Environmental Engineering Reference
In-Depth Information
we can define an
equilibrium constant
for each step
[
ML
i
]
K
eq,
i
=
(5.175)
[
ML
i
−
1
][
L
]
and a
stability constant
for each complex
[
ML
i
]
β
i
=
i
.
(5.176)
[
M
][
L
]
Using these definitions one can write for the Fe(II) system discussed here (see
Morel and Herring [1993] for details)
H
+
]
β
2
K
w
/
H
+
]
2
)
k
0
+[
[
]+[
[
]
k
1
(K
1
K
w
/
)
k
2
(
k
obs
=
.
(5.177)
H
+
]
H
+
]
β
2
K
w
/
2
)
[
1
+
(K
1
K
w
/
[
)
+
(
[
]
10
−
8
s
−
1
, 3.2
10
−
2
s
−
1
, and
Typical values of
k
0
,
k
1
, and
k
2
at 298 K are 1
×
×
10
4
s
−
1
, respectively. Since
k
o
1
k
2
, we can see why predominantly
hydroxo species of Fe(II) are formed. Competition for ligands (e.g., Cl
−
and SO
2
4
)
will significantly lower the rate of oxidation. Therefore, iron oxidation is far more
favorableinfreshwatersthaninopenmarinesystems.Reportedrateconstantinmarine
systems are a 100 times lower than in freshwater systems.
The redox reaction as discussed above proceeds with transfer of electrons between
molecules.There are two known mechanisms of electron transfer between the oxidant
and reductant. Both involve the formation of an activated complex.The distinguishing
feature is the type of activated complex. In the first variety, the hydration shells of
the two ions interpenetrate each other sharing a common solvent molecule. This is
called the
inner sphere (IS) complex.
In the second type, the two hydration shells are
separated by one or more solvent molecules, this being termed the
outer sphere (OS)
complex.
In the OS complex, the solvent will mediate the electron transfer. The two
mechanisms can be distinguished from one another since, in the IS case, the rates
will depend on the type of ligand forming the bridged complex. Electron transfer
reactions are generally slower than other reactions because of the rearrangements and
orientations of the solvent molecule required for the reaction to proceed.
A formal theory of
e
−
transfer in reactions is provided by the well-known
Marcus
theory
. The basic tenet of the theory is that the overall free energy of activation for
electron transfer is made up of three components (Marcus, 1963). The first involves
the electrostatic potential (
×
k
1
G
elec
) required to bring two ions together. The second
is the free energy for restructuring the solvent around each ion (
Δ
G
solv
)
. The last
and final term arises from the distortions in bonds between ligands in products and
reactants (
Δ
G
lig
)
.
Δ
G
AB
= Δ
G
elec
+ Δ
G
solv
+ Δ
G
lig
.
Δ
(5.178)
Marcus derived expressions for the free energy terms and combined them to give the
overall free energy. This resulted in the following equation for the rate of electron
transfer
kT
h
·
e
−
(
Δ
G
AB
/RT)
.
k
AB
= κ
(5.179)
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