ELECTROCHEMICAL METHODS Fundamentals and Applications - Allen.J.Bard

24 Chapter 1. Introduction and Overview of Electrode Processes
r lmt
'Hct
r lrxn
Figure 1.3.7 Processes in an
electrode reaction represented as
resistances.
the slowness with which a rate-determining step disposes of their products or creates their
reactants.
Each value of current density, j, is driven by a certain overpotential, 77. This overpotential
can be considered as a sum of terms associated with the different reaction steps: Tj mt
(the mass-transfer overpotential), r) ct (the charge-transfer overpotential), r] rxn (the overpotential
associated with a preceding reaction), etc. The electrode reaction can then be represented
by a resistance, R, composed of a series of resistances (or more exactly,
impedances) representing the various steps: R m , R ct , etc. (Figure 1.3.7). A fast reaction
step is characterized by a small resistance (or impedance), while a slow step is represented
by a high resistance. However, except for very small current or potential perturbations,
these impedances are functions of E (or /), unlike the analogous actual electrical elements.
1.3.4 Electrochemical Cells and Cell Resistance
Consider a cell composed of two ideal nonpolarizable electrodes, for example, two SCEs
immersed in a potassium chloride solution: SCE/KC1/SCE. The i-E characteristic of this
cell would look like that of a pure resistance (Figure 1.3.8), because the only limitation on
current flow is imposed by the resistance of the solution. In fact, these conditions (i.e.,
paired, nonpolarizable electrodes) are exactly those sought in measurements of solution
conductivity. For any real electrodes (e.g., actual SCEs), mass-transfer and charge-transfer
overpotentials would also become important at high enough current densities.
When the potential of an electrode is measured against a nonpolarizable reference
electrode during the passage of current, a voltage drop equal to iR s is always included in
the measured value. Here, R s is the solution resistance between the electrodes, which, unlike
the impedances describing the mass transfer and activation steps in the electrode reaction,
actually behaves as a true resistance over a wide range of conditions. For example,
consider once again the cell in Figure 1.3.4. At open circuit (/ = 0), the potential of the
cadmium electrode is the equilibrium value, £ eq ,cd (about —0.64 V vs. SCE). We saw earfc
appl
Hg/Hg 2CI 2/K + , CI7Hg 2CI 2/Hg
© 0
1 Ideal electrodes
• Real electrodes
Figure 1.3.8 Current-potential curve for a cell composed of two electrodes approaching ideal
nonpolarizability.