36 II. METHODS OF INVESTIGATION 



7.2.4. Combination of Oxidant and Reductant with Other 

 Substances. The simple metalloporphyrins, as will be seen later, 

 possess the capacity of combining with a variety of other substances. 

 When the linkage occurs by coordination with the metal atom, such' 

 combination, as in the hemochromes, is usually characterized by a 

 measurable, often high, dissociation constant, so that the energj'^ 

 change contributes to the oxidation-reduction potential. Clark and 

 collaborators H53) were the first to develop equations describing 

 these systems, and have carried out detailed studies {If,5l,536,27Jf9, 

 2872) in an endeavor to establish the nature of the equilibria met 

 with in practice. The results of their work are discussed in Chapter V, 

 Sections 4, 6, and 7. The development of the equations is somewhat 

 involved, and several simplifying assumptions are made. Since 

 Clark's papers are of fundamental importance, and present great 

 difficulty to the nonmathematical student on account of the highly 

 condensed form of the mathematical treatment, an attempt will be 

 made to supply the details of the algebra. The following derivation, 

 and also Chapter V, should be read in conjunction with the papers 

 of Clark and collaborators. 



Oxidation and reduction of a metalloporphyrin are assumed to follow 

 equation 26. The typography will henceforth be simplified by abbreviating 

 Red to R and Ox to 0. The pH is kept constant, so that the electrode equa- 

 tion in terms of concentrations may be written: 



Eh = E'^ ^-' In I^ - (28) 



» nF [R^y 



The addition of a nitrogenous base, B, results in its independent coordina- 

 tion with both oxidant and reductant. The equations are: 



0„ + qB^ 0„B, (29) 



R„, + rB^ R^B, (30) 



in which no change of aggregation of either oxidant or reductant is assumed 

 to occur on combination with B. From equation ^O we have: 



[On] W 



[o,A] 



And from equation 30 it follows that: 



[/U [BY 

 [R„M 



= Ko (31) 



= K« (32) 



