Decomposition of A is a first order reaction at $\mathrm{T}(\mathrm{K})$ and is given by $\mathrm{A}(\mathrm{g}) \rightarrow \mathrm{B}(\mathrm{g})+\mathrm{C}(\mathrm{g})$. In a closed 1 L vessel, 1 bar $\mathrm{A}(\mathrm{g})$ is allowed to decompose at $\mathrm{T}(\mathrm{K})$. After 100 minutes, the total pressure was 1.5 bar. What is the rate constant (in $\min^{-1}$) of the reaction? ($\log 2=0.3$)

JEE Main · 2026 · 21 Jan 2026 · Shift 2 · Chemical Kinetics

Decomposition of A is a first order reaction at

T (K)

and is given by

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

. In a closed 1 L vessel, 1 bar

A (g)

is allowed to decompose at

T (K)

. After 100 minutes, the total pressure was 1.5 bar. What is the rate constant (in

min^{- 1}

) of the reaction? (

lo g 2 = 0.3

)

Answer: (B)

Let

p

be the pressure of A that has decomposed; the stoichiometry makes the total pressure

(1 - p) + p + p = 1 + p

. Setting

1 + p = 1.5

gives

p = 0.5

bar, so the pressure of A remaining is

0.5

bar. For a first-order reaction

k = \frac{2.303}{t} lo g \frac{p _{0}}{p _{A}} = \frac{2.303}{100} lo g \frac{1}{0.5} = \frac{2.303 \times 0.3}{100}

. Evaluating gives

k = 6.9 \times 1 0^{- 3} mi n^{- 1}

JEE Main · 2026 · 21 Jan 2026 · Shift 2 · Single correct option