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

[JEE Main 2024, 29 Jan (Shift 1)]

Question

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

[JEE Main 2024, 29 Jan (Shift 1)]

YESPYQ · Accepted Answer

Correct answer: a) 30. By applying Arrhenius equation $K = \frac{K_1 \cdot K_2}{K_3} = \frac{A_1 \cdot A_2}{A_3} \cdot e^{-\frac{(E_{a1} + E_{a2} - E_{a3})}{RT}}$ $A \cdot e^{-E_a/RT} = \frac{A_1 A_2}{A_3} \cdot e^{-\frac{(E_{a1} + E_{a2} - E_{a3})}{RT}}$ $E_a = E_{a1} + E_{a2} - E_{a3} = 40 + 50 - 60$ $= 30 \text{ kJ/mole}$

For a reaction taking place in three steps at same temperature, overall rate constant \(\mathrm{K}=\frac{\mathrm{K}_{1} …

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