Radiometric Measurements of Constants of Indicators. 69 



The concentration of phenolphthalein is not a factor in the variations 

 of the constants in the different tables. The following shows that it is 

 possible to determine K t without knowing the concentration of the 

 indicator. 



If we consider equation 21 



LH X OH K, 

 Q + ~ K,- 



and represent the total concentration of phenolphthalein by T, and that 

 of the quinoid salt by Q, we have from equation 24 



In (I/I ) X T 



In (I/Io)' 

 LH is then equal to (T Q) or 



= Q 



TTT / T O x T In (I /Io) X T 



LH = (T - Q) - T - ln (I/Io) , (27) 



Substituting these values in the hydrolysis equation, we have 



x OH 



T T _ 

 L 



In (I/Ip) X T K,- 



In (I/Io)' 



, 9Q , 



Simphfying, T, the concentration of the phenolphthalein disappears, 

 and we have 



QH[ln (I/I y - In (I/I )] K w 

 In (I/Io) " K, 



K, : , calculated from equation 29, gives the same value as when calcu- 

 lated from the equations previously derived. 



Since it is not necessary to know the concentration of the indicator to 

 determine its ionization constant, the variation of K t , shown by the 

 different tables, must be due to other causes. It will be noticed from 

 the separate tables that K; decreases with the hydroxyl ion concentra- 

 tion. This is in accordance with the results of previous investigators. 

 When the hydroxyl ion concentration, or the ratio of ammonium 

 chloride to ammonium hydroxide remains the same, K; shows a marked 

 decrease with decreasing amounts of neutral salts. If we consider 

 solutions III and I in tables 40 and 44, respectively, it will be seen that 

 decreasing the concentration of the neutral salt four times changes K t 

 from 1.6XKT 10 to 0.9 XlO" 10 . This is in accord with the results of 

 Rosenstein, who has made a very careful study of the effect of neutral 

 salts on the ionization constant of phenolphthalein. It will, therefore, 

 be seen that the discrepancies in the value of K, are due in part at least 



