The rate of a reaction quadruples when the temperature changes from...

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

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

$\ln \left(\dfrac{{k}_{2}}{{k}_{1}}\right) = \dfrac{{E}_{a}}{R}\left(\dfrac{1}{{T}_{1}} - \dfrac{1}{{T}_{2}}\right)$

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

$2 \times 0 . 693 = \dfrac{{E}_{a}}{R}\left(\dfrac{10}{300 \times 310}\right)$

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