FORM OF THE CONDUCTANCE FUNCTION 83 



given substance in different solvents or in the same solvent at different 

 temperatures, the value of D is practically constant, while the values of 

 m and K vary. It follows, therefore, that the y, Cy-curves for all such 



solutions pass through the point Cy = 1, Y = n _i_ i ^is relation is of 



importance in interpreting the influence of temperature on the conduct- 

 ance of solutions. 



The further discussion of the relation between the conductance and 

 the concentration is greatly simplified by introducing the function K' and 

 examining the manner in which K' varies as a function of the ion concen- 

 tration. Differentiating, we have the equations: 



A W 

 (24) 



^-JMPtJP* 



If D were zero, that is, if the mass-action law held, we should have: 



. 



or K' = constant. 



On the other hand, when the D term is present, K' will always increase 

 with the concentration. The form of the K', CA-curve is determined 

 mainly by the constant m. When m = 1, we evidently have: 



(26) = Dm or 



In this limiting case, therefore, K' varies as a linear function of the 

 specific conductance CA. 



The form of the curves for values of m greater and less than unity 

 may readily be determined by means of the second differential coefficients. 

 W^e have: 



( 27 ) 3^T5= D (-1) 



When m < 0, 



(28) 



and the K, Cy-curve is everywhere concave toward the axis of Cy. When 



