Question

For a reaction taking place in three steps, the rate constants are $ k_{1}, k_{2} $ and $ k_{3} $ and overall rate constant is $ k=\frac{k_{1}k_{3}}{k_{2}}\cdot $ If the energies of activation $ E_{1}, E_{2} $ and $ E_{3} $ are $ 60 $ , $ 30 $ and $ 10 \, kJ \, mol^{-1} $ , respectively, then the overall energy of activation is

• A. $ 30 \,kJ\, mol^{- 1} $
• B. $ 40 \,kJ\, mol^{- 1} $
• C. $ 60 \,kJ\, mol^{- 1} $
• D. $ 100 \,kJ\, mol^{- 1} $

Answer 1

Answer: (B)

Given, $K=\frac{k_{1}k_{3}}{k_{2}}$
From Arrhenius equation, $k=Ae^{-E_{a}/RT}$
$Ae^{-E_{a} /RT}=\frac{Ae^{-E_{1} /RT}\cdot Ae^{-E_{3} /RT}}{Ae^{-E_{2} /RT}}$
$\therefore E_{a}=E_{1}+E_{3}-E_{2}=60+10-30$
$=70-30=40\,kJ \,mol^{-1}$