Unformatted text preview: his gives
D H æ DT ö
x B = fus m ç 2f ÷ ,
R è Tf ø
which can be further simplified to yield (see the text above Eq. 5.119)
RT 2 M A
m or DT f = K f m B ,
DT f =
D fus H m B
where Kf is called the cryoscopic constant of the solvent. Boiling Point Elevation:
By considering the liquid-vapor equilibrium in which the vapor contains only the
component A, we can derive an expression analogous to that obtained above:
RT 2 M A
DT b =
m or DT b = K b m B ,
D vap H m B
where Kb is called the ebullioscopic constant of the solvent.
The elevation of boiling point is a rather weak effect compared to the depression
of freezing point. Therefore, the latter property is overwhelmingly used for the
practical applications of colligative properties.
Problems 5.37, 5.38, 5.44
These equations are useful to determine the freezing points or boiling points of
various solutions of nonvolatile solutes.
A somewhat “liberal” interpretation of Eq. (5.115) or (5.116) can be used to
calculate the solubility of various solutes at temperature T in a solvent whose
enthalpy of fusion and freezing point are known.
The “simplified” forms are also useful to determine the molar masses of
unknown solutes using Eq. (5.122).
Problems 5.50, 5.53
Colligative properties depend on number of “particles” in solution rather than
actual “concentration.” For instance, a 1 m solution of NaCl leads to a 2 m
solution of ions (Na+ and Cl–). Such a solution, therefore, will yield twice the
expected ∆Tf. This effect must be taken into account when dealing with ionic
substances (See problem 5.24)....
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