LAWS OF ELECTROLYTIC DISSOCIATION 77 



we perceive that A must increase with increasing values of x. For 

 A = °o , X must have its maximum value, which, according to the 

 last italicized rule above, may only be that of the isoelectric point. 

 In other words, the more concentrated the ampholj^te solution the 

 closer does its [H+] approach that of the isoelectric point of the 

 ampholyte. For A = we obtain, on the other hand, the other 

 limiting value, x = Vkw, or the neutral reaction. 



By applying the above outlined general solution of equation 

 (VII) and the rules developed from it, the value of x may be es- 

 timated for any special case. By substituting this estimated value 

 in equation (VII) together with the appropriate values for ka, kb 

 and kw, it becomes possible to determine whether one or more 

 terais of the expression become extremely small in respect to the 

 other terms, and may then be disregarded. Thus approximate 

 values for x are obtained, which may be verified by substitution in 

 (VII), and, whenever necessary, corrected by actual trial. By 

 this method S0rensen made the following calculations for pure 

 aqueous solutions of glycocoll, for which ka = 1.8 X 10~^", kb = 

 2.7 X 10-12, kw = 10-14; 



Concentration of the solution: 



A °° 1 10-1 10-2 10-3 10-4 



pH 6.088 6.089 6.096 6.155 6.413 6.782 



The isoelectric point is at pH = 6.088. 



21. The hydrogen ion concentration and the solubility of weak acids 



This problem takes us back again to the simple electrolytes. It 

 is commonly known that free acids are less soluble than their alkali 

 salts and that bases are less soluble than their chlorides. Since, as 

 was shown above, the relative amounts of free acids and of their ions, 

 as well as of salts, depends upon the hydrion concentration, it 

 follows, therefore, that the hydrion concentration of a solution 

 must have an effect upon the solubility of the electrolytes. Let us 

 next define the concept of solubility. We shall choose for illustra- 

 tive purposes the solution of a fairly insoluble acid. When water 

 is saturated with solid benzoic acid a system is finally obtained which 

 has the following composition: A sediment of solid benzoic acid 

 which is not electrolytically dissociated to any measurable extent. 



