74 Conductivities and Viscosities in Pure and in Mixed Solvents. 



If a large excess of alkali 1 is added to the indicator solution Ci = 0, and 

 equation 2 reduces to 



ln(I/Io)"=-Kc =- KT (4) 



where T equals the total concentration of the indicator in solution. If 

 the percentage transmissions are determined for the same depth of 

 solution and for the same wave-length of light, and if the total concen- 

 tration of the indicator is the same in all solutions, then the values of 

 the constants K and K' given by equations 3 and 4 can be substituted 

 in equation 2, whence 



TXln (I/Io) =ln (I/I )"Xc +ln (I/I )'X * (5) 



Since the total concentration of the indicator T is always equal to the 

 sum of the two components, T = c +c\, equation 5 reduces to 



In (I/Io)' In (I/Ip) (6) 



In (I/Io) -In (I/I )" 



The ratio c/Ci = (In)/HIn) can be determined from equation 6. 

 (I/Io) is the percentage transmission for some given depth of the 

 incompletely transformed solution under investigation, for some wave- 

 length of light; (I/Io)' the percentage transmission of the indicator 

 solution completely transformed into the yellow component for the 

 same wave-length; and (I/Io)" the percentage transmission for the 

 same depth of indicator solution completely transformed into the red 

 component, for the same wave-length of light. The total concentra- 

 tion of the indicator in these three solutions must, of course, be the 

 same, but the total concentration need not be known. 



Returning now to equation 1, the method of obtaining all the data 

 necessary for calculating the ionization constant is known, except that 

 for determining the concentration of the hydrogen ion. This was fixed 

 by solutions of disodium phosphate containing varying amounts of 

 hydrochloric acid. The addition of hydrochloric acid converts the 

 hydrophosphate ion almost quantitatively into the dihydrophosphate 

 ion. The hydrogen ion concentration is given in such a solution by 2 



1.95 X 10- 7 (H 2 P0 4 ) 



(HP0 4 ) 



If we represent by a the concentration of the added hydrochloric acid, 

 and by 6 the concentration of the disodium phosphate, then equation 7 

 becomes 



1.95 X IP" 7 X a tti 



/7 



(o a) ct 2 



where ai and a 2 represent respectively the dissociations of the mono- 

 and disodium phosphates present at equilibrium. 



'By "a large excess" is meant sufficient alkali to convert the indicator entirely into its red 

 component. 



2 The value of the constant was taken from the work of Abbott and Bray: Journ. Amer. Chem. 

 Soc., 31, 760 (1909). 



