Environmental Engineering Reference
In-Depth Information
molecule and two water molecules:
2
e
−
{
p
}+
3H
+
{
el
}+
HSO
4
{
el
}→
PbO
2
+
PbSO
4
+
2H
2
O
(4.16)
The net reaction in the storage battery is the sum of the cathode and anode reactions, equations (4.15)
and (4.16):
H
+
{
el
}+
HSO
4
{
el
}
)
→
e
−
{
n
}−
e
−
{
p
}
)
Pb
+
PbO
2
+
2
(
2PbSO
4
+
2H
2
O
+
2
(
(4.17)
In the discharge reaction of the lead-acid battery, equation (4.17), both electrode surfaces are each
converted to lead sulfate while sulfuric acid is removed and water is added to the electrolyte,
diluting it.
14
When both electrode surfaces are completely covered with lead sulfate, there is no
difference between the electrodes and no further electric work may be drawn from it.
In the discharge reaction, equation (4.17), the electrical work of moving the two electrons
through the external circuit equals 2
q
e
(
p
−
n
)
, where
q
e
is the magnitude of the electron charge.
When this discharge occurs very slowly at fixed temperature and pressure, the electrical work is
then equal to the reduction of free energy per unit mass
(
f
)
la
when the reactants Pb
+
PbO
2
+
2(H
+
+
HSO
4
) are converted to the products 2PbSO
4
+
2H
2
O. As a consequence, the battery
potential difference
p
−
n
can be written as
a
−
c
=
(
f
)
la
M
la
2
(4.18)
F
where
is the Faraday constant.
15
At usual
conditions, the lead-acid battery potential difference is 2.05 V. In the reaction of equation (4.17),
the free energy change per unit mass of reactants,
M
la
is the molecular weight of the reactants and
F
0.6 MJ/kg.
The advantage of the storage battery is that the discharge reactions, such as those of equa-
tions (4.15) and (4.16) for the lead-acid battery, can be reversed in direction by imposing an external
potential difference between the positive and negative electrodes that exceeds the equilibrium value
of equation (4.18). In so doing, the products of the discharge reaction are converted back to re-
actants, renewing the energy stored in the battery, with the energy increment being supplied by
electrical work from the external charging circuit. In the discharging and recharging of a storage
battery there is usually a net loss of energy because more electrical work is required to charge
the battery than is recovered in its discharge. This energy loss of the charge-discharge cycle is
dependent upon the charging and discharging rates: When these rates are higher, the loss is greater.
Some of the loss is caused by resistive heating resulting from the internal ion current of the battery,
while the rest is a consequence of electrochemical irreversibilities at the electrode surfaces.
The electrode reactions that release or absorb electrical work occur at the electrode surface.
The electrodes of storage batteries have a porous, sponge-like structure to maximize the ratio of
surface area to electrode volume. In this way the amount of energy stored per unit mass of electrode
material may be maximized and the cost of energy storage minimized.
(
f
)
la
, is 171 Wh/kg
=
14
The degree of discharge of the lead-acid battery can be determined by measuring the specific gravity of the
electrolyte, which decreases as the acid content is diluted.
15
See Table A.3.
