56 Conductivities and Viscosities in Pure and in Mixed Solvents. 



In a pure aqueous solution of methyl orange, or one containing an 

 excess of alkali, c = 0, therefore, equation 15 reduces to: 



ln(I/I )' = - K'c' = -KT (17) 



If to a solution of methyl orange sufficient sulphuric acid is added to 

 convert all of the azo-base into the quinoid salt and completely suppress 

 hydrolysis, c' = 0, and equation 15 becomes 



In (I/I )" = - Kc = - KT/2 (18) 



From equations 16, 17 and 18, K and K' can be eliminated, and 

 solving for c we obtain : 



T[ln (I/Ip) - In (I/Ip)'] 

 ' 2[ln (I/I )" - In (I/Io)'] 



In the above equation (I /To)' is the percentage transmission for the 

 solution of pure methyl orange for some given wave-length of light; 

 (I /Io)", the percentage transmission of the solution containing an excess 

 of acid for the same wave-length, and (I /To) the percentage transmission 

 for the same wave-length of the solution whose quinoid salt concen- 

 tration c is to be determined. 



Returning now to the fundamental hydrolysis equation for methyl 

 orange previously derived : 



H X AzOH K w 



Q + 



we can readily insert the proper values, knowing the total concentration 

 of methyl orange T, and having determined by radiometric means the 



quinoid salt concentration c. Q is equal to 2c. AzOH = c' = T 2c. 



+ 



H is given by 2(T' - c), where T' represents the total quantity of acid 



added. It is assumed that the dissociation of these extremely dilute 

 solutions is practically complete. The sulphonic acid group can have 

 but little effect on the hydrogen ion concentration, since benzenesul- 

 phonic acid 1 is as strong as sulphuric acid, being dissociated at 25 to the 

 extent of 90 per cent for a dilution v =32. As Stieglitz 2 has pointed 

 out, the whole behavior of methyl orange is that of a very weak base, 

 and the elimination of the sodium sulphonate group from it leaves 

 dimethylaniline azobenzene, which shows all the characteristics of 

 methyl orange as an indicator. 



It will be noticed from equation 10 that it is necessary to know the 

 ionization constant for water before the constant for the indicator can 

 be calculated from its hydrolysis constant. The generally accepted 

 value of K i( , at 25 is 1.2X10" 14 . It was desired to know the value of 

 the constant at 20, since, unless otherwise stated, it was at this tem- 



iCarnegie lust. Wash. Pub. N. 170, 128 (1912). 

 2 Journ. Amer. Chem. Soc., 25, 1117 (1903). 



