Chemistry Reference
In-Depth Information
¨
(
)
()
+
(
)
HO
-
O
-
OH
∑
[4.9]
2
ads
ads
ads
(
)
(
)
(
)
-
v
2
=
k
q
1
-
q
1
-
q
k
q
q
1
-
q
[4.16]
2
-
-
•
-
2
-
•
-
O
OH
O
OH
HO
HO
2
2
¨
(
)
()
+
OH
∑
+
OH
-
O
-
H O
[4.10]
2
ads
ads
(
)
-
(
)
v
=
k
q
c
1
-
q
k
q
1
-
q
[4.17]
3
3
•
-
-
-
3
-
•
OH
OH
O
O
OH
()
+
()
¨
(
)
+
OO
-
-
Oe
-
-
[4.11]
2
ads
ads
(
)
-
2
()
()
(
)
v
=
k
E
q
2
1
-
q
k
E
q
1
-
q
[4.18]
4
4
-
-
4
-
-
-
O
O
O
O
2
2
¨
(
)
O
-
O
+
e
-
[4.12]
2
2
ads
(
)
()
()
v
=
k
E
q
-
k
c
1
-
q
[4.19]
5
5
-
-
5
-
O
2
O
O
2
2
The factors (1 -q) express that the reaction involved can take place only on
the fraction of the electrode surface that is not covered.
In order to determine whether mechanism 1 is compatible with the exper-
imental evidence and to indentify which of the five sub-stages is the rate-
determining one, Equations 4.15-4.19 are of no use in practice, because the
degrees of coverage are not experimentally accessible. If one of the sub-
stages is assumed to be rate-determining step, it is then possible to trans-
form the rate equation of the stage involved into the form:
a
F
a
F
a
k
r
E
r
E
[4.20]
vc
@
ke
-
ke
c
R
T
R
T
aA
¢
kB
¢
where
c
is the concentration of a bulk component (hydrogen peroxide,
hydroxide ion or oxygen), k
a
and k
k
are reaction rate constants with the ref-
erence potential, and
E
is the working electrode potential versus the same
reference potential. The value of
r
is either zero or one. If no chemical reac-
tion stages occur in the sequence of sub-reactions,
r
= 1 always applies,
and the potential dependence is represented by classical Butler-Volmer
exponents. If chemical stages are present, the anodic or cathodic term
of Equation 4.20 can be potential-independent (
r
= 0). The transformation
is possible by assuming that the four sub-stages which are not rate-
determining are in virtual balance, and their net reaction rate can be set
equal to zero. This is a realistic assumption: being not rate-determining sup-
poses sufficiently high k,
c
or q values, or in other words, for electrochemi-
cal reactions, a relatively high
i
0
and hence a relatively small overpotential
or a quasi-equilibrium situation. In what follows, the sign of approximate
equality (Equation 4.20) is replaced by the equals sign.
Hence, the followed procedure involves subsequently considering every
sub-stage of a postulated mechanism as the rate-determining stage and
