582 



SCIENCE. 



[N. S. Vol. XX. No. 514. 



or 1 — y = ii(cy)^ where y is the degree 

 of ionization, c the concentration, and K a 

 constant. The first of three functions was 

 proposed by Kohlrausch, the second by 

 Barmwater. Owing to the relatively 

 small variation of the ionization, these two 

 functions can not differ much as to their 

 constancy, but on the whole the experi- 

 mental data indicate that the second func- 

 tion is somewhat more constant. The aver- 

 age deviations of the actual measurements 

 from the values corresponding to this func- 

 tion are i per cent, in the case of ten uni- 

 univalent salts, ^ per cent, in the ease of 

 nine uni-bivalent salts and also ^- per cent, 

 in the case of three uni-tri and uni- 

 quadrivalent salts. The maximum devia- 

 tions are two or three times as great. It 

 is of interest to note that the strong min- 

 eral acids, hydrochloric and nitric, behave 

 like salts in this respect. These functions 

 have been shown to apply to potassium 

 and sodium chlorides through a range of 

 temperature extending from 18° to 306°. 

 They do not apply at all closely to such 

 salts of the bi-bivalent type as magnesium 

 and copper sulphates, perhaps owing to 

 appreciable hydrolysis. Nor do they rep- 

 resent satisfactorily the experimental data 

 for any kind of salts at the very low con- 

 centrations lying between 1/100,000 and 

 1/2,000 normal, nor at concentrations 

 higher than 1/5 normal. 



The experimental results are also well 

 expressed by the statement that in the 

 case ioth of uni-univalent and uni-'bivalent 

 salts hetiveen the concentrations of 1/10,- 

 000 and 1/5 normal, the concentration of 

 the un-ionized molecules is proportional to 

 the concentration of the ions raised to a 

 constant power, varying someivhat with 

 the salt and the temperature, hut as a ride 

 only hetiveen the limits of 1.43 and 1.56. 

 That is, 



c(l — y) =^(0-)", where n> 1.43 and <1.56. 



This general function was first applied 

 by Storch, and was afterwards further dis- 

 cussed by Euler and Bancroft. It has the 

 advantage over the previous ones that it 

 represents the data with accuracy even up 

 to the highest dilutions, and therefore can 

 be used for obtaining the limiting con- 

 ductivity at zero concentration. 



The applicability to the salts of different 

 types of either of these principles govern- 

 ing the change of ionization with the con- 

 centration leads to the important conclu- 

 sion that the form of the concentration 

 function is independent of the number of 

 ions into which the molecules of the salt 

 dissociates. This remarkable fact, though 

 previously recognized, has not been suffi- 

 ciently emphasized, and it has been often 

 ignored in discussions of the cause of the, 

 deviation of the ionization of salts from 

 the requirements of the mass action law. 

 It seems to me to show almost conclusively 

 that chemical mass action has no appre- 

 ciable influence in determining the equilib- 

 rium between ions and un-ionized mole- 

 cules. How complete the contradiction 

 with the mass action law is, may be illus- 

 trated by citing the specific facts that for 

 di-ionic, tri-ionic and tetra-ionic salts this 

 law requires that the concentration of the 

 un-ionized molecules be proportional to 

 the square, the cube, and the fourth power, 

 respectively, of the concentration of the 

 ions, while the experimental data show that 

 it is approximately proportional to the 3/2 

 power of that concentration, whatever may 

 be the type of salt. 



Having seen in what manner the degree 

 of ionization varies when the concentra- 

 tions of both ions of the salt are simultane- 

 ously varied by dilution, it is of interest to 

 determine the effect of changing the con- 

 centi-ation of either ion separately. A 

 study of the conductivity and the freezing- 

 point of mixtures of two salts having one 

 ion in common throws much light upon 



