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JEE Main 24-Jan-2025 Paper - Shift 2 — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEEJEE Main 24-Jan-2025 Paper - Shift 24 Marks
Question
Consider a complex reaction taking place in three steps with rate constants $k _1, k _2$ and $k _3$ respectively. The overall rate constant $k$ is given by the expression $k=\sqrt{\frac{k_1 k_3}{k_2}}$. If the activation energies of the three steps are 60,30 and $10 kJ mol ^{-1}$ respectively, then the overall energy of activation in $kJ mol ^{-1}$ is ___________ . (Nearest integer)
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Answer

(20)
Sol. $K=\sqrt{\frac{ K _1 K_3}{K_2}}$
$
A \cdot e^{-E_2 / RT}=\sqrt{\frac{A_{e} e^{-E_1 / RT} \times A_3 e^{-Ea_3 / RT}}{A_2 e^{-E_2 / RT}}}
$
By comparinig exponential term
$
\begin{array}{l}
\frac{E_3}{R T}=\frac{1}{2} \times\left(\frac{E_{2_1}}{R T}+\frac{E_{2_3}}{R T}-\frac{E_{2_2}}{R T}\right) \\
E_a=\left(E_{a_1}+E_{a_3}-E_{a_2}\right) / 2 \\
E_a=(60+10-30) / 2=20 kJ mol^{-1}
\end{array}
$
Ans. 20

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