Colligative Properties: Calculations and Concepts

Posted on Jan 27, 2025 in Chemistry

Colligative properties are physical properties of solutions that depend on the concentration of solute particles, but not on the identity of the solute. These properties are crucial in understanding solution behavior.

Key Concepts

  1. Definition: Colligative properties depend on the number of solute particles in a solution.
  2. Physical Properties: These properties are affected by the physical characteristics of the solution.
  3. Four Main Properties:
    • Vapor pressure lowering
    • Boiling point elevation
    • Freezing point depression
    • Osmotic pressure

Vapor Pressure

The vapor pressure of a solution is affected by the presence of a nonvolatile solute. Here’s how:

  1. Nonvolatile Solute: The presence of a nonvolatile solute lowers the vapor pressure of the solvent.
  2. Intermolecular Forces:
    • If solute-solvent forces are weaker, vapor pressure increases.
    • If solute-solvent forces are stronger, vapor pressure decreases.

Ideal Solutions

An ideal solution is one where the interactions between solute and solvent molecules are similar to those between solute-solute and solvent-solvent molecules.

Calculations and Examples

Example 1: Glycerol Solution

Calculate the vapor pressure of a solution containing 65.0 mL of glycerol (density 1.26 g/mL) in 750 mL of water at 25°C. The vapor pressure of pure water at 25°C is 23.8 torr.

Example 2: Two-Component Solution

A solution is prepared by mixing 4.5 moles of substance A and 7.0 moles of substance B. Calculate the vapor pressure of the solution and the mole fraction of A in the vapor. Given: PA° = 53 torr and PB° = 34 torr.

Example 3: Glucose Solution

The vapor pressure of pure water at 110°C is 1070 torr. Calculate the vapor pressure of a solution containing 3.5 moles of glucose in 700 mL of water at 110°C.

Example 4: Lactose Solution

Calculate the vapor pressure of water above a solution prepared by adding 15.0 g of lactose to 100 mL of water at 25°C (P° = 23.8 torr).

Example 5: Ethanol Solution

At 53.5°C, the vapor pressure of water is 175 torr, and ethanol is 400 torr. A solution is prepared by mixing 500 mL of water and 5 moles of ethanol.

  • a) What is the mole fraction of ethanol in the solution?
  • b) Assuming ideal solution behavior, what is the vapor pressure of the solution at 53.5°C?
  • c) What is the mole fraction of ethanol in the vapor above the solution?

Example 6: Propylene Glycol Solution

Calculate the mass of propylene glycol needed to be added to 500 mL of water to reduce the vapor pressure by 4.5 torr at 25°C (P° = 23.8 torr).

Example 7: Glucose vs. Sucrose

Compare the vapor pressure of two solutions: one with 10g of glucose in 10L of water and another with 10g of sucrose in 1L of water at 20°C (P° = 75 torr). Are the vapor pressures the same? Justify your answer.

Boiling and Freezing Points

Example 8: NaCl Solution

A solution of NaCl (a nonvolatile solute) has a concentration of 3 mol/kg. Calculate the freezing point and boiling point of this solution. Given: Kb = 0.51 °C kg/mol and Kf = 1.86 °C kg/mol.