Page 29 - Battery Reference Book

1/14 Introduction to battery technology

1.5 Free energy changes and possible to evaluate the heat change of the reaction
electromotive forces in cells occurring in the cell. The result may be compared with
that obtained by direct thermal measurement; good
More recent work has regarded the processes occur- agreement would then confirm the view that -nFE is
ring in a cell in terms of free energy changes. The equal to the free energy increase, since Equation 1.20
free energy change accompanying a process is equal is based on this postulate.
to the reversible work, other than that due to a vol- Using Equation 1.20 it is possible, having the e.m.f.
ume change, at constant temperature and pressure. of a cell on open circuit at a particular temperature,
When a reversible cell operates, producing an infinites- the temperature coefficient of dEldT and the emf.,
imal current, the electrical work is thermodynamically to calculate the heat change accompanying the cell
reversible in character, and does not include any work reaction AH:
due to a volume change. Furthermore, since the tem-
[ (3J
perature and pressure remain constant, it is possible AH=nF E-T - VC
to identify the electrical work done in a reversible
cell with the free energy change accompanying the
chemical or other process taking place in the cell. The -
- -"F [. - T
work done in a cell is equal to the product of the e.m.f. 4.183 cal
and the quantity of electricity passing. The practical
unit of electrical energy is defined as the energy devel- For example, the open circuit voltage of a lead-acid
oped when one coulomb is passed under the influence cell is 2.01V at 15°C (288K) and its temperature
of an e.m.f. of one volt; this unit is called the volt- coefficient of resistance is dEldT = 0.000 37 VIK, n =
coulomb, and is equivalent to one international joule. 2. The heat change accompanying the cell reaction in
The calorie defined by the US Bureau of Standards calories is
is equivalent to 4.1833 international joules, and hence
one volt-coulomb is equivalent to U4.1833, Le. 0.2390 AH = -2 x 96500 (2.01 - 288 x 0.000 37)
(defined), calorie. 4.18
If the e.m.f. of a reversible cell is E volts, and the = -87500cai = -87.5kcal
process taking place is associated with the passage of
n faradays, i.e. nF coulombs, the electrical work done which is in quite good agreement with the calorimet-
by the system is consequently n FE volt-coulombs or rically derived value of -89.4 kcal.
international joules. The corresponding increase of free Similarly, in the Clark cell, the reaction
energy (AF) is equal to the electrical work done on
the system; it is therefore possible to write Zn(ama1gam) + Hg2S04(s) + 7Hz0
AF = -nFE (1.23) = ZnS04.7HzO(s) + 2Hg(1)
This is an extremely important relationship, which gives rise to 2F of electricity, i.e. n = 2, the open
forms the basis of the whole treatment of reversible circuit voltage is 1.4324 V at 15°C and the temperature
cells. coefficient is 0.000 19, hence:
The identification of the free energy change of a
chemical reaction with the electrical work done when AH = -2 x 96 540 (1.4324 - 288 x 0.001 19)
the reaction takes place in a reversible cell can be 4.18
justified experimentally in the following manner. By = 81.92kcal
the Gibbs-Helmholtz equation,
which agrees well with the calorimetric value of
(1.24) 8 1.13 kcal.

where AH is the heat change accompanying the cell 1.6 Relationship between the energy
reaction and T is temperature in kelvins. If AF is changes accompanying a cell reaction
(a
replaced by -nFE, the result is and concentration of the reactants
-nFE = AH - nFT - It is important when studying the effect of concentra-
tions of reactants in a cell on the e.m.f. developed by
AH = nF [. - T ( g)p] the cell to consider this in terms of free energies (AF).
Free energy (AF) is defined by the following
(1.25)
expression:
It can be seen from Equation 1.20 that if the e.m.f. -AF = w - PAV
of the reversible cell, i.e. E, and its temperature coef-
ficient dEldT, at constant pressure, are known, it is at constant temperature and pressure.