Nernst’s law

When a metal is in contact with its metal ion in solution, an equilibrium potential is established commonly referred to as Nernst potential (Er). Metal deposition occurs at potentials negative of Er, and dissolution for E > Er. However, when a metal is deposited onto a foreign metal substrate, which will always be the case for the initial stages of deposition, it is frequently observed that the first monolayer on the metal is deposited at potentials which are positive of the respective Nernst potential [37, 38]. This apparent violation for Nernst s law simply arises from the fact that the interaction between deposit metal and substrate is stronger than that between the atoms of the deposit. This effect has been termed underpotential deposition (upd), to contrast deposition processes at overpotentials. (One should keep in mind, however, that despite the symmetrical technical terms the physical origins of both effects are quite different. While the reason for an overpotential is solely due to kinetic hindrance of the deposition process, is that for underpotential deposition found in the energetics of the adatom-substrate interaction.)... 

Since the electron transfer reaction remains at equilibrium during the entire scan, the amounts of A and B per unit surface area, EA and / B, obey Nernst s law ... 

The first formulation is more directly suited to the case of reactants in solution and the second to attached reactants. In the first case, the rate constants have the dimensions length time typically cm s, whereas in the second case, they have the dimensions of time-1, typically s When these rate constants are very large, equilibrium is achieved, corresponding to Nernst s law ... 

In addition to this, and in contrast with the homogeneous case discussed in Section 5.2.2, the diffusion of P and Q is therefore not perturbed by any homogeneous reaction. If, furthermore, the P/Q electron transfer at the electrode is fast and thus obeys Nernst s law, the diffusive contribution to the current in equations (5.11) and (5.12) is simply equal to the reversible diffusion-controlled Nernstian response, idif, discussed in Section 1.2. The mutual independence of the diffusive and catalytic contributions to the current, expressed as... 

The integral relationships above are valid for any transient technique other than cyclic voltammetry, since at this stage of the derivation, the fact that the potential is a linear function of time has not yet been introduced. It is also valid in the case where charge transfer is not fast and together with diffusion, kinetically governs the electrochemical response. In the present case, the linear relationship between potential and time comes into play through Nernst s law, leading to... 

Application of Nernst s law to equations (6.20) and (6.23) finally leads to the dimensionless expression of the voltammogram in the general case (KG zone in Figure 2.1) reported in Table 6.4. 

Application of Nernst s law as an y = 0 boundary condition thus leads to... 

That is, in the original plane and taking Nernst s law into account, we have... 

We consider now the case where the kinetics of the electrode electron transfer may interfere. Equations (6.213) and (6.214) are still valid and Nernst s law is replaced by equation (4.9). Combination of these three equations leads to equation (4.10), and from it, to equation (4.11). 

As Lyklema (1987) points out, the congruence observation implies the applicability of Nernst s law for the oxides under consideration (Figs. 3.4 and 3.17) ... 

Discuss some of the consequences of Fig. 3.4. Why does the congruence of surface charge vs ApH imply the applicability of Nernst s law for oxides ... 

The voltage is related to the activity of the electroactive component by Nernst s law which then provides the following relation... 

Now the voltage provides information on the activity according to Nernst s law whereas Eqs (8.53) and (8.54) indicate the time dependence of the concentration. This may be overcome by expanding Eqn (8.54) by d and by introducing the relation between changes in the concentration and the stoichiometry, dCj = (NJVff) d, where A/ is Avogadro s number... 

As discussed in Section 8.2 the relation between the chemical diffusion coefficient and diffusivity (sometimes also called the component diffusion coefficient) is given by the Wagner factor (which is also known in metallurgy in the special case of predominant electronic conductivity as the thermodynamic factor) W = d n ajd In where A represents the electroactive component. W may be readily derived from the slope of the coulometric titration curve since the activity of A is related to the cell voltage E (Nernst s law) and the concentration is proportional to the stoichiometry of the electrode material ... 

Therefore, the distribution ratio of B remains constant only if the ratio of the activity coefficients is independent of the total concentration of B in the system, which holds approximately in dilute solutions. Thus, although solutions of metal chelates in water or nonpolar organic solvents may be quite nonideal, Nernst s law may still be practically obeyed for them if their concentrations are very low (JCchehte< 10" ). Deviations from Nernst s law (constant D ) will in general take place in moderately concentrated solutions, which are of particular importance for industrial solvent extraction (see Chapter 12). 

The mass distribution constant is not affected by the concentration of the component of interest in either liquid or gas, which is a reasonable assumption when the concentration is sufficiently low (Nernst s law range). 

Figure 10,1 (A) Activity-molar concentration plot. Trace element concentration range is shown as a zone of constant slope where Henry s law is obeyed. Dashed lines and question marks at high dilution in some circumstances Henry s law has a limit also toward inhnite dilution. The intercept of Henry s law slope with ordinate axis defines Henry s law standard state chemical potential. (B) Deviations from Nernst s law behavior in a logarithmic plot of normalized trace/carrier distribution between solid phase s and ideal aqueous solution aq. Reproduced with modifications from liyama (1974), Bullettin de la Societee Francaise de Mineralogie et Cristallographie, 97, 143-151, by permission from Masson S.A., Paris, France. A in part A and log A in part B have the same significance, because both represent the result of deviations from Henry s law behavior in solid.

Figure 10,2 Deviations from Nernst s law in crystal-aqueous solution equilibria, as obtained from application of various thermodynamic models. (A and B) Regular solution (liyama, 1974). (C) Two ideal sites model (Roux, 1971a). (D) Model of local lattice distortion (liyama, 1974). Reprinted from Ottonello (1983), with kind permission of Theophrastus Publishing and Proprietary Co.

Figure 10.4 shows normalized Ba/K and Sr/K distributions between sanidine and a hydrothermal solution (liyama, 1972), Li/K between muscovite and a hydrothermal solution (Voltinger, 1970), and Rb/Na between nepheline and a hydrothermal solution (Roux, 1971b), interpreted through the local lattice distortion model, by an appropriate choice of the Nernst s law mass distribution constant K and the lattice distortion propagation factor r. 

Deviations from Nernst s law in log-distribution diagrams such as figure 10.5 are represented by the simple equation ... 

We have already seen that, within the range of Nernst s law, the solid/liquid partition coefficient differs from the thermodynamic constant by the ratio of the Henry s law activity coefficients in the two phases—i.e.,... 

If the original liquids are mutually soluble and the third component is soluble in only one of them, the mutual solubility will be diminished by its addition—according to Nernst s law, at low concentrations. The rise or fall of interfacial tension will thus depend on two superimposed effects, the change of surface tension of the better solvent owing to addition of the solute, and that in each of the two liquids due to diminished concentration of the other. The latter effect tends to increase the tension while the former may work in either direction. 

With any electrochemical technique to study kinetics, the electrode-solution interface is perturbed from its initial situation. The initial conditions may be such that the system is in a chemical equilibrium and this usually means that the interfacial potential difference is determined by Nernst s law holding for the two components O and R of a redox couple being present... 

These expressions can be simplified to the so-called d.c.-reversible , or Nernstian , expressions if kf is sufficiently large to omit the terms in aQjkt. In that case, the charge transfer process is no longer co-determining the reaction rate and it is easily seen that, in fact, the rate equation is replaced by Nernst s law holding for c 0 and Cr ... 

This cell uses Ag/AgCN electrodes which are reversible towards CN. The potential difference between the electrodes is then given by Nernst s law... 

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