A solution was prepared by dissolving 2.500 g of a non-dissociating solute in 125 g of pure water. The resulting solution has a freezing point of -0.190°C. The Kf of water is 1.86°C/m. What is the molar mass of the unknown solute?

• A. 125 g/mol
• B. 245 g/mol
• C. 58.5 g/mol
• D. 186 g/mol

Answer: (B)

Verified step by step guidance

1. Step 1: Understand the concept of freezing point depression. The freezing point of a solution is lower than that of the pure solvent due to the presence of a solute. The change in freezing point (ΔTf) can be calculated using the formula: ΔTf = i * Kf * m, where i is the van't Hoff factor (which is 1 for non-dissociating solutes), Kf is the freezing point depression constant, and m is the molality of the solution.
2. Step 2: Calculate the change in freezing point (ΔTf). Since the freezing point of the solution is -0.190°C and the freezing point of pure water is 0°C, the change in freezing point is ΔTf = 0°C - (-0.190°C) = 0.190°C.
3. Step 3: Use the formula for freezing point depression to find the molality (m) of the solution. Rearrange the formula to solve for m: m = ΔTf / (i * Kf). Substitute the values: m = 0.190°C / (1 * 1.86°C/m).
4. Step 4: Calculate the number of moles of solute using the molality. Molality (m) is defined as moles of solute per kilogram of solvent. Rearrange the definition to solve for moles of solute: moles of solute = m * mass of solvent (in kg). Convert the mass of water from grams to kilograms: 125 g = 0.125 kg. Substitute the values to find the moles of solute.
5. Step 5: Determine the molar mass of the solute. Molar mass is defined as the mass of solute divided by the number of moles of solute. Use the mass of the solute (2.500 g) and the moles of solute calculated in the previous step to find the molar mass: molar mass = mass of solute / moles of solute.