1904.] Theory of Amphoteric Electrolytes. 277 



of pronouncedly basic character. The detailed investigation of these 

 methyl derivatives is at present proceeding in my laboratory. 



Turning now to the theoretical discussion of the simple case in which 

 the product kjc-b remains constant in a series of amphoteric acids, we 

 find that the dilution at which a given ionisation occurs, becomes 

 greater as the constants approximate, or, in other words, that at a given 

 dilution the unionised proportion uv increases as fa approaches k a in 

 value. From the table on p. 274 it will be seen that the influence of 

 dilution on the proportion unionised is comparatively small at ordinary 

 dilutions when the value of fa is considerable. From this it follows that 

 in the region considered a ten -fold increase in k a with a corresponding 

 diminution of fa may have no appreciable effect on the product uv at 

 the same v, although from equation (4) the proportion of H+ compared 

 with HX + will be greatly increased. Here then we have with a 

 nearly constant unionised proportion, considerable variation in the 

 relative proportions of the ions present, not only in the case of 

 a given acid at different dilutions, but also at the same dilution in 

 a series of acids with varying constants, if the product of the acid and 

 basic constants remains invariable. This comparative constancy of uv 

 often greatly simplifies its evaluation in a given case. Suppose that in 

 the series of amphoteric substances with constant k a fa we consider 

 that one for which k a = fa. This substance will be absolutely neutral, 

 and its ionisation, and therefore its uv, will be the same at all dilutions 

 (compare previous paper, p. 159). Here the calculation of uv is easy, 

 since c + d = 2d gives the ionised quantity, and a = b ^/K. 

 Equation (4) then becomes d = ku/ ^/K, and since v~ l = u + 2d, 



Now at 25 3 K = 1-2 x 10^ 14 , so that for this temperature 



1 -095x10-7 



uv = - 



(5). 



To exemplify this mode of calculation we may take the case con- 

 sidered on p. 276. We wish to know the value of uv, for k a = 10~ 3 y 

 fa/K = 100, and i; = 1C. Here fa = l-2x 10- 12 and Wfc = 1'2 x 10~ 15 . 

 A substance with the same product k a fa but with k a = fa would have 

 k = \/l 7 2 x 10- 15 = 0-3465 x 1Q- 7 . Applying formula (5) we obtain 

 uv = 0*613, a very close approximation to the true value 0'612. 



The method of calculation here indicated becomes inapplicable only 

 at great dilutions and in cases where the two constants are very 

 widely apart. In any case it affords a useful first approximation to 

 the value of u, and gives the limit to which uv may attain in maximo 

 at increasing concentrations. 



