Colligative Properties - Osmotic Pressure

Osmotic Pressure

The osmotic pressure of a solution is the difference in pressure between the solution and the pure liquid solvent when the two are in equilibrium across a semipermeable membrane, which allows the passage of solvent molecules but not of solute particles. If the two phases are at the same initial pressure, there is a net transfer of solvent across the membrane into the solution known as osmosis. The process stops and equilibrium is attained when the pressure difference equals the osmotic pressure.

Two laws governing the osmotic pressure of a dilute solution were discovered by the German botanist W. F. P. Pfeffer and the Dutch chemist J. H. van’t Hoff:

1. The osmotic pressure of a dilute solution at constant temperature is directly proportional to its concentration.
2. The osmotic pressure of a solution is directly proportional to its absolute temperature.

These are analogous to Boyle's law and Charles's Law for gases. Similarly, the combined ideal gas law, has as analog for ideal solutions, where is osmotic pressure; V is the volume; n is the number of moles of solute; R is the molar gas constant 8.314 J K-1 mol-1; T is absolute temperature; and i is the Van 't Hoff factor.

The osmotic pressure is then proportional to the molar concentration, since

The osmotic pressure is proportional to the concentration of solute particles ci and is therefore a colligative property.

As with the other colligative properties, this equation is a consequence of the equality of solvent chemical potentials of the two phases in equilibrium. In this case the phases are the pure solvent at pressure P and the solution at total pressure P + π.