Thermodynamics reference half-cells

Chapter 2) apply. The standard reference half-cell is reaction 15.6, the standard hydrogen electrode (SHE), and the standard conditions are those listed in Section 2.3, although for our purposes the molar concentration scale (mol L 1) can generally be used without significant loss of precision. We will simplify matters further, for illustrative purposes, by equating activities with molar concentrations our numerical results will therefore be only approximate, except where concentrations are very low. A thermodynamically acceptable treatment would require the calculation or measurement of ionic activities or, at the very least, maintenance of constant ionic strength, as outlined in Section 2.2. 

Among the secondary reference half cells which have been employed in work on many melt types, the Ag/Ag system has proved most popular, although the Pt/Pt is also useful in higher-melting media. Even in halide melts, however, these series may be slightly restricted because the metals are disposed to dissolve in their own salt melts, e.g., Na in NaCl. This causes a lowering of their thermodynamic activity, resulting in deposition at more noble potentials than that predicted on the basis of the defined standard state of unit activity. 

The conversion to the aqueous standard hydrogen electrode as reference half-cell requires an extra-thermodynamic assumption, either the assumption of a solvent independent reference redox system or other assumptions employed in calculating single-ion transfer properties. Details about the procedure and data for univalent cationimetal systems were published [13]. The redox couple ferrocenium ion/ferrocene as reference electrode system is not very suited for such a conversion as the ferrocenium cation undergoes interactions with water and thus impairs the extra-thermodynamic assumption for aqueous solutions. This becomes apparent when... 

We will now look at the effects of Ej on thermodynamic calculations, and then decide on the various methods that can be used to minimize them. One of the most common reasons for performing a calculation with an electrochemical cell is to determine the concentration or activity of an ion. In order to carry out such a calculation, we would first construct a cell, and then, knowing the potential of the reference electrode, we would determine the half-cell potential, i.e. the electrode potential E of interest, and then apply the Nemst equation. 

If we choose a set of standard conditions (cf. Section 2.3) and one convenient half-cell to serve as a reference for all others, then a set of standard half-cell EMFs or standard electrode potentials E° (Appendix D)1-9 can be measured while drawing a negligible electrical current, that is, with the cell working reversibly so that the equations of reversible thermodynamics... 

The American convention would assign a positive value to E° for the Zn Zn2+(aq) half cell written as an oxidation, but a negative sign if written as a reduction. It is seen that the European convention refers to the invariant electrostatic potential of the electrode with respect to the SHE, whereas the American convention relates to the thermodynamic Gibbs free energy which is sensitive to the direction of the cell reaction. 

Reactive electrodes refer mostly to metals from the alkaline (e.g., lithium, sodium) and the alkaline earth (e.g., calcium, magnesium) groups. These metals may react spontaneously with most of the nonaqueous polar solvents, salt anions containing elements in a high oxidation state (e.g., C104 , AsF6 , PF6 , SO CF ) and atmospheric components (02, C02, H20, N2). Note that ah the polar solvents have groups that may contain C—O, C—S, C—N, C—Cl, C—F, S—O, S—Cl, etc. These bonds can be attacked by active metals to form ionic species, and thus the electrode-solution reactions may produce reduction products that are more stable thermodynamically than the mother solution components. Consequently, active metals in nonaqueous systems are always covered by surface films [46], When introduced to the solutions, active metals are usually already covered by native films (formed by reactions with atmospheric species), and then these initial layers are substituted by surface species formed by the reduction of solution components [47], In most of these cases, the open circuit potentials of these metals reflect the potential of the M/MX/MZ+ half-cell, where MX refers to the metal salts/oxide/hydroxide/carbonates which comprise the surface films. The potential of this half-cell may be close to that of the M/Mz+ couple [48],... 

As indicated previously, it is desirable to consider the individual electrode reactions independently. One might suppose that this could be achieved by characterizing the individual electrodes as described in Section 3.1.3. However, for reasons of sound thermodynamics, another method has been established. It was decided to relate all electrode reactions to one common reference electrode. Electrochemists have chosen the H+/H2 reaction under standard conditions (ct 1+ = 1M p 12 = 1 bar) as such a general reference electrode. It is termed the normal hydrogen electrode or the standard hydrogen electrode (SHE). Thus, whenever E and E° values are presented for individual electrode reactions (half cells), it is understood that these values pertain to a complete cell in which the SHE constitutes the second electrode. 

In order to satisfy the necessary criteria, a reversible redox couple is utilized in the reference electrode half-cell reaction. The potential of a reversible reference electrode is thermodynamically defined by its standard electrode potential, EP (see for example Compton and Sanders, 1996, for further discussion). Currently, the most commonly used reference electrode in voltammetric studies is the silver/silver chloride electrode (3), which has overtaken the calomel electrode (see for example Bott, 1995) for which the reaction is (4). 

The sensing mechanism was studied in detail by Hotzel and Weppner from a thermodynamic point of view. Under open circuit conditions, the equilibrium half cell electrochemical reaction at the reference electrode is... 

In thermodynamics, only energy differences are measurable absolute energies are not. Therefore, energies (or enthalpies or free energies) are defined relative to a reference state for which these quantities are arbitrarily set at 0 by international agreement. The same reasoning applies to half-cells Because only differences are measured, we are free to define a reference reduction potential for a particular half-cell and measure other half-cell reduction potentials relative to it. The convention used is to define %° for the half-cell reduction of Hilg) to H30 (d (j ) to be 0 at all temperatures, when the gas pressure at the electrode is 1 atm and the -iiO aq) concentration in solution is I M (Fig. 17.3). 

An electrode potential is a measure of the thermodynamics of a redox reaction. It may be expressed as the difference between two half-cell potentials, which by convention are measured against a hydrogen electrode. Tabulated values refer to standard conditions (ions at unit activity). 

Also known as the standard hydrogen electrode (SHE), it is a redox reference electrode which forms the basis of the thermodynamic scale of oxidation-reduction potentials. The potential of the NHE is defined as zero and based oti equilibrium of the following redox half-cell reaction, typically on a Pt surface 2H+(aq) + 2e H2(g). The activities of both the reduced form and the oxidized form are maintained at unity. That implies that the pressure of hydrogen gas is 1 atm and the concentration of hydrogen ions in the solution is 1 M. 

The second point is the assumption that the potential of a half-cell containing the reference redox system is—within experimental error— independent of the nature of the solvent. This assumption is outside the realm of exact thermodynamics and thus open to discussion. As for any extra-thermodynamic assumption it is impossible to prove its validity. This point should be kept in mind especially when discussing single-ion transfer properties. 

Although the thermodynamic analysis has given results with clear contributions from each of the electrodes, the observed EMF cannot be separated into these contributions by experiment. As was seen in the previous section, the solution to this problem has been to choose the SHE as a reference and to quote the standard potentials of all other half-reactions with respect to this point on the redox potential scale. In order to illustrate the application of this concept using absolute electrode potentials, the following cell is considered ... 

Any study of an electrochemical system should be started with the equilibrium mode. In such a mode, the electrodes should not be called the cathode or the anode, and both half-reactions should be shown as reduction reactions. It is because, by common convention, the reference data on the (standard) electrode potentials are given for the reduction reactions. The convention will be discussed in Chapter 4. However, one electrode of an electrochemical cell should be more positive than another one, and the polarity can be experimentally found using the high-resistance electrometer. Also, the polarity of the electrodes in the equilibrium cell can theoretically be calculated using thermodynamic data. This will also be discussed in Chapter 4. 

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