Question

Enzymes are highly efficient catalyst. An enzyme 'catalase' increases the rate of decomposition of $H_2{O}_2\left(aq\right)$ into $H_{2}O\left(1\right)$ and $O_2\left(g\right)e^{20}$ times at $300K$. The activation energy of enzyme catalysed reaction is $2.0kcal/mol$. Which of the following information(s) is/are correct assuming that the value of pre-exponential factor is unaffected by temperature change or use of catalyst and the activation energy is independent of temperature.

• A. The activation energy of uncatalysed reaction is $14.0kcal/mol$
• B. Uncatalysed reaction is an elementary (single step) reaction
• C. Catalysed reaction is a complex (multi step) reaction
• D. On increasing the temperature, the ratio of rates of catalysed and uncatalysed reactions becomes less than $e^{20}$

Answer 1

Answer: (A), (B), (D)

On increasing the temperature, the ratio of rates of catalysed and uncatalysed reactions becomes less than $e^{20}$

$\left(a\right)\frac{k_{cat}}{k_{uncat}}=e^{20}=\frac{A{e}^{-E_a^{\prime }/RT}}{A{e}^{-E_a/RT}}=e^{(E_a-E_a^{\prime })/RT}$

$\therefore 20=\frac{E_a-E_a^{\prime }}{RT}=\frac{E_a-2kcalmo{l}^{-1}}{\frac{2}{1000}kcal{K}^{-1}mol-1\times 300K}$

$\therefore E_a=14kcalmo{l}^{-1}$

$\left(b\right),\left(c\right)$
$\text{Reaction:}2H_2{O}_2\left(aq\right)\to 2H_{2}O\left(1\right)+O_2\left(g\right)\text{is a first order reaction.}$

$\left(d\right)$
Rate of uncatalysed reaction increases to greater extent on increasing temperature because its activation energy is high.