Stoichiometric correlations

Cross-sectionai area. The combustor cross section can be determined by dividing the volumetric flow at the combustor inlet by a reference velocity which has been selected as being appropriate for the particular turbine conditions on the basis of proven performance in a similar engine. Another basis for selecting a combustor cross section comes from correlations of thermal loading per unit cross section. Thermal loading is proportional to the primary zone air flow because fuel and air mixtures are near stoichiometric in all combustors. 

A fireball is assumed to bum with a constant temperature in the isothermal fireball model of Lihou and Maund (1982). Combustion is controlled by the supply of air and ceases after a time which is correlated empirically with the mass of flammable gas in the initial vapor sphere. It is assumed that a fraction (1 — /c) of the fuel is used to form soot, and the remaining fractionbums stoichiometrically, producing an increase of /ij moles per mole of flammable gas. The stoichiometric molar ratio of air to flammable gas is p, and dVIdt is the volumetric rate of air entrainment. The rate of increase of volume can now be written as ... 

NaOMe solutions, no correlation was found between reaction rates and either or stoichiometric base concentration but where the rates were successfully correlated by a linear free energy equation similar to those given above. 

For nonideal solutions, the thermodynamic equilibrium constant, as given by Equation (7.29), is fundamental and Ei mettc should be reconciled to it even though the exponents in Equation (7.28) may be different than the stoichiometric coefficients. As a practical matter, the equilibrium composition of nonideal solutions is usually found by running reactions to completion rather than by thermodynamic calculations, but they can also be predicted using generalized correlations. 

Equation (7.28) may not provide a good fit for the equilibrium data if the equilibrium mixture is nonideal. Suppose that the proper form for Kkmetic is determined through extensive experimentation or by using thermodynamic correlations. It could be a version of Equation (7.28) with exponents different from the stoichiometric coefficients, or it may be a different functional form. Whatever the form, it is possible to force the reverse rate to be consistent with the equilibrium constant, and this is recommended whenever the reaction shows appreciable reversibility. 

Experimental Materials. All the data to be presented for these illustrations was obtained from a series of polyurethane foam samples. It is not relevant for this presentation to go into too much detail regarding the exact nature of the samples. It is merely sufficient to state they were from six different formulations, prepared and physically tested for us at an industrial laboratory. After which, our laboratory compiled extensive morphological datu on these materials. The major variable in the composition of this series of foam saaqples is the aaK>unt of water added to the stoichiometric mixture. The reaction of the isocyanate with water is critical in determining the final physical properties of the bulk sample) properties that correlate with the characteristic cellular morphology. The concentration of the tin catalyst was an additional variable in the formulation, the effect of which was to influence the polymerization reaction rate. Representative data from portions of this study will illustrate our experiences of incorporating a computer with the operation of the optical microscope. 

Another important characteristic of inhibitors is the time of their inhibition action. If an inhibitor is consumed only in chain termination reactions, this time is determined by the initial concentration [InH]0, stoichiometric coefficient of inhibition / and Vj. In this case, the rate of inhibitor consumption is vInH = v //. Side reactions of InH with dioxygen and hydroperoxide shorten the inhibitory period and increase the rate of inhibitor consumption. Therefore, an inhibitor is efficient when it provides a minimal chain length v and its own loss in side reactions w is low. Assuming that an efficient inhibitor has w < 0.25, we get the inequality 4k 2[InH][02] < v which can be transformed, by substituting the correlation equation from Table 14.7, into the following equation... 

The correlation between 02 fraction and stoichiometric value X is given with the equation... 

Where R is the gas constant, T is the temperature, and F is the Faraday constant. Caused by the logarithmic correlation between the gas concentration and the voltage signal, the potentiometric measurement is best suited for measurements of small amounts of oxygen. A well-known application of this principle has been realized in the so called lambda-probe for automotive applications where they are used to control the lambda value within a small interval around 1 = 1. The lambda-value is defined by the relation between the existing air/fuel ratio and the theoretical air/fuel ratio for a stoichiometric mixture composition ... 

First-order estimates of entropy are often based on the observation that heat capacities and thereby entropies of complex compounds often are well represented by summing in stoichiometric proportions the heat capacities or entropies of simpler chemical entities. Latimer [12] used entropies of elements and molecular groups to estimate the entropy of more complex compounds see Spencer for revised tabulated values [13]. Fyfe et al. [14] pointed out a correlation between entropy and molar volume and introduced a simple volume correction factor in their scheme for estimation of the entropy of complex oxides based on the entropy of binary oxides. The latter approach was further developed by Holland [15], who looked into the effect of volume on the vibrational entropy derived from the Einstein and Debye models. 

In 1986, Puchot et al.104 studied the nonlinear correlation between the enantiomeric excess of a chiral auxiliary and the optical yield in an asymmetric synthesis, either stoichiometric or catalytic. Negative NLEs [(—)-NLEs] were observed in the asymmetric oxidation of sulfide and in [.S ]-proline-mediated asymmetric Robinson annulation reactions, while a positive NLE [(+)-NLEs]... 

Reported flame speed results for most fuels vary somewhat with the measurement technique used. Most results, however, are internally consistent. Plotted in Fig. 4.21 are some typical flame speed results as a function of the stoichiometric mixture ratio. Detailed data, which were given in recent combustion symposia, are available in the extensive tabulations of Refs. [24-26], The flame speeds for many fuels in air have been summarized from these references and are listed in Appendix F. Since most paraffins, except methane, have approximately the same flame temperature in air, it is not surprising that their flame speeds are about the same (—45 cm/s). Methane has a somewhat lower speed (<40 cm/s). Attempts [24] have been made to correlate flame speed with hydrocarbon fuel structure and chain length, but these correlations... 

From these correlations it would be natural to expect that the maximum blowoff velocity as a function of air-fuel ratio would occur at the stoichiometric mixture ratio. For premixed gaseous fuel-air systems, the maxima do occur at this mixture ratio, as shown in Fig. 4.56. However, in real systems liquid fuels are injected upstream of the bluff-body flame holder in order to allow for mixing. Results [60] for such liquid injection systems show that the maximum... 

In the random-walk model, the individual ions are assumed to move independently of one another. However, long-range electrostatic interactions between the mobile ions make such an assumption unrealistic unless n is quite small. Although corrections to account for correlated motions of the mobile ions at higher values of n may be expected to alter only the factor y of the pre-exponential factor Aj., there are at least two situations where correlated ionic motions must be considered explicitly. The first occurs in stoichiometric compounds having an = 1. but a low AH for a cluster rotation the second occurs for the situation illustrated in Fig. 3.6(c). 

In higher acidity, the rate constant may correlate better with (the Hammet-Deyrup acidity scale) than with the stoichiometric concentration of H+. Since nearly all the studies involve hydrolysis reactions, the depletion of the reagent water may be an important consideration also. 

The impressive increase in the ee values achieved in stoichiometric reactions compared to those in catalytic runs strongly indicates that the configuration at the metal correlates with the stereochemistry of the catalytic outcome only if (R, Rc)-9 and (Sj, Rc)-9 diverge in enantioselection, it is possible to achieve zero ee working with / jr,/ c/5ir,/ c mixtures and up to 93.5% ee using pure (Sir,Rc)-9 as catalyst. 

The first example of a chiral Lewis base promoted allylation was given by Denmark and coworkers in 1994 [45], Stoichiometric amounts of chiral phospho-ramide R,R)-20 facilitated the enantioselective allylation (Scheme 15). There was a complete stereochemical correlation between the geometry (ElZ) of allylsilane and the diastereomeric ratio (synlanti) of the products. 

There is no clear evidence to identify the active material for SO2 removal in a MgAl20 stoichiometric system. Figure 13 shows results for a 50-50 mole% magnesia-alumina material prepared from magnesium hydroxide and alumina sol and calcined at various temperatures. An attempt was made to correlate SO2 removal with compound formation, as measured by X-ray diffraction, and surface area. As indicated in the figure, SO2 removal ability decreased with Increasing calcination temperature as did surface area. X-ray diffraction analysis showed spinel formation increases as... 

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