Electrode kinetics, reaction orders

In chemical kinetics, reaction orders are the most important parameters in determining reaction mechanisms. Reaction orders were first introduced into electrode kinetics by Vetter (64). For determination of reaction orders, double layer effects are suppressed by working in excess of supporting electrolyte and rates are compared at constant electrode potential V (i.e., constant potential drop across the metal-solution interface) as a function of concentration. Then,... 

The concept of stoichiometric number was introduced in electrochemistry by Horiuti and Ikusima [42, 43] for the hydrogen electroreduction reaction. We need to introduce the stoichiometric number V in complex multielectron electrode kinetics in order to distinguish different possible mechanisms. The International Union of Pure and Applied Chemistry (lUPAC) defines the stoichiometric number in electrochemistry as a positive integer that indicates the number of identical activated complexes formed and destroyed in the completion of the overall reaction as formulated with the charge number, n [44, 45]... 

The rate of an electrochemical process can be limited by kinetics and mass transfer. Before considering electrode kinetics, however, an examination of the nature of the iaterface between the electrode and the electrolyte, where electron-transfer reactions occur, is ia order. 

Thus, worldwide efforts have focused on the elucidation of the reaction mechanism. For this purpose, knowledge about the following items is vital (1) identification of reaction products and the electrode kinetics of the reactions involved, (2) identification of adsorbed intermediate species and their distribution on the electrode surface, and (3) dependence of the electrode kinetics of the intermediate steps in the overall and parasitic reactions on the structure and composition of the electrocatalyst. It is only after a better knowledge of the reaction mechanisms is obtained that it will be possible to propose modifications of the composition and/or structure of the electrocatalyst in order to significantly increase the rate of the reaction. 

CI2 evolution reaction, 38 56 electrochemical desorption, 38 53-54 electrode kinetics, 38 55-56 factors that determine, 38 55 ketone reduction, 38 56-57 Langmuir adsorption isotherm, 38 52 recombination desorption, 38 53 surface reaction-order factor, 38 52 Temkin and Frumkin isotherm, 38 53 real-area factor, 38 57-58 regular heterogeneous catalysis, 38 10-16 anodic oxidation of ammonia, 38 13 binding energy quantification, 38 15-16 Haber-Bosch atrunonia synthesis, 38 12-13... 

In Chapter 7 general kinetics of electrode reactions is presented with kinetic parameters such as stoichiometric number, reaction order, and activation energy. In most cases the affinity of reactions is distributed in multiple steps rather than in a single particular rate step. Chapter 8 discusses the kinetics of electron transfer reactions across the electrode interfaces. Electron transfer proceeds through a quantum mechanical tunneling from an occupied electron level to a vacant electron level. Complexation and adsorption of redox particles influence the rate of electron transfer by shifting the electron level of redox particles. Chapter 9 discusses the kinetics of ion transfer reactions which are based upon activation processes of Boltzmann particles. 

The kinetics of MeOH oxidation of a 1 1 PfRu in an MEA has been well established by Vidakovic, Christov, and Sundmacher. At low overpotentials, the MeOH oxidation reaction was found to be zero order in MeOH concentration, indicating that CO oxidation is the rate-determining step. A Tafel slope of 50-60 mV dec was found at 60°C. At higher overpotentials, positive reaction orders were found, suggesting that MeOH adsorption becomes rate determining. An activation energy of 55 kj moP was found this agrees well with the values found for similar bulk PtRu electrodes. 

The second-order reaction with adsorption of the ligand (2.210) signifies the most complex cathodic stripping mechanism, which combines the voltammetric features of the reactions (2.205) and (2.208) [137]. For the electrochemically reversible case, the effect of the ligand concentration and its adsorption strength is identical as for reaction (2.205) and (2.208), respectively. A representative theoretical voltammo-gram of a quasireversible electrode reaction is shown in Fig. 2.86d. The dimensionless response is controlled by the electrode kinetic parameter m, the adsorption... 

Hendrikx et al. [36] investigated the reaction kinetics and mechanism of zinc and amalgamated zinc electrode in KOH solutions in the concentration range 1.5-10 M using galvanostatic methods. On the basis of Tafel slopes and reaction orders for OH , the following rate determining step (rds) in anodic and cathodic processes was postulated ... 

In electrode kinetics, however, the charge transfer rate coefficient can be externally varied over many orders of magnitude through the electrode potential and kd can be controlled by means of hydrodynamic electrodes so separation of /eapp and kd can be achieved. Experiments under high mass transport rate at electrodes are the analogous to relaxation methods such as the stop flow method for the study of reactions in solution. 

In electrode kinetics, the reaction order with respect to the species k can be defined by... 

Notice that, because of the strong dependence of the kinetics on electrode potential, the determination of the electrochemical reaction order requires that the partial cathodic or anodic current densities are measured at constant potential in addition to the activities of the other species remaining constant. 

Also, in complex electrode reactions involving multistep proton and electron transfer steps, the electrochemical reaction order with respect to the H+ or HO may also vary with pH, indicating a change of mechanism with pH. In this respect, the use of schemes of squares outlined in Sect. 2.2 is very useful in the analysis of these complex kinetics [13]. 

An electrocatalytic reaction is an electrode reaction sensitive to the properties of the electrode surface. An electrocatalyst participates in promoting or suppressing an electrode reaction or reaction path without itself being transformed. For example, oxygen reduction electrode kinetics are enhanced by some five orders of magnitude from iron to platinum in alkaline solutions or from bare carbon to carbon electrodes modified with Fe phthalocyanines or phenylporphyrins. For a comprehensive discussion of the subject, the reader is referred to refs. (76, 95, and 132-136). 

The goal of this chapter is to describe the application of hydrodynamic electrodes to the study of electrode kinetics and the kinetics of electrode and coupled homogeneous reactions. In order to do this, it is important to describe first the mass transport and how to fulfil experimentally the conditions described by the mass transport equations, i.e. electrode construction and operation. 

In order to distinguish the different Me-H interactions (such as size effects and electronic effects) in transition metal hydrides, the thermodynamics of H solutions have been carefully studied. Hydrogen activities can be established electrochemically at metal surfaces by using the metal as a hydrogen electrode (cathode). If the proton activity (pH) has been predetermined in an appropriate aqueous solution, the equilibrium hydrogen activity is determined through the electrochemical reaction H+(aq) + e (Me) = H. However, when we study the kinetics of the hydrogen electrode, various reaction steps such as... 

Quantitatively, the rate of hydrogen production is second order in [Pt] or [Au]232-234 and, although this has been attributed to particle-particle interactions,232 it is found that, if the particles are considered as microelectrodes, spherical electrode kinetics will explain this behaviour, (at least for particles above 100 A in diameter), whereas homogeneous reaction kinetics will... 

It is convenient at this juncture to introduce a concept that, in electro analytical chemistry, sometimes is referred to as the reaction order approach. Consider first the half-life-time, t1/2> which in conventional homogeneous kinetics refers to the time for the conversion of half of the substrate into product(s). From basic kinetics, it is well known that t /2 is independent of the substrate concentration for a reaction that follows a first-order rate law and that 1/t j2 is proportional to the initial concentration of the substrate for a reaction that follows a second-order rate law. Similarly, in electro analytical chemistry it is convenient to introduce a parameter that reflects a certain constant conversion of the primary electrode intermediate. In DPSCA, it is customary to use ti/2 (or to.s), which is the value of (f required to keep the value of Ri equal to 0.5. The reaction orders (see Equation 6.30) are then given by Equations 6.35 and 6.36, where Ra/b = a + b, and Rx = x (in reversal techniques such as DPSCA, in which O and R are in equilibrium at the electrode surface, it is not possible to separate the... 

A distinguishing aspect in electrode kinetics is that the heterogeneous rate constants, kred and kox, can be controlled externally by the difference between the inner potential in the metal electrode (V/>M) and in solution (7/>so1) that is, through the interfacial potential difference E = electrode setup (typically, a three-electrode arrangement and a potentiostat), the E-value can be varied in order to distort the electrochemical equilibrium and favor the electro-oxidation or electro-reduction reactions. Thus, the molar electrochemical Gibbs energy of reaction Scheme (l.IV), as derived from the electrochemical potentials of the reactant and product species, can be written as (see Eqs. 1.32 and 1.33 with n = 1)... 

Figure 12(b) shows the local current distribution of first and second order reactions and applied over potentials ° for the coupled anode model without the mass transfer parameter y. The figure also shows the effect of a change in the electrode kinetics, in terms of an increase in the reaction order (with respect to reactant concentration) to 2.0, on the current distribution. Essentially a similar variation in current density distribution is produced, to that of a first order reaction, although the influence of mass transport limitations is more severe in terms of reducing the local current densities. 

The same equation had previously been derived by Fronaeus and Ostman [249]. These workers made two further important contributions to the theory. Taking it for granted that the catalysed exchange proceeded by an electron transfer mechanism, they related ucat to the concentrations of Ox and Red by the theory of electrode kinetics. For simple redox couples whose electrochemical reaction orders are unity, this leads to... 

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