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Multiple Choice
The freezing point of ethanol is -114.6°C. The molal freezing point depression constant for ethanol is 2.00°C/m. What is the freezing point of a solution prepared by dissolving 50.0 g of glycerin (C3H8O3, a nonelectrolyte) in 200.0 g of ethanol?
A
-115.4°C
B
-113.0°C
C
-116.2°C
D
-117.8°C
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1
Identify the given values: the freezing point of pure ethanol is -114.6°C, the molal freezing point depression constant (Kf) is 2.00°C/m, the mass of glycerin is 50.0 g, and the mass of ethanol is 200.0 g.
Calculate the molality of the solution. First, determine the moles of glycerin using its molar mass (C3H8O3). The molar mass of glycerin is calculated as follows: (3 * 12.01 g/mol for C) + (8 * 1.01 g/mol for H) + (3 * 16.00 g/mol for O).
Convert the mass of ethanol to kilograms to use in the molality formula. Since 200.0 g of ethanol is given, convert it to kg by dividing by 1000.
Use the formula for molality (m): m = moles of solute / kilograms of solvent. Substitute the moles of glycerin and the kilograms of ethanol to find the molality of the solution.
Apply the freezing point depression formula: ΔTf = Kf * m, where ΔTf is the change in freezing point. Subtract ΔTf from the freezing point of pure ethanol to find the new freezing point of the solution.