100 HYDROGEN ION CONCENTRATION 



Second case: Titration of a weak acid with a strong base. Ten cubic 

 centimeters of N acetic acid are diluted with water to 100 cc. and 

 titrated with iV NaOH. Again we construct a curve which repre- 

 sents the change in pH with increasing quantities of added base. 



To calculate the pH values in this case the following principles are 

 applied : 



1. The pH of the pure acetic acid solution is calculated from equa- 

 tion (la) page 40. 



[H+] = Vk X [A] 



2. On the addition of NaOH we have in solution a mixture of free 

 'acetic acid + sodium acetate. The pH of these mixtures is derived 

 from equation (1), page 44. 



_ [free acetic acid] 

 [sodium acetate] 



3. As soon as an equivalent quantity of the base had been added 

 we have a 0.1 A'' solution of pure sodium acetate. At this state the 

 pH value is calculated from the hydrolj^sis formulae (see table, page 

 90). 



4. When an excess of base had been added we deal with a dilute 

 NaOH solution; assuming total dissociation the pOH and hence pH 

 may be obtained. 



In this manner the middle curve in figure 12 is obtained. 



The end point in this titration is also characterized by a sudden 

 rise in the pH curve. But here also the transformation point of the 

 nitrophenol (pH 5.0 to 6.0) bears no relation to this sudden rise of the 

 curve. This rise covers the range of pH 7.0 to 11.0. Neither nitro- 

 phenol (pH range 5.0 to 6.0) nor litmus (pH 7.0) but phenolphthalein 

 alone (pH 8.0 to 8.5) can be used as an indicator for reaching the 

 true end-point of this titration. The dissociation constant of phe- 

 nolphthalein is pk = 9.7 and hence its transformation point is at 

 about pH 8.0 to 8.5. 



Among the weak acids acetic acid (k = 2 X 10~^) is a fairly strong 

 one. If instead of acetic acid a still weaker acid, such as boric acid 

 or phenol (pk = 10), then an entirely different curve is obtained 

 (upper curve in figure 12). 



In this case the pH values are calculated just as in the case of 

 acetic acid from the equations stated above. 



