Verified Solution • 2025–26 Session moderate

QJEEM24Cha9c6: JEE Main 2024 Chemistry - Class 12 JEEM24Cha9c6 Solution: For a reaction taking place in three steps at same temperature, …

For a reaction taking place in three steps at same temperature, overall rate constant K=K1 K2 K3\mathrm{K}=\frac{\mathrm{K}_1 \mathrm{~K}_2}{\mathrm{~K}_3} . If Ea1,Ea2\mathrm{Ea}_1, \mathrm{Ea}_2 and Ea3\mathrm{Ea}_3 are 40, 50 and 60 kJ/mol60 \mathrm{~kJ} / \mathrm{mol} respectively, the overall Ea\mathrm{Ea} is ________ kJ/mol\mathrm{kJ} / \mathrm{mol} .

Step-by-Step Verified Solution

amp;K=K1⋅K2 K3=A1⋅A2 A3⋅e−(Ea1+Ea2−Ea3)RTamp; A⋅e−Ea/RT=A1 A2 A3⋅e−(Ea1+Ea2−Ea3)RT\begin{aligned} & \mathrm{K}=\frac{\mathrm{K}_1 \cdot \mathrm{K}_2}{\mathrm{~K}_3}=\frac{\mathrm{A}_1 \cdot \mathrm{A}_2}{\mathrm{~A}_3} \cdot \mathrm{e}^{-\frac{\left(\mathrm{E}_{\mathrm{a}_1}+\mathrm{E}_{\mathrm{a}_2}-\mathrm{E}_{\mathrm{a}_3}\right)}{R T}} \\ & \mathrm{~A} \cdot \mathrm{e}^{-\mathrm{E}_{\mathrm{a}} / \mathrm{RT}}=\frac{\mathrm{A}_1 \mathrm{~A}_2}{\mathrm{~A}_3} \cdot \mathrm{e}^{-\frac{\left(\mathrm{E}_{\mathrm{a}_1}+\mathrm{E}_{\mathrm{a}_2}-\mathrm{E}_{\mathrm{a}_3}\right)}{R T}}\end{aligned}

Ea=Ea1+Ea2−Ea3=40+50−60=30 kJ/mole.\mathrm{E}_{\mathrm{a}}=\mathrm{E}_{\mathrm{a}_1}+\mathrm{E}_{\mathrm{a}_2}-\mathrm{E}_{\mathrm{a}_3}=40+50-60=30 \mathrm{~kJ} / \mathrm{mole} .

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