Environmental Engineering Reference
In-Depth Information
electrolyte is
2H
+
{
el
}+
2
e
−
{
a
}
H
2
→
(3.47)
where
el
is the electric potential of the electrolyte and
a
is that of the anode. In this reaction
a
while the ion moves into the electrolyte at the
the electron moves into the anode at its potential
el
. At the cathode, the oxidizing reaction is
potential
1
2
O
2
→
2H
+
{
el
}+
2
e
−
{
c
}+
H
2
O
(3.48)
where
c
is the cathode electric potential. The net effect of both of the electrode reactions in the
production of water and the movement of a charge through the external circuit, found by adding
(3.47) and (3.48), is
1
2
O
2
→
2
e
−
{
a
}−
2
e
−
{
c
}
H
2
+
H
2
O
+
(3.49)
In this overall reaction the hydrogen and the oxygen molecules produce water molecules. In the
process, for each hydrogen molecule two electrons flow from the low anode potential to the high
cathode potential in the external circuit, producing electrical work. If
q
e
is the magnitude of the
charge of an electron and
m
H
2
is the mass of a hydrogen molecule, then the electrical work work
per unit mass of fuel in the reaction is
w
=
(
2
q
e
/
m
H
2
)(
c
−
a
)
. Multiplying the numerator and
denominator of the first factor of this expression by Avogadro's number (see Table A.3), we find
2
F
M
H
2
w
=
(
c
−
a
)
(3.50)
where
F
=
9
.
6487
E
(
4
)
coulomb/mole is the Faraday constant and
M
H
2
is the molecular mass (g)
of a mole of diatomic hydrogen (H
2
).
The second law limits the electrode potential difference
c
−
a
that can be achieved, because
the work
w
cannot exceed the free energy change
f
available in the oxidation reaction
w
≤
(
f
)
H
2
(3.51)
(
)
H
2
M
H
2
2
f
(
c
−
a
)
≤
F
where (3.50) has been used to eliminate
in the second line of (3.51). The right-hand side of
(3.51) is thus the maximum possible electrode potential difference. For a hydrogen-oxygen fuel
cell at 20
◦
C and one atmosphere of pressure, using the values of Table 3.1, this is calculated to
be 1.225 V.
The maximum potential difference of a fuel cell, determined by the free energy change of
the fuel oxidation reaction as in equation (3.51), is only reached when the cell is operated in a
reversible manner by limiting the current to extremely low values, in effect zero current or open
external circuit. For finite current draw, there will be a voltage drop at the electrode surfaces and
within the electrolyte that is needed to move the fuel ions to the cathode at a finite rate, along with
a corresponding decline in the electrode potential difference. The thermodynamic efficiency
w
η
fc
of a fuel cell may then be defined as the ratio of the actual electric work
w
delivered by the cell to
