Kinetics autocatalytic

While we have taken some liberties with the numerical values that we will subsequently employ, the following set of mechanistic equations has been proposed in an effort to explain the observed autocatalytic kinetic behavior (13). 

The presence of N-atoms in the aromatic part of the aldehyde appears essential for chiral amplification. With only one nitrogen, such as in the case of 3-pyridine carbaldehyde, autocatalytic kinetics but no chiral amplification effect has been observed [24,25]. In the case of 3-quinoline carbaldehyde, i.e., in the presence of two nucleophilic centers, autocatalysis as well as moderate chiral amplification were reported [26,27]. Highest amplification capacity is observed in the presence of two N-atoms in the aromatic part of the aldehyde, where for the substituent at the 2-position the amplification capacity increases H < CH3 < f- Bu - C=C -, i.e., with the size and rigidity of this group. So far, detailed studies that could relate the given observations to the possible mechanism of chiral amplification in Soai s reaction are still to be carried out. 

Taking into account basic experimental information, such as the observation of autocatalytic kinetics and the formation of dimers, the Soai reaction was expressed by a minimal kinetic model (Scheme 6) that was considered foremost to consist of chemically realistic steps [69] ... 

The key problems in a polymerization CSTR are the determination and characterization of micro- and macromixing, and the possibility of multiple steady states due to the exothermic nature of the reactions. Recent studies of CSTRs for bulk or solution free-radical polymerization indicate the possibility of multiple steady states due to the large heat evolution and difficult heat transfer that are characteristic of the reactors. Furthermore, even in simple solution polymerization (for example, in methyl methacrylate polymerization in ethyl acetate solvent), autocatalytic kinetics can lead to runaway conditions even with perfect temperature control for certain combinations of solvent concentration and reactor residence time. In practice, the heat evolution can be an additional source of autocatalytic behavior. 

It should be noted that for non-isothermal case (and also for isothermal case with autocatalytic kinetics) the local equation may have multiple solutions. When this occurs, the averaged model obtained by the L-S method captures the complete set of solutions of the full CDR equations only within the region of convergence of the local equation. For example, for the wall-catalyzed non-isothermal reaction case, we have shown that the averaged two-mode model can capture only the three azimuthally symmetric solutions of the full CDR equation. The latter has three symmetric solutions (of which two are stable) as... 

Velocity constant for autocatalytic kinetics of second order (s" )... 

AcAc system was investigated at different tenqieratures. At each temperature, an autocatalytic kinetic model was utilized to obtain the reaction order and the rate constant. The model can be expressed as [20] ... 

Traditional Isothermal Kinetics Measurements of conversion-rate of conversion-time data by isothermal method 1 and conversion-time data by isothermal method 2 were described earlier in this section. Isothermal method 1 measurements have the advantage of simultaneously measuring conversion (a) and rate of conversion (daJdt), which allows use of derivative forms of the rate equation such as Eqs. (2.82) and (2.86). Both conversion and rate of conversion data are necessary to model autocatalytic kinetics [e.g., using Eq. (2.86)]. Isothermal method 2 yields both Tg and conversion at a series of times and temperatures (see Rg. 2.70 as an example). However, the measurements are time-consuming, and since the reaction rate is not measured, it must be calculated mathematically, or integrated forms of the rate equation such as Eqs. (2.83)-(2.85) must be used. To perform these analyses generally requires use of a spreadsheet. 

The chemistry for a stoichiometrically balanced reaction suggests that m = 1 and n = 2 in Eq. (2.86). For real systems, values are often close to these values but not identical. In the epoxy-amine reaction the alcohol, which may be present initially in small concentrations but is also a product of the reaction, catalyzes further reaction, resulting in autocatalysis. Since there are four unknowns ki, k2, m, and n) nonlinear regression analysis must be employed, although ki can be evaluated independently as the extrapolated reaction rate at a = 0. Autocatalytic kinetics are usually evaluated by the derivative form of the autocatalytic rate equation [Eq. (2.86)] with data coUected by isothermal method 1 measurements. Activation energy E and preexponential factor A are measured from the Arrhenius equation... 

This reaction is very slow and it has extraordinary autocatalytic kinetics (independent of chlorine concentration). The system can thus be treated as a homogeneous liquid-phase system, for which the mass transfer effects are negligible. 

Equation [A] is solved numerically giving y = 0.55. Finally, we obtain xb = y > xb = 0.3025. This is less than what was obtained for the CSTR (xb.cstr = 0.76), which is a direct consequence of the autocatalytic kinetics. 

Products of attack by OH radicals rather than hydrolysis by supercrihcal water occur when 4-nitrophenyl acetate is sonolysed in argon-saturated water. " Hydrolyses of substituted benzoic acid esters in near-critical water (250-300 °C) show autocatalytic kinetic behaviour and surprisingly give the same rate constant regardless of substituent, suggesting that an acid-catalysed mechanism predominates. ... 

This pH dependence is consistent with a predominance of autocatalytic kinetics at pH 4 and intramolecular activation below pH 3 as long as the protein concentration is 1 mg/ml or less. 

The kinetics of the polymerization of pyrrole can be followed by measuring the disappearance of the reactants. Pyrrole concentrations can be determined by gas chromatography [10]. The depletion of iron can be followed by the titration of the iron(III) chloride with a complexing agent, and the disappearance of the sulfur-containing doping agents can be determined by inductively coupled plasma (ICP) [47]. Experiments reveal that the reaction follows second-order autocatalytic kinetics [ 10]. A plot of the concentrations of pyrrole monomer (surface and no surface) versus time at room temperature is shown in Fig. 35.5. The surface resistance of the polypyrrole-coated textiles can be controlled by... 

The selective a-chlorination of propionic acid was achieved by heating the acid with a mixture of chlorine, chlorosulfonic acid and oxygen in a semibatch reactor at 70-110 °C. The kinetics of the chlorination were autocatalytic, when the concentration of the chlorosulfonic acid catalyst was kept constant. The primary product was sulfopropionic acid and the autocatalytic kinetics were explained by a mechanism involving acid-catalysed enolization of the key intermediate, propanoyl chloride, as the rate-determining step. ° ... 

Autocatalytic kinetic model of Chen and Reagan with experimental data at 370°C, 1 atm... 

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