Question

A certain reaction proceeds in sequence of three elementary steps with rate constant k₁, k₂& k₃. If k_obs= $\left( \frac{k_{1}}{k_{2}} \right)^{1/2}$. k₃ the observed E_a is –

• A. $\frac{1}{2}\left( \frac{E_{1}}{E_{2}} \right) + E_{3}$
• B. $\frac{E_{3} + E_{1}}{2}$
• C. $E_{3}\left( \frac{E_{1}}{E_{2}} \right)^{1/2}$
• D. E₃ + $\frac{1}{2}$ [E₁ –E₂]

Answer 1

Answer: (D)

E₃ + $\frac{1}{2}$ $E₁ –E₂$

Answer 2

k₀ = $\left( \frac{K_{1}}{K_{2}} \right)^{1/2}$× k₃……..(1)

k = A e ^–ta/RT ……..(2)

from (1) & (2)

Ae^–Ea/RT = $\left( \frac{A_{1}e^{–Ea/RT}}{A_{2}e^{–Ea_{2}/RT}} \right)^{1/2} \cdot A_{3}e^{–Ea_{3}/RT}$i.e.

E_a = $\frac{1}{2}$ [Ea₁ – Ea₂] + Ea₃