312 PHYSICAL CHEMISTRY 



assisted in the preparation of the material upon which this paper is 

 based by Dr. J. W. Brown and Dr. M. S. Sherrill, of the Massachusetts 

 Institute of Technology. 



The principles to be first presented have reference to two of the 

 main hypotheses which are commonly employed in quantitative 

 applications of the ionic theory. One of these hypotheses is that the 

 migration-velocities of the ions of a salt do not vary appreciably with 

 its concentration, at least up to a moderate concentration; and conse- 

 quently, that the degree of ionization is equal to the ratio of the equi- 

 valent conductivity at the concentration in question to the limiting value 

 of the equivalent conductivity at zero concentration a ratio which 

 I will hereafter call simply the conductivity-ratio. The other hypothe- 

 sis is that ions, and also the un-ionized molecules accompanying them, 

 produce an osmotic pressure substantially equal to the pressure exerted 

 by the same number of gaseous molecules at the same temperature, at 

 least up to a moderate concentration; an hypothesis which may be more 

 briefly expressed by the statement that the osmotic pressure-constant 

 for dissolved electrolytes is identical with the gas-constant. It is evi- 

 dent that with the help of this hypothesis we can calculate, either from 

 measurements of osmotic pressure or from those of any other property 

 which is thermodynamically related to osmotic pressure, the number 

 of mols in the solution resulting from one formula weight of salt, that 

 is, the quantity which van't Hoff has represented by the letter i. 

 From the latter, provided the ionization is not complicated by the 

 formation of complex molecules or ions, the degree of ionization is 

 readily derived. 



The first of these hypotheses cannot be independently tested, 

 because no direct method of determining the change of migration- 

 velocity with the concentration is known. But the following princi- 

 ple, which has an important significance with reference to the relative 

 influence of concentration on the velocities of different ions, has been 

 established by measurements of the concentration-changes at the 

 electrodes attending the electrolysis of salt solutions. 



The transference number, or ratio of the conductivity of one ion to 

 the sum of the conductivities of both ions, is constant within one per 

 cent, between the concentrations of ~-^ and -^ normal, for all salts 

 thus far accurately investigated, except lithium chloride, the halides of 

 bivalent metals, and cadmium sulphate. 



This principle holds true, according to the results of various inves- 

 tigators, in the case of potassium and sodium chlorides, hydrochloric 

 and nitric acids, silver nitrate, barium nitrate, potassium sulphate, 

 and copper sulphate thus in the case of salts of the three different 

 ionic types, which I will speak of as the uni-univalent, the uni-bi- 

 valent, and the bi-bivalent types, in correspondence with the valences 

 of the two ions composing the salt. 



