Radiometric Measurements of Constants of Indicators. 53 



sary to modify the Ostwald view as to the cause of color. The facts 

 and relations brought out by these investigations have been correlated 

 and interpreted by Stieglitz 1 in the so-called chromophoric theory of 

 color. A. A. Noyes 2 , in a quantitative application of the theory of 

 indicators to volumetric analysis, has also fully explained the signifi- 

 cance of the chromophoric theory. According to this theory it is 

 necessary to consider an indicator solution as containing a mixture of 

 two tautomeric substances of different structural types. The ioni- 

 zation constants of the two forms, and the equilibrium relations between 

 them, are such that when the indicator exists as a slightly ionized acid 

 or base, one form is present in greatly predominating quantity. The 

 other form largely predominates when the indicator exists as a highly 

 ionized salt. 



Considering phenolphthalein, the ionization constant K,-, according to 

 the Ostwald conception, is expressed by the simple equilibrium equation 



HXP = K,-XPH (1) 



The chromophoric theory, as Stieglitz 3 has shown, requires two such 

 equations, (a) and (6) : 



LHXfc = QH (a) 



QXH = K'XQH (6) 



where k is the stability constant expressing the equilibrium relation 

 between the two tautomeric acids. The acid represented by LH is 

 assumed to be a pseudo- or an extremely weak acid; and that by QH 

 is the true acid. Its ionization constant K' is of such a magnitude that 

 the quinoid salt is formed in greatly predominating quantity in the 

 presence of alkalies, the stability constant k acting so as to maintain 

 the equilibrium relation between the two tautomeric acids. The 

 ionization constant for phenolphthalein is the product of the stability 

 constant k, and the ionization constant K' of the acid QH ; or, combining 

 a and 6 and incorporating k and K' into K> we have 



QXH = K,XLH (2) 



The above equations illustrate the fundamental differences between 

 the two color theories; and accepting the Stieglitz interpretation of K, 

 according to equation 2, the theory underlying the calculation of the 

 dissociation constant of methyl orange from radiometric measurements 

 will be discussed. 



Methyl orange is in reality a weak base. Noyes 4 has deduced a 

 general expression for the equilibrium relations of any pair of tauto- 

 meric bases and their ions. This deduction involves three fundamental 



Uourn. Amer. Chem. Soc., 25, 1112 (1903). 3 Ibid., 32, s.5S (1910). 



*Ibid., 32, 815 (1910). 4 Ibid., 32, 818 (1910). 



