Half-cell reactions definition

It is very often necessary to characterize the redox properties of a given system with unknown activity coefficients in a state far from standard conditions. For this purpose, formal (solution with unit concentrations of all the species appearing in the Nernst equation its value depends on the overall composition of the solution. If the solution also contains additional species that do not appear in the Nernst equation (indifferent electrolyte, buffer components, etc.), their concentrations must be precisely specified in the formal potential data. The formal potential, denoted as E0, is best characterized by an expression in parentheses, giving both the half-cell reaction and the composition of the medium, for example E0,(Zn2+ + 2e = Zn, 10-3M H2S04). 

All the oxidation-reduction reactions used in examples (a) to (e) proceed in one definite direction e.g. Fe3+ can be reduced by Sn2+, but the opposite process, the oxidation of Fe2+ by Sn4+ will not take place. That is why the single arrow was used in all the reactions, including the half-cell processes as well. If however we examine one half-cell reaction on its own, we can say that normally it is reversible. Thus, while Fe3+ can be reduced (e.g. by Sn2+) to Fe2+, it is also true that with a suitable agent (e.g. MnO ) Fe2+ can be oxidized to Fe3+. It is quite logical to express these half-cell reactions as chemical equilibria, which also involve electrons, as... 

The foregoing example illustrates how equilibrium constants for overall cell reactions can be determined electrochemically. Although the example dealt with redox equilibrium, related procedures can be used to measure the solubility product constants of sparingly soluble ionic compounds or the ionization constants of weak acids and bases. Suppose that the solubility product constant of AgCl is to be determined by means of an electrochemical cell. One half-cell contains solid AgCl and Ag metal in equilibrium with a known concentration of CP (aq) (established with 0.00100 M NaCl, for example) so that an unknown but definite concentration of Kg aq) is present. A silver electrode is used so that the half-cell reaction involved is either the reduction of Ag (aq) or the oxidation of Ag. This is, in effect, an Ag" Ag half-cell whose potential is to be determined. The second half-cell can be any whose potential is accurately known, and its choice is a matter of convenience. In the following example, the second half-cell is a standard H30" H2 half-cell. 

Table 19.1 lists standard reduction potentials for a number of half-cell reactions. By definition, the SHE has an E° value of 0.00 V. Above the SHE the negative standard reduction potentials increase, and below it the positive standard reduction potentials increase. It is important to know the following points about the table ... 

Equation (18.16) could also be considered to represent a half-cell reaction, except that the electron is not shown. If you have followed our discussion of the single-ion and SHE conventions, you will not be surprised to leam that it does not matter what value the chemical potential of the electron is considered to have because it always cancels out in balanced reactions, and that by convention it is given the value zero. This means that the Nemst equation applies to half-cell reactions as well as cell reactiohs, as do equations (18.15). And if you have followed all this, you now know what Eh is, because (18.17) when applied to half-cells is the definition of Eh. Thus... 

Equation (5) or (11) can be applied directly to half-cell reactions such as (6) and (7) and the resulting potentials obtained will be identical to those obtained from the overall reactions (9) and (10) because of the definition of the SHE as the universal standard. A selection of standard potentials of half-cell reactions is shown in Table 1 [5]. By international convention, electrode reactions in thermodynamic tables are always written as reduction reactions, so the more noble metals have a positive standard potential. Lists such as that in Table 1 are also called electromotive force series or tables of standard reduction potentials. 

When applying the Vetter s definition to a reversible electrode (or half-cell) reaction, it is no longer able to use the conventional scale as the reference of the free energy change and the... 

The most widely used reference electrode, due to its ease of preparation and constancy of potential, is the calomel electrode. A calomel half-cell is one in which mercury and calomel [mercury(I) chloride] are covered with potassium chloride solution of definite concentration this may be 0.1 M, 1M, or saturated. These electrodes are referred to as the decimolar, the molar and the saturated calomel electrode (S.C.E.) and have the potentials, relative to the standard hydrogen electrode at 25 °C, of 0.3358,0.2824 and 0.2444 volt. Of these electrodes the S.C.E. is most commonly used, largely because of the suppressive effect of saturated potassium chloride solution on liquid junction potentials. However, this electrode suffers from the drawback that its potential varies rapidly with alteration in temperature owing to changes in the solubility of potassium chloride, and restoration of a stable potential may be slow owing to the disturbance of the calomel-potassium chloride equilibrium. The potentials of the decimolar and molar electrodes are less affected by change in temperature and are to be preferred in cases where accurate values of electrode potentials are required. The electrode reaction is... 

Further standard voltages could be measured and placed into an electrochemical sequence with other pairs of half-cells, as can be found in many chemistry teaching books. The extent of the introduction of the hydrogen half-cell as a standard electrode can be determined in each individual lesson. If one consequently describes all redox reactions in relation to the metal sequence, redox or electrochemical sequence with ions and offers the students model drawings (see Figs. 8.3 and 8.4), then the electron transfer and the redox definition, in terms of involved smallest particles, becomes even clearer and the mixing at the language level of substances and that of particles can be effectively suppressed. 

Any cell reaction can be considered to be an electron transfer between two coupled half-cells. The measured potential corresponds to the difference of the electron energy. The arbitrary definition of a reference electrode raises the question of whether the electrochemical potential scale can be correlated with energy scales of electrons in surface physics. If measuring work functions or electron affinities, the reference value is the free electron in vacuum. Mehl and Lohmann calculated for the electron affinity of a hydrogen electrode —4.5 eV using the following Bom-Haber process... 

The two solid metals tiiat are connected by the external circuit are called electrodes. By definition, flie electrode at which oxidation occurs is called the anode the electrode at which reduction occurs is called the cathode. Each of die two compartments of die voltaic cell is called a half-cell. One half-cell is the site of die oxidation half-reaction and the other is the site of the reduction halfreaction. In our present example Zn is oxidized and Cu is reduced ... 

The most acceptable method of obtaining standard electrode potentials is by comparing tbe electrode potential of metals with the standard hydrogen electrode. Since the SHE has zero electrode potential at all temperatures by definition, the electrode potential of a metal is numerically equal to the emf of the cell formed by SHE and the metal electrode. In other words, the emf of the cell represents the electrode potential of the half cell formed by the metal with respect to the standard hydrogen electrode. In such a cell, reaction on the hydrogen electrode is oxidation and reaction on the other electrode is reduction. Such a cell can be expressed as ... 

An important conclusion to be made here is related to the definition of the standard electrode potential given in the lUPAC manual [1] The standard potential of an electrochemical reaction, abbreviated as standard potential, is defined as the standard potential of a hypothetical cell, in which the electrode (half-cell) on the left of the cell diagram is the SHE and the electrode at the right is the electrode in question. Note that E of a half-reaction (or a total electrochemical reaction) as an intensive variable does not depend on the number of electrons nsed in the half-reaction. 

Many half-reactions of interest to biochemists involve protons. As in the definition of AG °, biochemists define the standard state for oxidation-reduction reactions as pH 7 and express reduction potential as E °, the standard reduction potential at pH 7. The standard reduction potentials given in Table 13-7 and used throughout this book are values for E ° and are therefore valid only for systems at neutral pH Each value represents the potential difference when the conjugate redox pair, at 1 m concentrations and pH 7, is connected with the standard (pH 0) hydrogen electrode. Notice in Table 13-7 that when the conjugate pair 2ET/H2 at pH 7 is connected with the standard hydrogen electrode (pH 0), electrons tend to flow from the pH 7 cell to the standard (pH 0) cell the measured E ° for the 2ET/H2 pair is -0.414 V... 

These laws (determined by Michael Faraday over a half century before the discovery of the electron) can now be shown to be simple consequences of the electrical nature of matter. In any electrolysis, an oxidation must occur at the anode to supply the electrons that leave this electrode. Also, a reduction must occur at the cathode removing electrons coming into the system from an outside source (battery or other DC source). By the principle of continuity of current, electrons must be discharged at the cathode at exactly the same rate at which they are supplied to the anode. By definition of the equivalent mass for oxidation-reduction reactions, the number of equivalents of electrode reaction must be proportional to the amount of charge transported into or out of the electrolytic cell. Further, the number of equivalents is equal to the number of moles of electrons transported in the circuit. The Faraday constant (F) is equal to the charge of one mole of electrons, as shown in this equation ... 

You have probably worked with tables of standard reduction potentials before. These tables provide the reduction potentials of various substances. It describes an oxidized species s ability to gain electrons in a reduction half-reaction (like copper in the voltaic cell example). According to this definition, we can use a value from the table to represent the E°red in the expression above, but how do you find the E°ox ... 

Conversion efficiency is definitely affected by the large void fraction, which is apparent in the results from changes in the total throughput, or space velocity (0.56 versus 1.11 sec ), shown in Fig. 7. In this comparison, the concentration of unconverted hexane increased tenfold when the flow rate was doubled. The impact of improvements in conductive heat transfer, combined with the mass transfer limitations associated with the cell size and honeycomb design, and a catalyst loading that was nearly one-half Chat of commercial pellet catalysts (average, 11.5% versus 19.2%) suggested that both carbon formation and steam/hydrocarbon reactions were better controlled with monolithic supports under the conditions employed. This comparison was made where the extent of the endothermic reaction is equal between the pellet bed and the hybrid cordierite/metal monolith bed. 

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