32 MORRIS LOEB 



for different substances the corresponding coefficients may 

 differ. 



1. The first application of this hypothesis affects Kohl- 

 rausch's law of conduction; 1 the conducting power of an elec- 

 trolyte is no longer the sum of the velocities of all the ions, 

 but of that proportion which are free to move. Only for 

 extreme dilutions do we find a rigorous adherence to the 

 equation \=u+v, which becomes in less dilute solutions 

 \ = a(u +v) (I), where a expresses the "coefficient of ac- 

 tivity," or that proportion of the whole number of mole- 

 cules which is dissociated. Experiments having given very 

 reliable results for u and v in the case of quite a number of 

 ions, and X being known for a large number of compounds 

 at various degrees of concentration, the respective values of 

 a are readily obtained. 



2. The number of molecules in the solution is increased by 

 the dissociation. If each molecule is dissociated into k con- 

 stituent ions, and n\ molecules are thus broken up, while n 

 remain associated, the osmotic pressure must correspond to 

 the presence of n+krii molecules, instead of n+ni. We shall 

 have for the relation of the true osmotic pressure to that 

 calculated upon the assumption that the molecules remain 



intact, i 



The definition of the coefficient of activity has introduced 

 the value a= > whence 



-l)a (II) 



This explains the fact, alluded to in a recent review, that 

 the molecular weight of an electrolyte, as determined by any 

 of the "osmotic" methods, must be found smaller than 



1 Compare Am. Chem. Journ. 11, 116 (1889). 



