Consider the following transformation involving first order elementary reaction in each step at constant temperature as …
Consider the following transformation involving first order elementary reaction in each step at constant temperature as shown below.
\(\mathrm{A}+\mathrm{B}\underset{\mathrm{Step}2}{\overset{\mathrm{Step}1}{⇌}}\mathrm{C}\overset{\mathrm{Step}2}{\to }\mathrm{P}\)
Some details of the above reactions are listed below.
Step Rate constant \((se{c}^{-1})\) Activation energy {\(kJmo{l}^{-1}\))
1 \({k}_{1}\) \(300\)
2 \({k}_{2}\) \(200\)
3 \({k}_{3}\) \({\mathrm{Ea}}_{3}\)
If the overall rate constant of the above transformation (k) is given as \(k=\frac{{k}_{1}{k}_{2}}{{k}_{3}}\)and the overall activation energy \(\left({E}_{a}\right)\) is \(400kJmo{l}^{-1}\), then the value of \(E{a}_{3}\) is _______ \(\mathrm{kJ}{\mathrm{mol}}^{-1}\) (nearest integer)
[JEE Main 2024, 4 Apr (Shift 1)]
100
\(\mathrm{Arrhenius}\mathrm{Relation}:\\ \mathrm{k}={\mathrm{Ae}}^{\frac{-{\mathrm{E}}_{\mathrm{a}}}{\mathrm{RT}}}\\ {\mathrm{E}}_{\mathrm{a}}={\mathrm{E}}_{\mathrm{a}1}+{\mathrm{E}}_{\mathrm{a}2}+{\mathrm{E}}_{\mathrm{a}3}\\ {\mathrm{E}}_{\mathrm{a}}=400\mathrm{kJ}{\mathrm{mol}}^{-1}\\ {\mathrm{E}}_{\mathrm{a}1}=300,{\mathrm{E}}_{\mathrm{a}2}=200\\ 400=300+200-{\mathrm{E}}_{\mathrm{a}3}\\ 400=500-{\mathrm{E}}_{\mathrm{a}3}\\ {\mathrm{E}}_{\mathrm{a}3}=500-400=100\mathrm{kJ}{\mathrm{mol}}^{-1}\\\)
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