The rate of a reaction quadruples when temperature changes from $27^{\circ} \mathrm{C}$ to $57^{\cir

Question

The rate of a reaction quadruples when temperature changes from $27^{\circ} \mathrm{C}$ to $57^{\circ} \mathrm{C}$. Calculate the energy of activation. Given $R=8.314 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}, \log 4=0.6021$

Professor PC Thomas Classes · Answer

(a) : $T_1=27^{\circ} \mathrm{C}=300 \mathrm{~K}, T_2=57^{\circ} \mathrm{C}=330 \mathrm{~K}$ It is given that, $k_2=4 k_1$, We know, $\log \frac{k_2}{k_1}=\frac{E_a}{2.303 R}\left[\frac{T_2-T_1}{T_1 T_2}ight]$ Therefore, $\log \frac{4 k_1}{k_1}=\frac{E_a}{2.303 	imes 8.314}\left[\frac{330-300}{300 	imes 330}ight]$ \ $ \begin{aligned} & \Rightarrow \quad 0.6021=\frac{E_a 	imes 30}{2.303 	imes 8.314 	imes 300 	imes 330} \ & \Rightarrow \quad E_a=38044.03 \mathrm{~J} \mathrm{~mol}^{-1}=38.04 \mathrm{~kJ} \mathrm{~mol}^{-1} \end{aligned} $