68 



PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 



be observed that in this equation the mass-action function K' is expressed 

 as a function of the ion concentration raised to the ra'th power. The 

 equation may be tested very simply by graphical methods. It may be 

 written in the form: 



(10) (2 m) log (C Y ) log [C (1 Y ) ] = log D. 



If, therefore, we plot the logarithms of (7(1 y) against the logarithms 

 of the ion concentrations Cy or the specific conductances, the experi- 

 mental points should lie on a straight line, provided the equation holds. 

 This method of treatment was first proposed by Bancroft 2 and has 

 proved extremely useful in determining the behavior of very concen- 

 trated solutions. In Figure 7 are shown the curves for potassium chloride 

 and potassium nitrate in water at 18. It will be observed that the points 

 lie very nearly on a straight line. 



0.0 



5.0 



2.0 



0.0 



3.0 



LogC (1 Y). 

 FIG. 7. Plot of Storch Equation for Aqueous Solutions of Binary Electrolytes. 



It is evident, however, that an equation of this type cannot apply 

 generally, since it does not approach the mass-action expression as a 

 limiting form. As we have seen, dilute solutions in non-aqueous solvents 

 approach the mass-action function at low concentrations. It has there- 

 fore been proposed 3 to express the relation between the conductance and 

 the concentration by means of the equation: 



(ii) 



K'= 



0(1 



2 Bancroft, Ztschr. f. phys. Chem. SI, 188 (1899). 



Kraus, Proc. Am. Chem. Soc. 1909, p. 15; Bray, Science 35, 433 (1912) ; Trans. Am. 

 Electro-Ch. Soc. 21, 143 (1912) ; MacDougall, J. Am. Chem. Soc. 34, 855 (1912) ; Kraus 

 and Bray, J. Am. Ohem. Soc. 35, 1315 (1913). Somewhat similar four-constant equations 



