Pseudo-kinetic rate constant

Pseudo Kinetic Rate Constant Method for Copolymers with Long Branches... 

In this paper, the pseudo-kinetic rate constant method in which the kinetic treatment of a multicomponent polymerization reduces to that of a hcmopolymerization is extensively applied for the statistical copolymerization of vinyl/divinyl monomers and applications to the pre- and post-gelation periods are illustrated. 

The pseudo-kinetic rate constant method for multicomponent polymerization has been applied in some copolymerization studies (3-5), and its derivation and specific approximations have been made clear (6,7). The pseudo-kinetic rate constants basically... 

Symbols used are defined at the end of this paper. The definitions of other pseudo-kinetic rate constants can be found in earlier papers (6,7). 

Necessary conditions for the validity of the pseudo-kinetic rate constants are ... 

Applying the pseudo-kinetic rate constants, the explicit formulation of the kinetics of a multicomponent polymerization reduces to that of a homopolymerization. 

Application of the Method of Mcanents. In order to apply the method of moments (6,7), the pseudo-kinetic rate constant for the crosslinking reaction should be defined as follows. 

The basic reaction scheme for free-radical bulk/solution styrene homopolymerization is described below. A complete description of copolymerization kinetics involving styrene is not given here however, the homopolymerization kinetic scheme can be easily extended to describe copolymerization using the pseudo-kinetic rate constant method [6]. Such practice has been used by many research groups [7-10] and has been used extensively for modelling of copolymerization involving styrene by Gao and Penlidis [11]. In this section, all rate constants are defined as chemically controlled, i.e. they are only a function of temperature. 

Since the polymerization kinetic constants appear as weighted sums in Equation 2.96, this equation can be rewritten using pseudo-kinetic rate constants ... 

We will first show how to derive such population balances for living polymer chains, but instead of applying the same approach to all other species we will introduce the concept of pseudo-ldnetic rate constants [63, 64]. When pseudo-kinetic rate constants are defined, the equations derived for homopolymerization can also be used for copolymerization with only one minor modification, thus considerably simplifying the time required for model development. 

Upon addition of a solution of sulfuric acid in D20 the reaction of A-acetoxy-A-alkoxyamides obeys pseudo-unimolecular kinetics consistent with a rapid reversible protonation of the substrate followed by a slow decomposition to acetic acid and products according to Scheme 5. Here k is the unimolecular or pseudo unimolecular rate constant and K the pre-equilibrium constant for protonation of 25c. Since under these conditions water (D20) was in a relatively small excess compared with dilute aqueous solutions, the rate expression could be represented by the following equation ... 

Worked Example 8.17 The following kinetic data were obtained for the second-order reaction between osmium tetroxide and an alkene, to yield a 1,2-diol. Values of k are pseudo-order rate constants because the 0s04 was always in a tiny minority. Determine the second-order rate constant k2 from the data in the following table ... 

The amount of TiO was varied, and the assembly was tested for its photocata-lytic activity using degradation of 2,4-xylidine as test reaction probe. The decrease in the concentration of xylidine and the corresponding increase in oxalate concentration were monitored through HPLC. A pseudo-first order kinetics was ob served in the photodegradation process based on the Langmuir-Hinshelwood mechanism. An inverse correlation was observed between the kinetic rate constant and the obtained Light-Induced Optoacoustic Spectroscopy (LIOAS) frequency maxima. 

The kinetic parameters chosen for comparison are rate constants and t1/2. Radiation influences and the effect of reactor design are usually identical when these kinetic data are compared between the various AOPs tested. The values for pseudo first-order kinetics and half-lives for various processes are given in Table 14.3. In most cases, the values of f3/4 are equal to two times those of t1/2 therefore, the reactions obey a first-order kinetics. Figure 14.5. shows that Fenton s reagent has the largest rate constant, e.g., approximately 40 times higher than UV alone, followed by UV/F C and Os in terms of the pseudo first-order kinetic constants. Clearly, UV alone has the lowest kinetic rate constant of 0.528 hr1. 

The pseudo first-order kinetic rate constants for processes based on the application of ozone are given in Table 14.7. Figure 14.9 presents the pseudo first-order rate constants of p-hydroxybenzoic degradation. The degradation rates follow the increasing order ... 

This steady-state equation leads to the expressions that relate the apparent pseudo first-order rate constants A3(app) and A4(app) with the kinetic rate constants... 

Table 5.6 provides information taken from the kinetic reaction profile for Br" in Figure 5.7b. Use this information to determine a value for the pseudo-order rate constant in Equation 5.22. 

The kinetic rate constant kj corresponds to the kinetics of heterogeneous surface-catalyzed chemical reactions in the boundary conditions, whereas the rate law is written on a pseudo-volumetric basis when chemical reaction terms are included in the mass transfer equation. 

The Hougen-Watson rate law lEinw, with units of moles per area per time, is written on a pseudo-volumetric basis using the internal surface area per mass of catalyst S , and the apparent mass density of the pellet Papp. k is the nth-order kinetic rate constant with units of (volume/mole)" per time when the rate law is expressed on a volumetric basis using molar densities. 

Example. Determine the best value of the pseudo-first-order kinetic rate constant that provides the closest match between the actual rate law and the first-order irreversible rate law. 

The LLSA prescription for the best pseudo-first-order kinetic rate constant is... 

Methodology. Pseudo-first-order kinetic rate constants that are consistent with nth-order kinetics and Hougen-Watson models are calculated as follows ... 

Step 1. Use the integral form of a linear-least squares analysis to determine the best value of the pseudo-first-order kinetic rate constant, i, that will linearize the reaction term in the mass transfer equation. It is necessary to apply the Leibnitz rule for differentiating a one-dimensional integral with constant limits to the following expression ... 

The adsorption/desorption equilibrium constant for each component is Kf = 0.25 atm and forward is the kinetic rate constant for the forward chemical reaction on the catalytic surface with units of moles per area per time. The reason that forward has the same units as Ehw is because rate laws for heterogeneous catalysis are written in terms of fractional surface coverage by the adsorbed species that participate in the reaction. Langmuir isotherms are subsequently used to express fractional surface coverage of the reacting species in terms of their partial pressures. The best value for the pseudo-first-order kinetic rate constant is calculated from... 

Figure 15-1 Total pressure dependence of the best pseudo-first-order kinetic rate constant when a first-order rate law approximates a Hougen-Watson model for dissociative adsorption of diatomic A2 on active catalytic sites. Irreversible triple-site chemical reaction between atomic A and reactant B (i.e., 2Acr - - Bcr -> products) on the catalytic surface is the rate-limiting step. The adsorption/desorption equilibrium constant for each adsorbed species is 0.25 atm. ...

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