EFFECT OF pH 33 



From the second part of equation 15, we have: 



[ Ox+] [QH-] ^^ ^ [0^+] K;r ^^gx 



[OxOll] "" [OxOH][H+] 



whence : 



[OxOW] = f^^ (17) 



Let So be the concentration of total oxidant, and Sr that of total reductant; 

 then: 



Sr = [Red] (18) 



and: 



So = [Ox+] + [Oa;OH] (19) 



Substituting in equation 19 the value of [OjOH] from equation 17 and 

 solving for [0.r+], we have: 





(20) 



Hence by substitution in equation 14: 



£, = £o - — ln^ + ^ In , j"^^^^ (21) 



F So F [H+]Ko + K, 



If the ;)H is kept constant, the last term of equation 21 is constant, 

 whence : 



E, = K - ^ln|-^ (22) 



t bo 



This is the equation commonly employed in oxidation-reduction potential 

 studies at constant pH. It may be treated graphically in the same manner 

 as equation 14. 



To visualize the effect of change of pH, make So equal to Sr in equa- 

 tion 21. Then: 



E, = £o + — In , j^^'^^o (23) 



F [H+]Ko + K„. 



In general, Ko will be much larger than Kw- At low pH values, when [H +] Kq 

 is also much greater than Kir, the last term of equation 23 becomes zero, 

 and the potential is invariant. As the hydrogen ion concentration is reduced, 

 a point is reached where [H"'"] Ko = Kjf. In the neighborhood of this point, 

 the second term acquires a finite negative value, and Eh becomes more 

 negative with increasing pH. When the value of [H+] is such that [H+] Ko 

 is much smaller than Kr', the second term of equation 23 approximates: 



RT^jm]Ko 



F K„ 



