A.J. Bard, L.R. Faulkner - Electrochemical methods - Fundamentals and Applications (794273), страница 80
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From these values, determinea, and k°f (i.e., the value of kf at E = 0.0 V vs. NHE). (b) Use the treatment of Meites and Israel toobtain the same information, (c) Calculate CQ(0, t) for each /. Plot C o (0, t) as a function of potential. On the same graph plot the i values listed above.7.3 Consider a material A, which can be reduced at a dropping mercury electrode to form B. A 1-mMsolution of A in acetonitrile shows a wave with Ещ at -1.90 V vs.
SCE. The wave slope is 60.5mV at 25°C and (/) m a x = 2.15 in the usual units. When dibenzo-15-crown-5 is added to the solution,the polarographic behavior changes.Dibenzo-15-crown-5 (C)304Chapter 7. Polarography and Pulse VoltammetryThe following observations were made:Concentration of C, M-31010 - 210 - 1Em, VWave Slope, mV(/)„-2.15-2.21-2.2760.359.859.82.032.022.04What interpretation can be made of these results? Can any thermodynamic data be derived from thedata? Can you suggest the identity of species A?7.4 A polarogram of molecular oxygen in air-saturated 0.1 M KNO 3 is like that of Figure 5.6.2.
The=concentration of O 2 is about 0.25 mM. At E = -0.4 V vs. SCE, (/a)max 3.9 fiA, r m a x = 3.8 s, andm= 1.85 mg/s. At E = -1.1 У vs. SCE, (/ d ) m a x = 6.5 fiA, r m a x = 3.0 s, and m = 1.85 mg/s. Calculate (/) max at each potential. Is the ratio of the two values what you expect? Explain any discrepancyin chemical terms.
Calculate the diffusion coefficient for O 2 using the more appropriate constant.Defend your choice of the two.7.5 Consider an analysis for the toxic ion T1(I) in waste water that also contains Pb(II) and Zn(II) in 10to 100-fold excesses. Outline any obstacles that would impede a polarographic determination andsuggest means for circumventing them without implementing separation techniques.
For 0.1 M KC1,£1/2(T1+/T1) = -0.46 V, £ 1/2 (Pb 2+ /Pb) = -0.40 V, and £ 1/2 (Zn 2+ /Zn) = -0.995 V vs. SCE.7.6 Sketch the normal pulse voltammogram expected for a substance undergoing an irreversible electrode reaction at a gold disk (e.g., O 2 —> H 2 O 2 in 1 M KC1). Assume that the reduced form is not initially present and that no electrolysis occurs at the base potential in the starting solution. Explain theshape of the trace.
(Note that the location of the trace on the potential axis is not of interest here.)Do the same for the case in which the electrode reaction is reversible. How would the curves differif the disk were rotated during the recording of the polarograms?7.7 (a) Show that the derivative of a reversible sampled-current voltammetric wave isdidE_ n2F2AC*1/2 1/2RTTT Tgfl(1 +{в)2(b) Show that (7.3.19) approaches this form for 61/ДЯ « di/dE as A£ -» 0.8CONTROLLED-CURRENTTECHNIQUES8.1 INTRODUCTIONWe discussed in Chapters 5-7 methods in which the potential of an electrode was controlled (or was the independent variable), while the current (the dependent variable) wasdetermined as a function of time.
In this chapter we consider the opposite case, where thecurrent is controlled (frequently held constant), and the potential becomes the dependentvariable, which is determined as a function of time. The other conditions assumed inChapters 5-7, such as small ratio of electrode area to solution volume and semi-infinitediffusion, are also assumed here. We do not treat UMEs, because the behavior in thesteady-state regime is not a function of whether the applied signal is a controlled potential or current. The experiment is carried out by applying the controlled current betweenthe working and auxiliary electrodes with a current source (called a galvanostai) andrecording the potential between the working and reference electrodes (e.g., with arecorder, oscilloscope, or other data acquisition device) (Figure 8.1.1). These techniquesare generally called chronopotentiometric techniques, because E is determined as a function of time, or galvanostatic techniques, because a small constant current is applied tothe working electrode.8.1.1 Comparison with Controlled-Potential MethodsSince the general aspects of controlled-potential and controlled-current experimentsare so similar, we might consider the basic differences between the two types of experiments and the relative advantages of each.
The instrumentation for controlled-currentexperiments is simpler than the potentiostats required in controlled-potential ones,since no feedback from the reference electrode to the control device is required. Although constant-current sources constructed from operational amplifiers are frequentlyused, a simple circuit employing a high-voltage power supply (e.g., a 400-V powersupply or several 90-V batteries) and a large resistor can be adequate.
The mathematical treatment also differs from what we have already seen. In controlled-current exper-1Controlledcurrentsource1f^ J RefT WorkingPotential-recordingdeviceFigure 8.1.1 Simplified blockdiagram of apparatus forchronopotentiometricmeasurements.305306Chapter 8. Controlled-Current Techniquesiments, the surface boundary condition is based on the known current or fluxes (i.e.,the concentration gradients) at the electrode surface, while in controlled-potentialmethods, the concentrations at x = 0 (as functions of E) provide the boundary conditions. Usually the mathematics involved in solving the diffusion equations in controlled-current problems are much simpler, and closed-form analytical solutions areusually obtained.A fundamental disadvantage of controlled-current techniques is that double-layercharging effects are frequently larger and occur throughout the experiment in such a waythat correction for them is not straightforward.
Treating data from multicomponent systems and step wise reactions is also more complicated in controlled-current methods, andthe waves observed in E-t transients are usually less well-defined than those of potentialsweep i-E curves.Controlled-current methods can be of particular value when the process being studiedis the background process, such as solvated electron formation in liquid ammonia or reduction of quaternary ammonium ion in an aprotic solvent.
A simple method for determinationof the thickness of metal films is by anodic stripping at constant current. Working withbackground processes in a controlled-potential mode is often difficult.8.1.2Classification and Qualitative DescriptionDifferent types of constant-current techniques are illustrated in Figure 8.1.2.
Let us firstconsider constant-current chronopotentiometry (Figure 8.1.2a) in the context of the anthracene (An) system used as an example in Section 5.1.1. The steady current, /, appliedto the electrode causes the anthracene to be reduced at a constant rate to the anion radical, An7.
The potential of the electrode moves to values characteristic of the couple andvaries with time as the An/An7 concentration ratio changes at the electrode surface. Theprocess can be regarded as a titration of the An in the vicinity of the electrode by thecontinuous flux of electrons, resulting in an E-t curve like that obtained for a potentiometric titration (E as a function of titrant added, i-i). Eventually, after the concentrationof An drops to zero at the electrode surface, the flux of An to the surface is insufficient toaccept all of the electrons being forced across the electrode-solution interface.
The potential of the electrode will then rapidly shift toward more negative values until a new,second reduction process can start. The time after application of the constant currentwhen this potential transition occurs is called the transition time, r. It is related to theconcentration and the diffusion coefficient and is the chronopotentiometric analogue ofthe peak or limiting current in controlled-potential experiments. The shape and locationof the E-t curve is governed by the reversibility, or the heterogeneous rate constant, ofthe electrode reaction.Instead of a constant current, one can apply a current that varies as a known functionof time (e.g., / = fit, a current ramp; Figure 8.1.2/?). Although this technique, called programmed current chronopotentiometry, can be treated theoretically with little difficulty, ithas been employed infrequently. The current can also be reversed after some time (current reversal chronopotentiometry, Figure 8.1.2c).
For example, if in the case consideredabove, the current is suddenly changed to an anodic current of equal magnitude at, or before, the transition time, the An7formed during the forward step will start oxidizing.The potential will move in a positive direction as the An/An7 concentration ratio increases. When the An7 concentration falls to zero at the electrode surface, a potential transition toward positive potentials occurs, and a reverse transition time can be measured. Inan extension of this technique the current can be continuously reversed at each transition,resulting in cyclic chronopotentiometry (Figure 8.1.2d). Finally, as in the treatment of8.2 General Theory of Controlled-Current Methods < 307ResponseExcitationFigure 8.1.2 Different typesof controlled-current techniques.(a) Constant-currentchronopotentiometry.(b) Chronopotentiometry withlinearly increasing current.(c) Current reversalchronopotentiometry.(d) Cyclic chronopotentiometry.(с)Е(d)controlled-potential data, the derivatives of the E-t curves can be obtained or differential1methods can be employed.8.2 GENERAL THEORY OF CONTROLLEDCURRENT METHODS8.2.1Mathematics of Semi-Infinite Linear DiffusionWe again consider the simple electron-transfer reaction, О + ne —> R.
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