Electrode first order

The overpotential of an electrode process (Eq. (5.1.11)) is given in the case of a simple first-order electrode reaction as... 

The metals that display reversible half reactions with their respective ions and are found to be suitable for employing as first-order electrodes are Ag, Hg, Cu, Cd, Zn, Bi, Pb and Sn. However, several other metals like Fe, Co, Cr and W are not useful due to the following reasons ... 

Using a different convention, a simple metal in contact with its cations is also commonly termed an electrode of the first kind, or a class I or first-order electrode, while an electrode covered with an insoluble salt, e.g. AgCI I Ag for determining u(Cr), is termed an electrode of the second kind, or a class II or second-order electrtxle. In this latter convention, inert electrodes fur following redox reactions (cf. Chapter. 4) are somewhat confusingly termed redox electrodes. 

According to eqn. (79) for a first-order electrode reaction, the transfer coefficient can be obtained from... 

The simplest situation occurs if a metal (phase 1) is immersed in an electrolyte solution (phase 2), for example, Zn(s) Zn +(aq). An electrode and its electrolyte make up a half-cell compartment or a so-called first-order electrode, the potential of which is given in Eq. (7) ... 

In this equation, Cqx,s Cred,s represent, respectively, the concentrations of et Bred 1 the electrode surface. The expression (4.26) represents the Butler-Volmer equation for any first-order electrode reaction. Its rate, by definition, is proportional to the reactant concentration at the electrode surface. 

K. Darowicki, P. Slepski, Dynamic electrochemical impedance spectroscopy of the first order electrode reaction, J. Electroanal. Chem., 2003,547, pp. 1-8. 

K. Darowicki, J. Majewska, The effect of a polyharmonic structure of the perturbation signal on the results of harmonic analysis efthe current of a first-order electrode reaction, Electrochim. Acta, 1998 44, pp. 483-490. 

This difference is a measure of the free-energy driving force for the development reaction. If the development mechanism is treated as an electrode reaction such that the developing silver center functions as an electrode, then the electron-transfer step is first order in the concentration of D and first order in the surface area of the developing silver center (280) (Fig. 13). Phenomenologically, the rate of formation of metallic silver is given in equation 17,... 

In this scheme the reversible conversion of A to O is the reaction whose rate is to be studied, whereas the reduction of O to R is the electrode process. Scheme XIV can also represent a pseudo-first-order formation of O. A specific example is the acid-base equilibrium of pyruvic acid, shown in Scheme XV. 

This equation is that of a first-order reaction process, and thus the fraction of material electrolysed at any instant is independent of the initial concentration. It follows that if the limit of accuracy of the determination is set at C, = 0.001 C0, the time t required to achieve this result will be independent of the initial concentration. The constant k in the above equation can be shown to be equal to Am/ V, where A is the area of the pertinent electrode, V the volume of the solution and m the mass transfer coefficient of the electrolyte.20 It follows that to make t small A and m must be large, and V small, and this leads to the... 

Figure 4.2 shows the computer simulation results of such a dynamic aeration experiment. The y-axis shows the response fraction with respect to time. The gas phase response is typically first-order, and the liquid phase shows some lag or delay on the signal. The electrode response is much more delayed for a slow-acting electrode.4... 

Consider again the electron-transfer reaction O + ne = R the actual electron transfer step involves transfer of the electron between the conduction band of the electrode and a molecular orbital of O or R (e.g., for a reduction, from the conduction band into an unoccupied orbital in O). The rate of the forward (reduction) reaction, Vf, is first order in O ... 

Moreover, the product of an electrode process may also vary with the substrate concentration. In particular, this occurs when the reactive intermediate can further react by either a first-order or a higher-order chemical process or when the intermediate is able to react with molecules of the starting material. Examples of the latter type of reaction are... 

Consider the case when the equilibrium concentration of substance Red, and hence its limiting CD due to diffusion from the bulk solution, is low. In this case the reactant species Red can be supplied to the reaction zone only as a result of the chemical step. When the electrochemical step is sufficiently fast and activation polarization is low, the overall behavior of the reaction will be determined precisely by the special features of the chemical step concentration polarization will be observed for the reaction at the electrode, not because of slow diffusion of the substance but because of a slow chemical step. We shall assume that the concentrations of substance A and of the reaction components are high enough so that they will remain practically unchanged when the chemical reaction proceeds. We shall assume, moreover, that reaction (13.37) follows first-order kinetics with respect to Red and A. We shall write Cg for the equilibrium (bulk) concentration of substance Red, and we shall write Cg and c for the surface concentration and the instantaneous concentration (to simplify the equations, we shall not use the subscript red ). 

When only taking into account the concentration polarization in the pores (disregarding ohmic potential gradients), we must use an equation of the type (18.15). Solving this equation for a first-order reaction = nFhjtj leads to equations exactly like (18.18) for the distribution of the process inside the electrode, and like (18.20) for the total current. The rate of attenuation depends on the characteristic length of the diffusion process ... 

A semi-empirical, second-order response lag is used. This consists of a first-order lag equation representing the diffusion of oxygen through the liquid film on the surface of the electrode membrane... 

Early studies of ET dynamics at externally biased interfaces were based on conventional cyclic voltammetry employing four-electrode potentiostats [62,67 70,79]. The formal pseudo-first-order electron-transfer rate constants [ket(cms )] were measured on the basis of the Nicholson method [99] and convolution potential sweep voltammetry [79,100] in the presence of an excess of one of the reactant species. The constant composition approximation allows expression of the ET rate constant with the same units as in heterogeneous reaction on solid electrodes. However, any comparison with the expression described in Section II.B requires the transformation to bimolecular units, i.e., M cms . Values of of the order of 1-2 x lO cms (0.05 to O.IM cms ) were reported for Fe(CN)g in the aqueous phase and the redox species Lu(PC)2, Sn(PC)2, TCNQ, and RuTPP(Py)2 in DCE [62,70]. Despite the fact that large potential perturbations across the interface introduce interferences in kinetic analysis [101], these early estimations allowed some preliminary comparisons to established ET models in heterogeneous media. 

Although there are differences in the approach curves with the constant-composition model, it would be extremely difficult to distinguish between any of the K cases practically, unless K was below 10. Even for K = 10, an uncertainty in the tip position from the interface of 0. d/a would not allow the experimental behavior for this rate constant to be distinguished from the diffusion-controlled case. For a typical value of Z)Red, = 10 cm s and electrode radius, a= 12.5/rm, this corresponds to an effective first-order heterogeneous rate constant of just 0.08 cm s. Assuming K,. > 20 is necessary... 

Typical theoretical concentration profiles, observed at a probe electrode, for the consumption of a receptor phase species in a first-order interfacial reaction are shown in Fig. 16. The simulation involved solving Eq. (30) with appropriate boundary conditions. 

The rate of the electrode process—similar to other chemical reactions— depends on the rate constant characterizing the proportionality of the rate to the concentrations of the reacting substances. As the charge transfer reaction is a heterogeneous process, these constants for first-order processes are mostly expressed in units of centimetres per second. 

Electrocatalysis employing Co complexes as catalysts may have the complex in solution, adsorbed onto the electrode surface, or covalently bound to the electrode surface. This is exemplified with some selected examples. Cobalt(I) coordinatively unsaturated complexes of 2,2 -dipyridine promote the electrochemical oxidation of organic halides, the apparent rate constant showing a first order dependence on substrate concentration.1398,1399 Catalytic reduction of dioxygen has been observed on a glassy carbon electrode to which a cobalt(III) macrocycle tetraamine complex has been adsorbed.1400,1401... 

This value represents the upper limit of a first order reaction rate constant, k, which may be determined by the RHSE. This limit is approximately one order of magnitude smaller that of a rotating electrode. One way to extend the upper limit is to combine the RHSE with an AC electrochemical technique, such as the AC impedance and faradaic rectification metods. Since the AC current distribution is uniform on a RHSE, accurate kinetic data may be obtained for the fast electrochemical reactions with a RHSE. 

In potentiometry, the variation of the potential of a Pt electrode relative to a calomel reference electrode represents the time-dependent bromine concentration. Available [Br2] is about 2 x 10-5-10-4 m pseudo-first-order conditions ([Ol] [Br2]) have to be used. Rate constants up to 104 5 m- 1 s 1 can thus be obtained (Atkinson and Bell, 1963 Dubois et ai, 1968). 

---