Electrode potentials diffusion

In addition, the temperature dependence of the diffusion potentials and the temperature dependence of the reference electrode potential itself must be considered. Also, the temperature dependence of the solubility of metal salts is important in Eq. (2-29). For these reasons reference electrodes with constant salt concentration are sometimes preferred to those with saturated solutions. For practical reasons, reference electrodes are often situated outside the system under investigation at room temperature and connected with the medium via a salt bridge in which pressure and temperature differences can be neglected. This is the case for all data on potentials given in this handbook unless otherwise stated. 

The electrode current depends on the rates of the coupled reactions, but by suitable adjustment of the electrode potential (into the diffusion current region for the electrode reaction) the rate of the reduction reaction can be made so fast that the current depends only on the rate of the prior chemical reaction. The dependence of the observed current on the presence of the chemical reaction is a measure of the rate. 

The equilibrium potentials and E, can be calculated from the standard electrode potentials of the H /Hj and M/M " " equilibria taking into account the pH and although the pH may be determined an arbitrary value must be used for the activity of metal ions, and 0 1 = 1 is not unreasonable when the metal is corroding actively, since it is the activity in the diffusion layer rather than that in the bulk solution that is significant. From these data it is possible to construct an Evans diagram for the corrosion of a single metal in an acid solution, and a similar approach may be adopted when dissolved O2 or another oxidant is the cathode reactant. 

Under certain conditions, it will be impossible for the metal and the melt to come to equilibrium and continuous corrosion will occur (case 2) this is often the case when metals are in contact with molten salts in practice. There are two main possibilities first, the redox potential of the melt may be prevented from falling, either because it is in contact with an external oxidising environment (such as an air atmosphere) or because the conditions cause the products of its reduction to be continually removed (e.g. distillation of metallic sodium and condensation on to a colder part of the system) second, the electrode potential of the metal may be prevented from rising (for instance, if the corrosion product of the metal is volatile). In addition, equilibrium may not be possible when there is a temperature gradient in the system or when alloys are involved, but these cases will be considered in detail later. Rates of corrosion under conditions where equilibrium cannot be reached are controlled by diffusion and interphase mass transfer of oxidising species and/or corrosion products geometry of the system will be a determining factor. 

The sign of the electrode potential is arbitrarily defined as follows. A kation electrode (e.g., Zn in ZnS04 aq.) is said to be positive when it is positive to a unimolar (f — 1) solution of its ions an anion electrode e.g., CI2 in KC1) is said to be positive when it is positive to a unimolar solution of its ions. If a cell is made up of electrodes reversible with respect to any kinds of ions, its electromotive force is the algebraic difference of its electrode potentials, provided the electromotive force at the contact of the two solutions, due to diffusion (cf. Jahn, Elcktro-chcmie) is neglected. 

Anodic shipping voltammetry (ASV) is the most widely used form of stripping analysis, hi this case, the metals are preconcenhated by elechodeposition into a small-volume mercury electrode (a tiiin mercury film or a hanging mercury drop). The preconcenhation is done by catiiodic deposition at a controlled tune and potential. The deposition potential is usually 0.3-0.5 V more negative than E° for the least easily reduced metal ion to be determined. The metal ions reach die mercury electrode by diffusion and convection, where diey are reduced and concentrated as amalgams ... 

Figure 18 shows the dependence of the activation barrier for film nucleation on the electrode potential. The activation barrier, which at the equilibrium film-formation potential E, depends only on the surface tension and electric field, is seen to decrease with increasing anodic potential, and an overpotential of a few tenths of a volt is required for the activation energy to decrease to the order of kBT. However, for some metals such as iron,30,31 in the passivation process metal dissolution takes place simultaneously with film formation, and kinetic factors such as the rate of metal dissolution and the accumulation of ions in the diffusion layer of the electrolyte on the metal surface have to be taken into account, requiring a more refined treatment. 

The EMIRS and SNIFTIRS methods provide the IR vibrational spectra (really the difference spectra - see later) of all species whose population changes either on the electrode surface or in the electrical double layer or in the diffusion layer in response to changing the electrode potential. Spectra will also be obtained for adsorbed species whose population does not change but which undergo a change in orientation or for which the electrode potential alters the Intensity, the position or shape of IR absorption bands. Shifts in band maxima with potential at constant coverage (d nax 6 very common for adsorbed species and they provide valuable information on the nature of adsorbate/absorbent bonding and hence also additional data on adsorbate orientation. 

The changes in surface concentrations of the components caused by current flow have two important effects They produce a change in electrode potential, and they imply that there is an upper limit to the cell currents when the diffusion flux attains its iimiting value. The first of these effects is considered in Section 6.3 the second, in the present section. 

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.)... 

Equilibrium electrode potentials are readily established when metal electrodes are in contact with melts. However, two difficnlties arise in attempts to measnre them suitable, sufficiently corrosion-resistant reference electrodes must be selected, and marked diffusion potentials develop at interfaces between different melts. 

The equation obtained can be used when the electrode potential can be varied independent of solution composition (i.e., when the electrode is ideally polarizable). For practical calculations we must change from the Galvani potentials, which cannot be determined experimentally, to the values of electrode potential that can be measured E = ( q + const (where the constant depends on the reference electrode chosen and on the diffusion potential between the working solution and the solution of the reference electrode). When a constant reference electrode is used and the working solutions are sufficiently dilute so that the diffusion potential will remain practically constant when their concentration is varied, dE (i(po and... 

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... 

The surface concentration Cq Ajc in general depends on the electrode potential, and this can affect significantly the form of the i E) curves. In some situations this dependence can be eliminated and the potential dependence of the probability of the elementary reaction act can be studied (called corrected Tafel plots). This is, for example, in the presence of excess concentration of supporting electrolyte when the /i potential is very small and the surface concentration is practically independent of E. However, the current is then rather high and the measurements in a broad potential range are impossible due to diffusion limitations. One of the possibilities to overcome this difficulty consists of the attachment of the reactants to a spacer film adsorbed at the electrode surface. The measurements in a broad potential range give dependences of the type shown in Fig. 34.4. 

This book seeks essentially to provide a rigorous, yet lucid and comprehensible outline of the basic concepts (phenomena, processes, and laws) that form the subject matter of modem theoretical and applied electrochemistry. Particular attention is given to electrochemical problems of fundamental significance, yet those often treated in an obscure or even incorrect way in monographs and texts. Among these problems are some, that appear elementary at first glance, such as the mechanism of current flow in electrolyte solutions, the nature of electrode potentials, and the values of the transport numbers in diffusion layers. 

Indicator electrodes, reference electrodes and diffusion potentials... 

If we consider the limiting current ( ,) to be confined to a merely diffusion-limited current (id), we can consider its value as follows. As an example we take the cathodic reduction of a Zn2+ solution with a considerable amount of KC1. We chose an Eapp value greater than Eiecomp of Zn2+ and less than decomp of K +, so that only Zn2+ is reduced. The transport of electricity is completely provided for by the excess of K+ and Cl ions and hence Zn2+ ions can reach the cathode only by diffusion. Suppose [Zn2+ ] in the bulk of the solution is equal to C and at the cathode surface is equal to c the latter therefore determines the electrode potential. For diffusion perpendicular to the electrode surface we have Fick s first law ... 

The case of the prescribed material flux at the phase boundary, described in Section 2.5.1, corresponds to the constant current density at the electrode. The concentration of the oxidized form is given directly by Eq. (2.5.11), where K = —j/nF. The concentration of the reduced form at the electrode surface can be calculated from Eq. (5.4.6). The expressions for the concentration are then substituted into Eq. (5.2.24) or (5.4.5), yielding the equation for the dependence of the electrode potential on time (a chronopotentiometric curve). For a reversible electrode process, it follows from the definition of the transition time r (Eq. 2.5.13) for identical diffusion coefficients of the oxidized and reduced forms that... 

In an ideal case the electroactive mediator is attached in a monolayer coverage to a flat surface. The immobilized redox couple shows a significantly different electrochemical behaviour in comparison with that transported to the electrode by diffusion from the electrolyte. For instance, the reversible charge transfer reaction of an immobilized mediator is characterized by a symmetrical cyclic voltammogram ( pc - Epa = 0 jpa = —jpc= /p ) depicted in Fig. 5.31. The peak current density, p, is directly proportional to the potential sweep rate, v ... 

Fig. 5.46 The dependence on time of the instantaneous current / at a dropping mercury electrode in a solution of 0.08 m Co(NH3)6C13 + 0.1 m H2SO4 + 0.5m K2S04 at the electrode potential where -7 -/d (i.e. the influence of diffusion of the electroactive substance is negligible) (1) in the absence of surfactant (2) after addition of 0.08% polyvinyl alcohol. The dashed curve has been calculated according to Eq. (5.7.23). (According to J. Kuta and I.

As demonstrated in Section 5.2, the electrode potential is determined by the rates of two opposing electrode reactions. The reactant in one of these reactions is always identical with the product of the other. However, the electrode potential can be determined by two electrode reactions that have nothing in common. For example, the dissolution of zinc in a mineral acid involves the evolution of hydrogen on the zinc surface with simultaneous ionization of zinc, where the divalent zinc ions diffuse away from the electrode. The sum of the partial currents corresponding to these two processes must equal zero (if the charging current for a change in the electrode potential is neglected). The potential attained by the metal under these conditions is termed the mixed potential Emix. If the polarization curves for both processes are known, then conditions can be determined such that the absolute values of the cathodic and anodic currents are identical (see Fig. 5.54A). The rate of dissolution of zinc is proportional to the partial anodic current. 

The basic theory of mass transfer to a RHSE is similar to that of a RDE. In laminar flow, the limiting current densities on both electrodes are proportional to the square-root of rotational speed they differ only in the numerical values of a proportional constant in the mass transfer equations. Thus, the methods of application of a RHSE for electrochemical studies are identical to those of the RDE. The basic procedure involves a potential sweep measurement to determine a series of current density vs. electrode potential curves at various rotational speeds. The portion of the curves in the limiting current regime where the current is independent of the potential, may be used to determine the diffusivity or concentration of a diffusing ion in the electrolyte. The current-potential curves below the limiting current potentials are used for evaluating kinetic information of the electrode reaction. 

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