Maximum concentration of intermediate

This equation indicates that the maximum becomes more pronounced as k2/kl becomes smaller. If kx is known and the maximum concentration of intermediate is measured, k2 may... 

Figure 3.11 shows the general characteristics of the concentration-time curves for the three components A decreases exponentially, R rises to a maximum and then falls, and S rises continuously, the greatest rate of increase of S occurring where R is a maximum. In particular, this figure shows that one can evaluate k and k2 by noting the maximum concentration of intermediate and the time when this maximum is reached. Chapter 8 covers series reactions in more detail. 

The maximum concentration of intermediate and the time at which it occurs is given by... 

The maximum concentration of intermediate, CRj ax the time when this occurs is found to be... 

When an experiment like that shown in Fig. 4 was carried out at 50°C, a similar behavior of the intermediate was observed, except that both formation and decay were six times faster. Experiments were also followed at 50°C in which 0.5 M excess P(OEt)3 was added initially, or when the intermediate rc-allyl complex was at a maximum. In the latter case, the rate of disappearance of the intermediate was essentially the same as in the control, consistent with rate-determining reductive elimination in 4 with m = 2 the rate of consumption of HCN and BD decreased abruptly, however, when excess L was added. In the experiment with L added initially, the overall rate of product formation was only about half that of the control the smaller maximum concentration of intermediate is consistent with a greater inhibiting effect of added L on the rate for formation of the intermediate than on its rate of decay. 

The Bodenstein approximation recognises that, after a short initial period in the reaction, the rate of destruction of a low concentration intermediate approximates its rate of formation, with the approximation improving as the maximum concentration of intermediate decreases (see Chapters 3 and 4). Equating rates of formation and destruction of a non-accumulating intermediate allows its concentration to be written in terms of concentrations of observable species and rate constants for the elementary steps involved in its production and destruction. This simplifies the kinetic expressions for mechanisms involving them, and Scheme 9.3 shows the situation for sequential first-order reactions. The set of differential equations... 

Figure 9 shows the characteristic curves for the accumulation of these species in the reaction between thiophenol and liquid elemental sulfur at thiol-sulfur ratios of 1 18.8, 1 8, and 1 3 at I30°C. Several facts are qualitatively apparent from Figures 8 and 9. Irrespective of the relative amounts of HS -H and SxH the concentration of HSjH becomes dominant compared with the other intermediate species HSJi when the relative concentration of SH to sulfur is increased in the reaction mixture. The buildup to a maximum concentration of intermediates is associated with the induction period. Similar behavior was observed in the NMR spectra of reaction mixtures of other thiophenols with sulfur. However, such intermediates were not observed to form in the cases of p-amino and p-nitrothiophenol, further suggesting that these thiols react by a different mechanism. 

There are a few other points worthy of note that become evident on closer inspection of the equations developed in Illustrations 9.2 and 9.3. First, except for the case where 2/ 1 = 1 Plug flow or batch reactor requires a lower space or holding time than a CSTR to achieve the maximum concentration of intermediate. The more this ratio departs from unity, the greater the difference in space times. This fact becomes evident on substitution of numerical values into equations (C) and (G) of Illustrations 9.2 and 9.3, respectively, or when plots of Cv/Cao versus kiT are prepared for various ratios of 2/ 1 [see, e.g., Lev-enspiel (5)]. In general, for series reactions, the maximum possible yields of intermediates are obtained when fluids of different compositions (different stages of conversion) are not allowed to mix. 

It is seen that the intermediate product, in the very early stages of the reaction, accumulates exponentially with time. At later stages of the reaction, competition of CH2O for the active centers HO and OH must be taken into account as was done in Section 5.4 when the problem of the maximum concentration of intermediate CH2O was considered. This aspect of the problem will be taken up again soon but in the meantime we shall focus our attention on the early stages of reaction where formaldehyde is still at too low a concentration for competing effectively with methane for the active centers HO2 and OH. 

To find the time corresponding to the maximum concentration of intermediate, we differentiate eqn 7.12 and look for the time at which d[I]/df = 0. First we obtain... 

By an approximate evaluation of this expression, starting from e.g. the initial partial pressures Pa° = 0.1 atm and pn — 0-9 atm and the above mentioned values of the constants, we obtain S = 14 the maximum concentration of the intermediate product corresponding to this value is about 80%, in agreement with the experimental results in Fig. 7. 

More recently, Bagal and coworkers (Luchkevich et al., 1991) obtained similar results in a kinetic investigation of the coupling reactions of some substituted benzenediazonium ions with 1,4-naphtholsulfonic acid, and with 1,3,6-, 2,6,8-, and 2,3,6-naphtholdisulfonic acids. The kinetic results are consistent with the transient formation of an intermediate associative product. The maximum concentration of this product reaches up to 94% of the diazonium salt used in the case of the reaction of the 4-nitrobenzenediazonium ion with 1,4-naphtholsulfonic acid (pH 2-4, exact value not given). The authors assume that this intermediate is present in a side equilibrium, i. e., the mechanism of Scheme 12-77 mentioned above rather than that of Scheme 12-76, and that the intermediate is the O-azo ether. 

The first approach is based on equation 5.3.7 and makes use of the fact that the time at which the maximum concentration of the intermediate B is reached is a function only of the two rate constants and initial concentrations. For the case where no B is present initially, equations 5.3.7 and 5.3.6 can be written as... 

The role of Ca2+ in inducing refolding of a-lactalbumin is reflected in clean two-stage kinetics, with rate constants 6.0 and 1.3 s-1. The maximum concentration of the intermediate, monitored by stopped-flow fluorescence and time-resolved photo-CIDNP NMR, occurs at about 200 ms (327). 

Since the maximum concentration of 07 is about an order of magnitude greater than that of 0 , one can easily follow the formation of stable intermediates using IR spectroscopy. As shown in Figure 3, after the reaction of 07 with ethane, a band appeared at 1095 cm 1, which is attributed to a surface ethoxide ion. 

Thus, time at which the concentration of intermediate is maximum, will depends on the rate constants k and k2. 

A chemical reaction can be designated as oscillatory, if repeated maxima and minima in the concentration of the intermediates can occur with respect to time (temporal oscillation) or space (spatial oscillation). A chemical system at constant temperature and pressure will approach equilibrium monotonically without overshooting and coming back. In such a chemical system the concentrations of intermediate must either pass through a single maximum or minimum rapidly to reach some steady state value during the course of reaction and oscillations about a final equilibrium state will not be observed. However, if mechanism is sufficiently complex and system is far from equilibrium, repeated maxima and minima in concentrations of intermediate can occur and chemical oscillations may become possible. 

Figure 8.9 shows that the concentration of intermediate in reversible series reactions need not pass through a maximum, while Fig. 8.10 shows that a product may pass through a maximum concentration typical of an intermediate in the irreversible series reaction however, the reactions may be of a different kind. A comparison of these figures shows that many of the curves are similar in shape, making it difficult to select a mechanism of reaction by experiment, especially if the kinetic data are somewhat scattered. Probably the best clue to distinguishing between parallel and series reactions is to examine initial rate data—data obtained for very small conversion of reactant. For series reactions the time-concentration curve for S has a zero initial slope, whereas for parallel reactions this is not so. 

Again, as with the two-reaction set, we find that a plug flow reactor yields a higher maximum concentration of any intermediate than does a mixed flow reactor. 

Fig. 5.11. Excitability in a chemical system, (a) The nullclines /(a, 0) = 0 and g(a,0) = 0 intersect just to the left of the maximum. A suitable perturbation must make a full circuit, as shown by a typical trajectory, before returning to the stable stationary state, (b), (c) The corresponding evolution of the concentration of intermediate A and the temperature excess in time showing the large-amplitude excursion.

There is an initial fast equilibrium in which the alcohol interacts with IBX, leading to a small concentration of intermediate 45. This intermediate evolves slowly to IBA and the desired carbonyl compound. As expected, the presence of water displaces the initial equilibrium to the left and produces a decrease on the oxidation speed. Thus, although IBX oxidations can be made in the presence of water, it is better to perform them under dry conditions for maximum velocity. 

The bromination of dibenzoazepine 63 in 1,2-dichloroethane gives the /raw.v-dibromide 64 as the only product. The reaction was monitored spectrophotometrically and found to exhibit a third-order kinetics (second-order in Br2). A significant conductivity has also been found during the course of bromination. Both spectrophotometric and conductometric measurements are consistent with the presence of Br3- salt intermediates at a maximum concentration of ca 2% of that of the initial reactants. The X-ray structure of dibromide 64 shows a considerable strain at carbons bearing bromine atoms. The strain appears to be responsible for an easy, spontaneous debromination of 64, as well as for high barrier for the formation of 64 from the bromonium-tribromide intermediate. That makes possible the cumulation of the intermediate itself during the bromination of 63119. 

While solid matrices have been employed successfully, they may be less than ideal for controlled mechanistic studies. A more appropriate technique for controlled doublet photochemistry appears to be two-photon excitation in solution. In this experiment, the first photon is used to initiate radical ion formation, whereas the second photon, appropriately delayed to coincide with the maximum concentration of the radical cation so generated and tuned to its absorption maximum, serves to excite these intermediates. However, we hasten to add that the benefits of this technique have yet to be demonstrated. The photoinduced rearrangement of radical cations very likely will benefit substantially from a mismatch between (quartet vs. doublet) potential surfaces, much as triplet sensitized isomer-izations can be ascribed to mismatches between triplet and ground state surfaces. 

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