THE HYDRATE THEORY OF SOLUTIONS 221 



this has been done the changes of ionic radius can be deduced. 

 In the case of potassium chloride the relationship 



r = r oo ( 1 + B/i - i) - * 

 was deduced for the radius of the ion and was shown to hold 

 good up to a concentration of N/5, where h = number of 

 molecules of water added to each molecule of salt, B = a 

 constant : the change of radius appears therefore to proceed 

 in a regular manner and according to perfectly definite laws. 



Further evidence of variations in the size of the ion (and 

 therefore, incidentally, of the existence of a variable water- 

 atmosphere) has recently been obtained in the case of the 

 hydrogen ion itself. In the case of most of the ions Arrhenius's 

 assumption that the mobility is independent of the concentration 

 holds good for solutions of moderate dilution. The hydrogen 

 ion, however, gave discordant values when the mobility was 

 determined (a) from transport values at moderate dilutions and 

 (b) from conductivity measurements at extreme dilutions. These 

 discrepancies were traced by Noyes and Kato (Journ. Amer. 

 Chem. Soc. 1908, 30, 318-334) to variations of mobility taking place 

 at dilutions considerably greater than those at which the mobili- 

 ties of the other ions become constant, and as concordant values 

 were obtained from independent observations with nitric and 

 hydrochloric acid there can be little doubt of their correctness. 



Ionic Mobility of Hydrogen at Different Dilutions 



Collateral evidence in reference to the hydration of the ions 

 has been obtained from a study of electrolysis in mixed solvents, 

 e.g. silver nitrate in aqueous methyl alcohol, and of aqueous 

 solutions containing a salt and an inert solute, but the results 

 obtained have not been very decisive, and in any case can only 

 be used to indicate differences in the hydration of anion and 

 kathion. The method, although of great value in the study of 

 other complex ions, has therefore not proved of equal value in 

 the investigation of hydrates and a passing reference to it must 

 here suffice. 



