A.J. Bard, L.R. Faulkner - Electrochemical methods - Fundamentals and Applications (794273), страница 19
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the potential of afree electron in vacuum). This interest arises, for example, if one would like to estimaterelative potentials of metals or semiconductors based on their work functions. The absolute potential of the NHE can be estimated as 4.5 ± 0.1 V, based on certain extrathermodynamic assumptions, such as about the energy involved in moving a proton from thegas phase into an aqueous solution (10, 29).
Thus, the amount of energy needed to removean electron from Pt/H2/H+(a = 1) to vacuum is about 4.5 eV or 434 kJ. 1 5 With this value,the standard potentials of other couples and reference electrodes can be expressed on theabsolute scale (Figure 2.1.1).2.3 LIQUID JUNCTION POTENTIALS2.3.1Potential Differences at an Electrolyte-Electrolyte BoundaryTo this point, we have examined only systems at equilibrium, and we have learned thatthe potential differences in equilibrium electrochemical systems can be treated exactly bythermodynamics. However, many real cells are never at equilibrium, because they featuredifferent electrolytes around the two electrodes.
There is somewhere an interface betweenthe two solutions, and at that point, mass transport processes work to mix the solutes. Unless the solutions are the same initially, the liquid junction will not be at equilibrium, because net flows of mass occur continuously across it.Such a cell isCu/Zn/Zn 2+ /Cu 2+ /Cu'a(2.3.1)/3for which we can depict the equilibrium processes as in Figure 2.3.1. The overall cell potential at null current is thenСиE = (ф ' -фР)~15Си(фаа- ф ) + (фР - ф )(2.3.2)The potential and the Fermi energy of an electrode have different signs, because the potential is based onenergy changes involving a positive test charge, while the Fermi energy refers to a negative electron.64Chapter 2.
Potentials and Thermodynamics of CellsCuZne—eaZn2 +_Zn 2 +PCu'Cu 2 +—Cu 2 +Figure 2.3.1 Schematic view of the phases in cell (2.3.1). Equilibrium is established for certaincharge carriers as shown, but at the liquid junction between the two electrolyte phases a and /3,equilibrium is not reached.Obviously, the first two components of E are the expected interfacial potential differencesat the copper and zinc electrodes. The third term shows that the measured cell potentialdepends also on the potential difference between the electrolytes, that is, on the liquidjunction potential.
This discovery is a real threat to our system of electrode potentials, because it is based on the idea that all contributions to E can be assigned unambiguously toone electrode or to the other. How could the junction potential possibly be assigned properly? We must evaluate the importance of these phenomena.2.3.2Types of Liquid JunctionsThe reality of junction potentials is easily understood by considering the boundary shownin Figure 23.2a.
At the junction, there is a steep concentration gradient in H + and Cl~;hence both ions tend to diffuse from right to left. Since the hydrogen ion has a muchlarger mobility than Cl~, it initially penetrates the dilute phase at a higher rate. Thisprocess gives a positive charge to the dilute phase and a negative charge to the concentrated one, with the result that a boundary potential difference develops. The corresponding electric field then retards the movement of H + and speeds up the passage of Cl~ untilthe two cross the boundary at equal rates.
Thus, there is a detectable steady-state potential, which is not due to an equilibrium process (3, 24, 30, 31). From its origin, this interfacial potential is sometimes called a diffusion potential.Lingane (3) classified liquid junctions into three types:1.Two solutions of the same electrolyte at different concentrations, as in Figure2.3.2a.2.Two solutions at the same concentration with different electrolytes having an ionin common, as in Figure 2.3.2b.3.Two solutions not satisfying conditions 1 or 2, as in Figure 2.3.2c.We will find this classification useful in the treatments of junction potentials that follow.Typei0.01 MHCIType 20.1 MHCI0.1 MHCIТуреЗ0.05 MKNO;0.1 MKCI• H+•cr©0(a)00(b)(c)Figure 2.3.2 Types of liquid junctions.
Arrows show the direction of net transfer for each ion,and their lengths indicate relative mobilities. The polarity of the junction potential is indicated ineach case by the circled signs. [Adapted from J. J. Lingane, "Electroanalytical Chemistry," 2nd ed.,Wiley-Interscience, New York, 1958, p. 60, with permission.]2.3 Liquid Junction Potentials < 65Even though the boundary region cannot be at equilibrium, it has a composition thatis effectively constant over long time periods, and the reversible transfer of electricitythrough the region can be considered.Conductance, Transference Numbers, and MobilityWhen an electric current flows in an electrochemical cell, the current is carried in solutionby the movement of ions.
For example, take the cell:++0Pt/H 2 (l atm)/H , СГ/Н , СГ/Н 2 (1 atm)/Pt'©(«i)where a2 > a^trode,16K}(*2)When the cell operates galvanically, an oxidation occurs at the left elec+H 2 -> 2H (a) + 2e(Pt)(2.3.4)and a reduction happens on the right,2H+(j3) + 2e(Pt') -> H 2(2.3.5)Therefore, there is a tendency to build up a positive charge in the a phase and a negativecharge in p.
This tendency is overcome by the movement of ions: H + to the right and Cl~to the left. For each mole of electrons passed, 1 mole of H + is produced in a, and 1 moleof H + is consumed in /3. The total amount of H + and Cl~ migrating across the boundarybetween a and /3 must equal 1 mole.The fractions of the current carried by H + and Cl~ are called their transference numbers (or transport numbers). If we let t+ be the transference number for H + and t- be thatfor Cl~, then clearly,t+ + t- = 1(2.3.6)In general, for an electrolyte containing many ions, /,(2.3.7)Schematically, the process can be represented as shown in Figure 2.3.3. The cell initiallyfeatures a higher activity of hydrochloric acid (+ as H + , — as Cl~) on the right (Figure(«)и/н 2 /! 1/ t i l l1 _/H 2 /R(с)/!+_ !! !/H2/PIFigure 2.3.3 Schematic diagram showing the redistribution of charge during electrolysis of asystem featuring a high concentration of HCl on the right and a low concentration on the left.16A cell like (2.3.3), having electrodes of the same type on both sides, but with differing activities of one orboth of the redox forms, is called a concentration cell.66Chapter 2.
Potentials and Thermodynamics of Cells2.3.3a); hence discharging it spontaneously produces H + on the left and consumes it onthe right. Assume that five units of H + are reacted as shown in Figure 233b. For hydrochloric acid, t+ ~ 0.8 and t- ~ 0.2; therefore, four units of H + must migrate to theright and one unit of Cl~ to the left to maintain electroneutrality. This process is depictedin Figure 2.3.3c, and the final state of the solution is represented in Figure 2.3.3d.A charge imbalance like that suggested in Figure 233b could not actually occur, because a very large electric field would be established, and it would work to erase the imbalance. On a macroscopic scale, electroneutrality is always maintained throughout thesolution.
The migration represented in Figure 2.3.3c occurs simultaneously with the electron-transfer reactions.Transference numbers are determined by the details of ionic conduction, which areunderstood mainly through measurements of either the resistance to current flow in solution or its reciprocal, the conductance, L (31, 32). The value of L for a segment of solutionimmersed in an electric field is directly proportional to the cross-sectional area perpendicular to the field vector and is inversely proportional to the length of the segment along thefield.
The proportionality constant is the conductivity, к, which is an intrinsic property ofthe solution:L = KA/1(2.3.8)The conductance, L, is given in units of Siemens (S = fl" 1 ), and к is expressed in S cm" 1or ft"1 cm" 1 .Since the passage of current through the solution is accomplished by the independentmovement of different species, к is the sum of contributions from all ionic species, /. It isintuitive that each component of к is proportional to the concentration of the ion, the magnitude of its charge |ZJ|, and some index of its migration velocity.That index is the mobility, щ, which is the limiting velocity of the ion in an electricfield of unit strength.
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