nship between electrical energy and energy
content of a cell
1/12
1.5 Free energy changes and electromotive forces in
cells
1/14
1.6 Relationship between the energy changes
accompanying a cell reaction and concentration of the
reactants
1/14
1.7 Single electrode potentials
1/15
1.8 Activities of electrolyte solutions
1/18
1.9 Inuence of ionic concentration in the electrolyte on
electrode potential
1/22
1.10 Effect of sulphuric acid concentration on e.m.f. in the
leadacid battery
1/24
1.11 End-of-charge and end-of-discharge e.m.f.
values
1/26
1.12 Effect of cell temperature on e.m.f. in the leadacid
battery
1/27
1.13 Effect of temperature and temperature coefcient of
voltage dE/dT on heat content change of cell
reaction
1/28
1.14 Derivation of the number of electrons involved in a
cell reaction
1/28
1.15 Thermodynamic calculation of the capacity of a
battery
1/29
1.16 Calculation of initial volume of sulphuric acid
1/31
1.17 Calculation of operating parameters for a leadacid
battery from calorimetric measurements
1/32
1.18 Calculation of optimum acid volume for a cell
1/34
1.19 Effect of cell layout in batteries on battery
characteristics
1/34
1.20 Calculation of energy density of cells
1/42
1.21 Effect of discharge rate on performance
characteristics
1/44
1.22 Heating effects in batteries
1/47
1.23 Spontaneous reaction in electrochemical cells
1/56
1.24 Pressure development in sealed batteries
1/61
Electromotive force
1/3
1.1 Electromotive force
A galvanic or voltaic cell consists of two dissimilar
electrodes immersed in a conducting material such as
a liquid electrolyte or a fused salt; when the two elec-
trodes are connected by a wire a current will ow. Each
electrode, in general, involves an electronic (metallic)
and an ionic conductor in contact. At the surface of
separation between the metal and the solution there
exists a difference in electrical potential, called the
electrode potential. The electromotive force (e.m.f.)
of the cell is then equal to the algebraic sum of the
two electrode potentials, appropriate allowance being
made for the sign of each potential difference as fol-
lows. When a metal is placed in a liquid, there is,
in general, a potential difference established between
the metal and the solution owing to the metal yielding
ions to the solution or the solution yielding ions to the
metal. In the former case, the metal will become neg-
atively charged to the solution; in the latter case, the
metal will become positively charged.
Since the total e.m.f. of a cell is (or can in many
cases be made practically) equal to the algebraic sum
of the potential differences at the two electrodes, it
follows that, if the e.m.f. of a given cell and the value
of the potential difference at one of the electrodes are
known, the potential difference at the other electrode
can be calculated. For this purpose, use can be made
of the standard calomel electrode, which is combined
with the electrode and solution between which one
wishes to determine the potential difference.
In the case of any particular combination, such as
the following:
Zn/
N
ZnSO
4
/Hg
2
Cl
2
in
N
KCl/Hg
the positive pole of the cell can always be ascertained
by the way in which the cell must be inserted in the
side circuit of a slide wire potentiometer in order to
obtain a point of balance, on the bridge wire. To obtain
a point of balance, the cell must be opposed to the
working cell; and therefore, if the positive pole of the
latter is connected with a particular end of the bridge
wire, it follows that the positive pole of the cell in the
side circuit must also be connected with the same end
of the wire.
The e.m.f. of the above cell at 18
°
C is 1.082 V and,
from the way in which the cell has to be connected to
the bridge wire, mercury is found to be the positive
pole; hence, the current must ow in the cell from
zinc to mercury. An arrow is therefore drawn under
the diagram of the cell to show the direction of the
current, and beside it is placed the value of the e.m.f.,
thus:
Zn/
N
ZnSO
4
/Hg
2
Cl
2
in
N
KCl/Hg
!
1.082
It is also known that the mercury is positive to the
solution of calomel, so that the potential here tends to
produce a current from the solution to the mercury.
This is represented by another arrow, beside which is
placed the potential difference between the electrode
and the solution, thus:
Zn/
N
ZnSO
4
/Hg
2
Cl
2
in
N
KCl/Hg
!
0.281
!
1.082
Since the total e.m.f. of the cell is 1.082 V, and since
the potential of the calomel electrode is 0.281 V, it
follows that the potential difference between the zinc
and the solution of zinc sulphate must be 0.801 V,
referred to the normal hydrogen electrode, and this
must also assist the potential difference at the mercury
electrode. Thus:
Zn/
N
ZnSO
4
/Hg
2
Cl
2
in
N
KCl/Hg
!
!
0.801
0.281
!
1.082
From the diagram it is seen that there is a tendency
for positive electricity to pass from the zinc to the solu-
tion, i.e. the zinc gives positive ions to the solution, and
must, therefore, itself become negatively charged rel-
ative to the solution. The potential difference between
zinc and the normal solution of zinc sulphate is there-
fore
0.801 V. By adopting the above method, errors
both in the sign and in the value of the potential dif-
ference can be easily avoided.
If a piece of copper and a piece of zinc are placed
in an acid solution of copper sulphate, it is found, by
connecting the two pieces of metal to an electrometer,
that the copper is at a higher electrical potential (i.e.
is more positive) than the zinc. Consequently, if the
copper and zinc are connected by a wire, positive
electricity ows from the former to the latter. At the
same time, a chemical reaction goes on. The zinc
dissolves forming a zinc salt, while copper is deposited
from the solution on to the copper.
Zn C CuSO
4
(aq.) D ZnSO
4
(aq.) C Cu
This is the principle behind many types of electrical
cell.
Faradays Law of Electrochemical Equivalents holds
for galvanic action and for electrolytic decomposition.
Thus, in an electrical cell, provided that secondary
reactions are excluded or allowed for, the current of
chemical action is proportional to the quantity of elec-
tricity produced. Also, the amounts of different sub-
stances liberated or dissolved by the same amount of
electricity are proportional to their chemical equiva-
lents. The quantity of electricity required to produce
one equivalent of chemical action (i.e. a quantity of
chemical action equivalent to the liberation of 1 g of
hydrogen from and acid) is known as the faraday (F).
One faraday is equivalent to 96 494 ampere seconds 1/4
Introduction to battery technology
or coulombs. The reaction quoted above involving the
passage into solution of one equivalent of zinc and
the deposition of one equivalent of copper is there-
fore accompanied by the production of 2 F (192 988 C),
since the atomic weights of zinc and copper both con-
tain two equivalents.
1.1.1 Measurement of the electromotive force
The electromotive force of a cell is dened as the
potential difference between the poles when no current
is owing through the cell. When a current is owing
through a cell and through an external circuit, there is
a fall of potential inside the cell owing to its internal
resistance, and the fall of potential in the outside circuit
is less than the potential difference between the poles
at open circuit.
In fact if R is the resistance of the outside cir-
cuit, r the internal resistance of the cell and E its
electromotive force, the current through the circuit is:
C D
E
R C r
1.1
The potential difference between the poles is now
only E
0
D
CR, so that
E
0
/E D R/R C r
The electromotive force of a cell is usually measured
by the compensation method, i.e. by balancing it
against a known fall of potential between two points
of an auxiliary circuit. If AB (Figure 1.1) is a uniform
wire connected at its ends with a cell M, we may nd
a point X at which the fall of potential from A to X
balances the electromotive force of the cell N. Then
there is no current through the loop ANX, because
the potential difference between the points A and X,
tending to cause a ow of electricity in the direction
ANX, is just balanced by the electromotive force of N
which acts in the opposite direction. The point of bal-
ance is observed by a galvanometer G, which indicates
when no current is passing through ANX. By means of
such an arrangement we may compare the electromo-
tive force E of the cell N with a known electromotive
force E
0
of a standard cell N
0
; if X
0
is the point of
balance of the latter, we have:
AX
AX
0
D E
E
0
1.2
Figure 1.1 The Poggendorf method of determining electromotive
force
1.1.2 Origin of electromotive force
It is opportune at this point to consider why it comes
about that certain reactions, when conducted in gal-
vanic cells, give rise to an electrical current. Many
theories have been advanced to account for this phe-
nomenon. Thus, in 1801, Volta discovered that if two
insulated pieces of different metals are put in con-
tact and then separated they acquire electric charges
of opposite sign. If the metals are zinc and copper, the
zinc acquires a positive charge and the copper a neg-
ative charge. There is therefore a tendency for negative
electricity to pass from the zinc to the copper. Volta
believed that this tendency was mainly responsible for
the production of the current in the galvanic cell. The
solution served merely to separate the two metals and
so eliminate the contact effect at the other