40 II. METHODS OF INVESTIGATION 



A further assumption, in conformity with experience with base metal- 

 loporphyrins, is made, namely that the affinity of the reduced form for base 

 is much higher than that of the oxidized, i.e., Kq > K^. 



Inspection of equation 49 suggests that there are three values of [B] 

 {i.e. of Sb — ZS) in terms of K© and K^ which will give unique values of 

 Ea - E^. 



(/) When [/?p = Kft : i.e., {Sb - ZS)^ = Kr : 



En- E', = 0.06 log ^ ^^^^^ 



by substitution in equation 49. Since it has been assumed that K/? < Ko, 

 (K/e)2 is negligible in relation to KqKr. Then Eh -E'o = 0.06 log ^2 =0.0181 v. 

 From equation 43, it follows that r = 2, and [0] = 2 [7?]; and from equations 

 32 and 3.3, [/?] = [RBo] == 0.5 Sr. But, since So = Sr under the conditions 

 chosen, we have from equation 42, Sr = 0.5 »S, i.e., [RB-^l = 0.5 Sr = 0.25 S. 

 Further, from equations 34 and 35, [0] + [OB2] -[/?] -[RB2] = 0, from which 

 by substitution for [0] and [/^/^a], [Oi^2] 4= 0. Hence one quarter of the metal- 

 loporphyrin is combined with base, and the base metalloporphyrin is prac- 

 tically entirely in the reduced condition. Proceeding, since [OB-i] = 0, from 

 equation 44, y = 0. Then by substitution for .r and ?/ in equation 48, Z = 0.5. 



Also: 



[BY - Kr = {Sb - 0.5 Sy 

 and: 



Sb = VKr + 0.5 S* 



li q = r, but has a value other than 2, the point where [BY = Kr satisfies 

 the above conditions, except that Z = r/4 and: 



Sb = r^lKR +^5 



{3) When [B]-* = KoKr, we obtain by substitution in equation 49: 



I.e., 



Eh = K + 0.0601 log^i^ + 0.0601 log ^^^+ ^^gS g- 

 Eh = E. + 0.0601 log 



Kb + VKoKb 



Ko + VKoKr 

 from equation 39. Adding these two equations, and dividing by 2 : 



* Note typographical error in Clark's paper (It5S, p. 552) where Sg is equated to 

 Kb— 0.5 S. The correct result, as given above, is used throughout the rest of Clark's 

 discussion. Note also in Clark's equation 19 on the same page, a figure 2 has been 

 omittefl from the denominator. 



