[macgregor] conductivity OF ELECTROLYTES 79 



which there are {p — 1) {'p -\- q — 1), similar equations may then be 

 deduced froui thein for all groups of the electrolytes consisting of two 

 with no common ion and the products of their double decomposition. 



That the above 2p (/> + '7 — — *? equations form the only condi- 

 tions may be shown by deducing from them the equations obtained by 

 applying the law of equilibrium to each electrolyte throughout the whole 

 volume, as, for example, 



e, h ^ /^i + /^4 + A, + /Ao + etc. A + /:^, + /^; + etc. 



V V ' 



or, without this trouble, by showing, as is done below, that these equa- 

 tions are sutficient to determine the state of dissociation. 



Arrhenius ^ says with regard to this general case : " It is easy to see 

 that if we mix any number ion of combinations of in positive and n neg- 

 ative ions, equilibrium will not be disturbed, provided these mn electro- 

 lytes formed isohydric solutions among one another before the mixing, and 

 the product of the active masses [i.e., quantities of dissociated ions] of two 

 electrolytes J,,,./,, I^.J^, is equal to the product of the active masses of 

 I,„J^, and I„J,^. This will be the case if the volumes of the isohydric solu- 

 tions are related to one another as the surfaces in the annexed diagram," 

 in which diagram the surfaces, so far as the eye can judge, are equal. It 

 is obvious that if the volumes occupied by the various electrolytes in the 

 solutions were equal, the second set of equilibrium conditions would be 

 satisfied ; but equality of volumes is not necessary for their satisfaction. 



For determining the quantities of the various electrolytes present in 

 the solution, and their ionisation coefficients, we have the following 

 equations : 



(a) from the equilibrium conditions, 



ai a., • 



-y = -rf — etc., P (.P ~\~ 'l) — 1 equations. 



- - ' ' . .1 . . . . Q, + ,^ _ 1) (y, _ 1) equations, 



etc. ,1 



(h) from the volume relation, 



JV-i Vi 4- •^'l'T 2 4- etc. = V 1 equation, 



(e) from the relation of ionisation to dilution, 



T^ = .^ ( 1 i), ' l> (.P + 'J) equations, 



' i 



etc., J 



((/) from the conservation of mass, 



/', 4- /'in + etc. = N, + N, + etc. + 7V„ + etc.l 



/ho = i\"iu + iV,, + ^V,_, + etc.. I . ,(2p + q — l) eqns., 



etc., J 



ill all 3// (j) -\- q) equations for determining p (p 4- q) as. p {p -\- q) i\'''s, 

 aiidj» {p -\- q) F's. 



1 Ztschr. f. physikal. Chemie, vol. il., p. 284 (1888). 



