The Valency of the Radioelements. 391 



them. It will be shown in the present paper that it is pos- 

 sible to deduce the number of! charges borne by the cation, 

 i. e. its valency, from the velocity with which it diffuses in 

 presence of a large excess of the anion. The diffusion con- 

 stant of a cation has also been determined by measuring its 

 mobility in an electric field. This second method acts as a 

 check on the first one. Before proceeding to describe the 

 methods employed in this research, the subject of diffusion 

 of electrolytes will be discussed from a general point of 

 view. 



§ 2. Diffusion of Electrolytes. 



When dilute hydrochloric acid diffuses in pure water, the 

 H and CI ions are borne from points of - higher to points of 

 lower osmotic pressure by the osmotic forces. The smaller 

 the frictional resistance offered to the migrating ion, the 

 more rapidly, does it move. Xow a hydrogen ion has to 

 overcome a frictional resistance which is only about 1/5 of 

 that to be overcome by the chlorine atom. It is therefore, 

 to be expected that the rapidly moving H ion, when allowed 

 to diffuse, would soon leave the slowly moving CI ion^ and 

 be completely separated from it. This, however, does not 

 take place. The polar ions are not capable of being separated 

 by diffusion, for as Xernst showed in his fundamental theory 

 of diffusion of electrolytes, the foremost hydrogen ion gives 

 a positive charge to the water layer, and a negative charge 

 to the residual ion. A compensating potential difference is 

 thus produced, which accelerates the motion of the CI ions, 

 so that the resultant velocity of diffusion of the CI ions is the 

 same as that of the H ions. For this reason the diffusion of 

 an electrolyte depends both on the mobility of the cation 

 and of the anion. 



The numerical relation between the diffusion constant and 

 the mobility of an ?z-valent electrolyte may be derived as 

 follows. 



The effect of the osmotic forces is that in unit time 



dF 



K'k=— "D"-,— cations 

 ax 



and ,^, ^dF 



dx 



£s a= — V-y— anions 



pass unit cross-section *. IT and V are proportional to the 

 mobilities of the cation and the anion respectively, c is the 

 concentration, and n the valency. 



* Nernst, Zeit. phys. C/iem. vol. ii. p. 614 (1888). 



