Chemical reaction multiple

Consider a simple system 1 consisting of n components and subject to r chemical reaction mechanisms, and having specified values U of energy, V of volume, and values of V, As,. Ay of the amounts of components that are obtained from given values Nla, N2a,Nar. Such a system permits a very large number of states. But the second law requires that among all these states, the chemical equilibrium state is the only stable equilibrium state. In this state, we have 

The values of U, V, N.r and v determine uniquely the values of the entropy. S, the reaction coordinate e, and each Nj0 

The entropy of system 1 is a function of time. If. S cq is the entropy at stable equilibrium, the values of d (i) are smaller than the value. S cq. The rate of entropy production d in the isolated system 1 is given by 

Since each of the functions d and A - depends solely on the reaction coordinate c,p we have 

This equation indicates that the r X r matrix with elements (dXk/dBj )vy N v e is symmetric for the matrix e. From the Jacobian properties, the matrix with elements (dek ldXt )UFN vXis symmetric also for both zero and nonzero values of X, and we have 

---

As illustrated by the examples above, the possibility of removing the generated heat from the reaction zone decreases with an increase in reactor size. As proven above, it can happen that the temperature of the reaction mixture in a full-scale reactor becomes higher than in the laboratory flask reactor. If multiple chemical reactions of distinctly different temperature sensitivities take place, differences in yields and selectivities between small and large reactors will be observed. This has a large influence on safety also. The laboratory reactor might still show satisfactory performance, while the industrial reactor might even explode. 

Ung S, Doherty MF. Vapor-liquid equilibrium in systems with multiple chemical reactions. Chem Eng Sci 1995 50 23 18. 

It is important to remember that in the calculation of property degradation kinetics, the constants Ea and A do not imply any information regarding the chemical processes occurring. Multiple chemical reactions may give rise to an effective "activation energy" that is useful for comparison purposes only. 

Equation 3.39 holds valid for the system in which only a single process or reaction is occurring. In a system in which multiple chemical reactions are simultaneously occurring, Eq. 3.27 for the uncompensated heat can be expressed by the sum of the products of all independent affinities and their conjugated reaction rates as given in Eq. 3.40 ... 

This equation 4.13 can be used for studying the stability of chemical equilibria of multiple chemical reactions. 

Dissolution kinetics. In contrast to the degradation of organic matter, the dissolution of CaC03 in sediments relies on abiotic dissolution which ought, in principle, to be more conservative across regions of the ocean. A complication is that CaCOs dissolution into seawater is comprised of multiple chemical reactions such as... 

Devolatilization is very complicated, involving multiple chemical reactions coupled with transport processes, and it is very difficult to describe the process theoretically. In practice we resort to the use of a simplified global devolatilization model, which can be an effective approach if properly used.27... 

In the preceding section we noted fliat when multiple chemical reactions take place, only a set of independent chemical reactions should be considered to determine the species composition. As indicated, flie summations in Eq. 2.3.3 and Eq. 2.3.11 are taken over a set of independent chemical reactions and not over all the reactions that take place. This point deserves a closer examination. 

When multiple chemical reactions take place, the chemical reaction whose stoichiometric coefficients are used in Eqs. 2.5.1a and 2.5.1b is the stoichiometric relation that ties the reactants fed to the desirable product. This is illustrated in Example 2.11. 

When multiple chemical reactions take place simultaneously, species j may participate in several reactions, formed hy some and consumed hy others. The change in the molar content of species j in the reactor relates to its formation hy all chemical reactions. Using the definition of the reaction extent (Eq. 2.3.1), the molar content relates to the reaction extents hy... 

Equation 4.3.8 is the reaction-based, differential design equation of an ideal batch reactor, written for the mth-independent reaction. As will be discussed below, to describe the operation of a reactor with multiple chemical reactions, we have to write Eq. 4.3.8 for each of the independent reactions. Note that the reaction-based design equation is invariant of the specific species used in the derivation. For an ideal batch reactor with a single chemical reaction, Eq. 4.3.8 reduces to... 

As discussed in Chapter 4, in order to describe the operation of a reactor with multiple chemical reactions, we have to write the design equation (Eq. 6.1.1) for each independent chemical reaction. Also, to solve the design equations (to obtain relationships between Z s and t), we have to express V/ (t) and the rates of the chemical reactions, r s and r s, in terms of Z s, and t. The auxiliary relations needed to express the design equations explicitly in terms of Z s, and T, are derived next. 

Discussed the design of isothermal operations with multiple chemical reactions. 

A recycle reactor is a mathematical model describing a steady plug-flow reactor where a portion of the outlet is recycled to the Met, as shown schematically in Figure 9.5. Although this reactor configuration is rarely used in practice, the recycle reactor model enables us to examine the effect of mixing on the operations of continuous reactors. In some cases, the recycle reactor is one element of a complex reactor model. Below, we analyze the operation of a recycle reactor wifii multiple chemical reactions, derive its design equations, and discuss how to solve fiiem. 

Equation 9.4.5 is the dimensionless design equation of a recycle reactor, written for the mth-independent reaction. To describe the operation of a recycle reactor with multiple chemical reactions, we have to write Eq. 9.4.5 for each of the independent reactions. 

For most operations with single chemical reactions, the profit function is expressed in terms of relatively simple functions of these parameters, and Eq. 10.1.3 can be solved analytically. For operations with multiple chemical reactions, we have to determine the optimal parameters numerically. 

Runaway Reactions in a CSTR 540 Nonisothemnal Multiple Chemical Reactions 543... 

We now shift our discussion to chemical reactions in which bonds, primarily covalent bonds in reactant chemicals, are broken and new bonds are formed to generate reaction products. At any one time several hundred different kinds of chemical reactions are occurring simultaneously in every cell, and many chemicals can, in principle, undergo multiple chemical reactions. Both the extent to which reactions can proceed and the rate at which they take place determine the chemical composition of cells. 

---