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Kinetic modeling convenience kinetics

As far back as 1960 Winstein and L. de Vries noted a high anchimeric acceleration (10 °) in the solvolysis of pentamethylcyclopentadienylcarbinol tosylate 484 as compared with neopentyl tosylate chosen as a model convenient for comparison. The kinetically controllable products in this reaction were olefine 485 and... [Pg.203]

Predicting the solvent or density dependence of rate constants by equation (A3.6.29) or equation (A3.6.31) requires the same ingredients as the calculation of TST rate constants plus an estimate of and a suitable model for the friction coefficient y and its density dependence. While in the framework of molecular dynamics simulations it may be worthwhile to numerically calculate friction coefficients from the average of the relevant time correlation fiinctions, for practical purposes in the analysis of kinetic data it is much more convenient and instructive to use experimentally detemiined macroscopic solvent parameters. [Pg.849]

Measurements of overall reaction rates (of product formation or of reactant consumption) do not necessarily provide sufficient information to describe completely and unambiguously the kinetics of the constituent steps of a composite rate process. A nucleation and growth reaction, for example, is composed of the interlinked but distinct and different changes which lead to the initial generation and to the subsequent advance of the reaction interface. Quantitative kinetic analysis of yield—time data does not always lead to a unique reaction model but, in favourable systems, the rate parameters, considered with reference to quantitative microscopic measurements, can be identified with specific nucleation and growth steps. Microscopic examinations provide positive evidence for interpretation of shapes of fractional decomposition (a)—time curves. In reactions of solids, it is often convenient to consider separately the geometry of interface development and the chemical changes which occur within that zone of locally enhanced reactivity. [Pg.17]

Chiral sulphoxides are the most important group of compounds among a vast number of various types of chiral organosulphur compounds. In the first period of the development of sulphur stereochemistry, optically active sulphoxides were mainly used as model compounds in stereochemical studies2 5 6. At present, chiral sulphoxides play an important role in asymmetric synthesis, especially in an asymmetric C—C bond formation257. Therefore, much effort has been devoted to elaboration of convenient methods for their synthesis. Until now, optically active sulphoxides have been obtained in the following ways optical resolution, asymmetric synthesis, kinetic resolution and stereospecific synthesis. These methods are briefly discussed below. [Pg.284]

Multi-State Models. In studies of copolymerization kinetics and polymer microstructure, the use of reaction probability models can provide a convenient framework whereby the experimental data can be organized and interpreted, and can also give insight on reaction mechanisms. (1.,2) The models, however, only apply to polymers containing one polymer component. For polymers with mixtures of different components, the one-state simple models cannot be used directly. Generally multi-state models(11) are needed, viz. [Pg.175]

Note in Table 5.10 that many of the integrals are common to different kinetic models. This is specific to this reaction where all the stoichiometric coefficients are unity and the initial reaction mixture was equimolar. In other words, the change in the number of moles is the same for all components. Rather than determine the integrals analytically, they could have been determined numerically. Analytical integrals are simply more convenient if they can be obtained, especially if the model is to be fitted in a spreadsheet, rather than purpose-written software. The least squares fit varies the reaction rate constants to minimize the objective function ... [Pg.89]

Because the more complicated model that required numerical solution still neglected important effects, we chose to use a simple analytical model for convenience. We chose Oddson s because its major features had been verified by Huggenberger (15, 16) for lindane, one of the compounds in our study. Oddson included the kinetics of adsorption by assuming that the rate of adsorption is proportional to the difference between the amount that has already adsorbed and the equilibrium value ... [Pg.202]

The standard approach to modeling PDRs is to use a one-dimensional approach in which the radiation strikes perpendicularly. The region is divided into slabs, so that the equations of radiative transfer and chemical kinetics can be solved conveniently. The slabs can be homogeneous, or can have different gas densities. The radiation is scattered and absorbed by dust particles, but, in addition, both H2 and... [Pg.39]

What we shall be doing in the discussion that follows is comparing the effect that a particular Y would be expected to have on the rate of attack on positions o-/p- and m-, respectively, to the substituent Y. This assumes that the proportions of isomers formed are determined entirely by their relative rates of formation, i.e. that the control is wholly kinetic (cf. p. 163). Strictly we should seek to compare the effect of Y on the different transition states for o-, m- and p-attack, but this is not usually possible. Instead we shall use Wheland intermediates as models for the transition states that immediately precede them in the rate-limiting step, just as we have done already in discussing the individual electrophilic substitution reactions (cf. p. 136). It will be convenient to discuss several different types of Y in turn. [Pg.151]

Nowadays, studies of direct electrochemistry of redox proteins at the electrodesolution interface have held more and more scientists interest. Those studies are a convenient and informative means for understanding the kinetics and thermodynamics of biological redox processes. And they may provide a model for the study of the mechanism of electron transfer between enzymes in biological systems, and establish a foundation for fabricating new kinds of biosensors or enzymatic bioreactors. [Pg.560]

In this chapter, the discussion has centred on the redox behaviour of the cyclic systems of a limited range of metal ions. Nevertheless, the examples are of sufficient breadth to illustrate that the redox behaviour of a particular system usually depends upon a fine balance between kinetic, thermodynamic and structural factors in which both the nature of the central metal ion and of the cyclic ligand are major influences. Of course, such considerations are not restricted to macrocyclic systems - however, the latter have provided convenient models for the elucidation of a variety of redox behaviour - much of which is of relevance to other areas and, for example, to many of the natural redox systems. [Pg.223]

As shown in Example 22-3, for solid particles of the same size in BMF, the form of the reactor model resulting from equation 22.2-13 depends on the kinetics model used for a single particle. For the SCM, this, in turn, depends on particle shape and the relative magnitudes of gas-film mass transfer resistance, ash-layer diffusion resistance and surface reaction rate. In some cases, as illustrated for cylindrical particles in Example 22-3(a) and (b), the reactor model can be expressed in explicit analytical form additional results are given for spherical particles by Levenspiel(1972, pp. 384-5). In other f l cases, it is convenient or even necessary, as in Example 22-3(c), to use a numerical pro-... [Pg.563]

In the studies described above the experimental conditions were chosen for experimental convenience, so they may differ greatly from those found in natural waters. To try to identify the factors that might influence Mn(II) oxidation on metal oxides surfaces in natural waters, the surface equilibria and kinetic models developed above can been used to predict the time scales for Mn(II) oxidation in these waters. [Pg.497]

In order to understand the BZ system Field, Koros and Noyes developed the so-called FKN mechanism. From this, Field and Noyes later derived the Oregonator model, an especially convenient kinetic model to match individual experimental observations and predict experimental conditions under which oscillations might arise. [Pg.95]

The tools we created in Chapter 3, Physical/Chemical Models, form the core of the fitting algorithms of this chapter. The model defines a mathematical function, either explicitly (e.g. first order kinetics) or implicitly (e.g. complex equilibria), which in turn is quantitatively described by one or several parameters. In many instances the function is based on such a physical model, e.g. the law of mass action. In other instances an empirical function is chosen because it is convenient (e.g. polynomials of any degree) or because it is a reasonable approximation (e.g. Gaussian functions and their linear combinations are used to represent spectral peaks). [Pg.101]

The use of transition state theory as a convenient expression of rate data is obviously complex owing to the presence of the temperature-dependent partition functions. Most researchers working in the area of chemical kinetic modeling have found it necessary to adopt a uniform means of expressing the temperature variation of rate data and consequently have adopted a modified Arrhenius form... [Pg.50]

The kinetics of a catalytic reaction is usually measured in a reactor under conditions relevant to the industrial process. The measured overall rates can then be fitted to a mathematical model, the macroscopic kinetics. This is extremely convenient for process design purposes. [Pg.81]

The model framework for describing the void problem is schematically shown in Figure 6.3. It is, of course, a part of the complete description of the entire processing sequence and, as such, depends on the same material properties and process parameters. It is therefore intimately tied to both kinetics and viscosity models, of which there are many [3]. It is convenient to consider three phases of the void model void formation and stability at equilibrium, void growth or dissolution via diffusion, and void transport. [Pg.185]

Over 30 man-years of effort were involved in developing the model, which is named KINPTR, an acronym for kinetic platinum reforming model. Since its development, KINPTR has had a major impact in Mobil s worldwide operations. It can be accessed by personnel at each of Mobil s locations throughout the world. Input requirements are simple and convenient making it very user friendly. Only feed characteristics, product quality targets, process configuration information, and process conditions are required for input. Output is informative and detailed. Overall and detailed yields, feed and product properties, and reactor performance data are given in the output. [Pg.194]

Our primary objective has been to present the experimental results in a convenient, combined form rather than to discuss their significance in great detail. In view of the extreme physical and chemical complexity of anthracite and the limited amount of experimental investigation to which the material has been subjected at present, an elaborate theoretical discussion would be pointless. Indeed, it is improbable that the kinetics of volatile matter release for such a complex material will ever submit to a satisfactory correlation by simple functional relationships. In spite of these difficulties, it is of interest to discuss some of the general trends exhibited by the experimental data and their interpretation by suggesting approximate theoretical and mathematical models for the release mechanism. [Pg.606]


See other pages where Kinetic modeling convenience kinetics is mentioned: [Pg.606]    [Pg.167]    [Pg.130]    [Pg.110]    [Pg.142]    [Pg.9]    [Pg.388]    [Pg.78]    [Pg.177]    [Pg.115]    [Pg.28]    [Pg.593]    [Pg.143]    [Pg.28]    [Pg.34]    [Pg.98]    [Pg.238]    [Pg.5]    [Pg.315]    [Pg.131]    [Pg.334]    [Pg.120]    [Pg.296]   
See also in sourсe #XX -- [ Pg.186 , Pg.188 ]




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