Question

In the decomposition of $H_2{O}_2$ at $300K$, the energy of activation was found to be $18kcalmo{l}^{-1}$, it is decreased to $6kcalmo{l}^{-1}$ when the decomposition was carried out in presence of catalyst at $300K$. How many times is the catalytic reaction faster than the uncatalysed one?

Answer 1

The relationship between the rate constant and the activation energy is $logk=logA-\frac{E_a}{2.303RT}$
For catalyzed reaction $logk=logA-\frac{18000}{2.303\times 2\times 300}$......(1)
For uncatalyzed reaction $log{k}^{\prime }=logA-\frac{6000}{2.303\times 2\times 300}$......(2)
Subtract equation (2) from equation (1),
$log\frac{k}{k^{\prime }}=\frac{-12000}{2.303\times 600}$

$k^{\prime }=4.8\times {10}^8=x\times {10}^8$
$x=4.8$
$10x=48$