Question
Enzymes are highly efficient catalyst. An enzyme ‘catalase’ increases the rate of decomposition of H2O2 (aq) into H2O(l) and O2(g) e20 times at 300 K. The activation energy of enzyme catalysed reaction is 2.0 kcal/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.
Options
Solution
$(a)\frac{K_{\text{cal}}}{K_{\text{uncat}}} = e^{20} = \frac{A.e^{E_{a'}/RT}}{A.e^{E_{a'}/RT}} = e^{\left( E_{a} - E_{a'} \right)/RT}$
$\therefore 20 = \frac{E_{a} - E_{a'}}{RT} = \frac{E_{a} - 2\text{Kcal}}{\frac{2}{1000} \times 300} $$$\Rightarrow E_{a} = 14\text{ Kcal/mol.}$$
(b), (c) Reaction: 2H2O2(aq) → 2H2O(l)+O2(g) is first order. (d) Rate of uncatalysed reaction increases to greater extent on increasing temperature because its activation energy is high.
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