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The first order conversion A(aq) -> B(aq) + C(aq) involves species that are all optically active. Initially only A is present in 500 mL of solution. Exactly 100 minutes after the start the solution becomes optically inactive (net rotation zero). Given specific rotations of +50 deg per molar for A, -20 deg per molar for B and +10 deg per molar for C, find the time (in minutes) for (875/9)% of the reaction to be completed.
- 100
- 150
- 200
- 300
Correct answer: 200
Solution
Setting net rotation 50(a-x) - 20x + 10x = 0 gives 50a = 60x, so x = (5/6)a, i.e. 83.33% reacted at 100 min. Since (875/9)% = 97.222% completion leaves fraction 1/36 remaining and 1/6 was left at 100 min, t = 100 * (log 36 / log 6) = 200 minutes.
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