It has been found that for a chemical reaction with rise in...

Arrhenius equation for the rate constant of a reaction in terms of energy of activation at two different temperatures is given by

$\log \left(\dfrac{{K}_{2}}{{K}_{1}}\right) = \dfrac{{E}_{a}}{2 . 3R}\left[\dfrac{1}{{T}_{1}} - \dfrac{1}{{T}_{2}}\right]$

Rise in temperature $= 9K$

Initial temperature $= 300K$

$\log \left(\dfrac{{K}_{309}}{{K}_{300}}\right) = \dfrac{{E}_{a}}{2 . 3R}\left[\dfrac{1}{300} - \dfrac{1}{309}\right]$

$\log 2 = \dfrac{{E}_{a}}{2 . 3R}\left[\dfrac{9}{300 \times 309}\right]$

${E}_{a} = \dfrac{2 . 3 \times 0 . 30 \times 300 \times 309}{9}$

${E}_{a} = 58 . 988 \times {10}^{3}J = 58 . 988kJ = 59kJ$