JEE Main · 2020 · Shift-ImediumCK-105

The rate of a certain biochemical reaction at physiological temperature (T) occurs 106 times faster with enzyme than…

Chemical Kinetics · Class 12 · JEE Main Previous Year Question

Question

The rate of a certain biochemical reaction at physiological temperature (T) occurs $10^6$ times faster with enzyme than without. The change in the activation energy upon adding enzyme is:

Options

a
$-6(2.303)RT$
✓
b
$-6RT$
c
$+6(2.303)RT$
d
$+6RT$

Correct Answera

$-6(2.303)RT$

Detailed Solution

$\frac{k_{\text{enzyme}}}{k_{\text{no enzyme}}} = 10^6$

$\frac{k_{\text{enzyme}}}{k_{\text{no enzyme}}} = e^{(E_{a,\text{uncat}} - E_{a,\text{cat}})/RT} = 10^6$

$\frac{\Delta E_a}{RT} = \ln 10^6 = 6\ln 10 = 6 \times 2.303$

$\Delta E_a = E_{a,\text{cat}} - E_{a,\text{uncat}} = -6(2.303)RT$

(Negative because enzyme lowers activation energy)

Answer: Option (1) — $-6(2.303)RT$

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