A certain reaction is $\displaystyle 50$% complete in $\displaystyle 20$ minutes at $\displaystyle 300$ K and the same reaction is $\displaystyle 50$% complete in $\displaystyle 5$ minutes at $\displaystyle 350$ K. Calculate the activation energy if it is a first order reaction. $\displaystyle 3$ $\displaystyle \left[\mathrm{R}=8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1} ; \log 4=0.602\right]$

t1/$\displaystyle 2$= 𝑘 k1= $\displaystyle 20$ = $\displaystyle 0.03465$ / $\displaystyle 3.465$ × $\displaystyle 10$-$\displaystyle 2$ min-$\displaystyle 1$ k2= $\displaystyle 5$ = $\displaystyle 0.1386$ / $\displaystyle 1.386$ × $\displaystyle 10$-$\displaystyle 1$ min-$\displaystyle 1$ log 𝐸𝑎 $\displaystyle 2.303$ ×$\displaystyle 8.314$ [$\displaystyle 350$−$\displaystyle 300$] [$\displaystyle 350$ ×$\displaystyle 300$] log $\displaystyle 4$ = 𝐸𝑎 [$\displaystyle 50$] [$\displaystyle 350$ ×$\displaystyle 300$] Ea = $\displaystyle 24209$ J mol-$\displaystyle 1$ or $\displaystyle 24.209$ kJ mol-$\displaystyle 1$