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# Colligative properties

Colligative properties are properties of solutions that depend on the number of particles in a given volume of solvent and not on the mass of the particles. Colligative properties include: lowering of vapor pressure; elevation of boiling point; depression of freezing point; osmotic pressure (see Osmosis; Reverse Osmosis). Measurements of these properties for a dilute aqueous solution of a non-ionized solute such as urea or glucose can lead to accurate determinations of relative molecular masses. Alternatively, measurements for ionized solutes can lead to an estimation of the percentage of ionization taking place.

## Vapor pressure

The relationship between the lowering of vapor pressure and concentration is given by Raoult's law, which states that:

The vapor pressure of an ideal solution is dependent on the vapor pressure of each chemical component and the mole fraction of the component present in the solution. (For details, see the article on Raoult's law.)

## Boiling point and freezing point

Both the boiling point elevation and the freezing point depression are proportional to the lowering of vapor pressure in a dilute solution

### Boiling point elevation

Boiling Pointtotal = Boiling Pointsolvent + ΔTb

where

ΔTb = molality * Kb, (Kb = constant kinetic energy, which is 0.51 for boiling point)

### Freezing point depression

Freezing Pointtotal = Freezing Pointsolvent - ΔTf

where :ΔTf= molality * Kf, (Kf = constant kinetic energy, which is 1.86 for freezing point)

## Osmotic pressure

For a fixed mass of 1 kg of solvent, the change in temperature is given by

ΔT = (K * m) / M

where m is the mass of solute, M is the mass percentage of solute, and K is the boiling-point constant or freezing-point constant for that particular solvent.

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, PV = nRT, has an analog for ideal solutions:

πV = nRT

where: π = osmotic pressure; V is the volume containing 1 mole of solute; T is absolute temperature; n is the number of moles of solute; R = 8.3145 J K-1mol-1, the molar gas constant.