Nemst-type equation

For the adsorption of a phenoxy radical, the opposite behavior is shown. The curves shift with concentration in parallel, in the horizontal direction. Full coverage is reached at each concentration, but the potential corresponding to any given coverage changes with concentration according to a Nemst type equation (cf. Eq. 19F). The difference between the two types of behavior shows clearly that dhe potential dependence of 0 observed in the two regions is due to entirely different physical phenomena. 

Now, we can write a Nemst-type equation for the absolute metal-solution potential difference at the reversible potential, namely... 

The majority of the published PAFC and HT-PEM fuel cell models use a Nemst type equation to calculate the open circuit potential. Alternatively, empirical expressions may be used to express the cell voltage for a given operating temperature (Table 18.5). 

Flow along uncharged surfaces has been considered in secs. I.6.4f and e. surface conduction in sec. I.6.6d and mixed transport phenomena, simultaneously involving electrical, mechanical and diffusion types of transport In sec. 1.6.7. Specifically the Nemst-Planck equation ((1.6.7.1 or 2]) is recalled, formulating ion fluxes caused by the sum-effect of diffusion, conduction and convection. 

The limits of integration are the oxygen partial pressures maintained at the gas phase boundaries. Equation (10.10) has general validity for mixed conductors. To carry the derivation further, one needs to consider the defect chemistry of a specific material system. When electronic conductivity prevails, Eqs. (10.9) and (10.10) can be recast through the use of the Nemst-Einstein equation in a form that includes the oxygen self-diffusion coefficient Dg, which is accessible from ionic conductivity measurements. This is further exemplified for perovskite-type oxides in Section 10.6.4, assuming a vacancy diffusion mechcinism to hold in these materials. 

If two ionic solutions are brought into contact via a permeable membrane, difference in concentration or type of ion will give rise to a liquid junction potential. This concept differs from the earlier ones in that it involves the Nemst-Planck equation which embraces a theory of the influence of both electrical and concentration gradients on the ionic distribution. ... 

Reverse osmosis can be used for the separation of ions om an aqueous solution. Neutral membranes are mainly used for such processes and the transport of ions is determined by their solubility and diffusivity in the membrane (as expressed by the solute permeability coefficient, see eq V 162). The driving force for ion transport is the concentration difference, but if charged membranes or ion-exchange membranes are used instead of neutral membranes ion transport is also affected by the presence of the fixed charge. Teoreil [45] and Meyer and Sievers [46] have used a fixed charge theory to describe ionic transport through these type of systems. This theory is based on two principles the Nemst-Planck equation and Dorman equilibrium. 

The type and concentration of defects in sohds determine or, at least, affect the transport properties. For instance, the -> ion conductivity in a crystal bulk is usually proportional to the -> concentration of -> ionic charge carriers, namely vacancies or interstitials (see also Nemst-Einstein equation). Clustering of the point defects may impede transport. The concentration and mobility of ionic charge carriers in the vicinity of extended defects may differ from ideal due to space-charge effects (see also -> space charge region). 

The disagreement often observed between the ionic conductivity values measured directly and calculated from diffusion coefficient measurements via the Nemst-Einstein equation originates from several factors. The main one is attributed to the difference in the contributing species between the measurements. Electrical conductivity detects the motion of charged ions regardless of the type. However, the diffusion coefficient measures all mobile species, wheUier they are dissociated ions, charged multiplets, or... 

Two types of hypothesis were invoked, which lead to position-independent parameters [c, (x) = constant], to anal5dically solve the Nemst Planck equations. Either relationships between the concentrations are supposed in addition to electroneutrality in the bulk film or the migration terms are neglected. 

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 ... 

When both solutions are binary and identical in nature and differ only by their concentration and the component E of the held strength is given by Eq. (4.18), the diffusion potential 9 can be expressed by Eq. (4.19). An equation of this type was derived by Walther Nemst in 1888. Like other equations resting on Eick s law (4.1), this equation, is approximate and becomes less exact with increasing concentration. For the more general case of multicomponent solutions, the Henderson equation (1907),... 

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.)... 

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... 

As an example, consider a simple reaction of the type (6.2) taking place under pure diffusion control. At all times the electrode potential, according to the Nemst equation, is determined by the reactant concentrations at the electrode surface. It was shown in Section 11.2.3 that periodic changes in the surface concentrations which can be described by Eq. (11.19) are produced by ac flow. We shall assume that the amplitude of these changes is small (i.e., that Ac electrode polarization. With this substitution and using Eq. (11.19), we obtain... 

Reversal potentials for LSD were also determined over a range of external K+ concentrations. According to the Nemst equation, reversal potentials should shift approximately 60 mV per 10-fold shift in K+ concentration if K+ were the ionic species involved in a conductance change. Reversal potentials of LSD were found to shift almost exactly to the extent predicted by the Nemst equation for a K+-dependent potential. Of course, there are several different types of K+ conductances that could be activated by LSD, including the Ca2+-dependent outward current. To evaluate the latter possibility, midbrain slices were exposed... 

The slope is important because it gives us the opportunity to perform simple back of the envelope -type calculations. All we need to know is the number of decades of concentration to which the analyte has been diluted from a = 1. (Remember that the Nemst equation is formulated in terms of activity, which is the concentration perceived by the electrode.) As an illustration, we can rewrite equation (3.8) as an equation of the following type ... 

Ag+.Ag s obtained after having accounted for the second electrode by using equation (3.3). The activity is then obtained from the Nemst equation (equation (3.8)) as XAg = 0.68. The mole fraction and activity are the same for solid mixtures of this type, so the amalgam filling is 68 mol% silver. 

The maximum open-circuit photo voltage, attainable in a dye-sensitized solar cell, is the difference between the Fermi level of the solid under illumination and the Nemst potential of the redox mediator. However, for these devices this limitation has not been achieved and Voc is in general much smaller. It appears that Voc is kinetically limited and the diode Equation 17.12 can be applied for an n-type semiconductor in a regenerative cell.23... 

The Ncrnst equation was given before (Eq. 10.115), and in this chapter the effect of pH on the reduction potential of the hydrogen ion has been mentioned, but the effect in general should be emphasized. There are several types of reactions in which concentrations of the reactants and products affect the stability of various oxidation states. This can be understood through application of the Nemst equation. The reduction potential of hydrogen will vary with the concentration of the hydrogen ion hence the commonly known fact that many reasonably active metals dissolve in acid but rot in base. 

In order to be able to distinguish between active and passive transport through biological membranes, P. Meares and H. H. Ussing (95) likewise made a study of the fluxes through a membrane under the influence of diffusion together with an electric current. They studied the influxes and the outfluxes of sodium- and chloride ions at a cation exchange resin membrane. They started from the Nemst-Planck flux equations of the type ... 

G. Scatchard (138) found that the requirements of the Nemst equations are met in the case of an anion- and cation selective membrane of the heterogeneous type in combination with HC1, NaCl and CaCl2 solutions in the concentration range of approx. 10 4 n to approx. 0.1 n. 

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