What is the freezing point of an aqueous solution that boils at 106.5 °C?

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Identify the boiling point elevation formula: \( \Delta T_b = i \cdot K_b \cdot m \), where \( \Delta T_b \) is the boiling point elevation, \( i \) is the van't Hoff factor, \( K_b \) is the ebullioscopic constant, and \( m \) is the molality.

Calculate the boiling point elevation: \( \Delta T_b = 106.5 \, ^\circ\text{C} - 100 \, ^\circ\text{C} \).

Use the boiling point elevation to find the molality \( m \) of the solution: \( m = \frac{\Delta T_b}{i \cdot K_b} \). Assume \( i = 1 \) for a non-electrolyte unless specified otherwise.

Identify the freezing point depression formula: \( \Delta T_f = i \cdot K_f \cdot m \), where \( \Delta T_f \) is the freezing point depression and \( K_f \) is the cryoscopic constant.

Calculate the freezing point of the solution: \( T_f = 0 \, ^\circ\text{C} - \Delta T_f \).

Key Concepts

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

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 and freezing point depression, which are crucial for understanding how solutes affect the phase changes of solvents.

Boiling Point Elevation

Boiling point elevation occurs when a non-volatile solute is added to a solvent, resulting in an increase in the boiling point of the solution compared to the pure solvent. This phenomenon can be quantified using the formula ΔT_b = i * K_b * m, where ΔT_b is the boiling point elevation, i is the van 't Hoff factor, K_b is the ebullioscopic constant, and m is the molality of the solution.

Freezing Point Depression

Freezing point depression is the decrease in the freezing point of a solvent when a solute is dissolved in it. Similar to boiling point elevation, it can be calculated using the formula ΔT_f = i * K_f * m, where ΔT_f is the freezing point depression, i is the van 't Hoff factor, K_f is the cryoscopic constant, and m is the molality of the solution. This concept is essential for determining the freezing point of the solution in the given question.

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Freezing Point Depression

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