Nemst equation applied

In the mechanism of the anodic iron dissolution, described in this section, the formation process of the intermediate of ferrous hydroxocomplexes, Eqn. 9-21a, is in the quasi-equilibrium state so that the Nemst equation applies between the adsorption coverage, 6p oa-, of the intermediate FeOH [d and the overvoltage, t). Accordingly, for the range of relatively low coverages of adsorption to which Langmuir s adsorption isotherm applies, we obtain Eqn. 9-22 ... 

The Nemst equation applies (if we neglect the activity coefficients of the ions, in keeping with PB theory) to the emf (electromotive force) of an electrochemical cell. The emf of such a cell and the surface potential of a colloidal particle are quantities of quite different kinds. It is not possible to measure colloidal particle with a potentiometer (where would we place the electrodes ), and even if we could, we have no reason to expect that it would obey the Nemst equation. We have been at pains to point out that all the experimental evidence on the n-butylam-monium vermiculite system is consistent with the surface potential being roughly constant over two decades of salt concentration. This is clearly incompatible with the Nemst equation, and so are results on the smectite clays [28], Furthermore, if the zeta potential can be related to the electrical potential difference deviations from Nemst behavior, as discussed by Hunter... 

Relaxed interfaces cannot be polarized unless special precautions are taken. Capacitances can of course be obtained as derived quantities by differentiating the surface charge with respect to the surface potentieil if changes In the latter are known, which is possible if the Nemst equation applies. We now discuss direct capacitance measurements on reversible interfaces. To start with, the response of such an interface to an applied field has to be considered. The basic problem is that not only are double layers built up, but also charge transfer across the interfaces takes place and diffusion of charge-determining ions to or from the surface starts to play a role. With regard to these physical processes only the sum-effect is measured, and this sum has to be divided into its parts to obtain the capacitance. Distinctions can be made because the three constituents mentioned react in a different way to the frequency of the external field. 

The Nemst equation applied to Reaction (15-2), written in terms of the formal potential and concentrations, is... 

The Nemst equation, applied to this reaction, produces the relationship ... 

Table 4.3 shows, however, that redox potentials often differ greatly from electrode potentials. Ion activities are only qualitatively related to redox potentials, except in rare circumstances. One reason is that the Nemst equation applies only to equilibrium. Redox reactions in soils are noiiequilibria, though in some cases for highly reduced soils, a steady state may be reached approximating equilibrium. Then only a few redox couples in the soil affect the platinum electrode and the result may approach a pseudo-equilibrium. 

For a reversible electron-transfer reaction, the Nemst equation applies, that is,... 

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... 

This form of corrosion occurs in the presence of stagnant corrosive solution near a hole, under a deposit, or any geometric shape that can form a crevice. It is also known as cavernous corrosion or underdeposit corrosion. This form of corrosion results from a concentration cell formed between the electrolyte within the crevice, which is oxygen starved, and the electrolyte present outside the crevice where plenty of oxygen is present. The metal within the crevice acts as anode, and the metal outside the crevice functions as the cathode. The difference in aeration produces a different equilibrium potential, given by the Nemst equation applied to the reaction... 

Thus the key experimental observation Equation (7.11), is satisfied in presence of spillover. When an external overpotential AUWR is applied, with a concomitant current, I, and O2 flux I/2F, although UWR is not fixed anymore by the Nemst equation but by the extremally applied potential, still the work function Ow will be modified and Equations (7.11) and (7.12), will remain valid as long as ion spillover is fast relative to the electrochemical charge transfer rate I/2F.21 This is the usual case in solid state electrochemistry (Figs. 7.3b, 7.3d) as experimentally observed (Figs. 5.35, 5.23, 7.4, 7.6-7.9). 

E = Faraday constant). The equilibrium potential E is dependent on the temperature and on the concentrations (activities) of the oxidized and reduced species of the reactants according to the Nemst equation (see Chapter 1). In practice, electroorganic conversions mostly are not simple reversible reactions. Often, they will include, for example, energy-rich intermediates, complicated reaction mechanisms, and irreversible steps. In this case, it is difficult to define E and it has only poor practical relevance. Then, a suitable value of the redox potential is used as a base for the design of an electroorganic synthesis. It can be estimated from measurements of the peak potential in cyclovoltammetry or of the half-wave potential in polarography (see Chapter 1). Usually, a common RE such as the calomel electrode is applied (see Sect. 2.5.1.6.1). Numerous literature data are available, for example, in [5b, 8, 9]. 

Abstract This chapter first explains the natural flotability of some minerals in the aspect of the crystal structure and demonstates the collectorless flotaiton of some minerals and its dependence on the h and pH of pulp. And then the surface oxidation is analysed eletrochemically and the relations of E to the composition of the solutions are calculated in accordance with Nemst Equation. The E h-pH diagrams of several minerals are obtained. Thereafter, electrochemical determination such as linear potential sweep voltammetry (LPSV) and cyclic voltammetry (CV) and surface analysis of surface oxidation applied to the sulphide minerals are introduced. And recent researches have proved that elemental sulfur is the main hydrophobic entity which causes the collectorless flotability and also revealed the relation of the amount of sulfur formed on the mineral surfaces to the recoveries of minerals, which is always that the higher the concentration of surface sulphur, the quicker the collectorless flotation rate and thus the higher the recovery. 

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. 

Note thai the true Nemst equation (equation (3.8)) has an electrode potential on the left-hand side, i.e. a potential that is measured (at equilibrium). The variant here does not have an electrode potential at all the term on the left-hand side is an imfmsed potential, i.e. it is applied through a power source such as a potentiostat. 

Applying Nemst equation, the electrode potential of the hydrogen electrode is given by... 

The second boundary condition involves a relation between the concentrations of A and D and the potential E. The simplest relation is obtained by (initially) assuming that there is charge-transfer equilibrium at the interface (a = 0), in which case the Nemst equation (7.47) can be applied ... 

Biochemists use the formal potential of a half-reaction at pH 7 (Eul) instead of the standard potential (E°), which applies at pH 0. E° is found by writing the Nemst equation for the half-reaction and grouping together all terms except the logarithm containing the formal concentrations of reactant and product. The combination of terms, evaluated at pH 7, is E°. ... 

E vs. log(id-i)/f which should be linear with a slope of 59.1/n mV at 25 °C if the wave is reversible. This method relies however upon a prior knowledge of n, and if this is not known then the method is not completely reliable as theory predicts that when the electron transfer process itself is slow, so that equilibrium at the electrode between the oxidized and reduced forms of the couple is established slowly and the Nemst equation cannot be applied, then an irreversible wave is obtained and a similar plot will also yield a straight line but of slope 54.2/ana mV at 25 °C (a = transfer coefficient, i.e. the fraction of the applied potential that influences the rate of the electrochemical reaction, usually cu. 0.5 na = the number of electrons transferred in the rate-determining step). Thus a slope of 59.1 mV at 25 °C could be interpreted either as a reversible one-electron process or an irreversible two-electron process with a = 0.45. If the wave is irreversible in DC polarography then it is not possible to obtain the redox potential of the couple. 

The chronoamperometric technique illustrates the principle that analytically useful current responses depend critically on the efficiency of analyte mass transport within the solution. The analyte mass transport in turn depends on the efficiency with which an applied voltage can maintain the surface concentrations of oxidized and reduced species at values specified by the Nemst equation. It is generally the case in chronoamperometry that the bulk concentration of one of the species is zero whereas the surface concentration of the other species is forced to zero by the applied potential, but this is not always so. 

For an electrode reaction to be considered reversible, it is necessary to compare the rate of the charge transfer process and the rate of the mass transport of electroactive species. When the mass transport rate is slower than the charge transfer one, the electrode reaction is controlled by the transport rate and can be considered as electrochemically reversible in that the surface concentration fulfills the Nemst equation when a given potential is applied to the electrode. In Electrochemistry, knowledge of the behavior of reversible electrode processes is very important, since these can be used as a benchmark for more complex systems (see Chap. 5 in [1] and Sect. 1.8.4 for a detailed discussion). 

In the preceding chapter, single pulse voltammetry and chronoamperometry were applied to the study of reversible electrode reactions of species in solution. Under these conditions, the surface concentrations fulfill Nemst equation and are independent of the duration of the experiment, regardless of the diffusion field... 

Buck, R.P. 1984. Kinetics of bulk and interfacial ionic motion Microscopic bases and limits of the Nemst-Planck equation applied to membrane systems. J. Membr. Sci. 17, 1-62. 

The standard potential applies to a half-cell when all the reactants are present at unit activity that is, when the solution species are near a concentration of 1 molar. The actual half-cell potential is a function of the solution concentrations and is related to these and to the standard potential E° by the Nemst equation. The Nemst equation for the generalized half-reaction... 

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