The following data were obtained during the first order thermal decomposition of a gas A at constant volume: A(g) → 2B(g) + C(g) | S.No | Time/s | Total pressure | |------|--------|----------------| | 1. | 0 | 0.1 | | 2. | 115 | 0.28 | The rate constant of the reaction is ____ × 10⁻² s⁻¹ (nearest integer)

JEE Main · 2024 · 01 Feb 2024 · Shift 2 · Chemical Kinetics

The following data were obtained during the first order thermal decomposition of a gas A at constant volume:
A(g) → 2B(g) + C(g)

S.No	Time/s	Total pressure
1.	0	0.1
2.	115	0.28

The rate constant of the reaction is ____ × 10⁻² s⁻¹ (nearest integer)

Answer: 2

For

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

, let

x

be the pressure of A that has decomposed at time

t

. Total pressure

= (0.1 - x) + 2 x + x = 0.1 + 2 x

. At

t = 115 s

0.1 + 2 x = 0.28 \Rightarrow x = 0.09

, so the pressure of A remaining is

0.1 - 0.09 = 0.01 atm

.

For a first-order reaction,

k = \frac{1}{t} ln \frac{P _{0}}{P _{t}} = \frac{1}{115} ln \frac{0.1}{0.01} = \frac{2.303}{115} = 0.0200 s^{- 1} = 2 \times 1 0^{- 2} s^{- 1}

JEE Main · 2024 · 01 Feb 2024 · Shift 2 · Integer answer