First order decay models

Chemical/Physical. Hydrolysis in distilled water at 25 °C produced c/5-3-chloro-2-propen-l-ol and HCl. The reported half-life for this reaction is 1 d (Milano et al., 1988 Kollig, 1993). Kim et al. (2003) reported that the disappearance of c/5-1,3-dichloropropylene in water followed a first-order decay model. At 25 and 35 °C, the first-order rate constants were 0.077 and 0.286/d, respectively. The corresponding hydrolysis half-lives were 9.0 and 2.4 d, respectively. 

The rate of physical mixing and volumetric expansion caused by carbon additions declines quickly with time. Soil carbon accumulation with time (Figure 7(d)) can be described by the following first-order decay model (Jenny et al., 1949) ... 

Doi et al (9) using a HgCl - supported catalyst showed that the decay rate was second order with respect to catalyst activity. Brockmeier (5) has reported an order of l.S, whilst Tait and Wang (6) have demonstrated that the decay can be better represented by a multi-centre first order decay model than by other models which were considered. 

The most widely accepted model to predict E-cat activity is based on a first-order decay type [7] ... 

Most published data deals with model solutions to assess the major factors influencing betalain stability, among which pH and temperature are most frequently addressed. Until recently, total color loss was assessed by spectrophotometric monitoring of the decline at the wavelength of maximum absorption. To predict color fading over time, kinetic data were derived therefrom, most often obeying first-order decay principles. 

In conclusion, the basic assumptions of the re-entry model (i.e., a linear relationship between application rate and ADFR and a first-order decay of the DFR) were confirmed. The relationship between the transfer factor and level of DFR and re-entry time should be explored further. Including foliage... 

Half-life estimates of approximately 28 days for thiophanate-methyl indicate a very slow decay compared to methiocarb with an estimate of half-life of about 11 days. The application of a model based on a first-order decay process resulted in fairly high R2 and significant fit. The results suggest that both pesticides are relatively stable compared to other compounds under similar environmental conditions (Brouwer et al., 1994). With respect to the objectives of the study and the proposed model, it can be stated that the results confirm the assumption of a linear relationship between application rate (for both application techniques) and the increase of dislodgeable foliar residue. This relationship holds for modeling purposes. The contribution of the crop density or total crop surface area to the process of interception cannot be quantified with the results of the present study. Because the interception factor ranges from about 0.35 to 0.9 (Willis and McDowell, 1987), the... 

Gradient diffusion was assumed in the species-mass-conservation model of Shir and Shieh. Integration was carried out in the space between the ground and the mixing height with zero fluxes assumed at each boundary. A first-order decay of sulfur dioxide was the only chemical reaction, and it was suggested that this reaction is important only under low wind speed. Finite-difference numerical solutions for sulfur dioxide in the St. Louis, Missouri, area were obtained with a second-order central finite-difference scheme for horizontal terms and the Crank-Nicolson technique for the vertical-diffusion terms. The three-dimensional grid had 16,800 points on a 30 x 40 x 14 mesh. 

Primary outputs are produced essentially by sedimentation and (to a much lower extent) by emissions in the atmosphere. The steady state models proposed for seawater are essentially of two types box models and tube models. In box models, oceans are visualized as neighboring interconnected boxes. Mass transfer between these boxes depends on the mean residence time in each box. The difference between mean residence times in two neighboring boxes determines the rate of flux of matter from one to the other. The box model is particularly efficient when the time of residence is derived through the chronological properties of first-order decay reactions in radiogenic isotopes. For instance, figure 8.39 shows the box model of Broecker et al. (1961), based on The ratio, normal-... 

When several temperature-dependent rate constants have been determined or at least estimated, the adherence of the decay in the system to Arrhenius behavior can be easily determined. If a plot of these rate constants vs. reciprocal temperature (1/7) produces a linear correlation, the system is adhering to the well-studied Arrhenius kinetic model and some prediction of the rate of decay at any temperature can be made. As detailed in Figure 17, Carstensen s adaptation of data, originally described by Tardif (99), demonstrates the pseudo-first-order decay behavior of the decomposition of ascorbic acid in solid dosage forms at temperatures of 50° C, 60°C, and 70°C (100). Further analysis of the data confirmed that the system adhered closely to Arrhenius behavior as the plot of the rate constants with respect to reciprocal temperature (1/7) showed linearity (Fig. 18). Carsten-sen suggests that it is not always necessary to determine the mechanism of decay if some relevant property of the degradation can be explained as a function of time, and therefore logically quantified and rationally predicted. 

Brown (1999b) reported formaldehyde and VOC emissions from new, unfinished particleboard and MDF (both using urea formaldehyde resins) in Ausbalia. Formaldehyde emissions over the first three weeks exhibited first-order decay behavior that predicted little to no formaldehyde emission after 6 months. However, further emission measurements at 8 months showed the products sbll emitted formaldehyde at approximately one-half the new product rate (also further unpublished measurement at 2 years showed the same emission rate as at 8 months). It was concluded that the wood-based panels emitted formaldehyde by a double-exponen-ttal model, the early- to late-term emissions including the free formaldehyde in the products but the long-term emissions consisbng of only the formaldehyde... 

Berner (1980) first introduced the following concept of a one-G model for determining first-order decay constants (k) of organic matter decomposition ... 

A two-dimensional numerical model was developed to describe the transport of dissolved organics originating from nonaqueous phase liquid pool dissolution in saturated porous media in the presence of dissolved humic substances. The model assumes that the dissolved contaminant (NAPL dissolved in the aqueous phase) may sorb onto the solid matrix as well as onto humic substances suspended in the aqueous phase, contaminant-humic particles and humic substances may sorb onto the solid matrix, the dissolved contaminant may undergo first-order decay, and humic substances are introduced into the aquifer from a line source. 

Both decay processes are due to minor side reactions of some of the same carbenium ions as those propagating the "fhiitful" reactions of cracking and isomerization. Their effects combine to yield an equation for the kinetics of catalyst decay which can be anywhere from first to second order in site concentration. In practice, small molecules of the type studied as model compounds generally exhibit almost pure second-order decay in site concentration, while the large molecules found in gas oils tend to show a lower kinetic order, often approaching first-order decay. 

The reason that gas-oil cracking has such a large component of first-order decay and the model compounds do not is no doubt connected to the presence of much more complex carbenium ions in gas-oil cracking processes. The ions present in these systems may well be able to form non-desorbable and therefore poisonous species by a series of monomolecular eliminations of various small paraffinic molecules (or hydrogen). 

In our efforts to determine the order of decay, we assume that the main reaction order is a known quantity. If it is not, a dual-model trial-and-error solution is necessary. The idea is to find the simplest model that fits the data. If we assume first-order decay. 

David and Augsburger (63) studied the decay of compressional forces for a variety of excipients, compressed with flat-faced punches on a Stokes rotary press. They found that initial compressive force could be subject to a fairly rapid decay and that this rate was dependent on the deformation behavior of the excipient for the materials studied, they found that maximum loss in compression force was for compressible starch and MCC, which was followed by compressible sugar and DCP. This was attributed to differences in the extent of plastic flow. The decay curves were analyzed using the Maxwell model of viscoelastic behavior. Maxwell model implies first order decay of compression force. 

The effect of humic materials on the photolytic micellar system was evaluated in DR s photodegradation. DR solubilized within Tween 80 micellar solution with or without humic materials was determined. In order to calculate the quantum yield, the molar absorptivity of DR was determined by spectrophotometry. The determination of the quantum yield and reaction rates was examined through a pseudo first-order decay rate expression. Quenching and catalytic effects resulting from the humic substances were examined through Stem-Volmer analysis. A reaction mechanism of photolytic decay of DR solubilized within surfactant micelles in the presence of various amount of humic materials was proposed for this purpose. The effect of high and low concentration of humic materials has been accounted for by a designed model. 

The important assumptions for the pesticide model are instantaneous, linear, reversible adsorption described by an adsorption partition coefficient, K, and first-order decay described by an overall decay rate, k. Parameters for the pesticide model include universal soil loss equation parameters (if erosion loss is to be modeled), pesticide application information (rate, date, and method of application), K, k, and a dispersion coefficient. 

Gaussian Distribution Model. As reported earlier (22), neither pyrene nor DPA fluorophore yields monoexponential unimolecular decays once adsorbed onto the silica gel surface. The low surface coverage and the absence of pyrene excimers indicate that the surface probe exists as an isolated species. Previously, deviations from the first-order decay kinetics... 

Solute transport with biodegradation modelled as a first-order decay process (simple, lumped-parameter approach),... 

BIOCHLOR (Aziz et al., 2000) is a screening model that simulates remediation by natural attenuation of dissolved solvents in groundwater. The software, programmed in the Microsoft Excel spreadsheet environment and based on the Domenico analytical solute transport model, has the ability to simulate 1-D advection, 3-D dispersion, linear adsorption, and biotransformation via reductive dechlorination (the dominant biotransformation process at most chlorinated solvent sites). Dissolved solvent degradation is assumed to follow a sequential first order decay process. 

Solute transport with biotransformation modelled as a sequential first-order decay process with 2 different reaction zones (i.e., each zone has a different set of rate coefficient values). 

The plasma concentration versus time equation for the two-compartment first-order absorption model contains three exponential decay terms, and three corresponding phases in Figure 10.80. The first exponential decay term contains the larger hybrid rate constant (/li), which dominates just after t ax during the distribution phase. Hence li is called the hybrid distribution rate constant. The second exponential decay term contains the smaller hybrid rate constant I2), which dominates at later times during the elimination phase. The third exponential decay curve contains and dominates the early rising absorption phase. The two-compartment elimination half-lrfe is then written in terms of as... 

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