For a reaction taking place in three steps, the rate constants are $k_{1}, k_{2}$ and $k_{3}$ . The overall rate constant $k = \frac{k_{1} k_{2}}{k_{3}}$ . If the energy of activation values for the first, second and third stages are $40, 50$ and $60$ $k J$ ${m o l}^{- 1}$ respectively, then the overall energy of activation in $k J$ ${m o l}^{- 1}$ is:

30

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40

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60

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50

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Solution

The correct option is A $30$
$k = \frac{k_{1} k_{2}}{k_{3}}$
$A e^{- E_{a} / R T} = \frac{A e^{- E_{a_{1}} / R T} \times A e^{- E_{a_{2}} / R T}}{A e^{- E_{a_{3}} / R T}}$
$e^{- E_{a} / R T} = e^{(- E_{a_{1}} - E_{a_{2}} + E_{a_{3}}) / R T}$
$E_{a} = E_{a_{1}} + E_{a_{2}} - E_{a_{3}}$
$= 40 + 50 - 60 = 30$ $k J$ ${m o l}^{- 1}$

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