J 904.] Theory of Amphoteric Electrolytes. 159 



proportion is small compared with the unionised, then u is approxi- 

 mately equal to 1 /v, where v is the number of litres in which one gramme- 

 molecule is dissolved, and the concentrations of the positive ions will 

 become equal when v is approximately equal to Tc^jK. At greater 

 dilutions a is greater than cl ; at less dilutions d is greater than a. 



In order to see clearly how different an amphoteric electrolyte is in 

 its conductivity relations from a simple electrolyte, whether acid, base, 

 or salt, we may consider the case for which Jc a = h, i-e>, where the 

 substance is of the same strength as acid and as base. From (11) we 

 deduce a = b, and since from (5) the product ab is constant for all dilute 

 solutions, it follows that the concentration of hydrion and hydroxidion 

 is equal to the concentration of these ions in pure water, i.e., the 

 substance is at all dilutions absolutely neutral. Its solutions, therefore, 

 behave in this respect like those of a neutral salt, but differ from them in 

 the effect of dilution on the molecular conductivity. From (9) and (10) 

 namely, we find that c = d, and that c + d is proportional to u, since a is 

 here constant. The ionised proportion is thus a constant fraction of 

 the total dissolved substance independently of the concentration, and 

 consequently the molecular conductivity is independent of the dilution. 

 Comparing different substances of this type with each other, the 

 proportion ionised is seen to vary directly as k If a substance at 25° 

 had k a = h b = l-2 x 10 -7 , that is, if the acidic and basic constants were 

 more than 100 times less than those of acetic acid or ammonia, the 

 value of d derived from (9) would be l'lu, or the substance would be 

 ionised to the extent of 52 per cent, at all dilutions, and therefore a 

 good electrolyte. 



Comparing generally the expression a 2 — ^— ^ u deduced for an 



amphoteric electrolyte, with the expression a 2 = K+Jc a u deduced for a 

 simple acid with the same acid constant, we see that the former is 



equal to the latter divided by 1 + ^ u. When k h = 0, that is, when the 



electrolyte has no basic character, the divisor becomes equal to unity, 

 and the expression for a simple acid is obtained. When l-b/K and u 

 have finite values, it is obvious that the amphoteric electrolyte cannot 

 strictly obey Ostwald's dilution law. If, however, either h^lK or u is 

 very small, Ostwald's dilution law is approximately followed, for then 

 the values of a from the simple and amphoteric formulae become nearly 



equal, and the expression d = ^ ua for the concentration of the other 



positive ion nearly vanishes. The smaller the basic dissociation constant, 

 then, and the greater the dilution, the more likely is the amphoteric 

 electrolyte to follow the dilution law characteristic of simple acids and 

 bases. 



