Osmotic Pressure and the van’t Hoff Factor
The most sensitive of the colligative properties, and the only one practical for measuring the molar mass of very large molecules.
What osmotic pressure is
Separate pure solvent from a solution by a membrane that passes solvent but not solute. Solvent flows into the solution. Osmotic pressure is the pressure that must be applied to the solution to stop that flow exactly.
The driving force is the difference in chemical potential of the solvent on the two sides. Adding solute lowers the solvent's chemical potential, so solvent moves to where its potential is lower — the same reasoning that underlies every colligative property.
The van't Hoff equation
The formal resemblance to the ideal gas equation is striking, and it is not accidental — both describe the behaviour of a dilute species distributed through a volume. It holds for dilute solutions; concentrated ones require correction terms.
Why it is the most sensitive colligative property
| Property | Suitable for | Practical limitation |
|---|---|---|
| Freezing point depression | Small molecules | Effect too small for macromolecules |
| Boiling point elevation | Small molecules | Solute may decompose at the boiling point |
| Osmotic pressure | Macromolecules, proteins, polymers | Needs a suitable membrane; slow to equilibrate |
Molar mass determination
Rearranging with concentration expressed as mass per unit volume:
Measure the osmotic pressure of a solution of known mass concentration, and the molar mass follows. For polymers this gives the number average molar mass specifically, because colligative properties count particles regardless of their size — a point worth stating, since other methods give different averages.
The van't Hoff factor
Colligative properties depend on the number of particles, so a solute that dissociates produces a larger effect than its formula concentration suggests, and one that associates produces a smaller one.
| Solute behaviour | i | Example situation |
|---|---|---|
| No dissociation or association | 1 | A simple molecular solute |
| Dissociates into n particles | Approaches n | A strong electrolyte |
| Partially dissociates | Between 1 and n | A weak electrolyte |
| Associates into dimers | Approaches 0.5 | A carboxylic acid in a non-polar solvent |
The association case is the one most often missed. A carboxylic acid dimerises through hydrogen bonding in a non-polar solvent, halving the particle count and giving i near 0.5. A question reporting a factor below one is testing whether association is recognised.
From i, the degree of dissociation or association follows, which makes colligative measurements a route to equilibrium constants for weak electrolytes.
Where osmosis matters practically
- Cells must be kept in solutions of matching osmotic pressure, or they swell or shrink.
- Reverse osmosis applies pressure exceeding the osmotic pressure to force solvent the other way, which is how water is desalinated.
- Preservation by high sugar or salt concentration works by drawing water out of microorganisms.
Frequently asked questions
Why is osmotic pressure so much larger than other colligative effects?
Because of the size of the proportionality constant. The same molar concentration that changes a freezing point imperceptibly produces an easily measurable pressure.
Why is it preferred for polymers?
Because a polymer's high molar mass means very few moles per gram, so all other colligative effects are too small to measure. Osmotic pressure remains measurable.
Can the van't Hoff factor be less than one?
Yes, when the solute associates. Dimerisation halves the particle count and gives a factor near 0.5.
Why does the equation resemble the ideal gas law?
Because both describe a dilute species spread through a volume, with the same entropic origin. The resemblance is formal but reflects genuinely similar physics.
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