For a reaction taking place in three steps at same temperature, overall rate constant K=frac K_1 K_2 K_3. If Ea_1, Ea_2 and Ea_3 are 40, 50 and 60 kJ / mol respectively, the overall Ea is ________ kJ / mol.

K=frac K_1 * K_2 K_3=frac A_1 * A_2 A_3 * e^-frac( E_ a_1+ E_ a_2- E_ a_3)R T \ A * e^- E_ a / RT=frac A_1 A_2 A_3 * e^-frac( E_ a_1+ E_ a_2- E_ a_3)R T\ E_ a= E_ a_1+ E_ a_2- E_ a_3=40+50-60=30 kJ / mole .

For a reaction taking place in three steps at same temp... | null (Chemistry)

\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}

\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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