Environmental Engineering Reference
In-Depth Information
reservoir, which is at the electrostatic potential f
e
. However, since the electrode
potential influences electrons and nuclei of the bulk electrode in the same way,
there is no net effect on the neutral metal atoms. Consequently, m
me
(T, a
me
, f
e
)
can be replaced by the potential-independent Gibbs free energies of the bulk
electrode reservoir, g
bulk
me
(T, a
me
).
†
The term N
e
m
e
(f
e
) accounts for the excess charges transferred from the reference
electrode at the electrostatic potential f
ref
(which we have already defined as the
energy zero) to the electrode. Thus, with (5.11) this term can be rewritten as
q
e
(f
e
F
=
e), where we have introduced the total excess charge at the electrode
q
e
¼
N
e
e.
†
The terms N
a
m
a
(T, a
a
, f
S
) and N
c
m
c
(T, a
c
, f
S
): for the bulk electrolyte reser-
voir, the condition
m
a
(T, a
a
, f
S
)
þ
y
x
m
c
(T, a
c
, f
S
)
¼
m
ac
(T, a
ac
)
(5
:
16)
holds, where m
ac
describes entire salt molecules of the type (c
x
þ
)
y/x
(a
y -
) [e.g.,
(H
þ
)
2
SO
2-
], which are overall neutral and therefore potential-independent.
Within the electrode/electrolyte interface, however, the amounts of anions and
cations differ, leading to
N
a
m
a
(T, a
a
, f
S
)
þ
N
c
m
c
(T, a
c
, f
S
)
¼
N
a
m
ac
(T, a
ac
)
þ
N
c
y
m
c
(T, a
c
, f
S
)
(5
:
17)
x
N
a
Here, the last term accounts for the excess ions in the interfacial region, which
compensate the excess charge q
e
on the electrode surface and keep the overall
interface electroneutral. What in electrochemical terms is often described as a
polarizable active electrode and an unpolarizable reference electrode ensures
that any change of the number of ions in the electrochemical half-cell under
consideration, caused by an electrochemical reaction, is just compensated by a
corresponding counter-reaction at the reference electrode.
Including these considerations, the interfacial free energy (5.15) becomes
h
GT,
g(T, a
n
, a
me
, a
ac
, a
c
, f
e
, f
S
)
¼
1
A
ð
a
fg
,
N
fg
Þ
N
n
m
n
(T, a
n
)
N
me
g
bulk
me
(T, a
me
)
q
e
(f
e
F
=
e)
N
a
m
ac
(T, a
ac
)
N
c
y
m
c
(T, a
c
, f
S
)
i
(5
:
18)
x
N
a
As mentioned above, the last term in this equation represents the overall charge com-
pensation within the interface. Therefore, with (5.13), we finally obtain the following
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