DISSOCIATION OF STRONG ELECTROLYTES 119 



If the electrol}i:e solution be diluted, then the mean ionic distance is 

 altered and consequently also the autopotential changed. Therefore, 

 at infinite dilution an amount of electric work is performed to the 



extent of —> where e is the electric elementary quantum (the charge 



on one ion), D the dielectric constant and r is the original mean ionic 



distance. Furthermore r = \ ^z^ (where No is the number of 



y 2JNo 



molecules per liter, and V the volume of the solution), hence 



^ No e2 Ay2l7o 

 A = 



and therefore, 



D \/v 

 No e2 \/^ 



D VV 



° = 2 RT In a. 



From the last expression the value of a may be calculated, and 

 then one finds good agreement between observed and calculated 

 values of a. for a large number of strong electrolytes, provided it is 

 assumed at the same time that their dissociation is complete at each 

 concentration used. 



32. The effect of the ionic charge upon the lowering of the 



freezing point 



In two excellent papers Milner^ shows that in a mixture containing 

 equal numbers of positive and negative ions the electrostatic forces 

 exercise a characteristic effect upon the average spatial distribution 

 of the ions. Milner applied a theorem proposed by Boltzman: 

 when a large number of molecules is distributed in a defined space, 

 then any two neighboring molecules in a given period of time are 

 separated by varying distances for which a quite definite statistical 

 mean can be determined. When these molecules are conceived to 

 be ions, and, furthermore, when the numbers of positive and negative 

 ions are equal, then we find that the distance between any two 

 neighboring ions of the same charge, which always repel each other, 



9 S. R. Milner, The Virial of a Mixture of Ions. Phil. Mag. 23, II, 551 (1912) ; 

 The Effect of Interionic Forces on the Osmotic Pressure of Electrolytes. Ibid. 

 25, II, 742 (1913). 



