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  4. The rate of a certain biochemical reaction at physiological temperature (T) occurs 106 times faster with enzyme than without. The change in the activation energy upon adding enzyme is :

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Q. 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 :

JEE MainJEE Main 2020Chemical Kinetics

Solution:

$K=Ae^{\frac{-E_{a}}{RT}}$
$K '=Ae^{\frac{-E_{a}}{RT}}=10^{6}K$
$Ae^{\frac{-E_{a}}{RT}}=10^{6}\times Ae^{\frac{-E_{a}}{RT}}$
$\frac{-E'_{a}}{RT}=\frac{-E_{a}}{RT}+In\,10^{6}$
$E'_{a}=E_{a}-RT\,In\,10^{6}$
$E'_{a}-E_{a}=-RT\,In\,10^{6}$
$=-6RT\times2.303$