Rate constants of a reaction at 500 K and 700 K are $0.04 \mathrm{~s}^{-1}$ and $0.14 \mathrm{~s}^{-

Question

Rate constants of a reaction at 500 K and 700 K are $0.04 \mathrm{~s}^{-1}$ and $0.14 \mathrm{~s}^{-1}$, respectively; then, activation energy of the reaction is (Given : $\log 3.5=0.5441, R=8.31 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$ )

Professor PC Thomas Classes · Answer

(c) $: \log \frac{k_2}{k_1}=\frac{E_a}{2.303 R}\left[\frac{T_2-T_1}{T_1 T_2}ight]$ Given, $k_1=0.04 \mathrm{~s}^{-1}, k_2=0.14 \mathrm{~s}^{-1}, T_1=500 \mathrm{~K}$, \ $ \begin{aligned} & T_2=700 \mathrm{~K}, R=8.31 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1} \ & \log (3.5)=\frac{E_a}{2.303 	imes 8.31}\left[\frac{700-500}{700 	imes 500}ight] \ & E_a=0.5441 	imes 2.303 	imes 8.31 	imes \frac{35 	imes 10^4}{200}=18222.65 \mathrm{~J} \end{aligned} $