USING COLLIGATIVE PROPERTIES TO DETERMINE MOLAR MASS
The colligative properties of nonelectrolyte solutions provide a means of determining the molar mass of a solute. Theoretically, any of the four colligative properties are suitable for this purpose. In practice, however, only freezing-point depression and osmotic pressure are used because they show the most pronounced changes. For example, osmotic pressure measurements are very useful for determining the molar masses of large molecules, such as proteins. Here we will cover only use of the freezing point depression.
Freezing Point Depression
The presence of solute molecules disturbs the formation
of ordered crystals as the temperature of a liquid is lowered. As a result
the freezing point of a solution will be below that of the pure solvent.
The amount of depression of the freezing point is governed by the following
equation.
DTf = Kfm
Example
A sample of an unknown organic molecule weighing 1.20 g is dissolved in 50.0
g of benzene. The resulting solution freezes at 4.92°C. Determine
the molecular weight of the unknown. Kf = 5.12°C/m
and T°f = 5.48°C
DTf
= 5.48°C - 4.92°C = 0.56°C
m = DTf/Kf
= 0.56°C/5.12°C/m = 0.11 m
moles of solute = 0.11 m(.0500 kg benzene) =
0.0055 mol solute
Mw = 1.20 g solute/0.0055 mol solute =
220 g/mol