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MCQEasyJEE 2023Order & Molecularity

JEE Chemistry 2023 Question with Solution

A student has studied the decomposition of a gas AB3AB_3 at 25∘C25^\circ \text{C}. He obtained the following data.

p (mm Hg)  50,100,200,400Relative t1/24,2,1,0.5p \, (\text{mm Hg}) \; 50, 100, 200, 400 \quad \text{Relative } t_{1/2} \quad 4, 2, 1, 0.5

The order of the reaction is:

  • A

    0.50.5

  • B

    22

  • C

    11

  • D

    00 (zero)

Answer

Correct answer:D

Step-by-step solution

Standard Method

Given: The decomposition of gas AB3AB_3 at 25∘C25^\circ \text{C} has initial pressures 50,100,200,400 mm Hg50, 100, 200, 400 \, \text{mm Hg} and corresponding relative half-lives 4,2,1,0.54, 2, 1, 0.5.

Find: The order nn of the reaction.

For a reaction, the half-life is related to the initial pressure by

t1/2∝(P0)1−nt_{1/2} \propto (P_0)^{1-n}

where nn is the order of the reaction.

Taking the ratio of half-lives at two pressures,

t1/2(P1)t1/2(P2)=(P2P1)n−1\frac{t_{1/2}(P_1)}{t_{1/2}(P_2)} = \left( \frac{P_2}{P_1} \right)^{n-1}

Using the given data,

t1/2(50)t1/2(100)=(10050)n−1\frac{t_{1/2}(50)}{t_{1/2}(100)} = \left( \frac{100}{50} \right)^{n-1}

Substituting the relative half-lives,

42=2n−1\frac{4}{2} = 2^{n-1}

So,

2=2n−12 = 2^{n-1}

Therefore,

n−1=1  ⟹  n=2n - 1 = 1 \implies n = 2

Thus, the order of the reaction is 22.

The solution concludes that the correct option is D, but this contradicts the working, which clearly gives n=2n = 2. Hence the defensible correct option from the listed choices is B.

Common mistakes

  • Using the listed option label from the solution without checking the working. This is wrong because the algebra in the solution gives n=2n = 2, not zero. Always trust the derivation over a mismatched option label.

  • Applying the half-life relation for first-order reactions directly. This is wrong because here the half-life changes with initial pressure, so the reaction cannot be first order. Use t1/2∝(P0)1−nt_{1/2} \propto (P_0)^{1-n} instead.

  • Writing the pressure ratio in the wrong order in the exponent relation. This gives an incorrect sign for n−1n-1. Carefully use the same order on both sides of the ratio formula.

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