OXIDATION-REDUCTION POTENTIALS 



in transporting an electron from the solution (at concentration [ej) to the electrode 

 at concentration [e^,]. That is : — 



Electrical work = EF 



r^-^i 1 



" Osmotic " work = KT / r-r d [e] = KT In [eJ + HT In^—n 



7 e, fe] "^ ' ^ "■' [eJ 



(3) Therefore EF - RT hi [eJ + RT In -^ 



where, R = gas constant ; T = absolute temperature ; In = natm'al logarithms. 

 Since the concentration of electrons in the electrode ([e„]) is a constant, equation 

 (3) may be rewritten as : — 



T-. T RT , 1 



(4) E = k,+ j^lnj^j 



where k^ is a constant. 

 From equation (2) 



[Fe®®] 



and substituting this value in equation (4), we obtain ; — 



RT [Fe®®®] 



(6) E = ka + ^ In -^e©J 



where kg is a constant. 



It is not possible to measure a single potential difference at an electrode as this 

 constitutes only a half-cell ; but if the circuit is completed by including a standard 

 half-cell the electromotive force of the completed cell may readily be measured. 

 The second half-cell to which electrode potentials are referred is the normal hydrogen 

 electrode, which is taken as the standard of reference. Electrode potentials referred 

 to this standard are measured in volts and designated E^. 



E^ = E — potential of normal hydrogen electrode (kg), and substituting the value 

 for E from equation (6). 



RT [Fe®®®] 



(7) E^ = kg + ^ In ^-pe®®] ~ ^^ 



Let kg — kg = Eq = constant for system. 



(8) E^ = Eo + -^ In -p^lej 



In order to make this equation more general in application, the ferrous-ferric ion 

 system may be replaced by the general reversible oxidation-reduction system : — 



Reduced form ^ oxidised form -fn electrons. 



(9) Red. ^ Ox. + ne. 



and applying equation (8) we obtain the important general electrode equation (Peters, 

 1898). 



