The rate of a particular reaction quadruples when the temperature increases from $\displaystyle 293$ K to $\displaystyle 313$ K. Calculate the energy of activation $\displaystyle \left(\mathrm{E}_{\mathrm{a}}\right)$ of the reaction assuming that it does not change with temperature.

log K = - Ea /$\displaystyle 2.303$ RT log 𝐸𝑎 $\displaystyle 2.303$ ×$\displaystyle 8.314$ [$\displaystyle 313$−$\displaystyle 293$] [$\displaystyle 313$ ×$\displaystyle 293$] log $\displaystyle 4$ = 𝐸𝑎 [$\displaystyle 20$] [$\displaystyle 313$ ×$\displaystyle 293$] Ea= $\displaystyle 0.602$ ×$\displaystyle 19.147$ ×$\displaystyle 313$ ×$\displaystyle 293$ =$\displaystyle 52850$ J mol-$\displaystyle 1$ / $\displaystyle 52.85$ kJ mol-$\displaystyle 1$