Chemistry Reference
In-Depth Information
-=
D
GTK
0
Rln
[2.6]
Beware of the fact that
E
0
values are valid only under equilibrium condi-
tions and for
a
O
=
a
R
= 1. In practice, this condition is, in most cases, not
fulfilled.
When Equations 2.2 and 2.4 are combined, the resulting equation relates
the half-cell potential to the effective activity of the redox couple:
R
F
T
n
a
a
R
T
a
a
R
O
0
0
EE
=-
ln
=+
E
ln
[2.7]
n
F
O
R
a relation better known as the Nernst equation. This quantity is equal to
the concentration of the species times a mean activity coefficient:
a
M
=
g
[2.8]
y
+
±
C
M
y
+
Although there is no straightforward and convenient method for evaluat-
ing activity coefficients for individual ions, the Debye-Hückel relationship
permits an evaluation of the mean activity coefficient (g
±
), for ions at low
concentrations (usually < 0.01 mol l
-1
):
I
2
[2.9]
log
g
±
=-
0 509
.
z
1
+
I
where
z
is the charge on the ion and
I
is the ionic strength given by:
Â
I
=
05
.
c
ii
2
[2.10]
The reaction of an electrochemical cell always involves a combination of
two redox half reactions such that one species oxidises a second species to
give the respective redox products. Thus, the overall cell reaction can be
expressed by a balanced chemical equation:
¨
-
a
Oe R
1
+
nc
E
[2.11]
1
1
¨
-
b
ROe
2
d
+
n
E
[2.12]
2
2
¨
a
OR RO
1
+
b c
+
d
K
[2.13]
2
1
2
However, electrochemical cells are most conveniently considered as two
individual half reactions, whereby each is written as a reduction in the form
indicated by Equations 2.11 and 2.12. When this is done and values of the
appropriate quantities are inserted, a potential can be calculated for each
half cell of the electrode system. Then the reaction corresponding to the
half cell with the more positive potential will be the positive terminal in a
galvanic cell, and the electromotive force of that cell will be represented by
the algebraic difference between the potential of the more-positive half cell
and the potential of the less-positive half cell:
