The rate constant of a reaction is  $1.5\text{'}{10}^{-7}{\mathrm{S}}^{-1} \mathrm{at} 50°\mathrm{C} \mathrm{and} 4.5\text{'} {10}^{-7} {\mathrm{S}}^{-1} \mathrm{at} 100°\mathrm{C}$ .The value of energy of activation is

$\log \frac{K_2}{K_1}=\frac{E_a}{2.303}\left[\frac{T_2-T_1}{T_1{T}_2}\right]$

$\mathrm{Log}\frac{4.5\times {10}^{-7}}{1.5\times {10}^{-7}}=\frac{{\mathrm{E}}_{\mathrm{a}}}{2.303\times 8.314}\left[\frac{373-323}{323\times 373}\right]$

$\Rightarrow \log 3=\frac{{\mathrm{E}}_{\mathrm{a}}}{2.303\times 8.314}\left[\frac{50}{323\times 373}\right]$

$\Rightarrow 0.4771=\frac{{\mathrm{E}}_{\mathrm{a}}}{2.303\times 8.314}\times \frac{50}{323\times 373}$

and then,${\mathrm{E}}_{\mathrm{a}}=\frac{0.4771\times 2.303\times 8.314\times 323\times 373}{50}$$\therefore {\mathrm{E}}_{\mathrm{a}}=2.2\times {10}^{-4}\mathrm{J} {\mathrm{mol}}^{-1}$