Nemst equations

Nevertheless, the earlier thermodynamic treatment left one significant equation still very much present and effective when a change toward the kinetic approach occurred. This equation (Nemst s law) is used today and probably will be used even when all electrochemical calculations are wrapped up inside various companies software offerings. Nemst s equation,11 which treats the electrode/solution interface at equilibrium in a thermodynamic way, is the subject of the following section. 

From the century s beginning, through its midpoint, the electrochemistry of electrodes was based upon the treatment given by Nemst (Section 7.2.36). This had been derived first, for an interface between a metal and its ions in solution, but the treatment had spread (Planck and Henderson, 1890-1907) to the potential difference between two liquids containing different concentrations of electrolytes. The first of these two treatments yields an equation (Nemst equation) identical in form to the... 

These equations become more complex when the limitations due to the charge transfer kinetics arise, and other overpotentials, such as that of the bubble formation/break-off and the crystal deposition/reconstructions have to be considered. In this chapter, some typical cases were considered, however, the resolution of the other equations (Nemst-Planck equations) with their continuity and the corresponding Navier-Stokes expressions have to be evaluated carefully for each real situation. 

When there is an oxidizer in the liquid and the concentration of this is increased, the corrosion potential is generally increased, as shown in Figures 6.1 and 6.2. The shift is due to the activity term in the reversible potential equation (Nemst s equation, (3.9)) increased activity of oxidizers gives increased reversible potential for the cathodic reaction. This may lead to an increase in corrosion rate, as shown on the right in Figures 6.1 and 6.2 for active and active-passive metals, respectively. 

Provided that the redox equilibrium (7.5) is electrochemically reversible under potentiometric conditions at the inert electrode, the electrode will assume a potential given by the following equation (Nemst equation) ... 

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... 

For more complicated redox reactions, a general fonn of the Nemst equation may be derived by analogy with A2.4.113. If we consider a stoichiometric reaction of the following type ... 

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 ... 

Combining equation 6 and 7 with the Van t Hoff isotherm the Nemst equation for electrochemicA reactions is obtained ... 

Equation 11 gives the conductivity for a particular ion having a transference number, in a crystal, which is the Nemst-Einstein relationship. 

The doped Zr02 stmctures are used as electrochemical sensors, as, for example, when used to detect oxygen in automotive exhaust (see Exhaust CONTROL, automotive). The sensor voltage is governed by the Nemst equation (eq. 17) where the activities are replaced by oxygen partial pressures and the air inside the chamber is used as reference. 

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. 

Smaller values of necessitate the appHcation of voltages greater than those calculated from the Nemst equation to obtain a corresponding set of surface concentrations of electroactive species. These voltages are called overpotentials and iadicate chemically related difficulties with the electrolysis. In other words, electron exchange between the electrode and the electroactive species is impeded by the chemistry of the process itself. 

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. 

Equation 14 is a form of the Nemst equation. The overall chemical reaction for the passage of 2 Earadays of charge in the external circuit from right to left... 

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... 

These three terms represent contributions to the flux from migration, diffusion, and convection, respectively. The bulk fluid velocity is determined from the equations of motion. Equation 25, with the convection term neglected, is frequently referred to as the Nemst-Planck equation. In systems containing charged species, ions experience a force from the electric field. This effect is called migration. The charge number of the ion is Eis Faraday s constant, is the ionic mobiUty, and O is the electric potential. The ionic mobiUty and the diffusion coefficient are related ... 

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... 

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