Zero-time concentrations

Table 1 Anticipated zero-time concentrations (mg kg ) as a function of soil core length...

Bound residues of tetracyclines may occur in bones of slaughtered animals for months after treatment. Theoretically, these could reach the food chain via contaminated (mechanically deboned) meat or meat and bonemeal. The accumulation of tetracyclines in tissues is illustrated by the findings of Toutain and Raynaud for oxytetracycline in calves (Table 2.8). Concentrations of oxytetracycline were relatively high in liver and kidney compared to the extrapolated zero-time concentration for serum (4.2 mg/1). The time required for residues to deplete to 0.1 mg/1 in serum was 143 hr, considerably shorter than the time required for residues to deplete to 0.1 mg/kg in liver and kidney, but similar to the depletion time for muscle. The data nicely illustrate the importance of tissue elimination half-life in determining decrease to the 0.1 mg/kg concentration despite an almost three-fold higher initial concentration... 

Formulation 20 mg/kg of a 20% w/v solution. Extrapolated zero-time concentration. 

The nitric acid used in this work contained 10% of water, which introduced a considerable proportion of acetic acid into the medium. Further dilution of the solvent wnth acetic acid up to a concentration of 50 moles % had no effect on the rate, but the addition of yet more acetic acid decreased the rate, and in the absence of acetic anhydride there was no observed reaction. It was supposed from these results that the adventitious acetic acid would have no effect. The rate coefficients of the nitration diminished rapidly with time in one experiment the value of k was reduced by a factor of 2 in i h. Corrected values were obtained by extrapolation to zero time. The author ascribed the decrease to the conversion of acetyl nitrate into tetranitromethane, but this conversion cannot be the explanation because independent studies agree in concluding that it is too slow ( 5.3.1). 

In the case of tracer from a vessel that contained an initial average concentration C°, the area under a plot of E(t) = Cgff[ygj,/C° between the ordinates at tj and tj is the fraction of the molecules that have residence times in this range. In the case of step constant input of concentration Cf to a vessel with zero initial concentration, the ratio F(t) = Cgff ygj,/Cf at tj is the fraction of molecules with residence time less than tj. 

With Eq. (2-42) the first-order rate constant can be calculated from concentrations at any two times. Of course, usually concentrations are measured at many times during the course of a reaction, and then one has choices in the way the estimates will be calculated. One possibility is to let r, be zero time for all calculations in this case the same value c° is employed in each calculation, so error in this quantity is transmitted to each rate constant estimate. Another possibility is to apply Eq. (2-42) to successive time intervals. If, as often happens, the time intervals are all... 

Since a first-order rate constant does not depend on [A]o, one need not know either the initial concentration or the exact instant at which the reaction began. This characteristic should not be used to rationalize experimentation on impure materials. These features do allow, however, a procedure in which measurements of slower reactions are not taken until the sample has reached temperature equilibrium with the thermostating bath. The first sample is simply designated as t = 0. Likewise, for rapidly decaying reaction transients, knowing the true zero time is immaterial. 

We emphasize that the conditions subscripted with a zero (time, initiator and monomer concentration) are not the beginning of a reaction, but rather some point well advanced in the polymerization process when the remaining amount of monomer is small in absolute terms but large compared to the desired end state of the polymerization (Mg M ). The amount of initiator Ig is to be achieved by addition to any present immediately before time zero, and the final monomer concentration, M, is set by production specifications. We do not set any predetennined bounds on upper and lower temperature limits. In practice the upper limit will be detennined by either reaction variables (depropagation and initiator depletion) or by process variables (heat exchange), while the lower temperature limit will be determined by process variables (solubility, heat exchange). We do not here consider the process variables to be constraints. 

No indication is given of the reaction of Co(ril) polymers although these are present in the reaction solutions . It is noteworthy that the intercepts of the above plots do not coincide with the values obtained from the initial Fe(ri) concentration. The zero-time oxidation is believed to arise from a finite quenching time together with a rapid reaction of hydrolysed species of the reactants. The rate of reaction is inversely proportional to the concentration of hydrogen ions. This result is taken as implying competitive reactions between CoOH -t-Fe and Co " -l-Fe, as described by the rate law... 

However, the intercepts of log [Fe(II)]/[Ce(IV)] versus time plots deviate from the values expected for the initial concentrations of the reactants. This apparent zero-time oxidation , which is reproducible, is believed to result from a finite quenching time, and the reaction of Fe(ll) with a very reactive Ce(IV) species. Added amounts of Ce(III) and Fe(lII) leave the rate unaffected. At constant ionic strength, k varies inversely with hydrogen-ion concentration in the range 0.05 to 1.00 M for [H" "] > 1.0 M, k increases with increasing In general... 

By measuring the optical rotation as it changes with time, after a gelatin solution is rapidly cooled to the temperature of interest, and extrapolating back to zero time, one can determine the initial specific rotation. It is approximately constant with the concentration, but varies with temperature. This initial specific rotation probably represents that of the sol molecule at that temperature before it is converted into the gel form. 

The relation between E and t is S-shaped (curve 2 in Fig. 12.10). In the initial part we see the nonfaradaic charging current. The faradaic process starts when certain values of potential are attained, and a typical potential arrest arises in the curve. When zero reactant concentration is approached, the potential again moves strongly in the negative direction (toward potentials where a new electrode reaction will start, e.g., cathodic hydrogen evolution). It thus becomes possible to determine the transition time fiinj precisely. Knowing this time, we can use Eq. (11.9) to find the reactant s bulk concentration or, when the concentration is known, its diffusion coefficient. 

For example, the expected zero-time soil concentration (Co) of a compound applied at a rate of 2.2kga.i.ha would be calculated by dividing the application rate (mga.i.ha ) by the total weight of a 15-cm depth of soil. Assuming a soil bulk density of 1500 kg m , the total weight of a 15-cm layer of soil is 2.24 x 10 kgha ... 

Proper sample collection and handling are the key to acceptable agrochemical recovery at zero time. The zero-time sample interval is defined as the first sample collected after application. Zero-time soil samples should be collected within 3h after application. Zero-time soil core concentrations, such as those given in Table 3,... 

Table 3 Summary of zero-time soil concentration and application verification (AV) monitor results for Pyraclostrobin applied at two field sites... 

Empirical evidence supporting the role of soil micro-layer losses in zero-time issues is given by the often-seen rise in post zero-time residue recoveries. The improved recoveries likely result from the micro-layer residue redistribution that reduces losses of the highly concentrated surface residues. There has been some speculation that zerotime core recoveries may be due to volatilization losses not measured by standard laboratory studies. If this were the case, however, increases in residue concentrations would not occur over time since volatilized residues would be lost to the atmosphere. ... 

In PAMPA measurements each well is usually a one-point-in-time (single-timepoint) sample. By contrast, in the conventional multitimepoint Caco-2 assay, the acceptor solution is frequently replaced with fresh buffer solution so that the solution in contact with the membrane contains no more than a few percent of the total sample concentration at any time. This condition can be called a physically maintained sink. Under pseudo-steady state (when a practically linear solute concentration gradient is established in the membrane phase see Chapter 2), lipophilic molecules will distribute into the cell monolayer in accordance with the effective membrane-buffer partition coefficient, even when the acceptor solution contains nearly zero sample concentration (due to the physical sink). If the physical sink is maintained indefinitely, then eventually, all of the sample will be depleted from both the donor and membrane compartments, as the flux approaches zero (Chapter 2). In conventional Caco-2 data analysis, a very simple equation [Eq. (7.10) or (7.11)] is used to calculate the permeability coefficient. But when combinatorial (i.e., lipophilic) compounds are screened, this equation is often invalid, since a considerable portion of the molecules partitions into the membrane phase during the multitimepoint measurements. 

The potential-decay method can be included in this group. Either a current is passed through the electrode for a certain period of time or the electrode is simply immersed in the solution and the dependence of the electrode potential on time is recorded in the currentless state. At a given electrolyte composition, various cathodic and anodic processes (e.g. anodic dissolution of the electrode) can proceed at the electrode simultaneously. The sum of their partial currents plus the charging current is equal to zero. As concentration changes thus occur in the electrolyte, the rates of the partial electrode reactions change along with the value of the electrode potential. The electrode potential has the character of a mixed potential (see Section 5.8.4). 

Figure 5 shows the diffusion of a solute into such an impermeable membrane. The membrane initially contains no solute. At time zero, the concentration of the solute at z = 0 is suddenly increased to c, and maintained at this level. Equilibrium is assumed at the interface of the solution and the membrane. Therefore, the corresponding membrane concentration at z = 0 is Kc1. Since the membrane is impermeable, the concentration on the other side will not be affected by the change at z = 0 and will still be free of solute. This abrupt increase produces a time-dependent concentration profile as the solute penetrates into the membrane. If the solution is assumed to be dilute, Fick s second law Eq. (9) is applicable ... 

Figure 5 Diffusion into a semi-infinite membrane. The membrane initially contains no solute. At time zero, the concentration of the solution at z = 0 is suddenly increased to and maintained at cx. This abrupt increase produces time-dependent concentration profiles as the solute penetrates into the membrane.

In this section we want to discuss unsteady diffusion across a permeable membrane. In other words, we are interested in how concentration and flux change before reaching the steady state discussed in Section IV.B. The membrane is initially free of solute. At time zero, the concentrations on both sides of the membrane are increased, to C and c2. Equilibrium between the solution and the membrane interface is assumed therefore, the corresponding concentrations on the membrane surfaces are Kc, and Kc2. Fick s second law is still applicable ... 

Plots of the concentration of carboxylate formed vs. time were drawn for each copolymer, and the initial rates of hydrolysis were determined by measurement of the slope of the tangent to the curve at zero time. The pseudo-unimolecular rate constant (K) is given by ... 

Yoshimura et al. [132] studied the pharmacokinetics of primaquine in calves of 180—300 kg live weight. The drug was injected at 0.29 mg/kg (0.51 mg/kg as primaquine diphosphate) intravenously or subcutaneously and the plasma concentrations of primaquine and its metabolite carboxyprimaquine were determined by high performance liquid chromatography. The extrapolated concentration of primaquine at zero time after the intravenous administration was 0.5 0.48 pg/mL which decreased with an elimination half-life of 0.16 0.07 h. Primaquine was rapidly converted to carboxyprimaquine after either route of administration. The peak concentration of carboxyprimaquine was 0.5 0.08 pg/mL at 1.67 0.15 h after intravenous administration. The corresponding value was 0.47 0.07 pg/mL at 5.05 1.2 h after subcutaneous administration. The elimination half-lives of carboxyprimaquine after intravenous and subcutaneous administration were 15.06 0.99 h and 12.26 3.6 h, respectively. 

---