Second-Order Chemical Kinetic Mechanisms

In the previous chapter coupled chemical reactions that follow first-order chemical kinetics under the experimental conditions were considered. Although the resolution of the problem is more complex since (in general) we deal with coupled equation systems and the spatial and temporal grids may need to be refined when fast chemical processes occur, the mathematical problem nevertheless still consists of linear equations. 

To introduce the problematic nature of non-linear equation systems we study the second-order catalytic mechanism where species Y and Z are electroinactive in the range of potentials of the experiments and their concentrations are not in large excess compared to the electroactive ones  

In the initial and bulk conditions we assume that only species A and Y are initially present in solution at the concentrations and Cy, respectively  

Otherwise, and assuming that equilibrium conditions apply at the beginning of the experiment, the initial concentrations of the species at the beginning of the simulation are calculated from the corresponding chemical speciation problem. 

Regarding the surface conditions, these reflect the electroactivity of the species in the potential range of the study  

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The applications of this simple measure of surface adsorbate coverage have been quite widespread and diverse. It has been possible, for example, to measure adsorption isothemis in many systems. From these measurements, one may obtain important infomiation such as the adsorption free energy, A G° = -RTln(K ) [21]. One can also monitor tire kinetics of adsorption and desorption to obtain rates. In conjunction with temperature-dependent data, one may frirther infer activation energies and pre-exponential factors [73, 74]. Knowledge of such kinetic parameters is useful for teclmological applications, such as semiconductor growth and synthesis of chemical compounds [75]. Second-order nonlinear optics may also play a role in the investigation of physical kinetics, such as the rates and mechanisms of transport processes across interfaces [76]. 

According to the definition given, this is a second-order reaction. Clearly, however, it is not bimolecular, illustrating that there is distinction between the order of a reaction and its molecularity. The former refers to exponents in the rate equation the latter, to the number of solute species in an elementary reaction. The order of a reaction is determined by kinetic experiments, which will be detailed in the chapters that follow. The term molecularity refers to a chemical reaction step, and it does not follow simply and unambiguously from the reaction order. In fact, the methods by which the mechanism (one feature of which is the molecularity of the participating reaction steps) is determined will be presented in Chapter 6 these steps are not always either simple or unambiguous. It is not very useful to try to define a molecularity for reaction (1-13), although the molecularity of the several individual steps of which it is comprised can be defined. 

Cristol, S. J. (1947) The kinetics of the alkaline dehydrochlorination of the benzene hexachloride isomers. The mechanisms of second-order elimination reactions. Journal of the American Chemical Society, 69, 338-342. 

A distinction between "molecularity" and "kinetic order" was deliberately made, "Mechanism" of reaction was said to be a matter at the molecular level. In contrast, kinetic order is calculated from macroscopic quantities "which depend in part on mechanism and in part on circumstances other than mechanism."81 The kinetic rate of a first-order reaction is proportional to the concentration of just one reactant the rate of a second-order reaction is proportional to the product of two concentrations. In a substitution of RY by X, if the reagent X is in constant excess, the reaction is (pseudo) unimolecular with respect to its kinetic order but bimolecular with respect to mechanism, since two distinct chemical entities form new bonds or break old bonds during the rate-determining step. 

The investigation of the kinetics of a chemical reaction serves two purposes. A first goal is the determination of the mechanism of a reaction. Is it a first order reaction, A—or a second order reaction, 2A— Is there an intermediate A—>/— and so on. The other goal of a kinetic investigation is the determination of the rate constant(s) of a reaction. 

This set includes all reaction mechanisms that contain only first order reactions, as well as very few mechanisms with second order reactions. Any textbook on chemical kinetics or physical chemistry supplies a list. A few examples for such mechanisms are given below ... 

However, if it is known from kinetic or other evidence that a reaction M + N - Product is a simple elementary reaction, i.e., if it is known that its mechanism is simply the interaction between a molecule of M and a molecule of N, then the molecular theory of reaction rates predicts that the rate of this elementary step is proportional to the concentration of species M and the concentration of species N, i.e. it is second order overall. The reaction is also said to be bimolecular since two molecules are involved in the actual chemical transformation. 

For our present purposes, we use the term reaction mechanism to mean a set of simple or elementary chemical reactions which, when combined, are sufficient to explain (i) the products and stoichiometry of the overall chemical reaction, (ii) any intermediates observed during the progress of the reaction and (iii) the kinetics of the process. Each of these elementary steps, at least in solution, is invariably unimolecular or bimolecular and, in isolation, will necessarilybe kinetically first or second order. In contrast, the kinetic order of each reaction component (i.e. the exponent of each concentration term in the rate equation) in the observed chemical reaction does not necessarily coincide with its stoichiometric coefficient in the overall balanced chemical equation. 

A distinctive characteristic of styrene polymerization is its thermal selfinitiation at high temperatures (without the presence of a chemical initiator). The mechanism of styrene thermal initiation was first described by Mayo [12]. The kinetics of thermal initiation were described by Weickert and Thiele [13] as a second-order reaction, while Hui and Hamielec [14], Husain and Hamielec... 

Of the three SECM modes that can be used to study electrode reaction mechanisms—the TG/SC, feedback, and SG/TC modes—the former is the most powerful for measuring rapid kinetics. With this approach, fast followup and sandwiched chemical reactions can be characterized under steady-state conditions, which are difficult to study even with rapid transient techniques such as fast scan cyclic voltammetry or double potential step chronoamperometry, where extensive corrections for background currents are often mandatory (44). At present, first- and second-order rate constants up to 105 s 1 and 1010 M 1 s, respectively, should be measurable with SECM. The development of smaller tip and substrate electrodes that can be placed closer together should facilitate the detection and characterization of electrogenerated species with submirosecond lifetimes. In this context, the introduction of a fabrication procedure for spherical UMEs with diameters... 

Hydrated electrons react with certain water-soluble metalloporphyrin complexes, reducing the porphyrin ligands to pi-radical species. When the metal centers are Zn(II), Pd(II), Ag(II), Cd(II), Cu(II), Sn(IV), and Pb(II), the radical complexes are produced at diffusion-controlled rates and decay with second-order kinetics.188 Fe(III) porphyrins, on the other hand, yield Fe(II) porphyrins.189 Rather different behavior is seen in the reaction of e (aq) with [Ru(bpy)3]3 + here, parallel paths generate the well-known luminescent excited-state [ Ru(bpy)3]2 + and another reduced intermediate, both of which decay to the ground-state [Ru(bpy)3]2+, 190 In a direct demonstration of the chemical mechanism of inner-sphere electron transfer, [Coni(NH3)5L]2+ complexes where L = nitrobenzoate and dinitrobenzoate react with e (aq) to form Co(III)-ligand radical intermediates, which then undergo intramolecular electron transfer to yield Co(II) and L.191... 

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