Quantitative kinetic molecular

Appendix 1 Mathematical Procedures A1 Al.l Exponential Notation A1 A1.2 Logarithms A4 A1.3 Graphing Functions A6 A1.4 Solving Quadratic Equations A7 A1.5 Uncertainties in Measurements AlO Appendix 2 The Quantitative Kinetic Molecular Model A13... 

We now have enough information to turn our qualitative ideas about a gas into a quantitative model that can be used to make numerical predictions. The kinetic model ( kinetic molecular theory, KMT) of a gas is based on four assumptions (Fig. 4.23) ... 

We have chosen the PVC diad and triad compounds 2,4-dichloropentane (DCP) and 2,4,6-trichloroheptane(TCH) as subjects for our attempt to obtain quantitative kinetic data characterizing their (n-Bu)3SnH reduction in the hope that they will serve as useful models tor the reduction of PVC to E-V copolymers. Unlike the polymers (PVC and E-V), DCP and TCH are low molecular weight liquids whose high resolution 13C NMR spectra can be recorded from their concentrated solutions in a matter of minutes. Thus, it is possible to monitor their (n-Bu)3SnH reduction directly in the NMR tube and follow the kinetics of their dechlorination. 

Beginning with these assumptions, it s possible not only to understand the behavior of gases but also to derive quantitatively the ideal gas law (though we ll not do so here). For example, let s look at how the individual gas laws follow from the five postulates of kinetic-molecular theory ... 

The interaction of H2S, organic sulfides, and other sulfur compounds may involve a number of consecutive steps including reversible molecular adsorption of the sulfur compound, its dissociation, reorientation or reconstruction of the metal surface, formation of a 2-D surface sulfide, and at still higher H2S/H2 ratios, formation of a three-dimensional (3-D) (bulk) metal sulfide. Kinetic information about these processes may generally be helpful in elucidating the adsorption mechanism. Unfortunately, such quantitative kinetic information is not adequately available, with one exception, formation of bulk sulfides (9, 96). 

In the next sections the quantitative effect of reactions (1), (3), (4), and (5) which can be considered as various deviations from ideal systems, on kinetics, molecular weights, and polydispersities, will be presented. The magnitude of only one variable will be changed each time to demonstrate clearly the effect of slow initiation, termination, transfer, and slow exchange on the polymerization rates and properties of the resulting polymers. 

Gas-phase epr studies have proved useful in the qualitative way described above, and they have been used also in quantitative kinetic studies. Low pressure discharge flow methods are eminently suitable, and the microwave cavity can be incorporated in the flow tube. Krongelb and Strandberg used the method to measure the rate of recombination of atomic oxygen. The spectrometer was calibrated using molecular oxygen that this procedure is valid was shown later by Westenberg and de Haas , who checked the calibration for both O and N by titration with NOj and NO (see Section 5). 

We can apply the kinetic-molecular theory quantitatively to phase changes by means of a heating-cooling curve, which shows the changes that occur when heat is added to or removed from a particular sample of matter at a constant rate. As an example, the cooling process is depicted in Figure 12.3 for a 2.50-mol sample of gaseous water in a closed container, with the pressure kept at 1 atm and... 

The determination of absolute rate coefficients of transfer reactions of bromine atoms is much more favourable than for the corresponding reactions of fluorine or chlorine atoms. This arises because the dissociation constant of molecular bromine is high at normal experimental temperatures and the chain lengths in bromination are relatively short. The rate constant of the reaction of bromine atoms with molecular hydrogen was the first quantitative kinetic study of a radical reaction [96]. Fettis and Knox [52] evaluated the data for the Br—Hj reaction and their results are given in Table 7. Trotman-Dickenson [1] has pointed out that the subsequent data of Timmons and Weston [80] for the reaction with Hj, HD and HT are not fully compatible with the conclusions of Pettis and Knox [52]. 

Let us now suppose that molecular bromine, formed in the above manner, reacts with the alkene to generate a bromonium ion. Because of the low-concentration of Bt2 in the system, the bromonium ion is also formed in low concentration. For Br2 addition to occur, a bromide anion would now have to attack the bromonium ion. Bromide anions, however, are also rare species in the system, given that HBr is formed only in low concentration. Thus, depending as it does on two low-concentration species, a bromonium ion and bromide, this reaction channel is an improbable one and cannot compete with the radical pathway, which explains the absence of Br2 addition under these conditions. This picture is backed by quantitative kinetic evidence, which we won t go into. 

Quantitative kinetic studies of lysozyme-catalysed hydrolyses can be achieved only in limited circumstances for example, the use of chromophoric substrates is beset by difficulties and no substrate of low molecular weight has gained acceptance in standard assays. An efficient and rapid assay of the lysozyme-catalysed hydrolysis and transglycosylation of [ C]chito-oligosaccharides uses h.p.l.c. to separate the products and liquid scintillation counting to determine their concentrations. 

We have just seen how each of the gas laws conceptually follows from kinetic molecular theory. We can also derive the ideal gas law from the postulates of kinetic molecular theory. In other words, the kinetic molecular theory is a quantitative model that implies PV = nRT. Let s now explore this derivation. 

Kinetic molecular theory is a quantitative model for gases. The theory has three main assumptions (1) the gas partieles are negligibly small, (2) the average kinetic energy of a gas particle is proportional to the temperature in kelvins, and (3) the collision of one gas particle with another is completely elastic (the particles do not stick together). The gas laws all follow from the kinetic molecular theory. 

Photo-oxidation of some aaylic-urethane thermoset networks was induced by chromophoric impurities that absorb UV light and produce radicals, initiating a radical oxidation of the polymer [145]. The authors introduced a quantitative kinetic model based on the identified mechanisms and a multi-scale approach from the molecular to the macroscopic level. 

Calculations of the above type have not yet been applied to reactive systems" and there is clearly a perceived need for both quantitative kinetic measurements and complementary molecular mechanics/dynamics simulations for model intrazeolite reactions. In what follows, we describe the first experiments designed to fill this void. 

For a quantitative description of the behavior of gases, we will employ some simple gas laws and a more general expression called the ideal gas equation. These laws will be explained by the kinetic-molecular theory of gases. The topics covered in this chapter extend the discussion of reaction stoichiometry from the previous two chapters and lay some groundwork for use in the following chapter on thermochemistry. The relationships between gases and the other states of matter— liquids and solids—are discussed in Chapter 12. 

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