Rate constants of a reaction at 500 K and 700 K are 0.04 ~s^ -1 and...

$\mathrm{K}=A e^{-E_a / R T}$ After taking In both side $\ln K=\ln A-\frac{E_a}{R T}$ $\operatorname{In} \mathrm{K}_1=\ln \mathrm{A}-\frac{\mathrm{E}_{\mathrm{a}}}{\mathrm{RT}_1}$ at temp. $\mathrm{T}_1$...(i) $\operatorname{In} \mathrm{K}_2=\ln \mathrm{A}-\frac{\mathrm{E}_{\mathrm{a}}}{\mathrm{RT}_2}$ at temp. $\mathrm{T}_2$,,(ii) (ii) - (i) $\operatorname{In} K_2-\operatorname{InK} K_1=\frac{E_a}{R}$\left[\frac{1}{T_1}-\frac{1}{T_2}\right] \ln \frac{\mathrm{K}_2}{\mathrm{~K}_1}=\frac{\mathrm{E}_{\mathrm{a}}}{\mathrm{R}}$\left[\frac{1}{500}-\frac{1}{700}\right]$ $\ln \frac{0.14}{0.04}=\frac{E_a}{R}$\left[\frac{700-500}{500 \times 700}\right] \ln \frac{14}{4}=\frac{E_a}{R}$\left[\frac{200}{500 \times 700}\right]$ $\log 3.5=\frac{E_a}{2.303 \times R}$\left[\frac{1}{250 \times 7}\right] 0.5441=\frac{E_a}{2.303 \times 8.31}$\left[\frac{1}{250 \times 7}\right]$ $E_a=0.5441 \times 8.31 \times 250 \times 7 \times 2.303$ $=0.5441 \times 83.1 \times 25 \times 7 \times 2.303$ $=18222.65$ $\approx 18219 \mathrm{~J}$