Question

In the decomposition of $H_2{O}_2$ at 300 K, the energy of activation was found to be 18 kcal/mol while it decreases to 6 kcal/mol when the decomposition was carried out in the presence of a catalyst at 300 K. If the number of times is the catalysed reaction faster than uncatalysed one is $x\times {10}^8$. The nearest integer value of $x$ is:

Answer 1

The Arrhenius equation is $k=A{e}^{-E/RT}$.
Here, k is the rate constant and E is the activation energy.
For uncatalyzed reaction, $k_u=A{e}^{-E_u/RT}$......(1)
For catalyzed reaction,$k_c=A{e}^{-E_c/RT}$......(2)
Divide equation (2) with equation (1)
$\frac{k_c}{k_u}=\frac{A{e}^{-E_c/RT}}{A{e}^{-E_u/RT}}=e^{(E_u-E_c)/RT}=e^{(18000-6000)/(2\times 300)}=e^{20}=5\times {10}^8=x\times {10}^8$.
Hence, $x=5$.