Reversible series reactions

Equations 5-81, 5-82 and 5-83 are first order differential equations that ean be solved simultaneously using the Runge-Kutta fourth order method. Consider two eases  

The developed bateh program BATCH53 simulates the eoneentra-tions of A, B, and C witli time step At = 0.05 hr for 1 hour. Eigures 5-9 and 5-10 show plots of the eoneentrations versus time for both eases. 

Introduction to Reactor Design Fundamentals for Ideal Systems 289 

Equations 5-88, 5-89, and 5-90 are first order differential equations and the Runge-Kutta fourth order method with the boundary eonditions is used to determine the eoneentrations versus time of the eomponents. 

An industrial example of a eonseeutive reversible reaetion is the eatalytie isomerization reaetions of n-hexane to 2-methyl pentane and 3-methyl pentane and is represented as  

Consider an irreversible chemical reactions scheme of the form 

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Figure 8.9 shows that the concentration of intermediate in reversible series reactions need not pass through a maximum, while Fig. 8.10 shows that a product may pass through a maximum concentration typical of an intermediate in the irreversible series reaction however, the reactions may be of a different kind. A comparison of these figures shows that many of the curves are similar in shape, making it difficult to select a mechanism of reaction by experiment, especially if the kinetic data are somewhat scattered. Probably the best clue to distinguishing between parallel and series reactions is to examine initial rate data—data obtained for very small conversion of reactant. For series reactions the time-concentration curve for S has a zero initial slope, whereas for parallel reactions this is not so. 

An example of where recycling can be effective in improving selectivity is in the production of benzene from toluene. The series reaction is reversible. Hence recycling diphenyl to the reactor can be used to suppress its formation at the source. 

The standard manufacturing method for tetraalkyl titanates, such as TYZOR TPT, or tetra- -butyi titanate, TYZOR TBT [5593-70 ] involves the addition of TiCl to an alcohol. In a series of reversible displacement reactions, the alkoxy substitution products and hydrochloric acid form as follows ... 

Consecutive reactions are those in which the product of one reaction is the reactant in the next reaction. These are also called series reactions. Reversible (opposing) reactions, autocatalytic reactions, and chain reactions can be viewed as special types of consecutive reactions. 

The chemical composition of many systems can be expressed in terms of a single reaction progress variable. However, a chemical engineer must often consider systems that cannot be adequately described in terms of a single extent of reaction. This chapter is concerned with the development of the mathematical relationships that govern the behavior of such systems. It treats reversible reactions, parallel reactions, and series reactions, first in terms of the mathematical relations that govern the behavior of such systems and then in terms of the techniques that may be used to relate the kinetic parameters of the system to the phenomena observed in the laboratory. 

This section discusses the kinetic implications of series reactions. We will be concerned only with those cases where the progress of the various stages of the overall transformation is not influenced by either parallel or reverse reactions. The discussion will again be limited to constant volume systems. 

The following example illustrates a combination of semibatch and semicontinuous operation for an irreversible reaction, with one reactant added intermittently and the other flowing (bubbling) continuously, that is, a combination of Figures 12.3(a) and 12.4(a). Chen (1983, pp. 168-211, 456-460) gives several examples of other situations, including reversible, series-reversible, and series-parallel reactions, and nonisothermal and autothermal operation. 

In this chapter, we develop some guidelines regarding choice of reactor and operating conditions for reaction networks of the types introduced in Chapter 5. These involve features of reversible, parallel, and series reactions. We first consider these features separately in turn, and then in some combinations. The necessary aspects of reaction kinetics for these systems are developed in Chapter 5, together with stoichiometric analysis and variables, such as yield and fractional yield or selectivity, describing product distribution. We continue to consider only ideal reactor models and homogeneous or pseudohomogeneous systems. 

These are almost identical to the irreversible series reactions solved previously except that now the first reaction is assumed to be reversible. The mass-balance equations for A, B,... 

We can next solve the series reactions where both reactions are reversible... 

Anderson and his coworker carried out a series quantum chemistry studies of oxygen reduction reactions.52-57 Anderson and Abu first studied reversible potential and activation energies for uncatalyzed oxygen reduction to water and the reverse oxidation reaction using the MP2/6-31G method. The electrode was modeled by a non-interacting electron donor molecule with a chosen ionization potential (IP). The primary assumption is that when the reactant reaches a point on the reaction path where its electron affinity (EA) matched the donor IP, an electron transfer is initialized. The donor s IP or reactant s EA was related to the electrode potential by,... 

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