A.J. Bard, L.R. Faulkner - Electrochemical methods - Fundamentals and Applications (794273), страница 85
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The change in the open-circuit potential, AEb andits relaxation with time are used to obtain kinetic information about the electrode reaction. A number of different phenomena come into play to cause the potential shift withtemperature (e.g., temperature dependence of the double-layer capacitance and the Soretpotential arising from the temperature gradient between the electrode and the bulk electrolyte), but the response can be treated by a general master equation (40):AEt = atsi* + kmb P exp[-* m (f - r)] AT? dr(8.7.15)Jowhere AT?is the temperature change normalized by a factor that accounts for heat lossesand temperature distribution, aATfrepresents the initial potential response in the absenceof interfacial electron transfer, and the second term accounts for the electron-transfer relaxation and its associated rate constant, km. The time dependence of the temperaturechange can be treated by a least-squares procedure to extract values of a, b, and km.
Thisapproach has been used, for example, to measure the effect of alkyl chain length in amixed organized film of alkyl thiols, some with ferrocene terminations (see Section14.5.2), on the rate of electron transfer from the ferrocene moiety, where km values on theorder of 107-108 s" 1 were found (43).Digital Scope1 •-./ 1 DiffuserNDLaserFigure 8.7.5 Schematic diagram of apparatus employed for the temperature-jump method. Thelaser pulse is passed through a neutral density filter (ND) and irradiates the thin film electrode at thebottom of the cell. The dark rectangles are an auxiliary electrode and a QRE for measurement ofthe potential change.
The potentiostat (Pot.), which adjusts the electrode potential beforeirradiation, is disconnected immediately before the laser pulse. The change in potential is measuredwith a fast amplifier (Amp.). [Reprinted from J. F. Smalley, L. Geng, S. W. Feldberg, L. C. Rogers,and J. Leddy, /. Electroanal. Chem., 356, 181 (1993), with permission from Elsevier Science.]328Chapter 8. Controlled-Current Techniques8.8 REFERENCES1. H. J. S. Sand, Phil. Mag., 1, 45 (1901).2.
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W. Feldberg, C. E. D. Chidsey,M. R. Linford, M. D. Newton, and Y. P. Liu,/. Phys. Chem., 99, 13141 (1995).8.9 PROBLEMS8.1 Derive equation 8.3.13 under the assumptions given in the text.8.2 For current reversal chronopotentiometry involving the forward reduction of a species О under conditions of semi-infinite linear diffusion, the reverse transition time can be made equal to forward3298.9 Problemselectrolysis time by a proper choice of currents during the forward (reduction) reaction, /f, and thereverse (oxidation) reaction, ir. Find the ratio if/ir that will yield, r r = tf.8.3 An analyst determines a mixture of lead and cadmium at a mercury pool cathode by chronopoten2+tiometry.
In the cell used in the determination, a 1.00 mM solution of P b reduced at a current of2+273 mA yielded т - 25.9 s and Ет/4 = -0.38 V vs. SCE. A 0.69 mM solution of Cd reduced with a2+current of 136 mA gave т = 42.0 s and £ т/4 = —0.56 V vs. SCE. An unknown mixture of P b and2+Cd reduced at a current of 56.5 mA produced a double wave, with r\ = 7.08 s and r 2 = 7.00 s.
Cal2+2+culate the concentrations of P b and Cd in the mixture. Neglect double-layer and other background effects.28.4 Show that if one uses programmed current chronopotentiometry with i(t) = /3/^ , then the stepwisereduction of a substance with щ = п^ gives т\ = т 2 .8.5 Examine the results in Figure 8.4.1. Estimate the transition times and work up the data to yield information about the electrode reaction.8.6 Consider the circuit in Figure 8.9.1, which is characteristic of that used for the injection of charge ina coulostatic experiment.
Сщ is initially charged completely with a 10-V battery. At equilibrium,after the switch is closed, how much charge will reside on Q and on Cmfl About how long will ittake to charge C$8.7 Solve (8.7.6) by the Laplace transform method to yield (8.7.7).8.8 Derive the equation for the large-step coulostatic response in the diffusion limited region, analogousto (8.7.14), for a spherical indicator electrode.8.9 Consider a 1 mM solution of cadmium in 0.1 M HC1, which is being examined coulostatically at ahanging mercury drop 0.05 cm 2 in area. The formal potential for the Cd 2+ /Cd(Hg) couple is —0.61V vs.
SCE. Suppose the electrode is initially at rest at —0.4 V vs. SCE, then a sufficient charge isapplied to shift its potential instantaneously to —1.0 V vs. SCE. Assume the differential and integraldouble-layer capacitances to be 10 /iF/cm2. How much charge is required for the initial potentialexcursion? How long would it take for the potential to fall back to -0.9 V after the charge injection? Take D = 10" 5 cm2/s.8.10 Barker et al. [Faraday Disc.
Chem. Soc, 56, 41 (1974)] performed experiments in which 15-nspulses from a frequency-doubled ruby laser were used to illuminate a mercury pool working electrode. Each light pulse caused ejection of electrons from the electrode. Ejected electrons seem totravel about 50 A before becoming solvated and available for reaction.When electrons are emitted into a solution of N 2 O in water containing 1 M KC1, the followingreaction occurs:ещN 2 O + H2O -> OH- + N 2 + OHThe hydroxyl radicals are easily reduced at the electrode at potentials more negative than — 1.0 Vvs. SCE., = 100Q100200Time after flash, nsecFigure 8.9.1Figure 8.9.2300330 » Chapter 8.
Controlled-Current TechniquesThe response of the illuminated working electrode to the flash is followed coulostatically.Curves like those shown in Figure 8.9.2 can be obtained. Explain their shapes. AE is measured withrespect to the initial potential.8.11 Barker's technique (Problem 8.10) can also be used to create hydrogen atoms and to study theirelectrochemistry. The reaction producing them in acid media isInvestigators studying the hydrogen discharge reaction have often suggested that H* is an intermediate and that hydrogen gas is produced by reducing it further in a fast heterogeneous process:+(H-)free + e + H 3 O -^ H 2 + H 2 O(a)or(H-)ads + e + H 3 0 + " ^ H 2 + H 2 0Whether H* is free or adsorbed has been debated.
Barker addressed the question by comparing, ineffect, the rate of H- electroreduction to the rate of its homogeneous reaction with ethanol (leadingto electroinactive products). He found [Ber. Bunsenges. Phys. С hem., 75, 728 (1971)] that the fraction of H* undergoing electroreduction was independent of potential from —0.9 V to —1.3 V vs.SCE. What do his observations tell us about the choice between (a) and (b)?CHAPTER9METHODS INVOLVINGFORCED CONVECTION—HYDRODYNAMICMETHODS9.1 INTRODUCTIONThere are many electrochemical techniques in which the electrode moves with respectto the solution. These involve systems where the electrode is itself in motion (e.g., rotating disks, rotating wires, streaming mercury electrodes, rotating mercury electrodes,vibrating electrodes) or ones where there is forced solution flow past a stationary electrode (conical, tubular, screen, and packed-bed electrodes in fluid streams, channelelectrodes, bubbling electrodes).
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