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.

검증된 단계별 안내

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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주요 개념

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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.