Half-life concentration dependence

For second-order reactions, the half-life does depend on the reactant concentration. We calculate it using the following formula ... 

IM— iutramuscular Systemic availability may be less than 100%, reduced peak concentrations compared to IV administration, potentially delayed and reduced biologic effects, less invasive than IV route, half-life may depend on absorption... 

Unlike the first-order case, this half-life time depends on the initial concentration. This is not surprising For example, in the reaction A I A - products, two A molecules must collide, and this is more likely at higher [A]0 values. 

The insecticide aminocarb has also been used extensively in eastern Canada on budworm control operations. Fenitrothion has been applied as a water emulsion (New Brunswick) and an oil solution (Quebec), but aminocarb because of its formulation characteristics, has been only applied operationally as an oil solution. Analysis of spruce foliage (7) showed aminocarb had a half life of 5 to 6 days with complete disappearance by 64 days post spray. Subsequent work (8) confirmed the short half life of aminocarb on coniferous foliage (3.2 to 6.9 days), and showed that the half life was dependant on the initial concentration of the insecticide. The material was found to be highly labile and dissipated rapidly and the authors made the statement that with these characteristics... 

In spite of its instability in the liquid state, cobalt hydrocarbonyl can be carried from one vessel to another as a vapor highly diluted with carbon monoxide or any other inert gas at room temperature and pressure. A semiquantitative study of the rate of decomposition in both the vapor state and in hexane solution indicates that the half-life is dependent on the initial concentration (Sternberg, Wender, Friedel, and Orchin, 29). It can be absorbed in water at 0° and behaves as a strong mineral acid. The ionization provides a cobalt carbonyl anion ... 

The zero-order rate constant corresponds to the slope of the non-logarith-mic presentation of the kinetics. The respective half-life, however, depends on the concentration. Second-order kinetics are relevant for bimolecular reactions when the concentrations of both reactants are rate-determining. When the concentration of the environmental reaction partner is sufficiently large to be assumed to be constant as compared to the concentration of the contaminant, the kinetics are simplified to pseudo first order. 

For zero-order reactions, the half-life is dependent upon the initial concentration of the reactant. However, in contrast to the second-order reaction, as a zero-order reaction proceeds, each half-life gets shorter. 

Notice that, for a zero-order reaction, the half-life also depends on the initial concentration however, unlike in the second order case, the two are directly proportional—the half-life gets shorter as the concentration deaeases. 

The half-life is dependent on the concentration of initiator used. In general, the lower the molar concentration, the longer tv. ... 

Many proteins and enzymes within the cell appear to have a half-life that depends upon their amino acid structures. Alterations in the amino acid sequence may increase the liability to denaturation. Various mechanisms exist to stabilize the enzymes and protect them from the destabilizing factors in their environment. Destabilization becomes more evident when protein biosynthesis, which maintains the enzymes at a steady-state concentration, decreases for whatever reason. Thus, when there is decreased replacement of protein and enzymes, destabilization is aggravated by the loss of enzymes necessary to maintain the stabilizing systems. 

Commercial condensed phosphoric acids are mixtures of linear polyphosphoric acids made by the thermal process either direcdy or as a by-product of heat recovery. Wet-process acid may also be concentrated to - 70% P2O5 by evaporation. Liaear phosphoric acids are strongly hygroscopic and undergo viscosity changes and hydrolysis to less complex forms when exposed to moist air. Upon dissolution ia excess water, hydrolytic degradation to phosphoric acid occurs the hydrolysis rate is highly temperature-dependent. At 25°C, the half-life for the formation of phosphoric acid from the condensed forms is several days, whereas at 100°C the half-life is a matter of minutes. 

Disopyr mide. Disopyramide phosphate, a phenylacetamide analogue, is a racemic mixture. The dmg can be adininistered po or iv and is useful in the treatment of ventricular and supraventricular arrhythmias (1,2). After po administration, absorption is rapid and nearly complete (83%). Binding to plasma protein is concentration-dependent (35—95%), but at therapeutic concentrations of 2—4 lg/mL, about 50% is protein-bound. Peak plasma concentrations are achieved in 0.5—3 h. The dmg is metabolized in the fiver to a mono-AJ-dealkylated product that has antiarrhythmic activity. The elimination half-life of the dmg is 4—10 h. About 80% of the dose is excreted by the kidneys, 50% is unchanged and 50% as metabolites 15% is excreted into the bile (1,2). 

Time to peak plasma concentration depends on the rate of IV dosing but is usually achieved in 45—90 seconds. Therapeutic plasma concentrations are 1.5—5.0 )J.g/mL, and concentrations above 5 )J.g/mL maybe toxic. The elimination half-life after a bolus iv dose is 8 min the elimination half-life after a 24 h iv infusion is about 100 min. The dmg is eliminated by the kidneys. Ten percent is unchanged and the remainder is in the form of inactive metabolites... 

Nicardipine is almost completely absorbed after po adrninistration. Administration of food decreases absorption. It undergoes extensive first-pass metaboHsm in the Hver. Systemic availabiHty is dose-dependent because of saturation of hepatic metaboHc pathways. A 30 mg dose is - 35% bioavailable. Nicardipine is highly protein bound (>95%). Peak plasma concentrations are achieved in 0.5—2.0 h. The principal path of elimination is by hepatic metaboHsm by hydrolysis and oxidation. The metaboHtes are relatively inactive and exert no pharmacological activity. The elimination half-life is 8.6 h. About 60% of the dose is excreted in the urine as metaboHtes (<1% as intact dmg) and 35% as metaboHtes in the feces (1,2,98,99). 

The functional dependence of the half-life on reactant concentration varies with the reactant order. From the integrated rate equations we obtain these results ... 

On the basis of the general reaction scheme (see p. 248) the kinetic dependence is caused by the fact that the rate of the 8 2 reaction, Eq. (7), is dependent on the concentration of diazomethane but that the rate of the SkI reaction, Eq. (6), is not. (For unimolecular reactions, the half-life does not depend on the concentration but it does in the case of bimolecular reactions. We have, assuming fast pre-equilibrium ... 

Reality Check In (b), reducing the amount present to 15% takes more time than two half-lives (i.e., more than the time to reduce to 25%). The answer is larger than 2(6.60 X 103), as it should be. In (c), the rate is dependent on the initial concentration, unlike the half-life in (a)—which is independent of the initial amount... 

Dark Decay of UDMH in Air, UDMH was observed to undergo a gradual dark decay in the 30,000-liter Teflon chamber at a rate which depended on humidity. Specifically, at 41 C and 4% RH the observed UDMH half-life was " 9 hours (initial UDMH 4.4 ppm) and at 40 C and 15% RH, the half-life was -6 hours (initial UDMH 2.5 ppm). The only observed product of the UDMH dark decay was NH3, which accounted for only -5-10% of the UDMH lost. In particular, no nitrosamine, nitramine, or hydrazone were observed. Formaldehyde dimethyIhydrazone was observed in previous studies which employed higher UDMH concentrations and reaction vessels with relatively high surface/volume ratios (, ) ... 

The half-life is thus seen to depend on the initial concentration for the second order reaction considered. This is in contrast to first-order reaction where the half-life is independent of concentration. For this reason half-life is not a convenient way of expressing the rate constant of second-order reactions. 

PbB concentrations reflect the absorbed dose of lead. However, the interpretation of PbB data depends on a knowledge of the past history of exposure to lead. This is because in the body, bone constitutes the major lead sink and this results in lead having a long body half-life. Thus, in the absence of intense exposure to lead for a considerable period up to its body half-life, the PbB concentrations reflect recent lead exposures. However, if intermittent exposure to lead is occurring in several distinct environments, the PbB concentration reflects both recent and past exposures to lead. Thus, biological effects for populations with the same PbB concentrations may not be the same since different exposure times scales may be involved. This is the reason why free erythrocyte protoporphyrin (FEP) and erythrocyte zinc protoporphyrin (ZPP) have been used as additional biological markers since their elevation is more related to chronic lead exposure than acute lead exposure (see Section 2.7). 

The original proposal of the approach, supported by a Monte Carlo simulation study [36], has been further validated with both pre-clinical [38, 39] and clinical studies [40]. It has been shown to be robust and accurate, and is not highly dependent on the models used to fit the data. The method can give poor estimates of absorption or bioavailability in two sets of circumstances (i) when the compound shows nonlinear pharmacokinetics, which may happen when the plasma protein binding is nonlinear, or when the compound has cardiovascular activity that changes blood flow in a concentration-dependent manner or (ii) when the rate of absorption is slow, and hence flip-flop kinetics are observed, i.e., when the apparent terminal half-life is governed by the rate of drug input. 

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