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Rate Constant

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 are $40, 60, 50$ 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 D $25$
As we know,
$k = A e^{- E_{a} / R T}$

$l n k = l n A - \frac{E_{a}}{R T}$

So, according to given value of $k$ , overall energy of activation, $E_{a} = E_{2} - E_{3} + \frac{1}{2} \times (E_{1} - E_{5}) = 60 - 50 + (\frac{1}{2}) \times 40 - (\frac{1}{2}) \times 10 = 25 k J / m o l$

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