Page 239 - Academic Press Encyclopedia of Physical Science and Technology 3rd Chemical Engineering

P1: FYK/GJK P2: FJU Final Pages
Encyclopedia of Physical Science and Technology EN005B-205 June 15, 2001 20:24

146 Electrochemical Engineering

TABLE I Standard Electrode Potentials Variations with pressure are given by
0
Electrode reaction E (V) ∂ G
= V (7)
∂P
Au 3+ + 3e = Au 1.50 T
or
+
O 2 + 4H + 4e = 2H 2 O 1.23

Fe 3+ + e = Fe 2+ 0.77 ∂E V
=− , (8)
O 2 + 2H 2 O + 4e = 4OH − 0.40 ∂P T nF
Cu 2+ + 2e = Cu 0.34
where V is the volume change of the reaction. If ideal
+ 0.00
2H + 2e = H 2
behavior can be assumed,
Fe 2+ + 2e = Fe −0.44
∂E NRT
Zn 2+ + 2e = Zn −0.76
=− , (9)
Al 3+ + 3e = Al −1.60 ∂P nFP
T
where N is the change in the number of moles of gaseous
constituents and R is the gas constant. For condensed
+
2H + 2e = H 2 , (4) phases, pressure corrections are usually neglected.
Concentration corrections can be estimated from the
where the hydrogen ions are at unit activity, and the hy- Nernst equation. For a reaction
drogen gas is at unit fugacity; the reversible potential for
this electrode is defined as zero. Several standard electrode aA + bB = cC + dD,
potentials are listed in Table I. By convention all electrode the Nernst equation is
reactions are written as reductions. c d
RT [C] [D]
The theoretical cell potential under standard conditions E = E − ln , (10)
0
a
can be calculated by combining any two reactions of in- nF [A] [B] b
terest. The reversible cell potential is given by subtracting where the quantities in brackets refer to concentrations.
the more negative number from the more positive. The In this equation, activity coefficient corrections and liquid
reaction associated with the more positive potential pro- junction potentials are neglected.
ceeds spontaneously in the direction indicated in Table I.
An overall reaction can be indicated by reversing the reac- E. Reference Electrodes
tion associated with the more negative potential and mul-
In principle, we can measure the potential of an electrode
tiplying one of the reactions by a constant if the electrons
with a hydrogen reference electrode. We can also calculate
participating in each reaction are not equal.
the reversible potential of the cell composed of the elec-
Operation of an actual electrochemical process invari-
trode of interest and the hydrogen reference electrode. In
ably takes place under conditions other than those speci-
practice, a hydrogen electrode is difficult to operate prop-
fied for the standard electrode potentials. Since electrode
erly and is rarely used in engineering measurements. In-
potentials generally vary with temperature, pressure, and
stead, commercially available reference electrodes (e.g.,
concentration, it is necessary to calculate the reversible po-
calomel, Ag/AgCl, and Hg/HgO) are used.
tential under appropriate conditions. Frequently, the dif-
Because of irreversibilities associated with electrode
ferences are small, and approximate methods are used to
kinetics and concentration variations, the potential of an
calculate the corrections.
electrode is different from the equilibrium potential. This
The variation in Gibbs-free-energy change with tem-
departure from equilibrium, known as the overpotential,
perature at constant pressure is given by
can be measured with a reference electrode. So that sig-
∂ G nificant overpotential at the reference electrode can be
=− S, (5) avoided, the reference electrode is usually connected to the
∂T
P
working electrode through a high-impedance voltmeter.
where S is the entropy change of the reaction. Combin- With this arrangement the reference electrode draws neg-
ing this with Eq. (2), we obtain ligiblecurrent,andalloftheoverpotentialcanbeattributed
to the working electrode.
∂E S
= . (6)
∂T nF
P F. Ion Conduction
As an approximation, the entropy change can be treated Conduction in electrolytes is due to the movement of pos-
as a constant, and the change in reversible potential can itive and negative ions in an electric field. The conductiv-
be calculated directly. ity is proportional to the density and mobility of charge