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  4. If the activation energy of a reaction is 80.9 kJ mol -1, the fraction of molecules at 700 K having enough energy to react to form products is e -x. The value of x is (Rounded off to the nearest integer) [. Use .R=8.31 J K -1 mol -1]

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Q. If the activation energy of a reaction is $80.9 kJ$ $mol ^{-1},$ the fraction of molecules at $700 K$ having enough energy to react to form products is $e ^{-x}$. The value of $x$ is___
(Rounded off to the nearest integer)
$\left[\right.$ Use $\left.R=8.31 J K ^{-1} mol ^{-1}\right]$

JEE MainJEE Main 2021Chemical Kinetics

Solution:

Fraction of molecules to have enough energy to react $= e ^{- E a / RT }$

So, $x=\frac{E_{a}}{R T}$

$=\frac{80.9 \times 10^{3}}{8.31 \times 700}$

$=13.9$