ON ELECTKOLTSIS IN ITS PHYSICAL AND CHEMICAL BEARINGS. 371 



that the quantity present of each ion, I, or Jj, is not altered by the reactions ; 

 lience it follows that — 



2(.>i\> = 0, and S^V^'O = 0- 



These are n+v fresh equations, one more than is required, but one of them is 

 not independent. 



Thus we have all the equations necessary for the solution of the problem. 

 The general equation of the system (A) is — 





or — 



This equation contains the following proposition : — 



(32) When equilibrium i^ established among any numbei- of electrolytes, the 



product of the active masses of two conjugate electrolytes is equal to 

 the product of the active masses of their tivo opposites, just as if no 

 other electrolytes were present. 



This extremely simple proposition contains the solution of the general problem 

 — if one mixes a number of electrolytes together in any proportion, what 

 reactions will occur? By a discussion similar to that preceding prop. 24, one 

 recognises easily that — 



(33) Bodies possessing the smallest coefficients of activity are most likely to 



he formed at the expense of opposite bodies. 



§ 9. Applications of the foregoing paragraph. 



In practice the case which most often presents itself is that of two electrolytes, 

 -whose four ions are different, put to react on each other in a slightly active solvent 

 (most commonly water). We will consider some important special cases. 



Case 1. The two electrolytes are a very active acid, and the salt of a less 

 active acid. Let the initial quantities be n and 1. If no water were present, the 

 equation of equilibrium would be — 



(«-.r) (l-.r) aS = .r^/3y 2a 



But, by reason of the presence of water, the salts, of which the quantities will 

 be 1 — .V and .r, get into equilibrium with the water and their respective acids and 

 bases. So minute quantities are decomposed by the water, and the quantities 1 — x 

 and .V will be a little diminished — especially 1 — .r, the salt of the less active acid. 

 Let us write these so reduced quantities — 



Izfiand^ 

 X ^• 



Similarly the quantity of reacting acids n — x and x will be a little increased, 

 especially the latter. Call the actual quantities — 



X (n — x) and px. 



Calculation indicates that the greatest of the quantities x and y}/, X and p, does not 

 differ appreciably from 1 unless afi is excessively great in comparison with j3y. 

 So, writing ^'>^lpx=T, we have proved that T£tl if 0y is comparable to aS. If, 

 on the other hand, a8ll3y is very big, r will differ from unity, but stiU t • adj^y will 

 be enormously great, and hence in the equation — 



{n—x) (l—x) T = x^ 



/3y 



it is still necessary to suppose x almost equal to n or to 1, whichever is least. The 

 role of the water consists in delaying the process a little, and can, from a broad 



B B 2 



