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Provides students with solutions to problems in the 3rd edition of the classic textbook Electrochemical Methods: Fundamentals and Applications
Electrochemical Methods is a popular textbook on electrochemistry that takes the reader from the most basic chemical and physical principles, through fundamentals of thermodynamics, kinetics, and mass transfer, all the way to a thorough treatment of all important experimental methods. Holistically, it offers comprehensive coverage of all important topics in the field. To aid in reader comprehension, exercises are included at the end of each chapter which extend concepts introduced in the text or show how experimental data are reduced to fundamental results. This book provides worked solutions for many of the end-of-chapter exercises and is a key resource for any student who makes use of the original textbook.
Cynthia G. Zoski, Research Professor of Chemistry and Associate Director of the Center for Electrochemistry, The University of Texas at Austin, USA, is co-author of the solutions manual for the 2nd and 3rd editions of Electrochemical Methods. Her current research focuses on electrochemistry at the micro- and nanoscale in order to understand practical chemical, physical, materials, and biologically-related problems.
Johna Leddy, Associate Professor, The University of Iowa, USA is co-author of the solutions manual for the 2nd edition of Electrochemical Methods. Her electrochemical research interests range from fundamentals through measurements to build of electrochemical energy systems. Of special focus are classical modeling methods, modified electrodes, and magnetic effects on electron transfer.
Preface vii
1. Overview of Electrode Processes 1
2. Potentials and Thermodynamics of Cells 13
3. Basic Kinetics of Electrode Reactions 23
4. Mass Transfer by Migration and Diffusion 33
5. Steady-state Voltammetry at Ultramicroelectrodes 37
6. Transient Methods Based on Potential Steps 41
7. Linear Sweep and Cyclic Voltammetry 61
8. Polarography, Pulse Voltammetry, and Square-wave Voltammetry 73
9. Controlled-current Techniques 77
10. Methods Involving Forced Convection - Hydrodynamic Methods 83
11. Electrochemical Impedance Spectroscopy and AC Voltammetry 89
12. Bulk Electrolysis 101
13. Electrode Reactions with Coupled Homogeneous Chemical Reactions 117
14. Double-layer Structure and Adsorption 125
15. Inner-sphere Electrode Reactions and Electrocatalysis 137
16. Electrochemical Instrumentation 143
17. Electroactive Layers and Modified Electrodes 151
18. Scanning Electrochemical Microscopy 157
19. Single-particle Electrochemistry 161
20. Photoelectrochemistry and Electrogenerated Chemiluminescence 171
A. Mathematical Methods 175
B. Basic Concepts of Simulations 189
Problem 1.1© (a). In approaching this kind of problem, it is useful to list all the couples in Table C. 1 that are relevant to the system.
Alternatively, a graphical representation may prove useful. Here, the standard or formal potentials for each redox couple are plotted on a potential axis. The species present in solution are underlined. Note the reduced half of the couple is noted toward more negative potentials. The vertical line indicates the approximate potential range where both halves of the redox couple can exist. For electrode potentials positive of a given line, the oxidized half of the couple is stable at the electrode surface; for electrode potentials negative of the line, the reduced form is stable. Note that for n = 1, electrode potentials within 118 mV of E0 require no less than 1% of either the oxidized or reduced halves of the couple as given by .
The composition of the system dictates that the rest (zero current) potential be more positive than and more negative than or , i.e., between about 0.34 V and 1.2 V vs. NHE. Graphically, this is apparent because this is the voltage range over which the oxidized (Cu2+) and reduced species (Pt or H2O) present in the solution are most adjacent on the graph. This defines a zone of stability set by the oxidized and reduced species. (Note that the cell would not be at equilibrium if oxidized and reduced species of two or more couples were present such that they were on the outer sides of the lines. For example, if the solution contained Cu and O2, there would be a thermodynamic driving force for these species to react spontaneously to form water and Cu2+.) In the rest potential range, the potential is not well defined in a thermodynamic sense; the electrode is not well poised, because no couple has both oxidized and reduced forms present. Calculation of the equilibrium potential by the Nernst equation cannot be made.
Current will flow when the potential is moved negatively from the rest potential to about 0.340 V (or 0.340 + (-0.2412) = 0.099 V vs. SCE) so that Cu2+ is reduced at the electrode surface first.
A positive movement from the rest potential first causes significant current flow when platinum and water are oxidized.
Actually, Pt would form a thin oxide film, then it would stabilize, and only the oxygen evolution reaction would occur, with a significant negative (anodic) current flow due to the oxidation of water, which marks the positive background limit. The current-potential curve would look like the following with a transition from a limiting positive (cathodic) current flow due to Cu2+ reduction to Cu metal that plates onto the Pt UME to a significant cathodic current beginning at -0.1 V vs SCE due to H+(2 M in solution) reduction, which marks the negative background limit. Although Cd2+ is present in the solution, its reduction to Cd cannot be observed, because this reduction occurs at about -0.6 V vs. SCE, far beyond the negative background limit.
The reader may be puzzled regarding the locations of the background limits, which are less extreme than the related standard potentials. One must remember that a background curve represents just the foot of an enormous wave supported by a highly available electroreactant (in this case, H+or H2O). The half-wave potential for that wave might be near the standard potential of the couple, but on the current scale that allows observation of voltammetric features of interest, one never approaches the standard potential before the background current becomes prohibitive. In general, a background limit based on a reversible or quasireversible couple is less extreme than the corresponding standard potential by about 0.1 V.
(b). The couples to be considered from Table C. 1 are as follows:
The graphical representation is as follows.
Because both Sn4+ and Sn2+ are present, the system is poised and a well-defined thermodynamic equilibrium potential exists. From the Nernst equation (1.3.13), the equilibrium potential is 0.15 V vs. NHE or -0.09 V vs. SCE. Moving negatively from this potential favors Sn2+ at the electrode and requires reduction of Sn4+.
Likewise, a move positive of the rest potential favors Sn4+ at the electrode and drives oxidation.
The current potential curve resembles the following where the equilibrium potential (-0.09 V vs SCE) for the Sn4+/Sn2+ couple is shown because both tin cations are present in the electrochemical cell at the same concentration. Moving negative from this potential for Sn4+/Sn2+ and positive from this potential for Sn2+/Sn4+ leads to a cathodic and anodic limiting current respectively that are equal but opposite in sign. Moving yet more negative in potential from the cathodic limiting current leads to a significant increase in cathodic current at -0.1 V vs SCE due to proton (1 M) reduction, which corresponds to the negative background limit. The limiting current for reduction of Sn4+ is not fully resolved from the current rise at this limit. Moving more positive in potential from about +0.9 V from the anodic limiting current leads to a significant excursion of the anodic current due to water oxidation, which corresponds to the positive background limit.
(c) The couples to be considered from Table C. 1 are as follows:
The graphical representation is shown.
As in (a), the system is unpoised and the rest potential is not well defined, but exists between vs. NHE and at 0.26816 V vs. NHE; that is, between -0.2412 V and 0.02696 V vs. SCE. The first oxidation occurs when the potential is drawn to more positive values than ~ - 0.1 V vs. SCE, where the following reaction begins.
The chart and diagram predict that the first reduction will be the evolution of hydrogen.
However, this reaction is extremely slow on mercury (i.e., it has a high overpotential; see Section 1.1.7(c) and Chapters 1 and 3) and does not occur at an appreciable rate until far more negative potentials are reached. Thus, the first reduction of significance is the deposition of cadmium into the mercury to form the amalgam.
This is an example of kinetics superseding thermodynamic expectation during dynamic perturbation of an electrochemical system. The overpotential of hydrogen on mercury significantly widens the range of accessible potentials (i.e., the "potential window") in water, and is one reason mercury was long-favored for electrochemical analysis and thermodynamic evaluations despite its toxicity. The reduction waves for Cd2+ and Zn2+ can both be observed at a mercury electrode.
The reduction of Cd2+ will lead to a limiting current at -0.59 V vs SCE, followed by a limiting current of similar height for the reduction of Zn2+ at about -1.0 V vs. SCE. Finally, the reduction of H+begins at approximately -1.1 V vs. SCE with a cathodic current that appears infinite on the current scale due to the H+concentration of 1 M.
The current-potential curve resembles the following where the anodic current due to the oxidation of Hg at 0.0 V vs SCE appears practically infinite on the current scale. This oxidation defines the anodic background limit.
The negative background limit in this case is not due to a reversible or quasireversible couple, but, rather, the highly...
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