Basic Stoichiometric Concepts

There are many eqnivalent ways of writing the stoichiometric eqnation for a reaction. For example, one conld write the oxidation of carbon monoxide in our notation as 

This second form is preferred, provided that one keeps in mind the proper sign convention for the stoichiometric coefficients. For the example above, Vqq = -2, Vq = -1, andvco, =2. 

The choice is a matter of personal convenience. The essential point is that the ratios of the stoichiometric coefficients are unique for a specific reaction. In terms of the two forms of the chemical equation above. 

Because the reaction stoichiometry can be expressed in various ways, one must always write down a stoichiometric equation for the reaction under study during the initial stages of the analysis and base subsequent calculations on this reference equation. If a consistent set of stoichiometric coefficients is used throughout the calculations, the results can be readily understood and utilized by other workers in the field. 

This equation is valid for all species A,, a fact that is a consequence of the law of definite proportions. The molar extent of reaction is a time-dependent extensive variable that is measured in moles. It is a useful measure of the progress of the reaction because it is not tied to any particular species A,. Changes in the mole numbers of two species i and j can be related to one another by eliminating between two expressions that may be derived using equation (1.1.4)  

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Efforts to understand the effects of CO2 emissions on the atmosphere will no doubt continue throughout your lifetime. It is a complex problem, but our understanding of it continues to progress. The next time you read an article on global climate change or the greenhouse effect, keep in mind that basic stoichiometric concepts are at the heart of aU the lengthy calculations in the various sophisticated mathematical models used in scientific studies. 

These calculations are so basic to the field that you should go back and carefully review the two examples in this section the calculation of weight percents in N2O and the inference of the formula for aluminum oxide. Then you can practice stoichiometric calculations on the following pair of problems, which are answered and explained in Appendix A. Many such practice exercises are included in this book so you can determine whether you understand the major concepts of chemistry. It is well worth your time to study these examples and their explanations in Appendix A until you can do the calculations correctly. 

So far we have discussed the basic concept of non-stoichiometry without showing real examples. Here we shall consider case studies in order to understand the non-stoichiometry appearing in various kinds of substances. To construct phase diagrams which contain non-stoichiometric compounds, it is indispensable to know the relationship between the deviation from stoichiometry <5, the partial pressure of coexisted gas, (for diatomic gases),... 

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. 

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. 

In 1879 Guldberg and Waage substituted the above formulation for the basic law of chemical reactions by its modem version in terms of the concept of mobile equilibrium. For the interaction between the initial substances A, B, C, taken in the stoichiometric ratio of a to to y, i.e. aA + / B + yC, the reaction rate, W, was expressed as... 

The theory of steady-state reactions operates with the concepts of "a path of the step , "a path of the route , and "the reaction rate along the basic route . Let us give their determination in accordance with ref. 16. The number of step paths is interpreted as the difference of the number of elementary reaction acts in the direct and reverse directions. Then the rate for the direct step is equal to that of the paths per unit time in unit reaction space. One path along the route signifies that every step has as many paths as its stoichiometric number for a given route. In the case when the formation of a molecule in one of the steps is compensated by its consumption in the other step, the steady-state reaction process is realized. If, in the course of this step, no final product but a new intermediate is formed, then it is this... 

The state of equilibrium in ion exchange chromatography is currently described by stoichiometric models where the solute, for example a protein, displaces a stoichiometric number of salt ions bound on the ion exchanger. A basic concept is the stoichiometric displacement model developed by Kopaciewicz et al. (1983). For monovalent counterions the reaction is described as follows ... 

We shall now apply the concept of the basic rate of each reaction as defined in Chapter 5. Thus, for a given reaction of the system, say reaction 1, we postulate a product with a stoichiometric coefficient of +1 for that reaction and zero for all other reactions (i.e., t u = 1, i i2 = 3 = = 0)- The summation in Equation 11.14 then reduces to the simple equation... 

Applied General Chemistry—study of the general concepts of chemistry with an emphasis on industrial applications. Students measure physical properties of matter, perform chemical calculations, describe atomic and molecular structures, distinguish periodic relationships of elements, name and write inorganic formulas, write equations for chemical reactions, demonstrate stoichiometric relationships, and demonstrate basic laboratory skills. 

Many of the difficulties associated with the application of whole cells as catalyst can be avoided using isolated enzymes. The necessary in situ regeneration and high conversion of NADH/NADPH can be accomplished in different ways [12]. In every case the stoichiometric link between coenzyme consumption and product formation is shifted toward the consumption of a cosubstrate and the concomitant production of a second product. The basic concept is derived from the metabolism but is simplified from the network to a single reaction step, which is more amenable to optimization by reaction engineering techniques [9,13]. 

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