Environmental Engineering Reference
In-Depth Information
The potential in standard conditions (E) of other electrochemical pairs can be
obtained with respect to Eq.
3.4
, permitting the compilation of a list of semi-
reaction potentials (electrochemical series). In this list, all the semi-reactions are
written in such a way to evaluate the tendency of the oxidized forms to accept
electrons and become reduced forms (positive potentials correspond to spontaneous
reductions) [
2
]. These potentials can be correlated to thermodynamic quantities if
the electrochemical system behaves in a reversible way from a thermodynamic
point of view, i.e., when the electrochemical system is connected against an external
cell with the same potential, no chemical reaction occurs, while any infinitesimal
variation of the external potential either to produce or to absorb current is exactly
inverted when the opposite variation is applied (reversible or equilibrium poten-
tials, E
eq
). When the equilibrium of the semi-reaction considered is established
rapidly, its potential against the reference can be experimentally determined.
Any redox reaction is accompanied by a change of free energy (DG) at a given
temperature and pressure. However, when the reaction is carried out in an elec-
trochemical way, the transport of electric charges due to a total potential difference
is associated with an electric work, which is given by:
W
el
¼
qE
ð
3
:
5
Þ
where E is the difference between cathode and anode potentials (E
c
- E
a
), and q is
the total charge transported, which can be expressed as a product of number of
moles of electrons transferred in the simplest balanced equation for the reaction in
question (n) by the Faraday constant (F, amount of charges on 1 mol of electrons):
q
¼
nF
ð
3
:
6
Þ
On the other hand, a fundamental thermodynamic equation defines the change
of free energy of a reaction as:
DG
¼
W
rev
PDV
ð
3
:
7
Þ
where -DG represents the total reversible work obtainable from the reaction (W
rev
),
diminished by the work associated with any possible volume change in the reaction
system (PDV, work of expansion). Since in an electrochemical reaction neither work
of expansion nor any other form of work are involved, from Eqs.
3.5
to
3.7
:
DG
¼
W
el
;
rev
ð
3
:
8
Þ
Hence, if the electrochemical system is reversible (or has no losses, all the free
energy can be converted into electric energy):
DG
¼
nFE
eq
ð
3
:
9
Þ
from which
E
eq
¼
DG
nF
ð
3
:
10
Þ
