FORM OF THE CONDUCTANCE FUNCTION 81 



preaches at zero concentration. At higher concentrations the tangent 

 will decrease; that is, the ionization will increase less rapidly for a given 



increase in the ion concentration, because both K' and -^ ,.~ > in- 



crease with the concentration. 



If we introduce A and CA as variables, Equation 15 has the form: 



dA A* /CA dJC' 



- 2 '' d(CA) 



The plot of A against the specific conductance in dilute solution will 

 therefore be a curve convex toward the axis of specific conductances, and 

 as the concentration decreases it will approach a line whose tangent is 



provided the conditions mentioned in the preceding paragraph are 

 K. 



fulfilled. 



In order to follow up the form of the curve at higher concentrations, 

 we may introduce the conductance function 11. On differentiating this 

 function we have: 



(17) " A2 



Since K' approaches K at low concentrations, it follows that the tangent 

 approaches the value -= as a limit. At higher concentrations, the 



tangent decreases, since K' decreases. Ultimately the form of the curve 

 depends upon the value of m. If m is less than 1, then the tangent will 

 always have a negative value; in other words, the equivalent conduct- 

 ance will always decrease with increasing values of the specific con- 

 ductance. On the other hand, when m is greater than unity, the tangent 

 will become zero, when: 



(18) 



J.\. 



that is, at this point the conductance passes through a minimum value 

 after which it increases with increasing values of the specific conduct- 



(CA\ m 

 -r 1 + K, and denoting by C' 



and A' the values of the concentration and the equivalent conductance at 

 the minimum point, we have: 



(19) 



D(m-D) 



