Independent chemical reactions example

Example 7.17 illustrates the utility of the reaction coordinate method for solving equilibrium problems. There are no more equations than there are independent chemical reactions. However, in practical problems such as atmospheric chemistry and combustion, the number of reactions is very large. A relatively complete description of high-temperature equilibria between oxygen and... 

To avoid unnecessary complications in the analysis of multiple reactions, we restrict the following discussion to sets of independent chemical reactions. Consequently, we need a.method of identifying a set of independent reactions from a larger collection of reactions. When only a few reactions are involved, as in the foregoing example, this can be done by inspection. If many reactions occur, the methods of matrix algebra can be used to determine a set of independent reactions, though we will employ a simpler procedure developed by Denbigh. ... 

As a last example, we consider the regular linear fluid mixture of atomic and molecular oxygen and ozone O, O2, O3 as ideal gases denoted by a = 1,2,3 respectively, i.e. the simplification (4.475) is valid. Here two independent chemical reactions take place, e.g. (4.48)... 

A fruitful approach to the thermodynamic treatment of chemical vapor deposition has been developed by Sirtl et al. and Ban et al. for the technologically important epitaxial deposition of Si from tetrachlorosilane and hydrogen [24, 25]. Hurle and MulHn developed a related concept for the deposition of III-V compound mixed-crystal layers [26]. The general approach consists in the numerical solution of a set of equations that is obtained from the law-of-mass-action expressions for all the independent chemical reactions between the different chemical species present in the deposition region and the conditions for the conservation of masses. Following Hurle and Mullin [26], the deposition of epitaxial layers of GaAsi- P, as applied in LED production, is used as an example. 

The number of independent chemical reactions we need to specify can be obtained by using the Gibbs phase rule for reacting systems. The phase rule for reacting systems is obtained by counting the total number of variables in the system and making sure we have the same number of independent equations. It is accomphshed in much the same way we accounted for variables for nonreacting systems in Example 6.17. 

Step 4 of the thermal treatment process (see Fig. 2) involves desorption, pyrolysis, and char formation. Much Hterature exists on the pyrolysis of coal (qv) and on different pyrolysis models for coal. These models are useful starting points for describing pyrolysis in kilns. For example, the devolatilization of coal is frequently modeled as competing chemical reactions (24). Another approach for modeling devolatilization uses a set of independent, first-order parallel reactions represented by a Gaussian distribution of activation energies (25). 

Until the second half of the twentieth century, the structure of a substance—a newly discovered natural product, for example—was determined using information obtained from chemical reactions. This information included the identification of functional groups by chemical tests, along with the results of experiments in which the substance was broken down into smaller, more readily identifiable fragments. Typical of this approach is the demonstration of the presence of a double bond in an alkene by catalytic hydrogenation and subsequent determination of its location by ozonolysis. After-considering all the available chemical evidence, the chemist proposed a candidate structure (or structures) consistent with the observations. Proof of structure was provided either by converting the substance to some already known compound or by an independent synthesis. 

Some progress has been made in developing theoretical expressions for rj(6) for deactivation processes such as coking. Deactivation by loss of active sites can be modeled as a chemical reaction proceeding in parallel with the main reaction. It may be substantially independent of the main reaction. Site sintering, for example, will depend mainly on the reaction temperature. It is normally modeled as a second-order reaction ... 

Gases that participate in chemical reactions typically are at pressures different from one bar. Substances in solution are likely to be at concentrations different from one molar. For example, a biochemist who wants to know what processes are spontaneous under physiological conditions will find that the substances dissolved in biological fluids are rarely at one molar concentration. How does AG vary with changes in molarity and pressure Recall that enthalpy is virtually independent of concentration but that entropy obeys Equation ... 

Enthalpies are often used to describe the energetics of bond formations. For example, when an amide forms through the condensation reaction between an ester and an amine, the new C-N bond, has an enthalpy of formation of -293 kj/mole. The higher the negative value for the bond enthalpy of formation, the stronger the bond. An even more useful concept is the enthalpy of a reaction. For any reaction, we can use the fact that enthalpy is a state function. A state function is one whose value is independent of the path traveled. So, no matter how we approach a chemical reaction, the enthalpy of the reaction is always the same. The enthalpy of... 

Minimal bounds on the production quantity are most often process dependent. Typically, a minimal campaign length is required if for example a critical mass is necessary to initiate a chemical reaction. The same is valid for maximal bounds on the production quantity. The rationale here is that a cleaning operation may be required every time a certain amount has been produced. Finally, batch size restrictions often arise in the chemical industry, if for example the batch size is determined by a reactor load or, as discussed above, the processing time for a certain production step is independent of the amount of material processed. In these scenarios, when working with model formulations using a discrete time scale, it is important that the model formulation takes into account that lot sizes may comprise of production in several adjacent periods. 

For a complex system, determination of the stoichiometry of a reacting system in the form of the maximum number (R) of linearly independent chemical equations is described in Examples 1-3 and 14. This can be a useful preliminary step in a kinetics study once all the reactants and products are known. It tells us the minimum number (usually) of species to be analyzed for, and enables us to obtain corresponding information about the remaining species. We can thus use it to construct a stoichiometric table corresponding to that for a simple system in Example 2-4. Since the set of equations is not unique, the individual chemical equations do not necessarily represent reactions, and the stoichiometric model does not provide a reaction network without further information obtained from kinetics. 

The simplest case of this parameter estimation problem results if all state variables jfj(t) and their derivatives xs(t) are measured directly. Then the estimation problem involves only r algebraic equations. On the other hand, if the derivatives are not available by direct measurement, we need to use the integrated forms, which again yield a system of algebraic equations. In a study of a chemical reaction, for example, y might be the conversion and the independent variables might be the time of reaction, temperature, and pressure. In addition to quantitative variables we could also include qualitative variables as the type of catalyst. 

For a nonlinear molecule consisting of N atoms, the potential energy surface depends on 3N - 6 independent coordinates and depicts how the PE changes as relative coordinates of the atomic nuclei involved in the chemical reaction are varied. For example, consider the water molecule (Fig. 9.10). 

This example also shows that the amount of kinetic information needed to complete the set of equations (one equation in this case) depends on the number of independent irreversible reactions (one) and not on the number of chemical species involved only in the irreversible reactions (two) or on the number of these species appearing as unknowns. 

In Chapter 3, we defined a new function, the internal energy U, and noted that it is a thermodynamic property that is, dU is an exact differential. As Q was defined in Equation (3.12) as equal to At/ when no work is done, the heat exchanged in a constant-volume process in which only PdV work is done is also independent of the path. For example, in a given chemical reaction carried out in a closed vessel of fixed volume, the heat absorbed (or evolved) depends only on the nature and condition of the initial reactants and of the final products it does not depend on the mechanism by which the reaction occurs. Therefore, if a catalyst speeds up the reaction by changing the mechanism, it does not affect the heat exchange accompanying the reaction. 

Because each half-reaction can behave like an independent chemical process, ping pong enzymes catalyze exchange reactions. For example, yeast NDPK catalyzes an ADP ATP exchange reaction ... 

Two Different Reactants. A set of two or more first-order reactions, the reactants of which are independent of each other, generating at least one product that is common for each chemical reaction. For example, consider the following set of parallel reactions ... 

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