Time required to reach half

Figure 2.3 Plot of the three phases of SPMD uptake, illustrating first-order exchange kinetics. Time is given in halflives or ti/2, which in this case is the time required to reach half of the equilibrium concentration of a chemical. This figure is reproduced courtesy of the American Petroleum Institute (Huckins et al., 2002).

Ca sensitivity is taken as the ratio of the time required to reach half-maximal superprecipitation in the absence of Ca + to that in the presence of Ca. Values for original cardiac troponins ranged from 20 to 27. For other details see Ebashi (1974a,b). 

Figure 3. The time required to reach half of the steady-state current Is plotted against the position of the electrode from the center of the tube. The asterisk symbol represents a single measurement whereas the solid line is that predicted by pure convection.

From the increase in H invariant with time (see Figure 5.35) after a temperature drop from 150 °C, it is possible to estimate the rate of crystallization for example, ti/2, where ti/2 is the time required to reach half of the invariant s maximum level. The rate of crystallization described by ri/2 as a function of crystallization temperature is plotted in Figure 5.36 notably, crystallization is faster at lower temperatures. 

Equation links time and concentration through the rate constant, and Equation links the rate constant to the half-life. Knowing a half-life, we can calculate the rate constant using Equation. Then the value of the rate constant and Equation can be used to determine the time required to reach a certain concentration. 

So U depends on the time, called the blend time, and on k. The longer the blend time, the higher the uniformity. The blend time to achieve U = 99 %, which is considered sufficient for many cases, t99, ranges from seconds in small reactors to minutes in large reactors of tens of cubic metres volume. A uniformity of 90 % is achieved at only half the mixing time required to reach U = 99% while mixing to a uniformity of 99.9999 % requires three times as much mixing time... 

Given the half-life or rate constant and the initial concentration, calculate the time required to reach a specified lower concentration. 

Principle Chlorophyll fluorescence is a sensitive and early indicator of damage to photosynthesis and to the physiology of the plant resulting from the effect of allelochemicals, which directly or indirectly affects the function of photosystem II (Bolhar-Nordenkemf et ah, 1989, Krause and Weiss 1991). This approach is convenient for a photosynthesis analysis in situ and in vivo and quick detection of otherwise invisible leaf damage. The photosynthetic plant efficiency was measured using the method of induced chlorophyll fluorescence kinetics of photosystem II [Fo, non-variable fluorescence Fm, maximum fluorescence Fv=Fm-Fo, variable fluorescence t /2, half the time required to reach maximum fluorescence from Fo to Fm and photosynthetic efficiency Fv/Fm]. 

N2 injection rapidly increases the methane production rate. The timing and magnitude depends on the distance between injection and production wells, on the natural fracture porosity and permeability, and on the sorption properties. N2 breakthrough at the production well occurs at about half the time required to reach the maximum methane production rate in this ideal case. The N2 content of the produced gas continues to increase until it becomes excessive, i.e., 50% or greater. 

Roughly half of the data on the activities of electrolytes in aqueous solutions and most of the data for nonelectrolytes, have been obtained by isopiestic technique. It has two main disadvantages. A great deal of skill and time is needed to obtain reliable data in this way. It is impractical to measure vapor pressures of solutions much below one molal by the isopiestic technique because of the length of time required to reach equilibrium. This is generally sufficient to permit the calculation of activity coefficients of nonelectrolytes, but the calculation for electrolytes requires data at lower concentrations, which must be obtained by other means. 

The time required to reach steady-state accumulation during multiple constant dosing depends on the rate of elimination. As a rule of thumb, a plateau is reached after approximately three elimination half-lives (ti/2). 

The half-life (t V2) of a drug is the time taken for the amount of a drug in the body to fall to one half of its original value. It is useful as it determines the amount of time taken for the body to eliminate a drug and also determines the time required to reach steady-state concentrations of drug following continuous administration. It is calculated from the following equation ... 

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. 

The complete data on the l-butene-NOa system (see Table II) are scattered because of the varying l-butene NO ratios in these runs, but certain trends are apparent. Adding CO decreased the time required to reach the NO2 maximum concentration and the half-life of the 1-butene. Also the amount of O3 produced seemed to increase with increasing CO concentration. The data also show that adding water vapor decreased the peak ozone concentration this result agrees with the results of Wilson and Levy (13) who also observed that less ozone was produced by irradiating 1-butene with NO. at higher relative humidities. 

The kinetics of the oxidation of iodide by the oxidized state of c -[Ru (dcbpy)2-(NCS)2] sensitizer adsorbed on nanocrystalline Ti02 films was measured by transient laser spectroscopy [92]. Figure 16 shows the transient absorption kinetics recorded in propylene carbonate with various electrolytes added. In all cases, the recovery of the ground-state absorption of the dye, after the fast electron injection into the solid, does not follow a simple kinetic law. In the absence of any electrolyte (trace a), the time needed to reach half of the initial absorbance (/1/2) through back electron transfer is 2 ps. Total recovery of the initial absorption, however, requires several hundreds of microseconds to milliseconds. Traces b, c, and d were recorded after addition of a common concentration of 0.1 m of iodide in the form of tetra-butylammonium (TBA+), Li+, and Mg + salts, respectively. Addition of the electrolyte in all three cases led to a considerable acceleration of the dye regeneration with ti/2 < 200 ns and complete suppression of the slow kinetic tail. 

Intramuscular injections of scopolamine hydrobromide at 26 pg/kg and of atropine sulfate at 175 ug/kg Induced approximately equal decrements In performance In the Number Facility Test, except that the maximal effect after scopolamine was attained in about half the time required to reach that after atropine. Intravenously Injected scopolamine hydrobromide produced Its maximal effect even more rapidly than that Injected Intramuscularly. Scopolamine mett lbromlde was slower In exerting Its maximal tachycardlsd. effect than scopolamine faydrobromlde, but no Information about the rapidity of Its action on performance In the Number Facility Test was provided In any of the three reports (24,165,166). The Increase In heart rate Induced by scopolamine methylbromlde was greater than those Induced by the same amounts of scopolamine hydrobromide or atropine sulfate. 

The reaction half time t- j2 is the time required to reach 50% attainment of equilibrium (F = 0.5). The half times for particle and film diffusion control are equal when both mechanisms proceed at the same rate in which case the ratio of the i/2 values will equal unity. Under infinite volume boundary conditions and counter-ions of equal mobility a dimensionless rate parameter is obtained from equations 6.12 and 6.21 given by ... 

As we did in Example 26-3, we determine the specific rate constant k from the known half-life. The time required to reach the present fraction of the original activity is then calculated from the first-order decay equation. 

GHB exhibits zero-order (constant rate) elimination kinetics after an intravenous dose. Since GHB exhibits zero-order kinetics, it has no true half-life. The time required to eliminate half of a given dose increases as the dose increases. A daily therapeutic dose of 25 mg kg has an apparent half-life of about 30 min in humans, as determined in alcohol dependent patients under GHB treatment (Ferrara et al., 1992). In contrast, an apparent half-life of 1-2 h was observed in dogs when they were given high intravenous doses of GHB. In humans it has been documented that there is increased rate of absorption if GHB is administered on an empty stomach, resulting in a reduced time to reach the maximum plasma concentration of GHB (Borgen et al., 2001). 

By increasing the temperature from 25°C to 85°C, the time required to reach the maximum cure rate has been decreased by one-half. In all photoinitiated cationic polymerizations employing either diaryl iodoni urn or triarylsulfoniurn salt photoinitiators, cure at the highest temperature the substrate will allow will give the highest cure rates. Obviously, certain trade offs must be made between the cure temperature and loss of the monomer through volatilization. 

Half-life is the time required for serum concentrations to decrease by one-half after absorption and distribution are complete. Half-life is important because it determines the time required to reach steady state and the dosage interval. Half-life is a dependent kinetic variable because its value depends on the values of clearance and volume of distribution. 

The half-life is a useful kinetic parameter for therapeutic molecules, as it defines the dosing interval at which drugs should be administered. Half-life also describes the time required to reach steady state, or to decay from steady-state conditions after a change in the administration regimen. However, as an indicator of the processes involved in drug elimination or distribution the half-life has only limited value. It must be mentioned that, for many proteins and peptides, the glomerular filtration rate is high, and has more impact on the elimination of a biopharmaceutical than does the hepatic first-pass effect [7]. 

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