Ch.14 - Solutions

Problem 83

Chapter 14, Problem 83

A glucose solution contains 74.2 g of glucose (C6H12O6) in 455 g of water. Determine the freezing point and boiling point of the solution.

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insert step 1> Calculate the molality of the solution by dividing the moles of glucose by the mass of water in kilograms. First, find the moles of glucose using its molar mass (C_6H_{12}O_6).

insert step 2> Use the freezing point depression formula: \( \Delta T_f = i \cdot K_f \cdot m \), where \( i \) is the van't Hoff factor (which is 1 for glucose, a non-electrolyte), \( K_f \) is the freezing point depression constant for water, and \( m \) is the molality calculated in step 1.

insert step 3> Subtract the \( \Delta T_f \) from the normal freezing point of water (0°C) to find the new freezing point of the solution.

insert step 4> Use the boiling point elevation formula: \( \Delta T_b = i \cdot K_b \cdot m \), where \( K_b \) is the boiling point elevation constant for water, and \( m \) is the molality calculated in step 1.

insert step 5> Add the \( \Delta T_b \) to the normal boiling point of water (100°C) to find the new boiling point of the solution.

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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 occur when a solute is added to a solvent, affecting the temperature at which the solvent freezes or boils.

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 dissolved in it. The extent of freezing point depression can be 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 of the solvent, and m is the molality of the solution.

Boiling Point Elevation

Boiling point elevation is another colligative property that refers to the increase in the boiling point of a solvent when a solute is added. This phenomenon can be quantified using the formula ΔTb = i * Kb * m, where ΔTb is the change in boiling point, i is the van 't Hoff factor, Kb is the boiling point elevation constant of the solvent, and m is the molality of the solution.

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