Page 33 - Analytical Electrochemistry 2d Ed - Jospeh Wang

18 FUNDAMENTAL CONCEPTS

an idealized curve). Values of a close to 0.5 are common for metallic electrodes with
a simple electron transfer process. The barrier for reduction at E is thus given by

z
z
DG ˆ DG c;0 ‡ anFE 1-36†
c
Similarly, examination of the ®gure reveals also that the new barrier for oxidation,
z
z
DG a is lower than DG :
a;0
DG ˆ DG z a;0 1 a†nFE 1-37†
z

a
z
By substituting the expressions for DG (equations 1-36 and 1-37) in equation
(1-34), we obtain for reduction
z
k ˆ A exp‰ DG =RTŠ exp‰ anFE=RTŠ 1-38†
f c;0
and for oxidation

z
k ˆ A exp‰ DG =RTŠ exp‰ 1 a†nFE=RTŠ 1-39†
b
a;0
The ®rst two factors in equations (1-38) and (1-39) are independent of the potential,
and thus these equations can be rewritten as

k ˆ k exp‰ anFE=RTŠ 1-40†
f
f

k ˆ k exp‰ 1 a†nFE=RTŠ 1-41†
b b
When the electrode is at equilibrium with the solution, and when the surface
concentrations of O and R are the same, E ˆ E , and k and k are equal:

f b

k exp‰ anFE=RTŠˆ k exp‰ 1 a†nFE=RTŠˆ k 1-42†
f b
and correspond to the standard rate constant k . By substituting for k and k (using

f
b
equation 1-42) in equations (1-40) and (1-41), one obtains equations (1-18) and
(1-19) (which describe the effect of the operating potential upon the rate constants).
1-3 THE ELECTRICAL DOUBLE LAYER
The electrical double layer is the array of charged particles and/or oriented dipoles
that exists at every material interface. In electrochemistry, such a layer re¯ects the
ionic zones formed in the solution to compensate for the excess of charge on the
electrode (q ). A positively charged electrode thus attracts a layer of negative ions
e
(and vice versa). Since the interface must be neutral, q ‡ q ˆ 0(where q is the
s
s
e
charge of the ions in the nearby solution). Accordingly, such a counterlayer is made