The rate of a reaction triples when temperature changes from ${20}^{°}\mathrm{C} \mathrm{to} {50}^{°}\mathrm{C}.$Energy of activation for the reaction is $\left(\mathrm{R}=8.314{\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1}\right)$

The Arrhenius equitation is

$\mathrm{Log} \frac{{\mathrm{K}}_2}{{\mathrm{K}}_1}=\frac{\mathrm{Ea}}{\mathrm{R}\times 2.303}\left[\frac{{\mathrm{T}}_2-{\mathrm{T}}_1}{{\mathrm{T}}_1{\mathrm{T}}_2}\right]$

Given that $\frac{{\mathrm{K}}_2}{{\mathrm{K}}_1}=3 and R R=8.314 J{K}^{-1}mo{l}^{-1}$

${\mathrm{T}}_1=20+273=293\mathrm{K}$

${\mathrm{T}}_2=50+273=323\mathrm{K}$

$\log 3=\frac{E_a}{8.314\times 2.303}\left[\frac{323-293}{323\times 293}\right]$

$\Rightarrow {\mathrm{E}}_{\mathrm{A}}=\frac{2.303\times 8.314\times 323\times 293\times 0.477}{30}$

$=288811.8 \mathrm{J} {\mathrm{moL}}^{-1}$

$\therefore {\mathrm{E}}_{\mathrm{a}}=28.81\mathrm{KJ} {\mathrm{mol}}^{-1}$