What is the freezing point in °C of each of the solutions in Problem 13.102? For water, Kf = 1.86 °C·kg/mol.

Verified step by step guidance

1. Step 1: Identify the formula for freezing point depression, which is \( \Delta T_f = i \cdot K_f \cdot m \), where \( \Delta T_f \) is the change in freezing point, \( i \) is the van't Hoff factor, \( K_f \) is the freezing point depression constant, and \( m \) is the molality of the solution.
2. Step 2: Determine the van't Hoff factor \( i \) for the solute in the solution. This factor depends on the degree of dissociation of the solute in the solvent. For non-electrolytes, \( i = 1 \). For electrolytes, \( i \) is equal to the number of ions the solute dissociates into.
3. Step 3: Calculate the molality \( m \) of the solution using the formula \( m = \frac{\text{moles of solute}}{\text{kilograms of solvent}} \). You need the mass of the solute and the solvent to find this value.
4. Step 4: Substitute the values of \( i \), \( K_f \), and \( m \) into the freezing point depression formula to find \( \Delta T_f \).
5. Step 5: Subtract \( \Delta T_f \) from the normal freezing point of the solvent (0°C for water) to find the new freezing point of the solution.

Key Concepts

Freezing Point Depression

Freezing point depression is a colligative property that describes the decrease in the freezing point of a solvent when a solute is added. The extent of this depression depends on the number of solute particles in the solution rather than their identity. This phenomenon can be quantified using the formula ΔTf = Kf * m, where ΔTf is the change in freezing point, Kf is the 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 directly relates to the number of solute particles in a given mass of solvent. Unlike molarity, which is volume-based, molality remains unaffected by temperature changes, making it ideal for freezing point depression calculations.

Freezing Point Depression Constant (Kf)

The freezing point depression constant (Kf) is a property specific to each solvent that indicates how much the freezing point of the solvent decreases per mole of solute added per kilogram of solvent. For water, Kf is 1.86 °C·kg/mol, meaning that for every mole of solute dissolved in one kilogram of water, the freezing point will decrease by 1.86 °C. This constant is essential for calculating the new freezing point of solutions.