Nemst equation potential

We now consider briefly the matter of electrode potentials. The familiar Nemst equation was at one time treated in terms of the solution pressure of the metal in the electrode, but it is better to consider directly the net chemical change accompanying the flow of 1 faraday (7 ), and to equate the electrical work to the free energy change. Thus, for the cell... 

The Nemst equation above for the dependence of the equilibrium potential of redox electrodes on the activity of solution species is also valid for uncharged species in the gas phase that take part in electron exchange reactions at the electrode-electrolyte interface. For the specific equilibrium process involved in the reduction of chlorine ... 

Once current passes tluough the interface, the Galvani potential difference will differ from that expected from the Nemst equation above the magnitude of the difference is temied the overpotential, which is defined heiiristically as... 

For a simple electron transfer reaction containing low concentrations of a redox couple in an excess of electrolyte, the potential established at an inert electrode under equilibrium conditions will be governed by the Nemst equation and the electrode will take up the equilibrium potential for the couple 0/R. In temis of... 

Cyclic voltammetry provides a simple method for investigating the reversibility of an electrode reaction (table Bl.28.1). The reversibility of a reaction closely depends upon the rate of electron transfer being sufficiently high to maintain the surface concentrations close to those demanded by the electrode potential through the Nemst equation. Therefore, when the scan rate is increased, a reversible reaction may be transfomied to an irreversible one if the rate of electron transfer is slow. For a reversible reaction at a planar electrode, the peak current density, fp, is given by... 

The expression for the mass-transport-limiting current density may be employed together with the Nemst equation to deduce the complete current-potential response in a solution containing only oxidized or reduced species... 

Gibbs values and the effective electrode potential follows the Nemst equation (see section C2.11). For the oxidation (anodic) reaction, the potential (E ) of the Nemst equation can be written as ... 

Corrosion occurs even if the two reactants involved are not at standard conditions. In this case the nonstandard equiUbrium potential for each reaction, often referred to as the reversible potential, can be calculated from the Nemst equation. Additional information on thermodynamic aspects of corrosion can be found in Reference 10. 

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 appHed 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 appHed potential, but this is not always so. 

Each reactant and product appears in the Nemst equation raised to its stoichiometric power. Thermodynamic data for cell potentials have been compiled and graphed (3) as a function of pH. Such graphs are known as Pourbaix diagrams, and are valuable for the study of corrosion, electro deposition, and other phenomena in aqueous solutions.Erom the above thermodynamic analysis, the cell potential can be related to the Gibbs energy change... 

As the Nemst equation suggests, concentration variations in the electrolyte lead to potential differences between electrodes of the same kind. These potential differences are concentration polarizations or concentration overpotentials. Concentration polarizations can also affect the current distribution. Predicting these is considerably more difficult. If concentration gradients exist, equations 25 and 27 through 29 must generally be solved simultaneously. 

The actual potential of the couple is given by the Nemst equation,... 

Nemst Equation the thermodynamic relationship between the equilibrium potential of an electrochemical reaction and the activities of the species involved in that reaction. 

The transmembrane potential derived from a concentration gradient is calculable by means of the Nemst equation. If K+ were the only permeable ion then the membrane potential would be given by Eq. 1. With an ion activity (concentration) gradient for K+ of 10 1 from one side to the other of the membrane at 20 °C, the membrane potential that develops on addition of Valinomycin approaches a limiting value of 58 mV87). This is what is calculated from Eq. 1 and indicates that cation over anion selectivity is essentially total. As the conformation of Valinomycin in nonpolar solvents in the absence of cation is similar to that of the cation complex 105), it is quite understandable that anions have no location for interaction. One could with the Valinomycin structure construct a conformation in which a polar core were formed with six peptide N—H moieties directed inward in place of the C—O moieties but... 

Otherwise it has been shown that the accumulation of electrolytes by many cells runs at the expense of cellular energy and is in no sense an equilibrium condition 113) and that the use of equilibrium thermodynamic equations (e.g., the Nemst-equation) is not allowed in systems with appreciable leaks which indicate a kinetic steady-state 114). In addition, a superposition of partial current-voltage curves was used to explain the excitability of biological membranes112 . In interdisciplinary research the adaptation of a successful theory developed in a neighboring discipline may be beneficial, thus an attempt will be made here, to use the mixed potential model for ion-selective membranes also in the context of biomembrane surfaces. 

From the foregoing discussion it will be clear that the stoichiometry of the oxidation [n in Eq. (1)] has no thermodynamic significance. It should not be used in the Nemst equation to describe the potential dependence of the equilibrium shown in Eq. (1). It is therefore better to describe n as the degree of oxidation of the polymer (i.e., the average number of holes per monomer unit), n is a potential-dependent parameter,... 

This isotherm is consistent with the modified electrochemical Langmuir isotherm, the Nemst equation and the potential-work function equivalence. For intermediate 0j and Pj values the isotherm of Eq. (6.58) is well approximated both by the Fowler-Guggenheim and by the Temkin isotherms. 

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). 

The Nemst equation describes the dependence of the half-cell potential on concentration ... 

Reducing and oxidizing conditions m a sediment determine the chemical stability of the solid compounds and the direction of spontaneous reactions. The redox state can be recognized as a voltage potential measured with a platinum electrode. This voltage potential is usually referred to as E or Eh defined by the Nemst equation, which was introduced in Chapter 5, Section 5.3.1 ... 

The thermodynamically stable oxidation state of a metal in a given environment is a function of the prevailing oxidation potential. The value of the potential is given by the Nemst equation, which is described in Chapter 5 for the generic reduction half-cell ... 

E = E °-------In Q The Nemst equation is used to convert between standard cell potentials and potentials of... 

As the Nemst equation describes, cell potentials are linked quantitatively to concentrations. One practical consequence of this relationship is that potential measurements can be used to determine concentrations of ions in... 

Atmospheric O2 has a partial pressure of 0.20 bar, and atmospheric water vapor is saturated with carbon dioxide. This dissolved CO2 forms carbonic acid, which generates a hydronium ion concentration of about 2.0 X 10 M. The Nemst equation allows calculation of the half-cell potential for the reduction of 02(g) under these... 

Electrode reactions are heterogeneous since they occur at interfaces between dissimilar phases. During current flow the surface concentrations Cg j of the substances involved in the reaction change relative to the initial (bulk) concentrations Cy p Hence, the value of the equilibrium potential is defined by the Nemst equation changes, and a special type of polarization arises where the shift of electrode potential is due to a change in equilibrium potential of the electrode. The surface concentrations that are established are determined by the balance between electrode reaction rates and the supply or elimination of each substance by diffusion [Eq. (4.9)]. Hence, this type of polarization, is called diffusional concentration polarization or simply concentration polarization. (Here we must take into account that another type of concentration polarization exists which is not tied to diffusion processes see Section 13.5.)... 

The concentration of one of the components, and hence its limiting current density, is zero. In this case the Nemst equation is not applicable for the equilibrium potential therefore, we must use a kinetic equation that is written in terms of potential rather than polarization. When an oxidizing agent is not present in the solution Cy.ox = 0> oiily anodic currents are possible in the system, and these produce an oxidizing agent. It then follows from Eq. (6.32) that... 

It is not a trivial point that 0fj vs. E curves are practically linear. In a reversible system the electrode potential can be linked to the activities (concentrations) of the potential-determining substances. In the system being discussed, this substance is atomic hydrogen. According to the Nemst equation we have E = const - (RTIF) X In Cjj. It follows that the degree of coverage, 0, is linearly related to the logarithm of concentration c in the solution ... 

Equation (11.2) remains valid as the first boundary condition in this case. The surface concentrations, c, of the reactants will remain constant, in accordance with the Nemst equation, when the electrode potential is held constant during current flow (and activation polarization is absent). Hence, the second boundary condition can be formulated as... 

A theoretical analysis of the functions obtained is mathematically difficult, hence a simplified analysis is given here. In reversible reactions, the reactant surface concentrations are related to potential in an unambiguous way. For reactions of the type Ox + ne Red, it follows from the Nemst equation and Eq. (12.5) that... 

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