Question Detail
Question
It takes 42.0 min for the concentration of a reactant in a first-order reaction to drop from 0.45 M to 0.32 M at 25 °C. How long will it take for the reaction to be 90% complete?
Correct Answer
Option D is the correct answer.
Detailed Explanation
First-order: k = (1/t) ln([A]₀/[A]) = (1/42) ln(0.45/0.32) = (1/42) × 0.341 = 0.00812 min⁻¹. For 90% complete, 10% remains: [A] = 0.1[A]₀. t = (1/0.00812) ln(1/0.1) = 123.15 × 2.3026 = 283.6 min ≈ 284 min.
Hint
Use the integrated rate law for first-order kinetics: ln([A]₀/[A]) = kt.