Radiometric Measurements of Constants of Indicators, 55 



Having determined the hydrolysis constant according to equation 10, 

 the ionization constant K; of methyl orange as a base can readily be 



obtained. The procedure, then, is to determine by radiometric meas- 



+ + 

 urements, the concentrations of Q, H, and AzOH in solutions of methyl 



orange containing varying amounts of these constituents. A method 



+ 



was developed whereby the concentration of the quinoid ions Q in 

 equation 10 could be determined from the light transmitted by the 

 indicator solutions. The percentage transmissions for these solutions 

 were given by the radiomicrometer deflections. The method will be 

 made clear by the following theoretical considerations applied to 

 methyl orange. 



If we consider light to pass through an absorbing solution of depth /, 

 the solvent itself having no absorption, the rate of change of intensity 

 dl is given by 



dl = -kldl (11) 



The constant k depends only on the wave-length of light and the 

 nature of the absorbing medium. If I denotes the intensity of the 

 incident light, then, when I = 0, IQ = I = constant. Integrating, the 

 intensity of the transmitted light I, given by an absorbing solution of 

 depth I, and concentration c, is 



I = I e~ Wc (12) 



If the solution has a second absorbing component, the light trans- 

 mitted by it will be 



Ii = Io e- k ' 1 '*' (13) 



Since the total transmission is the product of the separate trans- 

 missions, we have for the actual percentage transmission of a solution 

 containing two absorbing components such as methyl orange 



I/I = e~ klc ~ k ' l ' c> ] or In (I/I ) = - klc - k'l'c' (14) 



Since the depth of solution was maintained constant (20 mm.), the 

 above equation becomes 



In (I/I ) = - Kc - K'c' (15) 



Applying this equation to methyl orange, let c represent the con- 

 centration of the quinoid salt or Q in equation 10, and c' that of the 

 azo-base. If T is the total quantity of methyl orange in solution, then 

 c' = (T c) ; or, since a dibasic acid was used, viz, sulphuric acid, 

 c' = (T 2c) . When a pure solution of methyl orange is slightly 

 acidified with sulphuric acid, and not all of the azo-base converted into 

 the quinoid salt, both c and c' are present. The light transmitted by 

 such a solution will be: 



In (I/To) = - Kc - K'(T - 2c) (16) 



