Stoichiometrically unknown compounds

Stoichiometrically unknown compounds can be examined, by treating the indices as unknown quantities, e.g., 

Nonlinear equations are obtained in this case. However, we observe that during the solution of the above equations, the values m = 1 are forced and/or n = 2. If we put further y CmOn, then we obtain still n = 2m, as the relative composition of the compound and further ym = 1. So the stoichiometric factor y is fixed besides the uncertainty of a hypothetical m-mer of carbon dioxide. 

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The stoichiometric calculations of Chapters 12 and 13 are based on the mole as the fundamental chemical unit in reactions. An alternative method of calculation utilizes the equivalent as a fundamental chemical unit. There are two kinds of equivalents, the type depending on the reaction in question we shall refer to them as acid-base equivalents (or simply as equivalents) and electron-transfer equivalents (or E-T equivalents). The concept of an equivalent is particularly useful when dealing with complex or unknown mixtures, or when working out the structure and properties of unknown compounds. In addition, it emphasizes a basic characteristic of all chemical reactions that is directly applicable to all types of titration analyses. 

One of the possibilities is to study experimentally the coupled system as a whole, at a time when all the reactions concerned are taking place. On the basis of the data obtained it is possible to solve the system of differential equations (1) simultaneously and to determine numerical values of all the parameters unknown (constants). This approach can be refined in that the equations for the stoichiometrically simple reactions can be specified in view of the presumed mechanism and the elementary steps so that one obtains a very complex set of different reaction paths with many unidentifiable intermediates. A number of procedures have been suggested to solve such complicated systems. Some of them start from the assumption of steady-state rates of the individual steps and they were worked out also for stoichiometrically not simple reactions [see, e.g. (8, 9, 5a)]. A concise treatment of the properties of the systems of consecutive processes has been written by Noyes (10). The simplification of the treatment of some complex systems can be achieved by using isotopically labeled compounds (8, 11, 12, 12a, 12b). Even very complicated systems which involve non-... 

Compounds in the P/P" family permit not only fast Na ion diffusion but also rapid transport of other monovalent ions (e.g., K, Ag, Cu", Cs, Rb ), hydronium ions (HsO ), divalent ions (e.g., Ca ", Ba " ) and trivalent cations . As it turns out, the Na ion has the highest mobility in these two structures. The sodium -alumina and /)"-alumina compounds are nonstoichiometric aluminates that are derivatives of the yet unknown stoichiometric sodium aluminate, NaAlnOi (Na20 IIAI2O3), with an excess of Na20. 

The mechanism of the Ley oxidation is complex and the exact nature of the species involved in the catalytic cycle is unknown. The difficulty in establishing an exact mechanism arises from the fact that the complexes of Ru ", Ru ", Ru , Ru and Ru are all capable of stoichiometrically oxidizing alcohols to carbonyl compounds. The TRAP reagent can oxidize alcohols stoichiometrically as a three-electron oxidant and can also be used as a catalyst when a co-oxidant is present (e.g., NMO, TMAO, or hydroperoxides). Data suggests that the oxidation proceeds via the formation of a complex between the alcohol and TRAP (ruthenate ester). It was also found that the stoichiometric oxidation of isopropyl alcohol with TRAP is autocatalytic and the catalyst is suspected to be colloidal RUO2. Small amounts of water decrease the degree of autocatalysis. This observation is supported by the finding that the addition of molecular sieves improves the efficiency of the reaction. 

However, in the case of C02—metal complexes, the model compounds that have been well-characterized are not catalytically, or even stoichiometrically, active toward C02 reduction. Rapid and efficient homogeneous catalysts for the reduction of C02 by more than two electrons (e.g., to formate or CO) are currently unknown. Clearly, fundamental structure/reactivity relationships are not yet well understood. Efforts now are focused on trying to combine the current information about structural and electronic properties of the model compounds and available information about low-efficiency catalytic processes into strategies that will accomplish the goal of C02 fixation. Certainly, processes that could utilize sunlight to promote the necessary electron transfer reactions needed for C02 reduction are most desirable. 

This is all true when the stoichiometric disulfides are considered. What happens to chemical bonding upon sulfiir loss remains unknown. A possible solution of the problem appeared when the structures of SmSi.90 (Podberezskaya et al. 1999, Tamazyan et al. 2000b), DySi.84 (Podberezskaya et al. 1998), and DyS 7 (Tamazyan et al. 1994) were resolved. Formally, the chemical bonding may be characterized by the ionic formulas and by the interatomic distances in the structural series of the RS2 RS1.90 RSi.g4 RS].76 compounds. These distances are compared with the known radii (metallic, ionic, covalent) taken firom the Table of ionic radii in the ICSD databank (CRISTIN 1986). Considering the structures as alternating square nets, -(S2)-R-S-S-R-(S2-, two types of distances, within each layer (-(S2)-(S2)- R-R S-S ) and between the layers (R-S S-(S2) S-S), have been analyzed. In the sheet (R-S-S-R) or (RS)+ all the R-R and S-S distances are close to the sum of the appropriate metallic radii for R and ionic radii for and the R-S distances are close to the smn of the ionic radii of these elements. This means that the chemical bonding in this sheet is preferably ionic. 

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