Equilibrium electrode

As demonstrated in Section 3.1, electrode equilibrium is a distribution equilibrium of charged species (including the electron) between the metal... 

The chlorine electrode behaves reversibly, i.e. electrode equilibrium is... 

In the multi-electrode reaction coupled system, the mixed potential E always locates between the highest and the lowest equilibrium potential. That is to say, at least there is an electrode equilibrium potential lower or higher than the mixed potential. 

In redox electrodes an inert metal conductor acts as a source or sink for electrons. The components of the half-reaction are the two oxidation states of a constituent of the electrolytic phase. Examples of this type of system include the ferric/ferrous electrode where the active components are cations, the ferricyanide/ferrocyanide electrode where they are anionic complexes, the hydrogen electrode, the chlorine electrode, etc. In the gaseous electrodes equilibrium exists between electrons in the metal, ions in solution and dissolved gas molecules. For the half-reaction... 

Figure 2. Energy scheme for different surfaces of a semiconductor electrode equilibrium with the same redox system...

The following table lists the standard electrode potentials (in V) of some electrodes of the first kind.1-3 These are divided into cationic and anionic electrodes. In cationic electrodes, equilibrium is established between atoms or molecules of the substance and the corresponding cations in solution. Examples include metal, amalgam, and the hydrogen electrode. In anionic electrodes, equilibrium is achieved between molecules and the corresponding anions in solution. The potential of the electrode is given by the Nemst equation in the form... 

Electrodes of the first kind These are based on a potential determining equilibrium such as Ag+ + e Ag or iQ2 + e C1 where, for cationic electrodes , equilibrium is established between atoms or molecules and their corresponding cations in solution or, for anionic electrodes , their corresponding anions. 

To yireparc electrodes both metals and nonmctals can be applied. Iodine in a solid state in contact with iodide solution can, for example, become an electrode reversible with respect to the iodide ions. When making such an electrode the iodine is placed into a glass vessel and the iodide solution poured over it current connection is made by a platinum wire, which is in contact with the iodine and acts as an indifferent electrode. Equilibrium at the electrode is attained according to the formula ... 

The electrode equilibrium potential, Veq.e, as related to the half-reaction Ox -I- ne — Red, is given by the the Nernst equation ... 

At the electrode equilibrium potential Feq e the cathodic current, ic, and the anodic one, 4, which represent the reduction and oxidation reaction rates at the electrode-solution interphase, respectively, are equal and the net current i = jid - /a is zero the ic = 4 value is called the exchange current, iq. The passage of net current i 0) through the cell causes some changes with respect to equilibrium, and these are generically indicated by the term polarizations . The differenee between the value of the electrode potential under flowing current, Fi g, and that of the equilib-... 

The exchange current density, which governs the rate of attainment of electrode equilibrium, varies enormously from one potential-determining redox couple to another. It varies not only with the initial concentration but also with the ratio of oxidant to reductant [Equation (14-14)]. In titrations performed at great dilution, the equilibrium near the end point may be reached slowly. Therefore, it may be advantageous to select a method of end-point detection that is not dependent on equilibrium near the end point. 

EXAMPLE 15-1 Consider the titration of arsenic(III) with bromate. In a hydrochloric add solution containing excess bromide, the end point can be determined potentiometrically by using the bromine-bromide couple as the potential-determining system. Alternatively, the same titration can be followed amperometrically by measuring the diffusion-controlled current due to excess bromine slightly beyond the end point. At an initial concentration of 5 x 10 M arsenic(III), the potentiometric titration can barely be carried out, because several minutes are required for electrode equilibrium at each point of the titration. The amperometric method gives a successM end point even at 5 x 10 M arsenic(III), the whole titration taking only a few minutes. ////... 

The potentiometric titration curves and indicators for the Fe(II)-dichromate reaction are discussed in Section 15-3. In general, from curves such as in Figure 15-2, the dichromate potential has been found to increase with acidity, as expected. The variations with the nature of the acid, however, have not yet been explained. In particular, the dichromate potential is so low in 0.1 M perchloric acid that the potential break is barely discernible. From the practical viewpoint it should be emphasized that the rate of attainment of electrode equilibrium, particularly near the end point and beyond it, becomes slower with increasing dilution. Nevertheless, the reaction itself proceeds quantitatively and reasonably rapidly even at extreme dilution. As little as 1 ng of chromium in 100 ml of solution ( 10 M dichromate) has been successfully titrated with an accuracy of 1% by use of an amperometric end point. 

These two processes add to give the overall electrode equilibrium expressed by equation (9.2.23). As a result the silver silver chloride responds to the activity of the chloride ion in solution. 

These have been obtained as photoemission work function w (cf. Fig. 1) at the electron electrode equilibrium potential (which for hexamethylphosphotriamide and liquid ammonia was measured by experiment, and, for water, calculated from the thermochemical data ) by making a correction for the ideal gas entropy according to Eq. (3) ri . It should be noted that the aforementioned value, computed in this manner, is independent of the solvated electron concentration (for the same standard concentration of localized and delocalized electrons). 

A knowledge of the electron-electrode equilibrium potential is necessary to form a judgement about the primary or secondary nature of the generation process (see Sect. 7) and the place of this process among other electrode reactions. 

A reversible electron electrode for liquid ammonia was known long ago Recently, the electron electrode equilibrium in liquid ammonia has been studied anew by a number of authors in a series of works on the electrochemistry of solvated electrons. 

Table 5 compares the standard potential of the electron electrode in hexamethylphosphotriamide (5 °C) with the standard potentials of alkali metals (25 °C). Data for liquid ammonia are also given. In both solvents the rubidium electrode potential serves as a reference point since it depends very little on the solvent. It is seen from the Table that in both solvents the standard equilibrium potential of the electron electrode is more positive than that of a lithium electrode and is close to the potentials of other alkali metals. In the course of experiment, cathodic production of dilute solutions (10 — 10 mol/1) of solvated electrons takes place and this makes the electron electrode equilibrium potential more positive compared to the standard value. In case of hexamethylphosphotriamide the same happens when electrons are bound in strong non-paramagnetic associates by the cations of all alkali metals except lithium (see Sect. 4). This enables one to assume that under the conditions of the experiments the electron-electrode equilibrium potential in liquid ammonia and hexamethylphosphotriamide is more positive than the equilibrium potential of all alkali metals. This makes thermodynamically possible primary cathodic generation of solvated electrons in solutions of all alkali metal salts in the two solvents. 

Before considering the theoretical ideas that relate the current to the overvoltage, we should understand the principle of the measurement of overvoltage. A cell is shown schematically in Fig. 34.5. A measured current is passed between the two electrodes A and B. The reference electrode R is the same kind of electrode as B. Matters are arranged so that the same electrode equilibrium is established at both B and R. When i = 0,B and R both have the same potential. When the current passes into B, this electrode has a potential measured on the potentiometer P that is different from that of R, which carries no current. This difference in potential is the measured overvoltage, rjm = The value of rj ... 

The cathodic polarization curve is constructed using the oxygen electrode equilibrium potential and the cathodic slope, 6<- = —0.05V/decade. The equilibrium cathode potential, geq,c is calculated by applying the Nemst equation to the oxygen reduction reaction, Eq. (4.13), for an oxygen concentration of 1.0x10 mol/1 at pH= 11. 

Equilibrium potential (also termed the reversible potential) for an electrode process measured versus a reference electrode Equilibrium potential of the anode reaction versus a reference electrode Equilibrium potential of the cathode reaction versus a reference electrode... 

Measurements are taken when the electrode equilibrium is attained and no diffusion flux passes in the system. 

Two groups of methods can be applied to this task equilibrium, which have already been considered above, and non-equilibrium ones. The latter, in turn, can be divided into stationary and nonstationary methods. The non-equilibrium methods can be applied only to Nemstian systems, which means that the electrode equilibrium is attained. Of course, the intervalence equilibria have also to be established. The whole system, however, is non-equilibrium because of the presence of diffusion fluxes of E(/) and B(/). These fluxes are constant at stationary conditions ... 

Equilibrium on a silver electrode Equilibrium on a platinum electrode ... 

Activation polarization is caused by electrode kinetics while concentration polarization is caused by concentration gradients in the electrode. Equilibrium potential is described by the Nemst equation (Hirschenhofer et al, 1998) ... 

Species j in the bulk of the electrolyte Species j near the electrode Equilibrium constant = k/k ... 

The sulfur dioxide electrode works on exactly the same general principle as the ammonia electrode. Equilibrium is established between the sulfite level in the sample and the sulfite level in the proprietary filling solution. Hydrogen ions formed in the internal filling solution according to the reaction of SO2 and HjO... 

As mentioned previously, two electrodes are required in potentiometric sensors. In the most simple case, the reference point is an electrode exposed to a gas with a well-known partial pressure. For example, in oxygen gauges, air can be used. Equation (10.9b) for each electrode equilibrium leads to the following relation,... 

The theory and practical aspect of potentio- and galvanostatic measurements of selective dissolution of homogeneous alloys are developed quite good [24-27], but not all the possibilities of chronovoltammetry are utilized. This is primarily determined by the fact that a solution of even a simplest diffusion problem for a perfectly smooth electrode at the linear potential trace is given by an integral equation [28, 29]. Obviously, accounting such complex nonlinear effects of non-equilibrium vacancy subsystem relaxation and alloy / solution interface displacement is hardly possible without the use of labor-intensive numerical calculations. At the same time the surface roughness of an electrode, equilibrium solid-phase adsorption accumulation of alloy components before selective dissolution, and ability of the mixed kinetic control can be taken into account in the analytieal solution of the voltammetric problem. 

By applying the Nemst equation to the hydrogen electrode equilibrium it is seen that the potential of a hydrogen electrode is given by... 

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