The difference in energy of activation for uncatalysed reaction and catalysed reaction is 20 kJ/mol. How many times the rate constant of catalysed reaction will increase over the uncatalysed reaction?

Solution

we have to count the difference between uncatalysed and catalysed reaction.
thus we know that,

k_{1} = {Ae}^{- Ea / RT} k_{2} = {Ae}^{- Ea (c) / RT}

\log \frac{k_{2}}{k_{1}} = \frac{Ea - Ea (c)}{2.303 RT} \log \frac{k_{2}}{k_{1}} = \frac{20, 0000}{2.303 \times 8.314 \times 300} = 3.48 \frac{k_{2}}{k_{1}} = 3020

Thus, the reaction rate has increased nearly by 3020.

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