126 HYDROGEN ION CONCENTRATION 



of the ion. In the cations the free charge is located on the atomic 

 nucleus. The greater the atomic radius the greater the distance from 

 the unbound water-molecules and the smaller is the attraction. On 

 the other hand, in the anions the free charge is on the periphery in 

 the form of the valence electron, and its attraction for the water is 

 but slightly influenced by the size of the atomic radius insofar as the 

 greater or smaller distance of the positive nucleus weakens more or 

 less the electric field of the electron. The attraction between the 

 ions and the water had been conceived as an electrostatic one. A 

 water-molecule is to be considered as being electroneutral when 

 viewed remotely, so to speak, but more closely considered, it has 

 electropositive as well as electronegative places, and positive ions 

 are attracted to the negative places and conversely. Therefore, it 

 may be readily imagined that each ion is first surrounded by a 

 spherical layer of water-molecules and then by a second and perhaps 

 by a third laj'er which are progressively less closely attached. The 

 number of water-molecules which are firmly held in the inner layer 

 depends upon spatial possibilities, much in the manner of Werner's 

 coordination number. The hydrogen ion, in spite of its free positive 

 charge, can, because of its small atomic radius, bind less water than 

 any other ion. 



With these intimations we must end our discussion of the devia- 

 tions in concentrated solutions from Bjerrum's theory, especially 

 in view of the incomplete state of knowledge of the subject and of the 

 limited scope of this book.^^^ 



We see then that the underlying basis of the activity theory is 

 beset with many difficulties. Nevertheless it leads us to an impor- 

 tant and fundamentally quite well established result. It is only 



"* The activity theory has been recently greatly advanced and developed 

 in the experimental work of G. N. Lewis and his collaborators, the theoretical 

 studies of N. Bjerrum, and particularly through the fundamental work by 

 Debye and Huckel. These developments have been so wide in scope that they 

 can scarcely be summarized in a supplement. For an extensive study of these 

 the reader is referred to G. N. Lewis and M. Randall, Thermodynamics, N. Y., 

 1923, wherein the methods of determination of activity coefficients as well as 

 their thermodynamic derivation are particularly well given ; also to the excel- 

 lent summary of Debye's theories in E. Huckel, Zur Theorie der Electrolyte in 

 Ergebn. d. exact, naturwiss., Vol. 3, Berlin, 1924, both of which books pre- 

 suppose a good knowledge of electrophysics and of thermodynamics. 



