A.J. Bard, L.R. Faulkner - Electrochemical methods - Fundamentals and Applications (794273), страница 4
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In Section 1.4 and in laterchapters, we will be more quantitative. We first might consider simply the potential wewould measure when a high impedance voltmeter (i.e., a voltmeter whose internal resistance is so high that no appreciable current flows through it during a measurement) isplaced across the cell. This is called the open-circuit potential of the cell.1For some electrochemical cells, like those in Figure 1.1.1, it is possible to calculatethe open-circuit potential from thermodynamic data, that is, from the standard potentialsof the half-reactions involved at both electrodes via the Nernst equation (see Chapter 2).The key point is that a true equilibrium is established, because a pair of redox formslinked by a given half-reaction (i.e., a redox couple) is present at each electrode.
In Figure1.1.1/?, for example, we have H + and H 2 at one electrode and Ag and AgCl at the other.2The cell in Figure 1.1.3 is different, because an overall equilibrium cannot be established. At the Ag/AgBr electrode, a couple is present and the half-reaction isAgBr + e ±± Ag + Br= 0.0713 Vvs. NHE(1.1.6)Since AgBr and Ag are both solids, their activities are unity. The activity of Br can befound from the concentration in solution; hence the potential of this electrode (with respect to NHE) could be calculated from the Nernst equation.
This electrode is at equilibrium. However, we cannot calculate a thermodynamic potential for the Pt/H+,Br~electrode, because we cannot identify a pair of chemical species coupled by a given halfreaction. The controlling pair clearly is not the H2,H+ couple, since no H 2 has been introduced into the cell. Similarly, it is not the O 2 ,H 2 O couple, because by leaving O 2 out ofthe cell formulation we imply that the solutions in the cell have been deaerated. Thus, thePt electrode and the cell as a whole are not at equilibrium, and an equilibrium potential*In the electrochemical literature, the open-circuit potential is also called the zero-current potential or the restpotential.2When a redox couple is present at each electrode and there are no contributions from liquid junctions (yet to bediscussed), the open-circuit potential is also the equilibrium potential.
This is the situation for each cell inFigure 1.1.1.Chapter 1. Introduction and Overview of Electrode Processesdoes not exist. Even though the open-circuit potential of the cell is not available fromthermodynamic data, we can place it within a potential range, as shown below.Let us now consider what occurs when a power supply (e.g., a battery) and a microammeter are connected across the cell, and the potential of the Pt electrode is mademore negative with respect to the Ag/AgBr reference electrode. The first electrode reaction that occurs at the Pt is the reduction of protons,+2H + 2 e - * H 2(1.1.7)The direction of electron flow is from the electrode to protons in solution, as in Figure1.12a, so a reduction (cathodic) current flows. In the convention used in this book, ca3thodic currents are taken as positive, and negative potentials are plotted to the right.
Asshown in Figure 1.1.4, the onset of current flow occurs when the potential of the Pt elec+trode is near E° for the H /H 2 reaction (0 V vs. NHE or -0.07 V vs. the Ag/AgBr electrode). While this is occurring, the reaction at the Ag/AgBr (which we consider thereference electrode) is the oxidation of Ag in the presence of Br~ in solution to formAgBr. The concentration of Br~ in the solution near the electrode surface is not changedappreciably with respect to the original concentration (1 M), therefore the potential of theAg/AgBr electrode will be almost the same as at open circuit. The conservation of chargerequires that the rate of oxidation at the Ag electrode be equal to the rate of reduction atthe Pt electrode.When the potential of the Pt electrode is made sufficiently positive with respect to thereference electrode, electrons cross from the solution phase into the electrode, and the oxPt/H+, ВГ(1 M)/AgBr/AgCathodic11I11.5Onset of H +reduction on Pt.\i: /\y-0.50/\1 \//LOnset of Br"oxidation on PtCell PotentialAnodicFigure 1.1.4 Schematic current-potential curve for the cell Pt/H + , Br~(l M)/AgBr/Ag, showingthe limiting proton reduction and bromide oxidation processes.
The cell potential is given for the Ptelectrode with respect to the Ag electrode, so it is equivalent to £ P t (V vs. AgBr). Since ^Ag/AgBr =0.07 V vs. NHE, the potential axis could be converted to EPt (V vs. NHE) by adding 0.07 V to eachvalue of potential.3The convention of taking / positive for a cathodic current stems from the early polarograhic studies, wherereduction reactions were usually studied. This convention has continued among many analytical chemists andelectrochemists, even though oxidation reactions are now studied with equal frequency. Otherelectrochemists prefer to take an anodic current as positive.
When looking over a derivation in the literatureor examining a published i-E curve, it is important to decide, first, which convention is being used (i.e.,"Which way is up?").1.1 Introduction7idation of Br~ to Br2 (and Br^~) occurs. An oxidation current, or anodic current, flows atpotentials near the E° of the half-reaction,Br2 + 2 e ^ 2 B r ~(1.1.8)which is +1.09 V vs.
NHE or +1.02 V vs. Ag/AgBr. While this reaction occurs (rightto-left) at the Pt electrode, AgBr in the reference electrode is reduced to Ag and Br~ isliberated into solution. Again, because the composition of the Ag/AgBr/Br~ interface(i.e., the activities of AgBr, Ag, and Br~) is almost unchanged with the passage of modestcurrents, the potential of the reference electrode is essentially constant.
Indeed, the essential characteristic of a reference electrode is that its potential remains practically constantwith the passage of small currents. When a potential is applied between Pt and Ag/AgBr,nearly all of the potential change occurs at the Pt/solution interface.The background limits are the potentials where the cathodic and anodic currents startto flow at a working electrode when it is immersed in a solution containing only an electrolyte added to decrease the solution resistance (a supporting electrolyte). Moving thepotential to more extreme values than the background limits (i.e., more negative than thelimit for H2 evolution or more positive than that for Br2 generation in the example above)simply causes the current to increase sharply with no additional electrode reactions, because the reactants are present at high concentrations.
This discussion implies that one canoften estimate the background limits of a given electrode-solution interface by considering the thermodynamics of the system (i.e., the standard potentials of the appropriate halfreactions). This is frequently, but not always, true, as we shall see in the next example.From Figure 1.1.4, one can see that the open-circuit potential is not well defined inthe system under discussion. One can say only that the open-circuit potential lies somewhere between the background limits.
The value found experimentally will dependupon trace impurities in the solution (e.g., oxygen) and the previous history of the Ptelectrode.Let us now consider the same cell, but with the Pt replaced with a mercury electrode:Hg/H + ,Br-(l M)/AgBr/Ag(1.1.9)We still cannot calculate an open-circuit potential for the cell, because we cannot define aredox couple for the Hg electrode. In examining the behavior of this cell with an appliedexternal potential, we find that the electrode reactions and the observed current-potentialbehavior are very different from the earlier case.
When the potential of the Hg is madenegative, there is essentially no current flow in the region where thermodynamics predictthat H2 evolution should occur. Indeed, the potential must be brought to considerablymore negative values, as shown in Figure 1.1.5, before this reaction takes place.
The thermodynamics have not changed, since the equilibrium potential of half-reaction 1.1.7 is independent of the metal electrode (see Section 2.2.4). However, when mercury serves asthe locale for the hydrogen evolution reaction, the rate (characterized by a heterogeneousrate constant) is much lower than at Pt. Under these circumstances, the reaction does notoccur at values one would predict from thermodynamics. Instead considerably higherelectron energies (more negative potentials) must be applied to make the reaction occur ata measurable rate.
The rate constant for a heterogeneous electron-transfer reaction is afunction of applied potential, unlike one for a homogeneous reaction, which is a constantat a given temperature. The additional potential (beyond the thermodynamic requirement)needed to drive a reaction at a certain rate is called the overpotential. Thus, it is said thatmercury shows "a high overpotential for the hydrogen evolution reaction."When the mercury is brought to more positive values, the anodic reaction and the potential for current flow also differ from those observed when Pt is used as the electrode.8 • Chapter 1. Introduction and Overview of Electrode ProcessesHg/I-Г, ВГ(1 M)/AgBr/AgCathodicOnset of H +reduction ,0.5-1.5-0.5Onset of HgoxidationAnodicPotential (V vs.
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