A.J. Bard, L.R. Faulkner - Electrochemical methods - Fundamentals and Applications (794273), страница 51
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Because the system is reversible,one can rely on reversed electrolysis at the base potential imposed before each step to restore the initialconditions in each cycle. This point is discussed in Section 7.2.3.188Chapter 5. Basic Potential Step MethodsSubstituting (5.4.77) and (5.4.78) into (5.4.73), we obtaincE -F El 2'++RTnF l n- i(0l(5.4.79)L «(o jwithEM2 ~El -Цыкс-(5.4.80)cnFIt is clear now that the wave shape is the same as that for the simple redox processО + ne ^ R, but the location of the wave on the potential axis depends on Kc and C^, inaddition to the formal potential of the metal/amalgam couple.
For a given Kc, increasedconcentrations of the complexing agent shift the wave to more extreme potentials. In thespecific chemical example that we have been discussing, the effect of complexation byammonia is to stabilize Zn(II), that is, to lower the standard free energy of its predominantform. A consequence is that the change in free energy required for reduction of Zn(II) toZn(Hg) is made larger. Since this added energy must be supplied electrically, the wave isdisplaced to more negative potentials (Figure 5.4.2). The stronger the binding in the complex (i.e., the larger Kc), the larger the shift from the free metal potential E^.
Conveniently, Kc can be evaluated from this displacement:0'-(5.4.81)In a practice, E^ is usually identified with the voltammetric half-wave potential for themetal in a solution free of X, so that_JM_RTRTRT,-. r*ЛГ,, RTтм(5.4.82)From a plot of Eyy22 vs. In C^ one can determine the stoichiometric number p. Equation 5.4.80 shows that such a plot should have a slope of -pRT/nF. Much that is knownZn 2 + iniMKCI/^ _ — _1.0Zn 2 + in IMNH3+ IMNH4CI0.8Shift uponcomplexations 3 0.60.40.2n/I-0.8J I-1.01-1.2E/V vs.
SCE/Г/I-1.4-1.1Figure 5 A 2 Shift of a reversible wave upon complexation of the reactant. Left curve is thereduction wave for Zn 2 + in 1 M KC1 at a Hg electrode (EV2 = -1.00 V vs. SCE). Right curve is2+for Zn in 1 M NH 3 + 1 M NH4CI (E1/2 = -1.33 V vs. SCE). Complexation by ammonia lowersthe free energy of the oxidized form, so that it is no longer possible to reduce Zn(II) to the amalgamat the potentials of the wave recorded in the absence of ammonia.
By applying a more negativepotential, the combined free energy of Zn(II) plus the 2e on the electrode is elevated to match thatof Zn(Hg) and interconversion between Zn(II) and Zn(Hg) becomes possible.5.4 Sampled-Current Voltammetry for Reversible Electrode Reactions *4 189about the stoichiometry and stability constants of metal complexes has been determinedfrom voltammetric measurements of the kind suggested here.In the example just considered, the important feature was a shift in the wave positioncaused by selective chemical stabilization of one of the redox forms.
In a reversible system the potential axis is a free energy axis, and the magnitude of the shift is a direct measure of the free energy involved in the stabilization. These concepts are quite general andcan be used to understand many chemical effects on electrochemical responses. Any equilibrium in which either redox species participates will help to determine the wave position, and changes in concentrations of secondary participants in those equilibria (e.g.,ammonia in the example above) will cause an additional shift in the half-wave potential.This state of affairs may seem confusing at first, but the principles are not complicatedand are very valuable:1. If the reduced form of a redox couple is chemically bound in an equilibriumprocess, then the reduced form has a lowered free energy relative to the situation where the binding is not present.
Reduction of the oxidized form consequently becomes energetically easier, and oxidation of the reduced formbecomes more difficult. Therefore, the voltammetric wave shifts in a positivedirection by an amount reflecting the equilibrium constant (i.e., the change instandard free energy) for the binding process and the concentration of the binding agent.2.If the oxidized form is chemically bound in an equilibrium process, then the oxidized form is stabilized. It becomes energetically easier to produce this speciesby oxidation of the reduced form, and it becomes harder to reduce the oxidizedform.
Accordingly, the voltammetric wave shifts in a negative direction by a degree that depends on the equilibrium constant for the binding process and theconcentration of the binding agent. This is the situation that we encountered inthe example involving Zn(NH3)4+ just above (Figure 5.4.2).3o Increasing the concentration of the binding agent enlarges the equilibrium fraction of bound species, therefore the increase reinforces the basic effect and enhances the shift in the wave from its original position. We saw this feature in theexample given above when we found that there is a progressive negative shift inthe voltammetric wave for reduction of Zn(II) as the ammonia concentration iselevated.4.Secondary equilibria can also affect the wave position in ways that can be interpreted within the framework of these first three principles. For example, theavailability of ammonia in the buffer considered above is affected by the pH.
Ifthe pH were changed by adding HC1, the concentration of free ammonia wouldbe lessened. Thus the added acid would tend to lower the fraction of complexation and would consequently cause a positive shift in the wave from its positionbefore the change of pH, even though neither H + nor Cl~ is involved directly inthe electrode process.5.When both redox forms engage in binding equilibria, both are stabilized relativeto the situation in which the binding processes are absent. The effects tend to offset each other.
If the free energy of stabilization were exactly the same on bothsides of the basic electron-transfer process, there would be no alteration of thefree energy required for either oxidation or reduction, and the wave would notshift. If the stabilization of the oxidized form is greater, then the wave shifts inthe negative direction, and vice versa.Chapter 5. Basic Potential Step MethodsA very wide variety of binding chemistry can be understood and analyzed withinthis framework. Obvious by the prior example is complexation of metals. Another casethat we will soon encounter is the formation of metal amalgams, which produces usefulpositive shifts in waves for analytes of interest in polarography (Section 7.1.3). Generally important are acid-base equilibria, which affect many inorganic and organic redoxspecies in protic media.
The principles discussed here are also valid in systems involvingsuch diverse phenomena as dimerization, ion pairing, adsorptive binding on a surface,coulombic binding to a polyelectrolyte, and binding to enzymes, antibodies, or DNA.Detailed treatments like the one developed for the zinc-ammonia system are easilyworked out for other types of electrode reactions, includingО + mH + + ne «± R + H 2 OО + ne *± R(adsorbed)(Problem 5.7)(Chapter 14)Similar treatments can be developed for systems which do not involve the binding phenomena emphasized here, but which differ from the simple process О + ne ^ R and yetremain reversible.
Such examples include30 + ne<±RО + ne <± R(insoluble)(Problem 5.13)(Problem 5.5)Details are often available in references on polarography and voltammetry (28-30).Reversible systems have the advantage of behaving as though all chemical participants are at equilibrium, thus they can be treated by any set of equilibrium relationshipslinking the species that define the oxidized and reduced states of the system. It is not important to treat the system according to an accurate mechanistic path, because the behavior is controlled entirely by free energy changes between initial and final states, and themechanism is invisible to the experiment. In the case involving the zinc ammine complexdiscussed above, we formulated the chemistry as though the complex would become reduced by dissociating to produce Zn(II), which then would undergo conversion to theamalgam. This sequence probably does not describe the events in the real electrodeprocess, but it offers a convenient thermodynamic cycle based on quantities that we canmeasure easily in other experiments, or perhaps even find in the literature.In practical chemical analysis, one can obviously use half-wave potentials to identifythe species giving rise to the observed waves; however the foregoing paragraphs illustratethe fact that the wave for a given species, such as Zn(II) can be found in different positions under different conditions.
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