Q80 · CSIR-NET Chemistry, December 2011
Paper: CSIR-NET December 2011 · Subject: Physical Chemistry · Chapter: Chemical Kinetics · Topic: Steady State Approximation · Marks: 2 · Difficulty: Medium
The overall rate of the following complex reaction, \[ \begin{array}{l} 2 \mathrm{A} \stackrel{\mathrm{k}_{1}}{\underset{\mathrm{k}_{2}}{\rightleftharpoons}} \mathrm{A}_{2} \quad \text{(fast equilibrium)} \\ \mathrm{A}+\mathrm{B} \stackrel{\mathrm{k}_{2}}{\rightleftharpoons} \mathrm{C} \quad \text{(fast equilibrium)} \\ \mathrm{A}_{2}+\mathrm{C} \stackrel{\mathrm{k}_{3}}{\rightleftarrows} \mathrm{P}+2 \mathrm{A} \quad \text{(slow)} \end{array} \]
by steady state approximation would be (a)$\mathrm{K}_{1} \mathrm{K}_{2} \mathrm{k}_{3}[\mathrm{A}]^{3}[\mathrm{B}]$
(b)$\mathrm{K}_{2} \mathrm{K}_{1} \mathrm{k}_{3}[\mathrm{A}][\mathrm{B}]^{3}$
(c)$\mathrm{K}_{1} \mathrm{K}_{2} \mathrm{k}_{3}[\mathrm{A}][\mathrm{B}]^{2}$
(d)$\mathrm{K}_{1} \mathrm{K}_{2} \mathrm{k}_{3}[\mathrm{A}][\mathrm{B}]$
Answer
Answer: A ✓ checked by 4AB · confidence high
The source book printed no answer; this one was worked out and checked — see the explanation.
Explanation
Rate = k₃[A₂][C], with the pre-equilibria [A₂] = K₁[A]² and [C] = K₂[A][B]. Rate = K₁K₂k₃[A]³[B] (a).
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