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ROYAL SOCIETY OF CANADA 



calculated values of an}' solution, it might be better to proceed other- 

 wise, viz., by determining the constitution of a complex solution of the 

 electrolytes 1, 2, 3, 4 Avith a known common concentration of ions. For 

 this purpose select an}^ value of the concentration of ions and read off 

 from the experimental curves referred to above the corresponding values 

 of the dilutions Fi, Vo, V^, V^, of simple solutions of 1, 2, 3, 4, selecting 

 a concentration of ions characteristic of dilute solutions so as to avoid the 

 complication which would be introduced by change of volume on mixing. 

 If simple solutions of these dilutions ai-e mixed in proper proportions as 

 to volume, there will be no change of ionisation on mixing. To find the 

 proper proportions, select arbitrarily any value of i\ the volume of the 

 solution of 4 which is to be mixed with the others. It will contain 

 K^ — Vi/ Vi gramme-equivalents of 4. From equations (rf) above we 

 must have N^ = iV,. Hence the volume of 3 to be mixed with the others 

 will be Un = V^Vi/ F4. Next select arbitrarily any value of V2. Then in 

 order that there may be no change of ionisation on mixing we must have 



The volumes of the simple solutions of dilutions Fj. V^, F, F4. which must 

 be mixed in order to form a comj^lex solution with the selected concen- 

 tration of ions, are Ijius known. The solution may therefore be prepared 

 and its conductivity experimentally determined. The conductivity may 

 also be cakndated. For the concentrations of the simple solutions and the 

 volumes of them which are mixed being known, the iV's may be found ; 

 and the common concentration of ions and the dilutions being known, the' 

 a's may be found. If the densities of the simple solutions are known, 

 either from the data of published tables or from preliminary experiments, 

 the numbers, ?ii, îh, of gramme-equivalents of 1 and 2 which must l)e 

 added, sa}^ to a kilogramme of water in order to produce the required 

 complex solution, may be calculated, and the solution may thus be pre- 

 pared by three weighings, the eri'ors due to measurements of volume 

 being thus avoided. 



In this case there wil 



Case IV. —Solutions cont.\ining Three Electholytes having no 



(JOMMON Ion. 

 1 ill general he nine ek;el rolytes in the solution, 

 as illustrated in the diagram, in which the 

 numbers are given by which we shall indicate 

 the various electrolytes. 



The application of the law of equilibrium 

 to each electrolyte throughout its own region 

 gives nine equations, such as, 



., ''J ^ É1 . A. 



' ^1 l-l Vl 



Applied to each electrolyte throughout the 



