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

The Arrhenius equitation is

$\log \frac{{\text{k}}_{\text{2}}}{{\text{k}}_{\text{1}}}=\frac{\text{Ea}}{R\times 2.303}\left[\frac{{\text{T}}_{\text{2}}-{\text{T}}_1}{{\text{T}}_{\text{1}}{\text{T}}_{\text{2}}}\right]$

$\text{Given that }\frac{{\text{k}}_{\text{2}}}{{\text{k}}_{\text{1}}}=3and\text{ R = 8}{\text{.314 JK}}^{-1}{\text{mol}}^{-1}$

${\text{T}}_{\text{1}}=20+273=293\text{K}$

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

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

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

           $=28811.8{\text{ J mol}}^{-1}$

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