Half-order kinetic relationship

In addition to the elimination rate constant, the half-life (T/i) another important parameter that characterizes the time-course of chemical compounds in the body. The elimination half-life (t-1/2) is the time to reduce the concentration of a chemical in plasma to half of its original level. The relationship of half-life to the elimination rate constant is ti/2 = 0.693/ki,i and, therefore, the half-life of a chemical compound can be determined after the determination of k j from the slope of the line. The half-life can also be determined through visual inspection from the log C versus time plot (Fig. 5.40). For compounds that are eliminated through first-order kinetics, the time required for the plasma concentration to be decreased by one half is constant. It is impottant to understand that the half-life of chemicals that are eliminated by first-order kinetics is independent of dose. ... 

Drug elimination may not be first order at high doses due to saturation of the capacity of the elimination processes. When this occurs, a reduction in the slope of the elimination curve is observed since elimination is governed by the relationship Vmax/(Km- -[conc]), where Vmax is the maximal rate of elimination, Km is the concentration at which the process runs at half maximal speed, and [cone] is the concentration of the drug. However, once the concentration falls below saturating levels first-order kinetics prevail. Once the saturating levels of drugs fall to ones eliminated via first-order kinetics, the half time can be measured from the linear portion of the In pt versus time relationship. Most elimination processes can be estimated by a one compartment model. This compartment can... 

Studies on workers in an occupational setting showed a dose-response relationship between the concentration of acrylonitrile of inspired air and the recovery of metabolites in the urine (Houthuijs et al. 1982 Sakurai et al. 1978). In a controlled study using human volunteers, urinary metabolite data suggested that the elimination of acrylonitrile followed first-order kinetics, with a half- life of seven to eight hours (Jakubowski et al. 1987). 

At 2 h after dosing, the plasma concentration was 4.6 mg/mL at 5 h, the concentration was 2.4 mg/mL. Therefore, the plasma concentration of this aminoglycoside decreased to one-half in approximately 3 h—its half-life. In addition, drug elimination usually occurs according to first-order kinetics (i.e., a linear relationship is obtained when the drug concentration is plotted on a logarithmic scale vs. time on an arithmetic scale (a semilogarithmic plot)]. 

Phenyltrimethyldisilene (15) and (E)- and (Z)-l,2-dimethyl-l,2-diphenyldisilene (16) were also observed as transient absorption spectra by laser flash photolysis of the precursors in methylcyclohexanes28. The absorption band at 380 nm, assigned to the disilene 15, reached maximum intensity at ca 10 ns after the excitation and then started to decrease. The half-life assigned to 15 was 700 ns. The logarithm of the decay profile of the transient absorption at 380 nm versus time shows a very good linear relationship, indicating that the decay of the transient absorption fits first-order kinetics. This result shows that intramolecular isomerization or proton abstraction from the solvent is the origin for the decay of the disilene 15, which survives in solution only for several nanoseconds. 

When first-order kinetics hold, a simple relationship exists between the penetration rate constant, K, and f0.s (time necessary for one-half of the applied dose to penetrate) ... 

Correct answer = D. Drugs with zero-order kinetics of elimination show a linear relationship between drug concentration and time. In most clinical situations the concentration of a drug is much less than the Michaelis-Menten constant (Km). A decrease in drug concentration is linear with time. The half-life of the drug increases with dose. A constant amount of drug is eliminated per unit time. 

The reactivity of the model phenols and benzyl alcohols with phenyl isocyanate was determined in the presence of a tertiary amine (DMCHA) and a tin catalyst (DBTDL) by measurement of the reaction kinetics. The experimental results based on initial equal concentrations of phenyl isocyanate and protic reactants showed that the catalyzed reactions followed second order reaction with respect to the disappearance of isocyanate groups (see Figure 1). It was also found that a linear relationship exists between the experimental rate constant kexp, and the initial concentration of the amine catalyst (see Figure 2). In the case of the tin catalyst, the reaction with respect to catalyst concentration was found to be one-half order (see Figures 3-4). A similar relationship for the tin catalyzed urethane reaction was found by Borkent... 

Drug information resources will not provide data on the elimination half-life of ethanol because, in the case of this drug, it is not constant. The elimination of ethanol follows zero-order kinetics because the drug is metabolized at a constant rate irrespective of its concentration in the blood (see Chapter 3). The pharmacokinetic relationship between elimination half-life, volume of distribution, and clearance, given by... 

The rates for sunlight-caused photodecomposition of picloram in aqueous solutions were determined by five experiments. The photolysis follows pseudo first-order kinetics for concentrations up to 4.14 X 10 M and in circulating solutions as deep as 3.65 m. Hazy sunlight and water impurities had only a small effect on rate in the systems in which they were studied. A linear relationship relates the photochemical half-life of picloram to solution depth for solutions from 0.292-. 65 m deep. 

For drugs that exhibit non-linear or dose dependent kinetics, the fundamental pharmacokinetic parameters such as clearance, the apparent volume of distribution and the elimination half life may vary depending on the administered dose. This is because one or more of the kinetic processes (absorption, distribution and/or elimination) of the drug may be occurring via a mechanism other than simple first-order kinetics. For these drugs, therefore, the relationship between the AUC or the plasma concentration at a given time at steady state and the administered dose is not linear (Fig. 15.2). 

First, it s important to realize that radioactivity is essentially a first-order kinetics problem. Knowing the percentage of counts as a fraction of that seen for living organisms allows us to set up the ratio, I/T, which is equal to e. To use this relationship, we need to know the value of k or of the half-life, and then we can solve Ibr time, f, which will be the age of the artifect. 

Equations 3 to 5 employ first-order, one-compartment kinetics constants where k, is the uptake constant, k-2 is the elimination constant, both in units of day", and T.,/2 is the half-life of elimination in days. These kinetics constants, derived from time-toxicity data, were regressed, via the geometric mean functional regression method, against log KQyj, producing a quantitative structure-kinetics relationship (QSKR) which is analogous to a QSAR. 

Radioactive decay is a first-order process. To relate it to the first-order kinetics that we studied in Chapter 20, think of the activity as corresponding to a rate of reaction the number of atoms as corresponding to the concentration of a reactant and the decay constant. A, as corresponding to a rate constant, k. This correspondence can be carried further by writing an integrated radioactive decay law and a relationship between the decay constant and the half-life of... 

Kinetics. Madinaveitia and Quibell (112) and McClean and Hale (106) stated that the reaction time R to the half-viscosity is independent of the substrate concentration and inversely proportional to the enzjrme concentration. Actually, a graph of the data (112) shows a linear relationship between R and enzyme concentration only for reaction times up to 20 minutes. Similar observations were made by Haas (57) and by Dorfman (26). It is obvious that the enzyme should be assayed at concentrations high enough to give reaction times R < 20 minutes in order to avoid serious errors. Dalgaard (23), for the same reason, used a reaction time of 300 seconds. 

While the studies performed provide a reasonably complete quantitative description of the kinetics of CT-3, the nature of this charge-transfer reaction has yet to be identified. The influence of pH upon the kinetics of this charge-transfer reaction have not been analysed in detail. However, preliminary indications are that this reaction exhibits a reaction order of one half with respect to the proton concentration. For reaction CT-3 at 25°C, the relationship between the logarithm of flux and potential is linear with a slope of -340 50 mV.decade ". The activation energy of reaction CT-3 was found to be 41 kJ.mor at a potential of -600 mV vs SCE. 

The kinetics of the electron-transfer reactions between oxalatocobalt(m) complexes and iron(n) have been described. For cationic complexes, the rates decrease in the order (ox = oxalate) [Co(ox)(phen)J+>[Co(ox)(bipy)2] > [Co(ox)(NH3)4]+> [Co(ox)(en)2]+> [Co(oxXtrien)]+ the variation in reactivity is attributed to changes in the enthalpy of activation, a linear relationship being observed between and log k (k = observed rate constant). The much faster reactions of the phenanthroline and bipyridyl complexes are also considered to derive from the eflSciency of these ligands as electron mediators in reactions of this type. A relationship has also been observed between log k and the half-wave potential of the polarographic reduction of the cobalt(iii)... 

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