Calculate the freezing point and the boiling point of each...

Calculate the freezing point and the boiling point of each of the following aqueous solutions. (Assume complete dissociation.)
a. $0.050 \mathrm{~m} \mathrm{MgCl}_{2}$
b. $0.050 \mathrm{~m} \mathrm{FeCl}_{3}$

Key Concepts

Colligative Properties

Colligative properties are characteristics of solutions that depend on the number of dissolved particles rather than on their identity. These include changes in boiling point, freezing point, vapor pressure, and osmotic pressure, and are fundamental to understanding how solutes influence the physical properties of solvents.

Freezing Point Depression

Freezing point depression is a colligative property where the addition of a solute to a solvent lowers the freezing point of the resulting solution compared to the pure solvent. This depression is proportional to the molal concentration of the particles in solution and is calculated using the freezing point depression constant of the solvent along with the van’t Hoff factor for solute dissociation.

Boiling Point Elevation

Boiling point elevation is another colligative property where the addition of a non-volatile solute to a solvent raises the boiling point of the solution relative to the pure solvent. This effect is likewise proportional to the molal concentration of dissolved particles and involves the boiling point elevation constant of the solvent combined with the effective number of particles from solute dissociation.

Van't Hoff Factor

The van’t Hoff factor represents the number of particles into which a solute dissociates in solution. For substances that undergo complete dissociation, like many ionic compounds, the van’t Hoff factor is an essential part of calculating colligative property effects. It quantifies the effective concentration of solute particles that alter the boiling and freezing points of the solvent.

Molality

Molality is a concentration unit defined as the number of moles of solute per kilogram of solvent. It is particularly useful in colligative property calculations because it is independent of temperature, allowing for precise determination of freezing point depression and boiling point elevation in solutions.

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