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Arrhenius Equation

A hydrogenati...

Question

A hydrogenation reaction is carried out at 500 K. If the same reaction is carried out in presence of a catalyst at the same rate, the temperature required is 400 K. Calculate the activation energy of the reaction if the catalyst lowers the activation barrier by 20 KJ ${m o l}^{- 1}$ .

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Solution

we have
$E_{500} = \frac{E_{400}}{4} \times 5 ⟶ 1 a l s o E_{500} = E_{400} + 20 ⟶ 2 e q u a t i n g r i g h t s i d e o f b o t h e q^{n} E_{400} + 20 = \frac{E_{400}}{4} \times 5 (\frac{S}{4} = 1.25) E_{400} + 20 = E_{400} \times 1.25 1.25 E_{400} - E_{400} = 20 0.25 E_{400} = 20 E_{400} = \frac{20}{0.25} = 80 E_{400} = 80 K J m o l s u b s t i t u t e t h i s i n {e q}^{n} 2 E_{500} = E_{400} + 20 = 80 + 20 E_{500} = 100 K J m o l$

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