42 ir. METHODS OF INVESTIGATION 



Then from equation 44, y # 0.5 and [RB^] = 2 [OB2]; also from equation 

 31, [0\ = [OBn}; but since S^ = S^: 



[0] + [OBo] - [/?] - [RB,] = 



I.e., [/?] = 0. From equation 43, .r = 00 , and from equation 48, as j: — )• <» , 

 Z = 1.5. Then: 



[B] = ylK~o =^ Sb - 1.5S 



i.e., Sb =f >Ko + 1.5 5. From equations 34, 35 and 42: 



S = [0] + [OBo] + [/?] + [RBo] = 4 0J5o = 2 /?^2 



Hence at this point, three quarters of the metalloporphyrin is combined 

 with base ([0^2] + [BB:] = \ S) while practically no reduced metallopor- 

 phyrin remains uncombined ([/?] — > 0). As in cases (1) and (2), if g = r, but 

 does not equal 2, the point where [7^]'' = Ko satisfies the above conditions, 

 except that Z = 1.5 r/2, and: 



Sb = r^Ko-^^—S 



2 



It will be seen that at these three points relations exist expressing the 

 dissociation constants Ko and K/j in terms of measurable quantities, i.e., 

 Sb> the total base added, and S, the total metalloporphyrin. On making 

 measurements of the oxidation-reduction potential of the system under the 

 conditions specified, that is with constant pH, 50% reduction, and at 30°C., 

 the base concentration being the only variable, the values of £0 (at zero base 

 concentration) and Ei (the limiting potential at high base concentration, if 

 the system is sucli that equal numbers of molecules of base combine with 

 oxidant and reductant) and a series of values of Eh corresponding to various 

 values of Sb may be found. 



It has to be determined how best to plot the data so obtained, in order 

 to locate the three unique points. Usually, such results are plotted with 

 Eh as ordinate and Sb as abscissa. However, Clark shows that this does 

 not lead to the best results. 



By differentiation of equation 49 with respect to log {Sb — S), substi- 

 tuting in the result the condition at the second unique point that {Sb — S)^^ 

 = KoK/f, and making the usual approximations on the assumption that 

 Ko>K;?, it may be shown that, at this second point: 



^^'^ = 0.0601 r (50) 



d log (Sb - S) 



Hence in the present case, where r = 2 



dEh 



- = 0.12 



d log {Sb - S) 



