Zero-order kinetic model

If the derivative of concentration of NaBH with respect to time is equal to reaction rate and is constant, the reaction has zero order kinetics. In other words, if the consumption of NaBH with respect to time is equal to reaction rate, we could define this reaction as having zero order kinetics. That is, the rate of the reaction is independent of NaBH concentration [107,110]. 

Here C is the concentration, r is the rate of reaction, and k is the reaction rate constant based on the solution volmne. 

For the reactor volume V, and amount of catalyst m, the reaction rate kg is normalized and kg can be described as Equation 5.45 [ 110]. 

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A constant rate (zero-order kinetic behaviour) maintained during all, or the greater part of the process may be accounted for [487] by the following reaction models, illustrated in Fig. 5. These alternatives may be distinguished by microscopic observations. 

An overly simplified model of fluidized-bed combustion treats the solid fuel as spherical particles freely suspended in upward-flowing gas. Suppose the particles react with zero-order kinetics and that there is no ash or oxide formation. It is desired that the particles be completely consumed by position z = L. This can be done in a column of constant diameter or in a column where the diameter increases or decreases with increasing height. Which approach is better with respect to minimizing the reactor volume Develop a model that predicts the position of the particle as a function of time spent in the reactor. Ignore particle-to-particle interactions. 

Write the model in dimensionless form. What are the governing parameters for first and zero-order kinetics Verify by simulation. 

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... 

Isomerization of jS-isophorone to a-isophorone has been represented as a model reaction for the characterization of solid bases 106,107). The reaction involves the loss of a hydrogen atom from the position a to the carbonyl group, giving an allylic carbanion stabilized by conjugation, which can isomerize to a species corresponding to the carbanion of a-isophorone (Scheme 9). In this reaction, zero-order kinetics has been observed at 308 K for many bases, and consequently the initial rate of the reaction is equal to the rate constant. The rate of isomerization has been used to measure the total number of active sites on a series of solid bases. Figueras et al. (106,107) showed that the number of basic sites determined by CO2 adsorption on various calcined double-layered hydroxides was proportional to the rate constants for S-isophorone isomerization (Fig. 3), confirming that the reaction can be used as a useful tool for the determination of acid-base characteristics of oxide catalysts. 

The formation of brown pigments via the Maillard reaction, especially in model systems (e.g. glucose-glycine), usually follows zero-order kinetics, but the loss of reactants has been found to follow first- or second-order kinetics in foods and model systems. Activation energies of 109, 116 and 139 kJ mol-1 have been reported for the degradation of lysine, the formation of brown pigments and the production of hydroxymethylfurfural (HMF), respectively. 

NACs in a laboratory column system containing aquifer material from the banks of a river-groundwater infiltration site (Fig. 14.11). The columns were run under ferrogenic conditions. Note that zero-order kinetics suggests that the reactive sites were always saturated such as encountered in enzyme kinetics at saturation (Box 12.2). In this system, all model compounds as well as other NACs including again TNT, ADNTs, and DANTs (data not shown, see Hofstetter et al., 1999) reacted at virtually the same rate. However, when present in mixtures, the compounds showed competition for the reactive sites. A competition quotient, Qc (competition with the reference compound 4-C1-NB present at about equal concentrations) was determined for all model compounds ... 

Kinetic Considerations. The reaction kinetics are masked by a desorption process as shown below and are further complicated by rate deactivation. The independence of the 400-sec rate on reactant mole ratio is not indicative of zero-order kinetics but results because of the nature of the particular kinetic, desorption, and rate decay relationships under these conditions. It would not be expected to be more generally observed under widely varying conditions. The initial rate behavior is considered more indicative of the intrinsic kinetics of the system and is consistent with a model involving competitive adsorption between the two reactants with the olefin being more strongly adsorbed. Such kinetic behavior is consistent with that reported by Venuto (16). Kinetic analysis depends on the assumption that quasi-steady state behavior holds for the rate during rate decay and that the exponential decay extrapolation is valid as time approaches zero. Detailed quantification of the intrinsic kinetics was not attempted in this work. 

The buccal permeability of the non-steroidal antiinflammatory drug, diclofenac sodium, has been evaluated in a dog model. The dog was selected because of the similarity of its buccal mucosa to that of man. Analysis of the buccal data indicated that diclofenac sodium permeability followed an essentially zero-order kinetic process with a minimal lag phase. Permeability of the drug was estimated to be 3 mg/cm2.h but significant differences were observed between animals. The absorption rate with the transbuccal delivery device decreased with time whereas the corresponding rate with a saturated solution was constant. This difference was attributed to the time dependency of drug delivery from the device and was modeled on the basis of release from a membrane-dispersed monolith combined with constant buccal permeability. The predictions of the model showed excellent agreement with the experimental data. 

Wiist WF, Kober R, Schlicker O, Dahmke A. Combined zero- and first-order kinetic model of the degradation of TCE and cis-DCE with commercial iron. Environ Sci Technol 1999 33 4304 4309. 

Analysis of Kinetic Data. To gather the data necessary for this type of analysis, yet another set of phenolysis experiments was carried out this time in a small Parr bomb that was immersed in an oil bath maintained at 220 °C for relatively short periods of time. The data collected and summarized in Table VI were correlated for zero, first, and second order kinetic models by the use... 

TABLE 1 Theophylline Release Rates from Asymmetric-Membrane Tablet Coatings, Results of Fitting Release Profiles to Zero-Order Kinetics, and Precipitation Times Determined from Model Predictions... 

Vinyl-terminated polydimethyl siloxanes react with hydrogen silanes according to second order kinetics. The same kinetics are found in model reactions on monofunctional reactants at a lower concentration range. Also, a direct proportionality between the rate of reaction and platinum concentration is observed in both cases. Network formation does not inhibit the reaction. Polymers with lateral vinyl groups and very short chain polymers with vinyl end groups have q)proximately zero order kinetics with... 

Figure 3.30 shows clearly the effect of m and z on the reactant transformation degree for a SPMR. Only for a zero-order kinetics process, does the slip flow not affect the degree of the reactant transformation. For other Xf values, each graphic construction based on Fig. 3.30 shows the same rules of evolution (at m<0.5, z and X increase simultaneously, and, when n increases, X increases slowly for m>0.5, X keeps a constant value determined by z). When the PM core of SPMR is exchanged with a CFM model, we obtain a special SPMR type in which the performances can be appreciated by the model developed above. 

As previously discussed, Harrison and Thode (1958) invoked a two-step model to account for the range of isotopic fractionation encountered during sulfate reduction by D. desulfuricans. Rees (1973) developed a steady-state multi-step model for isotope fractionation during bacterial reduction. His approach differed from previous attempts in that he included the possibility of zero-order kinetics for describing the uptake of sulfate. His reaction scheme is basically of the form... 

Thus, first order kinetics and zero order kinetics appear as special cases of the more general kinetics which have been derived on the basis of the zipper mechanism. The zipper model does not invoke the steady state assumption but allows the number of producing sites to increase during the acceleratory period as more zip chains start production and to decrease during the de-celeratory period as more chains are terminating than are starting. 

The kinetics of product evolution in a typical reaction of adamantane hydroxylation showed an initial induction period followed by a fast, apparently zero-order phase with the maximum rate and highest efficiencies (Fig. 2). Deviation from linear behavior took place only after 90% oxygen donor and 80% of the substrate had been consumed. When Ru (TPFPP)(0)2, prepared by reaction of Ru"(TPFPP)(CO) with 3-chloroperbenzoic acid was used as the catalyst, no induction time was detected and zero-order kinetics were observed as well. The well defined and characteristic UV-vls spectra of metalloporphyrins provide an invaluable tool for the mechanistic studies. Thus, monitoring the state of the metalloporphyrin catalysts during the course of both model reactions by UV-vis spectroscopy revealed that the initial form of the catalyst remained the predominant one throughout the oxidation, i.e. in the Ru°(TPFPP)(CO) catalyzed reaction c.a. 80% of the porphyrin catalyst existed as Ru"(TPFPP)(CO) and in Ru (TPFPP)(0)2 catalyzed reaction more than 90% of... 

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