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62 g of ethylene glycol is dissolved in 500 g of water and placed in a refrigerator at 263 K. What mass of ice (in grams) separates out at this temperature? (Kf for water = 1.86 K per unit molality)

1. 100 g
2. 200 g
3. 314 g
4. 400 g

Correct answer: 314 g

Solution

Ethylene glycol (MW = 62 g/mol). Moles = 62/62 = 1 mol. The refrigerator is at 263 K, so Delta_Tf = 273 - 263 = 10 K. As ice forms, solute concentrates in remaining liquid. Let w g of ice form. Remaining water = (500 - w) g. Molality = 1 mol / ((500-w)/1000 kg) = 1000/(500-w). Delta_Tf = Kf * m: 10 = 1.86 * 1000/(500-w). 500 - w = 186. w = 314 g.

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