Reaction stoichiometry Description

Reaction stoichiometry Description of the quantitative relationships among substances as they participate in chemical reactions. 

Mechanism I illustrates an important requirement for reaction mechanisms. Because a mechanism is a summary of events at the molecular level, a mechanism must lead to the correct stoichiometry to be an accurate description of the chemical reaction. The sum of the steps of a mechanism must give the balanced stoichiometric equation for the overall chemical reaction. If it does not, the proposed mechanism must be discarded. In Mechanism I, the net result of two sequential elementary reactions is the observed reaction stoichiometry. 

The early chapters in this book deal with chemical reactions. Stoichiometry is covered in Chapters 3 and 4, with special emphasis on reactions in aqueous solutions. The properties of gases are treated in Chapter 5, followed by coverage of gas phase equilibria in Chapter 6. Acid-base equilibria are covered in Chapter 7, and Chapter 8 deals with additional aqueous equilibria. Thermodynamics is covered in two chapters Chapter 9 deals with thermochemistry and the first law of thermodynamics Chapter 10 treats the topics associated with the second law of thermodynamics. The discussion of electrochemistry follows in Chapter 11. Atomic theory and quantum mechanics are covered in Chapter 12, followed by two chapters on chemical bonding and modern spectroscopy (Chapters 13 and 14). Chemical kinetics is discussed in Chapter 15, followed by coverage of solids and liquids in Chapter 16, and the physical properties of solutions in Chapter 17. A systematic treatment of the descriptive chemistry of the representative elements is given in Chapters 18 and 19, and of the transition metals in Chapter 20. Chapter 21 covers topics in nuclear chemistry and Chapter 22 provides an introduction to organic chemistry and to the most important biomolecules. 

The term reaction mechanism is part of the everyday language of chemists, yet it conveys different things to different people. The IUPAC Gold book (www.goldbook.iupac.org) defines the mechanism of a reaction as A detailed description of the process leading from the reactants to the products of a reaction, including a characterization as complete as possible of the composition, structure, energy and other properties of reaction intermediates, products and transition states. An acceptable mechanism of a specified reaction (and there may be a number of such alternative mechanisms not excluded by the evidence) must be consistent with the reaction stoichiometry, the rate law and with all other available experimental data, such as the stereochemical course of the reaction. On the basis of Occam s razor (Section 3.7.4), one should always choose the simplest mechanism that is consistent with all available evidence. 

The overall reaction stoichiometry, Reaction 5.1, is explained as a linear combination of the five reactions in the proposed mechanism. By balancing the species in the overall stoichiometry, one can determine that the overall stoichiometry is produced by adding twice the third reaction to the remaining reactions. If the elementary reactions cannot be combined to form the overall stoichiometry, then the mechanism is not a valid description of the observed stoichiometry. ... 

No. Description Mixing = 1) i,kk Reaction (stoichiometry, /.J 9, react, rr Waste Product separation spliti.kk... 

For a quantitative description of the behavior of gases, we will employ some simple gas laws and a more general expression called the ideal gas equation. These laws will be explained by the kinetic-molecular theory of gases. The topics covered in this chapter extend the discussion of reaction stoichiometry from the previous two chapters and lay some groundwork for use in the following chapter on thermochemistry. The relationships between gases and the other states of matter— liquids and solids—are discussed in Chapter 12. 

The description presented in this section applies to a gas mixture that is not undergoing chemical reactions. As long as reactions do not occur, the number of moles of each gas is determined by the amount of that substance initially present. When reactions occur, the numbers of moles of reactants and products change as predicted by the principles of stoichiometry. Changes in composition must be taken into account before the properties of the gas mixture can be computed. Gas stoichiometry is described in the next section. 

The first step In balancing a redox reaction is to divide the unbalanced equation into half-reactions. Identify the participants in each half-reaction by noting that each half-reaction must be balanced. That Is, each element In each half-reaction must be conserved. Consequently, any element that appears as a reactant In a half-reaction must also appear among the products. Hydrogen and oxygen frequently appear in both half-reactions, but other elements usually appear In just one of the half-reactions. Water, hydronium ions, and hydroxide ions often play roles In the overall stoichiometry of redox reactions occurring in aqueous solution. Chemists frequently omit these species in preliminary descriptions of such redox reactions. 

The semi-empirical descriptions of adsorbate/solid interactions are based on net changes in system composition and, unlike surface complexation models, do not explicitly identify the details of such interactions. Included in this group are distribution coefficients (Kp) and apparent adsorbate/proton exchange stoichiometries. Distribution coefficients are derived from the simple association reaction... 

Though it is impossible to formulate a complete mathematical representation of the super-rate burning, it is possible to introduce a simplified description based on a dual-pathway representation of the effects of a shift in stoichiometry. Generalized chemical pathways for both non-catalyzed and catalyzed propellants are shown in Fig. 6.26. The shift toward the stoichiometric ratio causes a substantial increase in the reaction rate in the fizz zone and increases the dark zone temperature, a consequence of which is that the heat flux transferred back from the gas phase to the burning surface increases. 

In Chapter 7 we considered catalytic reactions on solid surfaces and foimd that transport steps are essential in describing these reactions because mass transfer of reactants and products between phases must accompany reaction. In this chapter we consider the reactions of solids in which the solid enters the stoichiometry of the reaction as a reactant or product or both. We remark that the texts of Levenspiel give excellent and thorough descriptions of the reactions of solids, and we will only summarize some of the features of reactions involving solids here. 

The first description of a bacterial FDPase was that of Fossitt and Bernstein (89), who purified the enzyme from extracts of Pseudomonas saccharophila and established the specificity of the enzyme and the stoichiometry of the reaction. Fructosediphosphatase has also been reported in Aerobacter aerogenes (90), where the enzyme is required for growth on D-fructose. Like the enzyme in E. coli, the Aerobacter FDPase exhibits optimum activity between pH 7 and 8. In this organism the obligatory pathway for fructose utilization is fructose - fructose 1-phosphate -> fructose 1,6-diphosphate. The presence of FDPase is required as a source of fructose 6-phosphate for biosynthetic pathways. 

The chemical equation for an elementary reaction is a description of an individual molecular event that involves breaking and/or making chemical bonds. By contrast, the balanced equation for an overall reaction describes only the stoichiometry of the overall process, but provides no information about how the reaction occurs. The equation for the reaction of N02 with CO, for example, does not tell us that the reaction occurs by direct transfer of an oxygen atom from an N02 molecule to a CO molecule. 

The latter difficulty is easily overcome by extrapolation. Furthermore, it is clear that if the mean content of a component in a compound is equal to 40-60 %, while the range of homogeneity is 1-2 % or less, then possible deviations from the quasistationary concentration distribution can hardly be expected to have any noticeable effect on the results of analytical description of layer-growth kinetics. This is especially so in the case of reaction diffusion. The layer of any chemical compound grows mainly at the expense of stoichiometry of that compound and not at the expense of its range of homogeneity. Therefore, for formal kinetics it does not matter,... 

The stoichiometric description of a chemical reaction requires answers to the following questions. How many equations are to be written How can we verify that they are independent How can we verify that they correctly describe the experimental results . Answers to these questions are provided by the criteria of Brinkley and Jouguet and by the theory of invariants. But, before this, the concepts of independent constituents and stoichiometries need to be defined. 

The stoichiometric description of a chemical system requires that s stoichiometric equations be written between c constituents involved in the reaction (for example, constituents which have been analytically detected). Even for systems which are not too complex, it may be feared that some reactions have been overlooked or are not independent. Thus, criteria allowing us to fix a priori the number of independent stoichiometries and to test their independence are needed. 

In terms of such an empirical description the particular reaction is said to have an order a with respect to species A, an order 3 with respect to species B, etc., and an over-all order given by the sum a + P + y + . The individual derivatives dCA/dt, dCBldt, and dCcfdt are referred to as the rate of the reaction with respect to species A, B, C, respectively, and are related by the stoichiometry of the chemical reaction. 

Given any P-dimensional vector b, the A-dimensional vector p b lies in the kernel of = b = 0. This, as will be seen, has important consequences in the theory of equilibrium. It is also important to realize that a description of the stoichiometry in terms of the condition = is in many senses equivalent to a description in terms of a, and in many formal manipulations it may be preferable when the number of species and/or reactions becomes very large, because the dimensions of stay at P no matter how complex the mixture may be. 

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