First-order system half-time

PROBABLE FATE photolysis C-C bond photolysis can occur, not important in aquatic systems, photooxidation by U.V. light in aqueous medium 90-95°C, time for the formation of CO2 (% theoretical) 24% 3 hr, 50% 17.4 hr, 75% 45.8 hr, photooxidation in air 9.24 hrs-3.85 days oxidation probably not an important process hydrolysis very slow, not important, first-order hydrolytic half-life 207 days volatilization not an important process, calculated half-life in water 4590 hr 25°C and 1 m depth, based on an evaporation rate of 1.5x10 m/hr sorption important for transport to anaerobic sludges, 30-40% adsorbed on aquifer sand 5°C after 3-100 hr equilibrium time, 75-100% disappearance from soils 3-10 yrs biological processes biotransformation is the most important process other reac-tions/interactions electrochemical reduction with products of benzene and gamma-TCCH has been studied... 

The only kinetic data reported are in a Ph.D. thesis (41). Integral order kinetics were usually not obtained for the reaction of a number of ketones with piperidine and a number of secondary amines with cyclohexanone. A few of the combinations studied (cyclopentanone plus piperidine, pyrrolidine, and 4-methylpiperidine, and N-methylpiperazine plus cyclohexanone) gave reactions which were close to first-order in each reactant. Relative rates were based on the time at which a 50% yield of water was evolved. For the cyclohexanone-piperidine system the half-time (txn) for the 3 1 ratio was 124 min and for the 1 3 ratio 121 min. It appears that an... 

The half-life, f1/2, of a substance is the time needed for its concentration to fall to one-half its initial value. Knowing the half-lives of pollutants such as chlorofluoro-carbons allows us to assess their environmental impact. If their half-lives are short, they may not survive long enough to reach the stratosphere, where they can destroy ozone. Half-lives are also important in planning storage systems for radioactive materials, because the decay of radioactive nuclei is a first-order process. 

In homogeneous catalysis, the quantification of catalyst activities is commonly carried out by way of TOF or half-life. From a kinetic point of view, the comparison of different catalyst systems is only reasonable if, by giving a TOF, the reaction is zero order or, by giving a half-time, it is a first-order reaction. Only in those cases is the quantification of activity independent of the substrate concentration utilized ... 

Cytochrome P-450 from rat or human liver microsome preparations is inactivated when incubated anaerobically with carbon tetrachloride in the presence of NADPH and an oxygen-scavenging system (Manno et al. 1988 1992). Inactivation involved destruction of the heme tetrapyrrolic structure, and followed pseudo first-order kinetics with fast and slow half lives of 4.0 and 29.8 minutes. When compared with rat liver microsomes, the human preparations were 6-7 times faster at metabolizing carbon tetrachloride, and only about one- eighth as susceptible to suicide inactivation (about 1 enzyme molecule lost for every 196 carbon tetrachloride molecules metabolized). 

Figure 18.7 (a) Relative concentration as a function of the nondimen-sional radius, r = r/r0 and the non-dimensional time, t = Dt/t2 (D diffusion coefficient), see Eq. 18-33. C°, C° initial concentration inside and outside the sphere, respectively. The concentration in B is kept constant. (b) Relative mass exchange between system B (environment) and system A (sphere) as a function of the nondimensional time t (Eq. 18-35). MM is the maximum possible mass exchange which is achieved if CA (r,f)= C°. At t m = 0.03, half of the potential mass exchange has occurred. The curve named first-order mass exchange model is discussed in Chapter 19.5. Adapted from Carslaw and Jaeger (1959). 

A 0.500 L reaction vessel equipped with a movable piston is filled completely with a 3.00% aqueous solution of hydrogen peroxide. The H202 decomposes to water and 02 gas in a first-order reaction that has a half-life of 10.7 h. As the reaction proceeds, the gas formed pushes the piston against a constant external atmospheric pressure of 738 mm Hg. Calculate the PV work done (in joules) after a reaction time of 4.02 h. (You may assume that the density of the solution is 1.00 g/mL and that the temperature of the system is maintained at 20°C.)... 

In this equation, 0.693 is a constant obtained during the derivation of the formula (log 0.5). If we substitute our hypothetical values as used above, we would obtain a t112 of approximately 14 minutes. This is an important value to know since the time required to reach a steady-state plateau, and maintain it, depends only on the half-life of the drug. In our case, therefore, it would take approximately 70 minutes (i.e., 5 half-lives) to reach approximately 97 percent of steady state. In first-order reactions t112 is independent of dose, since, under normal circumstances, i.e., therapeutic, the system is not saturated since dosage is in the subgram amount. 

CS is rapidly absorbed and distributed throughout the body after inhalation exposure. Pharmacokinetic studies show that CS is removed from circulation quickly with first-order kinetics, following inhalation exposure. CS half-life is just under 30 s (Olajos, 2004). Short half-lives in the circulatory system are also demonstrated for the major CS metabolites (2-chlorobenzyl malononitrile and 2-chlorobenzaldehyde) (Leadbeater, 1973). Currently, it is thought that significant amounts of CS, near the tolerable concentration around 10 mg/m, would not be absorbed following CS inhalation. The absorption of CS from the digestive tract in cases of exposure by ingestion is unknown at this time. Systemic toxicity... 

Dynamically raised processes in the dispersion, such as Brownian molecular motion, cause variations in the intensities of the scattered light with time, which is measured by PCS. Smaller the particle, higher the fluctuations by Brownian motion. Thus, a correlation between the different intensities measured is only possible for short time intervals. In a monodisperse system following first-order kinetics, the autocorrelation function decreases rather fast. In a half logarithmic plot of the auto correlation function, the slope of the graph enables the calculation of the hydrodynamic radius by the Stokes-Einstein equation. With the commercial PCS devices the z-average is determined, which corresponds to the hydrodynamic radius. 

Most elementary reactions involve either one or two reactants. Elementaiy reactions involving three species are infrequent, because the likelihood of simultaneous three-body encounter is small. In closed, well-mixed chemical systems, the integration of rate equations is straightforward. Results of integration for some important rate laws are listed in Table 2.7, which gives the concentration of reactant A as a function of time. First-order reactions are particularly simple the rate constant k has units of s , and its reciprocal value (1/k) provides a measure of a characteristic time for reaction. It is common to speak in terms of the half-life ( 1/2) for reaction, the time required for 50% of the reactant to be consumed. When... 

Whereas radioactive decay is never a reversible reaction, many first-order chemical reactions are reversible. In this case the characteristic life time is determined by the sum of the forward and reverse reaction rate constants (Table 9.5). The reason for this maybe understood by a simple thought experiment. Consider two reactions that have the same rate constant driving them to the right, but one is irreversible and one is reversible (e.g. k in first-order equation (a) of Table 9.5 and ki in first-order reversible equation (b) of the same table). The characteristic time to steady state tvill be shorter for the reversible reaction because the difference between the initial and final concentrations of the reactant has to be less if the reaction goes both ways. In the irreversible case all reactant will be consumed in the irreversible case the system tvill come to an equilibrium in which the reactant will be of some greater value. The difference in the characteristic life time between the two examples is determined by the magnitude of the reverse reaction rate constant, k. If k were zero the characteristic life times for the reversible and irreversible reactions would be the same. If k = k+ then the characteristic time for the reversible reaction is half that of the irreversible rate. 

The advantages of using non-compartmental methods for calculating pharmacokinetic parameters, such as systemic clearance (CZg), volume of distribution (Vd(area))/ systemic availability (F) and mean residence time (MRT), are that they can be applied to any route of administration and do not entail the selection of a compartmental pharmacokinetic model. The important assumption made, however, is that the absorption and disposition processes for the drug being studied obey first-order (linear) pharmacokinetic behaviour. The first-order elimination rate constant (and half-life) of the drug can be calculated by regression analysis of the terminal four to six measured plasma... 

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