SECTION III., 1900. { 37 ] Trans. R. S. C. 
IV.—On the Depression of the Freezing-Point in Solutions containing 
Hydrochloric and Sulphuric Acids. 
By JAMES BARNES, M.A., Dalhousie College, Halifax, N.S. 
(Communicated by Prof. J. G. MacGregor, and read May 29, 1900.) 
The work presented in the present paper was undertaken at the 
suggestion and under the kind direction of Professor MacGregor, to 
ascertain whether or not it is possible, by the aid of the dissociation 
theory, to calculate the depressions of the freezing-point in aqueous solu- 
tions formed by mixing solutions of hydrochloric and sulphuric acids, 
when sufficient data as to the depressions of the freezing-point and the 
conductivities of the constituent solutions are available. 
This calculation, in the case of a complex solution containing sul- 
phuric acid as one constituent, is of special interest, because this acid is 
supposed to have a mode of ionization which varies with the concentra- 
tion of the solution, its molecules in dilute solutions dissociating into three 
ions, namely H, H,and SO,, but in stronger solutions partly into two ions, 
Hand HSO,. Itis impossible to calculate the depression of the freezing- 
point of a complex solution, one of the constituents of which has a mixed 
mode of ionization. I have, therefore, regarded the mode of ionization 
in the solutions examined, which were of moderate dilution, to be the 
same as it is usually supposed to be at great dilution. On this supposi- 
tion I have been able, in a former paper,’ to calculate the conductivity 
of mixtures of moderately dilute solutions of these two acids. 
In a simple solution containing n gramme-molecules of an electrolyte 
per litre, if « is the ionization coefficient, the number of dissociated mole- 
cules is na, and the number of undissociated (1—«) n. If a molecule of 
this electrolyte breaks down into m ions, the number of free ions is nma, 
and thus the total number of undissociated molecules and free ions in this 
solution is 
(1— a) n + nma, or n(1+a(m—1)). 
On the assumption that a free ion produces the same amount of de- 
pression of the freezing-point as a molecule, and that in a solution the 
molecules are so far apart that no association of molecules occurs, if Ô is 
the depression of the freezing-point and M the molecular depression, 2.e., 
the depression produced by one gramme-molecule or one gramme-ion, we 
have 
M = “à M NS) 
n(1+a(m—1)) 
1Trans. N.S. Inst. Sci., 10, 129, 1899-1900. 

