Using data from Table 13.3, calculate the freezing and boiling points of each of the following solutions: (a) 0.25 m glucose in ethanol; (b) 20.0 g of decane, C₁₀H₂₂, in 50.0 g CHCl₃; (c) 3.50 g NaOH in 175 g of water, (d) 0.45 mol ethylene glycol and 0.15 mol KBr in 150 g H₂O.

Verified step by step guidance

1. Identify the solute and solvent in the solution. Here, decane (C_{10}H_{22}) is the solute, and chloroform (CHCl_{3}) is the solvent.
2. Calculate the molality (m) of the solution using the formula: \( m = \frac{\text{moles of solute}}{\text{kilograms of solvent}} \). First, find the moles of decane by dividing its mass by its molar mass.
3. 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 non-electrolytes like decane), \( K_f \) is the freezing point depression constant for chloroform, and \( m \) is the molality calculated in the previous step.
4. Calculate the new freezing point by subtracting \( \Delta T_f \) from the normal freezing point of chloroform.
5. 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 chloroform. Calculate the new boiling point by adding \( \Delta T_b \) to the normal boiling point of chloroform.

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 and freezing point depression, which are crucial for understanding how the addition of a solute, like decane, affects the phase changes of the solvent, in this case, chloroform.

Boiling Point Elevation

Boiling point elevation is a colligative property that describes how the boiling point of a solvent increases when a non-volatile solute is added. The extent of this elevation can be calculated using the formula ΔT_b = i * K_b * m, where ΔT_b is the change in boiling point, K_b is the ebullioscopic constant of the solvent, and m is the molality of the solution. Understanding this concept is essential for calculating the new boiling point of the chloroform solution.

Freezing Point Depression

Freezing point depression is another colligative property that indicates how the freezing point of a solvent decreases when a solute is added. This can be calculated using the formula ΔT_f = i * K_f * m, where ΔT_f is the change in freezing point, K_f is the cryoscopic constant of the solvent, and m is the molality. This concept is vital for determining how the addition of decane will lower the freezing point of chloroform.