192 
CHEMISTRY: WASHBURN AND READ 
sure pK of any constituent A in such a solution is proportional to the 
mole-fraction of that constituent in the solution. This law is ex- 
pressed in differential form by the equation: dp^ = kdxx. 
From this relation, with the aid of thermodynamics, we may derive 
the other laws of ideal solutions. Most of the experimental data at 
present available for illustrating the application of these laws to specific 
cases have been derived from direct measurements of the vapor-pres- 
sures themselves. It seemed therefore desirable to secure some addi- 
tional experimental data which would serve as examples illustrating the 
character of the results given by some of the other laws. 
The freezing-point-solubiHty law was chosen as the first one to be 
studied in this connection because it happens that this law offers a 
convenient as well as exact method for testing the accuracy with which 
a given solution obeys the laws of ideal solutions. 
For an ideal solution of two substances, A and B, it can be shown 
thermodynamically that the following equations express the change of 
freezing-point caused by an increase in the mole-fraction of each com- 
ponent: 
where R is the gas constant, T the absolute temperature, L the heat of 
fusion per mole, and x the mole-fraction, in solution, of the substance 
indicated by the subscript. At the eutectic point it is evident that 
these two equations must hold simultaneously; and by eliminating x^ 
and from them we can calculate the eutectic temperature for the 
system under consideration. The purpose of this investigation was to 
test in this way the vaHdity of these equations for the three two-com- 
ponent solutions which can be formed from the three substances ben- 
zene, diphenyl, and naphthalene. For this purpose it is necessary to 
know the heat of fusion and melting-point of each substance. 
Satisfactory values of the molar heats of fusion of beazene and naph- 
thalene were available; that of benzene had been determined by De- 
merliac and by J. Meyer to be 2370 calories, and that of naphthalene by 
Alluard and by Pickering as 4560 calories. It was, however, necessary 
to determine that of diphenyl. For this purpose, weighed amounts 
(about 30 grams) of diphenyl in stoppered test-tubes were transferred 
from a mercury bath at 71° to a calorimeter, consisting of a silvered 
vacuum-tube filled with water; and the rise in temperature (about 3°) 
was measured with a Beckmann thermometer. The calorimeter was then 
cooled to its original temperature by dropping in a weighed piece of dry 
dT RT^ dT 
dXj^ Lj^Xf^ dXj 
