Colligative Properties Reference Cheat Sheet

Key Facts

• Colligative properties depend on the number of solute particles in solution, not on the chemical identity of the solute.
• The van't Hoff factor $i$ represents the number of dissolved particles produced per formula unit of solute.
• Molality is defined as $m = \frac{\text{mol solute}}{\text{kg solvent}}$ and is used in boiling point and freezing point calculations.
• Boiling point elevation is calculated with $\Delta T_b = iK_bm$, so the solution boiling point is $T_b = T_b^{\circ} + \Delta T_b$.
• Freezing point depression is calculated with $\Delta T_f = iK_fm$, so the solution freezing point is $T_f = T_f^{\circ} - \Delta T_f$.
• Osmotic pressure is calculated with $\Pi = iMRT$, where $M$ is molarity and $T$ is temperature in kelvins.
• Vapor pressure lowering occurs because solute particles reduce the mole fraction of solvent, often described by $P_{\text{solution}} = X_{\text{solvent}}P_{\text{solvent}}^{\circ}$ for ideal solutions.
• For nonelectrolytes such as glucose, $i = 1$, while ideal $\text{NaCl}$ has $i \approx 2$ and ideal $\text{CaCl}_2$ has $i \approx 3$.

Vocabulary

Colligative property

A property of a solution that depends on the number of dissolved solute particles rather than their identity.

Molality

A concentration unit equal to moles of solute per kilogram of solvent, written as $m = \frac{\text{mol solute}}{\text{kg solvent}}$.

Van't Hoff factor

The factor $i$ that tells how many dissolved particles are produced from each formula unit of solute.

Boiling point elevation

The increase in a solution's boiling point compared with the pure solvent, calculated using $\Delta T_b = iK_bm$.

Freezing point depression

The decrease in a solution's freezing point compared with the pure solvent, calculated using $\Delta T_f = iK_fm$.

Osmotic pressure

The pressure needed to stop solvent from moving through a semipermeable membrane, calculated using $\Pi = iMRT$.