Quantitative Interpretation of Kinetic Data

Suppose that experimental rate data for the reaction A + B C were obtained over a wide range of total pressures, all at the same temperature. Comparison of a plot of the observed results with curves such as shown in Fig. 9-3 would be of value in establishing the most accurate rate equation. However, it is sometimes difficult to cover a wide enough range of pressures to observe all the changes in shape of the curves. 

To evaluate the rate and adsorption equilibrium constants in equations such as (9-32) rate data are needed as a function of concentrations in the fluid phase. Data are required at a series of temperatures in order to establish the temperature dependency of these constants. The proper concentrations to employ are those directly adjacent to the site. In the treatment that follows we shall suppose that these local concentrations have been established from the measurable concentrations in the bulk stream by the methods to be given in Chaps. 10 and 11. Our objective here is to find the most appropriate rate equation at a catalyst site. 

Statistical methods are required to obtain the best fit of the equation to the kinetic data. Minimizing the deviations between the observed rate and that predicted from the equation is straightforward as long as the constants are linearly related in the rate equation. When nonlinearities exist the analysis is more complicated. There are many illustrations of the method for evaluating the constants in equations such as (9-32) from experimental rate measurements. The sequence for this process is usually as follows  

Assume various mechanisms and controlling steps for each mechanism. Develop a rate equation for each combination of mechanism and controlling step. 

Determine the numerical values of the constants which -give the best fit of each equation to the observed rate data. 

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We would, therefore, agree with Bond s conclusion (3) that application of the transition state theory to heterogeneous reactions has not so far provided insight into the mechanisms of surface reactions and that the failures of the theory are generally more significant than the successes. We do not accept that the use of the theory of absolute reaction rates in the interpretation of kinetic data provides a general and reliable method for the estimation of the concentration of surface active sites but conclude that results should always be considered with reference to appropriate quantitative supporting evidence (133). 

In Fig. 5.26(a) and for Ecxe < E% one can see that PCI effects also exist for the 4d5/2 photoline, because towards the ionization threshold hv — kin(4d5/2) increases, i.e., ki (4d5/2) decreases. A quantitative interpretation of these data, however, will be omitted for two reasons. First, the study requires quantitative electron spectrometry at low kinetic energies which is difficult due to the cutoff problem in the spectrometer transmission (see Fig. 4.15). Second, the cumulative effects of all possible Auger decays following 4d5/2 photoionization, not just a single chosen one, contribute to the photoline. 

Except in very special circumstances (Section 6.4) electroneutrality is maintained in cationic polymerizations by the presence of a negatively charged counter-ion or gegenion, X . This species has no analogue in free radical polymerizations, and indeed much of the early work on cationic (and anionic) reactions was carried out with almost total disregard for the effect of counter-ion. In fact it turns out as we shall see that the counter-ion, and its physical relationship with the growing cation, is of vital importance in the interpretation of kinetic data derived from these systems. The present authors take the view that, while results obtained from polymerizations where such relationships are unknown are qualitatively useful, any quantitative data obtained must be treated with caution. 

It should be mentioned, however, that surface inhomogeneities of different dimensionality (cf. Section 2.1) significantly influence the kinetics of metal electrodeposition and the time-dependent surface morphology. Therefore, an exact analysis of corresponding EIS spectra is rather difficult. The necessary presumptions of stationarity and linearity for EIS measurements and quantitative interpretation of EIS data are often violated. The lack of direct local information on surface dynamics strongly hinders a quantitative analysis of the impedance behavior of time-dependent systems. Such considerations have been mainly disregarded in previous EIS data interpretations. In future, a combination of EIS measurements with in situ local probe... 

Water-soluble root exudates are most frequently collected by immersion of root systems into aerated trap solutions for a defined time period (Fig. 1 A). The technique is easy to perform and permits kinetic studies by repeated measurements over time using the same plants. While it is possible to get a first impression about qualitative exudation patterns and even quantitative changes in response to different preculture conditions, the technique also includes several restrictions that should be taken into account for the interpretation of experimental data. 

The large uncertainty in the quantitative interpretation of heterogeneous initiation phenomena results not only from the uncertainty of the kinetic parameters used (See section on Kinetic Data), but also from the large uncertainty of the temps of the initiation sites (hot spots)... 

Quantitative Interpretation of Intracrystalline Diffusional Effects. Since a qualitative effect of crystallite size upon selectivity was observed, the next step was to extract some quantitative values for the intracrystalline diffusional parameters. To do this, we must either know the intrinsic or diffusion-free kinetics or be able to make a simplifying assumption so that the diffusional parameters can be extracted from the available data. 

In these later sections, interpretations of quantitative data for product mixtures are emphasised, and the relationship between kinetics and product analysis will be developed. Mechanistic applications of kinetic data are limited to steps of reactions prior to and including the rate-determining step. As separate later steps often determine the reaction products, detailed product studies and investigations of reactive intermediates are important supplements to kinetic studies. Examples of solvolytic and related (SN) reactions have been chosen first because they provide a consistent theme, and second because SN reactions provide an opportunity to assess critically many of the mechanistic concepts of organic chemistry. Product composition in solvolytic reactions will be discussed next followed by product selectivities (Section 2.7.2) and rate-product correlations (Section 2.7.3). 

In the following Sections (3 and 6) more quantitative interpretations of the kinetic data will be discussed. 

It is at present clearly impossible to understand all the aspects of these systems. Nevertheless the mechanism and kinetics of some emulsion systems are reasonably well understood—those in which the monomer is water- insoluble and in which the polymer is soluble in the monomer. An outline is given of this mechanism and the kinetics of polymerization are developed on the basis of this mechanism. This theoretical kinetic behavior is then compared with experimental data, both from the literature and from unpublished results. Whenever possible, the influence of monomer water solubility and monomer solubility of the polymer is commented on. These comments are mostly of a qualitative nature and sometimes even speculative. The present state of our knowledge does not permit going beyond such comments, although recently the literature has given a few attempts at quantitative interpretation of emulsion polymerization of water-soluble monomers. 

The influence of background electrolyte concentration on the adsorption kinetics of SDS was studied by Fainerman (1978, 1986, 1991). With increasing electrolyte concentration the surface activity of the SDS is enhanced. However, a quantitative interpretation of the kinetic data is not... 

The primary data furnished by such detection then allows interpretation of kinetics and mechanisms and can serve as the basis for building specific quantitative, mechanistic models, as well as for controlling polymerization reactions. The ACOMP platform is one means of anbodying and employing any chosen set of such detectors, and these can also be complemented by widely used in situ detectors. 

Reactions 29 and 30 occur on sites free of C HpOq and OHad- It is likely that weakly bonded species participate. The difficulties of interpreting the kinetic data of methanol oxidation were pointed out in the preceding chapter. The anodic oxidation [4, 39, 84, 85, 88, 89] of higher alcohols and aldehydes is equally complex. Further experimental results are needed for a quantitative interpretation. 

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