54 Conductivities and Viscosities in Pure and in Mixed Solvents. 



equations. Expressing the equilibrium relation k, between the quinoid 

 and azo-base, it being understood that the symbols represent gram- 

 molecular or gram-ionic concentrations, we have 



AzOH 



The quinoid base and the azo-base are also in equilibrium with their 



ions, according to 4 and 5 : 



QXOH 

 ~QOlT 



X OH _ 



KAZOH 



AzOH 



Multiplying 3 by 4 and adding 5 to the product, we have 



Q X O"H + Az X 0~H 



4 QTT 



. 



= AC X -tt-QOH ' J^AzOH 



and substituting in the denominator for AzOH its value - j* 



it follows that 



Q X OH + Az X OH k X K QOH + K AzOH , 



AzOH + QOH 1 + k 



Letting the above equal K,-, we have 



OH(A + z + Q) _ 

 AzOH + QOH 



Noyes has called attention to the fact that for a satisfactory two-color 

 indicator such as methyl orange, the sum of the two tautomeric bases 



(AzOH + QOH) must be substantially equal to AzOH; and that the 



+ + + 



sum of the two ions (Q + Az) must be substantially identical with Q. 



It therefore follows that 



OHXQ _ . 



AzOH ~ 



where K t expresses the equilibrium relations of the two tautomeric bases 

 and their ions, and is substantially the equation derived by Stieglitz. 1 



_|_ 



Combining equation 9 with that of the ion product of water, H X OH 

 = K w , we get 



H X AzOH K w v 



Q + T7~ = -^(hydrolysis) 



which is in reality the familiar equation of Walker 2 ( - ,, kj. 



Mourn. Amer. Chem. Soc., 25, 1112 (1903). 2 Zeit. phys. Chem., 4, 324 (1889). 



