38 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 



ratio of the equivalent conductance at any concentration to the limiting 

 value of the equivalent conductance at low concentrations, is supported 

 by other important properties of these solutions. Raoult 25 had observed 

 that the freezing point depression produced by electrolytes in water is 

 greater than that of other substances at equivalent concentrations, van't 

 Hoff, 26 finally, supplied the theoretical foundation which made it pos- 

 sible to calculate from the measurements of Raoult the molecular weight 

 of substances in solution. Since in the case of aqueous salt solutions the 

 depression was found to be abnormal, van't Hoff introduced an arbitrary 

 factor i, which he apparently assumed to be a constant independent of 

 concentration. Arrhenius at once recognized the significance of van't 

 Hoff's factor and pointed out the relation between this factor and the 

 coefficients derived from conductance measurements. According to 

 Arrhenius, if electrolytes are dissociated, the freezing point depression of 

 their solutions as measured should be greater than that calculated ac- 

 cording to the method of van't Hoff, the molecular weight being assumed 

 equal to the formula weight of the dissolved substance. If we let 



M 



where M is the formula weight and MQ the molecular weight calculated 



from freezing point measurements, then, obviously, there exists between 

 i and y> the relation: 



(4) t=l+(n lh, 



where n is the number of ions resulting from the dissociation of a single 

 molecule. The values of y a s calculated from freezing point or other 

 similar determinations should thus agree with the values of y as calcu- 

 lated from conductance measurements. In Table VI 27 are given the 



TABLE VI. 



COMPARISON OF IONIZATION VALUES DERIVED FROM CONDUCTANCE AND 

 FROM FREEZING POINT MEASUREMENTS. 



Electrolyte Method 5 X 10 a 10- 2 2 X 10- 2 5 X 10- 2 10- 1 2 X 10- 1 5 X 10- 1 



KC1 ........ ... F .963 .943 .918 .885 .861 .833 .800 



C .956 .941 .922 .889 .860 .827 .779 



NH 4 C1 ......... F .947 .928 .907 .878 .856 .832 .... 



C .941 .921 



" C. R. 94, 1517; 95, 188 and 1030 (1882). 



van't Hoff, 8v. Vet.-Akad. Handlingar 91, No. 17 (1886), p. 



"Noyes and Falk, J. Am. Chem. 8oc. 3J,, 485 (1912). Th< 



148. 

 e concentrated solutions 

 have been corrected for the viscosity effects. (See footnote above, p. 35.) 



