# If the activation energy of a reaction is

Question:

If the activation energy of a reaction is $80.9 \mathrm{~kJ} \mathrm{~mol}^{-1}$, the fraction of molecules at $700 \mathrm{~K}$, having enough energy to react to form products is $\mathrm{e}^{-\mathrm{x}}$. The value of $\mathrm{x}$ is _________________ (Rounded off to the nearest integer)

$\left[\mathrm{Use} \mathrm{R}=8.31 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\right]$

Solution:

(14)

$\mathrm{E}_{\mathrm{a}}=80.9 \mathrm{~kJ} / \mathrm{mol}$

Eraction of molecules able to cross energy barrier $=\mathrm{e}^{-\mathrm{E}_{\mathrm{a}} / \mathrm{RT}}=\mathrm{e}^{-\mathrm{x}}$

$x=\frac{E_{a}}{R T}=\frac{80.9 \times 1000}{8.31 \times 700}=13.91$

$x \simeq 14 \mathrm{Ans}$