Abnormal Molar Masses
Quick Notes
- Some solutes show abnormal molar masses when determined via colligative properties.
- Abnormality arises due to either:
- Association of solute molecules (e.g. acetic acid in benzene),
- Dissociation of solute into ions (e.g. KCl in water).
- The van’t Hoff factor (i) is introduced to account for this abnormality.
- Modified formula for molar mass: Observed molar mass = Normal molar mass / i
- Colligative property expressions are corrected by multiplying with van’t Hoff factor (i).
- If i > 1 → dissociation (e.g. salts),
If i < 1 → association (e.g. carboxylic acids).
Full Notes
We can use colligative properties (like boiling point elevation or freezing point depression) to find the molar mass of a non-volatile solute. But sometimes, we get unusual (abnormal) results. This happens when solute particles join together (association) or split apart (dissociation) in solution.
Colligative Properties
Association or dissociation changes the number of solute particles in solution, which directly affects colligative properties.
Example: Association in non-aqueous solvent
Acetic acid in benzene forms dimers: 2 CH3COOH ⇌ (CH3COOH)2.
Fewer particles means smaller effect on properties and apparent molar mass appears higher.

Example: Dissociation in aqueous solution
Potassium chloride (KCl) in water dissociates: KCl → K+ + Cl−.
More particles means bigger effect on properties and apparent molar mass appears lower.

Abnormal Molar Mass
As seen above, when solute molecules associate (combine) or dissociate (split) in solution, the number of particles changes.
- This affects colligative properties (like ΔTb, ΔTf, etc.), leading to an abnormal molar mass.
- Association reduces particle number → lower effect → molar mass appears higher
- Dissociation increases particle number → higher effect → molar mass appears lower
van’t Hoff Factor (i)
To correct for these changes, van’t Hoff introduced a factor i, defined as:

- i = Normal molar mass / Abnormal molar mass
- i = Observed colligative property / Calculated colligative property
- i = (Total moles of particles after dissociation or association) / (Initial moles before dissociation or association)
Interpretation:
- If i < 1 → Association (fewer particles)
- If i > 1 → Dissociation (more particles)
Examples: Typical i values
- Ethanoic acid in benzene → i ≈ 0.5 (association)
- KCl in water → i ≈ 2 (dissociation)
Modified Colligative Property Formulas Using i
Relative lowering of vapour pressure

Elevation of boiling point

Depression of freezing point

Osmotic pressure

Key Point
The van’t Hoff factor allows chemists to account for deviations in colligative property-based molar mass calculations caused by molecular association or dissociation in solution. This correction is crucial when dealing with electrolytes and compounds forming aggregates in non-aqueous solvents.
Summary
- Association lowers particle number and makes molar mass appear higher.
- Dissociation raises particle number and makes molar mass appear lower.
- van’t Hoff factor i corrects colligative property formulas for abnormal molar masses.
- Use corrected expressions with i to determine accurate molar masses.