Concentration-yield curves

Figure 8. Yield Curves for Salt-To-Pu Ratio vs Concentration of MgC12 for Extraction of Americium From NaCi-CaCl2-MgCl2 Salt Using 2-Stage Counter-Current Extraction...

The concentration-time curve can be integrated numerically and yields the so-called area under the curve (AUC) ... 

The shape of the instantaneous yield curve determines the optimum reactor configuration and flow pattern for a particular reaction network. For cases where the instantaneous yield increases continuously with increasing reactant concentration, the optimum reactor configuration from a product selectivity viewpoint is a... 

The rate constants for micelle-catalyzed reactions, when plotted against surfactant concentration, yield approximately sigmoid-shaped curves. The kinetic model commonly used quantitatively to describe the relationship of rate constant to surfactant, D, concentration assumes that micelles, D , form a noncovalent complex (4a) with substrate, S, before catalysis may take place (Menger and Portnoy, 1967 Cordes and Dunlap, 1969). An alternative model... 

Commercial samples containing approximately 400 mg of ephedra per capsule yield roughly 5 mg of ephedrine, 1 mg of pseudoephedrine, and less than 1 mg of methylephedrine (White et al. 1997). For a dose of four capsules, yielding approximately 20 mg of ephedrine, the elimination half-life is 5.2 hours. The time to reach maxium concentration is 3.9 hours. Compared to pure ephedrine tablets, the elimination kinetics of ephedra are comparable. However, ephedra showed somewhat different absorption kinetics (e.g., lag time, area under the concentration-time curve, and maximum plasma concentration). So, ephedra tablets may vary from pure ephedrine in the onset of action, but the durations of action are grossly equivalent. 

Thereafter, and V ax values for substrate turnover are determined in the absence (controls) and presence of several concentrations of the inhibitor of interest. It is recommended that substrate turnover in the presence of at least four concentrations of inhibitor are examined, at concentrations between 1/3 x IC50 and 4 x IC50. Velocity data are then plotted versus substrate concentration, yielding a control plot and plots at each of the concentrations of inhibitor assessed. Hyperbolic curves are then fitted to data with the Michaelis-Menten equation, or with whichever variation of the Michaelis-Menten equation was found to describe control enzyme behavior most appropriately (see Section 4.1.4 etseq.). In this way, a pattern of changes in Km and Vmax> or both, should become apparent with changing inhibitor concentration. 

Therefore, plotting the ALIS MS response from a titration series versus the total ligand concentration yields a saturation binding curve that can be fit to this equation by nonlinear regression analysis to yield the of the ligand of interest. 

The slopes of the curves show an exponential rise consistent with the increasing volume percent of carbon that would increase the probability of finding carbon at the surface of the CoFoam (Figure 4.18). Plotting the slope against the reflectance data (which is related to the carbon concentration) yields results shown in Figure 4.19. Table 4.4 summarizes the data. 

The approximate linearity of the v/m = 20 cm /g plots in Figure 3 is of interest. These data points represent samples that had rather large amounts of zeolite present in comparison to the volume of the solution. In these preparations, the solution pH was determined by the Na Y zeolite but was moderated by the quantity of copper salt initially present. Increasing the solution volume by a factor of 10 yielded curves having an inflection point near a copper concentration of 0.01 H. Below this concentration, the curves are parallel to the corresponding v/m = 20 cm3/g curves and again reflect the presence of the zeolite. 

It is possible to use a preliminary dilution step of 1 100 when the pT-scale relies, for instance, on a < 20% effect endpoint measurement (e.g., determination of IC < 20 in non quantal tests with algae and bacteria). In this case, the pT-value should be calculated from the concentration-effect curve. The pT-value is determined by using the first sample concentration that generates an effect below 20%. If, for example, the concentration incurring a 19% effect is equated with a dilution factor of 1 3200, the pT-value is calculated with equation 5 as demonstrated below. The modulus for transforming decadic logarithms into binary ones, 1 / logio 2 , yields equation 6. For the 1 100 diluted wastewater example above, the pT-value can then be calculated with the help of equation 8. 

By measuring the absorbance of several solutions containing an analyte at various known concentrations, you can discern this relationship. Graphing the absorbance versus the concentration yields a calibration curve, as shown in Figure 10.19. If you measure the absorbance of an analyte solution of unknown concentration, the calibration curve gives the concentration of analyte that corresponds to that particular absorbance. 

In other cases, the UFs are multiplied, usually yielding low hazardous concentration values that are supposed to offer sufficient protection in worst-case conditions. In mixture assessments, the simple generic model consists of the use of point estimates from concentration-effect curves, in combination with the concentration addition model, to address mixture problems. 

Critical concentrations of elements in plants have been defined by Beckett and Davis (1977) and Davis and Beckett (1978) as those concentrations which cause toxic reactions and reduce yield (biomass). They presented yield curves of plants grown in the presence of toxic metals ... 

The effective local concentration determined from the longitudinal relaxation as mentioned above is roughly equal to the value of the bulk concentration where the dose-yield curve begins to deviate from the linear relationship. Assuming that the dose-yield curve starts to saturate at the bulk concentration of 8.4 mmol/dm3 or the radical-pair concentration of 4.2 mmol/dm3 due to the overlap of the spurs, the radius of the spur is estimated to be 4.5 nm. This value is in good agreement with the spur radius of 4.1 nm obtained from the relaxation measurement. This coincidence seems to support the general view that the... 

All of these reactions presumably arise through free radical mechanisms. The abstraction of hydrogen from tetralin by coal to produce naphthalene is of course expected. What sets this reaction apart from the rest is the linear dependence of naphthalene yield on coal concentration. From the slope of the yield curve, we calculate that hydrogen was removed from tetralin in the amount of 2.5 wt. percent of the added coal. This is a reasonable amount of hydrogen to be transferred to coal under liquefaction conditions. However, we note a recent report on the decomposition of 1,2-diphenylethane in tetralin in which Benjamin states that over twice the amount of naphthalene required in the formation of toluene was produced (11). Presumably, the excess appears as molecular hydrogen. In the present case, we cannot rule out the possibility that some fraction of the naphthalene was produced by a similiar mechanism. 

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