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Electrochemical Engineering 145

to produce desired products. It is important to recog-
nize that thermodynamic calculations yield information
regarding equilibrium states but tell us nothing about the
rate at which an equilibrium is attained. Calculation of
the rate, which is essential in a design calculation, must
be obtained from knowledge of the electrode kinetics and
mass-transport limitations.
A large body of thermodynamic data has been amassed
over the last century, and it is of obvious value to relate
electrochemical variables to these data. One such rela-
tion can be developed by recognizing that the maximum
work performed by a closed system at constant tempera-
ture and pressure is given by the change in Gibbs free en-
ergy ( G) of the system. In an ideal electrochemical sys-
tem the change in free energy, which results from chemical
reaction, must be equal to the product of the charge and
the potential difference through which the charge falls:
G =−nFE, (2)
FIGURE 1 Schematic of an electrochemical cell. Electrodes are where n is the number of electrons participating in the
immersed in electrolyte. The charge is transported by ions in the reaction and E is the reversible cell potential.
electrolyte and by electrons in the external circuit.
From thermodynamic considerations the maximum en-
ergy that can be derived from a specified mass of reactants
caused by rubbing glass on silk “positive.” Current flow can be calculated. This calculation is of particular interest
was originally defined in terms of the flow of posi- in the design of portable energy sources. The theoretical
tive charges. Although we now recognize that negative specific energy is the ratio of Gibbs free energy of the
electrons carry the charge in a conductor, the original con- reaction to the mass of the reactants:
vention is so well-established that its use is still universal. G
Theoretical specific energy = . (3)
M i
reactants
B. Faraday’s Law
In some calculations the mass of the reactants (especially
The correspondence between charge flow and chemical
oxygen derived from the air) that do not need to be trans-
reaction was established by Faraday:
ported is not added to the total mass.
MIt
m = , (1)
nF
D. Potential
where m is the mass of the substance produced, M the
atomic or molecular weight of the species, I the current, The reversible cell potential is the maximum potential that
t the time, n the number of electrons participating in the an ideal galvanic device can attain. Because of irreversibil-
electrode reaction, and F Faraday’s constant (96,500 C). ities, the potential difference of a practical galvanic device
The product of the current and time gives the total charge is always lower. To optimize cell performance, we want to
passed. If the current is not constant, the charge is calcu- minimize the irreversibilities at a specified current density.
latedbyintegratingthecurrentoverthetimeorismeasured A knowledge of the overall cell potential does not give us
with a coulometer. information regarding the sources of the irreversibilities;
detailed knowledge of the individual electrode processes
is required for this purpose. To calculate the losses at a
C. Thermodynamics
particular electrode, we need to know its reversible poten-
For engineering purposes, thermodynamic calculations tial, but this quantity cannot be uniquely specified because
are useful in several respects. First, they tell us whether there is no absolute zero of potential. As a way of over-
a proposed electrochemical system can proceed sponta- coming this difficulty, a specific electrode reaction has
neously in a given direction. Second, they tell us the been arbitrarily chosen as the standard to which all other
maximum work that can be derived from a given cell or, electrode systems can be referred. The universal reference
conversely, the minimum work that must be expended electrode is the hydrogen electrode: