Question

Consider the following transformation involving first order elementary reaction in each step at constant temperature as shown below.
$$\mathrm{A}+\mathrm{B} \underset{	ext { Step } 3}{\stackrel{	ext { Step } 1}{ightleftharpoons}} \mathrm{C} \xrightarrow{	ext { Step } 2} \mathrm{P}$$

Some details of the above reaction are listed below.

| Step | Rate constant $(\mathrm{sec}^{-1})$ | Activation energy $(\mathrm{kJ~mol}^{-1})$ |
|------|--------------------------------------|---------------------------------------------|
| 1    | $\mathrm{k}_{1}$                     | 300                                         |
| 2    | $\mathrm{k}_{2}$                     | 200                                         |
| 3    | $\mathrm{k}_{3}$                     | $\mathrm{Ea}_{3}$                           |

If the overall rate constant of the above transformation ( k ) is given as $\mathrm{k}=\frac{\mathrm{k}_{1} \mathrm{k}_{2}}{\mathrm{k}_{3}}$ and the overall activation energy ( $\mathrm{E}_{\mathrm{a}}$ ) is $400 \mathrm{~kJ} \mathrm{~mol}^{-1}$, then the value of $\mathrm{Ea}_{3}$ is _____ $\mathrm{kJ} \mathrm{mol}^{-1}$ (nearest integer)

Accepted Answer

100

Step	Rate constant $(sec^{- 1})$	Activation energy $(kJ mol^{- 1})$
1	$k_{1}$	300
2	$k_{2}$	200
3	$k_{3}$	$Ea_{3}$

JEE Main · 2024 · 04 Apr 2024 · Shift 1 · Chemical Kinetics

Solution

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