Chemistry Reference
In-Depth Information
and the redox system concerned has its specific formal potential. In that
case, the BV relation maintains the same general form as Equation 1.24.
Moreover, Bockris
1
has extended the validity of the BV relation to
reaction sequences comprising, besides electron-transfer steps, also
homogeneous reaction steps - rate-determining ones as well as non
rate-determining ones. In the general reaction scheme as above, they can
occur anywhere, without a limitation to their number. The BV relation for
multistep reactions, including homogeneous chemical reactions, which will
be referred to later on as the extended BV relation, is as follows:
F
R
F
R
Ó
˛
ah
ah
a
k
j
=
j
0
e
-
e
T
T
[1.33]
where
j
0
depends on the kinetic parameters of every sub-step. For the trans-
fer coefficients, the following applies:
n
vv
r
1
-=
-
nn
v
na
vo
a
=
b
-
b
r
[1.34]
a
n
v
v
=+
a
b
r
[1.35]
k
+=
n
v
aa
a
[1.36]
Here b is the cathodic symmetry factor of the rate-determining step and n
is a positive integral number indicating how many times the RDS is occur-
ring in the global electron-transfer reaction (mostly n=1). The parameter
r
takes into account a homogeneous chemical reaction, the rate of which is
not dependent on the potential, as RDS: when the RDS is a charge-
transfer step,
r
= 1 applies, and for a chemical RDS,
r
= 0.
The transfer coefficients are the ones determining how the electrode
potential influences the electrochemical reaction rate or, in other words, the
inclination of the relation between log
I
and the over-potential, also called
the Tafel slope, of a multistep reaction. The coefficients are an important
aid when unravelling the electrochemical reaction mechanisms, because the
experimentally determined Tafel slope should correspond to the value that
is calculated for the postulated sub-step sequence and RDS.
However, this method is not sufficient to validate quickly a possible reac-
tion mechanism because it cannot deliver the reaction order of a compo-
nent
not
occurring in the global reaction equation. Often H
+
ions or OH
-
ions are involved in the sub-steps where an intermediate is formed before
the RDS and is re-used in or after the RDS. This causes a pH dependency
of the global reaction, despite the fact that not necessarily H
+
or OH
-
appears in the overall reaction of the oxidation or reduction.
