34 II. METHODS OF INVESTIGATION 



The whole equation then becomes: 



^. = ^+ -^ln[H+] (24) 



F 



-'''"■■ E = E„+^. In Ka- 



F K^ 



i.e., a constant. At 30°C., and transformed to common logarithms, this is 

 equivalent to: 



Eh = E + 0.06 log [H+] (25) 



Consequently in this pH region the value of Eh becomes more negative with 

 increasing pH, by 0.06 v. per pH unit. 



In the case of systems other than that represented by equation 15, a 

 similar procedure to that followed above leads to equations of the same 

 general type, the effect of pVL on Eh. being determined by the form of the 

 last term. 



It is common practice to represent the relationship of Eh to pH graph- 

 ically, keeping So equal to Sr and plotting Eh as ordinate and pH as abscissa. 

 A series of such curves is shown on pp. 198, 199. In general, a change in 

 slope of the curve is found corresponding to each dissociation constant of 

 oxidant or reductant connected with the reduction process. The midpoint 

 of the transition gives the ;>K value of the dissociation. Between these 

 points, the curve approaches a straight line, the slope of which corresponds 

 to rates of change of Eh with pH of 0.06, 0.03, 0.00, etc. v. per pH unit, this 

 value depending on the value of n and the ionic change involved. 



If oxidant and reductant contain acidic or basic groups other than those 

 affected directly by the reduction process, these additional groups may 

 exhibit a difference in dissociation constant between the oxidized and 

 reduced forms. The energy change concerned in this must then be accounted 

 for, and the Eh/pH relationship assumes a more complicated form. In 

 hemoglobin such groups exist in the form of imidazole groups linking heme 

 to globin; cf. Chapter \T. The possible effect of side chain carboxylic acid 

 groups is discussed in Chapter V, Section 7.1.3. Two useful conclusions can 

 be drawn: (a) When other conditions are constant, demonstration of a 

 relationship between Eh and pH expressed by the equation: 



_ ^^ = 0.0601 (at 30°C.) 

 ApH 



indicates that the reductant must possess one more hydrogen ion (or one 

 less hydroxyl ion) than the oxidant for each electron necessary to convert 

 oxidant to reductant. (h) If, on increase of pK, x equivalents of hydrogen 

 ions per mole are dissociated from the reductant, the value of — (AE^/ApH) 

 will decrease by x(0.06)/n. If under the same conditions, dissociation of x 

 equivalents of hydrogen ion take place from the oxidant, the value of 

 — (AEh/ApH) will increa.'se l)y the same amount. The same argument holds 

 if dissociation of a hydrogen ion is replaced by the association of a hydroxyl 

 ion. The numerical value is of course for 30°C. 



