The van't Hoff factor for CaCl2 is 2.71. What is its mass % in an aqueous solution that has Tf = - 1.14 °C?

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 change in freezing point, \( i \) is the van't Hoff factor, \( K_f \) is the cryoscopic constant, and \( m \) is the molality.
2. Rearrange the formula to solve for molality \( m \): \( m = \frac{\Delta T_f}{i \cdot K_f} \).
3. Substitute the given values into the equation: \( \Delta T_f = 1.14 \text{ °C} \), \( i = 2.71 \), and use the known \( K_f \) for water, which is 1.86 °C kg/mol.
4. Calculate the molality \( m \) using the rearranged formula.
5. Use the definition of molality \( m = \frac{\text{moles of solute}}{\text{kg of solvent}} \) to find the mass of \( \text{CaCl}_2 \) and then calculate the mass percent using \( \text{mass percent} = \frac{\text{mass of solute}}{\text{mass of solution}} \times 100 \).

Key Concepts

van't Hoff Factor (i)

The van't Hoff factor (i) represents the number of particles into which a solute dissociates in solution. For ionic compounds like CaCl2, which dissociates into three ions (one Ca²⁺ and two Cl⁻), the theoretical van't Hoff factor is 3. However, the given value of 2.71 suggests some degree of ion pairing or incomplete dissociation in the solution.

Freezing Point Depression

Freezing point depression is a colligative property that describes how the freezing point of a solvent decreases when a solute is added. The relationship is given by the formula ΔTf = i * Kf * m, where ΔTf is the change in freezing point, Kf is the freezing point depression constant of the solvent, and m is the molality of the solution. This concept is essential for calculating the concentration of the solute based on the observed freezing point.

Mass Percent Concentration

Mass percent concentration is a way to express the concentration of a solute in a solution, defined as the mass of the solute divided by the total mass of the solution, multiplied by 100. It is crucial for determining how much of the solute is present in a given mass of solution, which can be derived from the molality and the density of the solution when solving problems related to colligative properties.