Using data from Table 13.3, calculate the freezing and boiling points of each of the following solutions: (a) 0.22 m glycerol (C₃H₈O₃) in ethanol, (b) 0.240 mol of naphthalene (C₁₀H₈) in 2.45 mol of chloroform, (c) 1.50 g NaCl in 0.250 kg of water, (d) 2.04 g KBr and 4.82 g of glucose (C₆H₁₂O₆) in 188 g of water.

검증된 단계별 안내

Identify the colligative properties involved: freezing point depression and boiling point elevation.

Use the formula for freezing point depression: \( \Delta T_f = i \cdot K_f \cdot m \), where \( i \) is the van't Hoff factor, \( K_f \) is the freezing point depression constant for chloroform, and \( m \) is the molality of the solution.

Calculate the molality \( m \) of the solution using the formula \( m = \frac{\text{moles of solute}}{\text{kilograms of solvent}} \). Here, the solute is naphthalene and the solvent is chloroform.

Use the formula for boiling point elevation: \( \Delta T_b = i \cdot K_b \cdot m \), where \( K_b \) is the boiling point elevation constant for chloroform.

Determine the new freezing and boiling points by subtracting \( \Delta T_f \) from the normal freezing point and adding \( \Delta T_b \) to the normal boiling point of chloroform.

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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 are crucial for calculating the changes in freezing and boiling points when a solute is added to a solvent.

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 can be calculated 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. Understanding this concept is essential for determining the new boiling point of the solution.