ELECTROCHEMICAL METHODS Fundamentals and Applications - Allen.J.Bard

32 * Chapter 1. Introduction and Overview of Electrode Processes
Cathodic
(-)• H-
Anodic
Figure 1.4.2 (a) Current-potential curve for a nernstian reaction involving two soluble species
with only oxidant present initially, (b) log[(// - /)//] vs. E for this system.
where Ещ is independent of the substrate concentration and is therefore characteristic of
the O/R system. Thus,
(1.4.16)
When a system conforms to this equation, a plot of E vs. log[(// — /)//] is a straight line
with a slope of 23RT/nF (or 59.1/л mV at 25°C). Alternatively (Figure 1.4.2b), log[(// -
i)li\ vs. E is linear with a slope of nF/23RT (or л/59.1 mV" 1
at 25°C) and has an ^-intercept
of Ещ. When m o
and m R
have similar values, Ещ ~ E°'.
(b) Both О and R Initially Present
When both members of the redox couple exist in the bulk, we must distinguish between a
cathodic limiting current, // c
, when CQ(X = 0) ~ 0, and an anodic limiting current, z /a
,
when C R
(x = 0) « 0. We still have CQ(X = 0) given by (1.4.11), but with // now specified
as // . The limiting anodic current naturally reflects the maximum rate at which R can be
c
brought to the electrode surface for conversion to O. It is obtained from (1.4.7):
(1.4.17)
(The negative sign arises because of our convention that cathodic currents are taken as
positive and anodic ones as negative.) Thus CR(X = 0) is given by
The i-E curve is then
0
C R
(x = 0) =
nFAm R
C R
(x = 0)_
- 1 — l
C R
> RT,
~n~F ln Щ
+ fjln( 1
- W
(1.4.18)
(1.4.19)
(1.4.20)
A plot of this equation is shown in Figure 1.4.3. When / = 0, E = E eq
and the system is at
equilibrium. Surface concentrations are then equal to the bulk values. When current flows,