158 



Prof. J. Walker. 



[Feb. 3, 



From (7a) and (5) we obtain 



From (6a) and (5) we obtain similarly 



c - (10). 



Now the sum of the concentrations of the positive ions must be equal 

 to the sum of the concentration of the negative ions, i.e., 



u + fZ = b + c, 



or, substituting the values of c and d from (9) and (10), 



(11 >- 



Multiplying both sides by a, and again making use of (5), we obtain 



« K+h a u 



h ■ < 12 >- 



or 



K+k a u 



From equation (5) we obtain J in terms of a ; the value of d is given 

 by (9) ; and finally from (10) and (5) we obtain 



c = & a ttft a 



We are now able to express the concentrations of the various ions 

 present in the aqueous solution of an amphoteric electrolyte if we 

 know, as is in many cases easily possible, the concentration of the 

 unionised substance, the dissociation constants of the substance acting 

 as acid and base respectively, and the ionisation constant of water. 



From the above formulae it is evident in the first place that the 

 electrical conductivity when treated in the ordinary way forms no 

 measure of the acidity or even of the ionisation of the dissolved 

 electrolyte, for besides hydrion there is the positive ion HX + , the 

 concentration of which may greatly exceed the concentration of the 

 hydrion, and whose velocity can only be about one-fifth of the velocity of 

 hydrion. The total conductivity is in fact the sum of four terms, each 

 consisting of an ionic concentration multiplied into the corresponding 

 ionic velocity. It may be seen from equation (9) that the concentrations 

 of the two positive ions are equal when u = K/Jc b . If the ionised 



