Single-electrode potential, calculation

R. Parsons, The Single Electrode Potential Its Significance and Calculation and Standard Electrode Potentials Units, Conventions and Methods of Determination, in Standard Potentials in Aqueous Solution, A. J. Bard, R. Parsons, and J. Jordan, eds. Chs. 1 and 2, Marcel Dekker, New York (1985). 

Single electrode potentials have been measured at Sn02 anodes and ITO cathodes for solutions in 50 v/v % aqueous CH3CN,. OIM in H2SO4, in which the photostationary ratio of TH to TH4 varied by a factor of more than 10 and the Fe(III) Fe(II) ratio varied by a factor of approximately six (J). The potential at the SnO anode paralleled the potential calculated for the TH" TH42 couple from known compositions with the aid of the Nernst potential equation. Measured values were, however. 

Gas-phase ionization energies or electron affinities for molecular species calculated by quantum mechanics do not include the thermodynamic properties of the free electron and can be compared directly to the tabulations of experimental data for these processes in the ion convention. To relate condensed- and gas-phase redox thermochemistry directly, however, a common convention must be adopted. Electrode potentials can be converted to the gas-phase convention for reaction in which there is a change in the number of electrons. The single electrode potential Es°) can be... 

Thermodynamic calculations are always based on an electrochemical cell reaction, and the derived voltage means the voltage difference between two electrodes. The voltage difference between the electrode and the electrolyte, the absolute potential , cannot exactly be measured, since potential differences can only be measured between two electronic conductors (2). Single electrode potential always means the cell voltage between this electrode and a reference electrode. To get a basis for the electrode-potential scale, the zero point was arbitrarily equated with the potential of the standard hydrogen electrode (SHE), a hydrogen electrode under specihed conditions at 25 °C (cf. Ref. 3). 

Parsons R (1985) The single electrode potential its significance and calculation. In Bard AJ, Parsons R, Jordan J (eds) Standard potentials in aqueous solution. Marcel Dekker,New York, p 13... 

Single-electrode potentials are important for some fundamental but unmeasurable quantities. The problem has been discussed in literature [2, 3]. Relative potential values (not absolute values which refer to an imaginary point in the universe ) can be calculated. Also single-electrode entropy values can be calculated by means of non-isothermal cells, but it is necessary to make use of some non-thermodynamic assumptions. 

By means of entropy calculations as mentioned above, fixup values of common reference electrodes have been calculated. On this basis, the non-isothermal temperature coefficient of some single-electrode potentials became available. Some results of such single-electrode potentials are given in Table 2.2. A comprehensive... 

The equilibrium potentials and E, can be calculated from the standard electrode potentials of the H /Hj and M/M " " equilibria taking into account the pH and although the pH may be determined an arbitrary value must be used for the activity of metal ions, and 0 1 = 1 is not unreasonable when the metal is corroding actively, since it is the activity in the diffusion layer rather than that in the bulk solution that is significant. From these data it is possible to construct an Evans diagram for the corrosion of a single metal in an acid solution, and a similar approach may be adopted when dissolved O2 or another oxidant is the cathode reactant. 

A reaction in an electrochemical cell comprises two half-cell reactions. Even when we want to focus on a single half-cell, we must construct a whole cell and determine its cell emf, which is dehned as (positive electrode) - E(negative electrode) - Only when we know both the emf and the value of one of the two electrode potentials can we calculate the unknown electrode potential. 

To express the absolute values of single potentials is made difficult by the fact that the absolute zero electrode is not known, in respect of which other elements could be measured. It is, therefore, necessary to be satisfied with comparative values. These will be obtained by referring each potential to an exactly defined arbitrary standard electrode the potential of which is conventionally taken as zero. Such comparative potential valuos, of course, do not prevent the calculation of the EMF s of cells composed of two elements because in such instance the zero electrode potential proper appears in the corresponding equation twice once with a positive, and once with the negative sign, so being annuled in the result. 

Norskov and coworkers have determined the stability of reaction intermediates (mostly oxygen) on many single crystals and alloys of noble metals. Energy corrections due to solvent, zero-point energy, and entropy effects afforded experimentally relevant free energies for each mechanistic step. Their calculations treated the electrode potential with the same approach as Anderson, whereby each proton transfer was coupled with an energy shift of -et/ U being the potential difference between... 

One effect of special interest to electrochemists is the potential-dependent chemisorption of ions and molecules on electrode surfaces. A particularly well-studied example is the adsorption of CO on platinum single-crystal electrodes. In collaboration with the Weaver group at Purdue, we have recently undertaken detailed DFT calculations of the potential-dependent chemisorption of CO on platinum-group (111) surfaces [47,54,55], modeled as clusters, for comparison with the extensive vibrational characterization of these systems as carried out by the Purdue group [56,57]. The electrode potential in these studies is modeled as a variable external electric held applied across the cluster, an approach many others have taken in the past. 

Calculations such as those in Example 22-2 permit us to find the differences in standard electrode potentials theoretically needed to determine one ion without interference from another. These differences range from about 0.04 V for triply charged ions to approximately 0.24 V for singly charged species. 

Not only is the value of jQ important in electrocatalysis but also the experimental Tafel slope at the operating electrode potential. As expected in an electrocatalytic process, this complex heterogeneous reaction exhibits at least one intermediate (reactant or product) adsorbed species. Therefore, a single or simple Tafel slope for the entire process is not expected, but rather surface coverage and electrolyte composition potential dependent Tafel slopes within the whole potential domain are expected. Instead of calculating the most proper academic Tafel slope, the experimental current vs. potential curve is required for the selected electrocatalysts [4,6]. 

The earlier sections of this chapter discuss the mixed electrode as the interaction of anodic and cathodic reactions at respective anodic and cathodic sites on a metal surface. The mixed electrode is described in terms of the effects of the sizes and distributions of the anodic and cathodic sites on the potential measured as a function of the position of a reference electrode in the adjacent electrolyte and on the distribution of corrosion rates over the surface. For a metal with fine dispersions of anodic and cathodic reactions occurring under Tafel polarization behavior, it is shown (Fig. 4.8) that a single mixed electrode potential, Ecorr, would be measured by a reference electrode at any position in the electrolyte. The counterpart of this mixed electrode potential is the equilibrium potential, E M (or E x), associated with a single half-cell reaction such as Cu in contact with Cu2+ ions under deaerated conditions. The forms of the anodic and cathodic branches of the experimental polarization curves for a single half-cell reaction under charge-transfer control are shown in Fig. 3.11. It is emphasized that the observed experimental curves are curved near i0 and become asymptotic to E M at very low values of the external current. In this section, the experimental polarization of mixed electrodes is interpreted in terms of the polarization parameters of the individual anodic and cathodic reactions establishing the mixed electrode. The interpretation then leads to determination of the corrosion potential, Ecorr, and to determination of the corrosion current density, icorr, from which the corrosion rate can be calculated. 

In the present work, the theory for single-electrode reactions (E), series reactions (E.E) and parallel reactions (E + E) only will be considered. This represents a minimum theory set that is necessary for model calculation and graphical display and for integration into the data analysis system. In the experimental section, all the data over the entire potential range has been tested against this theory to find the most appropriate theory with which to interpret the experiments. 

The first applications of ab initio quantum-chemical calculations to systems of electrochemical interest were concerned with the adsorption of halides at metal surfaces. The adsorption of halides is of great experimental and practical importance as many electrolyte solutions contain halide anions, which tend to adsorb specifically at the metal-water interface, especially at more positive electrode potentials. Issues of interest in halide chemisorption are the nature of chemical bond with the surface ( . e., covalent or ionic), the strength of the interaction of the different halides on different substrates, the preferred binding geometry on single-crystal surfaces, the effect of the electrode potential, and the importance of including the solvent (water) in correctly modeling the properties of the chemisorption bond. 

With slow kinetics of the involved processes or with interfaces where electrode potential modulation might be detrimental because of crystallographic changes in the metal surface, other spectroscopic techniques have to be used. The whole spectrum of interest can be scanned or registered within a few milliseconds with a rapid scan spectrometer or a multichannel (diode array) spectrometer. Repeated acquisition provides the required signal-to-noise ratio. After a potential step, the acquisition is repeated and spectral calculation yields AR/R. This single potential step procedure allows investigation of systems where repeated potential modulation has failed. 

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