Parallel reaction. See

Special cases such as that arising from a nuclide decaying by more than one process simultaneously are treated exactly as the case for parallel reactions (see Chapter 2). In nuclear chemistry, this situation is referred to as branching because the overall process is taking different courses. After any given time, the ratio of the product nuclides is the same as the ratio of the decay constant producing them (see Section 2.3). However, there are some situations that arise when describing the kinetics of radioactivity that deserve special mention. 

In fact, it is often possible with stirred-tank reactors to come close to the idealized well-stirred model in practice, providing the fluid phase is not too viscous. Such reactors should be avoided for some types of parallel reaction systems (see Fig. 2.2) and for all systems in which byproduct formation is via series reactions. 

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). 

Calculate activation energies for the three Diels-Alder reactions (energy of transition state - sum of energies of reactants). Which reaction has the smallest energy barrier Which has the largest energy barrier Do your results parallel the measured relative rates of the same reactions (see table at left) ... 

A corollary of this pattern for parallel reactions is that the one with the larger activation enthalpy grows relatively more important at higher temperatures. Also, the reaction that is slower below the isokinetic temperature is the faster one above it. One can also show that the logarithm of product yield, ln([P]]/tP2]), is a linear function of l/T (see Problem 7-13). 

Parallel reactions, 58-64, 129 Partitioning ratios, 79 Perturbation (see Chemical relaxation) pH profiles, 139-145 bell-shaped, 141-142 Phosphorous acid, oxidation of, 186-187 Physical methods for kinetics, 22-25 end point reading unknown, 25-28 sample calculation for, first-order,... 

Maleic anhydride is an important industrial fine chemical (see original citations in [43]). The oxidation of C4-hydrocarbons in air is a highly exothermic process, therefore carried out at low hydrocarbon concentration (about 1.5%) and high conversion. The selectivity of 1-butene to maleic anhydride so far is low. The reaction is composed of a series of elementary reactions via intermediates such as furan and can proceed to carbon dioxide with even larger heat release. As a consequence, hot spots form in conventional fixed-bed reactors, decrease selectivity and favor other parallel reactions. 

Oxides of Platinum Metals Anodes of platinum (and more rarely of other platinum metals) are used in the laboratory for studies of oxygen and chlorine evolution and in industry for the synthesis of peroxo compounds (such as persulfuric acid, H2S2O8) and organic additive dimerization products (such as sebacic acid see Section 15.6). The selectivity of the catalyst is important for all these reactions. It governs the fraction of the current consumed for chlorine evolution relative to that consumed in oxygen evolution as a possible parallel reaction it also governs the current yields and chemical yields in synthetic electrochemical reactions. 

The E-model was also applied to a system of parallel reactions (Baldyga and Bourne, 1990a). It was found that selectivity depends on compositions of both the initial reactor content and the stream added for chemically equivalent mixtures of three reactants (see reaction system given by Eqns. (5.4-143) and (5.4-144)). For an instantaneous reaction, the yield of 5 varies from 0 to 100 % depending on the mode of composing the feeding stream. 

Parallel reactions, i.sothermal reactor, oiai om2, aei aB2, see Table 5.4-43. 

Parallel reactions, omi = oa2, aai = am = 0, E < E2. The selectivity of the desired product decreases with temperature. However, a low temperature disfavours the reaction rate. A nonuniform temperature-time profile should be applied to maximize the reactor productivity (see Fig. 5.4-70). Initially the temperature should be low to avoid the formation of too much unwanted product. The temperature is gradually raised with time to increase the reaction rate until the maximum allowable temperature is reached. At T u the reaction is completed. 

If a chemical reaction regenerates the initial substance completely or partially from the products of the electrode reaction, such case is termed a chemical reaction parallel to the electrode reaction (see Eq. 5.6.1, case c). An example of this process is the catalytic reduction of hydroxylamine in the presence of the oxalate complex of TiIV, found by A. Blazek and J. Koryta. At the electrode, the complex of tetravalent titanium is reduced to the complex of trivalent titanium, which is oxidized by the hydroxylamine during diffusion from the electrode, regenerating tetravalent titanium, which is again reduced. The electrode process obeys the equations... 

As with parallel reactions, series reactions might not only lead to a loss of materials and useful products, but might also lead to byproducts being deposited on, or poisoning catalysts (see Chapters 6 and 7). 

As we have pointed out in Section 1.1 the mass signal response for a given reaction is proportional to the respective current (see Eq. 1.1). The result in Fig. 4.1 shows that at 0.58 V an increase in current by a factor of 7.5 is obtained. At the same time, the mass signal for C02 increases by a factor of 13 and that for HCOOCH3 by a factor of 3. This result indicates that tin affects the current efficiency for both parallel reaction pathways to a different extent. 

From a comparison of the qualitative results of modes 2 and 3, we see that the concentration level of B does not have a major influence on the product distribution and the reaction sequences involved. (It will, however, influence the overall conversion rate.) This behavior is characteristic of parallel reactions of the same order with respect to a particular species. From the viewpoint of species , reactions 9.3.3 and 9.3.4 may be regarded as... 

Most of the parallel reactions described in Schemes 4.23 and 4.24 were performed as dry-media reactions, in the absence of any solvent. In many cases, the starting materials and/or reagents were supported on an inorganic solid support, such as silica gel, alumina, or clay, that absorbs microwave energy or acts as a catalyst for the reaction (see also Section 4.1). In this context, an interesting method for the optimization of silica-supported reactions has been described [83], The reagents were co-spotted neat or in solution onto a thin-layer chromatographic (TLC) plate. 

Since the rate of chain oxidation of hydrocarbon is v v,1/2 and does not depend on [02] (see Chapter 2), the catalyst initiates the chains via two parallel reactions by the reaction with ROOH and by the reaction with dioxygen. The following mechanism was proposed ... 

The reactions of intramolecular isomerization occur and are important in the oxidation of natural and synthetic rubbers. The peroxyl radical addition to the double bond occurs very rapidly. For example, the peroxyl radical adds to the double bond of 2-methylpropene by 25 times more rapidly than abstraction of hydrogen atom from this hydrocarbon (see Chapter 4). Therefore, the oxidation of polymers having double bonds proceeds as a chain process with parallel reactions of P02 with double and C—H bonds including the intramolecular isomerization of the type [12] ... 

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