First-Order Kinetic Model

If the consumption of NaBH with respect to time is equal to reaction rate, the reaction has first order kinetics. Ihe reaction is dependent on NaBH concentration as given in Equation 5.48 [110]  

C(NaBH )() versus time gives a straight line, and the first-order rate constant can oe calculated from the slope of the line [111]. 

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Naiki H, Nakakuki K. First-order kinetic model of Alzheimer s beta-amyloid fibril extension in vitro. Lab Invest 1996 74 374-383. 

Several models have been developed for a kinetic approach to bioaccumulation that would model the trophic transfer of contaminant in animals from ingested food. A first-order kinetic model has been proposed, which considers uptake from both dissolved and particulate phases [95], A particular application of that model is to separate the pathways for metal uptake in marine suspension and deposit feeders since ... 

The First-Order Kinetic Model. Karickhoff (1, 68) has proposed a two-compartment equilibrium-kinetic model for describing the solute uptake or release by a sediment. This model is based on the assumption that two types of sorption sites exist labile sites, S, which are in equilibrium with bulk aqueous solution, and hindered sites, Sjj, which are controlled by a slow first-order rate process. Conceptually, sorption according to this model can be considered either as a two-stage process ... 

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... 

When a simple kinetic model is not enough, two separate first-order kinetic models for fast and slow degradation, respectively, have been used. But, it is difficult to define the time when the fast mechanism ends and the slow mechanism begins during cooking (Lee et al., 2007). However, the fractional conversion provides improved accuracy and reliability in determining... 

Pseudo-first-order kinetic model (Lagergren s rate equation) In this model, the kinetic rate in differential form and its analytical solution can be expressed as... 

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 ... 

Reilly, P.M., R. Bajramovic, G.E. Blau, D.R. Branson, and M.W. Sauerhoff. 1977. Guidelines for the optimal design of experiments to estimate parameters in first order kinetic models. Can. J. Chem. Eng. 55 614-622. 

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. 

Rate, A.W., McLaren, R.G. and Swift, R.S. (1992) Evaluation of a log-normal distribution first-order kinetic model for copper(II)-humic acid complex dissociation. Environ. Sci. Technol, 26,2477-2483. 

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-... 

It has been shown that changes in the UV and IR absorbance of unplasticized Cellophane films subjected to accelerated aging in a dry oven at 140 °C follow the behavior predicted by a first-order kinetic model, except for deviations in the early aging period, and that these deviations are most likely caused by oxidation products in the films. It has also been shown that, for Cellophane films, the changes in UV and IR absorbance follow the same kinetics as color change, and that these kinetics are nearly identical with those for rayon and cotton cloths aged under similar conditions. 

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. 

Under stationary conditions, i.e. constant concentration of H atoms as interstitial defects, the relaxation of a heat capacity for the Lu-H can be described within the frameworks of the first-order kinetics model,... 

Figure 1. Heat-capacity derivative, dCJdt, [6] and residual-resistivity, p, [8] dependences on time for LuH0.i48 (a) and LuH0180 (b) solid solutions at different annealing temperatures. In Fig. 1(b), —experimental data from Ref. [5], dash curve corresponds to the first-order kinetics model, and solid curve represents the second-order kinetics model.

Figure 5.20 shows concentration-time profiles for the decomposition of hydrocortisone butyrate at 60°C in a buffered aqueous propylene glycol (50 w/w%, pH 7.6). Consecutive, irreversible, first-order kinetic models [i.e., Equation (5.119a), Equation (5.119b), and Equation (5.119c)] fit reasonably well with the experimental... 

The association/dissociation curves are shown in Fig. 12(B). A common pseudo first-order kinetic model was applied to yield the kinetic constants (kon and ko ) and the affinity constants (KA and A D). The association curves could... 

As clearly illustrated in Figures 12.9 and 12.11, good descriptions of the effluent results from BC-I and BC-II were achieved when the first-order kinetic model was implemented. Furthermore, increased sorption was realized for the higher input concentration (C0 = 0.005 M) of the BC-I column than for BC-II. This finding is based on the ratio of the parameters (k, k2) that provided the best-fit model (see Table 12.3). For BC-I, the value of (k, k2) was 2.76 compared to a value of 0.98 for BC-II. Such trends are consistent with the upper Bs layer and indicate sorption dependency on the dominant concentration within the soil column as influenced by the S04 input (C0). 

Reaction rate data for first-order kinetic model. 

Positive values of AH show the endothermic nature of adsorption. Similar results have been reported for the adsorption of methylene blue by clay [19].The negative values of AG indicate the spontaneous nature of adsorption for mefriylene blue at 35, 40, 50 and 60 C. The positive values of AS suggest the increased randomness at the solid /solution interface during the adsorption of dye on coir pith carbon. Equilibrium data at different temperatures for the adsorption of dye on coir pith carbon do not follow the first order kinetic model but follows the second order kinetic model. The second order rate constants were in the range 0.357-0.879g/mg/min. 

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

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