The Colligative Properties of Solutions

Rucete ✏ Chemistry In a Nutshell

1. What are Colligative Properties?

• Properties that depend on the number of dissolved particles, not their identity.
• Examples:
1. Boiling Point Elevation
2. Freezing Point Depression
3. Vapor Pressure Lowering
4. Osmotic Pressure (not included in this text, but also a colligative property).

2. Van’t Hoff Factor ($i$)

• Represents the number of particles a solute dissociates into in solution.
• Example:
• NaCl dissociates into 2 particles ($N{a}^{+}$ and $C{l}^{-}$), so $i=2$.
• CaCl₂ dissociates into 3 particles ($C{a}^{2+}$ and $2C{l}^{-}$), so $i=3$.

3. Boiling Point Elevation ($\mathrm{\Delta }{T}_b$)

• Adding a non-volatile solute increases the boiling point.

• Formula:

  $$\mathrm{\Delta }{T}_b=i{K}_{b}m$$
  • $i$ = Van’t Hoff factor
  • $K_b$ = Boiling point elevation constant
  • $m$ = Molality of the solution

• Reason: Solute lowers the vapor pressure, requiring a higher temperature to boil.

4. Freezing Point Depression ($\mathrm{\Delta }{T}_f$)

• Adding a solute lowers the freezing point of the solvent.

• Formula:

  $$\mathrm{\Delta }{T}_f=i{K}_{f}m$$
  • $i$ = Van’t Hoff factor
  • $K_f$ = Freezing point depression constant
  • $m$ = Molality of the solution

• Reason: Solute disrupts the solid lattice, making it harder for the liquid to freeze.

5. Vapor Pressure Lowering (Raoult’s Law)

• A non-volatile solute lowers the vapor pressure of the solvent.

• Formula:

  $$P_{\text{solution}}=X_{\text{solvent}}{P}_{\text{solvent}}$$
  • $P_{\text{solution}}$ = Vapor pressure of the solution
  • $X_{\text{solvent}}$ = Mole fraction of the solvent
  • $P_{\text{solvent}}$ = Vapor pressure of pure solvent

• Reason: Solute particles block some solvent molecules from evaporating.

Example Problems

1. Find the freezing point of a 0.500 m CaCl₂ solution.
   • Answer: -2.79°C.
2. Find the vapor pressure of a mixture of 18.02 g water and 0.200 m sugar at 29°C.
   • Given vapor pressure of water = 30.0 torr.
   • Answer: 9.99 torr.

In a nutshell

• More solute = Higher boiling point.
• More solute = Lower freezing point.
• More solute = Lower vapor pressure.