First-order kinetics concentration profiles

FIG. 12 First-order kinetic profiles observed from CLM measurements of the diprotonation of H2TTP (a) and the demetalation of ZnTPP (b). The initial concentrations of H2TPP and ZnTPP were 1.71 x 10 and 8.9 x 10 moldm, respectively. The concentration of hydrochloric acid was 2.0moldm (Reprinted from Ref. 61. Cop5right 1998, American Chemical Society.)... 

Fig. 3.4 The substrate concentration profile with respect to the radial distance predicted by first-order kinetics (solid lines) and Michaelis-Menten kinetics with j3 = 5 (broken lines) for different values of Thiele s modulus ().

As previously discussed, compartmental models can be effectively used to project plasma concentrations that would be achieved following different dosage regimens and/or multiple dosing. However, for these projections to be accurate, the drug PK profile should follow first-order kinetics where various PK parameters such as CL, V,h T /2, and F% do not change with dose. 

In conclusion, pharmacokinetics is a study of the time course of absorption, distribution, and elimination of a chemical. We use pharmacokinetics as a tool to analyze plasma concentration time profiles after chemical exposure, and it is the derived rates and other parameters that reflect the underlying physiological processes that determine the fate of the chemical. There are numerous software packages available today to accomplish these analyses. The user should, however, be aware of the experimental conditions, the time frame over which the data were collected, and many of the assumptions embedded in the analyses. For example, many of the transport processes described in this chapter may not obey first-order kinetics, and thus may be nonlinear especially at toxicological doses. The reader is advised to consult other texts for more detailed descriptions of these nonlinear interactions and data analyses. 

Time profiles of the formation of fullerene radical anions in polar solvents as well as the decay of 3C o obey pseudo first-order kinetics due to high concentrations of the donor molecule [120,125,127,146,159], By changing to nonpolar solvents the rise kinetics of Go changes to second-order as well as the decay kinetics for 3C o [120,125,133,148], The analysis of the decay kinetics of the fullerene radical anions confirm this suggestion as well. In the case of polar solvents, the decay of the radical ion absorptions obey second-order kinetics, while changing to nonpolar solvents the decay obey first-order kinetics [120,125,127,133,147]. This can be explained by radical ion pairs of the C o and the donor radical cation in less polar and nonpolar solvents, which do not dissociate. The back-electron transfer takes place within the ion pair. This is also the reason for the fast back-electron transfer in comparison to the slower back-electron transfer in polar solvents, where the radical ions are solvated as free ions or solvent-separated ion pairs [120,125,147]. However, back-electron transfer is suppressed when using mixtures of fullerene and borates as donors in o-dichlorobenzene (less polar solvent), since the borate radicals immediately dissociate into Ph3B and Bu /Ph" [Eq. (2)][156],... 

The disappearance of melphalan from aqueous solutions has been shown to follow first-order kinetics [62,82,85] and the concentration profile during hydrolysis is consistent with a mechanism consisting of two consecutive pseudo first-order reactions (Scheme III A) [53]. 

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... 

Fig. 7.14. Concentration profiles in a liquid phase with a homogeneous catalyst for irreversible first-order kinetics at different values of the Hatta number. Reactant A has to be transferred from...

By using a resonant mirror biosensor, the binding between YTX and PDEs from bovine brain was studied. The enzymes were immobilized over an aminosilae surface and the association curves after the addition of several YTX concentrations were checked. These curves follow a typical association profile that fit a pseudo-first-order kinetic equation. From these results the kinetic equilibrium dissociation constant (K ) for the PDE-YTX association was calculated. This value is 3.74 p,M YTX (Pazos et al. 2004). is dependent on YTX structure since it increases when 44 or 45 carbons (at C9 chain) group. A higher value, 7 p,M OH-YTX or 23 p,M carboxy-YTX, indicates a lower affinity of YTXs analogues by PDEs. 

The catalytic mechanism in solution phase described by Equations (3.1) and (3.2) is usually described in terms of a reversible electron transfer for the Cat system (Equation (3.3)) followed by a reaction operating under conditions of pseudo first-order kinetics (Nicholson and Shain, 1964). Thus, the shape of cyclic voltammo-grams (CVs) depends on the parameter X = kc, t, where k is the rate constant for reaction (3.2) and c at is the concentration of catalyst. For low A, values, the catalytic reaction has no effect on the CV response and a profile equivalent to a singleelectron transfer process is approached. For high X values, s-shaped voltammetric curves are observed that can be described by (Bard and Faulkner, 2001) ... 

Figure 2 - Concentration profiles of a-pinene, and camphene, Hydration reaction over USY in aqueous acetone at 55 °C. The lines represent the fit to a first order kinetics.

The reaction term R in Eq. (6.12) is determined as follows. Mn " is produced by the dissolution of solid-phase Mn oxide and is subject to reprecipitation as either an oxide or reduced phase. Because oxide reduction begins very close to the sediment-water interface, I assume that little reprecipitation as an oxide actually takes place within the deposit or that reprecipitation takes place so near to the interface that it cannot be differentiated from a boundary condition. Therefore, the Mn distribution can be considered as influenced dominantely by production and anoxic precipitation reactions over most of the sampled interval. The production term was shown in the previous section to be of the form R = Ro exp(-our) where Rq and oi are constants and x is the depth in the deposit. Precipitation reactions are commonly assumed to follow first-order or pseudo-first-order kinetics such that R = ki(C - Ceq) where /t, is a first-order rate constant and represents a depth-dependent equilibrium concentration (Holdren et al., 1975 Robbins and Callender, 1975). In LIS sediments the concentrations of many anions such as HCOs", which might precipitate with Mn, are roughly constant over the top —20 cm of sediment. This is true in particular at NWC and DEEP (Part 1). It will therefore be assumed that Ce, is constant over the depth interval of interest and that its value is the concentration to which a profile asymptotes at depth. Taken together these considerations suggest that an appropriate reaction term for Mn in the present case is... 

Under the hypothesis of first-order kinetics, the dimensionless concentration profile is calculated with the assumption that j3 1 ... 

Under conditions where absorbance is due to only the primary reactant or product, it is of interest to examine how the complex mechanism affects the E.R.-time profile. A convenient parameter to use for this purpose is the time ratio io.s/ O.OS where to s and to os are the times forE.R. to equal 0.5 and 0.05, respectively. For a simple single-step mechanism io.5/. 05 is a constant, 13.51, independent of the magnitude of the microscopic rate constant (fel) for the reaction. For the complex mechanism shown in Scheme 1.1, there are three rate constants (% k, and fep). Since in this chapter we are dealing with pseudo-first-order kinetics, rather than expressing the forward rate as fef, we adopt the term fef[B]o where [B]o is the initial concentration of the reactant in excess (B), which is assumed to remain constant in the kinetic experiment or calculation. The intermediate in the reaction is called the reactant complex since it is most often a noncovalendy bound complex between reactants A and B. 

Consider the case of a nonisothermal reaction A B occurring in the interior of a spherical catalyst pellet of radius R (Figure 6.4). We wish to compute the effect of internal heat and mass transfer resistance upon the reaction rate and the concentration and temperature profiles within the pellet. If Z)a is the effective binary diffusivity of A within the pellet, and we have first-order kinetics, the concentration profile CA(f) is governed by the mole balance... 

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