PROBLEMS Ybm
3.1 Consider the electrode reaction O ne R. Under the conditions that Cr Cq 1 mM, k 10 7 cm s, a 0.3, and n 1 a Calculate the exchange current density, jo iq A, in xA cm2. b Draw a current density-overpotential curve for this reaction for currents up to 600 A cm2 anodic and cathodic. Neglect mass-transfer effects. c Draw log j vs. rj curves Tafel plots for the current ranges in b . 3.2 A general expression for the current as a function of overpotential, including mass-transfer effects, can be...
Scanning Electrochemical Microscopy
SECM is an electrochemical scanning probe technique where the measured current is caused by an electrochemical reaction at the tip 15 . The overall apparatus for SECM is similar to that used for ESTM, that is, a bipotentiostat is used to control the tip potential and frequently also that of the substrate , and the tip is moved by piezo controllers. However the principles of operation and the type of information obtained by SECM differ from those of ESTM 16-18 . For electrodes with radii of 1 to...
Problems 1
2.1 Devise electrochemical cells in which the following reactions could be made to occur. If liquid junctions are necessary, note them in the cell schematic appropriately, but neglect their effects. c 2PbS04 2H20 lt Pb02 Pb 4H 2SO d AnT TMPD An TMPD in acetonitrile, where An and An are anthracene and its anion radical, and TMPD and TMPD are and its cation radical. Use anthracene potentials for DMF solutions given in Appendix C.3 . e 2Ce3 2H BQ 2Ce4 H2Q aqueous, where BQ is p-benzoquinone and...
Modes of Mass Transfer
Let us now be more quantitative about the size and shape of current-potential curves. As shown in equation 1.3.4, if we are to understand , we must be able to describe the rate of the reaction, v, at the electrode surface. The simplest electrode reactions are those in which the rates of all associated chemical reactions are very rapid compared to those of the mass-transfer processes. Under these conditions, the chemical reactions can usually be treated in a particularly simple way. If, for...
T 1
Reference Auxiliary or counter electrodes Figure 1.3.10 Three-electrode cell and notation for the different electrodes. tions from the ohmic drop in solution. With such electrodes, currents of the order of 1 nA are typical hence Rs values even in the Mil range can be acceptable. In experiments where iRs may be high e.g., in large-scale electrolytic or galvanic cells or in experiments involving nonaqueous solutions with low conductivities , a three-electrode cell Figure 1.3.10 is preferable. In...
Scanning Tunneling Microscopy
The STM is useful for studying surfaces, particularly well-defined and atomically smooth surfaces. It is probably the only technique available that can provide true atomic resolution of electrode surfaces in an electrochemical environment. The technique is based on measurement of the tunneling current that flows between the electrode surface and a sharp metal tip W or Pt as the tip is brought close to the surface and scanned across it Figure 16.2.1 . Tunneling is a form of electronic conduction...
r r
Isotherms are sometimes written in terms of the fractional coverage of the surface, 0 iyrs the Langmuir isotherm in this form is The Langmuir isotherm can be written in terms of the concentration of species i in solution by including activity coefficients in the 3 term. This yields If two species, i and j, are adsorbed competitively, the appropriate Langmuir isotherms are where Tbs and Fj,s represent the saturation coverages of i and j, respectively. These equations can be derived from a...
REFERENCES Xcw
1. J. Heyrovsky, Chem. Listy, 16, 256 1922 . 2. I. M. Kolthoff and J. J. Lingane, Polarography, 2nd ed., Wiley-Interscience, New York, 1952, Chap. 17. 3. J. J. Lingane, Electroanalytical Chemistry, 2nd ed., Wiley-Interscience, New York, 1958, Chap. 11. 4. L. Meites, Polarographic Techniques, 2nd ed., Wiley-Interscience, New York, 1958, Chap. 2. 5. J. J. Lingane, Anal. Chim. Acta, 44, 411 1969 . 6. A. Bond, Modern Polarographic Methods in Analytical Chemistry, Marcel Dekker, New York, 1980. 7....
Info Ype
Figure 1.1.4 Schematic current-potential curve for the cell Pt H , Br l M lAgBr Ag, showing the limiting proton reduction and bromide oxidation processes. The cell potential is given for the Pt electrode with respect to the Ag electrode, so it is equivalent to EPt V vs. AgBr . Since EAg AgBr 0.07 V vs. NHE, the potential axis could be converted to Pt V vs. NHE by adding 0.07 V to each value of potential. 3The convention of taking i positive for a cathodic current stems from the early...
Info Tyy
Figure 13.3.6 a A view of the differential capacitance in the Gouy-Chapman-Stern GCS model as a series network of Helmholtz-layer and diffuse-layer capacitances. b Potential profile through the solution side of the double layer, according to GCS theory. Calculated from 13.3.23 for 10-2 M 1 1 electrolyte in water at 25 C. 4See 13.3.15b , 13.3.20b , and 13.3.21b for evaluations of the constants for aqueous solutions at 25 C. Figure 13.3.6 a A view of the differential capacitance in the...
PROBLEMS Pxb
4.1 Consider the electrolysis of a 0.10 M NaOH solution at platinum electrodes, where the reactions are anode 20H 02 H20 2e cathode 2H20 2 H2 20H Show the balance sheet for the system operating at steady state. Assume 20e are .passed in the external circuit per unit time, and use the Aq values in Table 2.3.2 to estimate transference numbers. 4.2 Consider the electrolysis of a solution containing 101 M Fe C104 3 and 101 M Fe C104 2 at platinum electrodes anode Fe2 - gt Fe3 e cathode Fe3 e Fe2...
General Considerations In Bulk Electrolysis
11.2.1 Extent or Completeness of an Electrode Process The extent or degree of completion of a bulk electrolytic process can be predicted for nernstian reactions from the applied electrode potential and a suitable form of the Nernst equation. a Both Forms Soluble in Solution Consider the overall reduction reaction where both O and R are soluble and R is initially absent. Let Q be the initial concentration of O, Vs be the volume of the solution, and x be the fraction of O reduced to R at the...
Problems
4. See, for example, G. J. Hoytink, J. Van Schooten, E. de Boer, and W. Aalbersberg, Rec. Trav. Chim., 73, 355 1954 , for an application of this type of method to the study of reactions coupled to the reduction of aromatic hydrocarbons. 1.1 Consider each of the following electrode-solution interfaces, and write the equation for the electrode reaction that occurs first when the potential is moved in 1 a negative direction and 2 a positive direction from the open-circuit potential. Next to each...
Info Ism
Figure 6.4.1 Variation of quasireversible current function, for different values of a as indicated on each graph and the following values of A I A 10 II A 1 III A 0.1 IV A 10-2. Dashed curve is for a reversible reaction. E UFACqDq2 nF RT mvm and A k Dlf2 F RT l 2vm for Dq Dr D . From H. Matsuda and Y. Ayabe, Z. Elektrochem., 59,494 1955 , with permission. Abscissa label adapted for this text. Figure 6.4.1 Variation of quasireversible current function, for different values of a as indicated on...
Classification Of Techniques
The methods can be classified by the controlled parameter .E or i and by the quantities actually measured or the process carried out. Thus in controlled-potential techniques the potential of the working electrode is maintained constant with respect to a reference electrode. Since the potential of the working electrode controls the degree of completion of an electrolytic process in most cases, controlled-potential techniques are usually the most desirable for bulk electrolysis. However, these...
REFERENCES Nuj
1. V. G. Levich, Physicochemical Hydrodynamics, Prentice-Hall, Englewood Cliffs, NJ, 1962. 2. R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport Phenomena, Wiley, New York, 1960. 3. J. N. Agar, Disc. Faraday Soc., 1, 26 1947 . 4. J. Newman, Electroanal. Chem., 6, 187 1973 . 5. J. S. Newman, Electrochemical Systems, 2nd ed., Prentice-Hall, Englewood Cliffs, NJ, 1991. 6. R. F. Probstein, Physicochemical Hydrodynamics An Introduction, 2nd ed., Wiley, New York, 1994. 7. A. C. Riddiford, Adv....
REFERENCES Wqz
1. R. W. Murray, Accts. Chem. Res., 13, 135 1980 . 2. R. W. Murray, Electroanal. Chem., 13, 1 1983 . 3. A. J. Bard, J. Chem. Educ., 60, 302 1983 . 4. L. R. Faulkner, Chem. Engr. News, 62 9 , 28 1984 . 5. M. S. Wrighton, Inorg Chem., 4, 269 1985 . 6. C. E. D. Chidsey and R. W. Murray, Science, 231, 25 1986 . 7. M. S. Wrighton, Science, 231, 32 1986 . 8. M. Fujihira in Topics in Organic Electrochemistry, A. J. Fry and W. E. Britton, Eds., Plenum, New York, 1986. 9. R. W. Murray, A. G. Ewing, and...
Spectroelectrochemistry And Other Coupled Characterization Methods
Recent years have seen high continued interest in studying electrode processes by experiments that involve more than the usual electrochemical variables of current, charge, and potential. Much of the motivation for this work has been to provide means for obtaining information about electrochemical systems that could not be gathered in purely electrochemical experiments. In this chapter, we will examine some of the more important approaches involving the coupling of nonelectrochemical...
O Sjb
amperometric titration curve dilution neglected for titration of Fe2 with Ce4 with the platinum indicator electrode held at E in Figure 11.5.4. potential of each will thus shift during a titration to maintain the condition ic a . For example, for the Fe2 -Ce4 titration with two platinum electrodes held at a potential difference, AE 50 mV Figure 11.5.4 , the titration curve that results is shown in Figure The shape of the two-electrode amperometric titration curve depends strongly on the...
Bulk Electrolysis Methods
The methods described in Chapters 5 to 10 generally employ conditions featuring a small ratio of electrode area, A, to solution volume, V. These allow the experiments to be carried out over fairly long time periods without appreciable changes of the concentrations of the reactant and the products in the bulk solution, and they allow the semi-infinite boundary condition e.g., C0 x, t Cq as x gt 00 to be maintained over repeated trials. For example, consider a 5 X 10-3 M solution of O with V 100...
Fundamentals Of Theory For Voltammetric And Chronopotentiometric Methods
The theoretical treatments for the different voltammetric methods e.g., polarography, linear sweep voltammetry, and chronopotentiometry and the various kinetic cases generally follow the procedures described previously. The appropriate partial differential equations usually the diffusion equations modified to take account of the coupled reactions producing or consuming the species of interest are solved with the requisite initial and boundary conditions. For example, consider the ErQ reaction...
Major Symbols
Listed below are symbols used in several chapters or in large portions of a chapter. Symbols similar to some of these may have different local meanings. In most cases, the usage follows the recommendations of the IUPAC Commission on Electrochemistry R. Parsons et al., Pure Appl. Chem., 37, 503 1974 . however there are exceptions. A bar over a concentration or a current e.g., C0 x, s indicates the Laplace transform of the variable. The exception is when i indicates an average current in...
Rotating Disk Electrode
The rotating disk electrode RDE is one of the few convective electrode systems for which the hydrodynamic equations and the convective-diffusion equation have been solved rigorously for the steady state. This electrode is rather simple to construct and consists of a disk of the electrode material imbedded in a rod of an insulating material. For example, a commonly used form involves a platinum wire sealed in glass tubing with the sealed end ground smooth and perpendicularly to the rod axis....
Theory For Transient Voltammetry And Chronopotentiometry
We examine here the theoretical treatments for cyclic voltarnmetry and other transient techniques chronoamperometry, chronopotentiometry for a broad set of reaction schemes, all of which are introduced in Section 12.2. When one wants to investigate an electrochemical reaction scheme, one almost always turns first to CV. Although all transient methods can, in principle, explore the same i-E-t space to obtain the needed data, cyclic voltarnmetry allows one to see easily the effects of E and t on...
Basic Potential Step Methods
The next three chapters are concerned with methods in which the electrode potential is forced to adhere to a known program. The potential may be held constant or may be varied with time in a predetermined manner as the current is measured as a function of time or potential. In this chapter, we will consider systems in which the mass transport of elec-troactive species occurs only by diffusion. Also, we will restrict our view to methods involving only step-functional changes in the working...
DoubleLayer Capacitance and Charging Current in Electrochemical Measurements
Consider a cell consisting of an IPE and an ideal reversible electrode. We can approximate such a system with a mercury electrode in a potassium chloride solution that is also in contact with an SCE. This cell, represented by Hg K , CF SCE, can be approximated by an electrical circuit with a resistor, Rs, representing the solution resistance and a capacitor, C j, representing the double layer at the Hg K ,C1 interface Figure 1.2.5 .5 Since
Chronocoulometry
To this point, this chapter has concerned either current-time transients stimulated by potential steps or voltammograms constructed by sampling those curves. An alternative, and very useful, mode for recording the electrochemical response is to integrate the current, so that one obtains the charge passed as a function of time, Q t . This chronocoulometric mode was popularized by Anson 41 and co-workers and is widely employed in place of chronoamperometry because it offers important experimental...
Coupled Irreversible Chemical Reactions
When an irreversible chemical reaction is coupled to a nernstian electron transfer, the i-E curves can be used to provide kinetic information about the reaction in solution. Consider a nernstian charge-transfer reaction with a following first-order reaction where k is the rate constant in s_1 for the decomposition of R. Note that k could be a pseudo-first-order constant, such as when R reacts with protons in a buffered solution and k amp 'CH . As an example of this sequence, consider the...