Environmental Engineering Reference
In-Depth Information
the reactions necessarily proceed at the same rate in both directions or at both
electrodes. This unsymmetrical reaction rate process will give rise to a different
charge acceptance rate (generally much lower) than the charge release rate (gen-
erally high), and noticeably temperature dependent.
Thermodynamics of battery systems are developed around the Gibbs free
energy of the constituent materials used in the electrodes and electrolyte. In the
ideal case this energy content,
D
G
(Btu, Cal, Joules) is defined as
D
G
¼
nFE
ð
J
=
mol
Þ
ð
10
:
1
Þ
where
n
is the number of electrons involved in the reaction,
F
is the Faraday's
constant
1
(96,474 C/mol, 26.8 Ah/equivalent, 23.06 kcal where 1 cal
¼
4.186 J) and
E
is the voltage. In an electrochemical cell the reaction kinetics determine the
potential, with available energy dependent on the amount of materials present to
take part in the reaction. As an example of cell voltage we consider a nickel-
cadmium (NiCd) system. The reaction is a two-electron exchange process that can
be written as follows:
Cd
þ
2NiOOH
¼
Cd
ð
OH
Þ
2
þ
2Ni
ð
OH
Þ
2
ð
10
:
2
Þ
D
G
þ
0
þ
2
ð
129
:
5
Þ¼ð
112
:
5
Þþ
2
ð
108
:
3
Þ
ð
10
:
3
Þ
D
G
¼
70
:
1
ð
kcal
Þ
ð
10
:
4
Þ
Using the energy value obtained in (10.4) in (10.1) results in the cell potential
of
70
:
1
10
3
2
23
:
06
10
3
¼
¼
D
G
nF
E
¼
1
:
52
ð
V
Þ
ð
10
:
5
Þ
According to (10.5) the NiCd system has a theoretical cell potential of 1.52 V.
Of course we don't get something for nothing. There are kinetics involved that will
diminish this internal potential, resulting in a lower potential of 1.35 V at the
terminals. The predominant loss kinetics involved in electrochemical cell thermo-
dynamics can be grouped into potential losses resulting from electrode reaction
kinetics (activation polarization), the availability of reactants (concentration
polarization) and Joule losses (ohmic loss in electrodes and electrolyte). These
polarization effects can be defined in terms of physical constants, number of
electrons involved in the reaction, exchange current and electrolyte concentration.
Activation polarization
arises from hindrances to kinetic transport in the
electrolyte of charge exchange during the reaction. The reaction rate at equilibrium
1
The Faraday constant is a convenient way to represent the ratio of Avagadro's number to the electron
charge,
N
A
/q
= 6.0221
10
23
/1.602
10
19
= 96,474 C/mol.
