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For a first order reaction, A → products, r = k[A] or k = r / [A]. If r = 1.5 × 10⁻² and [A] = 0.5, calculate k and t₁/₂.

1. k = 3 × 10⁻², t₁/₂ = 23.1 min
2. k = 3 × 10⁻³, t₁/₂ = 23.1 min
3. k = 3 × 10⁻², t₁/₂ = 45.1 min
4. k = 3 × 10⁻³, t₁/₂ = 45.1 min

Correct answer: k = 3 × 10⁻², t₁/₂ = 23.1 min

Solution

For a first-order reaction, k = r / [A]. Substituting r = 1.5 × 10⁻² and [A] = 0.5, k = (1.5 × 10⁻²) / 0.5 = 3 × 10⁻². The half-life for a first-order reaction is t₁/₂ = 0.693 / k. Substituting k = 3 × 10⁻², t₁/₂ = 0.693 / (3 × 10⁻²) = 23.1 min.

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