Section III., 1897. [ 69 ] Tkans. R. S. C 



V. — On the Calcnlation of the (^onduefioity of Aqueous Sobitiom con- 

 taining Sodium Ch/oride and Pofassiujn Sulphate. 



By E. H. Archibald, B.Sc, Dulhousie College, Halifax, N.S. 

 (Commun kated by Prof. J. G. MacGregor, and read June, 18î)7.> 



In a paper communicated to this society in 1896, Prof. J. G. Mac- 

 Gregor suggested a mode of testing the possibility of calculating, by the 

 aid of the dissociation theory of electrolytic conduction, the conductivity 

 of a solution containing two electrolytes with no common ion. The 

 peculiar difficulty of the calculation in this case is due to the fact that if 

 the solution contain two such electrolytes it will also contain other two 

 formed by double decomposition. 



It has been shown by Arrhenius that if su.ch a solution be formed by 

 mixing simple solutions of the four electrolytes, no appreciable change of 

 ionization will occur on mixing, provided (1) the solutions are so dilute 

 that no appreciable change of volume occurs. (2) the concentration of 

 ions of the simple solutions are the same, and (3) the volumes of the simple 

 solutions are such that the products of the volumes of the solutions of 

 electrolytes with no common ion are equal. 



Prof. MacGregor pi-oposed, thei-efore, to draw curves showing the 

 relation of ionic concentration to dilution for simple solutions of each of 

 the four electrolytes, by the aid of observations of their conductivity, and 

 to read olf from these curves the values of the dilutionsof those solutions 

 of the respective electrolytes which would have any desired common con- 

 centration of ions. These solutions might then be prepared. Their dilu- 

 tions ( F) and the number (iV) of gramme-equivalents of their electrolytes 

 in any volume (r), their ionic concentrations (a/V), and their ionization 

 coefficients (a) would thus be known. They ai-e then to be inixed in the 

 proper proi)ortions as to volume to ensure that no change of ionization 

 will occur on mixing. For this purpose, calling two of the electrolytes 

 with no common ion, 1 and 2 respectively, and the other two 3 and 4, 

 select arbitrarily any value of y^, the volume of the solution of 4 to be 

 mixed with the others. It will contain iV, = i' / V^ gramme-equivalents 

 of 4. Xow, if n, and n.^ be the number of gramme-equivalents of 1 and 2, 

 which would have to be added to water to make a solution of the same 

 constitution as the mixture, we have n, = iVj -f ^3 = ^i + ^t 

 and therefore A\ = N^. Hence the volume of 3 to be mixed with the 

 others will be r^ = F, ry V^. Next select arbitrarily any value of y,. 

 Then, in order that there may be no change of ionization on mixing, we 

 must have t\ = v^ vjc, — V., v// V, c^. As in all cases I selected r,= 

 t\, it is obvious that v. = i\. 



