Nernst coefficient

Nernst coefficient, Ettingshausen coefficient, Righi-Leduc coefficient,... 

When a heat current is made to flow in a conductor perpendicular to a magnetic field, an electric field is observed which is perpendicular to both the heat current and the magnetic field (Fig. lb). This effect was first observed in 1886 by Ettingshausen and Nernst. The Nernst coefficient, which defines this effect, is given by... 

In situations where trace element abimdance variations are large, the use of these distribution coefficients will certainly help to limit the possible ways in which the variations were generated. The fact that these distribution coefficients, particularly the Berthelot-Nernst coefficients, vary with P, T and composition, greatly limits their usefulness in situations where the variations in trace element chemistry are more subtle as could arise from P and T variations. For geothermometry and geobarometry, it is necessary to calculate true equilibrium constants and some possible approaches to this problem have been discussed here. 

The oxide solid elecU olytes have elecuical conductivities ranging from lO Q cm to 10 cm at 1000°C and these can be converted into diffusion coefficient data, D, for die oxygen ions by the use of the Nernst-Einstein relation... 

Standard potentials Ee are evaluated with full regard to activity effects and with all ions present in simple form they are really limiting or ideal values and are rarely observed in a potentiometric measurement. In practice, the solutions may be quite concentrated and frequently contain other electrolytes under these conditions the activities of the pertinent species are much smaller than the concentrations, and consequently the use of the latter may lead to unreliable conclusions. Also, the actual active species present (see example below) may differ from those to which the ideal standard potentials apply. For these reasons formal potentials have been proposed to supplement standard potentials. The formal potential is the potential observed experimentally in a solution containing one mole each of the oxidised and reduced substances together with other specified substances at specified concentrations. It is found that formal potentials vary appreciably, for example, with the nature and concentration of the acid that is present. The formal potential incorporates in one value the effects resulting from variation of activity coefficients with ionic strength, acid-base dissociation, complexation, liquid-junction potentials, etc., and thus has a real practical value. Formal potentials do not have the theoretical significance of standard potentials, but they are observed values in actual potentiometric measurements. In dilute solutions they usually obey the Nernst equation fairly closely in the form ... 

If the substance shared between two solvents can exist in different molecular states in them, the simple distribution law is no longer valid. The experiments of Berthelot and Jungfleiscli, and the thermodynamic deduction show, however, that the distribution law holds for each molecular state separately. Thus, if benzoic acid is shared between water and benzene, the partition coefficient is not constant for all concentrations, but diminishes with increasing concentration in the aqueous layer. This is a consequence of the existence of the acid in benzene chiefly as double molecules (C6H5COOH)2, and if the amount of unpolymerised acid is calculated by the law of mass action (see Chapter XIII.) it is found to be in a constant ratio to that in the aqueous layer, independently of the concentration (cf. Nernst, Theoretical Chemistry, 2nd Eng. trans., 486 Die Verteilnngssatz, W. Hertz, Ahrens h annulling, Stuttgart, 1909). 

Since can be expressed in terms of the Nernst equation (neglecting activity coefficients)... 

The interface separating two immiscible electrolyte solutions, e.g., one aqueous and the other based on a polar organic solvent, may be reversible with respect to one or many ions simultaneously, and also to electrons. Works by Nernst constitute a fundamental contribution to the electrochemical analysis of the phase equilibrium between two immiscible electrolyte solutions [1-3]. According to these works, in the above system electrical potentials originate from the difference of distribution coefficients of ions of the electrolyte present in the both phases. 

Equation (31) is true only when standard chemical potentials, i.e., chemical solvation energies, of cations and anions are identical in both phases. Indeed, this occurs when two solutions in the same solvent are separated by a membrane. Hence, the Donnan equilibrium expressed in the form of Eq. (32) can be considered as a particular case of the Nernst distribution equilibrium. The distribution coefficients or distribution constants of the ions, 5 (M+) and B X ), are related to the extraction constant the... 

Moreover, as the ratio uf/uf is by definition the partition coefficient of I, P , this parameter can be defined by putting into evidence the ratio of the ion activities in the Nernst equation ... 

As reversible ion transfer reactions are diffusion controlled, the mass transport to the interface is given by Fick s second law, which may be directly integrated with the Nernst equation as a boundary condition (see, for instance. Ref. 230 232). A solution for the interfacial concentrations may be obtained, and the maximum forward peak may then be expressed as a function of the interfacial area A, of the potential scan rate v, of the bulk concentration of the ion under study Cj and of its diffusion coefficient D". This leads to the Randles Sevcik equation [233] ... 

Most measurements include the determination of ions in aqueous solution, but electrodes that employ selective membranes also allow the determination of molecules. The sensitivity is high for certain ions. When specificity causes a problem, more precise complexometric or titri-metric measurements must replace direct potentiometry. According to the Nernst equation, the measured potential difference is a measure of the activity (rather than concentration) of certain ions. Since the concentration is related to the activity through an appropriate activity coefficient, calibration of the electrode with known solution(s) should be carried out under conditions of reasonable agreement of ionic strengths. For quantitation, the standard addition method is used. 

However, under most conditions the activity coefficients cannot be neglected, certainly for a single redox couple where the ox/red concentration ratio cannot be simply calculated from the true standard potential and the potential directly observed. In order to overcome this difficulty the concept of the formal potential was introduced, which represents a formal standard potential E ° measured in an actual potentiometric calibration and obeying the Nernst equation, E = E ° + (0.05916/n) log ([ox]/[red]) at 25° C, E"0 must meet the conditions under which the analytical measurements have to be made. Sometimes the formal potential values are decisive for the direction of the reaction between two redox couples even when the E° values do not differ markedly10. 

The ratio of the diffusion coefficient and the electrolytic mobility is given by the Nernst-Einstein equation (valid for dilute solutions)... 

Replacement of the diffusion coefficients by the electrolytic mobilities according to Eq. (2.3.22) yields the Nernst-Hartley equation ... 

It is very often necessary to characterize the redox properties of a given system with unknown activity coefficients in a state far from standard conditions. For this purpose, formal (solution with unit concentrations of all the species appearing in the Nernst equation its value depends on the overall composition of the solution. If the solution also contains additional species that do not appear in the Nernst equation (indifferent electrolyte, buffer components, etc.), their concentrations must be precisely specified in the formal potential data. The formal potential, denoted as E0, is best characterized by an expression in parentheses, giving both the half-cell reaction and the composition of the medium, for example E0,(Zn2+ + 2e = Zn, 10-3M H2S04). 

Definitive measurements by fundamental quantities complemented by an empirical factor, e.g. titre (titrimetry), as well as by well-known empirical (transferable) constants like molar absorption coefficient (spectrophotometry), Nernst factor (potentiometry, ISE), and conductivity at definite dilution (conductometry)... 

Depending on the type of relationships between the measured quantity and the measurand (analytical quantity) it can be distinguished (Danzer and Currie [1998]) between calibrations based on absolute measurements (one calibration is valid for all1 on the basis of the simple proportion y = b x, where the sensitivity factor b is a fundamental quantity see Sect. 2.4 Hula-nicki [1995] IUPAC Orange Book [1997, 2000]), definitive measurements (b is given either by a fundamental quantity complemented by an empirical factor or a well-known empirical (transferable) constant like molar absorption coefficient and Nernst factor), and experimental calibration. 

The mobility of eh was determined by measuring the equivalent conductance following pulse irradiation (Schmidt and Buck, 1966 Schmidt and Anbar, 1969). After correcting for the contribution of H30 and OH ions, they found the equivalent conductance of eh = 190 10 mho cm2. From this, these authors obtained the mobility p(eh) = 1.98 x 10"3 cm2/v.s. and the diffusion coefficient D(eh) = 4.9 x 10-5 cm2/s using the Nernst-Einstein relation, with about 5% uncertainty. The equivalent conductance of eh is the same as that for the OH - ion within experimental uncertainty. It is greater than that of the halide ion and smaller than that of eam... 

We need the Nernst equation to determine the change of the equilibrium potential with concentration. For this purpose the overall reaction is usually rewritten in such a way that all coefficients are integers, with negative stochiometric coefficients denoting the reactants. This results in an equation of the form ... 

The second boundary condition arises from the continuity of chemical potential [44], which implies - under ideally dilute conditions - a fixed ratio, the so-called (Nernst) distribution or partition coefficient, A n, between the concentrations at the adjacent positions of both media ... 

We consider, then, two media (1 for the cell-wall layer and 2 for the solution medium) where the diffusion coefficients of species i are /),yi and 2 (see Figure 3). For the planar case, pure semi-infinite diffusion cannot sustain a steady-state, so we consider that the bulk conditions of species i are restored at a certain distance <5,- (diffusion layer thickness) from the surface where c, = 0 [28,45], so that a steady-state is possible. Using just the diffusive term in the Nernst-Planck equation (10), it can be seen that the flux at any surface is ... 

If instead of semi-infinite diffusion, some distance (5m acts as an effective diffusion layer thickness (Nernst layer approximation), then a modified expression of equation (63) applies where ro is substituted by 1 / (1 /Vo + 1 /<5m ) (see equation (38) above). For some hydrodynamic regimes, which for simplicity, are not dealt with here, the diffusion coefficient might need to be powered to some exponent [57,58],... 

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