DETERMINATION OF ACIDITY AND ALKALINITY 107 



The maximum of the buffer value is then established when 



dp (S - 2 L) 



= 

 dL S • log e 



or, 



L.f (II) 



Therefore, it occurs in a mixture of equal concentrations of acetic 

 acid and sodium acetate. 



The numerical relation of the buffer value j/ in a mixture of a weak 

 acid and its salt may be obtained from equation (I) above: 



1 [bound acid] ... 



»» X log e = - = , ^ , — r X free acid (III) 



rs [total acidj 



If for the sake of simplicity we neglect the factor log e in the above 

 calculation permitting a shght alteration in the definition, and assume 

 V X log e to be equal to the buffer value where v has its former value 



dL , . . 



of "TTtj ^tien equation III gives us a very simple expression for the 



buffer value. This holds only for a mixture of an acid and its salt, 

 and that only within the limits within which the approximation 

 formula 



[free acid] 



[H+] = k 



salt] 



is applicable. This range may be approximately estimated between 

 the values pH = pk + 2 and pH = pk — 2. The reciprocal value tj 



may be designated as the "yielding power. "^'^ 



The dissociation constant of the acid does not enter into the expres- 

 sion III. Hence it follows that : 



The "yielding power" and with it the buffering effect of an acid-salt 

 mixture are independent of the nature of the acid. Thus the relatively 

 strong acetic acid and the very weak boric acid when appropriately 

 mixed with their respective sodium salts have the same buffering 

 effect, except that the ma.ximum of their buffer effects is at different 

 pH values. This maximum may be evaluated in the following way: 



1" "Nachgiebegkeit" — frequently used by the author in the sense of the 

 reciprocal of buffer value. — Translator. 



