JEE Main 2025 — Chemical Kinetics Question with Solution

${\mathrm{k}}_1,{\mathrm{k}}_2$ and ${\mathrm{k}}_3$ are given as rate constants of three steps of a complex reaction. Rate constant (k) of the overall reaction is given as $k=\sqrt{\frac{k_1{k}_3}{k_2}}$ Activation energies of the three steps are given as $\begin{aligned} & \mathrm{E}_{\mathrm{a}_1}=60 \mathrm{~kJ} \mathrm{~mol}^{-1}, \mathrm{E}_{\mathrm{a}_2}=30 \mathrm{~kJ} \mathrm{~mol}^{-1}, \\ & \mathrm{E}_{\mathrm{a}_3}=10 \mathrm{~kJ} \mathrm{~mol}^{-1} \end{aligned}$ From Arrhenius equation, we know that $\mathrm{k}={\mathrm{Ae}}^{-\mathrm{Ea}/\mathrm{RT}T}$ If $E_a$ is the activation energy of the overall reaction, then $\begin{aligned} & E_a=\frac{1}{2}\left[E_{a_1}+E_{a_3}-E_{a_2}\right] \\ & =\frac{1}{2}[60+10-30]=20 \mathrm{~kJ} \mathrm{~mol}^{-1} \end{aligned}$