Steady-state concentrations

Bromide ion acts as an inliibitor through step (9) which competes for HBr02 with the rate detennining step for the autocatalytic process described previously, step (4) and step (5). Step (8) and Step (9) constitute a pseudo-first-order removal of Br with HBr02 maintained in a low steady-state concentration. Only once [Br ] < [Br ] = /fo[Br07]//r2 does step (3) become effective, initiating the autocatalytic growth and oxidation. 

Figure A3.14.3. Example bifurcation diagrams, showing dependence of steady-state concentration in an open system on some experimental parameter such as residence time (inverse flow rate) (a) monotonic dependence (b) bistability (c) tristability (d) isola and (e) musliroom.

The distributions of excess, or injected, carriers are indicated in band diagrams by so-called quasi-Fenni levels for electrons or holes (Afp). These functions describe steady state concentrations of excess carriers in the same fonn as the equilibrium concentration. In equilibrium we have... 

As the temperature approaches the NTC zone, the reversibility of reaction 2 comes into play and the steady-state concentration of alkyl radicals rises. There is a competing irreversible reaction of oxygen with radicals containing an alpha hydrogen which produces a conjugate olefin (eq. 23). 

Once the steady-state concentration is known, the rate of dmg clearance determines how frequendy the dmg must be adininistered. Because most dmg elimination systems do not achieve saturation under therapeutic dosing regimens, clearance is independent of plasma concentration of the dmg. This first-order elimination of many dmgs means that a constant fraction of dmg is eliminated per unit time. In the simplest case, clearance can be deterrnined by the dose and the area under the curve (AUC) describing dmg concentration as a function of total time ... 

The variables are separable, but the plot is of a numerical solution. The steady state concentration is 1.1736. 

FIG. 24-24 Effect of recycle on steady-state concentrations of cell mass and limiting nutrient. 5-fold increase in cell concentration in separator. SiiLscripts denote fraction of cell concentrate recycled. 

Hydrophilic substances and/or compounds with a relatively high reactivity, present at a steady-state concentration in biota due to high external exposures. 

Is reactant accumulation possible Steady state concentrations Reaction calorimetry combined with analysis... 

It is important to emphasize that direet studies sueh as those earned out on the eyelopropylmethyl radieal ean be done with low steady-state eoneentrations of the radical. In the case of the study of the eyelopropylmethyl radical, removal of the source of irradiation leads to rapid disappearance of the EPR spectrum, because the radicals react rapidly and are not replaced by continuing radical formation. Under many conditions, the steady-state concentration of a radical intermediate may be too low to permit direct detection. Failure to observe an EPR signal, therefore, cannot be taken as conclusive evidence against a radical intermediate. 

Theoretical volume of distribution (Vj) of a chemical is the volume in which the chemical would be distributed if its concentration were equal to a theoretical steady-state plasma concentration (Cq) at time zero. The volume of distribution is thus obtained quite similarly as the steady state concentration of a compound in the workroom air ... 

VOCs are released during chemical cleaning of bonding surfaces. The extract system is designed on the basis of the steady-state concentration determined for maximum source strength and considering the mechanical extract ventilation only and no air-exchange with the assembly hail. Ehis concentration must be kept below the threshold concentration (TVL) which is set to 300 mg/kg in this example. 

Of course it is also possible for a reaction system not to belong to any of these classes of approximate description.) Only in class III can equilibrium be said to be a special case of the steady-state treatment. Note that, for class III systems, the steady-state concentration of intermediate is very large,whereas for class I it is very small. Zuman and Patel have discussed the equilibrium and steady-state approximations in terms similar to the present treatment. 

FIGURE 18.12 The use of inhibitors to reveal the sequence of reactions in a metabolic pathway, (a) Control Under normal conditions, the steady-state concentrations of a series of intermediates will be determined by the relative activities of the enzymes in the pathway, (b) Plus inhibitor In the presence of an inhibitor (in this case, an inhibitor of enzyme 4), intermediates upstream of the metabolic block (B, C, and D) accumulate, revealing themselves as intermediates in the pathway. The concentration of intermediates lying downstream (E and F) will fall. 

Steady-State Concentrations of Glycolytic Metabolites in Erythrocytes... 

The carbon-14 formed by this nuclear reaction is eventually incorporated into the carbon dioxide of the air. A steady-state concentration, amounting to about one atom of carbon-14 for every 1012 atoms of carbon-12, is established in atmospheric C02. More specifically, the concentration of C-14 is such that a sample containing one gram of carbon has an activity of 15.3 atoms/min. A living plant, taking in carbon dioxide, has this same activity, as do planteating animals or human beings. 

FIGURE 2.23 Schematic diagram showing the routes of possible removal of drug from the receptor compartment. Upon diffusion into the compartment, the drug may be removed by passive adsorption en route. This will cause a constant decrease in the steady-state concentration of the drag at the site of the receptor until the adsorption process is saturated. 

If the entry of a molecule into the body were simply a temporally restricted absorption process, then a steady-state concentration would be achieved given enough time for complete absorption. However, what in fact is observed in drug pharmacokinetics is a complex curve reflecting absorption of the drug into the body and the diminution of the concentration that is absorbed back down to negligible levels. The reason for this complex pattern of rise and fall in... 

FIGURE 8.25 Repeated oral administration of drags leads to steady-state plasma concentrations. If elimination is rapid and administration not often enough, then an elevated and therapeutically effective steady-state concentration may not be achieved (green lines). In contrast, if elimination is very slow (or administration too often), then an accumulation of the drag may be observed with no constant steady state (red line). Bine line shows a correct balance between frequency of administration and elimination. 

Anastrazole is a nonsteroidal, type H, aromatase inhibitor that is 200 times more potent than aminoglutethimide. It is eliminated primarily via hqDatic metabolism, has a terminal half life of 50 h with steady state concentrations achieved approximately 10 days with once daily dosing regimens. It is administered orally at a dose of 1 mg/day that achieves near maximal aromatase inhibition and hence estrogen suppression in breast cancer patients. No effect on adrenal steroidogenesis has been observed at up to ten times the daily recommended dose. When used in the metastatic setting, anastrozole has been shown... 

If a drug is given repetitively with a constant dose (D) and a constant administration interval (Tau) accumulation occurs until a steady-state concentration (Css) is obtained after 4.32 times the elimination half-life (/ss -4.32 Tl/2). 

The kinetics and mechanism of living radical polymerization have been reviewed by Fischer,21 Fukuda et at.,22 and Goto and Fuktida.23 In conventional radical polymerization, new chains are continually formed through initiation w hile existing chains are destroyed by radical-radical termination. The steady state concentration of propagating radicals is 10"7 M and an individual chain will have a lifetime of only 1-10 s before termination within a total reaction lime that is... 

Monomers not amenable to direct homopolymerization using a particular reagent can sometimes be copolymcrizcd. For example, NMP often fails with methacrylates (e.g. MMA, BMA), yet copolymerizalions of these monomers with S are possible even when the monomer mix is predominantly composed of the methacrylate monomer,15j This is attributed to the facility of cross propagation and the relatively low steady state concentration of propagating radicals with a terminal MMA (Section 7.4.3.1). MMA can also be copolymerized with S or acrylates at low temperature (60 C).111 Under these conditions, only deactivation of propagating radicals with a terminal MMA unit is reversible, deactivation of chains with a terminal S or acrylate unit is irreversible. Molecular weights should then be controlled by the reactivity ratios and the comonomer concentration rather than by the nitroxide/alkoxyamine concentration. 

As in the case of diazotization by N203 (Sec. 3.1), either the formation of XNO or the nitrosation of the amine (or of the aminium ion) may be rate-limiting. Under most experimental conditions the second alternative applies. If a steady-state concentration of XNO exists (which is however, not always the case) the reaction system of Schemes 3-26 and 3-27 yields the rate equation shown in Scheme 3-29 if it is the amine base (ArNH2) that is nitrosated. Xa is the acidity constant of the conjugate acid (ArNH3). 

Applying the steady-state approximation to both [VI] and [VIII] one obtains (29) for the steady-state concentration of VI and (30) for the steady-state concentration of VIII, viz. 

EPR spectroscopy is usually used to calibrate the clock (i.e., to determine kc). The method described here uses EPR to detect the two radicals. These are the parent (R1 ) and the product (R2 ) of its reaction, be it cyclization, decarbonylation, decarboxylation, rearrangement, or whatever. The radical R1 is produced photochemi-cally in the desired inert solvent by steady and usually quite intense light irradiation of the EPR cavity. Typically, R1 and R2 attain steady-state concentrations of 10-8 to 10 6 M. 

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