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 $\mathrm{e}^{-x}$. The value of $x$ is____________.
(Rounded off to the nearest integer)
[Use $R=8.31 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$ ]
Solution:
Fraction of molecules to have enough energy
to react $=e^{-E a / R T}$
So, $x=\frac{E_{\mathrm{a}}}{R T}$
$=\frac{80.9 \times 10^{3}}{8.31 \times 700}$
$=13.9$