Reaction $\mathrm{A}(\mathrm{g}) \rightarrow 2 \mathrm{~B}(\mathrm{~g})+\mathrm{C}(\mathrm{g})$ is a first order reaction. It was started with pure A | t/min | Pressure of system at time t/mm Hg | |-------|------------------------------------| | 10 | 160 | | ∞ | 240 | Which of the following option is incorrect?

(C) Rate constant of the reaction is $1.693 \mathrm{~min}^{-1}$

(A) Initial pressure of A is 80 mm Hg

(B) The reaction never goes to completion

(D) Partial pressure of A after 10 minute is 40 mm Hg

JEE Main · 2025 · 07 Apr 2025 · Shift 1 · Chemical Kinetics

Reaction

A (g) \to 2 B (g) + C (g)

is a first order reaction. It was started with pure A

t/min	Pressure of system at time t/mm Hg
10	160
∞	240

Which of the following option is incorrect?

(A)Initial pressure of A is 80 mm Hg
(B)The reaction never goes to completion
(C)Rate constant of the reaction is $1.693 min^{- 1}$ ✓ Correct
(D)Partial pressure of A after 10 minute is 40 mm Hg

Answer: (C)

Solution

At completion each mole of A yields three moles of gas, so the final pressure

3 P_{0} = 240

gives

P_{0} = 80 mm Hg

. At ten minutes the total pressure

P_{0} + 2 x = 160

gives

x = 40

, so the pressure of A is

80 - 40 = 40 mm Hg

. The first-order rate constant is

k = \frac{1}{t} ln \frac{P _{0}}{P _{A}} = \frac{1}{10} ln \frac{80}{40} = \frac{0.693}{10} = 0.0693 min^{- 1}

, and because a first-order reaction reaches completion only as time tends to infinity it never truly ends. The statement that the rate constant equals

1.693 min^{- 1}

is the incorrect one.

JEE Main · 2025 · 07 Apr 2025 · Shift 1 · Single correct option

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JEE Main · 2025 · 07 Apr 2025 · Shift 1 · Chemical Kinetics

Solution

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