Chapter 11 Electrochemical Methods Chapter Overview Section 11A Overview of Electrochemistry Section 11B Potentiometric Methods Section 11C Coulometric Methods Section 11D Voltammetric and Amperometric Methods Section 11E Key Terms Section 11F Chapter Summary Section 11G Problems Section 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 basic electrochemical signals, there are a 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, charge, or current 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. 667 Source URL: http://www.asdlib.org/onlineArticles/ecourseware/Analytical%20Chemistry%202.0/Text_Files.html Saylor URL: http://www.saylor.org/courses/chem108 Attributed to [David Harvey] Saylor.org Page 1 of 115 668 Analytical Chemistry 2.0 11A Overview of Electrochemistry The focus of this chapter is on analytical techniques that use a measurement of potential, charge, or current 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- istry outlined by Larry Faulkner in the form at the electrode’s surface; (2) the concentration of analyte at the elec- 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 reactions; (4) current is a measure of the rate of the analyte’s See also, Kissinger, P. T.; Bott, A. W. “Elec- trochemistry for the Non-Electrochemist,” oxidation or reduction; and (5) we cannot simultaneously control current Current Separations, 2002, 20:2, 51–53. and potential. 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 ladder diagrams for oxidation–reduction reaction. For an oxidation–reduction reaction, the potential determines the reactions in Section 6F.3. reaction’s position. Figure 11.1, for example, shows a ladder diagram for the Fe3+/Fe2+ and the Sn4+/Sn2+ equilibria. If we place an electrode in a solution of Fe3+ and Sn4+ and adjust its potential to +0.500 V, Fe3+ reduces to Fe2+, but Sn4+ remains unchanged. more positive E Fe3+ o Figure 11.1 Redox ladder diagram for Fe3+/Fe2+ and for Sn4+/ E Fe3+/Fe2+ = +0.771V 2+ Sn4+ Sn redox couples. The areas inblue 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+ o pink. Note that a more positive potential favors the oxidized E Sn4+/Sn2+ = +0.154 V forms. At a potential of +0.500 V (green arrow) Fe3+ reduces to 2+ 4+ Sn2+ Fe , but Sn remains unchanged. more negative Source URL: http://www.asdlib.org/onlineArticles/ecourseware/Analytical%20Chemistry%202.0/Text_Files.html Saylor URL: http://www.saylor.org/courses/chem108 Attributed to [David Harvey] Saylor.org Page 2 of 115 Chapter 11 Electrochemical Methods 669 (a) ] bulk 3+ solution [Fe (b) ] diffusion bulk 3+ 3+ layer solution Figure 11.2 Concentration of Fe as a function of [Fe distance from the electrode’s surface at (a) E = +1.00 V and (b) E = +0.500 V. The electrode is shown in gray distance from electrode’s surface 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, the Nernst equation for Fe3+ and Fe2+ is RT []Fe 2+ 0. 05916 [Fe 2++ ] EE= oo− log = E − log 11.1 nF []Fe3+ 1 []Fe3+ where E is the electrode’s potential and Eo is the standard-state reduction potential for the reaction Fe32++É Fe + 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 at the electrode's surface, not the concentrations in bulk solution. This distinction between surface concentrations and bulk concentra- tions 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, the concentration of Fe3+ remains the same at all distances from the electrode’s surface. If we change the electrode’s potential to +0.500 V, the concentra- tion of Fe3+ at the electrode’s surface decreases to approximately zero. As shown in Figure 11.2b, the concentration of Fe3+ increases as we move away 3+ We call the solution containing this concen- from the electrode’s surface until it equals the concentration of Fe in bulk tration gradient in Fe3+ the diffusion layer. solution. The resulting concentration gradient causes additional Fe3+ from We will have more to say about this in Sec- the bulk solution to diffuse to the electrode’s surface. tion 11D.2. THE ANALYTE MAY PARTICIPATE IN OTHER REACTIONS Figure 11.2 shows how the electrode’s potential affects the concentration of Fe3+, and how the concentration of Fe3+ varies as a function of distance from the electrode’s surface. The reduction of Fe3+ to Fe2+, which is governed by equation 11.1, may not be the only reaction affecting 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 of a metal–ligand complex in bulk solution, such as Fe(OH)2+, also affects the concentration of Fe3+. Source URL: http://www.asdlib.org/onlineArticles/ecourseware/Analytical%20Chemistry%202.0/Text_Files.html Saylor URL: http://www.saylor.org/courses/chem108 Attributed to [David Harvey] Saylor.org Page 3 of 115 670 Analytical Chemistry 2.0 CURRENT IS A MEASURE OF RATE The reduction of Fe3+ to Fe2+ consumes an electron, which is drawn from the electrode. The oxidation of another species, perhaps the solvent, at a second electrode serves as the source of this electron. The flow of electrons between the electrodes provides a measurable current. Because the reduc- 3+ 2+ The rate of the reaction tion of Fe to Fe consumes one electron, the flow of electrons between 32++− the electrodes—in other words, the current—is a measure of the rate of the FeÉ Fe + e reduction reaction. One important consequence of this observation is that 3+ is the change in the concentration of Fe 32++− as a function of time. the current is zero when the reaction FeÉ Fe + e is at equilibrium. WE CANNOT SIMULTANEOUSLY CONTROL BOTH CURRENT AND POTENTIAL If a solution of Fe3+ and Fe2+ 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 reduction of Fe3+ to Fe2+. Because the concentrations of Fe3+ and Fe2+ are constantly changing, the potential, as given by equation 11.1, also changes over time. In short, if we choose to control the potential, then we must ac- cept 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 consist- ing of two or more electrodes and the electronic circuitry for controlling and measuring the current and the potential.