Chemistry Reference
In-Depth Information
¨
(
)
HO
-
HO
-
k
k
[4.8]
2
2
1
-
1
¨
(
)
()
+
(
)
HO
-
O
-
OH
∑
k
k
[4.9]
2
2
-
2
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¨
(
)
()
+
OH
∑
+
OH
-
O
-
H O
k
k
[4.10]
2
3
-
3
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¨
()
+
(
)
O
-
O O
-
-
+
H
-
k
k
[4.13]
2
2
4
-
4
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¨
(
)
O
-
O
+
e
-
k
k
[4.12]
2
2
5
-
5
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Mechanism 2 is obtained from the same stages as mechanism 1, except for
stage 4 (Equation 4.13). Hence, the reaction rate constants of stage 4 have
been given a different symbol. In the global reaction:
¨
3
HO
-
2
O
+
H O
+
OH
-
+
2
e
-
[4.14]
2
2
2
and sub-stages in Equations 4.13 and 4.12 occur twice.
Sections 4.6 and 4.7 of this chapter provide calculations as to which
current-potential relations are theoretically expected for both mechanisms.
Section 4.8 then attempts to unify these relations into one single relation
and to verify the validity of this current-potential relation against the
experimentally obtained data.
4.6
Theoretical
I
-
E
relationship for mechanism 1
In the first instance, equations need to be formulated for the reaction rate
of the different sub-stages in the postulated mechanism. To keep the equa-
tions and calculations as simple and as clear as possible, a number of abbre-
viated notations will be used. For example, a rate constant k
n
(
E
) means that
it is potential dependent. Hence, the exponential potential-dependent
factor of the rate equation is integrated here. The rate constants of the reac-
tions in forward (from left to right) sense - i.e. in anodic sense for the elec-
trochemical reactions - are represented by k
1
,k
2
, up to k
n
.The constants for
the reactions in the opposite sense are k
-1
,k
-2
, up to k
-
n
.For the compo-
nents, which do not occur in the bulk of the solution, the reaction rate
cannot be expressed as a function of a concentration. Here, the degree of
coverage of the electrode surface (symbol q) is used. The reaction rates of
the five sub-stages (Equations 4.15-4.19) of mechanism 1 can be written as
follows (for easy reference, the reactions involved are noted once again):
¨
(
)
HO
-
HO
-
[4.8]
2
2
(
)
-
v
=
k
c
1
-
q
k
q
[4.15]
1
1
-
-
-
1
-
HO
HO
HO
2
2
2
