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Two first-order reactions have half-lives in the ratio 3:2. Let t1 be the time for the first reaction to reach 25% completion, and t2 be the time for the second reaction to reach 75% completion. Calculate the ratio t1: t2.
- 0.3: 1
- 0.5: 1
- 0.2: 1
- 0.1: 1
Correct answer: 0.3: 1
Solution
With half-life ratio 3:2, k1:k2 = 2:3. For 25% completion of reaction 1: t1 = ln(4/3)/k1. For 75% completion of reaction 2: t2 = ln(4)/k2 = 2*ln(2)/k2. The ratio t1/t2 = [ln(4/3)*k2] / [2*ln(2)*k1] = ln(4/3)/(2*ln(2)) * (3/2) ~ 0.287/1.386 * 1.5 ~ 0.311 ~ 0.3.
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