The Foundations of Chemistry

The freezing point depressions of solutions of nonelectrolytes have been found to be
equal to the molality of the solute times a proportionality constant called the molal
freezing point depression constant, Kf.

TfKfm

The values of Kffor a few solvents are given in Table 14-2. Each is numerically equal
to the freezing point depression of a one-molal idealsolution of a nonelectrolyte in that
solvent.

EXAMPLE 14-8 Freezing Point Depression

When 15.0 grams of ethyl alcohol, C 2 H 5 OH, is dissolved in 750. grams of formic acid, the
freezing point of the solution is 7.20°C. The freezing point of pure formic acid is 8.40°C. Eval-
uate Kffor formic acid.

Plan

The molality and the depression of the freezing point are calculated first. Then we solve the
equation TfKfmfor Kfand substitute values for mand Tf.

Kf

Solution

_?_ 0.435 m

Tf(Tf[formic acid])(Tf[solution])8.40°C7.20°C1.20°C (depression)

Then Kf2.76°C/m for formic acid.

You should now work Exercise 48.

EXAMPLE 14-9 Freezing Point Depression

Calculate the freezing point of the 1.25 msucrose solution in Example 14-2.

Plan

We first find the decreasein freezing point from the relationship TfKfm.The temperature
at which the solution freezes is lowerthan the freezing point of pure water by this amount.

Solution

From Table 14-2, Kffor H 2 O1.86°C/m,so

Tf(1.86°C/m)(1.25 m)2.32°C

The solution freezes at a temperature 2.32°C belowthe freezing point of pure water, or

Tf(solution)0.00°C2.32°C2.32°C

You should now work Exercise 56.

1.20°C



0.435 m

Tf



m

1 mol C 2 H 5 OH



46.0 g C 2 H 5 OH

15.0 g C 2 H 5 OH



0.750 kg formic acid

mol C 2 H 5 OH



kg formic acid

Tf



m

Tfis the depressionof freezing point.

It is defined as

TfTf(solvent)Tf(soln)

so it is always positive.

14-12 Freezing Point Depression 565

See the Saunders Interactive

General Chemistry CD-ROM,

Screen 14.8, Colligative Properties (2):

Boiling Point and Freezing Point.

Lime, CaO, is added to molten iron

ore during the manufacture of pig

iron. It lowers the melting point of

the mixture. The metallurgy of iron

is discussed in more detail in

Chapter 22.