Reaction order kinetic model

The glycolysis of PETP was studied in a batch reactor at 265C. The reaction extent in the initial period was determined as a function of reaction time using a thermogravimetric technique. The rate data were shown to fit a second order kinetic model at small reaction times. An initial glycolysis rate was calculated from the model and was found to be over four times greater than the initial rate of hydrolysis under the same reaction conditions. 4 refs. 

Klupinski et al. (2004) conclude that the reduction of nitroaromatic compounds is a surface-mediated process and suggest that, with lack of an iron mineral, reductive transformation induced only by Fe(II) does not occur. However, when C Cl NO degradation was investigated in reaction media containing Fe(II) with no mineral phase added, a slow reductive transformation of the contaminant was observed. Because the loss of C Cl NO in this case was not described by a first-order kinetic model, as in the case of high concentration of Fe(II), but better by a zero-order kinetic description, Klupinski et al. (2004) suggest that degradation in these systems in fact is a surface-mediated reaction. They note that, in the reaction system, trace amounts of oxidize Fe(II), which form in situ suspended iron oxide... 

As pointed out in Section 8.2, most physical and chemical processes, not just the chemical transformation of reactants into products, are accompanied by heat effects. Thus, if calorimetry is used as an analytical tool and such additional processes take place before, during, or after a chemical reaction, it is necessary to separate their effects from that of the chemical reaction in the measured heat-flow signals. In the following, we illustrate the basic principles involved in applying calorimetry combined with IR-ATR spectroscopy to the determination of kinetic and thermodynamic parameters of chemical reactions. We shall show how the combination of the two techniques provides extra information that helps in identifying processes additional to the chemical reaction which is the primary focus of the investigation. The hydrolysis of acetic anhydride is shown in Scheme 8.1, and the postulated pseudo-first-order kinetic model for the reaction carried out in 0.1 M aqueous hydrochloric acid is shown in Equation 8.22 ... 

Sufficient DO data were not obtained from basalt-synthetic Grande Ronde groundwater experiments to allow determination of a definitive rate law. A first order kinetic model with respect to DO concentration was assumed. Rate control by diffusion kinetics and by surface-reaction mechanisms result in solution composition cnanges with different surface area and time dependencies (32,39). Therefore, by varying reactant surface area, determination of the proper functional form of the integrated rate equation for basalt-water redox reactions is possible. 

A parallel reaction is introduced in the kinetic model (3.58). When the results obtained with first-order kinetics, shown in Fig. 3.5, are compared with the corresponding first-order kinetic model with reactions in series (Fig. 3.3), a slight im-... 

Fig. 5. Reaction of the basic system at 30 °C (second order kinetic model)...

Reaction rate data for first-order kinetic model. 

The first order kinetic model was based on the following reaction, with k and k the forward and reverse reaction rate constants, respectively ... 

The kinetic parameters for the n order kinetic model have been obtained using these definitions of reactivity for the pure steam gasification experiments of birch. All the activation energies lie between 228-238 kJ/mol and the reaction orders between 0.54 and 0.58, apart from definition 3. The frequency factors are somewhat more scattered, lying between 5-10 and 3-10 . Regarding the uncertainty of the calculation, definitions 2, 5 and 4 seem to give more precise results and it is interesting to notice that the error of the reaction order calculation does not depend on how a representative reactivity value is defined. 

Figure 1. Comparison of the extent of delignificatlon predicted by the homogeneous (first-order, second-order and third-order) models and by the reaction-diffusion kinetic model. The open circles are the measured Klason lignin contents In the residues obtained from methylamine extraction of red spruce at 276 bar, 185 C and 1 g/mln solvent flow rate.

Goud et al.141 studied the kinetics of deactivation of Pd/Zr02 catalyst in the steam reforming of n-hexadecane. A first-order kinetic model, with first-order deactivation rate, was used to obtain the best fit values for the reaction rate constant and the deactivation rate constant as a function of S/C ratio, temperature, and sulfur loading. They noticed that the reaction rate was enhanced by an increase in temperatures and S/C ratios, but decreased by the presence of sulfur. The catalyst deactivation was more rapid in the presence of sulfur, at low S/C ratios and at lower temperatures. 

Fig. 6-7. Kinetics of Ni + sorption and associated cation release by Paxton A horizon (0.040 mol L Ni " " added, soil/solution ratio = 1 100). (a) Ratio of Ni " remaining to added as a function of time. The model represents a first-order reversible reaction with kJ = 0.65 and kj 0.95 K = 0.68). (b) Difference between Ni remaining in solution and the first-order kinetic model (Fig. 7a), as a function of The line indicates the area of direct relationship, (c) Cation release during the reaction. The solid line represents (1 — C/Q) or the inverse of the first-order model presented as a solid line in Fig. 6-7a. (d) Difference between cation gain to solution and the first-order kinetic model (Fig. 6-7c), as a function of The line indicates the area of direct relationship. 

Figure 9.16 Reaction profile (points) of the on-chip derivatization of propyl isocyanate (11) ( ),benzyl isocyanate (12) (A) and toluene-2,4-disocyanate (13) ( ) with NBDPZ and corresponding fits to a second-order kinetics model (lines).

Second-order kinetics is assumed as the most probable mechanism for the investigated reactions, because the concentration of 10 is equal to the concentration of the isocyanates (5 x 10 6M). The same assumption is valid for diisocyanate 13, since the formation of the monoderivatized product is much faster than that of the bis-derivatized product, as confirmed by ESI-MS data. The experimental data were fitted to a second-order kinetic model (Figure 9.16) using the equation... 

In Table 9.4 the slopes of the linear part of the reaction profiles (u), the second-order kinetic rate constants (k) and the initial rate constants (/c0) are summarized. From Table 9.4 it is clear that for the reactions of NBDPZ with monoisocyanates 11 and 12 and diisocyanate 13 the rate constants calculated by fitting the data to second-order kinetics are in good agreement with those calculated based on initial rates only, supporting the second-order kinetics of the reactions. The experimental data were also fitted to a first-order kinetics model. From the fits, which are not shown here, and the residual values, it was clear that only the second-order reactions kinetics could describe the data well. 

In the longer term, the usual types of nth-order kinetic models used for gas phase and solution phase reactions will not suffice to describe the solid or liquid phase reactions at a burning surface. This is because the generally accepted... 

We and others have demonstrated that association of short strands containing a single guanine-repeat seems to obey a fourth-order kinetics model. Third or fourth-order reactions are not common in biochemistry, and the practical consequences of this reaction order are important. A fourth-order reaction does not imply that an elementary kinetic step involves a four-body collision. Such mechanism is extremely unlikely and other processes could lead to this fourth order. The structure of these elusive intermediates remains unknown Stefl et have recently demonstrated that a Hoogsteen G-G duplex is an improbable intermediate. Its identification will be experimentally difficult, as numerical simulations indicate that it may not be present at detectable levels. 

A final test of the intracellular fluxes determined by metabolite balancing was provided through comparison with the predictions of a first-order kinetic model describing the oxidation of pulsed [ C]-indene to all detectable indene derivatives in steady state cells. Assuming Michaelis-Menten kinetics for a typical reaction depicted in Fig. 4, the rate of labeled metabolite conversion by that reaction can be expressed as... 

The previous discussion dealt with Forces and potentials, i.e., equilibrium concepts, so that it indicated the possibility of occurrence of some events, not the velocity at which they could happen. These potential considerations may be brought into a kinetic model similar to a bimotecular reaction rate, in which the probability of coalescence is taken as a function of the repulsive potential. This leads to a second-order kinetic model first proposed by Smoluchovski in 1916. It is useful], to describe an emulsion ripening process in which the reciprocate of tlie number of drops in a given system increases linearly as time elapses. This model has been improved on to calculate the coalescence dynamics of nonde-formable drops (37,38) as well as deformable drops associated with a thin-film hydrodynamic drainage (39.40). 

The Arrhenius plot generated from cure kinetics parameters (Figure 3) for this system essentially is linear through the cure region. The excellent fit obtained with the linear least squares regression over the temperature range of the cure reaction confirms the validity of the nth order kinetic model used to describe the cure of the uncatalyzed gel coat resins. 

Chitosan bead was synthesized for the removal of a cationic dye malachite green (MG) from aqueous solution (Bekc et al. 2008). The kinetics of this reaction implies that sorption process obeys the pseudo-second-order kinetic model. The temperature strongly influenced the adsorption process. It is clear that the ql (maximum adsorption capacity for the pseudo-second-order adsorption) values are increased by increasing the temperature. From the thermodynamic study, it is obtained that activation energy value for MG sorption onto chitosan bead is greater than 40kJ mol". Therefore, this type of adsorption can be considered as chemical adsorption. 

Since cubic autocatalytic reaction requires reaction between three molecules, modelling autocatalytic reactions by cubic form often is criticized. Aris et al. have considered two different models of autocatalytic reactions [26]. The first model considers only two variables, but requires a third-order kinetic model ... 

Figure 7.4 Reactions in microfluidic chips coupled with a MS system, (a) Photograph of the two-inlet chip used to study reaction kinetics, (b) Reaction profile (markers) of the on-chip derivatization of different compounds with NBDPZ and corresponding fits to a second-order kinetics model (lines) [51]. Adapted with permission from Brivio, M., Liesener, A., Oosterbroek, R.E., Verboom, W., Karst, U., van den Berg, A., Reinhoudt, D.N. (2005) Chip-based On-line Nanospray MS Method Enabling Study of the Kinetics of Isocyanate Derivatization Reactions. Anal. Chem. 77 6852-6856. Copyright (2005) American Chemical Society...

The 1 order kinetic model used to test the order of the reaction is, as shown in Figure 2 below, a plot of -ln(l-X) versus time (where X represents the percentage conversion of Butyl bromide). The plot shown compares a STR and OBR trial, with the value of the rate constant given by the slope of the line. 

Two kinetic models, namely, pseudo-first-order and pseudo-second-order, were used to investigate the adsorption process of methyl orange, methyl blue and safranine T onto synthesised and commercial zeolite. Kinetic parameters along with correlation coefficient for the pseudo-second-order kinetic model are listed in Table A.3. The calculated correlation coefficient is closer to unity for the pseudo-second-order kinetic model than the pseudo-first-order kinetic model. Therefore, the sorption reaction can be approximated more favourably by the pseudo-second-order kinetic model for methyl orange, methyl blue and safranine T onto synthesised and commercial zeolite. MPSD error function values as shown in Table A.3 are also considerably lower for the pseudo-second-order kinetic model, reinforcing the applicability of the pseudo-second-order kinetic model. It may be seen that the initial sorption rate (h) continuously increased with increase in Cq. This is due to the increase in driving force due to the increase in Q. 

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