Nernsts law

For fast electron transfer kinetics, the surface concentrations of O and R are at dynamic equilibrium and assumed to obey the Nernst law... 

Consider now the case where the molecules A and B are free to move in the solution. Noting that the volume concentrations of the three reactants obey the same Nernst laws as in the attached reactants case, the preceding analysis may be used simply by replacing the normalized charge by the normalized convoluted current (as defined in Section 1.3.2), Thus,... 

Electrocatalysis and the Rate of Electrochemical Reactions For a given electrochemical reaction A + ne B, which involves the transfer of n electrons at the electrode/ electrolyte interface, the equilibrium potential, called the electrode potential, is given by the Nernst law ... 

The reversible oxidation potential at the anode where process (X-4) takes place can be expressed according to the Nernst law by the equation ... 

Tracer methods — [i] The application of radiotracer methods in electrochemistry dates back to the pioneering works by Hevesy in 1914. The aim of these studies was to demonstrate that isotopic elements can replace each other in both -> electrodeposition and equilibrium processes (Nernst law -> Nernst equation). Nevertheless, Joliot s fundamental work in 1930 is considered by electrochemists as a landmark in the application of -> radiochemical (nuclear) methods in electrochemistry. 

The capacity factor k can also be defined in terms of Nernst Law, i.e., in terms of the ratio ns/nm, where ns is the total number of moles of the biosolute associated with the stationary phase, and nm is the total number of moles of the biosolute in the mobile phase. Hence, k can be expressed as... 

Additional deviations from the Nernst law [Eq. (4)] can come from kinetic effects in other words, if the potential scan is too fast to allow the system to reach thermal equilibrium. Two cases should be mentioned (1) ion transport limitation, and (2) electron transfer limitation. In case 1 the redox reaction is limited because the ions do not diffuse across the film fast enough to compensate for the charge at the rate of the electron transfers. This case is characterized by a square-root dependence of the current peak intensity versus scan rate Ik um instead of lk u. Since the time needed to cross the film, tCT, decreases as the square of the film thickness tCT d2, the transport limitation is avoided in thin films (typically, d < 1 xm for u < 100 mV/s). The limitation by the electron transfer kinetics (case 2) is more intrinsic to the polymer properties. It originates from the fact that the redox reaction is not instantaneous in particular, due to the fact that the electron transfer implies a jump over a potential barrier. If the scan... 

The partition of all three types should obey the Nernst law, but in most cases the concentrations of extractable species are affected by chemical equilibria Involving them and other components of the system. These must be taken into account when calculating the optimum conditions for quantitative extraction or separation. 

When, although vis-a-vis the mass transfer rate, the chemical reaction is slow compared with the backward electron transfer, the reduction or oxidation in Eq. (120) remains at equilibrium. The electrode potential is then given by the Nernst law in Eq. (122) ... 

The metal chelate distributes itself between the aqueous and organic phases according to the Nernst law... 

Nernst law (Fig. 4, curve 3). However, when the pH of the NADH solution differed from the pH of the solution in the cell, then the pH in the cell changed at the very moment NADH was added. A transmembrane potential was generated, the value of which exceeded the one that could be expected from the pH gradient on both sides of the membrane. A comparison of the curves 2 and 3 reveals that the maximum value of the observed potential is 2-2.5 times greater than that determined by the Nernst law. How much greater it was depended on NADH concentration. 

The extent to which the dimer is favored over that of the monomer is determined by the magnitude of This added seeondary equihbrium, this time appearing in the organic phase, is shown in Figure 3.5. The fundamental basis for the partitioning of HOAc between ether and water as introduced by the Nernst law is not violated and still is given by Kj). The measurable concentrations [HOAcjether and [HOAcjaq will definitely differ with this added dimerization reaction. Let us define D for this distribution equilibrium involving weak acid dissociation of HOAc in the aqueous phase and, at the same time, dimerization of HOAc in the ether phase as follows ... 

The equilibrium constant in the Nernst law can be approximated by calculation if the real behavior of component i in the raffinate phase and in the extract phase ate known. According to the Wilson equation, the activity coefficient depends on concentration and on temperature. At a constant temperature - for the concentrations Xj, -> 0 and Ft logarithmized activity coeffident approaches a certain value called critical value ... 

If you begin by expressing the equilibrium potential difference across an interface where both elements of a redox couple are present, then you can derive the Nernst law which expresses the potential of the corresponding electrode vs a reference electrode. 

In most documents, the expression of the Nernst law that is commonly chosen uses the number n of electrons exchanged. This expression then implicitly corresponds to a half-reaction written in the direction of oxidation (the activity of the oxidant is in the numerator). We prefer a more general expression involving the algebraic stoichiometric... 

Ideally, the two extreme states of this material should correspond to the C0O2/UC0O2 couple. To express the Nernst law In this material In a simplified manner, one can consider only the equilibrium of lithium ions which keep their oxidation number -i-l. This implies that the insertion material is a sufficiently good electronic conductor for the Insertion limit to be ruled by the ionic insertion sites. The redox half-reaction can then be written ... 

It is important to know the thermodynamic characteristics of redox couples in order to understand and qualitatively draw the current-potential curves . Mentioned here are some particular cases which are frequently seen in practice. When protons or hydroxide ions take part in the redox half-reaction and when the solution is buffered, one can assume that the proton or hydroxide ion activity remains constant whatever extent the reaction has reached. This is also the case when components present in large quantities take part in the half-reaction. In this instance therefore, the Nernst law is expressed by defining an apparent standard potential for this specific medium. These types of example are frequently found in systems involving highly acidic or highly basic solutions where the pH can be considered constant. Here apparent standard potentials are therefore defined, corresponding to aqueous solutions with fixed pH. 

If the solution under study is highly acidic (or highly basic) or if the solution is buffered, the Nernst law can be written as follows ... 

A similar situation is also found in systems using insertion materials where there is a high concentration of the ion being exchanged. The notion of apparent standard potential is again used in writing the Nernst law, in which only the insertion rate appears. One also refers to insertion isotherm. 

The Nernst law can be written as a function of the insertion rate, y, of manganese oxide ... 

This type of E/pHdiagram, also called Pourbaix diagram, is frequently used for redox equilibria in solutions, and also in the field of corrosion studies. It is a graphic illustration of thermodynamic data which results from applying the Nernst law. Section 3.4.1.4 focuses on the example of a particular part of the Pourbaix diagram which deals with the chlorine element in aqueous solution. Numerous other examples can easily be found in scientific literature. 

In the particular case in point here, the two elements of a single redox couple are present and therefore the open-circuit potential corresponds to the equilibrium potential given by the Nernst law that is applied to that couple. In this case, we can use the term of overpotential instead of polarisation. 

---