JEE Main 2025 Jan 24 Shift 2, Chemistry Q23: Factors Affecting The Rate of a Chemical Reaction

JEE Main2025Jan 24, Shift 2Chemistry

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 $k = \frac{k _{1} k _{3}}{k _{2}}$ . 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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Solution

Substitute the Arrhenius form $k_{i} = A_{i} e^{- E_{a, i} / R T}$ into the given expression and take the logarithm:

$k = \frac{k _{1} k _{3}}{k _{2}} \Rightarrow A e^{- E_{a} / R T} = \frac{A _{1} A _{3}}{A _{2}} exp [- \frac{1}{2 R T} (E_{a, 1} + E_{a, 3} - E_{a, 2})]$

Comparing the exponents gives:

$E_{a} = \frac{1}{2} (E_{a, 1} + E_{a, 3} - E_{a, 2})$

$E_{a} = \frac{1}{2} (60 + 10 - 30) = \frac{40}{2} = 20 kJ mol^{- 1}$ .

Answer: 20

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JEE Main 2025 Jan 24 Shift 2, Chemistry Q23: Factors Affecting The Rate of a Chemical Reaction

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