Colligative properties

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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 vapour 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.

[edit] Vapor pressure

The relationship between the lowering of vapor pressure and concentration is given by Raoult’s law, which states that the relative lowering of the vapor pressure is equal to the mole fraction of the solute in the solution.

Here p0 is the vapor pressure of pure solvent; p is the vapor pressure of solution; n is the number of moles of solute; and N is the number of moles of solvent.

As this relationship is true only for very dilute solutions, in which n is very small by comparison with N, it can be approximated by:

The left-hand side of the equation corresponds to the relative lowering of vapour pressure—that is the actual lowering divided by the original vapor pressure. The right-hand side of the equation is the ratio of the number of solute particles to the number of solvent particles.

[edit] Boiling point and freezing point

Both the elevation of the boiling point and the depression of the freezing point are proportional to the lowering of vapour pressure, provided only dilute solutions are considered.

[edit] 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 relative molecular mass of solute, and K is the boiling-point constant or freezing-point constant. K is a constant for a 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:

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

These are analogous to Boyle’s law and Charles’ law for gases. A similar equation can be used:

pV = n RT

where: p = 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.