[BARNES] DEPRESSION OF THE FREEZING-POINT 58 
» 
ates, C, and C!, whose values when substituted in equation (7) (VW and J, 
being known in any mixture) satisfy this equation. We have thus 
found k,, C, and C,; k, is easily found from equation (6). The a’s, the 
jonization coefficients in the mixture, are then determined from the 
k 
UC" 

relation, a = 
RESULTS OF THE CALCULATIONS ON MIXTURES. 
Table VI gives the necessary data for the calculation of the depres- 
sion of the freezing-point of mixtures of the two acids, and it shows the 
agreement of the caleulated with the experimental values, these latter 
values being the observed values corrected for change in concentration 
according to equation (4). The ionization coefficients of the electrolytes 
in the mixtures are determined as above, and the molecular depressions 
are obtained as mentioned on page 38 of this paper. The concentrations 
and the freezing-point depressions are expressed as in Table IV. 








TABLE VI. 
Concentrations | Ionization Go | reculer Depres- | x Dépression 
Solutions. Mixture at 0°C| S102 M Mixture. Mixture. Dion: 
No) eco) HC! || 550, Observed | Caleulat 
0517 | -0203 | -965 | -647 | 1-837 | 1819 | ‘1366 | -1357 | —-0009 
« | 0508 | -962 | -622 | 1-836 | 1-818 | -1967 | -1968 |  +-0001 
« | -ogi1| -955 | -613 | 1:836 | 1-817 | ‘2584 | -2569 | —-0015 
« | -102 | -954 | -605 | 1-836 | 1817 | -2989 | -2975 | —-0014 
« | -993 | -o941 | -586 | 1-844 | 1812 | ‘4939 | “4921 | —-0018 
< 304 | -922 | -570 | 1:865 | 1:812 6810 6822 | +0012 
-305 | -0203| -918 | -560 | 1-857 | 1-812 5804 | 5820 | +-0016 
« | -9508] -917 | ‘558 | 1:866 | 1-812 6446 | -6431 | —-0015 
« | -og1| -915 | -556 | 1-871 | 1:812 7025 | ‘7018 | —-0007 
« | 102 | -o1 | -553 | 1:875 | 1°812 7420 | ‘7420 | +0000 
« | -993 | -907 | -543 | 1894 | 1:s16 | ‘9302 | -9353 | —-0039 
« | -304 | -903 | -533 | 1°912 | 1-818 | 1:1300 | 1-1259 | —-0041 



The observed values in the above table have a limit of error, as 
mentioned above, of about 0:0004 degree. There are also many sources 
of error in the calculations, and they do not admit of exact valuation. As 
a rough estimate, the limit of error due to both observation and calcula- 
