276 



. J- Walker. 



[Oct. 19, 



Finally, if we denote the reciprocal of k a by I, and divide throughout 

 by v, we have 



The coefficients of p are here homogeneous functions of v, r, and I of 

 degree zero, that is, we do not by altering v, r, and I in the same 

 ratio effect any change in the value of p. In other words, if we 

 increase the constant k a w-fold, and simultaneously diminish v and r (or 

 fa) in the same proportion, the unionised proportion remains unaltered. 



The following is an example of the employment of the preceding 

 table in conjunction with this result. Suppose it is desired to know the 

 value of u'v' for k' a = 10~ 3 , k' b /K = 100, v' = 10. The table gives the 

 values for k a = 10" 4 . We must therefore, in consulting the table, 

 increase k'i/K and v' in the same ratio as that in which k' a is diminished, 

 that is, we must find the value in the table for &&/K = 1000 and 

 v = 100. The number sought is uv = u'v' = 0'612, whence u' 0'0612. 



The conclusion that the unionised proportion is unaffected by a simul- 

 taneous change of l/k a , kb, and v in the same ratio is of importance in the 

 discussion of the ionisation of a series of amphoteric electrolytes in which 

 the product kjciis constant. Ostwald* ascertained that the influence of 

 a substituent on the dissociation constants of simple acids is of such a 

 character that the constant of each acid is increased or diminished for 

 a given substitution in a ratio, which, although not constant for 

 different acids, is usually of the same order in a series of similar 

 substances. The same rule no doubt holds good for bases, although in 

 this case accurate data are wanting. At all events we know that when 

 chlorine is substituted for hydrogen in a simple acid, the dissociation 

 constant of the acid is greatly increased, and we also know that when 

 the same substitution is made in a simple base, the strength of the base 

 is greatly diminished. Suppose now that the substitution takes place 

 in an amphoteric electrolyte. We might expect the primary effect to 

 be a considerable increase in the value of k a and a corresponding dimi- 

 nution in the value of &&. This primary effect would, however, in 

 many cases be complicated by stereo-chemical influences, and possibly 

 by the secondary influence which the change in the strength of the 

 acid group might exert on the strength of the basic group, and con- 

 versely. Winkelblech found in opposition to this, that the substitution 

 of methyl for hydrogen in glycine diminished the acidic and basic 

 constants simultaneously, and the same is true of the effect of isomerism 

 in the amino-benzoic acids. In these examples it may be that the 

 primary effect is masked by the superimposed secondary effects, for in 

 the analogous case of the continued methylation of the amino-benzoic 

 acids, the acid parent substances are finally converted into derivatives 

 * ' Zeitschrift fur phyaikal. Chexn.,' vol. 3, p. 171 (1889). 



