Parallel reactions general order

In general an analysis of a system in which noncompetitive parallel reactions are taking place is considerably more difficult than analyses of the type discussed in Chapter 3. In dealing with parallel reactions one must deal with the problems of determining reaction orders and rate constants for each of the individual reactions. The chemical engineer must be careful both in planning the experiment and in analyzing the data so as to obtain values of the kinetic con-... 

This illustration has provided us with a concrete example that indicates in quantitative form the validity of the general rule of thumb that we have stated for analyzing parallel reactions. High concentrations favor the higher-order reaction, and low concentrations favor the lower-order reaction. 

The experimentally observed pseudo-first order rate constant k is increased in the presence of DNA (18,19). This enhanced reactivity is a result of the formation of physical BaPDE-DNA complexes the dependence of k on DNA concentration coincides with the binding isotherm for the formation of site I physical intercalative complexes (20). Typically, over 90% of the BaPDE molecules are converted to tetraols, while only a minor fraction bind covalently to the DNA bases (18,21-23). The dependence of k on temperature (21,24), pH (21,23-25), salt concentration (16,20,21,25), and concentration of different buffers (23) has been investigated. In 5 mM sodium cacodylate buffer solutions the formation of tetraols and covalent adducts appear to be parallel pseudo-first order reactions characterized by the same rate constant k, but different ratios of products (21,24). Similar results are obtained with other buffers (23). The formation of carbonium ions by specific and general acid catalysis has been assumed to be the rate-determining step for both tetraol and covalent adduct formation (21,24). 

Various ways to modify ZSM-5 catalyst in order to induce para-selectivity have been described. They include an increase in crystal size (15,17,20) and treatment of the zeolite with a variety of modifying agents such as compounds of phosphorus (15,18), magnesium (15), boron (16), silicon (21), antimony (20), and with coke (14,18). Possible explanations of how these modifications may account for the observed selectivity changes have been presented (17) and a mathematical theory has been developed (22). A general description of the effect of diffusion on selectivity in simple parallel reactions has been given by Weisz (23). 

Thus, a mixed flow reactor operating at conditions of highest (p with separation and recycle of unused reactant gives the best product distribution. This result is quite general for a set of parallel reactions of different order. 

When reactions in series are considered, it is not possible to draw any very satisfactory conclusions without working out the product distribution completely for each of the basic reactor types. The general case in which the reactions are of arbitrary order is more complex than for parallel reactions. Only the case of two first-order reactions will therefore be considered ... 

However, in contrast to the Type 1 selectivity problem treated in the previous section, the effectiveness factors >11 and tj2 here cannot be determined separately, since the two parallel reactions share a common reactant, and do not obey the same kinetic order. Hence, t/, and rf2 are not independent of each other. Therefore, instead of eq 40, we may define a more general effectiveness factor which is related to the rate of disappearance of reactant Ai ... 

This scheme represents two independent parallel reactions of the enantiomers. A general treatment for thermal kinetic resolution was given by Kagan and Fiaud [42]. For unimolecular photoreactions first-order equations seem to be appropriate [40]. Accordingly the rates are... 

Most of the generated reactions were eliminated during the construction of the mechanism. The primary tool was the comparison of reaction rates for parallel reaction channels. This approach required careful planning of the order of generation of the reaction types. The program was used for the pyrolysis of C1-C4 hydrocarbons. Mechanisms for ethane, propane and butane contained 15, 49 and 76 species and 18, 115 and 179 reactions, respectively. These mechanisms were compared with schemes which had been proposed by human experts. Most of the reactions were identical, and, in general, the program proposed a superset of those presented in the literature. 

Mixing in general decreases the reactant conversion but it may improve selectivity. Thus, the yield of a low-order path in a parallel reaction scheme would improve in a MER, as indicated earlier. The uniform concentration and rate in a MER and the simple algebraic form of the continuity equations (107) make this reactor ideal for kinetic analysis of simple and complex electrocatalytic reactions. 

Secondary amines used for reactions with cyclic ketones may be aziridine (52X azetidine (53), pyrrolidine (54), piperidine (55), hexamethylenimine (56), morpholine (57), //-methylpiperazinc (58) and acyclic amines like dimethyla-mine (59). The general order of electrophilic attack of enamines as dependent on the nature of the amine moiety decreases in the sequence pyrrolidine (54) > dimethylamine (59) > hexamethylenimine (56) > piperidine (55) sk azetidine (53) > morpholine (57). This sequence seems to parallel the magnitude of conjugative interaction between the amino group and the C=C double bond as indicated by the H NMR chemical shift of the hydrogen at the jS-carbon. 

Wheeler classified multiple reaction networks into three types in order to discuss the effect of diffusion on selectivity. In the present work, we use this classification to discuss selectivity effects with deactivation in general. Type I selectivity refers to two independent parallel reactions ... 

Next, we shall consider the series-parallel reaction system. Here, we shall examine the case where the reactions are all first order. This keeps the math simple and allows us observe the general behavior of such a group of reactions. If the order of the rates of reaction becomes... 

Parallel reactions (nonreacting products) The general case Effect of reaction order One of the reactants undergoes a second reaction Parallel-consecutive reactions Plug-flow reactor with recycle The basic design equation Optimal design of RPR Use of RPR to resolve a selectivity dilemma Semibatch reactors... 

The overall or global selectivity over the time span 0-f during which the reacting species were in contact is obtained after integration. It is generally different from the instantaneous value, but in the particular case of parallel reactions with the same order the two are identical ... 

This review has concentrated on the information which has been obtained from very careful studies of the kinetics of stratospheric reactions. These studies have almost always involved spectroscopic measurements of the rates of disappearance of an atom or free radical under pseudo-first-order conditions, i.e. in the presence of excess of the other reagent. Product analyses have rarely been carried out because of the small amounts of product formed fixim the low concentrations of transient species employed. An important but rather neglected area of selectivity in atmospheric reactions is the possible occurrence of parallel reaction paths leading to different products. In some cases the alternative reaction path could have a significant effect on predicted ozone depletions. For instance, it is generally assumed that the reaction CIO + HO2 yields exclusively HOQ + O2 rather than the energetically feasible HQ + O3. Similarly the photolysis of HOCl is believed to yield exclusively HO + Cl rather than HQ + O. If HQ were formed in either of these processes its relatively high stability in the stratosphere would reduce the proportion of chlorine present as Q and QO and hence decrease the predicted ozone depletions. 

It is more convenient to transform these steady state data into a plot which is independent of residence times and feed composition. Levenspiel (10) gave a general time-independent, plot for second-order series-parallel reactions. However, it can be shown that such a plot is also valid for Langmuir-Hinshelwood kinetics, if the denominators are the same for both reactions. 

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