Determining species thermochemical properties

While we are ultimately interested in the chemical kinetics of the system under consideration, we must first consider the thermodynamics. This is important not only because thermodynamic equilibrium constrains the overall system, but also because for each elementary reaction, the forward and reverse reaction rates are related via the equilibrium constant. To compute the equilibrium constant, we must know the Gibbs energy of each species participating in the reaction, at the reaction conditions. However, the Gibbs energy is not usually tabulated directly. Rather, the thermochemical properties are usually specified by the standard enthalpy of formation at 298 K, the standard entropy at 298 K and 1 bar (1 atm in some cases), and the heat capacity as a function of 

As illustrated in Fig. 1, there are essentially four methods for obtaining thermochemical data for the species in our reaction mechanism. The first choice is to find the needed data in databases or in the literature in general. This includes both published experimental data and published quantum chemical calculations, which can also be a reliable source of thermochemical data. If no information on a substance is available in the literature, one should consider whether it can be treated by group additivity methods. If a well-constructed group additivity method is available for the class of molecules of interest, the results, which can be obtained with minimal effort, will be comparable in accuracy to those from the best quantum chemistry calculations. If group additivity is not applicable to the molecules of interest, then we may want to carry out quantum chemistry calculations for them, as discussed in detail in an earlier chapter. In some cases, the effort required to carry out the quantum chemical calculations may not be warranted, and we may want to make coarser, empirical estimates of thermochemical properties. 

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An accurate knowledge of the thermochemical properties of species, i.e., AHf(To), S Tq), and c T), is essential for the development of detailed chemical kinetic models. For example, the determination of heat release and removal rates by chemical reaction and the resulting changes in temperature in the mixture requires an accurate knowledge of AH and Cp for each species. In addition, reverse rates of elementary reactions are frequently determined by the application of the principle of microscopic reversibility, i.e., through the use of equilibrium constants, Clearly, to determine the knowledge of AH[ and S for all the species appearing in the reaction mechanism would be necessary. 

There have been numerous experimental as well as theoretical studies dealing with the structural and thermochemical properties of cationic silicon hydrides, Si Hm+ , and a detailed discussion of these species would certainly exceed the limited space available. We will therefore confine ourselves to the discussion of only a few exemplary cases. For further information on Si-ion thermochemistry the reader is referred to several reviews on the experimental2-4 as well as computational5 determination of thermodynamic properties of silicon-containing ions. 

Consequently, our first goal is to determine thermochemical properties of a number of species involving peroxy and peroxide groups (radicals and molecules) which are essential and required in this work. Because of the drastic lack of available data in the literature, we have extended our estimation to a wide range of peroxide species in order to gain in understanding... 

There are many other systems, particularly those important in the processing of inorganic materials, that could potentially be modeled with similar success using detailed chemical kinetic modeling. However, in these cases we generally have very few experimentally measured rate parameters and may not even have experimentally determined thermochemical properties (enthalpy of formation, standard entropy, etc.) for many of the important chemical species. While experiments are still the most reliable source for most of the needed data, they are also in many... 

Once we have established the thermochemical properties of all the chemical species in our reaction mechanism, we must determine rate parameters for all the reactions. Given the thermochemistry, we only have to find rate parameters for a given reaction in the forward ... 

The above analyses of species concentrations and net reaction rates clearly indicate which reactions and which chemical species are most important in this reaction mechanism, under the particular conditions considered. However, for purposes of refining a reaction mechanism by eliminating unimportant reactions and species and by improving rate parameter estimates and thermochemical property estimates for the most important reactions and species, it would be helpful to have a quantitative measure of how important each reaction is in determining the concentration of each species. This measure is obtained by sensitivity analysis. In this approach, we define sensitivity coefficients as the partial derivative of each of the concentrations with respect to each of the rate parameters. We can write an initial value problem like that given by equation (35) in the general form... 

The existence of dimer R2CI6 species has been nicely demonstrated by Hastie et al. (1968) who studied the vapor phase over the representative solid/liquid chlorides LaCl3, EUCI3 and LUCI3. They concluded that the proportion of dimer to monomer increases with increasing temperature and varies considerably with the nature of the metal. However there is still a critical lack of high-temperature measurements that will lead to reliable determinations of the thermochemical properties of the dimers. 

To find K, we typically use available thermochemical data (Agj, A/ij, or permutations of these pure species properties), which allow us to calculate the Gibbs energy of reaction. We then solve for K via Equation (9.15). We will first look at how to calculate K from Ag at298 K then we will examine how to determine Ag at any T. Appendix F pro-... 

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