JEE Main 2024 — Chemical Kinetics Question with Solution

Consider the following transformation involving first order elementary reaction in each step at constant temperature as shown below. $A+B\underset{\text{ Step 3 }}{\text{ Step }1}C\stackrel{\text{ Step 2 }}{\to }P$ Some details of the above reactions are listed below. $\begin{array}{ccc}\text{ Step }& \text{ Rate constant }\left({\mathbf{sec}}^{-1}\right)& \text{ Activation energy }\left({\mathbf{kJ}\mathbf{mol}}^{-1}\right)\\ 1& {\mathrm{k}}_1& 300\\ 2& {\mathrm{k}}_2& 200\\ 3& {\mathrm{k}}_3& {\mathrm{Ea}}_3\end{array}$ If the overall rate constant of the above transformation $(k)$ is given as $k=\frac{k_1{k}_2}{k_3}$ and the overall activation energy $\left({\mathrm{E}}_{\mathrm{a}}\right)$ is $400\mathrm{kJ}{\mathrm{mol}}^{-1}$, then the value of ${\mathrm{Ea}}_3$ is $\mathrm{kJ}{\mathrm{mol}}^{-1}$ (nearest integer)