Page 51 - Lindens Handbook of Batteries

2.8 PRINCIPLES OF OPERATION

TABLE 2.3 Values of Transfer Coefficients α at 25°C for Selected Systems 4
Electrode reaction Metal Electrode reaction α
+
-3
H + e  ½H Pt (smooth) 1.0 mol dm HCl 2.0
2
-3
+
H + e  ½H Ni 0.12 mol dm NaOH 0.58
2
+
H + e  ½H Hg 10.0 mol dm HCl 0.61
-3
2
-3
+
O + 4H + 4e  2H O Pt 0.1 mol dm H SO 4 0.49
2
2
2
-3
O + 2H O + 4e  4OH - Pt 0.1 mol dm NaOH 1.0
2
2
2+
-3
-3
Cd + 2e  Cd Cd/Hg 10 mol dm Cd(NO ) in
3 2
-3
1 mol dm KNO 3 5.0
2+
Cu + 2e  Cu Cu 1 mol dm CuSO 0.5
-3
4
exist, but because the system is at equilibrium, the rates are equal and thus there is no net current
flow; hence
i = f i = b i (2.15)
o
where i is the exchange current. From Eqs. (2.10) to (2.13), together with Eq. (2.15), the following
o
relationship is established:
( - α
)
nFE 
o
o
e
Ck exp   -α RT e  = Ck exp  1 RT nFE  (2.16)
 

Rb
Of
where E , is the equilibrium potential. Rearranging,
e
o
E = RT ln   k  + RT ln   C   (2.17)
O
f
o 
e
nF  k  nF  C 
b
R
o
From this equation we can establish the definition of formal standard potential E , where concentra-
C
tions are used rather than activities,
o
f
o
E = RT ln    k  (2.18)
0 
C
k 
nF
b
For convenience, the formal standard potential is often taken as the reference point of the poten-
tial scale in reversible systems. Combining Eqs. (2.17) and (2.18), we can show consistency with
the Nernst equation,
O
E = e E + C o RT ln    C   (2.19)
C 
nF
R
except that this expression is written in terms of concentrations rather than activities. From Eqs. (2.10)
and (2.12), at equilibrium conditions,
nFE 
i = o i = f nFAC k exp   -α RT e  (2.20)
o
Of