If the activation energy of a reaction is $80.9 \mathrm{~kJ} \mathrm{~mol}^{-1}$, the fraction of molecules at 700 K , having enough energy to react to form products is $\mathrm{e}^{-x}$. The value of $x$ is $\_\_\_\_$
(Rounded off to the nearest integer)
$\left[\right.$ Use $\left.\mathrm{R}=8.31 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right]$
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Solution
Fraction of molecules to have enough energy to react $=e^{-\mathrm{Ea}^2 / R T}$
$$
\begin{aligned}
& \text { So, } x=\frac{E_a}{R T} \\
& =\frac{80.9 \times 10^3}{8.31 \times 700} \\
& =13.9
\end{aligned}
$$
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