Instantaneous complexation reactions

Whereas in the MMA photoinitiated polymerization by quinoline-bromine CT complex the formation of radicals is preceded by an instantaneous complexation reaction between the CT complex initiator and the monomer [68], no evidence of this occurrence is observed in the case of the poly(NVC)-Br2 CT complex, probably due to the steric hindrance provided by the polymeric chain. The behaviour of the above system should however be compared with that of the corresponding low-molecular-weight A-alkyl carbazole-Bra CT complex in order to clarify this point. 

Rates of Reaction. The rates of formation and dissociation of displacement reactions are important in the practical appHcations of chelation. Complexation of many metal ions, particulady the divalent ones, is almost instantaneous, but reaction rates of many higher valence ions are slow enough to measure by ordinary kinetic techniques. Rates with some ions, notably Cr(III) and Co (III), maybe very slow. Systems that equiUbrate rapidly are termed kinetically labile, and those that are slow are called kinetically inert. Inertness may give the appearance of stabiUty, but a complex that is apparentiy stable because of kinetic inertness maybe unstable in the thermodynamic equihbrium sense. 

Chapter 2 treated multiple and complex reactions in an ideal batch reactor. The reactor was ideal in the sense that mixing was assumed to be instantaneous and complete throughout the vessel. Real batch reactors will approximate ideal behavior when the characteristic time for mixing is short compared with the reaction half-life. Industrial batch reactors have inlet and outlet ports and an agitation system. The same hardware can be converted to continuous operation. To do this, just feed and discharge continuously. If the reactor is well mixed in the batch mode, it is likely to remain so in the continuous mode, as least for the same reaction. The assumption of instantaneous and perfect mixing remains a reasonable approximation, but the batch reactor has become a continuous-flow stirred tank. 

Finally, to conclude our discussion on coupling with chemistry, we should note that in principle fairly complex reaction schemes can be used to define the reaction source terms. However, as in single-phase flows, adding many fast chemical reactions can lead to slow convergence in CFD simulations, and the user is advised to attempt to eliminate instantaneous reaction steps whenever possible. The question of determining the rate constants (and their dependence on temperature) is also an important consideration. Ideally, this should be done under laboratory conditions for which the mass/heat-transfer rates are all faster than those likely to occur in the production-scale reactor. Note that it is not necessary to completely eliminate mass/heat-transfer limitations to determine usable rate parameters. Indeed, as long as the rate parameters found in the lab are reliable under well-mixed (vs. perfect-mixed) conditions, the actual mass/ heat-transfer rates in the reactor will be lower, leading to accurate predictions of chemical species under mass/heat-transfer-limited conditions. 

Nauk (UkrainRSR) 1966(7), 871-74 CA 65, 19919 (1966) "Criterion of Uni-dimensional Instability of Gas Detonations (The criterion was derived by using Zel dovich-Von Neumann model, which represents a detonation wave in an ideal gas as a stationary complex consisting of a shock wave and the front of an instantaneously occurring reaction with a characteristic induction time that follows the shock wave at a definite distance. The results showed that the criterion assumes the form dependent... 

Coke oven gas consists mainly of a mixture of carbon monoxide, hydrogen, methane, and carbon dioxide. It is contaminated with a variety of organic and inorganic compounds that have to be separated in absorption columns before its further use as a synthesis gas. The selective absorption of coke plant gas contamination results from a complex system of parallel liquid-phase reactions. Instantaneous reversible reactions ... 

This shows that both the instantaneous and the overall selectivity of B relative to C are the same, and depends only on k, and k2. The two selectivities differ for most complex reactions. 

One method of overcoming this problem is to increase the space time during the experiment by adapting the feed rate, so as to keep the conversion at a constant level. This, however, necessitates an instantaneous effluent analysis, coupled with a control circuit adjusting the inlet flow rates. For the study of the deactivation of a complex reaction mechanism subject to rapid deactivation, such as catalytic cracking on a Y-zcolite catalyst, this would be a... 

In a deterministic approach, the instantaneous MWDs are calculated first, and then the accumulated MWD is obtained by integrating the instantaneous MWDs. However, in MC simulations, we can follow the reaction history of each polymer particle directly, and the full MWD is obtained by simulating a large number of polymer particles [263]. Therefore, highly complex reaction kinetics can be simulated directly in a straightforward manner. 

Sloot et al. [1990] presented a simplified isothermal CNMR/ORG model which assumes that the two chambers divided by the membrane are well mixed. In practical applications, the model needs to be incorporated into a more complex model which, for example, considers the effect of flow configuration (cocurrent or countercurrent mode). In their model, mass transfer in the direction perpendicular to a flat membrane (i.e., y-direction) is considered for a general instantaneous, reversible reaction... 

Chlorex is added to the overhead stream, and since the complexing reaction is practically instantaneous, the resulting mixture can be fed without delay into another evaporator. The overheads stream from this separation is essentially Ce to Cio olefins. Since the bottoms stream has previously been freed of nickel catalyst, it can be successfully distilled as long as reasonable temperature limits are met. The distillation overheads are composed of C12 olefin, the Cj4 olefin-TEA-Chlorex ternary azeotrope, and some of the TEA-Chlorex complex. This stream is sent to the buildup reactor. The still bottoms contain most of the TEA, freed of C12 and Ci4 olefins, and they can therefore be used to alkylate the Ce to Cio stream. An excess of the Ce to Cio cut is maintained as recycle to aid in alkylation. The alkylated stream is fed into the buildup reactor at about the halfway point. Actually, it would probably be best to alkylate the Cq to Cg olefins separately from the decene. This would allow splitting the recycle streams... 

Relate the instantaneous rate of a complex reaction to its reaction mechanism. 

Rate-determining step You have probably heard the expression, A chain is no stronger than its weakest link. Chemical reactions, too, have a weakest link in that a complex reaction can proceed no faster than the slowest of its elementary steps. In other words, the slowest elementary step in a reaction mechanism limits the instantaneous rate of the overall reaction. 

For a complex reaction, the rate-determining step limits the instantaneous rate of the overall reaction. 

In a complex reaction scheme, where only some of the steps are diffusion controlled, the course of the reaction can be changed by controlling the diffusion coefficients. The archetypal example here is polymerization. The effect of diffusion control on overall rate and the rates of the different steps is first discussed. A simplified equation, sufficient for a qualitative discussion, for the instantaneous rate of polymer formation is... 

The parameter

rate constant k becomes infinite (instantaneous chemical reaction). The dif-fusivity ratio Dg/Dji and the concentration ratio influence in a complex... 

For intermediate reaction rates the use of the enhancement factor is not consistent with the standard approach of diffusional limitations in reactor design and may be somewhat confusing. Furthermore, there are cases where there simply is no purely physical mass transfer process to refer to. For example, the chlorination of decane, which is dealt with in the coming Sec. 6.3.f on complex reactions or the oxidation of o-xylene in the liquid phase. Since those processes do not involve a diluent there is no corresponding mass transfer process to be referred to. This contrasts with gas-absorption processes like COj-absorption in aqueous alkaline solutions for which a comparison with C02-absorption in water is possible. The utilization factor approach for pseudo-first-order reactions leads to = tfikC i and, for these cases, refers to known concentrations C., and C . For very fast reactions, however, the utilization factor approach is less convenient, since the reaction rate coefficient frequently is not accurately known. The enhancement factor is based on the readily determined and in this case there is no problem with the driving force, since Cm = 0- Note also that both factors and Fji are closely related. Indeed, from Eqs. 6.3.C-5 and 6.3.C-10 for instantaneous reactions ... 

In 1952, that is, before the time of flow and relaxation methods, JB discovered that the reaction between iron(IIl) ions and thiocyanate ions, a reaction that is famous in analytical chemistry for its intensive, blood-red color, can be slowed down practically to a standstill if the reaction is performed in cold methanol. This mediod of m ing "instantaneous reactions measurable turned out to apply quite generally not only to complexation reactions but also to certain "fast redox reactions, for example, the reaction between copper(II) and cyanide ion. JB s observation was only follow up to a limited extent (21) though a number of novel results were obtained by the cooling method. There is not much doubt that this method would sooner or later have considerably influenced the subject of inorganic chemistry, had it not been because flow and relaxation methods, which were invented so soon after, gave similar information. 

Another, less widely appreciated idealization in chemical kinetics is that phenomena take place instantaneously—that a change in [A] at time t generates a change in [fi] time t and not at some later time t + z. On a microscopic level, it is clear that this state of affairs cannot hold. At the very least, a molecular event taking place at point x and time t can affect a molecule at point x only after a time of the order of x — x f jlD, where D is the relevant diffusion constant. The consequences of this observation at the macroscopic level are not obvious, but, as we shall see in the examples below, it may sometimes be useful to introduce delays explicitly in modeling complex reaction networks, particularly if the mechanism is not known in detail. 

There are obviously many reactions that are too fast to investigate by ordinary mixing techniques. Some important examples are proton transfers, enzymatic reactions, and noncovalent complex formation. Prior to the second half of the 20th century, these reactions were referred to as instantaneous because their kinetics could not be studied. It is now possible to measure the rates of such reactions. In Section 4.1 we will find that the fastest reactions have half-lives of the order 10 s, so the fast reaction regime encompasses a much wider range of rates than does the conventional study of kinetics. 

If the inhibitor combines irreversibly with the enzyme—for example, by covalent attachment—the kinetic pattern seen is like that of noncompetitive inhibition, because the net effect is a loss of active enzyme. Usually, this type of inhibition can be distinguished from the noncompetitive, reversible inhibition case since the reaction of I with E (and/or ES) is not instantaneous. Instead, there is a time-dependent decrease in enzymatic activity as E + I El proceeds, and the rate of this inactivation can be followed. Also, unlike reversible inhibitions, dilution or dialysis of the enzyme inhibitor solution does not dissociate the El complex and restore enzyme activity. 

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