Colligative properties

Colligative properties are properties of solutions that depend on the number of molecules in a given volume of solvent and not on the properties/identity (e.g. size or mass) of the molecules.^[1] Colligative properties include: relative lowering of vapor pressure; elevation of boiling point; depression of freezing point and osmotic pressure. 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 vapour pressure and concentration is given by Raoult's law, which states that:

The vapour pressure of an ideal solution is dependent on the vapour 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.) Colligative properties are mostly studied for dilute solutions.

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 Point_total = Boiling Point_solvent + ΔT_b

where

ΔT_b = molality * K_b * i, (K_b = ebullioscopic constant, which is 0.512°C kg/mol for the boiling point of water; i = Van 't Hoff factor)

Boiling point is achieved in the establishment of equilibrium between liquid and gas phase. At the boiling point, the number of gas molecules condensing to liquid equals the number of liquid molecules evaporating to gas. Adding any solute effectively dilutes the concentration of the liquid molecules, slowing the liquid to gas portion of this equilibrium. To compensate for this and re-attain the equilibrium, boiling point is achieved at higher temperature. Any description of a colligative property which includes steric occlusion, or blocking of the surface to reduce the vapor pressure has no basis in reality, despite the fact that this explanation is frequently taught. This is also why vapor pressure and boiling point are independent of a liquid's accessible surface area. Alternatively, measurements for ionized solutes can lead to an estimation of the percentage of ionization taking place.

Freezing point depression (cryoscopy)

Freezing Point_solution = Freezing Point_solvent - ΔT_f

where

ΔT_f = molality * K_f * i, (K_f = cryoscopic constant, which is 1.86°C kg/mol for the freezing point of water,; i = Van 't Hoff factor)

Freezing point, or the equilibrium between a liquid and solid phase is generally lowered in the presence of a solute compared to a pure solvent. The solute particles cannot enter the solid phase, hence, fewer molecules participate in the equilibrium. Again, re-establishment of equilibrium is achieved at a lower temperature at which the rate of freezing becomes equal to the rate of liquefying.

The freezing point of a substance is defined as the temperature at which the vapor pressure of its liquid is equal to the vapor pressure of the corresponding solid. Since the addition of a non-volantile solute always lowers the vapor pressure of solvent, therefore, it will be in equilibrium with solid phase at a lower pressure and hence at a lower temperature. The difference between the freezing points of the pure solvent and the solution is called depression in freezing point or cryoscopy.

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

πV = nRTi

where: π = osmotic pressure; V is the volume; n is the number of moles of solute; R = .08206 L atm mol-1 K-1, the molar gas constant; T is absolute temperature; i = Van 't Hoff factor.

This can be simplified to π = "i"MRT (M = Molarity).

References

1. ^ W.J. Moore Physical Chemistry Prentice-Hall 1972