78 



ROYAL SOCIETY OF CANADA 



(/>) from the volume relation, 



iVil'i + XT', + etc. = V 



((') trom the relation of ionisation to dilution, 



' 1 1 



, 1 equation, 

 p' equations, 



etc. 



. 2]) — 1 equations, 



((/) from the consei-vation of mass, 

 7ii = :\^ + X, + X + etc., ^1 



n, = N, + ^\ + ^\, H- etc., .... 



etc., i 



in all, therefore, Sp^ equations for determining p^ «-'s, ^r iV's, and p- Vs. 



Case VI. — Solutions containing any number of Electrolytes with 

 NO Common Ion, the products of their Double Decomposition, 

 and any other Electrolytes. 



It is obvious that if in preparing such a solution there are added to 



the solvent, j-) electro- 

 lytes Avith no common 

 ion and q other elec- 

 trolytes, having each, 

 therefore, one ion in 

 common with one of the 

 ]> electi'olytes. there will 

 hep^p -\- ^) electrolytes 

 in the solution. Thus, 

 if sodium chloride, hy- 

 drogen iodide, potas- 

 sium bromide and mag- 

 nesium chloride be dissolved in water, the solution will contain the elec- 

 trolytes specified in the diagram. 



As in the last case, it is unnecessary to obtain the conditions of equili- 

 brium. It will be obvious, on the grounds there specified, that Ave have, 

 as such conditions, 



A ^ /^ ^ A, ^ etc 



liions, and 



forming a set of (/v {p -\- </) 



- 1) equal 

 etc.. 



fonning a set of (/> — 1) (]< + '/ — 1) equations. That the equations of 

 this set are (p — 1) (/> -f 7 — 1) in number is obvious from the fact 

 that if such equations be written down for each group of four electrolytes 

 represented in the above diagram as occupying contiguous squares, of 



