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An aqueous solution of NaOH is 40% by weight (w/w) and has a density of 2 g/mL. If the ratio of molarity M to molality m of this solution is x: 1, find the value of 5x/3.
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Correct answer: 2
Solution
Take 100 g of solution: 40 g NaOH (molar mass 40 g/mol = 1 mol), 60 g water (solvent). Volume = 100/2 = 50 mL = 0.05 L. Molarity M = 1/0.05 = 20 mol/L. Molality m = 1/0.060 kg = 16.67 mol/kg = 50/3 mol/kg. Ratio x = M/m = 20/(50/3) = 20*3/50 = 6/5 = 1.2. So 5x/3 = 5*1.2/3 = 6/3 = 2. The correct answer is 2. Note: the original problem's options (5, 10, 15, 20) appear to be from a different version of this question with different density; the computed answer with d = 2 g/mL is unambiguously 2.
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