Chemistry - Chemical Kinetics Question with Solution | TestHub

${\mathrm{k}}_1,{\mathrm{k}}_2$ 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 $\begin{array}{rl}& {\mathrm{E}}_{{\mathrm{a}}_1}=60\mathrm{kJ}{\mathrm{mol}}^{-1},{\mathrm{E}}_{{\mathrm{a}}_2}=30\mathrm{kJ}{\mathrm{mol}}^{-1},\\ & {\mathrm{E}}_{{\mathrm{a}}_3}=10\mathrm{kJ}{\mathrm{mol}}^{-1}\end{array}$ 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 $\begin{array}{rl}& E_a=\frac{1}{2}\left[E_{a_1}+E_{a_3}-E_{a_2}\right]\\ & =\frac{1}{2}[60+10-30]=20\mathrm{kJ}{\mathrm{mol}}^{-1}\end{array}$