If the half-life (t1/2) for a first order reaction is 1 minute, then the time required for 99.9% com

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Question

If the half-life (t1/2) for a first order reaction is 1 minute, then the time required for 99.9% completion of the reaction is closest to :

Accepted Answer

Correct Answer: A — 10 minutesStep-by-step Solution:Method 1 (Half-life approach): For 99.9% completion, 0.1% (0.001 fraction) remains.After n half-lives: fraction remaining = (1/2)ⁿ → (1/2)ⁿ = 0.001 ≈ 1/1024 = (1/2)¹⁰ → n = 10t = 10 × t₁/₂ = 10 × 1 = 10 minutesMethod 2 (Formula): k = 0.693/1 = 0.693 min⁻¹t = (2.303/0.693) × log(1/0.001) = 3.322 × log(1000) = 3.322 × 3 ≈ 9.97 ≈ 10 minutesWhy other options are wrong: 2 min = only 2 half-lives (~75% complete); 4 min = 4 half-lives (~93.75%); 5 min = 5 half-lives (~96.9%).Key Concepts:Half-life (t₁/₂): t₁/₂ = 0.693/k (constant for first-order, independent of concentration)After n half-lives: [A]ₜ = [A]₀ × (1/2)ⁿ99.9% completion ≈ 10 half-lives (a useful rule of thumb)

If the half-life (t1/2) for a first order reaction is 1 minute, then the time required for 99.9% completion of the reaction is closest to :

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If the half-life (t1/2) for a first order reaction is 1 minute, then the time required for 99.9% completion of the reaction is closest to :

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