Negative order kinetics

Many elements of a mathematical model of the catalytic converter are available in the classical chemical reactor engineering literature. There are also many novel features in the automotive catalytic converter that need further analysis or even new formulations the transient analysis of catalytic beds, the shallow pellet bed, the monolith and the stacked and rolled screens, the negative order kinetics of CO oxidation over platinum,... 

For zeroth-order kinetics the maximum selectivities are identical, and for negative-order kinetics the CSTR wiU give a higher maximum selectivity. [What type of reactor will be better if one reaction is positive order and the other negative order ]... 

Therefore, we can generalize the previous discussion to say that aU qualitative features of multiple steady states in the CSTR remain unchanged for the nth-order irreversible reaction as long as is obeys positive-order kinetics. We will consider zeroth-order and negative-order kinetics in problems. 

One consequence of the negative-order kinetics is auto catalysis of the crystallization process. If the initial concentration is higher than that of the rate maximum, crystal growth will accelerate initially as the concentration decreases. This is illustrated in Fig. 13. Once past the concentration of the growth-rate maximum, the rate drops off. Interestingly, the positions of steepest slope in the time dependencies of crystal length and width do not coincide (Fig. 13), as the positions of the maxima in Guo and Gioo differ (Fig. 12). 

A minimum in growth rate occurs as a function of either crystallization temperature or solution concentration at all growth transitions b etween successive integer folded forms. The latter results in negative-order kinetics, the dilution wave effect, and autocatalytic crystallization. 

B. Crystallization Rate Minima and Negative Order Kinetics... 

Another manifestation of the self-poisoning effect is the anomalous negative order kinetics of crystallization from solution. In long alkanes, there is a supersaturation range in which crystal growth rate... 

For reactions with no volume change, outward flow of gas yields a higher conversion than inward flow for positive-order kinetics, whereas inward flow is superior for negative-order kinetics. 

Classical analysis has demonstrated that a given quantity of active material should be deposited over the thinnest layer possible in order to minimize diffusion limitations in the porous support. This conclusion may be invalid for automotive catalysis. Carbon monoxide oxidation over platinum exhibits negative order kinetics so that a drop in CO concentration toward the interior of a porous layer can increase the reaction rate and increase the effectiveness factor to above one. The relative advantage of a thin catalytic layer is further reduced when one considers its greater vulnerability to attrition and to the deposition of poisons. 

A temperature gradient would also be expected. For an isothermal case, with rj set equal to 1, multiple steady-state solutions may be found (see Figure 10), and the concentration gradient is very significant at temperatures above 427°C (800°F). The non-isothermal catalytic effectiveness factors for positive order kinetics under external and internal diffusion effects were studied by Carberry and Kulkarni (8) they also considered negative order kinetics. 

Would the batch startup procedure always be preferable if the main reaction is irreversible Even for negative-order kinetics What if the reaction is reversible ... 

This equation may be solved by any of the several methods discussed in Chapter 6 (see Illustration 6.4), with the result as shown in Figure 7.9. Now, this is an isothermal calculation, but it shows both of the prominent features of the nonisothermal results of Figure 7.8, i.e., effectiveness > 1 for some ranges of 4>s multiplicity for high values of the parameter K. We have not said much in the text discussions to this point about negative-order kinetics this example should help us to keep in mind that reaction order < 0 is a world away from > 0. 

An example with the characteristics of the coupled displacement is the reaction of azide ion with substituted 1-phenylethyl chlorides. Although the reaction exhibits second-order kinetics, it has a substantially negative p value, indicative of an electron deficiency at the transition state. The physical description of this type of activated complex is the exploded S 2 transition state. 

Equation 5-247 is a polynomial, and the roots (C ) are determined using a numerical method such as the Newton-Raphson as illustrated in Appendix D. For second order kinetics, the positive sign (-r) of the quadratic Equation 5-245 is chosen. Otherwise, the other root would give a negative concentration, which is physically impossible. This would also be the case for the nth order kinetics in an isothermal reactor. Therefore, for the nth order reaction in an isothermal CFSTR, there is only one physically significant root (0 < C < C g) for a given residence time f. 

F statistic, 239, 241 False negatives, 152—153 False positives, 152—153 Fenoximone, 188 First-order kinetics, 167 Fluorescence resonance energy transfer, 182... 

The kinetics of oxidation over noble metals is dramatically different and much more complex. Every chemical species has an inhibiting effect on the rate of oxidation of another species. Carbon monoxide is a particularly strong self-poison, so that its oxidation kinetics usually proceeds at a negative order with respect to CO concentration. The kinetics also... 

Oxidation kinetics over platinum proceeds at a negative first order at high concentrations of CO, and reverts to a first-order dependency at very low concentrations. As the CO concentration falls towards the center of a porous catalyst, the rate of reaction increases in a reciprocal fashion, so that the effectiveness factor may be greater than one. This effectiveness factor has been discussed by Roberts and Satterfield (106), and in a paper to be published by Wei and Becker. A reversal of the conventional wisdom is sometimes warranted. When the reaction kinetics has a negative order, and when the catalyst poisons are deposited in a thin layer near the surface, the optimum distribution of active catalytic material is away from the surface to form an egg yolk catalyst. 

These two parameters describe the change in fraction unconverted with a percentage change in kt or in c0. The first sensitivity is also the slope of the curves in Fig. 28. The values of these sensitivities are given in Table IX. In a piston flow reactor where the conversion level is c/c0 = 0.1, the value of Stt is —0.23 for the first-order kinetics, —0.90 for the zero-order kinetics, and —4.95 for the negative first-order kinetics. In the stirred tank reactor, the value of the sensitivities Skt is —0.09 for the first-order kinetics, — 0.90 for the zero-order kinetics, and +0.11 for the negative first-order kinetics. A positive sensitivity means that as kt is increased, the fraction unconverted also increases, clearly an unstable situation. 

Third-order kinetics, equation (166), have also been obtained330 for the iodination of mesitylene and pentamethylbenzene by iodine monochloride in carbon tetrachloride, the negative activation energies of —4.6 and —1.6 (from measurements at 25.2 and 45.7 °C) obtained being attributed to a mildly exothermic preformation of ArHICl complexes (c/. molecular bromination, p. 123) which subsequently react with two further molecules of iodine monochloride to give the products, viz. equilibria (167) and (168)... 

An interesting cycloheptatriene (182) synthesis has been described using thiophene 1, 1-dioxides (180) and cyclopropenes 181 (equation 121)ns. Concerted [4 + 2]cycloaddition and subsequent cheletropic extrusion of sulfur dioxide are suggested by the second-order kinetics (first in each reactant), and by the large negative activation entropy. 

The oxidation of CO on Pt is one of the best studied catalytic systems. It proceeds via the reaction of chemisorbed CO and O. Despite its complexities, which include island formation, surface reconstruction and self-sustained oscillations, the reaction is a textbook example of a Langmuir-Hinshelwood mechanism the kinetics of which can be described qualitatively by a LHHW rate expression. This is shown in Figure 2.39 for the unpromoted Pt( 111) surface.112 For low Pco/po2 ratios the rate is first order in CO and negative order in 02, for high pco/po2 ratios the rate becomes negative order in CO and positive order in 02. Thus for low Pcc/po2 ratios the Pt(l 11) surface is covered predominantly by O, at high pco/po2 ratios the Pt surface is predominantly covered by CO. 

Thus in Table 4.3 we add to Table 4.2 the last, but quite important, available piece of information, i.e. the observed kinetic order (positive order, negative order or zero order) of the catalytic reaction with respect to the electron donor (D) and the electron acceptor (A) reactant. We then invite the reader to share with us the joy of discovering the rules of electrochemical promotion (and as we will see in Chapter 6 the rules of promotion in general), i.e. the rules which enable one to predict the global r vs O dependence (purely electrophobic, purely electrophilic, volcano, inverted volcano) or the basis of the r vs pA and r vs pD dependencies. 

The kinetics depicted in Figures 9.4 in conjunction with Figure 9.5 and 4.30 provide an excellent example of promotional rules L2, and G2 (electrophilic behaviour), as well as rule G3 (volcano type behaviour). As long as the rate is negative order in C2H4 and positive order in po2 (Fig. 9.4)... 

Although many reaction-rate studies do give linear plots, which can therefore be easily interpreted, the results in many other studies are not so simple. In some cases a reaction may be first order at low concentrations but second order at higher concentrations. In other cases, fractional orders as well as negative orders are obtained. The interpretation of complex kinetics often requires much skill and effort. Even where the kinetics are relatively simple, there is often a problem in interpreting the data because of the difficulty of obtaining precise enough measurements. ... 

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