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Chapter 11
Electrochemical Methods
Chapter Overview
11A Overview of Electrochemistry
11B Potentiometric Methods
11C Coulometric Methods
11D Voltammetric and Amperometric Methods
11E Key Terms
11F Chapter Summary
11G Problems
11H Solutions to Practice Exercises
In Chapter 10 we examined several spectroscopic techniques that take advantage of the
interaction between electromagnetic radiation and matter. In this chapter we turn our attention
to electrochemical techniques in which the potential, current, or charge in an electrochemical
cell serves as the analytical signal.
Although there are only three fundamental electrochemical signals, there are many possible
experimental designs—too many, in fact, to cover adequately in an introductory textbook.
The simplest division of electrochemical techniques is between bulk techniques, in which we
measure a property of the solution in the electrochemical cell, and interfacial techniques, in
which the potential, current, or charge depends on the species present at the interface between
an electrode and the solution in which it sits. The measurement of a solution’s conductivity,
which is proportional to the total concentration of dissolved ions, is one example of a bulk
electrochemical technique. A determination of pH using a pH electrode is an example of an
interfacial electrochemical technique. Only interfacial electrochemical methods receive further
consideration in this chapter.
637
638 Analytical Chemistry 2.1
11A Overview of Electrochemistry
The focus of this chapter is on analytical techniques that use a measurement
of potential, current, or charge to determine an analyte’s concentration or
to characterize an analyte’s chemical reactivity. Collectively we call this area
of analytical chemistry electrochemistry because its originated from the
study of the movement of electrons in an oxidation–reduction reaction.
Despite the difference in instrumentation, all electrochemical tech-
niques share several common features. Before we consider individual ex-
amples in greater detail, let’s take a moment to consider some of these
similarities. As you work through the chapter, this overview will help you
focus on similarities between different electrochemical methods of analysis.
You will find it easier to understand a new analytical method when you can
see its relationship to other similar methods.
11A.2 Five Important Concepts
The material in this section—particularly To understand electrochemistry we need to appreciate five important and
the five important concepts—draws upon interrelated concepts: (1) the electrode’s potential determines the analyte’s
a vision for understanding electrochem- form at the electrode’s surface; (2) the concentration of analyte at the elec-
istry outlined by Larry Faulkner in the
article “Understanding Electrochemistry: trode’s surface may not be the same as its concentration in bulk solution;
Some Distinctive Concepts,” J. Chem. (3) in addition to an oxidation–reduction reaction, the analyte may partici-
Educ. 1983, 60, 262–264. pate in other chemical reactions; (4) current is a measure of the rate of the
See also, Kissinger, P. T.; Bott, A. W. analyte’s oxidation or reduction; and (5) we cannot control simultaneously
“Electrochemistry for the Non-Electro-
chemist,” Current Separations, 2002, 20:2, current and potential.
51–53.
THE ELECTRODE’S POTENTIAL DETERMINES THE ANALYTE’S FORM
You may wish to review the earlier treat- In Chapter 6 we introduced the ladder diagram as a tool for predicting
ment of oxidation–reduction reactions how a change in solution conditions affects the position of an equilibrium
in Section 6D.4 and the development of reaction. Figure 11.1, for example, shows a ladder diagram for the Fe3+/
ladder diagrams for oxidation–reduction 2+ 4+ 2+
reactions in Section 6F.3. Fe and the Sn /Sn equilibria. If we place an electrode in a solution
3+ 4+ 3+
of Fe and Sn and adjust its potential to +0.500 V, Fe is reduced to
2+ 4+ 2+
Fe but Sn is not reduced to Sn .
more positive
E
Fe3+
o
3+ 2+ 4+ E 3+ 2+ = +0.771V
Figure 11.1 Redox ladder diagram for Fe /Fe and for Sn / Fe /Fe
4+
2+ Sn
Sn redox couples. The areas in blue show the potential range +0.500 V
where the oxidized forms are the predominate species; the re-
duced forms are the predominate species in the areas shown in Fe2+
pink. Note that a more positive potential favors the oxidized o
E 4+ 2+ = +0.154 V
3+ Sn /Sn
forms. At a potential of +0.500 V (green arrow) Fe reduces
2+ 4+ 2+
to Fe , but Sn remains unchanged. Sn
more negative
Chapter 11 Electrochemical Methods 639
(a) ] bulk
3+e solution
[F
(b) ] diffusion bulk
3+ 3+
e layer solution Figure 11.2 Concentration of Fe as a function of dis-
[F tance from the electrode’s surface at (a) E = +1.00 V and
distance from electrode’s surface (b) E = +0.500 V. The electrode is shown in gray and
the solution in blue.
INTERFACIAL CONCENTRATIONS MAY NOT EQUAL BULK CONCENTRATIONS
In Chapter 6 we introduced the Nernst equation, which provides a math-
ematical relationship between the electrode’s potential and the concentra-
tions of an analyte’s oxidized and reduced forms in solution. For example,
3+ 2+
the Nernst equation for Fe and Fe is
2+ 2+
o RT []Fe 0.05916 []Fe
32++
EE=-ln = log 11.1
Fe /Fe nF 3+ 1 3+
[]Fe []Fe
o 32++
where E is the electrode’s potential and EFe /Fe is the standard-state re-
32++-
duction potential for the reaction Fe ()aq ? Fe ()aq + e . Because it is
the potential of the electrode that determines the analyte’s form at the
electrode’s surface, the concentration terms in equation 11.1 are those of
2+ 3+
Fe and Fe at the electrode's surface, not their concentrations in bulk
solution.
This distinction between a species’ surface concentration and its bulk
concentration is important. Suppose we place an electrode in a solution of
Fe3+ and fix its potential at 1.00 V. From the ladder diagram in Figure 11.1,
we know that Fe3+ is stable at this potential and, as shown in Figure 11.2a,
3+
the concentration of Fe is the same at all distances from the electrode’s
surface. If we change the electrode’s potential to +0.500 V, the concentra-
3+
tion of Fe at the electrode’s surface decreases to approximately zero. As
shown in Figure 11.2b, the concentration of Fe3+ increases as we move We call the region of solution that contains
3+ this concentration gradient in Fe3+ the dif-
away from the electrode’s surface until it equals the concentration of Fe
in bulk solution. The resulting concentration gradient causes additional fusion layer. We will have more to say about
Fe3+ from the bulk solution to diffuse to the electrode’s surface. this in Section 11D.2.
THE ANALYTE MAY PARTICIPATE IN OTHER REACTIONS
Figure 11.1 and Figure 11.2 shows how the electrode’s potential affects
3+ 3+
the concentration of Fe and how the concentration of Fe varies as a
3+
function of distance from the electrode’s surface. The reduction of Fe to
Fe2+, which is governed by equation 11.1, may not be the only reaction
that affects the concentration of Fe3+ in bulk solution or at the electrode’s
surface. The adsorption of Fe3+ at the electrode’s surface or the formation
640 Analytical Chemistry 2.1
of a metal–ligand complex in bulk solution, such as Fe(OH)2+, also affects
3+
the concentration of Fe .
CURRENT IS A MEASURE OF RATE
3+ 2+
The reduction of Fe to Fe consumes an electron, which is drawn from
The rate of the reaction the electrode. The oxidation of another species, perhaps the solvent, at a
32++- second electrode is the source of this electron. Because the reduction of
Fe ()aq ?Fe ()aq +e 3+ 2+
3+ Fe to Fe consumes one electron, the flow of electrons between the elec-
is the change in the concentration of Fe 3+
as a function of time. trodes—in other words, the current—is a measure of the rate at which Fe
is reduced. One important consequence of this observation is that the cur-
32++-
rent is zero when the reaction Fe ()aq ? Fe ()aq + e is at equilibrium.
WE CANNOT CONTROL SIMULTANEOUSLY BOTH THE CURRENT AND THE POTENTIAL
3+ 2+
If a solution of Fe and Fe is at equilibrium, the current is zero and the
potential is given by equation 11.1. If we change the potential away from
its equilibrium position, current flows as the system moves toward its new
equilibrium position. Although the initial current is quite large, it decreases
over time, reaching zero when the reaction reaches equilibrium. The cur-
rent, therefore, changes in response to the applied potential. Alternatively,
we can pass a fixed current through the electrochemical cell, forcing the
3+ 2+ 3+
reduction of Fe to Fe . Because the concentrations of Fe decreases
2+
and the concentration of Fe increases, the potential, as given by equation
11.1, also changes over time. In short, if we choose to control the potential,
then we must accept the resulting current, and we must accept the resulting
potential if we choose to control the current.
11A.2 Controlling and Measuring Current and Potential
Electrochemical measurements are made in an electrochemical cell that
consists of two or more electrodes and the electronic circuitry needed to
control and measure the current and the potential. In this section we intro-
duce the basic components of electrochemical instrumentation.
The simplest electrochemical cell uses two electrodes. The potential of
one electrode is sensitive to the analyte’s concentration, and is called the
working electrode or the indicator electrode. The second electrode,
which we call the counter electrode, completes the electrical circuit and
provides a reference potential against which we measure the working elec-
trode’s potential. Ideally the counter electrode’s potential remains constant
so that we can assign to the working electrode any change in the overall
cell potential. If the counter electrode’s potential is not constant, then we
replace it with two electrodes: a reference electrode whose potential
remains constant and an auxiliary electrode that completes the electri-
cal circuit.
Because we cannot control simultaneously the current and the poten-
tial, there are only three basic experimental designs: (1) we can measure
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