Stoichiometric notation

This book will help to tie all of these topies together, and bring them to bear on the study of Chemical Reactions and Chemical Reactors. Let s begin by taking a ftesh look at stoiehiometry, from the standpoint of how we ean use it to deseribe the behavior of a chemical reaction, and systems of chemical reactions. 

The molecule C3H6O is propylene oxide, an important raw material in the manufacture of unsaturated polyesters, such as those used for boat bodies, and in the manufacture of polyurethanes, such as the foam in automobile seats. Reaction (1-A) describes the stoichiometry of the chlorohydrin process for propylene oxide manufacture. This process is used for about one-half of the worldwide production of propylene oxide. 

The balanced stoichiometric equation for any chemical reaction can be written using a generalized form of stoichiometric notation 

In this equation. A represents a chemical species. For instance, in Reaction (1 -A), we might choose 

The stoichiometric coefficient for chemical species i is denoted v,-. Equation (1-1) involves a convention for writing the stoichiometric coefficients. The coefficients of the products of a reaction are positive, and the coefficients of the reactants are negative. Thus, for Reaction (1-A)  

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Since elementary reactions of the chain propagation are assumed as being far from the equilibrium state and this allows to ignore their reversible directions, the stoichiometric notations of elementary (2.115) and (2.116) and also the final reactions (2.118) and (2.119) do not limit in any way the use of an algorithm of construction of the kinetic models of the routes. Furthermore, formally it can always be assumed that elementary (2.115) and (2.116) and the final reactions (2.118) and (2.119) have an anpty composite substance, the concentration of which is equal to zero for example... 

A formalisation of the final algorithm of the kinetic models for route construction is wholly stored under this variant of the stoichiometric notations of the non-reversible... 

You may have used this stoichiometric notation in earlier courses, such as thermodynamics. For example, the standard Gibbs free energy change of a reaction (AG ) and the standard enthalpy change of a reaction (A/f ) can be written as... 

If the index k is used to denote one specific reaction in a system of R reactions, the generalized stoichiometric notation for a reaction becomes... 

Of course, in reactions (5.A) and (5.B) the hydrocarbon sequences R and R can be the same or different, contain any number of carbon atoms, be linear or cyclic, and so on. Likewise, the general reactions (5.C) and (5.E) certainly involve hydrocarbon sequences between the reactive groups A and B. The notation involved in these latter reactions is particularly convenient, however, and we shall use it extensively in this chapter. It will become clear as we proceed that the stoichiometric proportions of reactive groups-A and B in the above notation—play an important role in determining the characteristics of the polymeric product. Accordingly, we shall confine our discussions for the present to reactions of the type given by (5.E), since equimolar proportions of A and B are assured by the structure of this monomer. 

To a good approximation this structure can be regarded as f.c.c. based with (002) planes composed alternatively of Tl and Al the cubic crystallographic notation Is. therefore, commonly used. If we denote as c and a the lattice parameters In the [001) and 11001/1010) directions, respectively, the c/a ratio is 1.02 at the stoichiometric composition and Increases to 1.03 at Al-rich compositions (Duwez and Taylor 1952 Huang, et al. 1987). 

As a shorthand notation for indicating that a reaction is elementary, we shall include the rate constants in the stoichiometric equation. Thus, the reaction... 

To avoid vriting long equations with similar terms, we introduce a convenient shorthand notation for most of the expressions considered so far. X will denote the molecules A, B, etc. and Vi the stoichiometric coefficients, which are negative for reactants and positive for products. This yields the following set of equations ... 

Components are the most basic units (molecules or ions or atoms) that interact with each other. In the above example X, Y, and Z are components. All the resulting products of the interactions (molecules or ions or complexes) are called species. In the example, one of potentially many species is XxYyZz. To be consistent and to allow elegant and efficient notation and computer coding, the components themselves are also species. Their equilibrium constant is one. The equilibrium constants fixyz as defined in (3.22) are called formation constants. The composition of a particular species is defined by a set of three stoichiometric constants written as the indices x, y, and z. If a species is composed of only two components, the appropriate index is zero. 

A more complex notation is needed for non-stoichiometric phases. Selected simple examples are given below, and more detailed information will be reported when discussing crystal coordination formulae ... 

The carbomethoxy cycle starts with the attack of a methoxy group at a coordinated carbonyl group or a migratory insertion of CO in a palladium methoxy bond. Any type of methoxy species will have a low concentration in the acidic medium of the reaction. In Figure 12.20 many details of these reactions, discussed above in section 12.2, have been omitted and only a shorthand notation is presented. Subsequently insertion of ethene takes place. It is known from stoichiometric experiments that both reactions are relatively slow. In the final step a formal protonation takes place, which as we saw before, may actually involve enolate species. 

The reason for following this complex notation will become apparent shortly. The law of mass action, which is confirmed experimentally, states that the rate of disappearance of a chemical species i, defined as RRit is proportional to the product of the concentrations of the reacting chemical species, where each concentration is raised to a power equal to the corresponding stoichiometric coefficient that is,... 

B. LAW OF MASS ACTION. Using the conventional notation, we will define an overall reaction rate 31 as the rate of change of moles of any component per volume due to chemical reaction divided by that component s stoichiometric coefficient... 

Notation-. T is the temperature, Vi the fluid velocity, II,j the viscous pressure tensor, Jg the heat current density, p its chemical potential, the current density of molecular species a, v J the stoichiometric coefficient (13), and Wp the speed of reaction p. 

For propagation of a flame in a stoichiometric mixture, following the paper by Frank-Kamenetskii and the author [6], we obtain in our notation here... 

This shows that the solution s to the system of linear equations represented by equation 6.1-1 is made up of the stoichiometric numbers s that give the number of times the various biochemical reactions have to occur to accomplish the net reaction. Equation 6.1-1 is conveniently written in matrix notation as... 

The composition of these oxides normally departs from the precise stoichiometry, expressed in their chemical formulae. For example, in the case of a stoichiometric oxide, such as A05, where 8 = 0, we will have only thermal disorder, where the concentration of vacancies, and interstitials will be determined by the Schottky, Frenkel, and anti-Frenkel mechanisms [40-42] (these defects are explained in more detail in Chapter 5). In the case of the Schotky mechanism, the following equilibrium, described with the help of the Kroger-Vink notation, [43] develops [40]... 

Thus, the main problems concern firstly, the input of the reaction mechanism into the computer (problem of chemical notation) and secondly, the processing of the reaction mechanism itself (problem of chemical compiler). Let us point out that the knowledge of tile matrix of stoichiometric coefficients allows us to compute the partial derivatives of the reaction rates with respect to the concentrations, i.e. a Jacobian matrix which has been shown to play a central role in the numerical computations. 

The principle of mass conservation, on a macroscopic basis, using equations representing the conservation of total mass, the conservation of each chemical element and the mass balance for each of the molecular species was applied. Chemical reactions were taken into account in these equations. The stoichiometric coefficients of individual reactants were evaluated using Microsoft Excel software by expressing the equations in matrix notation. 

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