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Rate equations parallel reactions

A silica-supported Sn—V—P—O catalyst (Sn/V/P = 1/9/3) was investigated by Onsan and Trimm [244]. Working with a flow reactor at about 520°C, a maximum selectivity of 75% to acrylonitrile was reached at a contact time of ca. 230 g sec l-1 and an oxygen/propene/ammonia ratio of 2/1/1.75. The authors assume that the six principal products (acrylonitrile, acetonitrile, HCN, CO, C02, N2) are formed by six parallel reactions and in the first instance apply power rate equations. A more detailed analysis reveals that a Langmuir—Hinshelwood type rate equation, surface reaction being rate-determining, properly describes the production of acrolein plus acrylonitrile from propene, viz. [Pg.173]

This tendency to react with a range of nucleophiles is reflected in the general rate equation for reactions of this type, as seen for the hydrolysis of [Co(en)2(H2NCH2C02 Pr)]3+. Typically, a three-term rate equation is obtained. This is indicative of a process in which at least three parallel reaction pathways are being followed. In the case of the hydrolysis of [Co(en)2(H2NCH2C02 Pr)]3+, the kx term refers to attack of the chelated ester by water, the k2 term to attack by hydroxide and the /% term to general base attack by any other nucleophile which is present in solution. The rate is defined in terms of the loss of the starting complex cation, rather than the formation of any specific product of the reaction. [Pg.54]

Consider the system of parallel reactions from Eq. (2.4) with the corresponding rate equations. " ... [Pg.26]

When potassium fluoride is combined with a variety of quaternary ammonium salts its reaction rate is accelerated and the overall yields of a vanety of halogen displacements are improved [57, p 112ff. Variables like catalyst type and moisture content of the alkali metal fluoride need to be optimized. In addition, the maximum yield is a function of two parallel reactions direct fluorination and catalyst decomposition due to its low thermal stability in the presence of fluoride ion [5,8, 59, 60] One example is trimethylsilyl fluoride, which can be prepared from the chloride by using either 18-crown-6 (Procedure 3, p 192) or Aliquot 336 in wet chlorobenzene, as illustrated in equation 35 [61],... [Pg.190]

Parallel reactions give rate equations having sums of rate terms. Each term provides the transition state composition for a reaction path. Eor example, some acid-catalyzed reactions have the rate equation... [Pg.219]

In a special circumstance the rate equation for parallel reactions may be misleading.If two parallel reactions are catalyzed by a common catalyst, and if a significant fraction of the catalyst is tied up in the form of intermediates, then the two reactions are not independent, and the rate equation will not give the transition state composition. King has analyzed this case in terms of enzyme-catalyzed reactions. [Pg.219]

In contrast to consecutive reactions, with parallel competitive reactions it is possible to measure not only the initial rate of isolated reactions, but also the initial rate of reactions in a coupled system. This makes it possible to obtain not only the form of the rate equations and the values of the adsorption coefficients, but also the values of the rate constants in two independent ways. For this reason, the study of mutual influencing of the reactions of this type is centered on the analysis of initial rate data of the single and coupled reactions, rather than on the confrontation of data on single reactions with intergal curves, as is usual with consecutive reactions. [Pg.35]

For most real systems, particularly those in solution, we must settle for less. The kinetic analysis will reveal the number of transition states. That is, from the rate equation one can count the number of elementary reactions participating in the reaction, discounting any very fast ones that may be needed for mass balance but not for the kinetic data. Each step in the reaction has its own transition state. The kinetic scheme will show whether these transition states occur in succession or in parallel and whether kinetically significant reaction intermediates arise at any stage. For a multistep process one sometimes refers to the transition state. Here the allusion is to the transition state for the rate-controlling step. [Pg.126]

This reaction cannot be elementary. We can hardly expect three nitric acid molecules to react at all three toluene sites (these are the ortho and para sites meta substitution is not favored) in a glorious, four-body collision. Thus, the fourth-order rate expression 01 = kab is implausible. Instead, the mechanism of the TNT reaction involves at least seven steps (two reactions leading to ortho- or /mra-nitrotoluene, three reactions leading to 2,4- or 2,6-dinitrotoluene, and two reactions leading to 2,4,6-trinitrotoluene). Each step would require only a two-body collision, could be elementary, and could be governed by a second-order rate equation. Chapter 2 shows how the component balance equations can be solved for multiple reactions so that an assumed mechanism can be tested experimentally. For the toluene nitration, even the set of seven series and parallel reactions may not constitute an adequate mechanism since an experimental study found the reaction to be 1.3 order in toluene and 1.2 order in nitric acid for an overall order of 2.5 rather than the expected value of 2. [Pg.9]

In general the rate equation for a heterogeneous reaction accounts for more than one process. The present consideration is directed to the general problem of combining the rates for processes of different kinds. Let r1( r2,..., rn be the rates of changes for the individual processes that are to be accounted for by an overall rate. If the changes occur by parallel paths, then the overall rate will be greater than the rate for any individual path. In fact, if the different parallel paths are independent of each other, the overall rate will be simply the sum of all the individual rates, or... [Pg.307]

Crosslinking of many polymers occurs through a complex combination of consecutive and parallel reactions. For those cases in which the chemistry is well understood it is possible to define the general reaction scheme and thus derive the appropriate differential equations describing the cure kinetics. Analytical solutions have been found for some of these systems of differential equations permitting accurate experimental determination of the individual rate constants. [Pg.241]

There are few short-cut methods for analyzing simple parallel systems. One useful technique, however, is to use stoichiometric ratios of reactants so that the ratio of the time derivatives of the extents of reaction simplifies where possible. For higher-order irreversible simple parallel reactions represented by equations 5.2.41 and 5.2.42, the degenerate form of the ratio of reaction rates becomes... [Pg.146]

We illustrate the development of the model equations for a network of two parallel reactions, A -> B, and A - C, with kt and representing the rate constants for the first and second reactions, respectively. Continuity equations must be written for two of the three species. Furthermore, exchange coefficients (Kbc and Kce) must be determined for each species chosen (here, A and B). [Pg.590]

From Figure 4.54 it can he seen that the family of reciprocal plots obtained at different fixed concentrations of NADP are essentially parallel to one another. This is also indicated in Figure 4.55, where the value of the slopes of the tines seem to be approximately constant. These results imply that the velocity equation for the ping-pong mechanism [146] can be used to describe the rate of the reaction catalyzed by G6PDH. Although initial velocity studies alone cannot define the exact kinetic mechanism [146,147], we are more interested in the appropriate rate equation that describes the reaction progress. [Pg.100]

The term has also been applied to Hammett equations (See Selectivity Factor) and for other substituted reactants undergoing parallel reactions at different sites with the same rate law. [Pg.539]

Generalized Rate Equations. This last reaction is typical of a large class of reactions which may proceed simultaneously by several parallel paths. The rate can be expressed as the sum of several contributions from the uncatalyzed and catalyzed paths. The overall rate for the hydrolysis of an amino acid ester in the presence of a metal salt may be expressed as... [Pg.154]

The use of tracers in this manner has also been considered by Le Cardinal et al (56), with special reference to homogeneous systems, and discussed by Happel (57) and Le Cardinal (55). Such an approach parallels the viewpoint of Aris and Mah (42) in which they distinguished between the kinematics and kinetics of overall reactions. Rates of change of species are considered without reference to their correlation in terms of rate equations related to particular physical conditions. [Pg.320]

The ammoxidation of isobutene has not received much attention. The only contribution in this field is by Onsan and Trimm [2.44] for a rather unusual catalyst, a mixture of the oxides of Sn, V and P (ratio 1/9/3) supported on silica. At 520 C, a maximum selectivity to methacrylonitrile + methacrolein of 80% was reached with a Sn—V—P oxide catalyst (ratio 1/9/3), an isobutene/ammonia/oxygen ratio of 1/1.2/2.5 and a contact time of 120 g sec l ]. The kinetics are very similar to those for the pro-pene ammoxidation. Again, the data are initially analysed by means of (parallel) power rate equations, for which the parameters were calculated, while a more detailed analysis proves that a Langmuir—Hinshelwood model with surface reaction as the rate-controlling step provides the best fit with regard to the two main products. At 520° C, the equation which applies for the production of methacrolein plus methacrylonitrile is... [Pg.179]

Rusyanova [25] describe the oxidation of phenanthrene to various products (using the V2Os catalyst above) by power rate equations according to a parallel reaction scheme... [Pg.220]

The kinetics of the ammoxidation of xylenes over a vanadium catalyst and mixed vanadium catalysts were studied. The reaction rate data obtained were correlated with the parallel consecutive reaction scheme by the rate equations based upon the Langmuir-Hinshelwood mechanism where the adsorption of xylenes was strong. The reaction rates of each path are remarkably affected by the kind of xylene and catalyst. The results of the physical measurement of catalysts indicated that the activity and the selectivity of reaction were affected by the nature and the distribution of metal ions and oxygen ion on catalyst surface. [Pg.289]

The parametric approach, which is not strictly needed for a single Gray-Scott reaction, works very well for an arbitrary number of parallel reactions and for continuous mixtures. Figure 16 shows a case of two parallel reactions for which an isola and a mushroom coexist. Because the notions of continuous mixtures and reactions will be treated in Chapter 8, G H and in the group of papers listed in the Index of Subjects in Publications under the heading Continuous mixtures, we can be very brief and start with the nondimensional equations. Let x be the index of the mixture whose species are /4(x). The steady-state concentration of the material with index in (x, x + dx) is V(x)dx, the feed concentration a(x)dx and the conversion U(x) = 1 - V/(x)/a(x), the last being defined only for values of x for which a(x) is not zero. B, the autocatalytic agent, forms itself as an undifferentiated product whose concentration is W. The rate of the first reaction, and hence p,(x), depends on the... [Pg.57]

If a second reactant B is involved in a system of parallel reactions, then the same principles apply to B as to A. The rate equations are examined to see whether the order of the desired reaction with respect to B is higher or lower than that of the undesired reaction, and to decide whether high or low concentrations of B favour a high yield of desired product. [Pg.61]

The kinetic study assists in the development of a credible reaction mechanism which describes all aspects of the reaction - not just the kinetics [ 1 ]. The complete exercise involves empirical and theoretical considerations which run in parallel they are complementary and feedback between them is essential [2]. Aspects (i) and (ii) above were covered in the previous chapter, and we now focus first on the derivation of the rate law (rate equation) from a mechanistic proposal (the mechanistic rate law) for comparison with the experimental finding. In simple cases, the derivation is usually straightforward but can be mathematically challenging for complex reaction mechanisms. Once derived, the mechanistic rate law is compared with the experimental, and the quality of the agreement is one test of the applicability of the mechanism. Different mechanisms may lead to the same rate law (they are kinetically equivalent), and, whilst agreement between mechanistic and experimental rate laws is required, this alone is not a sufficient proof of the validity of the mechanism [3-7]. We conclude the chapter by working through several case histories. [Pg.79]

The latter strongly depends on the specific reaction mechanism, the stoichiometry, and the presence or absence of parallel reaction schemes (69). The rate expressions for Rt usually represent nonlinear dependences on the mixture composition and temperature. Specifically for the coupled reaction-mass transfer problems, such as Eqs. (A10), it is always essential as to whether or not the reaction rate is comparable to that of diffusion (68,77). Equations (A10) should be completed by the boundary conditions relevant to the film model. These conditions specify the values of the mixture composition at both film boundaries. For example, for the liquid phase ... [Pg.377]

Parallel reactions are very common in chemistry. They play a key role in catalysis, because the catalyst effectively creates a parallel alternative to the noncatalyzed reaction. In many cases a catalytic reaction will yield several products, because one of the catalytic intermediates can react via two different pathways. The general scheme for two parallel reactions is shown in Eq. (2.46), and the corresponding differential rate equations for B and C are Eq. (2.47). [Pg.57]

Most reactors used in industrial operations run isother-mally. For adiabatic operation, principles of thermodynamics are combined with reactor design equations to predict conversion with changing temperature. Rates of reaction normally increase with temperature, but chemical equilibrium must be checked to determine ultimate levels of conversion. The search for an optimum isothermal temperature is common for series or parallel reactions, since the rate constants change differently for each reaction. Special operating conditions must be considered for any highly endothermic or exothermic reaction. [Pg.475]

Similar rate equations can be developed for the parallel leaching of other minerals (see Eq. 3). The oxidation of intermediate sulfur compounds to sulfates such as Eq. 2 is a consecutive reaction to mineral leaching. Other reactions are virtually instantaneous, e.g., precipitation of insoluble ferric arsenates from soluble NH4H2ASO4 which is consecutive to Eq. 3. On the other hand, the instantaneous shift in the amonia -ammonium equilibrium,... [Pg.331]


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