A.J. Bard, L.R. Faulkner - Electrochemical methods - Fundamentals and Applications (794273), страница 15
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Similarly, thestandard emfs of the half-reactions:2H + + 2 e * ± H 2(2.1.31)have also been assigned values of zero at all temperatures (the thermodynamic standard).We can record half-cell potentials by measuring them in whole cells against theNHE.3 For example, in the systemPt/H2(a = l)/H + (a = l)//Ag+(a = 1)/Ag(2.1.32)the cell potential is 0.799 V and silver is positive. Thus, we say that the standard potentialof the Ag+IAg couple is +0.799 V vs. NHE. Moreover, the standard emf of the Ag+ reduction is also +0.799 V vs. NHE, but that of the Ag oxidation is -0.799 V vs. NHE.
Another valid expression is that the standard electrode potential ofAg+/Ag is +0.799 V vs.NHE. To sum all of this up, we write:4Ag + + e <=t AgE°Ag+/Ag = +0.799 V vs. NHE(2.1.33)For the general system, (2.1.16), the electrostatic potential of the R/O electrode (withrespect to NHE) and the emf for the reduction of О always coincide. Therefore, one cancondense the electrostatic and thermodynamic information into one list by tabulating electrode potentials and writing the half-reactions as reductions.
Appendix С provides somefrequently encountered potentials. Reference (5) is an authoritative general source foraqueous systems.Tables of this sort are extremely useful, because they feature much chemical andelectrical information condensed into quite a small space. A few electrode potentials cancharacterize quite a number of cells and reactions. Since the potentials are really indicesof free energies, they are also ready means for evaluating equilibrium constants, complexation constants, and solubility products. Also, they can be taken in linear combinations tosupply electrochemical information about additional half-reactions. One can tell from aglance at an ordered list of potentials whether or not a given redox process will proceedspontaneously.3Note that an NHE is an ideal device and cannot be constructed.
However, real hydrogen electrodes canapproximate it, and its properties can be defined by extrapolation.4In some of the older literature, the standard emfs of reduction and oxidation are, respectively, called the"reduction potential" and the "oxidation potential." These terms are intrinsically confusing and should beavoided altogether, because they conflate the chemical concept of reaction direction with the physical conceptof electrical potential.2.1 Basic Electrochemical Thermodynamics51It is important to recognize that it is the electrostatic potential (not the emf) that is experimentally controlled and measured.
When a half-reaction is chemically reversible, thepotential of its electrode will usually have the same sign, whether the reaction proceeds asan oxidation or a reduction. [See also reference (9), and Sections 1.3.4, and 1 A2(Z?).]The standard potential of a cell or half-reaction is obtained under conditions whereall species are in their standard states (10). For solids, like Ag in cell 2.1.32 or reaction2.1.33, the standard state is the pure crystalline (bulk) metal. It is interesting to considerhow many atoms or what particle size is needed to produce "bulk metal" and whetherthe standard potential is a function of particle size when one deals with metal clusters.These questions have been addressed (11-13); and for clusters containing n atoms(where n < 20), E® indeed turns out to be very different from the value for the bulkmetal (n » 20). Consider, for example, silver clusters, Ag n .
For a silver atom (n = 1),the value of E® can be related to E° for the bulk metal through a thermodynamic cycleinvolving the ionization potential of Ag and the hydration energy of Ag and Ag + . Thisprocess yieldsAg + (aq) + e «± Agt(aq)£ ? = -1.8 V vs. NHE(2.1.34)which is 2.6 V more negative than for bulk Ag.
This result implies that it is much easierenergetically to remove an electron from a single isolated Ag atom than to remove anelectron from Ag atoms within a lattice of other Ag atoms. Experimental work carried outwith larger silver clusters shows that as the cluster size increases, E® moves toward thevalue for the bulk metal. For example, for n = 2Ag + (aq) + Ag! (aq) + e ?± Ag2 (aq)£ 2 ° - 0 V vs. NHE(2.1.35)These differences in standard potential can be explained by the greater surface energy of small clusters compared to bulk metal and is consistent with the tendency of smallparticles to grow into larger ones (e.g., the dimerization of 2Agj into Ag2 or the Ostwaldripening of colloidal particles to form precipitates). Surface atoms are bonded to fewerneighbors than atoms within a crystal; thus an extra surface free energy is required to create additional surface area by subdivision of a metal.
Conversely, the total energy of asystem can be minimized by decreasing the surface area, such as by taking on a sphericalshape or by fusing small particles into larger ones. If one adopts a microscopic viewpoint,one can see that the tendency for surfaces to reconstruct (see Section 13.4.2) and for different sites on surfaces to etch at different rates implies that even the standard potentialfor reduction to the "bulk metal" is actually an average of E° values for reduction at thedifferent sites (14).2.1.5emf and ConcentrationConsider a general cell in which the half-reaction at the right-hand electrode isz/oO + ne±±vRR(2.1.36)where the v's are stoichiometric coefficients. The cell reaction is thenvH2 + ^oO -> ^RR + vH+(2.1.37)and its free energy is given from basic thermodynamics (2) byAG = &G° + RT\n* "(2.1.38)52Chapter 2.
Potentials and Thermodynamics of Cellswhere щ is the activity of species i.5 Since AG = —nFE and AG° =-nFE0,but since aH+ = ащ = 1,J?Tar?(2.1.40)This relation, the Nemst equation, furnishes the potential of the O/R electrode vs. NHE asa function of the activities of О and R. In addition, it defines the activity dependence ofthe emf for reaction 2.1.36.It is now clear that the emf of any cell reaction, in terms of the electrode potentials ofthe two half-reactions, is(2.1.41)where £right and £ left refer to the cell schematic and are given by the appropriate Nernstequation.
The cell potential is the magnitude of this value.2.1.6Formal PotentialsIt is usually inconvenient to deal with activities in evaluations of half-cell potentials, because activity coefficients are almost always unknown. A device for avoiding them is theformal potential, E°'. This quantity is the measured potential of the half-cell (vs. NHE)when (a) the species О and R are present at concentrations such that the ratio C^/C^ isunity and (b) other specified substances, for example, miscellaneous components of themedium, are present at designated concentrations. At the least, the formal potentialincorporates the standard potential and some activity coefficients, у±.
For example, considerFe3+ + e^±Fe2+(2.1.42)Its Nernst relation is simplyE = E + —=; Ine2+= E + —— In ——(2.1.43)which is£ = £Q' + ^ | l nnFe-J(2.1.44)[Fe2+]where£ u = £ " + '-£ in _£>5(2.1.45)For a solute i, the activity is ax = yx (Cj/C°), where C\ is the concentration of the solute, C° is the standardconcentration (usually 1 M), and y; is the activity coefficient, which is unitless.
For a gas, av = y{ (PJP0), whereP[ is the partial pressure of /, P° is the standard pressure, and yx is the activity coefficient, which is againunitless. For most of the published literature, including all before the late 1980s, the standard pressure was 1atm (101,325 Pa). The new standard pressure adopted by the International Union of Pure and AppliedChemistry is 105 Pa. A consequence of this change is that the potential of the NHE now differs from that usedhistorically. The "new NHE" is +0.169 mV vs.
the "old NHE" (based on a standard state of 1 atm). Thisdifference is rarely significant, and is never so in this book. Most tabulated standard potentials, including thosein Table C.I are referred to the old NHE See reference 15.2.1 Basic Electrochemical Thermodynamics53Because the ionic strength affects the activity coefficients, E0' will vary from mediumto medium. Table C.2 contains values for this couple in 1 M HC1, 10 M HC1, 1 MHC1O4, 1 M H 2 SO 4 , and 2 M H3PO4. The values of standard potentials for half-reactions and cells are actually determined by measuring formal potentials values at different ionic strengths and extrapolating to zero ionic strength, where the activitycoefficients approach unity.Often E° also contains factors related to complexation and ion pairing; as it doesin fact for the Fe(III)/Fe(II) couple in HC1, H 2 SO 4 , and H3PO4 solutions.
Both ironspecies are complexed in these media; hence (2.1.42) does not accurately describe thehalf-cell reaction. However, one can sidestep a full description of the complex competitive equilibria by using the empirical formal potentials. In such cases, E° containsterms involving equilibrium constants and concentrations of some species involved inthe equilibria.2.1.7Reference ElectrodesMany reference electrodes other than the NHE and the SCE have been devised for electrochemical studies in aqueous and nonaqueous solvents. Several authors have provideddiscussions on the subject (16-18).Usually there are experimental reasons for the choice of a reference electrode. Forexample, the systemAg/AgCl/KCl (saturated, aqueous)(2.1.46)has a smaller temperature coefficient of potential than an SCE and can be built more compactly.
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