Cell reaction, definition

With the definition of the Faraday constant (Eq. 13) the amount of charge for the cell reaction for one formula conversion is given by Eq. (18) ... 

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). 

Let us now suppose that the waveform of figure 16.3 is applied to study the reversible oxidation of a species R to R in a given solvent. The reaction occurs at the working electrode (anode), and /i°(R/R ) is the standard potential of the R/R- couple. Because the standard potential of the reference electrode in our cell is known accurately relative to the standard potential of the SHE (E° = 0 by definition), we can write the cell reaction and the Nernst equation as... 

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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 electromotive force of a galvanic cell is a measure of the electrical work which can be obtained from the reaction in the cell. The total or maximum work which can be obtained from the cell reaction includes also the work which is done against the external forces owing to the changes in volume (formation of gas, etc.) of the reacting substances. From the definition of affinity (p. 318) it follows, therefore, that the electromotive... 

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... 

LT is the standard cell potential difference, which is determined only by the reactants in definited standard states. This quantity results as the difference of standard electrode potentials. The power term Ila contains the corrected composition quantities a, (fugacities and activities) with the stoichiometric coefficients v, of the gases and condensed substances taking part in the cell reaction [10,12]. If a sensor at equilibrium delivers signals in agreement with Equation (25-7) then we have a reaction celt. In this case at solid electrolytes with oxide ion vacancies Vo> two reactions can be found besides... 

In Example 17.3, we computed the AH° for the cell reaction from the cell potential and its temperature coefficient. If the reaction were carried out irreversibly by simply mixing the reactants together, AH° is the heat that flows into the system in the transformation by the usual relation, AH = Qp. However, if the reaction is brought about reversibly in the cell, electrical work in the amount is produced. Then, by Eq. (9.4), the definition of AS,... 

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. 

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 sign in this equation stands for the definition of the voltage measurement (i) electrode I minus electrode II and (ii) direction of the cell reaction in Eq. (3.10). The sign changes if the conditions of the voltage measurements are altered. 

V and therefore the cell reaction occurs spontaneously. These cells are sometimes referred to as Mackereth sensors . Such galvanic sensors are also often termed fuel cell sensors and it is possible to measure either the resulting current or the cell voltage. In the former case, the term amperometric sensor in its widest definition is still correct, although the cell is fundamentally different from the usual Faradaic amperometric systems. Note that for the determination of atmospheric oxygen an alternative has become available in recent years in the form of optical sensors based on fluorescence. These sensors are very robust as they do not contain electrodes or a liquid phase and show very fast response times. 

By definition, electrolytes should be ionic conductors and electronic insulators. If they were not, then galvanic cells in which they were employed would self-discharge on standing because the cell reaction could proceed even on open circuit [106]. In practice many conventional solid electrolytes, especially those based on Cu systems, have a non-negligible electronic conductivity contribution from electrons and/or holes, but provided that this is small enough, a reasonable shelf-life can be obtained. 

Suppose we have a galvanic cell in a parricular zero-current equilibrium state. Each phase of the cell has the same temperature and pressure and a well-defined chemical composition. The activity of each reactant and product of the cell reaction therefore has a definite value in this state. 

Two features of this definition are worth noting. One is that EPH is defined as the heat of a reversible reaction, which essentially eliminates the various uncertainties arising from the irreversible factors such as overvoltage. Joule heat, thermal conductivity, concentration gradient and forced transfer of various particles like ions and electrons in electrical field, and makes the physical quantity more definite and comparable. This indicates that EPH is a characteristic measure of a cell reaction, because the term 8 (AG)/8T) p is an amoimt independent on reaction process, and only related to changes in the function of state. That is to say, EPH is determined only by the initial and the final states of the substances taking part in the reaction that occurs on the electrode-electrolyte interfaces, although other heats due to irreversible factors are accompanied. EPH is, unlike the heat of dissipation (Joule heat and the heats due to irreversibility of electrode processes and transfer processes), one of the fundamental characteristics of the electrode process. 

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 definition of EPH for the electrode reaction given by Eq. (7) or Eq. (8) is all similar to that of a cell reaction except on the absolute scale. These equations indicate that EPH of a halfcell, just like that of the cell reaction, is also a characteristic quantity that only relates to changes in the function of state, i.e. the entropies on the absolute scale, of substances taking part in the reaction. The heat effect occurs on the electrode-electrolyte interfaces. Evidently, when Eq. (7) or Eq.(8) is apphed to a cell reaction, the terms, (H /H2) in Eq. (5), common to both electrodes of the cell, does not appear exphdtly because they are deleted ultimately. 

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