Q. Consider a complex reaction taking place in three steps with rate constants $k_1,k_2$ and $k_3$ respectively. The overall rate constant $k$ is given by the expression $k=\sqrt{\frac{k_1k_3}{k_2}}$. If the activation energies of the three steps are $60,30$ and $10\ kJ\ mol^{-1}$ respectively, then the overall energy of activation in $kJ\ mol^{-1}$ is ....... (Nearest integer)
Numerical Question
This is a numerical-answer question. The correct answer is shown below.
Explanation
[Solution by Dr. Abubacker] $k=\left(\frac{k_1k_3}{k_2}\right)^{1/2}$ with $k=Ae^{-E/RT}$ gives $E_a=\frac12\left(E_1+E_3-E_2\right)=\frac12(60+10-30)=20$ kJ/mol. Answer: 20.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.