140 ON THE DEPRESSION OF THE FREEZING-POINT 



into m ions, then the number of free ions is n m a, and therefore 

 the total number of undissociated molecules and free ions in this 

 solution is 



(l a)n + nma, or n(l + a (m 1)Y 



On the assumption that a free ion produces the same amount of 

 depression 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 rf is the depression of the freezing-point and 

 M the molecular depression, i. e., the depression produced by 

 one gramme-molecule or one gramme-ion, we have 



_ 6 _ 



= n(\+a(m-\}} ................ (1) 



In the case of mixtures of simple solutions, according to the 

 above assumption, A the depression of the freezing-point will be 

 represented by the expression : 



= 



where 1, 2, etc., denote the electro ytes, the m's the numbers of 

 ions into which the molecules of the respective electrolytes break 

 down, them's the ion'7 !'> i coefficients in the mixture, the N's the 

 concentrations (in grain me-molecules per litre) of the mixture 

 with respect to the respective electrolytes, and the M's the 

 depressions produced by one gramme-molecule or one gramme. 

 ion of the undissociated and dissociated portions respectively of 

 the electrolytes. The as in this expression are given by the 

 method to be tested ; the m's in the case of the electrolytes 

 selected can have only one value ; and the N's are of course 

 known ; but what values the M's are to be regarded as having 

 is doubtful. It was found for simple solutions of the three 

 electrolytes employed, that the molecular depressions increased 

 as the solutions became more concentrated. This appears to 

 indicate that one molecule or one ion, when in the presence 

 of a large number of molecules and ions, produces a greater 

 depression than when it is in the presence of a smaller 

 number. Thus in the case of a solution made by mixing 

 simple solutions of different electrolytes, since the number 



