A solution prepared by dissolving 3.00 g of ascorbic acid (vitamin C, C6H8O6) in 50.0 g of acetic acid has a freez- ing point that is depressed by ΔT = 1.33 °C below that ofpure acetic acid. What is the value of the molal freezing- point-depression constant for acetic acid?

Verified step by step guidance

1. Identify the formula for freezing point depression: \( \Delta T_f = i \cdot K_f \cdot m \), where \( \Delta T_f \) is the freezing point depression, \( i \) is the van't Hoff factor, \( K_f \) is the molal freezing-point-depression constant, and \( m \) is the molality of the solution.
2. Since ascorbic acid is a non-electrolyte, the van't Hoff factor \( i \) is 1.
3. Calculate the molality \( m \) of the solution using the formula \( m = \frac{\text{moles of solute}}{\text{kilograms of solvent}} \). First, find the moles of ascorbic acid by dividing the mass of ascorbic acid (3.00 g) by its molar mass (176.12 g/mol).
4. Convert the mass of acetic acid (50.0 g) to kilograms to use in the molality calculation.
5. Rearrange the freezing point depression formula to solve for \( K_f \): \( K_f = \frac{\Delta T_f}{i \cdot m} \), and substitute the known values to find \( K_f \).

Key Concepts

Freezing Point Depression

Freezing point depression is a colligative property that describes the lowering of a solvent's freezing point when a solute is added. The extent of this depression is directly proportional to the number of solute particles in the solution, which can be calculated using the formula ΔT = Kf * m, where ΔT is the change in freezing point, Kf is the molal freezing-point depression constant, and m is the molality of the solution.

Molality

Molality (m) is a measure of concentration defined as the number of moles of solute per kilogram of solvent. It is particularly useful in colligative property calculations because it accounts for the mass of the solvent, allowing for accurate determination of how the addition of solute affects properties like freezing point and boiling point.

Molar Mass of Ascorbic Acid

The molar mass of ascorbic acid (C6H8O6) is essential for converting grams of the solute into moles, which is necessary for calculating molality. The molar mass can be determined by summing the atomic masses of all the atoms in the molecular formula, allowing for the correct application of the freezing point depression formula in the context of the given problem.