CHAPTER 12 EQUILIBRIUM CONDITIONS IN MULTICOMPONENT SYSTEMS
12.4 COLLIGATIVEPROPERTIES OF ADILUTESOLUTION 376
TfTbbcbcututH (^2) O(s)
H 2
solutionO(l)
H 2
O(g)
0
2
4
6
8
10
12
240 280 320 360 400
T=K
A
=kJ mol
^1
Figure 12.3 Freezing-point depression and boiling-point elevation of an aqueous so-
lution. Solid curves: dependence on temperature of the chemical potential of H 2 O (A)
in pure phases and in an aqueous solution at 1 bar. Dashed curves: unstable states. The
Avalues have an arbitrary zero. The solution curve is calculated for an ideal-dilute
solution of compositionxAD0:9.
at which H 2 O has the same chemical potential in both phases at this pressure. At these
temperatures, the chemical potential curves for the phases intersect, as indicated by open
circles in the figure. The presence of dissolved solute in the solution causes a lowering of
the H 2 O chemical potential compared to pure water at the same temperature. Consequently,
the curve for the chemical potential of H 2 O in the solution intersects the curve for ice at a
lower temperature, and the curve for steam at a higher temperature, as indicated by open
triangles. The freezing point is depressed byÅTf, and the boiling point (if the solute is
nonvolatile) is elevated byÅTb.
Sections12.4.1–12.4.4will derive theoretical relations between each of the four col-
ligative properties and solute composition variables in the limit of infinite dilution. The
expressions show that the colligative properties of a dilute binary solution depend on prop-
erties of the solvent, are proportional to the solute concentration and molality, but do not
depend on the kind of solute.
Although these expressions provide no information about the activity coefficient of a
solute, they are useful for estimating the solute molar mass. For example, from a measure-
ment of any of the colligative properties of a dilute solution and the appropriate theoretical
relation, we can obtain an approximate value of the solute molalitymB. (It is only approxi-
mate because, for a measurement of reasonable precision, the solution cannot be extremely
dilute.) If we prepare the solution with a known amountnAof solvent and a known mass of
solute, we can calculate the amount of solute fromnBDnAMAmB; then the solute molar
mass is the solute mass divided bynB.