114 HYDROGEN ION CONCENTRATION 



A second method of estimating the degree of dissociation is by 

 means of determining the lowering of the freezing point. From the 

 latter one may calculate the molar concentration of the solution, and 

 this may be related to that molar concentration which is to be 

 expected by assuming a total lack of dissociation. If the latter 

 concentration is c and the former c X i (i being "van't Hoff's coeffi- 

 cient"), then with binary electrolytes i — 1 = a. It is conspicuous 

 that values for a. obtained by this method 'do not agree exactly with 

 those obtained by the conductivity method. 



But there is still another method for the estimation of a, namely, 

 the concentration chain method. This method is appKcable to a 

 large series of electrolytes. By means of concentration chains one 

 can measure the concentration of H+, 0H~, Cl~ and some other ions 

 and hence determine the degree of dissociation of many acids, such 

 as HCl, HNO3 and of salts, such as KCl, NaCl, etc. Accurate investi- 

 gations by this method have been made but recently^ when the 

 technic has been considerably improved. Bjerrum^'* called attention 

 to the fact that the values of a jdelded by the three methods did not 

 agree. Table 20 taken from Bjerrum shows some of the evidence. 

 The apparent degree of dissociation obtained from the freezing point 

 method, fo, is designated as the osmotic factor; analogously f/x is the 

 conductivity factor; and that determined by the concentration chain 

 as the ''activity factor," fa. As is seen from table 20, at the lowest 

 concentrations the deviations do not appreciably exceed the limits 

 of experimental error, but at the higher concentrations they do exceed 

 it beyond all doubt. Since these different methods give series of 

 three different results, it is justifiable to entertain doubts as to the 

 reUabihty of all the three, or to doubt whether these three methods 

 of measurement yield actually degree of dissociation figures. 



The key to the solution of this enigma will be found in the following 

 considerations which are based on the investigations of Bjerrum,^^ 

 Milner^ and of Ghosh.^ 



The usual formula for the law of mass action is generally 



» It must be mentioned that O. Jahn (Zeitschr. f. physikal. Chem. 33, 545 

 and 35, 1 (1900)) had long since observed a lack of agreement between degree 

 of dissociation values of strong electrolytes calculated from conductivity 

 and concentration chain measurements. He also recognized that the con- 

 ductivity data were misleading, while he attached full value to his calcula- 

 tions from the concentration chain data. 



6a N. Bjerrum Zts. Elektrochem. 24, 321, 1918. 



