Chemistry Reference
In-Depth Information
4.9
Combination of rate equations of
both mechanisms
In consideration of a sensor based on the prewave, the highest ascending
part of this wave is not important from an analytical point of view. In a pos-
sible analytical application, the pseudo-limiting-current needs to be applied,
because the current is higher and because it is less sensitive to variations in
the potential of the reference electrode.
Before attempting to combine the two postulated mechanisms with each
other, it is useful to examine them in the light of the experimental data pre-
sented in Fig. 4.9. Here, the inclination of the log
I
vs. pH relation decreases
with an increasing hydrogen peroxide concentration, and this from 0.54 to
0.30. Stages 4 and 5 as RDS of mechanisms 1 and 2 in the pseudo-limiting-
current range predict for OH
-
reaction orders of 1 and -0.5, respectively.
Qualitatively, this means that with an increasing hydrogen peroxide con-
centration, the relative fraction of mechanism 2 in the total current
increases. Physically, this reasoning can be explained by means of the fourth
stage in the reaction sequence of both postulated mechanisms. In mecha-
nism 1, the adsorbed O
-
particles react with each other (Equation 4.11)
while in mechanism 2 these particles react with fresh hydrogen peroxide
(Equation 4.13). Therefore it is logical that, with an increasing hydrogen
peroxide concentration, more O
-
particles will react with hydrogen pero-
xide, resulting in an increase of the fraction of mechanism 2 in the total
current.
In order to quantify this effect of a shifting relative contribution of mech-
anisms 1 and 2 as a function of the hydrogen peroxide concentration, a
factor,
x
, is introduced. This factor depends only on the hydrogen peroxide
concentration and is equated to 1 if only mechanism 1 would occur and is
equated to zero if only mechanism 2 would occur. By means of this para-
meter,
x
, it appears possible to combine Equation 4.49 with Equation 4.52
and to transform it into the same relation.
(
)
(
)
(
)
(
)
(
)
12
x
+
12
12
x
+
12
12
x
+
12
K
¢¢
1
-
x
K
¢¢
1
-
x
InA
=
F
K
K
K
K
x
¢¢
4
1
2
3
4
5
F
R
(
)
05
.
EE
-
2
x
(
)
(
)
(
)
ref
32 12
-
x
32
x
-
12
(
)
c
c
1
-
q
1
-
q
e
[ .555]
4
T
-
-
-
-
O
O
OH
2
HO
2
or:
(
)
+-
(
)
(
)
log
I
=
log
Gx E
,
32
12
x
log
c
+
32
x
-
12
log
c
-
-
HO
OH
2
[4.56]
In the parameter
G
, all factors are incorporated from the right-hand part
of Equation 4.55, except for the bulk concentrations of hydrogen peroxide
and hydroxyl ions. With
E
= 0.45 V vs. SCE, the parameter is defined as G¢.
