Section 116. Summary and Discussion. 



327 



hydrogen-ion calculated from each transference number and from the most 

 probable values for nitrate-ion and chloride-ion (64.6 and 68.5, respect- 

 ively) at 20 and extreme dilution.* In the last row of the table are given 

 the corresponding values for zero concentration as derived from Goodwin 

 and Haskell's conductivity experiments. f 



Table 138. Final values of the transference-numbers and the equivalent conductance 



of hydrogen-ion. 



It will be seen from table 138 that, except at the highest concentration 

 (0.055 normal), there is substantial agreement between the values of the 

 equivalent conductance of the hydrogen-ion derived from the independent 

 transference experiments with the two different acids, and that the (nearly 

 constant) value for the concentration-interval between 0.018 and 0.006 

 normal is nearly 5 per cent larger than that derived from conductivity 

 measurements at extreme dilution. The reality of this divergence, first 

 discovered by Noyes and Sammet, confirmed as it is on the conductivity 

 side by the investigation of Goodwin and Haskell and on the transference 

 side by the recent determinations of Jahn, Joachim, and Wolff, and by 

 these new experiments with nitric acid, can, we believe, no longer rea- 

 sonably be doubted. It must therefore be concluded that the transference 

 number of the anion of acids, and therefore the ratio of the velocity of the 

 anions to that of the hydrogen-ion, is several per cent larger at very small 

 concentration (0.001 normal and less) than at moderate concentrations 

 (0.05 to 0.005 normal). Thus a change in the relative velocities takes 

 place even after the concentration of the solute has become so small that 

 as a medium the solution scarcely differs from the pure solvent. The fact 



*The value here given for the CI is that derived by Noyes and Sammet from 

 Kohlrausch's conductivity data and the existing transference data for potassium 

 chloride. That for the NOs ion we have obtained by subtracting from that for the 

 CI the difference for these two ions at 20 given by Kohlrausch (Sitzungsber. 

 konigl. preuss. Akad. der Wissensch., 1901, 1031). These values have then simply 

 been multiplied by (1 n)/n. 



fThese investigators found for A at 18 377.0 for HNO3 and 380.1 for HCl. 

 The corresponding values at 20 calculated with Deguisne's coefficients are 389.2 

 and 392.5 respectively. Subtracting from these the values for the NOs and CI ions 

 (64.6 and 68.5) one obtains the values for the hydrogen ion given in the table. 



