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  4. The rate constant is doubled when temperature increases from 27 ° C to 37 ° C. Activation energy in kJ is

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Q. The rate constant is doubled when temperature increases from $27\,{}^\circ C$ to $37\,{}^\circ C$. Activation energy in $kJ$ is

VITEEEVITEEE 2019

Solution:

$log \frac{K_{3}}{K_{1}}=\frac{E_{a}}{2.303R}\left[\frac{1}{T_{1}}-\frac{1}{T_{2}}\right]; If \frac{K_{2}}{K_{1}}=2$
$log\,2=\frac{E_{a}}{2.303\times8.314}\left[\frac{1}{300}-\frac{1}{310}\right]
E_{a}=0.3010 × 2.303 × 8.314\left(\frac{300\times310}{10}\right)$
$=53598.59\,Jmol^{-1}=54\,kj$