[MACGREGOR] DEPRESSION OF THE FREEZING-POINT 15 
The agreement between observed and calculated values in the above 
tables is closest in the case of the weaker sulphate solutions, as was to be 
expected, considering that these solutions are all of equal concentration 
with respect to the two electrolytes and that the more laborious method 
was employed in determining their ionization coefficients. The agree- 
ment is remarkably good up to a total concentration of 0-1, which is the 
concentration at which the data of Table I would lead us to expect 
divergence to begin to occur. 
In the case of the solutions containing two chlorides, the calculated 
values differ more widely from the observations ; but in the more dilute 
solutions of both series, the differences are either within or but little 
beyond the probable limit of experimental error. 
The solutions containing the two acids could not be expected to 
exhibit a good agreement through more than a narrow concentration 
range. The zero difference for the sixth solution is probably accidental. 
APPLICATION TO THE DETERMINATION OF THE DEPRESSION 
CONSTANTS FOR HLECTROLYTES. 
It is obvious from the form of the expression used above for the 
equivalent depression of dilute solutions : 
60 =k (l—a) + la, 
that the constants, k and /, if determined by observations on sufficiently 
dilute solutions, must be simply related to the depression constant for 
undissociated molecules, 7.e., the depression produced by each gramme- 
molecule of undissociated electrolyte, and the depression constant for the 
free ions, 7.¢., the depression produced by each gramme-ion of the free 
ions,—which we may indicate by D and d respectively. 
In the case of the chlorides, k being the depression produced by one 
gramme-equivalent of the undissociated salt, and each gramme-equivalent 
being also a gramme-molecule, we have k = D ; and / being the depres- 
sion produced by one gramme-equivalent of the dissociated salt, we have, 
on the assumption that both kinds of free ions are equally effective in 
lowering the freezing-point, / = 2d. 
In the case of the sulphates, if they be assumed to dissociate into 
three free ions, e.g.,2 Kand S O,, since each gramme-molecule contains 
two gramme-equivalents, we have k = D/2, and 1/1=3d/2. If however 
they be assumed to dissociate into two free ions, e.g., Kand K S O,, we 
have k = D/2, and 1 = d. 
Hence given the values of & and / we can find those of D and d. 
It is obvious however that in general k and / will have been 
determined with quite different degrees of accuracy. 
