A.J. Bard, L.R. Faulkner - Electrochemical methods - Fundamentals and Applications (794273), страница 21
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To consider these cases, one must imagine the junction region to besectioned into an infinite number of volume elements having compositions that rangesmoothly from the pure a-phase composition to that of pure /3. Transporting charge acrossone of these elements involves every ionic species in the element, and ttl\z^ moles ofspecies / must move for each mole of charge passed. Thus, the passage of positive chargefrom a toward /3 might be depicted as in Figure 2.3.7.
One can see that the change in electrochemical free energy upon moving any species is {tJz^cfjjL^ (recall that zj is a signedquantity); therefore, the differential in free energy ispdG = 2 j : dJLx(2.3.33)Integrating from the a phase to the /3 phase, we haverPС fi t-i ^aJa*(2.3.34)If jitf for the a phase is the same as that for the /3 phase (e.g., if both are aqueous solutions),2j-RTd\na{ + n>i \F \(2.3.35)Since 2 ^ = 1,(2.3.36)which is the general expression for the junction potential.It is easy to see now that (2.3.30) is a special case for type 1 junctions between 1:1electrolytes having constant tv Note that £j is a strong function of t+ and t-, and that it actually vanishes if t+ = t~. The value of Щ as a function of t+ for a 1:1 electrolyte withai/a2 = 10 isEi = 59.1- 1) mV(2.3.37)at 25°C.
For example, the cellAg/AgCl/KCl (0.1 M)/KC1 (0.01 M)/AgCl/Ag(2.3.38)has t+ = 0.49; hence E-} = -1.2 mV.While type 1 junctions can be treated with some rigor and are independent of themethod of forming the junction, type 2 and type 3 junctions have potentials that dependon the technique of junction formation (e.g., static or flowing) and can be treated only inan approximate manner. Different approaches to junction formation apparently lead to- f/zj mole ofeach cation-fj/z, mole ofeach anionLocationElectrochemicalpotentialx + dxFigure 2.3.7 Transfer of net positivecharge from left to right through aninfinitesimal segment of a junction region.Each species must contribute ty moles ofcharge per mole of overall chargetransported; hence t-\z-\ moles of thatspecies must migrate.72Chapter 2. Potentials and Thermodynamics of Cellsdifferent profiles of tx through the junction, which in turn lead to different integrals for(2.3.36).
Approximate values for E-} can be obtained by assuming (a) that concentrationsof ions everywhere in the junction are equivalent to activities and (b) that the concentration of each ion follows a linear transition between the two phases. Then, (2.3.36) can beintegrated to give the Henderson equation (24, 30):—[COS) - C;(a)]1F*У. \z{ «AWRT, iFv i MiCiO3)i(2.3.39)iwhere щ is the mobility of species /, and C\ is its molar concentration. For type 2 junctionsbetween 1:1 electrolytes, this equation collapses to the Lewis-Sargent relation'.(2.3.40)where the positive sign corresponds to a junction with a common cation in the two phases,and the negative sign applies to the case with a common anion.
As an example, considerthe cellAg/AgCl/HCl (0.1M)/KCl (0.1 M)/AgCl/Ag(2.3.41)for which Есец is essentially E-y The measured value at 25°C is 28 ± 1 mV, depending onthe technique of junction formation (30), while the estimated value from (2.3.40) and thedata of Table 2.3.2 is 26.8 mV.2.3.5Minimizing Liquid Junction PotentialsIn most electrochemical experiments, the junction potential is an additional troublesomefactor, so attempts are often made to minimize it. Alternatively, one hopes that it is smallor that it at least remains constant. A familiar method for minimizing £j is to replace thejunction, for example,HC1 (Ci)/NaCl (C2)(2.3.42)with a system featuring a concentrated solution in an intermediate salt bridge, where thesolution in the bridge has ions of nearly equal mobility.
Such a system isHC1 (Ci)/KCl (C)/NaCl (C2)(2.3.43)Table 2.3.3 lists some measured junction potentials for the cell,Hg/Hg2Cl2/HCl (0.1 M)/KC1 (С)/Ка (0(2.3.44)As С increases, £j falls markedly, because ionic transport at the two junctions is dominatedmore and more extensively by the massive amounts of KC1. The series junctions becomemore similar in magnitude and have opposite polarities; hence they tend to cancel. Solutions used in aqueous salt bridges usually contain KC1 (t+ = 0.49, t- = 0.51) or, whereCl" is deleterious, KNO3 (t+ = 0.51, t- = 0.49).
Other concentrated solutions with equitransferent ions that have been suggested (39) for salt bridges include CsCl (f+ = 0.5025),RbBr (t+ = 0.4958), and NH4I (t+ = 0.4906). In many measurements, such as the determination of pH, it is sufficient if the junction potential remains constant between calibra-2.3 Liquid Junction Potentials:73TABLE 2.3.3 Effect of a Salt Bridge on MeasuredJunction Potentials"Concentration of KC1, C(M)£j,mV0.10.20.51.02.52720138.43.43.54.2 (saturated)1.1<1aSee J.
J. Lingane, "Electroanalytical Chemistry," WileyInterscience, New York, 1958, p. 65. Original data from H. A.Fales and W. C. Vosburgh, / . Am. Chem. Soc. 40, 1291 (1918);E. A. Guggenheim, ibid., 52, 1315 (1930); and A. L. Ferguson,K. Van Lente, and R. Hitchens, ibid., 54,1285 (1932).tion (e.g., with a standard buffer or solution) and measurement. However, variations in Ejof 1-2 mV can be expected, and should be considered in any interpretations made frompotentiometric data.2.3.6Junctions of Two Immiscible LiquidsAnother junction of interest is that between two immiscible electrolyte solutions (40^-4).A typical junction of this type would beК + С Г (H2O)/TBA+C1O4 (nitrobenzene)phase a(2.3.45)phase /3where TBA+C1O^ is tetra-n-butylammonium perchlorate.
Of interest in connection withion-selective electrodes (Section 2.4.3) and as models for biological membranes are related cells with immiscible liquids between two aqueous phases, such asAg/AgCl/ KC1 (aq) /TBA+CIO^ (nitrobenzene) / KC1 (aq) /AgCl/Ag(2.3.46)where the intermediate liquid layer behaves as a membrane. The treatment of the potentials across junctions like (2.3.45) is similar to that given earlier in this section, except thatthe standard free energies of a species / in the two phases, fifa and /if^, are now different.The junction potential then becomes (40, 41)+RTln(f)where A^"nsr?r j * s * п е standard free energy required to transfer species / with charge i\between the two phases and is defined as* & & i = № ~ da(2 3 48)--This quantity can be estimated, for example, from solubility data, but only with anextrathermodynamic assumption of some kind.
For example, for the salt tetraphenylarsonium tetraphenylborate (TPAs + TPB~), it is widely assumed that the free energy of solvation (AGJ?olvn) of TPAs + is equal to that of TPB~, since both are large ions with mostof the charge buried deep inside the surrounding phenyl rings (45). Consequently, the in-74 : Chapter 2. Potentials and Thermodynamics of Cellsdividual ion solvation energies are taken as one-half of the solvation energy of the salt,which is measurable from the solubility product in a given solvent.
That is,AG° olvn (TPAs + ) = AG° olvn (TPB") = ±AG° o l v n (TPAs+ТРЩr, TPAS+ = AG» olvn (TPAs + , J8) - AG° olvn (TPAs + , a)(2.3.49)(2.3.50)The free energy of transfer can also be obtained from the partitioning of the salt betweenthe phases a and /3. For each ion, the value determined in this way should be the same asthat calculated in (2.3.50), if the intersolubility of a and /3 is very small.The rate of transfer of ions across interfaces between immiscible liquids is also of interest and can be obtained from electrochemical measurements (Section 6.8).2.4 SELECTIVE ELECTRODES (46-55)2.4.1Selective InterfacesSuppose one could create an interface between two electrolyte phases across which only asingle ion could penetrate.
A selectively permeable membrane might be used as a separator to accomplish this end. Equation 2.3.34 would still apply; but it could be simplified byrecognizing that the transference number for the permeating ion is unity, while that forevery other ion is zero. If both electrolytes are in a common solvent, one obtains by integration^^<П = 0(2.4.1)where ion i is the permeating species. Rearrangement gives1П£т=-5 <If the activity of species / is held constant in one phase, the potential difference betweenthe two phases (often called the membrane potential, Em) responds in a Nernst-like fashion to the ion's activity in the other phase.This idea is the essence of ion-selective electrodes. Measurements with these devicesare essentially determinations of membrane potentials, which themselves comprise junction potentials between electrolyte phases.
The performance of any single system is determined largely by the degree to which the species of interest can be made to dominatecharge transport in part of the membrane. We will see below that real devices are fairlycomplicated, and that selectivity in charge transport throughout the membrane is bothrarely achieved and actually unnecessary.Many ion-selective interfaces have been studied, and several different types of electrodes have been marketed commercially. We will examine the basic strategies for introducing selectivity by considering a few of them here.
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