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X mL of a 60% (by weight) alcohol solution with density 0.6 g/mL is used completely to prepare 200 mL of a 12% (by weight) alcohol solution with density 0.9 g/mL. Find the value of X.
- 20
- 40
- 60
- 80
Correct answer: 60
Solution
Final solution: volume = 200 mL, density = 0.9 g/mL. Total mass = 200 * 0.9 = 180 g. Mass of alcohol = 12% of 180 = 21.6 g. Initial solution: volume = X mL, density = 0.6 g/mL. Total mass = 0.6X g. Mass of alcohol = 60% of 0.6X = 0.36X g. Since all the alcohol from initial solution goes to final solution: 0.36X = 21.6. X = 21.6 / 0.36 = 60 mL.
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