14: OXIDATION-REDUCTION POTENTIALS 



At the same time one mol of Fe®® will disappear from I and appear in II, and 

 the work done is : — 



The total " osmotic " work done will be the sum of these two, and this total will 

 be equivalent to the electrical work done in the passage of one faraday of electrons (F) 

 across the cell with electromotive force E. Therefore : — 



fTTe,®®®! TFe ®®1 



(40) EF = RT In y^\ + ET In [|^,^j 



This may be rearranged as : — 



(41) E = RT [Feo®®] RT [Fe^®®®] 



F ^ [Feo®®®] F ^ [Fei®®] 

 TFe ®®®1 



(37) now [Ji-^-gj] = k 



so that equation (41) becomes : — 



"RT r"Pp ®©©i 



(42) E = k. + f ,n EIg-,^1 



If the general reaction be considered in place of the iron system : — 



Reduced form ^ Oxidised form + n electrons. 



(43) Ked. ^ Ox. + ne 



and the potential is referred to the normal hydrogen electrode, used as a standard 

 of reference, we obtain : — 



^^^^ ^"^ = ^0 + nF ^^ [R^ 



which is the general electrode equation (10) derived previously from totally different 

 considerations. That the same result is obtained when working with different 

 assumptions implies a fundamental unity in the underlying principles involved. 



Michaelis (1932) and Elema (1933) have developed mathematically the relevant 

 equations applying to oxidation-reduction reactions which occur in two consecutive 

 stages. The relations are complicated owing to the number of factors involved and 

 the different equilibrium constants of the various reactants. The complex relation- 

 ships are of some biological interest since certain biological pigments have been 

 found to undergo reversible " two-step " oxidation-reduction within certain ranges 

 of pH values. 



FREE ENERGY CHANGES AND STANDARD OXIDATION POTENTIALS 



The total amount of energy suppUed to a thermodynamic system is not all 

 recoverable in the form of work. The change in free or available energy (aF) differs 

 from the change in total energy (aH) by a factor involving the absolute temperature 

 (T) and the change in entropy of the system (aS) : — 



(45) aF = AH— T. aS 



The familiar terms exothermic and endothermic applied to chemical reactions 

 refer to reactions which give out or take up heat. Exergonic and endergonic were 



