The half life for the decomposition of gaseous compound A is 240 s when the gaseous pressure was 500 Torr initially. When the pressure was 250 Torr, the half life was found to be 4.0 min. The order of the reaction is...... (Nearest integer)
Answer: 1
Solution
For a reaction of order n, the half-life is related to initial concentration (or pressure) by:
t₁/₂ ∝ [A]₀^(1-n)
Given:
Since both half-lives are equal (4.0 min) despite different initial pressures, the half-life is independent of initial concentration/pressure. This is characteristic of a first-order reaction, where:
t₁/₂ = (ln 2)/k = constant (independent of [A]₀)
For first-order: 1 - n = 0, so n = 1
Answer: 1
t₁/₂ ∝ [A]₀^(1-n)
Given:
- At P₀ = 500 Torr: t₁/₂ = 240 s = 4.0 min
- At P₀ = 250 Torr: t₁/₂ = 4.0 min
Since both half-lives are equal (4.0 min) despite different initial pressures, the half-life is independent of initial concentration/pressure. This is characteristic of a first-order reaction, where:
t₁/₂ = (ln 2)/k = constant (independent of [A]₀)
For first-order: 1 - n = 0, so n = 1
Answer: 1
JEE Main · 2022 · 25 Jul 2022 · Shift 1 · Integer answer