A.J. Bard, L.R. Faulkner - Electrochemical methods - Fundamentals and Applications (794273), страница 13
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(a) What is El/2 (V vs. NHE)? (b) Sketch the expectedi-E curve for this system, (c) Sketch the "log plot" (see Figure 1.4.2b) for the system.1.8 Consider the system in Problem 1.7 under the conditions that a complexing agent, L~, which reactswith A 3 + according to the reactionA 3 + + 4L~ <± A L ^К = 10163+is added to the system.
For a solution at 25°C containing only 2.0 mM A and 0 . 1 M L " in excess3+inert electrolyte, answer parts (a), (b), and (c) in Problem 1.7. (Assume m0 is the same for A andAL4.)1.9 Derive the current-potential relationship under the conditions of Section 1.4.2 for a system where Ris initially present at a concentration C R and C o = 0. Consider both О and R soluble. Sketch theexpected i-E curve.1.10 Suppose a mercury pool of 1 cm 2 area is immersed in a 0.1 M sodium perchlorate solution.
Howmuch charge (order of magnitude) would be required to change its potential by 1 mV? How wouldthis be affected by a change in the electrolyte concentration to 10 M? Why?1.11 Rearrangement of equation 1.4.16 yields the following expression for / as a function of E, which isconvenient for calculating i—E curves for nernstian reactions:ilii = {1 + exp[(nF/RT)(E -El/2)]}-1(a) Derive this expression, (b) Consider the half-reaction Ru(NH3)£+ + e *± Ru(NH 3 )^ + .
The E°for this reaction is given in Appendix C. A steady-state i-E curve is obtained with a solution containing 10 mM Ru(NH 3 ) 6 + and 1 M KC1 (as supporting electrolyte). The working electrode is a Ptdisk of area 0.10 cm2 operating under conditions where m = 10~3 cm/sfor both Ru species. Use a spreadsheet program to calculate and plot the expected i-E curve.1.12 (a) Derive an expression for / as a function of E, analogous to that in Problem 1.11, from equation1.4.20, using (1.4.15) as the definition of Ец2, for use in solutions that contain both componentsof a redox couple, (b) Consider the same system as in Problem 1.11, but for a solution containing10 mM Ru(NH 3 )^ + and 5.0 mM Ru(NH 3 )^ + in 1M KC1.
Use a spreadsheet program to calculatethe i-E curve and plot the results, (c) What is 77conc at a cathodic current density of 0.48 mA/cm2?(d) Estimate Rmt.CHAPTER2POTENTIALSAND THERMODYNAMICSOF CELLSIn Chapter 1, we sought to obtain a working feeling for potential as an electrochemicalvariable. Here we will explore the physical meaning of that variable in more detail. Ourgoal is to understand how potential differences are established and what kinds of chemicalinformation can be obtained from them.
At first, these questions will be approachedthrough thermodynamics. We will find that potential differences are related to free energychanges in an electrochemical system, and this discovery will open the way to the experimental determination of all sorts of chemical information through electrochemical measurements. Later in this chapter, we will explore the mechanisms by which potentialdifferences are established. Those considerations will provide insights that will prove especially useful when we start to examine experiments involving the active control of potential in an electrochemical system.• 2.1 BASIC ELECTROCHEMICAL THERMODYNAMICS2.1.1ReversibilitySince thermodynamics can strictly encompass only systems at equilibrium, the concept ofreversibility is important in treating real processes thermodynamically. After all, the concept of equilibrium involves the idea that a process can move in either of two opposite directions from the equilibrium position.
Thus, the adjective reversible is an essential one.Unfortunately, it takes on several different, but related, meanings in the electrochemicalliterature, and we need to distinguish three of them now.(a) Chemical ReversibilityConsider the electrochemical cell shown in Figure l.l.lfe:+Pt/H2/H , СГ/AgCl/Ag(2.1.1)Experimentally, one finds that the difference in potential between the silver wire and theplatinum wire is 0.222 V when all substances are in their standard states. Furthermore, theplatinum wire is the negative electrode, and when the two electrodes are shorted together,the following reaction takes place:H 2 + 2AgCl -> 2Ag + 2H + + 2СГ(2.1.2)2.1 Basic Electrochemical Thermodynamics45If one overcomes the cell voltage by opposing it with the output of a battery or other direct current (dc) source, the current flow through the cell will reverse, and the new cell reaction is2Ag + 2H + + 2СГ -> H 2 + 2AgCl(2.1.3)Reversing the cell current merely reverses the cell reaction.
No new reactions appear, thusthe cell is termed chemically reversible.On the other hand, the systemZn/H + , SO|~/Pt(2.1.4)is not chemically reversible. The zinc electrode is negative with respect to platinum, anddischarging the cell causes the reactionZ n - ^ Z n 2 + + 2e(2.1.5)to occur there. At the platinum electrode, hydrogen evolves:Thus the net cell reaction is2H++2e^H2(2.1.6)Zn + 2H + -> H 2 + Z n 2 +(2.1.7)1By applying an opposing voltage larger than the cell voltage, the current flow reverses,but the reactions observed are2Н т + 2е ^ н(Zn electrode)2Н2 О - * ( } 2 +2 4Н + + 4е (Pt electrode)2Н2О ^ 2 Н 2 + о(Net)2(2.1.8)(2.1.9)(2.1.10)One has different electrode reactions as well as a different net process upon current reversal; hence this cell is said to be chemically irreversible.One can similarly characterize half-reactions by their chemical reversibility.
The reduction of nitrobenzene in oxygen-free, dry acetonitrile produces a stable radical anion ina chemically reversible, one-electron process:PhNO 2 + e<=±PhNO2T(2.1.11)The reduction of an aromatic halide, ArX, under similar conditions will often be chemically irreversible, since the radical anion product of the electron-transfer reaction rapidlydecomposes:ArX + e->Ar+X~"-(2.1.12)Whether or not a half-reaction exhibits chemical reversibility depends upon solution conditions and the time scale of the experiment.
For example, if the nitrobenzene reaction iscarried out in an acidic acetonitrile solution, the reaction will become chemically irreversible, because PhNO 2 ~ reacts with protons under these conditions. Alternatively, if thereduction of ArX is studied by a technique that takes only a very short time, then the reaction can be chemically reversible in that time regime:(2.1.13)lrThe net reaction will also occur without a flow of electrons in the external circuit, because H + in solution willattack the zinc.
This "side reaction," which happens to be identical with the electrochemical process, is slow ifdilute acid is involved.46 • Chapter 2. Potentials and Thermodynamics of Cells(b) Thermodynamic ReversibilityA process is thermodynamically reversible when an infinitesimal reversal in a drivingforce causes it to reverse direction. Obviously this cannot happen unless the system feelsonly an infinitesimal driving force at any time; hence it must essentially be always at equilibrium.
A reversible path between two states of the system is therefore one that connectsa continuous series of equilibrium states. Traversing it would require an infinite length oftime.A cell that is chemically irreversible cannot behave reversibly in a thermodynamicsense. A chemically reversible cell may or may not operate in a manner approaching thermodynamic reversibility.(c) Practical ReversibilitySince all actual processes occur at finite rates, they cannot proceed with strict thermodynamic reversibility. However, a process may in practice be carried out in such a mannerthat thermodynamic equations apply to a desired accuracy. Under these circumstances,one might term the process reversible.
Practical reversibility is not an absolute term; it includes certain attitudes and expectations an observer has toward the process.A useful analogy involves the removal of a large weight from a spring balance. Carrying out this process strictly reversibly requires continuous equilibrium; the "thermodynamic" equation that always applies iskx = mg(2.1.14)where k is the force constant, x is the distance the spring is stretched when mass m isadded, and g is the earth's gravitational acceleration.
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