Core Concept

Colligative Properties are physical properties of solutions that change when a solute is added to a solvent. These properties depend solely on the number of solute particles in a solution, not their identity. The main colligative properties include vapor pressure lowering, boiling point elevation, freezing point depression, and osmotic pressure.

Key Colligative Properties

1. Vapor Pressure Lowering:

   • Adding a non-volatile solute (one that doesn’t evaporate) to a solvent decreases the solution’s vapor pressure.

   • Raoult’s Law describes this relationship: $P_{\text{solution}} = X_{\text{solvent}} \times P^{\circ}_{\text{solvent}}$

   • Where:

     • $P_{\text{solution}}$: Vapor pressure of the solution

     • $X_{\text{solvent}}$​: Mole fraction of the solvent

     • $P^{\circ}_{\text{solvent}}$​: Vapor pressure of the pure solvent

   • As solute particles occupy space at the surface, fewer solvent molecules can escape into the gas phase, resulting in lower vapor pressure.

2. Boiling Point Elevation:

   • When a solute is added, the boiling point of the solution becomes higher than that of the pure solvent.

   • Boiling Point Elevation Formula: $\Delta T_b = i \cdot K_b \cdot m$

   • Where:

     • ΔTb​: Boiling point elevation

     • i: Van’t Hoff factor (number of particles the solute dissociates into)

     • Kb​: Boiling point elevation constant (unique to each solvent)

     • m: Molality of the solution (moles of solute per kilogram of solvent)

   • This occurs because the addition of solute particles reduces the solvent’s ability to enter the vapor phase, requiring a higher temperature to reach the boiling point.

3. Freezing Point Depression:

   • Adding a solute lowers the freezing point of the solution relative to the pure solvent.

   • Freezing Point Depression Formula: $\Delta T_f = i \cdot K_f \cdot m$

   • Where:

     • $\Delta T_f$: Freezing point depression

     • i: Van’t Hoff factor

     • $K_f$​: Freezing point depression constant (specific to each solvent)

     • m: Molality of the solution

   • Solute particles disrupt the formation of the orderly solid structure, so a lower temperature is required for the solution to freeze.

4. Osmotic Pressure:

   • Osmotic pressure is the pressure required to stop the flow of solvent into a solution through a semipermeable membrane.

   • Osmotic Pressure Formula: Π = i ⋅ M ⋅ R ⋅ T

   • Where:

     • Π: Osmotic pressure

     • i: Van’t Hoff factor

     • M: Molarity of the solution

     • R: Ideal gas constant ($0.0821 \, \text{L} \cdot \text{atm} \, \text{mol}^{-1} \, \text{K}^{-1}$)

     • T: Temperature in Kelvin

   • Osmosis occurs when solvent molecules move through a semipermeable membrane to equalize concentration. Adding solute to one side increases osmotic pressure.

Key Concept: Van’t Hoff Factor (i)

• The Van’t Hoff factor, i, represents the number of particles into which a solute dissociates in solution.

  • For non-electrolytes (e.g., glucose), i = 1 because they do not dissociate.

  • For electrolytes (e.g., NaCl), i depends on the degree of dissociation (e.g., NaCl dissociates into $\text{Na}^+$ and $\text{Cl}^-$, so i = 2).

• The value of i affects the magnitude of all colligative properties.