Physical Chemistry , 1st ed.

7.8 Colligative Properties

Consider the solvent of a solution. It is typically defined as the component with

the majority mole fraction, although with concentrated aqueous solutions this

definition is often relaxed. Compare the properties of a solution with a non-

volatile solute with the same properties of the pure solvent. In certain cases,

the physical properties are different. These properties differ because of the

presence of solute molecules. The properties are independent of the identityof

the solute molecules, and the change in the property is related only to the num-

berof solute molecules. These properties are called colligative properties,where

the word colligativecomes from the Latin words meaning “to bind together”

which is what the particles of solute and solvent are doing, in a sense. The four

common colligative properties are vapor pressure depression, boiling point el-

evation, freezing point depression, and osmotic pressure.

We have already addressed vapor pressure depression, in the form of Raoult’s

law. The vapor pressure of a pure liquid is lowered when a solute is added, and

the vapor pressure is proportional to the mole fraction of the solvent:

psolvxsolvp*solv

where psolvis the true pressure of the solvent,p*solvis the vapor pressure of the

pure solvent, and xsolvis the mole fraction of the solvent in the solution. Since

mole fractions are always 1 or less, the vapor pressure of a solvent in a solu-

tion is always less than the vapor pressure of the pure liquid.Notice, too, that

Raoult’s law doesn’t care what the solute is, it only depends on the mole frac-

tion of the solvent. This is one of the characteristics of a colligative property.

It’s not what, but how much.

Before considering the next colligative properties, we recall the concentration

unit molality.The molality of a solution is similar to molarity except that it is

defined in terms of the number of kilograms of solvent, not liters of solution:

molality  (7.40)

Molality, abbreviated molal or m, is useful for colligative properties because

it is a more direct ratio of molecules of solute to molecules of solvent. The

unit molarity automatically includes the concept of partial molar volumes

because it is defined in terms of liters ofsolution,not liters of solvent. It is

also dependent on the amounts of solvent and solute (in mole and kilogram

units), but independent of volume or temperature. Thus, as Tchanges, the

concentration in molality units remains constant while the concentration

number of moles of solute



number of kilograms of solvent

7.8 Colligative Properties 193

Heating coil

(a) (b)

Purified

material

Collected

impurities

Figure 7.26 In zone refining of silicon, a heating coil melts a small part of the boule at a time.

As the liquid slowly solidifies, impurities remain concentrated in the liquid phase. As the molten

zone passes along the boule, eventually the impurities are collected at one end, which can then

be removed from the pure material.