Question

An enzyme ‘catalase’ increases the rate of decomposition of $H_2{O}_2\left(aq\right)$ into $H_{2}O\left(l\right)$ and $O_2\left(g\right)$ by $e^{40}$ times at $300K$. The activation energy of enzyme catalysed reaction is $4.0kcal/mol$. The activation energy of uncatalysed reaction is

• A. $14kcal$
• B. $28kcal$
• C. $8kcal$
• D. $5kcal$

Answer 1

The correct option is B $28kcal$

$\frac{K_{cat}}{K_{uncat}}=e^{40}=\frac{A.e^{E_a/RT}}{A.e^{E_{a^{\prime }}/RT}}=e^{(E_a-E_{a^{\prime }})/RT}$
$\therefore 40=\frac{E_a-E_{a^{\prime }}}{RT}=\frac{E_a-4Kcal}{\frac{2}{1000}\times 300}$
$\Rightarrow E_a=28Kcal/mol$
Option B is correct.