OTHER PROPERTIES OF ELECTROLYTIC SOLUTIONS 283 



2. Density of Electrolytic Solutions. According to the ionic theory, 

 the properties of dilute solutions of electrolytes are additive functions of 

 the concentrations of the ions and of the un-ionized molecules. If Ji is 

 the value of a given property of such solutions and 



(81) 

 then: 

 (82) kn = Ay + B(l Y), 



where Jt is the value of the property at zero concentration, jc is its value 

 at the concentration C, y is the ionization of the electrolyte at this con- 

 centration, and A and B are constants relating to the ions and the un- 

 ionized molecules respectively. Ajt is evidently the percentage equivalent 

 property change due to the electrolyte at the concentration in question. 

 In applying this equation, it is tacitly assumed that the property is inde- 

 pendent of any interaction between the ions and the un-ionized molecule, 

 otherwise a term should be added involving the concentration and the 

 equation would no longer be linear. Equation 82 may evidently be 

 written: 



(83) Arc = B + A'y, 

 where 



(84) A' = A B. 



Ajt is thus a linear function of y, and from the known values of An the 

 values of y may be obtained. Such additive properties lend themselves 

 to a determination of YJ and a comparison with the value of y as derived 

 from conductance measurements might be expected to thus serve as a 

 check on the correctness of these values. A simpler method of com- 

 parison consists in plotting the measured values of A:t against those of y 

 as derived from conductance measurements. 4 If the two methods yield 

 concordant values of y, the graph should be a straight line. 



Unfortunately, this method of checking the results of conductance 

 measurements is restricted in its application owing to the fact that in 

 many cases the value of a given property for the un-ionized fraction does 

 not differ appreciably from the sum of those of its constituent ions. This 

 appears to be the case, for example, with many of the optical properties 

 of electrolytic solutions. 



Many properties of atomic and molecular complexes depend upon the 



* Heydweiller, Ann. d. Phya. 37, 739 (1912) ; ibid., SO, 873 (1909) ; Magie, Physical 

 Kevvew 25, 171 (1907). 





