38 II. METHODS OF INVESTIGATION 



It is important to recognize from this result that the change of potential 

 E2 — E'o accompanying the addition of a coordinating base to a fixed mixture 

 of reduced and oxidized metalloporphyrin is a measure of the ratio of the 

 two dissociation constants. The course of the curve between E'^ and Et 

 is determined by the absolute values of Kq and K^ and the concentration 

 of total metalloporphyrin S (see equation 36). Since at the conditions of 

 the limiting potential £2 full combination with base is approximated, the 

 electrode potential is given by the equation: 



Eh = E^-h 0.0601 log p^ (40) 



The last term of equation 36 is expressed in terms of the concentration 

 of free base [B]. In those cases where the concentration of total base (Sb) 

 is high in relation to the concentration of total metalloporphyrin, [B] is 

 negligibly different from Sb', at low concentrations of total base, however, 

 the difference may be great. • It is therefore necessary to transform equa- 

 tion 36 in terms of Sb instead of [B], since Sb can be measured. 



To do this, Clark uses the following definitions, in addition to the previ- 

 ous assumption that p = m = 11 = I: 



Sb = [B] + q[OB,] + r[RBr] (41) 



S = So-h Sr (42) 



(see equations 34 and 35) 



(from equation 28) : 



= f^j = antilog^^ ~ ^" (43) 



[R] 0.0601 



- [^^^'^ = ar^tilog?^-^^ (44) 



[RBr] 0.0601 



a = ^ (45) 



The problem is now to substitute for [B] in equation 36 so that the resulting 

 equation is in terms of measurable quantities. From equation 41: 



[B] = Sb- q[OB,] - r[RB,] 



= Sb — (qy + r) [RBr] from equation 44 

 [RBr] = {Sr - [R]) from equation 35 



= S — So — [/?] from equation 42 



= S — aS — - — - from equations 45 and 43 



X 



= S - aS - (^ - l^^\ from equation 34 

 \x X / 



