Page 374 - Physical Chemistry

lev38627_ch12.qxd 3/18/08 2:41 PM Page 355

355
ethylene glycol, and various sugars. For example, the glycerol concentration in larvae Section 12.3
of the goldenrod gall moth is near zero in summer months but increases to 19% by Freezing-Point Depression and
Boiling-Point Elevation
weight in winter months. An alternative strategy used by many fish, insects, and plants
is to have antifreeze proteins keep their fluids in a metastable supercooled liquid state
(Sec. 7.4) from 1 to 10 K below the freezing point. The antifreeze proteins bind to the
surface of small ice crystals, preventing their growth.

EXAMPLE 12.1 Molecular weight from freezing-point
depression

The molal freezing-point-depression constant of benzene is 5.07 K kg/mol. A
0.450% solution of monoclinic sulfur in benzene freezes 0.088 K below the freez-
ing point of pure benzene. Find the molecular formula of the sulfur in benzene.
The solution is very dilute, and we shall assume it to be ideally dilute.
100.000 g of solution contains 0.450 g of sulfur and 99.550 g of benzene. From
T k m , the sulfur molality is
f
f
B
¢T f 0.088 K
m 0.0174 mol>kg
B
k f 5.07 K kg>mol
But m n /w [Eq. (9.3)], so the number of moles of sulfur is
B
B
A
n m w 10.0174 mol>kg210.09955 kg2 0.00173 mol
B
A
B
The sulfur molar mass is
M w >n 10.450 g2>10.00173 mol2 260 g>mol
B
B
B
The atomic weight of S is 32.06. Since 260/32.06 8.1 8, the molecular for-
mula is S .
8
Exercise
For D O (where D H), the normal freezing point is 3.82°C and H (T*)
2
2
fus
f
m
6305 J/mol. (a) Find k for D O. (b) Find the freezing point of a solution of
f
2
0.954 g of CH COCH in 68.40 g of D O. Explain why your answer is approx-
3
3
2
imate. [Answers: (a) 2.02 K kg/mol; (b) 3.33°C.]
6
As a pure substance freezes at fixed pressure, the temperature of the system
remains constant until all the liquid has frozen. As a dilute solution of B in solvent A
freezes at fixed pressure, the freezing point keeps dropping, since as pure A freezes
out, the molality of B in the solution keeps increasing. To determine the freezing point
of a solution, one can use the method of cooling curves (Sec. 12.8).
Freezing points are usually measured with the system open to the air. The dis-
solved air slightly lowers the freezing points of both pure A and the solution, but the
depression due to the dissolved air will be virtually the same for pure A and for the
solution and will cancel in the calculation of T .
f
If there are several species in solution, then x in (12.8) equals 1
x , where
A i A i
the sum goes over all solute species. Equation (12.11) becomes ln g x
x .
A A i A i
For a dilute solution, we have x M m , and Eq. (12.15) becomes for several solute
i A i
species
¢T k m ideally dil. soln., pure A freezes out (12.17)
f
f
tot