Concentration time plots

The initial screening of the resin catalysts was done in a batch reactor at supercritical for butene-1 conditions of temperature 155 °C, pressure of 1000 psig and at molar ratio of 1-butene water of 5.5. The reaction was stopped after predetermined period of time and the products analyzed. It was found that under the standard reaction conditions, for all of the catalysts studied, a constant concentration in the sec-butanol concentration was achieved within a 1-2 hour reaction time. Using only the linear section of the concentration-time plot, the one hour result was used to evaluate the catalyst activity, which was normalized as mmol of SBA/ per proton/ per hour (a), as mmol of product/ per gram of dry catalyst/ per hour (b) and mmol of product/ per ml of wet catalyst/ per hour (c). 

Identical doses of a capsule preparation (X) and a tablet preparation (Y) of the same drug were compared on a blood concentration-time plot with respect to peak concentration, time to peak concentration, and AUC after oral administration as shown in the figure below This comparison was made to determine which of the following ... 

The oxidation of methyl tolyl sulfoxide, a representative substrate, was monitored by the buildup of the sulfoxide as a function of time under many sets of conditions (42). A representative concentration time plot is presented in Pig. 1. In this case, and in all the others, the buildup curves showed similar features, the most noticeable of which is a distinct induction period. Its length depends on the concentrations, decreasing with increasing [Bu OOH] and [1], At the same time the rate itself was... 

Fig. 2. Concentration-time plot for the reaction between a PyO (44.4 mM) and PPh3 (44.4 mM), showing the great effectiveness of the dimeric catalyst 6 over its monomer-phosphine form. Reactions were conducted in benzene at 298 K.

Equation (3.22) shows that c2, i.e. concentration of the intermediate will first increase and then decrease. The concentration-time plots for various species are given in Fig. 3.1. 

The disappearance of tritiated vindesine from the blood of rats has been reported to be biphasic, with half-life estimates of 15 min (distribution) and 10 hr (elimination) (59) it is likely that the prolonged elimination phase represents a hybrid between the second elimination phase described above for vincristine and the prolonged third phase evident on inspection of log concentration-time plots for vincristine in the rat. Biliary excretion contributes heavily to the elimination of vindesine in the rat. The bioavailability of vindesine in the rat appears to be very poor. The distribution of vincristine to different tissues in the mouse has been correlated with the estimated concentration of tubulin in the tissues (40). Tubulin concentration was measured by the capacity of a tissue to bind colchicine (40) comparable relationships between tissue concentrations of vincristine and colchicine binding capacity were observed for the dog and the monkey, but it should be emphasized that the correlations were based on the assumption that tissue tubulin content is closely similar in the mouse, dog, and monkey. 

Fig. 5.2 Descriptive pharmacokinetic parameters (a) plasma concentration-time plot and (b) semi-logarithmic plot.

The plasma elimination half-life can be determined from a semi-logarithmic plot of the plasma concentration-time plot (Figure 5.2b), following an intravenous dose, as the time taken for the plasma concentration to fall by 50%. The elimination half-life of some drugs is very short (seconds or minutes) whereas for others it may be very long (weeks). 

When a drug of single compartment distribution is given intravenously, a. semilog plasma concentration time plot is obtained (Fig. 1.3.4), which has two slopes, one is due to distribution and another which is due to the drug elimination. 

Again plotting concentration versus time using these integrated second-order rate laws gives linear plots only if the reaction is a second-order process. The rate constants can be determined from the slopes. If the concentration-time plots are not linear, then the second-order rate equations do not correctly describe the kinetic behavior. There are integrated rate laws for many different reaction orders. 

Figure 1.17. Concentration-time plot following 3-mg/kg IV administration of NiK-12192 to mice. The dashed line is an extrapolation of the plasma sample concentration. The elimination phase determined using HPLC-MS is clearly different from that obtained using UPLC-MS. (Reprinted with permission from Pedraglio et al., 2007.)...

An assumption concerning the number of compartments is, by nature, not required. For reliable results and precise parameter estimates, however, a relatively large number of data points per individual are required. Phase 1 studies of mAbs usually provide sufficient data for a noncompartmental analysis, but the assumption of linear pharmacokinetics is not valid for most mAbs. This prerequisite, however, was frequently neglected during the early years of therapeutic mAh development, and an overall estimate for CL, for example, was frequently reported in the literature. In dose-escalating studies, however, the concentration-time plots of the raw data clearly indicate that the slope of the terminal phase is not parallel for the different doses, but increases with increasing dose (Fig. 3.10). As a result, the listing of different clearance values for different doses can be found. For example, the clearance of trastuzumab was reported to be 88.3 mL/h for a 10-mg dose, 34.3 mL/h for a 50-mg dose, 25.0 mL/h for a 100-mg dose, 19.0 mL/h for a 250-mg dose, and 16.7 mL/h for a 300-mg dose. 

Figure 9.3 Representations of typical log concentration-time plots for a drug and metabolite exhibiting first order kinetics showing the general changes when (a) k> km and (b) k < km...

Derivation of Reaction Schemes Based on Experimental Results. Although numerous methods for evaluating reactions schemes have been developed ( 0-44), most of them (40-42) start with a hypothetical mechanism which is, by means of experiments, either confirmed or rejected. A newly developed method for the systematic elucidation of reaction schemes of complex systems requires no chemical considerations, but concentration-time measurements and system-analytical considerations (45). The method is based on the initial slope of the concentration-time profiles and when necessary the higher derivatives of these curves at t = 0. Reaction steps in which products are formed directly from reactants can be identified in a concentration-time plot by a positive gradient c. at t = 0 (zero order delay). dtJ... 

For the case with porous particles, the pore fluid can be treated as a mass transfer medium rather than a separate phase thus enabling it to be combined with the bulk fluid in the overall mass balance. Under plug flow transfer conditions, at the end of each time increment, the pore fluid was assumed to remain stagnant, and only the bulk fluid was transferred to the next section. Based on these assumptions and initial conditions, the concentrations of the polypeptide or protein adsorbate in both liquid and solid phase can be calculated. The liquid phase concentration in the last section C , is the outlet concentration. The concentration-time plot, i.e., the breakthrough curve, can then be constructed. Utilizing this approach, the axial concentration profiles can also be produced for any particular time since the concentrations in each section for each complete time cycle are also derived. 

If some of the reactant or product species are present in excessive quantities, then the fractional changes in their concentrations over the entire duration of the reaction may be immeasurably small. In such cases the concentrations of the reactants present in excess remain approximately constant and may be absorbed into the rate constant fe. A measurement of the order of the reaction from concentration-time plots then does not reveal the dependence of the rate on the concentrations of the overabundant species the measurement yields the pseudo molecularity of the reaction, that is, the sum of the orders with respect to the species that are not present in excess. Thus a number of higher-order reactions are found to be pseudounimolecular under certain conditions. This observation provides the basis for the isolation method of determining the order of a complex reaction with respect to a particular reactant in this method, the apparent overall order (pseudo-molecularity) of the reaction is measured under conditions in which all of the reactants except the one of interest are present in excess. 

D) Normalized concentration-time plot from (C) for a 50 nm copper layer on a steel base. 

To accomplish a quantitative treatment of the concentration-time plots it was first necessary to elucidate the reasons for the observed deviations after longer time intervals. A consecutive reaction of the a,jS-unsaturated ketones was expected. Because the cyclopentanone derivative 5, containing an exocyclic double bond, can undergo isomerization (Erskine and Waight, 1960) further attention was centred on phenyl vinyl ketone (7) formed in reaction (2b). In a separate study, reported on p. 25 it was found that phenyl vinyl ketone reacts imder the conditions used with hydroxide ions at a measurable rate at pH above about 9. Because the Mannich bases 4 and 6 have piT values of about 9-5 and 9-6, respectively, the rate of elimination was measurable with these compounds at pH > 8-5. Hence practically over the whole pH-range in which the elimination can be studied, the consecutive reaction of the phenyl vinyl ketone formed had to be taken into account. In preference to the development of a mathematical treatment for the system of consecutive reactions a more suitable Mannich base, for which such complications would be absent, was looked for. 

Figure 11 Effect of varying absorption rate constant (ka) on the concentration time plots for two hypothetical drugs with similar dose, bioavailability, clearance, and volume of distribution. Case 1 (smooth line) ka > ke and Case 2 (broken line) ka < ke (flip-flop situation).

FIGURE 14.3 Concentration-time plot for males (open circles) and females (closed circles). 

Figure 6. Concentration-time plots of selected compounds in the lowest NOx ambient ROG - NOx surrogate experiment in the initial evaluation experiments (NOx 1 ppb, ROG 300 ppbC.

Hydrogenation of crotonaldehyde was studied in liquid phase using Pd/C catalyst. The only product formed was n-but)iraldehyde under the reaction conditions of the present work. The concentration-time profiles were obtained under various operating conditions. The rate constants were evaluated by simulating the concentration-time plots. The model predictions and the experimental data were found to be in good agreement. 

Bioequivalence The equivalence of blood concentrations of two preparations of the same drug measured over time if the concentration-time plots for the two preparations are nearly superimposable (within certain statistical limits), the preparations are said to be bioequivalent one preparation may be safely substituted for the other... 

The experimental measurements produced concentration-time plots of ethylene oxide and ethylene glycol in the liquid phase, as shown in Figure 8.18. The physical picture of this reaction/reactor system is most closely approximated by the plug-flow gas phase, well-mixed batch liquid phase. The appropriate relationships to model this system are given in equations (8-176) to (8-178), (8-183), and (8-188). The bubble volume is variable, and the nature of the variation changes with the extent of conversion (i.e., concentration of glycol in the liquid phase), however, the pure oxide gas phase allows yg = l. The modified equations specific to this reactor are then... 

Ci = terminal phase y-axis intercept from tissue drug concentration-time plot... 

In colurim 1 of the table, the time values are recorded that correspond to the observed plasma concentrations. This is done only for the absorption phase. In colurim 2, the observed plasma concentration values provided only from the absorption phase are recorded (i.e. all values prior to reaching maximum or highest plasma concentration value). In column 3, the plasma concentration values obtained only from the extrapolated portion of the plasma concentration versus time plot are recorded (these values are read from the plasma concentration-time plot) and, in column 4, the differences in the plasma concentrations (Cp)diff between the extrapolated and observed values for each time in the absorption phase are recorded. 

We also know from Eqs 6.6 and 6.7 that the intercept (J) of the plasma concentration-time plot is given by ... 

Paz-Abuin et al. developed a method for quantifying the reactivity ratio from the concentration-time plots of amines (Paz-Abuin et al., 1997a). Considering the classical reaction mechanism, applying the condition for maximum to [A2], it is obtained that... 

Figure 5.23. Concentration/time plot representing the growth phase of a discontinuous culture of microorganisms (1) lag phase with = lag time and = 0, (2) exponential phase with (3) decay phase with /x = /(s), (4) stationary phase with fx = —k, ...

Figure 5.41. Concentration/time plot of the three basic types of microbial product formation (I) growth association, (II) mixed growth association, and (III) nongrowth association (Gaden, 1955).

Figure 5.67. Concentration/time plot of structured biomass model according to Williams (1967) Biomass G and K compartment (xq,Xk) and total biomass (x) and substrate (s) simulated on the basis of Equs. 5.228d-f with =0.0125...

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