Kinetic curves reactions

Anions of another group were derivatized with formation of gaseous chemiluminescing species. Chemical reaction - gas extraction has been used with chemiluminescence detection in the stream of canier gas in on-line mode. Rate of a number of reactions has been studied as well as kinetic curves of extraction of gaseous products. Highly sensitive and rapid hybrid procedures have been developed for the determination of lO, BrO, CIO, CIO, NO,, N03, CrO, CIO, Br, T, S, 803 with detection limits at the level of pg/L, duration of analysis 3 min. 

If the flow is accompanied with CBA decomposition, the G value in Eq. (5) should be substituted with its time function, G(t). In the general case, thermal decomposition of a solid substance with gas emission is a heterogeneous topochemical reaction [22]. Kinetic curves of such reactions are S -shaped the curves representing reaction rate changes in time pass a maximum. At unchanging temperature, the G(t) function for any CBA is easily described with the Kolrauch exponential function [20, 23, 24] ... 

The shape of the kinetic curves depends on the catalyst type and polymerization conditions (ethylene pressure, temperature, concentration of inhibitors in reaction medium) (89, 97, 98). The types of the kinetic curves obtained. at ethylene polymerization under various conditions are presented in Fig. 1. 

The change of shape of the kinetic curves with monomer and inhibitor concentration at ethylene polymerization by chromium oxide catalysts may be satisfactory described 115) by the kinetic model based on reactions (8)-(14). 

Kinetic measurements were performed on a Hitachi 150-20 UV/VIS spectrophotometer. Dehydrobrominations were studied in DMF solution using cyclohexyl amine (CHA) as the base. Applied CHA concentrations were 2, 2.5, 3, 3.5, 4 and 5 10 3 mole.dm-3, initial concentration of 1 was 5 10 5 mole.dm-3 in every case (pseudo-first-order conditions). Ionic strength was adjusted to lO l mole.dm 3 with potassium nitrate. Kinetic curves / D(t) / were recorded at fix wavelength, X = 290 ran and the temperature was maintained at 30, 35.5, 40°C. Stock solutions were made daily for la and freshly for every measurement of Ih. The reaction was started by injection of solution of 1 to the thermostated solution of CHA. 

The shape of kinetic curves shown by Figure 1 clearly indicates the complexity of the reaction which requires at least five-parameter correlation (Eqn. 1). 

The kinetic curve of the reaction starting from ds-3-bromoflavanone (Ih) may be derived similarly to give Equation 7. 

Recorded kinetic curves were fitted to the five-parameter Equation (1). The parameters pj with their errors and the standard deviation of regressions are summarized in Tables 1-6. Comparison of the data confirm the previously reported (refs. 8,12) similarity in the behavior of the two isomers in the presence of strong bases in spite of the different shape of the kinetic curves. The relatively good agreement of exponents p2, P4 computed for the diastereomers at the same temperature and amine concentration demonstrates the validity of the model used. From comparison of Equations (4) and (7) it follows that both reaction must give the same exponent. 

The catalyst reuse is carried out without treating Pd/ ACF between the runs. Negligible leaching (<10% within the experimental error) was observed after catalyst reuse. Figure 8 shows the initial reaction rate and the selectivity for several runs. After activity drops in the first run, it stabilizes at 0.085 0.008 kmolHj/kgp /s, while selectivity to 1-hexene is 94+1%. Kinetic curves are identical from the second to the sixth runs. 

The drop of the voltammetric crurent is associated with Pt surface oxidation, and the drop on the negative-going mn is due to Reaction (12.9) (surface poisoning by CO) and the Tafehan kinetics of Reaction (12.8). Further, the shift between curves in Fig. 12.13a and b indicates that in the potential range between 0.5 and 0.6 V, methanol oxidation occms with zero or low level atop CO smface intermediate. The amplitudes on Fig. 12.13 on both scans nearly equal to each other indicate a high level of preferential (111) crystallographic orientation of the poly crystalline Pt surface used for this work, as inferred from data in [Adzic et al., 1982]. 

In our previous work [63], we studied the hydrolysis kinetics of lipase from Mucor javanicus in a modified Lewis cell (Fig. 4). Initial hydrolysis reaction rates (uri) were measured in the presence of lipase in the aqueous phase (borate buffer). Initial substrate (trilinolein) concentration (TLj) in the organic phase (octane) was between 0.05 and 8 mM. The presence of the interface with octane enhances hydrolysis [37]. Lineweaver-Burk plots of the kinetics curve (1/Uj.] = f( /TL)) gave straight lines, demonstrating that the hydrolysis reaction shows the expected kinetic behavior (Michaelis-Menten). Excess substrate results in reaction inhibition. Apparent parameters of the Michaelis equation were determined from the curve l/urj = f /TL) and substrate inhibition was determined from the curve 1/Uj.] =f(TL) ... 

Furthermore, in the system with coupled lipase and lipoxygenase, the production rate of HP is governed by the first enzymatic reaction and mass transfer. When TL,- is small (0 to 1 mM equiv. 3 mM LA), the kinetic curve has a sigmoid shape due to surface active properties of LA and HP [25]. Hydrolysis of TL and the increase of LA favor the transfer of LA. Such a transfer allows the lipoxygenase reaction to progress. Since lipox-ygenation consumes LA and produces HP, catalysis and transfer demonstrates a reciprocal influence. 

When a PVC film is exposed to the UV-visible radiation of an incandescent lamp in the presence of pure chlorine, at room temperature, the chlorine content of the polymer increases from 56.8 % initially to over 70 I after a few hours of irradiation (8). As the reaction proceeds, the rate of chlorination decreases steadily as shown by the kinetic curves of figure 2, most probably because of the decreasing number of reactive sites on the polymer chain that remain available for the attack by chlorine radicals. 

When this resin was exposed as a thin film to the UV radiation of a medium pressure mercury lamp (80 W aiH), the crosslinking polymerization was found to develop extensively within a fraction of a second (18). The kinetics of this ultra-fast reaction can be followed quantitatively by monitoring the decrease of the IR absorption at 810 an-1 of the acrylic double bond (CHCH twisting). Figure 8 shows a typical kinetic curve obtained for a 20 pm thick film coated onto a NaCl disk and exposed in the presence of air to the UV radiation at a fluence rate of 1.5 x 10 6 einstein s-1 cm 2. 

Assuming zero order kinetics, the reaction rate constants can be calculated from the slope of the hydrogen uptake curve. Table 1 shows that the first three catalysts have similar rate constants on catalyst weight basis, from 5.6xl0"3 to... 

It should be observed that curve C (Fig. 31) which characterizes the steady activity of the catalyst surface may be directly compared to activity curves obtained by other techniques. The evolutions of heat as a function of time produced by the reaction of doses of reaction mixture at the surface of four different nickel oxide catalysts are, for instance, plotted on Fig. 32. These curves are very similar indeed to the kinetic curves obtained with the same catalysts in a classical static reactor (Fig. 33) (8). 

When a CL reaction is developed by using the CAR technique, the shape of the resulting CL signal-versus-time plots follows a differential equation that is a combination of the integrated Eq. (2) and (4), and is very difficult to obtain. However, the kinetic curve exhibits the characteristic initial concave and wide linear portions that correspond to a reaction (see Fig. 7c). Therefore, the maxi-... 

The oscillation regime is observed in the oxidation of the iodide ions by the BrCfi ions. The kinetics of this reaction and its mechanism were studied in detail by Citri and Epstein [223]. The process was studied in a jet reactor. The oscillating regime is observed when the concentration of iodide ions changes in an interval of 5 x 10 7 to 4 x 10 2 M (bromate was introduced in excess with respect to the iodide ions). The example of the oscillating kinetic curve can be seen in Figure 10.1. 

The model proposed by Brandt et al. is consistent with the experimental observations, reproduces the peculiar shape of the kinetic curves in the absence and presence of dioxygen reasonably well, and predicts the same trends in the concentration dependencies of t, p that were observed experimentally (80). It was concluded that there is no need to assume the participation of oxo-complexes in the mechanism as it has been proposed in the literature (88-90). However, the model provides only a semi-quantitative description of the reaction because it was developed at constant pH by neglecting the acid-base equilibria of the sulfite ion and the reactive intermediates, as well as the possible complex-formation equilibria between various iron(III) species. In spite of the obvious constraints introduced by the simplifications, the results shed light on the general mechanistic features of the reaction and could be used to identify the main tasks for further model development. 

Arguably the best way to accelerate the rate of a reaction catalyzed by a soluble transition metal catalyst is by preventing deactivation of the catalyst. Most chemists who have investigated the kinetics of transition metal-catalyzed reactions are familiar with kinetic curves that shoot off with dazzling speed during... 

All the kp+ calculated by the original workers for bulk polymerisations and those obtained at high monomer concentrations are wrong because they are second-order rate-constants, calculated on the assumption that the polymerisations are second-order reactions. This is a considerable curiosity because all the kinetic curves published showed clearly that the polymerisations were of zero order with respect to the monomer concentration (m). A new set of kp+ values is given here. 

The process was controlled by determination of active hydrogen in Si-H groups for several times [2, 6], The influence of the structure of dihydride monomers on the reaction rate, yield and properties of obtained polymers has been studied (table 1, figure 1). Based on kinetic curves (figure 1) of Si-H groups conversion, the reaction rate constants have been determined (table 1). The total reaction order equals to 2. 

The authors [1] studied kinetics of poly (amic acid) (PAA) solid phase imidization in the presence of nanofiller (Na+-montmorillonite) and in its absence. It was found out, that the kinetic curves conversion (imidization) degree Q versus reaction duration t were have typical for polymerization reactions shape with autodeceleration showing imidization rate reduction as time is passing. As it is known [2], such curves Q(t) are specific for reaction passing in heterogeneous medium and are described by the simple relationship ... 

In figure 1 the kinetic curves of reesterification reactions without catalyst and in the presence of TBT are shown. The attention is draw by itself both quantitative and qualitative differences of these Q(t) curves. The quantitative difference is expressed by much faster growth Q at t increase due to catalyst presence that was expected. The qualitative change is reflected in the Q(t) curve form change. If in the absence of TBT linear dependence was obtained, which indicates on the reaction proceeding in Euclidean (homogeneous) space [7], then in TBT presence a typical curvilinear 0(1) dependence was obtained with reaction rate dQ / dt decrease with t increase. Such reactions are typical for heterogeneous (fractal)... 

Figure 1. The kinetic curves conversion degree time (Q-t) for reesterification reaction without catalyst (1) and in TBT presence (2).

Let s note three important aspects followed from the model [4] application for description of reesterification reaction. At first as reesterification reactions with TBT and in it absence proceed in identical conditions, then from the comparison of figure 1 kinetic curves follows, that the reaction fractal-like behaviour in TBT presence is due to local fluctuations of catalyst distribution in reactive medium. Secondly the division of reaction duration into short and long... 

In case of reaction course in the Euclidean spaces the value D is equal to the dimension of this space d and for fractal spaces D is accepted equal to spectral dimension ds [6], By plotting p i=( 1 -O) (where O is conversion degree) as a function of t in log-log coordinates the value D from the slope of these plots can be determined. It was found, that the mentioned plots fall apart on two linear parts at t<100 min with small slope and at PT00 min the slope essentially increases. In this case the value ds varies within the limits 0,069-3,06. Since the considered reactions are proceed in Euclidean space, that is pointed by a linearity of kinetic curves Q-t, this means, that the reesterefication reaction proceeds in specific medium with Euclidean dimension d, but with connectivity degree, characterized by spectral dimension ds, typical for fractal spaces [5],... 

In the Figure 7 the kinetic curves for the model chains with some distribution of reactive croups along the chain are shown. The reaction was simulated for the degree of occupation of reactive groups 0.5 and... 

Fig. 7-S. Reaction rate as a function of reaction affinity curve (a) = regime of linear kinetics near reaction equilibrium curve (b) = regime of nonlinear exponential kinetics away from reaction equilibrium v = reaction rate A= affinity.

Kinetic curves relative to polymerization reactions in the solid state commonly show a sigmoidal shape with a slow initiation step followed by a steep increase, even by two orders of magnitude, of the reaction rate. A reaction with this kind of kinetic curve is said to have an autocatalytic behavior. 

The fundamental processes involved in a solid state reaction are twofold. First, there is the reaction itself - the breaking and forming of bonds. Second, there is the transport of matter to the reaction zone. A number of models aiming to describe solid state reactions exist. They are generally based on sigmoidal kinetic curves. The general form of the kinetic equation is as follows ... 

The two most popular methods of calculation of energy of activation will be presented in this chapter. First, the Kissinger method [165] is based on differential scanning calorimetry (DSC) analysis of decomposition or formation processes and related to these reactions endo- or exothermic peak positions are connected with heating rate. The second method is based on Arrhenius equation and determination of formation or decomposition rate from kinetic curves obtained at various temperatures. The critical point in this method is a selection of correct model to estimate the rate of reaction. 

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