colligative properties

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Colligative properties are properties of solutions that depend on the number of molecules in a given volume of solvent and not on the properties (e.g. size or mass) of the molecules.^[1] Colligative properties include: 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 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 Point_total = Boiling Point_solvent + ΔT_b

where

ΔT_b = molality * K_b * i, (K_b = ebullioscopic constant, which is 0.51°C kg/mol for the boiling point of water; i = Van 't Hoff factor)

Since boiling point is achieved in the establishment of equilibrium between liquid and gas phase, that is, the number of molecules entering the molecules of a system equals the number of vapor molecules leaving the system, then an addition of solute would cause to hinder some of the molecules to leave the system because they are covering in the surface. To compensate for this and re-attain the equilibrium, boiling point therefore is achieved at higher temperature.

Freezing point depression

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, this is very fine; 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, less molecules participate in the equilibrium. Again, re-establishment of equilibrium is achieved at a lower temperature at which the rate of freezing becomes equal at the rate of solidifying.

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; T is absolute temperature; n is the number of moles of solute; R = 8.3145 J K-1 mol-1, the molar gas constant; i = Van 't Hoff factor.

References

1. ^ W.J. Moore Physical ChemistryPrentice-Hall 1972