysed backward reaction is _______ kJ mol – 1 .

TestHub · Accepted Answer

As per the question
To determine the activation energy of the catalyzed backward reaction, we need to use the Arrhenius equation and the given information.
The Arrhenius equation is given by:
$k = {Ae}^{(- Ea / RT)}$
${Ae}^{- \frac{300 \times 10^{3}}{600 \times R}} = {Ae}^{\frac{- Ea}{300 \times R}}$
$\Rightarrow \frac{10^{3}}{2} = \frac{Ea}{300}$
$\Rightarrow E_{a} = 150 \times 10^{3} J {mol}^{- 1}$
$\Rightarrow E_{a} = 150 kJ {mol}^{- 1}$
$∴$ Activation energy of catalysed backward reaction
Energy of activation for backward reaction $E_{b} = E_{a} - ∆ H$
$= 150 - 20 = 130 kJ {mol}^{- 1}$

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