600 13 Chemical Reaction Mechanisms II: Catalysis and Miscellaneous Topicswould correspond to a current passing through the electrochemical cell. At equilibrium
no current is flowing but the two half-reactions can occur with nonzero rates and
produce anodic and cathodic currents that cancel. Theexchange currentis defined as
the equilibrium magnitude of each of these currents. The exchange current per unit
area is denoted byj 0 and is commonly expressed in A cm−^2 (amperes per square
centimeter).
If the exchange current is large, a relatively small change in either the anodic or
cathodic current can produce a sizable net current, so that the electrode can approximate
a nonpolarizable electrode. If the exchange current is small, only a small net current is
likely to occur, and the electrode can approximate an ideal polarizable electrode. The
magnitude of the exchange current depends on the temperature, and is different for
different electrode materials and different solution compositions. Typical values range
from 5. 4 × 10 −^3 Acm−^2 for 0.0200 mol L−^1 Zn^2 +against a zinc amalgam with mole
fraction 0.010, down to 10−^10 Acm−^2 for the oxygen electrode with a platinum surface
in acid solution.^31 The zinc amalgam electrode is said to be areversible electrode, since
it is possible to reverse the direction of the net current at this electrode with a small
change in potential. The oxygen electrode is called anirreversible electrode, since a
small change in potential produces a negligible change in net current, because of the
small size of the exchange current.The Overpotential
Theback e.m.f.is a voltage that opposes the passage of a current through an electrolytic
cell. There are three sources of the back e.m.f. The first is thereversible back e.m.f.
due to the cell reaction. For example, in a Daniell cell with unit activities the reversible
back e.m.f. is the equilibrium standard-state cell potential of 1.100 V. For activities
other than unit activities, the reversible back e.m.f. can be calculated from the Nernst
equation. For an infinitesimal electrolytic current, the reversible back e.m.f. is the only
contribution to the back e.m.f. For a finite current, the “IR drop” in the voltage across
the electrolyte solution due to its electrical resistance also contributes. In many cases,
we will be able to neglect this contribution. The third source of back e.m.f. for a finite
current is theoverpotential, which is due to the polarization of the electrode.
There are two principal contributions to the overpotential.^32 The first contribution
is the concentration overpotential, which is due to changes in concentration near the
surface of the electrodes due to the passage of the current. The second contribution is
the activation overpotential, related to the activation energy of the chemical reaction
at the electrode.0 x = d
x[Zn2+]s[Zn2+]b[Zn2+
]Figure 13.16 The Assumed Concen-
tration Profile in a Boundary Layer
Near an Electrode.
The Concentration Overpotential If a Daniell cell is undergoing electrolysis at a
nonzero rate, zinc ions are being reduced at the surface of the zinc electrode. If there
is no stirring, the zinc ions are replaced from the bulk solution by diffusion. As a
simplification, let us assume that the concentration of zinc ions near the zinc electrode
varies linearly, as represented in Figure 13.16, wheredis the effective thickness of the
boundary layer. The value ofddepends on the shape of the electrodes, the concentration
of the solutes, the value of the diffusion coefficient, and so on. We will not attempt to
evaluate it directly, but will express it in terms of a limiting current.(^31) H. A. Laitinen and W. E. Harris,Chemical Analysis, 2nd ed., McGraw-Hill, New York, 1975, p. 233.
(^32) Ibid., p. 258ff.