Page 113 - Instant notes
P. 113
Colligative properties 99
when a small amount of B is added and x B is small compared to 1. Under these
conditions, the change in the freezing temperature is also small and:
∆T f is the freezing point depression, the decrease in the freezing temperature of the
solvent A on adding B (defined as a positive value). Thus:
Usually, this equation is written in terms of the molality of B, m B (see Topic D1). At
these low concentrations, x B=m BM, where M is the mass of one mole of the solvent, or
the molar mass. The equation then becomes:
K f is the cryoscopic constant or the freezing point depression constant of the solvent A
(not to be confused with an equilibrium constant, see section C). K f can in principle be
calculated from the enthalpy of fusion and the freezing point of pure liquid A, but in
practice values have been measured experimentally and tabulated for a range of solvents.
This value can be used, along with the measured value of ∆T f, to determine m B and/or x B
for any solute.
Elevation of solvent boiling point
For the equilibrium corresponding to the physical transition of A between liquid and
vapor in an ideal-dilute solution:
the activity of the solvent A in the liquid is again given by a A=x A (see Topic D1). The
equilibrium constant for this process, which is again dominated by A, is (see Topic C1):
where , the standard pressure, has a value of 1 atmosphere. At the boiling point, the
pressure of the solvent, p A is also 1 atmosphere, and so K=1/x A. By analogy with the
freezing point equilibrium:
