Page 111 - Instant notes

D3
COLLIGATIVE PROPERTIES

Key Notes
A colligative property of a solution is a property that depends
only on the number of solute molecules present. Measurement of
one of these properties allows the determination of the molality
or the concentration of the solute, from which the molecular mass
of the solute can be calculated, if the mass of solute in solution
and the volume of the solution are known.

When a small amount of involatile solute B is added to a solvent
A to make an ideal-dilute solution, the depression of the freezing
point of A, ∆T f , is related to the molality of B, m B , by ∆T f =K f m B ,
where K f is the cryoscopic constant, or the freezing point
depression constant. K f is a constant for a given solvent, A.
When a small amount of involatile solute B is added to a solvent
A to make an ideal-dilute solution, the elevation of the boiling
point of A, ∆T b , is related to the molality of B, m B , by ∆T b =K b m B ,
where K b is the ebullioscopic constant, or the boiling point
elevation constant. K b is a constant for a given solvent, A.
The osmotic pressure, Π, established between pure a solvent, A,
and an ideal-dilute solution of a solute, B, across a membrane
permeable only to solvent is given by Π≈c B RT, where c B is the
concentration of solute B. Measurement of this osmotic pressure
allows c B to be determined.
Related topics Fundamentals of equilibria (C1) Solutions (D2)
Non-electrolyte solutions (D1)

Characterization using colligative properties

In an ideal-dilute solution, when an involatile solute, B, is added to a solvent, A (see
Topic D2) the chemical potential of the liquid solvent is lowered, as
, where x A is the mole fraction of A (unity for pure A and decreasing when B
is added) and is the standard chemical potential (or molar Gibbs free energy) of pure
liquid A. This effect is independent of the chemical nature of B, but merely depends upon
the number of moles of B added, determined by its mole fraction, x B, as x A=1−x B (see
Topic D1). This thermodynamic stabilization of the solvent results in measurable
changes, such as the depression of the solvent vapor pressure, a decrease in the freezing
temperature and an increase in the boiling point, which only depend on the number of
moles of B added, and not its chemical structure. Such properties are called colligative
properties. Measurement of one of these properties is useful when characterizing a