48 Conductivity of Aqueous Solutions. Part II. 



An examination of table 9 shows that the results obtained independently 

 by the various experimenters in this laboratory with different sets of ap- 

 paratus and different solutions agree in almost all cases within 0.2 to 0.3 

 per cent, except at the temperature of 30(3, but that at this temperature 

 there are several deviations of nearly 1 per cent. Except at this highest 

 temperature the agreement is entirely satisfactory and indicates a cor- 

 responding precision of the results ; and even at 306 it is probable that the 

 final values adopted are not in error by more than 0.3 per cent, since the 

 later measurements made in larger number and after more experience 

 by Mr. A. C. Melcher are probably more accurate than our own. 



17. CHANGE OF EQUIVALENT CONDUCTANCE WITH THE 



CONCENTRATION. 



It is a well-known fact that the mass-action law does not express even 

 approximately the change with the concentration of the ionization of salts 

 and strong acids and bases, when this, in accordance with the familiar 

 hypothesis of the ionic theory, is calculated from the conductance ratio 

 A/A . This has led to the proposal of numerous other functions,* which 

 have for their purpose an accurate representation of the experimental 

 values of the equivalent conductance and the ionization values deduced 

 therefrom. The extended discussion of the matter has not yet led to any 

 conclusion, so far as the theoretical explanation of the phenomenon is 

 concerned. There have, however, been discovered some simple empirical 

 formulas which at ordinary temperatures express the observed results 

 satisfactorily. 



Those which contain only a single arbitrary constantf have the follow- 

 ing form when expressed in terms of the equivalent conductance (A) at 

 any concentration C and the limiting conductance A at zero concentra- 

 tion : 



- K (Kohlrausch) A ?7~f = K (Barmwater) 



C* v * A* C* 



A ^~ C i = K (van't Hoff ) ^""o = K (Rudolphi) 



-Compare Kohlrausch, Wied. Ann., 26, 200 (18S5) ; 50, 394 (1893) ; MacGregory, 

 ibid., 51, 133 (1894) ; Barmwater, Z. phys. Chem., 28, 134, 428 (1899) ; Sabat, ibid., 

 41, 224 (1902); Muller, Compt. rend., 128, 505 (1899); Rudolphi, Z. phys. Chem., 

 17, 385 (1895) ; van't Hoff, ibid., 18, 300 (1895) ; Kohlrausch, ibid., 18, 662 (1895) ; 

 Storch, ibid., 19, 13 (1896) ; Bancroft, ibid., 31, 188 (1899) ; Jahn, ibid., 37, 499 

 (1901) ; 41, 265, 288 (1902) ; Nernst, ibid., 38, 493 (1901) ; Bousfield, ibid., 53, 263 

 (1905) ; Kohlrausch and Maltby, Wissensch. Abhandl. phys.-techn. Reichsanstalt, 3, 

 219 (1900) ; Kohlrausch, Sitzungsber., preus. Akad., 44, 1002 (1900) ; Kohlrausch 

 and Steinwehr, ibid., 1902, 581; Kohlrausch and Griineisen, ibid., 1904, 1215. 



fKohlrausch and Maltby (loc. cit, p. 219) and Kohlrausch and Griineisen (loc. cit.) 

 find that the formula A Az=A'C^ applies closely to the results with uni-univalent, 

 uni-bivalent, and bi-bivalent salts between 0.002 and 0.0001 normal, but that large 

 deviations exist at higher concentrations, even at 0.01 normal. 



