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Chemical Kinetics

Question

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

According to the Arrhenius equation
k= Ae^-Ea/RT
where Ea is activation energy, T is temperature.

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.