What is the freezing point in °C of a solution prepared by dissolving 7.40 g of MgCl2 in 110 g of water if the value of Kf for water is given in Table 13.4, and the van’t Hoff factor for MgCl2 is i = 2.7?

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Calculate the molar mass of MgCl_2 by adding the atomic masses of Mg and Cl (Mg: 24.31 g/mol, Cl: 35.45 g/mol).

Determine the number of moles of MgCl_2 by dividing the mass of MgCl_2 (7.40 g) by its molar mass.

Calculate the molality of the solution by dividing the moles of MgCl_2 by the mass of water in kilograms (110 g = 0.110 kg).

Use 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 freezing point depression constant, and \( m \) is the molality.

Subtract \( \Delta T_f \) from the normal freezing point of water (0°C) to find the freezing point of the solution.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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 extent of this depression depends on the number of solute particles in the solution, which is calculated using the formula ΔTf = i * Kf * m, where ΔTf is the change in freezing point, i is the van’t Hoff factor, Kf is the freezing point depression constant, and m is the molality of the solution.

Van't Hoff Factor (i)

The van't Hoff factor (i) indicates the number of particles into which a solute dissociates in solution. For ionic compounds like MgCl2, which dissociates into three ions (one Mg²⁺ and two Cl⁻), the van't Hoff factor is typically greater than one. In this case, the given i value of 2.7 suggests that the solute behaves in a way that results in more particles than expected, possibly due to ion pairing or other interactions.

Molality (m)

Molality is a measure of concentration defined as the number of moles of solute per kilogram of solvent. It is expressed as m = moles of solute / mass of solvent (kg). In this problem, calculating the molality of the MgCl2 solution is essential for determining the freezing point depression, as it directly influences the extent of the freezing point change when the solute is added to the solvent.