Radiometric Measurements of Constants of Indicators. 



81 



In addition, the equilibrium equations given below are to be considered : 

 (H+) (HIn) 



(H 2 In) 

 By combining these three equations we obtain 



c/Cl = H+(H++ KI) 



(H+) (In) 

 (HIn) Ka 



(10) 



(ii) 



In the second case, when the ion HIn is red and the ion In is yellow, 

 the ratio becomes 



HIn 



c/ci= z -== (12) 



H 2 In + In 



and from equation 10 



/ _ 



Cl " 



H 2 



(13) 



In the third case, i. e., when both ions HIn and In are red, the ratio is 

 given by 



HIn + In 



C / C 1= 



whence, c/Ci = 



H+ K! + 



(i) 



H +2 



(I 4 ) 



(15) 



These equations, 11, 13, and 15, were tested by substituting the 

 experimental values of the ratios c/Ci and the hydrogen ion concen- 

 trations given for solutions 1 and 4, table 51, in the equations, and 

 solving for the constants KI and K 2 . The constants were then used to 

 calculate the ratios for solutions 2 and 3. Table 52 gives the values 

 of the ratios c/c\ calculated from the various equations, and also the 

 observed experimental ratios which are the averages of those given in 

 table 51. 



TABLE 52. 



On the first assumption, namely, that the ion HIn is yellow and the 

 ion In is red, the ratios calculated by equation 11, for solutions 2 and 3, 

 do not at all agree with the experimentally determined values. On the 

 assumption that the intermediate ion HIn is red and the secondary ion 

 15 is yellow, the constant K 2 , equation 13, was found to be a negative 



lr The development is essentially the same as given by Rosenstein for phenolphthalein. Journ . 

 Amer. Chem. Soc., 36, 1124 (1912). 



