Colligative properties

[1] The number ratio can be related to the various units for concentration of a solution such as molarity, molality, normality (chemistry), etc.

Only properties which result from the dissolution of a nonvolatile solute in a volatile liquid solvent are considered.

[2] They are essentially solvent properties which are changed by the presence of the solute.

The solute particles displace some solvent molecules in the liquid phase and thereby reduce the concentration of solvent and increase its entropy, so that the colligative properties are independent of the nature of the solute.

The word colligative is derived from the Latin colligatus meaning bound together.

[3] This indicates that all colligative properties have a common feature, namely that they are related only to the number of solute molecules relative to the number of solvent molecules and not to the nature of the solute.

Measurement of colligative properties for a dilute solution of a non-ionized solute such as urea or glucose in water or another solvent can lead to determinations of relative molar masses, both for small molecules and for polymers which cannot be studied by other means.

Alternatively, measurements for ionized solutes can lead to an estimation of the percentage of dissociation taking place.

In fact, all of the properties listed above are colligative only in the dilute limit: at higher concentrations, the freezing point depression, boiling point elevation, vapor pressure elevation or depression, and osmotic pressure are all dependent on the chemical nature of the solvent and the solute.

A vapor is a substance in a gaseous state at a temperature lower than its critical point.

For an ideal solution, the equilibrium vapor pressure is given by Raoult's law as

The vapor pressure lowering relative to pure solvent is

, which represents the true number of solute particles for each formula unit.

The measured colligative properties show that i is somewhat less than 3 due to ion association.

These properties are colligative in systems where the solute is essentially confined to the liquid phase.

The boiling point of a liquid at a given external pressure is the temperature (

The boiling point of a pure solvent is increased by the addition of a non-volatile solute, and the elevation can be measured by ebullioscopy.

It is found that Here i is the van 't Hoff factor as above, Kb is the ebullioscopic constant of the solvent (equal to 0.512 °C kg/mol for water), and m is the molality of the solution.

The boiling point is the temperature at which there is equilibrium between liquid and gas phases.

Adding a solute dilutes the concentration of the liquid molecules and reduces the rate of evaporation.

To compensate for this and re-attain equilibrium, the boiling point occurs at a higher temperature.

At the boiling point, the chemical potential μA of the solvent in the solution phase equals the chemical potential in the pure vapor phase above the solution.

It is found that Here Kf is the cryoscopic constant (equal to 1.86 °C kg/mol for the freezing point of water), i is the van 't Hoff factor, and m the molality (in mol/kg).

At the lower freezing point, the vapor pressure of the liquid is equal to the vapor pressure of the corresponding solid, and the chemical potentials of the two phases are equal as well.

The equality of chemical potentials permits the evaluation of the cryoscopic constant as

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.

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.

, 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.

[8] The word colligative (Latin: co, ligare) was introduced in 1891 by Wilhelm Ostwald.