30 II. METHODS OF INVESTIGATION 



conducting path is arranged so that the pressure of electrons in it can be 

 exactly counterbalanced, as in the potentiometric method, the condition is 

 attained for measurement of the free energy change of a reversible process. 

 For the transfer of one faraday (F) of electrons from activity (€)h to 

 activity (e) we have: 



- AA = EF = RT\n^ (6) 



(e) 



A A is the change in free energy, and E is the electromotive force in volts 

 Substituting in equation 6 the value of (e)H from equation 5: 



E=^ \n J^ld^ (7) 



F (e) (H+) 



Putting: 



ylnKH = ^H (8) 



RT^ VP RT, , , ,„, 



If the conditions of the hydrogen electrode are now defined so that when 

 P = 1 and (H+) = 1, €h = 1, then from equation 5, Kh = 1 and from 

 equation 8, Eh = 0, and we have: 



RT 



£,= -'^1X1(6) (10) 



where Eh signifies that the E.M.F. is referred to the potential of the normal 

 hydrogen electrode as zero. 



Equation 10 may be regarded as the fundamental oxidation-reduction 

 potential equation since by substitution for e the value obtained from the 

 equilibrium equation of the particular system under consideration, the rela- 

 tionship of Eh to the factors determining the system can be found. 



In the present case, from equation 3: 



= (Ki^Y" (11) 



\ (Ox"+)/ 



whence from equation 10: 



Eh = E,-^\n^ (12) 



RT 



where Eo = — — Trln K, a constant for the system. When (Red) = (Ox"+), 

 nr 



Eh = Eo, giving the "characteristic potential" of the system. 



In the above derivation, we have expressed all the relationships in terms 



