Reaction rates multiple

Commercially, stabilization is accomplished by controlled heating in air at temperatures of 200—300°C. A variety of equipment has been proposed for continuous stabilization. One basic approach is to pass a fiber tow through heated chambers for sufficient time to oxidize the fiber. Both Mitsubishi and Toho patents (23,24) describe similar continuous processes wherein the fiber can pass through multiple ovens to increase temperature and reaction rate as the thermal stabiUty of the fiber is increased. Alternatively, patents have described processes where the fiber passes over hot roUs (25) and through fluidized beds (26) to provide more effective heat transfer and control of fiber bundle temperature. 

In Fig. 28, the abscissa kt is the product of the reaction rate constant and the reactor residence time, which is proportional to the reciprocal of the space velocity. The parameter k co is the product of the CO inhibition parameter and inlet concentration. Since k is approximately 5 at 600°F these three curves represent c = 1, 2, and 4%. The conversion for a first-order kinetics is independent of the inlet concentration, but the conversion for the kinetics of Eq. (48) is highly dependent on inlet concentration. As the space velocity increases, kt decreases in a reciprocal manner and the conversion for a first-order reaction gradually declines. For the kinetics of Eq. (48), the conversion is 100% at low space velocities, and does not vary as the space velocity is increased until a threshold is reached with precipitous conversion decline. The conversion for the same kinetics in a stirred tank reactor is shown in Fig. 29. For the kinetics of Eq. (48), multiple solutions may be encountered when the inlet concentration is sufficiently high. Given two reactors of the same volume, and given the same kinetics and inlet concentrations, the conversions are compared in Fig. 30. The piston flow reactor has an advantage over the stirred tank... 

The extension to multiple reactions is done by writing Equation (3.1) (or the more complicated versions of Equation (3.1) that will soon be developed) for each of the N components. The component reaction rates are found from Equation (2.7) in exactly the same ways as in a batch reactor. The result is an initial value problem consisting of N simultaneous, first-order ODEs that can be solved using your favorite ODE solver. The same kind of problem was solved in Chapter 2, but the independent variable is now z rather than t. 

The number of active sites is a multiplicative factor in the rate of the main reaction. See for example Equations (10.11) and (10.16). Thus, the decline in reaction rate can be modeled using a time-dependent effectiveness. A reasonable functional form for the time-dependent effectiveness factor is... 

Bis(imino)pyridine iron complex 5 acts as a catalyst not only for hydrogenation (see 2.1) but also for hydrosilylation of multiple bonds [27]. The results are summarized in Table 10. The reaction rate for hydrosilylations is slower than that for the corresponding hydrogenation however, the trend of reaction rates is similar in each reaction. In case of tra s-2-hexene, the terminal addition product hexyl (phenyl)silane was obtained predominantly. This result clearly shows that an isomerization reaction takes place and the subsequent hydrosilylation reaction dehvers the corresponding product. Reaction of 1-hexene with H2SiPh2 also produced the hydrosilylated product in this system (eq. 1 in Scheme 18). However, the reaction rate for H2SiPh2 was slower than that for H3SiPh. In addition, reaction of diphenylacetylene as an atkyne with phenylsilane afforded the monoaddition product due to steric repulsion (eq. 2 in Scheme 18). 

The stereoselective allylation of carbon-nitrogen multiple bonds have also been studied. The addition of allylzinc bromide to aromatic imines derived from (. S j-valine esters was affected by reversibility, which caused the lowering of the diastereoisomeric ratio with increasing reaction time. The retroallylation reaction could be avoided by performing the reaction in the presence of trace amounts of water or by using CeC - 7H2O as the catalyst with a decreased reaction rate.71... 

If the forward and reverse reactions are nonelementary, perhaps involving the formation of chemical intermediates in multiple steps, then the form of the reaction rate equations can be more complex than Equations 5.33 to 5.36. 

As a vessel of a given shape increases in size, both the surface area and the volume increase, but they do not increase at the same rate. For a sphere the surface area is a function of the diameter squared and the volume is a function of the diameter cubed. This is also true for a cylinder whose height is a multiple of its diameter. The polymerization of styrene is an exothermic reaction. The amount of energy released at any time is dependent on the volume of the reactor, and the rate of removal of that heat is dependent on the surface area. Unless the heat is removed, the temperature will rise and the reaction rate will increase. The result will be an uncontrolled reaction that not only may ruin the batch but could also damage the reactor and might cause a tire or explosion to occur. 

Equation 8.3.4 may also be used in the analysis of kinetic data taken in laboratory scale stirred tank reactors. One may directly determine the reaction rate from a knowledge of the reactor volume, flow rate through the reactor, and stream compositions. The fact that one may determine the rate directly and without integration makes stirred tank reactors particularly attractive for use in studies of reactions with complex rate expressions (e.g., enzymatic or heterogeneous catalytic reactions) or of systems in which multiple reactions take place. 

It is readily apparent that equation 8.3.21 reduces to the basic design equation (equation 8.3.7) when steady-state conditions prevail. Under the presumptions that CA in undergoes a step change at time zero and that the system is isothermal, equation 8.3.21 has been solved for various reaction rate expressions. In the case of first-order reactions, solutions are available for both multiple identical CSTR s in series and individual CSTR s (12). In the case of a first-order irreversible reaction in a single CSTR, equation 8.3.21 becomes... 

For reactor design purposes, the distinction between a single reaction and multiple reactions is made in terms of the number of extents of reaction necessary to describe the kinetic behavior of the system, the former requiring only one reaction progress variable. Because the presence of multiple reactions makes it impossible to characterize the product distribution in terms of a unique fraction conversion, we will find it most convenient to work in terms of species concentrations. Division of one rate expression by another will permit us to eliminate the time variable, thus obtaining expressions that are convenient for examining the effect of changes in process variables on the product distribution. 

The divinyl monomers can thus be found in macromolecules as units which bear pendant vinyl groups or which are involved in cycles, crosslinks or multiple crosslinks. Since the number of crosslinks necessary for the onset of macrogelation is very low [64], pendant vinyl groups in RCC are mainly consumed in cycles and multiple crosslinks. Therefore, the reaction rate of pendant vinyl groups is a very sensitive indicator for the formation of cycles and multiple crosslinks in finite species [100,147,157-160]. 

Enhancement of a rate by temperature can counteract the effect of falling concentration. Exothermic reaction rates in pores, as a consequence, can be much greater than at the surface condition. Another peculiarity that can arise with adiabatic reactions is multiple steady states. 

Thus, these studies again stress the multiple possibilities which arise from the use of FTIR spectroscopy and the analysis of reaction rates. 

In Eq. (149) we assume that allosteric regulation affects the reaction rates as a multiplicative factor h(I). Following Ref. [161], a generic functional form for an inhibitory effector is... 

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