Chemical rate constant

In these circumstances a decision must be made which of two (or more) kinet-ically equivalent rate terms should be included in the rate equation and the kinetic scheme (It will seldom be justified to include both terms, certainly not on kinetic grounds.) A useful procedure is to evaluate the rate constant using both of the kinetically equivalent forms. Now if one of these constants (for a second-order reaction) is greater than about 10 ° M s-, the corresponding rate term can be rejected. This criterion is based on the theoretical estimate of a diffusion-controlled reaction rate (this is described in Chapter 4). It is not physically reasonable that a chemical rate constant can be larger than the diffusion rate limit. 

FIGURE 2-6 Cyclic voltammograms for a reversible electron transfer followed by an irreversible step for various ratios of chemical rate constant to scan rate, k/a, where a = nFv/RT. (Reproduced with permission from reference 1.)... 

The first theoretical attempts in the field of time-resolved X-ray diffraction were entirely empirical. More precise theoretical work appeared only in the late 1990s and is due to Wilson et al. [13-16]. However, this theoretical work still remained preliminary. A really satisfactory approach must be statistical. In fact, macroscopic transport coefficients like diffusion constant or chemical rate constant break down at ultrashort time scales. Even the notion of a molecule becomes ambiguous at which interatomic distance can the atoms A and B of a molecule A-B be considered to be free Another element of consideration is that the electric field of the laser pump is strong, and that its interaction with matter is nonlinear. What is needed is thus a statistical theory reminiscent of those from time-resolved optical spectroscopy. A theory of this sort was elaborated by Bratos and co-workers and was published over the last few years [17-19]. 

Bellman, R., J. Jacquez, R. Kalaba, and S. Schwimmer, "Quasilinearization and the Estimation of Chemical rate Constants from Raw Kinetic Data", Math. Biosc. 7,71-76(1967). 

As for all chemical kinetic studies, to relate this measured correlation function to the diffusion coefficients and chemical rate constants that characterize the system, it is necessary to specify a specific chemical reaction mechanism. The rate of change of they th chemical reactant can be derived from an equation that couples diffusion and chemical reaction of the form (Elson and Magde, 1974) ... 

It is the ratio of the measured rate constant to the intrinsic chemical rate constant. 

Marcus RA (1963) On the theory of oxidation-reduction reactions involving electron transfer. V. Comparison and properties of electrochemical and chemical rate constants. J Phys Chem 67 853-857... 

The lack of precise measurements of environmentally relevant chemical rate constants limits the number of quantitative evaluations of the importance of complex dynamics on uptake fluxes. Nonetheless, examples involving bicarbon-ate-CC>2 conversion [69,88] and trace metal complexation [8,46,325] have been examined theoretically in the literature. For example, comparison of the diffu-sional and reactional timescale allowed Riebesell and collaborators [69,88] to show that bicarbonate conversion to CO2 did not generally enhance the... 

For isothermal, first-order chemical reactions, the mole balances form a system of linear equations. A non-ideal reactor can then be modeled as a collection of Lagrangian fluid elements moving independe n tly through the system. When parameterized by the amount of time it has spent in the system (i.e., its residence time), each fluid element behaves as abatch reactor. The species concentrations for such a system can be completely characterized by the inlet concentrations, the chemical rate constants, and the residence time distribution (RTD) of the reactor. The latter can be found from simple tracer experiments carried out under identical flow conditions. A brief overview of RTD theory is given below. 

In mixed (0.8 - a ) M NaCl04 + x M NaF supporting electrolyte the electroreduction of Cd(II) was also studied by Saakes etal. [25]. The kinetic parameters were analyzed using CEE mechanism. The obtained chemical rate constants at both steps, kg 1 and kg 2, decreased with increasing NaF concentration. The data were corrected for nonspecific double-layer effect (Frumldn correction). The interpretation of CEE mechanism with parallel pathways connected with coexisting cadmium complexes was presented. 

It is a simple exercise to show that the above result is identical to Equation (50). If p can be regarded as a constant, then W plays a role in Equation (51) that converts the latter to the form of the Arrhenius expression for ordinary chemical rate constants. 

Here kf and kb do not have solely their usual meanings as forward and backward chemical rate constants, because the free monomer concentration has been included as a factor in kf and the concentrations of the byproducts of the forward reaction (inorganic pyrophosphate and water) have been absorbed into kb. Since there are actually four different types of monomer, each template site specifying, according to the Watson-Crick base-pairing rules, which type is to be incorporated at that site, this use of the same kf for each step is strictly valid only if all four monomer concentrations are equal, as well as essentially invariant during the duration of the process, and if the true rate constant for the incorporation of each type of monomer is independent not only of the nature of the monomer to be added but also of the nature of the sequence already incorporated. 

Prior to this discussion, we would like to refer to a qualitative introduction given by Bard and Faulkner (ref. 21, Sect. 11.1.2 and 11.2.3). In a few pages they give a clear indication of the effect of the chemical reaction on the several characteristic electrochemical quantities (e.g. half-wave potential, limiting current, etc.). In addition, it is argued that a chemical rate constant, ft,-, is measurable by a given technique if its reciprocal value, 1/fc, falls within the experimental time range accessible for the technique (the so-called time window ). 

Further guidelines for the interpretation of chronopotentiometric results can be found in refs. 21 and 22. Its diagnostic value, especially, should be emphasized, as well as its sensitivity to a wide range of chemical rate constants, because its time window can be adapted by choosing proper values for the controlled current density j. The ECE mechanism, left out of the discussion here, is treated in detail in ref. 22. 

Figure 23.17 Ratio of ipc(2)/ipc(l) for ECE mechanism of Eq. 23.24-23.26 for different values of kcT, where kc is the intervening chemical rate constant of Eq. 23.25 and i is the time (in seconds) required to scan from E[/2(l) to E1/2(2). Taken with permission from Ref. 22.

I wish to thank Drs. Dale Hawley and Marcin Majda for helpful comments on this manuscript, and Dr. Kent Mann for providing the raw data that allowed calculation of the chemical rate constant for Equation 23.22. I am grateful to the National Science Foundation for research support during this period. 

It is rare that a catalyst can be chosen for a reaction such that it is entirely specific or unique in its behaviour. More often than not products additional to the main desired product are generated concomitantly. The ratio of the specific chemical rate constant of a desired reaction to that for an undesired reaction is termed the kinetic selectivity factor (which we shall designate by 5) and is of central importance in catalysis. Its magnitude is determined by the relative rates at which adsorption, surface reaction and desorption occur in the overall process and, for consecutive reactions, whether or not the intermediate product forms a localised or mobile adsorbed complex with the surface. In the case of two parallel competing catalytic reactions a second factor, the thermodynamic factor, is also of importance. This latter factor depends exponentially on the difference in free energy changes associated with the adsorption-desorption equilibria of the two competing reactants. The thermodynamic factor also influences the course of a consecutive reaction where it is enhanced by the ability of the intermediate product to desorb rapidly and also the reluctance of the catalyst to re-adsorb the intermediate product after it has vacated the surface. 

It Chemical rate constant for forward surface reaction (molecules per unit area and unit time) m-V l 2t ... 

Equation (5.50) is usually called the Rabinowitch model (Rabinowitch, 1937). Although in the particular selected example there is only one chemical rate constant, in the general case Eq. (5.50) must be written for every reaction step. This means that the faster chemical steps will be more affected by diffusional resistances than the slower chemical reactions. 

For high values of the chemical rate constant, i.e., under conditions of a diffusive-kinetic steady state (dcross potentials of the ADDPV curves,... 

The variation of the peak current in the presence of a coupled catalytic reaction differs from the above behavior due to the catalytic contribution. Thus, as the chemical rate constant increases and the frequency decreases, that is, as the catalytic component becomes more apparent, there is a deviation from the linear increase of / d sc>Pcak wjth f/2. This deviation is only significant for kx > 10s 1. When steady-state conditions are achieved (very small frequencies and/or large kinetic constants), the peak current becomes independent of the frequency, as shown in Fig. 7.37 for k = 100s-1 and f1 2 < 5 s-1/2. 

The SWV and SWVC curves for the EEC reaction schemes, calculated from Eqs. (7.154) and (7.157), can be seen in Figs. 7.59 and 7.60, respectively. These curves have been obtained for different values of the dimensionless chemical rate constant kc and A(i.e., the difference between the formal potentials of the electron transfer reactions). SWV proves highly sensitive for detecting the presence of the catalysis, since no measurable response is obtained in the absence of the same. From Fig. 7.59, it can be deduced that when catalysis takes place, route... 

Fig. 7.59 SWV curves corresponding to an EEC mechanism for its three possible routes calculated from Eq. (7.154). The values of the dimensionless chemical rate constant kc appear on the curves. A s = 5mV, sw = 50mV, T = 298 K...

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