Stoichiometric Considerations

Depending on the gasification process, reactions that take place in a gasifier include  

Most of the oxygen injected into a gasifier, either as pure oxygen or air, is consumed in reactions (1) through (3) to provide the heat necessary to dry the solid fuel, break up chemical bonds, and raise the reactor temperature to drive gasification reactions (4) through (9). 

Reactions (4) and (5), which are known as water-gas reactions, are the principal gasification reactions, are endothermic, and favor high temperatures and low pressures. 

Reaction (6), the Boudourd reaction, is endothermic and is much slower than the combustion reaction (1) at the same temperature in the absence of a catalyst. 

Reaction (7), hydro-gasification, is very slow except at high pressures. 

With a pure compound of known composition and molar mass, M, it is possible to calculate the molar mass Adgas of the ehminated gaseous elimination product of a step using the equation below, where n is the number of gas molecules for each original molecule  

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Of course, this is the same result that was obtained more simply in Eq. (5.4). The earlier result, however, was based on purely stoichiometric considerations and not on the detailed distribution as is the present result. 

Formulations should be based on stoichiometric considerations. Based on a knowledge of the hydroxyl value of the polyol the amount of isocyanate necessary to cause chain growth should be calculated. The gas evolved will depend on the water content and additional isocyanate must be incorporated corresponding to the water present. When the isocyanate used equals the theoretical amount the system is said to have a TDI index of 100. In practice a slight excess of isocyanate is used (TDI index 105-110) to ensure complete... 

In Section 3.4 we discussed the problem of reversibility of diazotization of aromatic and heteroaromatic amines. Simple stoichiometric considerations indicate that the reverse reaction (ArNJ -> ArNH2) may take place under strongly acidic conditions. Experimentally the reverse reaction was found only with heteroaromatic diazonium salts (Kavalek et al., 1989). Reaction conditions of hydroxy-de-diazonia-tion are comparable to those used for the reverse reactions of diazotization (e.g., 10 m H2S04, but at 0°C for the formation of 2-amino-5-phenyl-l,3,4-thiadiazol from the corresponding diazonium salt, Kavalek et al., 1979). So far as we know, however, amines have never been detected in aromatic hydroxy-de-diazoniations, not even in small amounts. 

The quantum yield is the number of bond scissions, S, which occur per photon absorbed. From stoichiometric considerations (7),... 

Other restrictions on the system may result from stoichiometric considerations. A very common stoichiometric restriction occurs in ionic solutions where charge neutrality must hold. Other restrictions can result if two species are produced only by the decomposition of the same molecule. If the number of stoichiometric restrictions is a, the degrees of freedom of the system become... 

Correspondingly, organic-electrochemical reactions sometimes offer so many alternative paths (at least as seen by simple stoichiometric considerations) that the best that can be done is to reduce the dozen or more possible rate-determining steps that formalistic consideration seems to show are possible, down to two or three alternatives. The degree of detail with which one may determine a mechanism is always a matter of what is available, the instrumentation (both electrochemical and spectroscopic), time, and funds. 

These data suggest that, at least at the micron level (using 20x or 40x objectives), there are no inaccessible regions. Incorporation at the molecular level is not ruled out by these data, although stoichiometric considerations may suggest otherwise. ... 

Yokata, O., Oku, Y., Sano, T., Hasegawa, N., Matsunami, J., Tsuji, M., Tamura, Y. (2000). Stoichiometric consideration of steam reforming of methane on Ni/A1203 catalyst at 650°C by using a solar furnace simulator. Int. 1. Hydrogen Energy 25,81-86. 

In many calculations the hydrogen ion concentration is more accessible than the activity. For example, the electroneutrality condition is written in terms of concentrations rather than activities. Also, from stoichiometric considerations, the concentrations of solution components are often directly available. Therefore, the hydrogen ion concentration is most readily calculated from equilibrium constants written in terms of concentration. When a comparison of hydrogen ion concentrations with measured pH values is required (in calculation of equilibrium constants, for example), an estimate of the hydrogen ion activity coeflScient can be made by application of the Debye-Huckel theory if necessary, an estimate of liquid-junction potentials also can be made. Alternatively, the glass electrode can be calibrated with solutions of known hydrogen ion concentration and constant ionic strength. " ... 

Another curious reaction, the cathodic formation of N2 from N3, has recently been discovered by Roscoe and Conway (Elementary chemical stoichiometric considerations require that such a process must be accompanied by formation of NH3 (or N2H4), namely. 

One is the formate pathway characteristic of the mixed acid fermentation by bacteria such as Escherichia coli. The pathway was proposed from stoichiometric considerations, such as the molar amount of formate at pH around 7 is equal to the molar amount of C02 and H2 at pH... 

The fractions can now be easily determined. If n is the number of CHjF molecules initially excited by the laser, simple stoichiometric considerations for path C yield immediately... 

Ageno and Valla equilibrated their solid phase with water under a carbon dioxide containing atmosphere in a closed vessel at 25°C. The Ni(II) concentration and the partial pressure of CO2 were determined experimentally. Column 2 of their table on carbonate solubilities is labelled incorrectly. Under the conditions prevailing in their study an elementary stoichiometric consideration prediets ... 

In several of the studies of aqueous chemistry of aluminum that have been made since about 1950, polynuclear complexing mechanisms have been proposed to identify and describe the dissolved aluminum hydroxide complex species (3, JO, 11). The formulae proposed have generally been based on stoichiometric considerations and pH measurements assuming the polynuclear species were ionic, and that equilibrium was attained. The complex ions reported by Hsu and Bates (8) were single six-mem-bered rings Ale (OH) 12 or multiples of this unit. Johansson (JO) identified a structural unit containing 13 aluminum and 40 oxygen atoms with various numbers of protons in crystalline basic aluminum sulfate. Because this solid formed readily, the same structural unit of aluminum was proposed as a solute species. Most of the proposed formulae for polynuclear complexes, however, have not been derived from structural considerations. 

When the introduced cation is divalent, the situation is more compH-cated. General stoichiometric considerations show that one cation should... 

Specific Growth Rates, Yieid Coefficients, and Stoichiometric Considerations... 

Chemistry, the study of chemical reactions, would be a much simpler (and less interesting) science if all chemical reactions went to completion. This is not the case, however chemistry cannot be based on stoichiometry alone. Many reactions are reversible and do not go to completion. In such mixtures, the final composition is quite different from that which could be expected from stoichiometric considerations. A detailed knowledge of the composition, i.e., the concentration of each species present, of such mixtures is essential for the understanding of their chemistry. Short of actually measuring the amount of each and every species present, the only way to obtain this knowledge is from a consideration of the appropriate equilibria. 

Both thermodynamic and stoichiometric considerations are taken into account in maximizing the formation of SO3. The Le Chatelier-Braun principle is usually taken into account in deciding how to optimize the equilibrium. This states that when an equilibrium system is subjected to stress, the system will tend to adjust itself in sueh a way that part of the stress is relieved. These stresses are, for example, variations of temperature, pressure, or concentration of a reactant. 

The main problem in applying stoichiometric considerations to bioprocessing (beyond quantification in non-open-reactor systems) arises from the complex metabolic reaction network. In simple reactions stoichiometry is trivial, and complex reactions can only be handled with the aid of a formal mathematical approach analogous to the approach for complex chemical reactions (Schubert and Hofmann, 1975). In such a situation, an elementary balance equation must be set up. Due to complexity, it is not surprising that the approach first used in the quantification of bioprocesses was much simpler— the concept of yield factors Y. This macroscopic parameter Y cannot be considered a biological constant. 

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