1902-3.] Freezing-Point Depression in Electrolytic Solutions. 375 
II. 
Depression. 
Concentration. 
Acetic acid . 
0*1853 
0 0974 
Malonic acid 
0*1825 
0*08665 
The first experiment may be used to exemplify the mode of 
calculating the ionisation value from the cryoscopic data. An 
acetic acid solution of the concentration 0 '09 33 7 normal gives a 
depression of 0*1775°. Now we know from conductivity measure- 
ments that such a solution is ionised to the extent of 0'012. A 
solution of a non-ionised substance which would give the same 
depression would therefore have the concentration 0-09337 x T012 
= 0*0945 normal. But the depression given by the malonic acid 
solution is 0'1779°. According to Blagden’s law, that the de- 
pression is proportional to the concentration, a solution of a non- 
ionised substance which would give this depression would have the 
concentration 0*0947 normal. We may therefore say that a 
0*08445 normal solution of malonic acid has the same freezing- 
point depression as a 0*0947 normal solution of a non-electrolyte, 
i.e ., that these solutions contain the same number of molecules. 
The degree to which the malonic acid solution is ionised is there- 
fore 0 - - - - - = 0*121. In this calculation the change of 
0*08445 & 
the degree of ionisation of the acetic acid with concentration has 
been neglected, since it is so small that the final result is not 
thereby appreciably affected. A change on the concentration of 
the acetic acid solutions which is less than 20 per cent, will have 
no noticeable effect on the calculation. 
The second experiment with malonic acid yields the ionisation 
value 0*120. Calculating now the ionisation value m from 
Ostwald’s dilution formula, we obtain the numbers 0*121 and 0*120 
respectively for the two experiments. Here the concordance 
is absolute, but this absolute agreement is accidental, as these 
ionisation values are affected with an uncertainty of approximately 
5 units in the third decimal place. In any event the accordance 
of the numbers gives ample evidence of the validity of our method. 
Further to test the matter, we made experiments with approxi- 
mately 0*05 normal solutions of the same substances. Here the 
relative error of our method is greater owing to the smaller 
depressions observed. 
