For a reversible reaction A B, the . The activation energy of the uncatalysed forward reaction is 300 kJ . When the reaction is catalysed keeping the reactant concentration same, the rate of the catalysed forward reaction at 27°C is found to be the same

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Solution

Q.
For a reversible reaction A $⇌$ B, the $Δ H_{forward reaction} = {20 kJ mol}^{- 1}$ . The activation energy of the uncatalysed 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 the same as that of the uncatalysed reaction at 327°C. The activation energy of the catalysed backward reaction is ______ kJ ${mol}^{- 1}$ . [2023]

Ans.
(130)

$E_{a} = 300 kJ/mol$

$(\frac{E_{a}}{T}) = {(\frac{E_{a}^{'}}{T'})}_{cat}$

$\frac{300}{600} = \frac{{(E_{a}^{'})}_{f}}{300}$

${(E_{a}^{'})}_{f} = 150$

$Δ H = {(E_{a}^{'})}_{f} - {(E_{a}^{'})}_{b}$

$20 = 150 - {(E_{a}^{'})}_{b}$

${(E_{a}^{'})}_{b} = 130 kJ/mol$

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