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Arrhenius Equation

A reaction ta...

Question

A reaction takes place in various steps. The rate constant for first, second, third and fifth steps are $k_{1}, k_{2}, k_{3}$ and $k_{5}$ respectively. The overall rate constant is given by,
$k = \frac{k_{2}}{k_{3}} [\frac{k_{1}}{k_{5}}]^{1 / 2}$
If activation energy is $40, 60, 50$ and $10 k J / m o l$ respectively, the overall energy of activation $(k J / m o l)$ is :

A

10

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B

20

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C

25

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D

none of these

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Solution

The correct option is C $25$
The relationship between the energy of activation of overall reaction and the energy of activation of individual steps is
$E_{a} = (E_{a 2} - E_{a 3}) - \frac{E_{a 1} - E_{a 5}}{2}$
Substitute values in the above expression.
$E_{a} = (60 k J / m o l - 50 k J / m o l) + (\frac{40 k J / m o l - 10 k J / m o l}{2})$
$= 10 k J / m o l + 15 k J / m o l$
$= 25 k J / m o l$

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