For a reaction taking place in three steps at same temperature, overall rate constant . If , and are 40, 50 and 60 kJ/mol respectively, the overall Ea is ________ kJ/mol.

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Solution

Q.
For a reaction taking place in three steps at same temperature, overall rate constant $K = \frac{K_{1} K_{2}}{K_{3}}$ . If ${Ea}_{1}$ , ${Ea}_{2}$ and ${Ea}_{3}$ are 40, 50 and 60 kJ/mol respectively, the overall Ea is ________ kJ/mol. [2024]

Ans.
(30)

$k = \frac{k_{1} k_{2}}{k_{3}}$

$A e^{(\frac{- E_{a}}{R T})} = \frac{A_{1} e^{(\frac{- E_{a 1}}{R T})} A_{2} e^{(\frac{- E_{a 2}}{R T})}}{A_{3} e^{(\frac{- E_{a 3}}{R T})}} [Arrhenius equation]$

$A e^{(\frac{- E_{a}}{R T})} = \frac{A_{1} e^{(\frac{- 40}{R T})} A_{2} e^{(\frac{- 50}{R T})}}{A_{3} e^{(\frac{- 60}{R T})}}$

$A e^{(\frac{- E_{a}}{R T})} = \frac{A_{1} A_{2}}{A_{3}} e^{(\frac{- 40 - 50 + 60}{R T})}$

$A e^{(\frac{- E_{a}}{R T})} = \frac{A_{1} A_{2}}{A_{3}} e^{(\frac{- 30}{R T})}$

Thus $E_{a}$ for overall reaction is 30 kJ/mol.

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