The rate of a reaction quadruples when the temperature changes from 300   to 310   K . The…

The activation energy, rate constant and temperature can be related using Arrhenius equation.

$\mathrm{k}={\mathrm{Ae}}^{-\frac{{\mathrm{E}}_{\mathrm{a}}}{\mathrm{RT}}}$

$\ln \left(\frac{{\mathrm{k}}_2}{{\mathrm{k}}_1}\right)=\frac{{\mathrm{E}}_{\mathrm{a}}}{\mathrm{R}}\mathrm{ }\left(\frac{1}{{\mathrm{T}}_1}-\frac{1}{{\mathrm{T}}_2}\mathrm{ }\right)$

$\ln \left(4\right)=\frac{{\mathrm{E}}_{\mathrm{a}}}{\mathrm{R}}\mathrm{ }\left(\frac{1}{300}-\frac{1}{310}\mathrm{ }\right)$

$2\times 0.693=\frac{{\mathrm{E}}_{\mathrm{a}}}{\mathrm{R}}\mathrm{ }\left(\frac{10}{300\times 310}\mathrm{ }\right)$

${\text{E}}_{\text{a}} = \frac{2\times 0.693\times 300\times 310\times 8.314}{10} = 107.2 \text{kJ/mol}$