10 OXIDATION-REDUCTION POTENTIALS 



in which may be substituted the value of [Ox.]/[R0] derived from the mass action 

 equation (23). 



(25) E, = E|] + ^ In ^^ 



That is to say, the electrode potential may be regarded as being established by the 

 equilibrium between hydrogen ions and hydrogen atoms. The hydrogen concen- 

 tration ([H]) is a function of the partial pressure of hydrogen gas (P), and, in fact, 



(26) [H] = Ki VP 

 so that the potential equation (25) becomes : — 



(27) E, = E'i' + ^ In tS 



To obtain the value of the constant, E'^', we may consider the normal hydrogen 

 electrode, which is a special type of oxidation-reduction cell, in which E^ = ; 

 [H®] = 1 ; and P = 1, and substituting these values in the equation (27) we find 

 E"' = 0, so that equation (27) becomes :— 



(28) E, = ^^ In m 



or, transferring from Naperian to common Briggsian logarithms : — 



RT [H®1 



(29) Eh = 2-3026 ^ log "^.J 



V / ix F & ^p 



Since pH = log rTj®! and rH = log p 



(30) E, = 2-3026 1^ (rH - 2pH) 



For simplicity, let the temperature be 30°C., then : — 



(31) Eh = 0-03 (rH - 2pH) 



This equation gives the simple relation between E^, rH and pH in the reversible 

 system considered ; from it rH may be derived when E^ and pH are known, and E^ 

 may be obtained when rH and pH are given. Results quoted in terms of rH may 

 thus be readily converted to terms of Ej,. 



It follows from the equation also that the electrode potential, in a reversible 

 oxidation-reduction system at constant pH, is a function of the partial pressure of 

 hydrogen in equilibrium with the system. This gives us a fresh aspect on the 

 mechanism of establishment of electrode potentials ; hydrogen may be regarded as 

 being built up at the electrode mitil a partial pressure is reached which is in equili- 

 brium with the system, and the system is neither reduced nor oxidised. 



The hydrogen electrode used for pH measurements is a special form of oxidation- 

 reduction electrode in which the hydrogen pressure is kept constant (P = 1 atmo- 

 sphere) by bubbling hydrogen at one atmosphere pressure through the system, the 

 value of rH is therefore zero and the only variations in potential are due to alterations 

 in hydrogen ion concentration, i.e., equation (31) becomes (at 30°C.) : — 



(32) K= - 0-06 pH 



