Use the van't Hoff factors in Table 13.9 to calculate each colligative property: a. the melting point of a 0.100 m iron(III) chloride solution

Verified step by step guidance

1. Identify the colligative property to be calculated: the melting point depression.
2. 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 cryoscopic constant, and \( m \) is the molality of the solution.
3. Determine the van't Hoff factor \( i \) for iron(III) chloride (FeCl₃). When FeCl₃ dissociates in water, it forms one Fe³⁺ ion and three Cl⁻ ions, so \( i = 4 \).
4. Look up the cryoscopic constant \( K_f \) for the solvent, which is typically water. For water, \( K_f \) is approximately 1.86 °C/m.
5. Substitute the values into the formula: \( \Delta T_f = 4 \cdot 1.86 \cdot 0.100 \) to find the change in freezing point, and subtract \( \Delta T_f \) from the normal freezing point of water (0 °C) to find the new freezing point.

Key Concepts

Colligative Properties

Colligative properties are physical properties of solutions that depend on the number of solute particles in a given amount of solvent, rather than the identity of the solute. These properties include boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure. Understanding these properties is essential for calculating changes in physical states when solutes are added to solvents.

van't Hoff Factor (i)

The van't Hoff factor (i) is a dimensionless number that represents the number of particles a solute dissociates into when dissolved in a solvent. For ionic compounds like iron(III) chloride (FeCl3), which dissociates into four ions (one Fe³⁺ and three Cl⁻), the van't Hoff factor is 4. This factor is crucial for accurately calculating colligative properties, as it directly influences the extent of property changes.

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 freezing point depression can be calculated using 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 vital for determining the new freezing point of a solution containing iron(III) chloride.