98 



HYDROGEN ION CONCENTRATION 



It follows then that a as well as F are functions of the pH, of the 

 type of the dissociation curve. 



Figure 11 shows one of such curves for p-nitrophenol, which has 

 already been discussed on page 54. As will be readily seen this 

 indicator is practically colorless in the pH range of to 5.0. The 

 pH at which it begins to show color depends upon its concentration. 

 It may be stated in a general way that with concentrations of indica- 

 tors usually employed in titrations the color becomes noticeable when 

 the indicator is 5 per cent dissociated. In this particular case, this 

 occurs at about pH 5.2, at most at pH 6.0. This so-called transfor- 

 mation point of the indicator does not in any way correspond with the 



neutral reaction, pH 7.0. 



Let us now consider the 

 significance of this pH value 

 of 5.2 to 6.0 in a titration. 

 Three cases must be distin- 

 guished. 



First case: Titration of a 

 strong acid with a strong base. 

 Let us assume that we add 

 to 10 cc. of N HCl increas- 

 ing amounts of N NaOH. 

 The acid had been diluted 

 with water to a volume of 

 100 cc. This volume is so 

 little altered in the process 

 of the titration that we may- 

 consider it as remaining constant. This assumption simplifies the 

 calculation and introduces no marked error. In figure 12 the amount 

 of the alkali added in cubic centimeters is shown on the abscissa and 

 the resulting pH on the ordinate. The latter is calculated on the 

 assumption that the acid, the alkali and the salt formed are always 

 completely dissociated and that the amount of indicator added is so 

 small that it does not influence the state of equilibrium between the 

 acid and the base. 



In the beginning of the experiment we have 0.1 A'' HCl, therefore 

 the pH = 1.0. After the addition of 1 cc. of the base we have a 

 0.09 N HCl solution, or pH = 1.05. In this manner we may con- 

 tinue our calculation until we approach the vicinity of the neutral 



Fig. 11. The abscissa represent pH val- 

 ues and the ordinates represent the color 

 intensity of p-nitrophenol. The curve as 

 drawn is the calculated theoretical disso- 

 ciation- (a)-curve of the indicator, the 

 circles are the experimentally observed 

 values. 



