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Chemical Kinetics and Nuclear Chemistry question

2024 · 4 Apr · Shift 1 · Q23
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Chemical Kinetics and Nuclear Chemistry question

2024 · 4 Apr · Shift 1 · Q23

JEE MainChemistryChemical Kinetics and Nuclear ChemistryNumerical+4 / −1

Consider the following transformation involving first order elementary reaction in each step at constant temperature as shown below.

JEE Main 2024 (Online) 4th April Morning Shift Chemistry - Chemical Kinetics and Nuclear Chemistry Question 34 English

Some details of the above reactions are listed below.

Step Rate constant (sec −1^{-1}−1) Activation energy (kJ mol −1^{-1}−1)
1 k1\mathrm{k_1}k1​ 300
2 k2\mathrm{k_2}k2​ 200
3 k3\mathrm{k_3}k3​ Ea3\mathrm{Ea_3}Ea3​

If the overall rate constant of the above transformation (k) is given as k=k1k2k3\mathrm{k=\frac{k_1 k_2}{k_3}}k=k3​k1​k2​​ and the overall activation energy (Ea)(\mathrm{E}_{\mathrm{a}})(Ea​) is 400 kJ mol m−1400 \mathrm{~kJ} \mathrm{~mol} \mathrm{~m}^{-1}400 kJ mol m−1, then the value of Ea3\mathrm{Ea}_3Ea3​ is ‾\underline{\hspace{2cm}}​ integer)

Numerical answer
View written solutionFree

Correct answer: 100

  1. For each elementary first-order step, use the Arrhenius equation:

ki=Aie−Ea,i/RTk_i = A_i e^{-E_{a,i}/RT}ki​=Ai​e−Ea,i​/RT

  1. The overall rate constant is given as:

k=k1k2k3k = \frac{k_1 k_2}{k_3}k=k3​k1​k2​​

Substitute Arrhenius forms:

k=A1e−Ea1/RT⋅A2e−Ea2/RTA3e−Ea3/RTk = \frac{A_1 e^{-E_{a1}/RT} \cdot A_2 e^{-E_{a2}/RT}}{A_3 e^{-E_{a3}/RT}}k=A3​e−Ea3​/RTA1​e−Ea1​/RT⋅A2​e−Ea2​/RT​

k=A1A2A3e−Ea1+Ea2−Ea3RTk = \frac{A_1A_2}{A_3} e^{-\frac{E_{a1}+E_{a2}-E_{a3}}{RT}}k=A3​A1​A2​​e−RTEa1​+Ea2​−Ea3​​

  1. Comparing with the Arrhenius form of overall rate constant,

k=Ae−Ea/RTk = A e^{-E_a/RT}k=Ae−Ea​/RT

we get

Ea=Ea1+Ea2−Ea3E_a = E_{a1}+E_{a2}-E_{a3}Ea​=Ea1​+Ea2​−Ea3​

  1. Now substitute the given values:

400=300+200−Ea3400 = 300 + 200 - E_{a3}400=300+200−Ea3​

400=500−Ea3400 = 500 - E_{a3}400=500−Ea3​

Ea3=500−400=100E_{a3} = 500 - 400 = 100Ea3​=500−400=100

  1. Therefore, the required integer value is:

100\boxed{100}100​

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