A.J. Bard, L.R. Faulkner - Electrochemical methods - Fundamentals and Applications (794273), страница 40
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Equation 4.3.1 holds, with migration in this case being in thesame direction as diffusion.For mixtures of charged species, the fraction of current carried by the 7th species is Ц\and the amount of the total current, /, carried by theyth species is t}i. The number of molesof the 7th species migrating per second is tf/zjF. If this species is undergoing electrolysis,the number of moles electrolyzed per second is \tji\/nF, while the number of moles arriving at the electrode per second by migration is ± im/nF, where the positive sign applies toreduction of 7, and the negative sign pertains to oxidation.
Thus,/±J^td= -1=nF(4.3.2)zfor(4.3.3)im=±\t-jFrom equation 4.3.1,(4-3.4)(4.3.5)where the minus sign is used for cathodic currents and the positive sign for anodic currents. Note that both / and z} are signed.In this simplified treatment, we assume that the transference numbers are essentiallythe same in the bulk solution and in the diffusion layer near an electrode. This will be truewhen the concentrations of ions in the solution are high, so that only small fractionalchanges in local concentration are caused by the electrolytic generation or removal ofions.
This condition is met in most experiments. If the electrolysis significantly perturbsthe ionic concentrations in the diffusion layer compared to those in the bulk solution, theЦ values clearly will differ, as shown by equation 4.2.10 (12).Example 423+3Consider the electrolysis of a solution of 10" M Cu(NH 3 )| , 10" M Cu(NH 3 )J, and 33X 10~ M Cl~ in 0.1 M NH 3 at two Hg electrodes (Figure 43.3a). Assuming the limitingequivalent conductances of all ions are equal, that is,^Cu(II)=^Cu(I)=^Cl-=^(4.3.6)==we obtain the following transference numbers from (4.2.10): fcu(ii) 1/3, ^cu(i) 1/6 and=*ci~1/2- With an arbitrary current of 6e per unit time being passed, the migration current in bulk solution is carried by movement of one Cu(II) and one Cu(I) toward the cathode, and three Cl~ toward the anode.
The total balance sheet for this system is shown inFigure 4.3.3/7. At the cathode, one-sixth of the current for the electrolysis of Cu(II) is provided by migration and five-sixths by diffusion. The NH 3 , being uncharged, does not con-4.3 Mixed Migration and Diffusion Near an Active Electrode31433-Hg/Cu(NH3)4CI2(1 (Г М), Cu(NH3)2 С1(1(Г М), NH 3 (0.1 M)/Hg(a)Q(Cathode)6Cu(II) + 6e -» 6Cu(I)6Cu(II)6Cu(II)6Cu(I)6Cu(I)(Anode)6CU(I) - 6e -> 6CU(II)3d"diffusiondiffusion5Cu(II)5Cu(II)7Cu(I)7Cu(I)ЗСГЗСГFigure 4.3.3 Balance sheet for electrolysis of the Си(П), Cu(I), NH3 system, (a) Cell schematic.(b) Various contributions to the current when 6e are passed in the external circuit per unit time;/ = 6, n = 1.
For Cu(II) at the cathode, |i m | = (l/2)(l/3)(6) = 1 (equation 4.3.3), /d = 6 - 1 = 5(equation 4.3.4). For Cu(I) at the anode, |/J = (l/l)(l/6)(6) = 1, /d = 6 + 1 = 7.tribute to the carrying of the current, but serves only to stabilize the copper species in the+1 and + 2 states. The resistance of this cell would be relatively large, since the total concentration of ions in the solution is small.4.3.2 Effect of Adding Excess ElectrolyteExample 43Let us consider the same cell as in Example 4.2, except with the solution containing 0.10M NaClO 4 as an excess electrolyte (Figure 4.3.4a).
Assuming that ANa+ = А с ю ^ = ^»we obtain the following transference numbers: tNa+ = ^107 » = 0.485, fcu(n) = 0.0097,*Cu(D = °- 0 0 4 8 5 > 'ci- = 0.0146. The N a + and СЮ4 do not participate in the electrontransfer reactions; but because their concentrations are high, they carry 97% of thecurrent in the bulk solution. The balance sheet for this cell (Figure 4.3.4Z?) shows thatmost of the Cu(II) now reaches the cathode by diffusion, and only 0.5% of the totalflux is by migration.Thus, the addition of an excess of nonelectroactive ions (a supporting electrolyte)nearly eliminates the contribution of migration to the mass transfer of the electroactivespecies.
In general, it simplifies the mathematical treatment of electrochemical systems byelimination of the Чф or дф/дх term in the mass transport equations (e.g., equations 4.1.10and 4.1.11).In addition to minimizing the contribution of migration, the supporting electrolyteserves other important functions.
The presence of a high concentration of ions decreases144Chapter 4. Mass Transfer by Migration and DiffusionЭ• Hg/Cu(NH3)4CI2(10~3 M), Cu(NH3)2 CI(10~3 M)/Hg NH 3 (0.1 M), NaCIO4 (0.10 M)Cu(NH 3 )f (10- 3 M), Cu(NH3)2 (10- 3 M),Ions in cell:СГ(3 x 10~3 M), Na + (0.1 M), CIO4 (0.1 M)Г\(Cathode)Q(Anode)6e6Cu(II) + 6e -» 6Cu(I)6Cu(I) - 6e -> 6Cu(II)6Cu(II)6Cu(I)2.91 Na +2.91 CIO70.0291 Cu(II)0.0291 Cu(I)0.0873 СГdiffusiondiffusion5.97Cu(II)5.97Cu(II)6.029Cu(I)2.92Na +2.92Na+2.92CIO42.92CIO4(b)Figure 4.3.4 Balance sheet for the system in Figure 4.3.3, but with excess NaC104 as a supportingelectrolyte, (a) Cell schematic, (b) Various contributions to the current when 6e are passed in theexternal circuit per unit time (/ = 6, n = 1). fCu(II) = [(2 X 10 ~ 3 ) A/(2 X 1(Г 3 + 1(Г 3 + 3 X 1(Г 30.2)Л] = 0.0097.
For Си(П) at the cathode, |/J = (l/2)(0.0097)(6) = 0.03, i d = 6 - 0.03 = 5.97.the solution resistance, and hence the uncompensated resistance drop, between the working and reference electrodes (Section 1.3.4). Consequently, the supporting electrolyte allows an improvement in the accuracy with which the working electrode's potential iscontrolled or measured (Chapter 15). Improved conductivity in the bulk of the solutionalso reduces the electrical power dissipated in the cell and can lead to important simplifications in apparatus (Chapters 11 and 15). Beyond these physical benefits are chemicalcontributions by the supporting electrolyte, for it frequently establishes the solution composition (pH, ionic strength, ligand concentration) that controls the reaction conditions(Chapters 5, 7, 11, and 12).
In analytical applications, the presence of a high concentration of electrolyte, which is often also a buffer, serves to decrease or eliminate sample matrix effects. Finally, the supporting electrolyte ensures that the double layer remains thinwith respect to the diffusion layer (Chapter 13), and it establishes a uniform ionic strengththroughout the solution, even when ions are produced or consumed at the electrodes.Supporting electrolytes also bring some disadvantages.
Because they are used insuch large concentrations, their impurities can present serious interferences, for example,4.3 Mixed Migration and Diffusion Near an Active Electrode25Ii145Ia_20 -15 -10 О5 --0.6//77//JJI-0.8I-1.0E/Vbс _di-1.2-1.4Figure 4.3.5 Voltammograms for reduction of 0.65 mM T12SO4 at a mercury film on a silverultramicroelectrode (radius, 15 jam) in the presence of (a) 0, (b) 0.1, (c) 1, and (d) 100 mM LiClO4.The potential was controlled vs. a Pt wire QRE whose potential was a function of solutioncomposition.
This variability is the basis for the shifts in wave position along the potential axis.[Reprinted with permission from M. Ciszkowska and J. G. Osteryoung, Anal. С hem., 67, 1125(1995). Copyright 1995, American Chemical Society.]by giving rise to faradaic responses of their own, by reacting with the intended productof an electrode process, or by adsorbing on the electrode surface and altering kinetics.Also, a supporting electrolyte significantly alters the medium in the cell, so that its properties differ from those of the pure solvent.
The difference can complicate the comparison of results obtained in electrochemical experiments (e.g., thermodynamic data) withdata from other kinds of experiments where pure solvents are typically employed.Most electrochemical studies are carried out in the presence of a supporting electrolyte selected for the solvent and electrode process of interest. Many acids, bases, andsalts are available for aqueous solutions. For organic solvents with high dielectric constants, like acetonitrile and N,N-dimethylformamide, normal practice is to employ tetraл-alkylammonium salts, such as, Bu 4 NBF 4 and Et 4 NClO 4 (Bu = «-butyl, Et = ethyl).Studies in low-dielectric solvents like benzene inevitably involve solutions of high resistance, because most ionic salts do not dissolve in them to an appreciable extent. Insolutions of salts that do dissolve in apolar media, such as Hx 4 NC10 4 (where Hx = nhexyl), ion pairing is extensive.Studies in very resistive solutions require the use of UMEs, which usually pass lowcurrents that do not give rise to appreciable resistive drops (see Section 5.9.2).
The effectof supporting electrolyte concentration on the limiting steady-state current at UMEs hasbeen treated (12-14). Typical results, shown in Figure 4.3.5, illustrate how the limitingcurrent for reduction of Tl + to the amalgam at a mercury film decreases with an increasein LiClO 4 concentration (15). The current in the absence of LiClO4, or at very low concentrations, is appreciably larger than at high concentrations, because migration of thepositively charged T1(I) species to the cathode enhances the current. At high LiClO 4 concentrations, Li + migration replaces that of Tl + , and the observed current is essentially apure diffusion current. A similar example involving the polarography of Pb(II) withKNO 3 supporting electrolyte was given in the first edition.11First edition, p.
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