Colligative Properties

Definition

• Colligative Property: A property that depends on the concentration of solute particles, not their identity.

Types of Colligative Properties

1. Boiling Point Elevation
2. Freezing Point Depression
3. Osmotic Pressure
4. Vapor Pressure

1. Boiling Point Elevation

• Concept: Adding solute increases boiling point of the solution.
• Example:
  • Pure water boiling point = 100°C (at 1 atm).
  • Adding salt (NaCl) increases boiling point.
  • Boiling points for different NaCl molalities:
    • 1M NaCl: 101°C
    • 5M NaCl: 105.1°C
    • 10M NaCl: 110°C
• Formula:
  [ \Delta T = K_b \times m \times i ]
  • ( K_b ) = boiling point elevation constant (0.51 for water).
  • ( m ) = molality.
  • ( i ) = Van't Hoff factor (2 for NaCl due to Na⁺ and Cl⁻ ions).
• Calculation Example:
  • For 5M NaCl:
    • ( \Delta T = 0.51 \times 5 \times 2 = 5.1 )
    • New boiling point = 100 + 5.1 = 105.1°C.

2. Freezing Point Depression

• Concept: Adding solute decreases the freezing point of the solution.
• Formula:
  [ \Delta T_f = -K_f \times m \times i ]
  • Negative sign indicates freezing point decreases.
  • ( K_f ) = freezing point depression constant (-1.86 for water).
• Example:
  • Pure water freezes at 0°C.
  • 1M NaCl:
    • ( \Delta T_f = -1.86 \times 1 imes 2 = -3.72 )
    • New freezing point = 0 - 3.72 = -3.72°C.
• Higher Concentration Effect:
  • 5M NaCl: Freezing point decreases by a factor of 5.

3. Vapor Pressure

• Concept: Vapor pressure of a solution is affected by the concentration of solute particles.
• Formula:
  [ P_{solution} = X_{solvent} imes P^{0}_{solvent} ]
  • ( P_{solution} ) = vapor pressure of the solution.
  • ( X_{solvent} ) = mole fraction of the solvent.
• Relationship:
  • As solute concentration increases, vapor pressure decreases (inverse relationship)._

4. Osmotic Pressure

• Formula:
  [ \pi = MRT imes i ]
  • ( \pi ) = osmotic pressure.
  • ( M ) = molarity.
  • ( R ) = gas constant (0.08206 L·atm/(mol·K)).
  • ( T ) = temperature in Kelvin.
• Relationship:
  • Osmotic pressure increases with increasing solute concentration (direct relationship).

Summary of Relationships

• Direct Relationships:
  • Boiling Point Elevation: Increases with solute concentration.
  • Osmotic Pressure: Increases with solute concentration.
• Inverse Relationships:
  • Freezing Point Depression: Decreases with solute concentration.
  • Vapor Pressure: Decreases with solute concentration.

Example Problems

Boiling Point Calculation

• Problem: 20g NaOH in 200g water.
  • Kb = 0.51.
  • Calculate molality:
    • Molar mass NaOH = 40g/mol.
    • Moles = 20g / 40g/mol = 0.5 moles.
    • kg solvent = 0.2kg.
    • Molality = 0.5 moles / 0.2kg = 2.5 m.
  • Calculate boiling point:
    • ( \Delta T = 0.51 \times 2.5 \times 2 = 2.55 ).
    • New boiling point = 100 + 2.55 = 102.55°C.

Freezing Point Calculation

• Problem: 400g AlCl3 in 1600g water.
  • Kf = 1.86.
  • Molar mass AlCl3 = 133.33g/mol.
  • Calculate molality:
    • Moles = 400g / 133.33g/mol = 3 moles.
    • kg solvent = 1.6kg.
    • Molality = 3 moles / 1.6kg = 1.875 m.
  • Calculate freezing point:
    • ( \Delta T_f = -1.86 imes 1.875 imes 4 = -13.95 ).
    • New freezing point = 0 - 13.95 = -13.95°C.

Final Problem: Highest Boiling Point

• Options: A, B, C, D - calculate MI values to determine highest.
  • Example Calculations:
    • A: 0.35 (m) x 4 (i) = 1.4
    • B: 0.75 (m) x 1 (i) = 0.75
    • C: 0.50 (m) x 3 (i) = 1.5
    • D: 0.80 (m) x 2 (i) = 1.6
  • Conclusion: Answer choice D has the highest boiling point due to the highest MI value.