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. It was found that the catalysed reaction was $e^y$ times faster than uncatalysed one. Then value of $y$ is:

Answer 1

Decomposition of $H_2{O}_2$ is a first order reaction
$H_2{O}_2\to H_{2}O+\frac{1}{2}{O}_2$
we know
$k=A{e}^{\frac{-E_a}{RT}}$
For uncatalysed reaction
$k_1=A{e}^{\frac{-E_a}{RT}}$
$k_1=A{e}^{\frac{-18\times {10}^3}{2\times 300}}$ ...{1}
For catalysed reaction
$k_2=A{e}^{\frac{-E_a}{RT}}$
$k_2=A{e}^{\frac{-6\times {10}^3}{2\times 300}}$ ...{2}
Divide 2 by 1
$\frac{k_2}{k_1}=e^{\frac{(18-6)\times {10}^3}{2\times 300}}$
$\frac{k_2}{k_1}=e^{20}$
Catalysed reaction is $e^{20}$ faster than uncatalysed reaction.