Stoichiometry fundamentals

Section 2.6 provides a summary of the important concepts and relationships that may prove useful as a study guide or quick reference. References for further study are provided at the end of the chapter. Exercises are provided in Section 2.7 for reinforcing the concepts and to further develop one s understanding. The last several exercises introduce new material and show how the stoichiometry fundamentals presented in this chapter lead into other interesting topics. The reactor analysis book by Axis f l] influenced several sections of this chapter. 

At present, intercalation compounds are used widely in various electrochemical devices (batteries, fuel cells, electrochromic devices, etc.). At the same time, many fundamental problems in this field do not yet have an explanation (e.g., the influence of ion solvation, the influence of defects in the host structure and/or in the host stoichiometry on the kinetic and thermodynamic properties of intercalation compounds). Optimization of the host stoichiometry of high-voltage intercalation compounds into oxide host materials is of prime importance for their practical application. Intercalation processes into organic polymer host materials are discussed in Chapter 26. 

As depicted in Figure 2.3, electrons are transferred from the oxidation step to the reduction step of the redox reaction. The number of electrons exchanged is the fundamental basis for establishing the stoichiometry of the redox process. This fact is crucial when establishing a mass balance, as will be done by modeling sewer processes (cf. Chapters 5 and 6). The OX value is, by definition, a key element in determination of this number. 

Fermentation systems obey the same fundamental mass and energy balance relationships as do chemical reaction systems, but special difficulties arise in biological reactor modelling, owing to uncertainties in the kinetic rate expression and the reaction stoichiometry. In what follows, material balance equations are derived for the total mass, the mass of substrate and the cell mass for the case of the stirred tank bioreactor system (Dunn et ah, 2003). 

The presence of the OH group in alcohols makes alcohol combustion chemistry an interesting variation of the analogous paraffin hydrocarbon. Two fundamental pathways can exist in the initial attack on alcohols. In one, the OH group can be displaced while an alkyl radical also remains as a product. In the other, the alcohol is attacked at a different site and forms an intermediate oxygenated species, typically an aldehyde. The dominant pathway depends on the bond strengths in the particular alcohol molecule and on the overall stoichiometry that determines the relative abundance of the reactive radicals. 

Stoichiometry. The measurement of reactants and products of a chemical reaction. Fundamentals, rule that the combined weights of reactants will equal combined weights of products in reactions going to completion. 

An integer indicating the molecular stoichiometry of an elementary reaction. A fundamental assumption in chemical kinetics is that the kinetic form of a one-step reaction will be identical to its stoichiometric form. In terms of transition-state theory, molecularity equals the number of molecules (or entities) that are used to form the activated complex. For reactions in solution, solvent molecules are counted in the molecularity only if they enter into the overall process, not if they only exert an environmental or solvent effect ". ... 

The authors established that the main reaction product has a LiC2H2 stoichiometry and ascribed six of the observed fundamentals to this species (Table 3) . The presence of only... 

On a molecular level, reactions occur by coUisions between molecules, and the rate is usually proportional to the density of each reacting molecule. We will return to the subject of reaction mechanisms and elementary reactions in Chapter 4. Here we define elementary reactions more simply and loosely as reactions whose kinetics agree with their stoichiometry. This relationship between stoichiometry and kinetics is sometimes called the Law of Mass Action, although it is by no means a fundamental law of nature, and it is frequently invalid. 

In the case of coneentrated solutions of defects, i.e. large departures from stoichiometry, a fundamental fact in encountered AHimer and ASconf are strongly correlated, i.e. 

Although there are many features common to synthetic oxides and minerals, fundamental studies of the charge-transfer processes in mixed-valence compounds can only be systematically carried out on synthetic oxides of controlled stoichiometry and impurity concentration. However, with the exception of Seebeck coefficients, transport measurements require single-crystal data if quantitative interpretations are to be made. Nevertheless, conductivity data for polycrystalline samples of cubic phases are useful if the samples are dense and care has been taken to eliminate any segregation of impurities into the grain boundaries. 

However, structural chemistry in oxides with large departures from stoichiometry cannot be solely explained by point defects. Defects cannot remain isolated and interactions between them begin to occur. Our discussion therefore begins with a general description of the fundamental knowledge about nonstoichiometry in oxides. Understanding such disorder and the complex defect... 

In a related application, polyelectrolyte microgels based on crosslinked cationic poly(allyl amine) and anionic polyfmethacrylic acid-co-epoxypropyl methacrylate) were studied by potentiometry, conductometry and turbidimetry [349]. In their neutralized (salt) form, the microgels fully complexed with linear polyelectrolytes (poly(acrylic acid), poly(acrylic acid-co-acrylamide), and polystyrene sulfonate)) as if the gels were themselves linear. However, if an acid/base reaction occurs between the linear polymers and the gels, it appears that only the surfaces of the gels form complexes. Previous work has addressed the fundamental characteristics of these complexes [350, 351] and has shown preferential complexation of cationic polyelectrolytes with crosslinked car-boxymethyl cellulose versus linear CMC [350], The departure from the 1 1 stoichiometry with the non-neutralized microgels may be due to the collapsed nature of these networks which prevents penetration of water soluble polyelectrolyte. 

This example illustrates the qualitative nature of information that can be gleaned from macroscopic uptake studies. Consideration of adsorption isotherms alone cannot provide mechanistic information about sorption reactions because such isotherms can be fit equally well with a variety of surface complexation models assuming different reaction stoichiometries. More quantitative, molecular-scale information about such reactions is needed if we are to develop a fundamental understanding of molecular processes at environmental interfaces. Over the past 20 years in situ XAFS spectroscopy studies have provided quantitative information on the products of sorption reactions at metal oxide-aqueous solution interfaces (e.g., [39,40,129-138]. One... 

Water, carbon dioxide, olefin hydrocarbons, and alcohols are shown as products. It is obvious that other equations could be written showing the formation of hydrocarbons of other types—that is CH4, C2H6—and of the other oxygenates produced in this synthesis. Although Equations 8, 9, and 10 do not represent the reaction mechanism but simply express the stoichiometry of the system, they do indicate certain fundamental actions that... 

The relation between the non-stoichiometry and the equilibrium oxygen pressure mentioned in Section 1.1 can be deduced from the phase rule. For the purpose of the derivation of the phase rule, we shall review fundamental thermodynamics. Gibbs free energy G is defined by the relation... 

Chapter 1 deals with classical non-stoichiometric compounds. By classical, the author means that the basic concept of the phase stability has been well established from a thermodynamical point of view, and does not mean that research in this field has been fully completed. In these compounds the origin of non-stoichiometry is point defects . In the first half of the chapter, the fundamental relation between point defects and non-stoichiometry is described in detail, based on (statistical) thermodynamics, and in the second half various examples, referred to the original papers, are shown. 

Chemists ask three fundamental questions when they study chemical reactions What happens To what extent does it happen How fast does it happen The answer to the first question is given by the balanced chemical equation, which identifies the reactants, the products, and the stoichiometry of the reaction. The answer to the second question is addressed in Chapter 13, which deals with chemical equilibrium. In this chapter, we ll look at the answer to the third question—the speeds, or rates, at which chemical reactions occur. The area of chemistry... 

Oxidation by dioxygen has a fundamental difficulty. The molecule has a diatomic structure, while in most cases only one atom is needed for selective oxidation of organic compounds. Even in the case of more complex reactions, the stoichiometry of which requires several (and sometimes many) oxygen atoms, the oxidation process on a catalyst surface is likely to proceed step by step, involving consecutively one oxygen atom after another. 

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