FORM OF THE CONDUCTANCE FUNCTION 69 



In this equation y is written for the ratio -r- for the sake of brevity. An 



A 



inspection of this equation shows that at low concentrations the first 

 term of the right-hand member, involving the ion concentration Cy, will 

 diminish as the concentration decreases, and will ultimately become neg- 

 ligible in comparison with the constant K. On the other hand, at higher 

 concentrations, the constant K will become negligible in comparison with 

 the term involving the ion concentration. In other words, at high con- 

 centrations this equation approaches the Storch Equation 9 as a limiting 

 form. 



Obviously, this equation involves the four constants A , K, D and ra. 

 These constants may in most cases be determined readily by graphical 

 means. If conductance data are available at very low concentrations, 

 the second term of the right-hand member may be neglected, in which 

 case the reciprocal of the equivalent conductance becomes a linear func- 

 tion of the ion concentration; that is, the equation degenerates into the 

 form of Equation 7. The value of A and of K may therefore be de- 

 termined with a considerable degree of precision from this plot. Hav- 

 ing determined these two constants, the values of m and D may be de- 

 termined from data at higher concentrations. At very high concentra- 

 tions K may be neglected and from a plot of Equation 10, which is 

 linear if the equation holds, the values of ra and D may be determined. 

 In case the constant K is not negligible at higher concentrations, it is 

 necessary to take this into account. This may be done by means of a 

 second approximation. It is seen from Equation 11 that the mass-action 



Cv* 

 function K' = _ is a linear function of the ion concentration raised 



to the ra'th power. If the value of ra in the more concentrated solutions, 

 as determined by the first approximation, is correct, then the values of 

 K and D may be corrected by means of a plot of K' against (Cy) m . 

 The value of K is then determined by extrapolating to the concentration 

 zero and the value of D is determined from the slope of the line. The 

 values of the constants having been determined, it is possible to calcu- 

 late the conductance of a given electrolyte at any desired concentration 

 and to compare the calculated with the experimental values. 



In Figure 8 is shown a plot of the reciprocal of the equivalent con- 

 ductance against the specific conductance or ion concentration for solu- 

 tions of potassium amide in liquid ammonia. 4 This plot yields for A 



have been proposed by Bates (J. Am. Chem. Soc. 37. 1431 (1915)) and bv de 

 (Medd. K. Vet. Akad's Nobelinstitut, Vol. 3, Nos. 2 and 11 (1914)) While 



equations represent the course of the conductance curve fairly well in the case of aaueoua 

 solutions, they are not generally applicable to non-aqueous solutions 

 Franklin, Ztschr. f. phys. Chem. 69, 290 



