Pseudo-first-order processes

Fortunately, most ADME processes behave as pseudo-first-order processes—not because they are so simple, but because everything except the drug concentration is constant. For example, the elimination of a drug from the body may be written as follows ... 

If everything except the concentration of drug in the body is constant, the elimination of the drug will be a pseudo-first-order process. This may seem to be a drastic oversimplification, but most in vivo drug processes, in fact, behave as pseudo-first-order processes. 

Therefore, if In C is plotted against t, as shown in Fig. 2, the plot will be a straight line with an intercept (at t = 0) of In Co, and the slope of the line (m) will be — k. Such plots are commonly used to determine the order of a reaction that is, if a plot of In C versus time is a straight line, the reaction is assumed to be a first-order or pseudo-first-order process. 

Whereas the fugacity approach was used by Mackay for the computation of mass flows and the concentration levels, the SimpleBox adopt the concentration-based piston velocity type mass transfer coefficients (ms-1). This is, mainly, because most scientific papers express the mass transfer in these terms, rather than in terms of the fugacity-based conductivity type coefficients (mol h 1 Pa-1). Furthermore, the transfer and transformation phenomena are treated as simple pseudo first-order processes, similar to Mackay models. 

Is the reaction a pseudo first-order process The question says that the half-life t /2 of reaction is independent of initial concentration of ester, so the reaction must behave as though it was a first-order reaction in terms of [ester]. In other words, NaOH is in excess and its concentration does not vary with time. 

Here we observe Pbf cleavage from Fmoc-protected arginine under typical conditions, which proceeds as a (pseudo) first order process. Mass spectra from t = 0 and t = 10 min appear in Fig. 2. The reaction took 20 min to go to completion. 

If it is assumed that Z0 is very large, that is Y(o) > Z(o), it can be easily shown that the bimolecular process changes to a pseudo-first-order process. 

Several options were possible for modeling Equation (6.131) and Equation (6.132), and the choice of an appropriate model depended on the relationship between the rate constants and the degree of accuracy desired. When the substrate was not strongly associated with the solid phase or when the reaction rate was much lower than the desorption rate, it was possible to model the transformation as a pseudo first-order process, based on the assumption that Reaction 6.131 was insignificant relative to the reaction shown in Equation (6.132) (i.e., [PCB] = PCB(0(). The transformation rate was then approximated by Equation (6.133). 

Sequential Processes. In many cases (anhydride cured-epoxies, amine-cured epoxies, etc.), thermal degradation curves, for instance gravimetric ones, exhibit two distinct stages (Lehuy et al., 1991). The first one corresponds to a relatively fast, pseudo-first-order process, whereas the sec-... 

We consider first the situation in which the chemical reaction is considered as irreversible. It is assumed that the surface concentration of species Csoi remains constant and equal to their bulk value, c c (in such a way that the process can be considered as a pseudo-first order process),... 

Relaxation times become important when studying the approach to equilibrium either directly or as a result of a small perturbation from equilibrium. They also emerge directly from ultrasonic relaxation techniques for studying single and multiple equilibria (Section 2.6). However, they only apply to first order or pseudo- first order processes (Section 3.15). 

Reaction (49b) was the rate-limiting step that could be treated as a pseudo-first-order process in the presence of excess PhOH (0.1-0.43 M). The tip electrode (a 7-pm C fiber) and the substrate (a 60-pm Au electrode) were placed at a fixed separation distance, which was evaluated from the positive feedback current of decamethylferrocene. A series of current-distance curves for a range of PhOH concentrations showed the decrease in feedback with increasing [PhOH], This is because the consumption of AC in the gap caused a diminution of positive feedback for AC/AC couple. Fitting of the approach curves confirmed a DISP1 mechanism for the reduction of anthracene. In the presence of phenol. The results yielded a psudo-first-order rate constant for reaction (49b), ku from which the second-order rate constant, fc2 = k / [PhOH] = 4.4 0.4 x 103M-1s-1 was obtained. 

An important step towards treatment of SO2 conversion to sulfate and deposition of both species that avoids absolute uncertainties of dispersion and deposition rates was taken by Lewis and Stevens, who investigated the mathematical basis of one form of hybrid receptor modeling (.16). Their model assumes that one measures concentrations of SO2 and SO4 relative to that of some species borne by particles from the plant. They assumed that (1) dispersion, deposition and transformation of the three species (SO2, SO4 and fine primary particles) are linear or pseudo first-order processes, but may have complex dependences on time (2) dispersion affects all three pollutants identically (3) dry deposition is the only type of deposition which occurs (4) deposition velocity is the same for all fine particles, but may be different for SO2 (5) secondary sulfate is produced only by homogeneous oxidation of SO2. 

We should also note that Arney et al. (7), have shown recently that the loss of some properties of paper could be represented as the sum of two pseudo first-order processes, one oxygen independent and one linearly dependent on the oxygen concentration. The model corresponding to this result would then be Equation 18, which is equivalent to the conventional Equation 1... 

To be efficient in a photoprotective sense, the chlorophyll triplet species must be quenched on a time scale which is short in comparison with the pseudo first order process ... 

The inset of Figure 7.13a shows that the initially attained absorption at 350 nm corresponding to [Fen(CN)5NO]3 decays subsequently in excess of NO, suggesting decomposition (see below). Independent of this complication, the faster traces reflect a well-behaved pseudo-first-order process. The values of kobs depend linearly on the concentration of NO, and a value of kon = 250 M 1 s 1 can be derived. This value is similar to others measured for the coordination of several ligands (CO, NH3, py, etc.) into [Fe(CN)5H20]3, reflecting a dissociative mechanism (probably of D type) in... 

A number of processes that have been studied show a linear relationship between the log of the amount of substance present versus the time. Many of these processes do not arise from simple first-order chemical reactions, or the chemistry of the process may be unclear. Nevertheless, since they empirically fit the model for a first-order chemical reaction, they are commonly called pseudo first order processes. The slope of the log (concentration) versus time plot is called the apparent first order... 

Many pseudo first order processes also follow the Arrhenius relationship. In these cases the apparent activation energy can be calculated because of the excellent fit of the data to the Arrhenius equation. 

The striking features of Figure 1 are the initial linear relationship with a steep slope and the later linear relationship with a shallow slope. Although inconsistent with a simple apparent first order process, this relationship is entirely consistent with two pseudo first order processes with different rate constants occurring simultaneously. One process is rapid and the other process is slow. 

Rosen et al. (298) have presented evidence for involvement of methionine in the activity and regulation of bovine GDH. At pH 5.6-6.0 the enzyme is inactivated by lASA in a pseudo-first-order process. At these... 

In direct analogy to the Michaelis-Menten mechanism for reaction of enzyme with a substrate, the inactivator, I, binds to the enzyme to produce an E l complex with a dissociation constant K. A first-order chemical reaction then produces the chemically reactive intermediate with a rate constant k. The activated species may either dissociate from the active site with a rate constant to yield product, P, or covalently modify the enzyme ( 4). The inactivation reaction should therefore be a time-dependent, pseudo-first-order process which displays saturation kinetics. This is verified by measuring the apparent rate constant for the loss of activity at several fixed concentrations of inactivator (Fig. lA). The rate constant for inactivation at infinite [I], itj act (a function of k2, k, and k4), and the Ki can be extracted from a double reciprocal plot of 1/Jfcobs versus 1/ 1 (Fig. IB) (Kitz and Wilson, 1962 Jung and Metcalf, 1975). A positive vertical... 

Thus, unlike some kinetic models with many parameters that must be determined implicitly by curve fitting, the present equivalent circuit model offers a stringent test of the validity of our electrochemical analysis. The previously published (34, 36) derivation of the equivalent circuit implies that the equivalent circuit is intended for a photocurrent that arises from a single relaxation process that is, either first-order or pseudo-first-order processes. Thus, a composite photosignal that consists of both B1 and B2 is not expected to agree with the equivalent circuit. Therefore, a prerequisite to test the validity of the equivalent circuit analysis is to devise a successful method to separate the two components, for example, by elimination of the B2 component completely but leaving the B1 component intact. 

Internal conversion is a pseudo-first-order process by which the singlet excited state Sb energy is lost by collisions with solvent molecules or else by transfer between vibrational modes. Inevitably, the rate he will increase with increasing temperature and vice versa. Quenching is a similar deactivation process, in which collision with solute molecules leads to loss in singlet... 

Al-HMS mesoporous molecular sieves with Si/Al ratio in the range 10-40 were synthesized by using dodecylamine as template. They were characterized by XRD, N2 adsorption, MAS NMR, and DRIFT, and their acid properties were determined by pyridine (PY) adsorption. Aniline methylation was a pseudo-first-order process with respect to aniline concentration. Alkylation is a sequential reaction process, in which methylation of aniline produces N-methylaniline (NMA), then N,N-dimethylaniline (NNDMA) and subsequently N,N-dimethyltoluidines (NNDMT, p- > o-). N-methylation products (NMA+NNDMA) were predominant with a selectivity over 97 mol% at 573 K. 

Theoretical treatments for analysis based on second-order kinetics are considerably more involved than those for first-order or pseudo-first-order processes. Therefore, whenever possible, the conditions of a bimolecular reaction are adjusted so that the reaction follows pseudo-first-order kinetics a 50-fold or greater excess of reagent (Region I) or reactants (Region VII) is necessary. There are systems, however, for which pseudo-first-order conditions cannot be employed—for example, with a large excess of either reagent or reactants, the reactions of interest may be too fast for practical measurements. 

If experimental conditions are carefully selected so that all individual steps are either first-order or pseudo-first-order processes, then, under transient or pre-steady-state conditions, the reaction time courses will take the form of a sum of exponentials (i.e., a linear combination of the individual rate equations for each relaxation), such that the observable, time-dependent changes in absorbance, AZ, are given by the relationship... 

Our a - Ki (in Reference 1 ) our B - K2 (in Reference ). a is an exponential rate constant characterizing true or pseudo first-order processes and B - K(2)/c Is a second-order rate constant divided by molar extinction coefficient characterizing radical-radical decay processes important at high intensities, but not under low-intensity illumination conditions. Aq initial optical density. 

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