Concentration dependent distribution method

This radiochemical method is based on the utilization of calibration curves showing the dependence of the distribution ratio of the element of interest in a two-phase system on the total concentration of the element The concentration-dependent distribution method is applied to the simultaneous determination of chemically similar elements. This method uses a competitive reaction and is based on calibration curves obtained by two substoichiometric systems for a known and fixed total concentration of the two similar elements. In system (1), the concentration of element A serves as the independent variable and the concentration of element B is a constant parameter for each curve. In system (2) the opposite is used. The substoichiometric separation is carried out in both systems and calibration curves are drawn. The shape of the calibration cur ve has been theoretically derived and the influence of experimental conditions on the determination error and optimum labeling substances, yielding minimal error, have been discussed in connection with extraction amstants It is possibile to expand this idea to the simultaneous determination of three or four chemically similar elements, but the use of calibration curves and grajdiical treatment cannot be applied to more than two elements without much loss of simplicity and clarity. The sub- and super-equivalence method is superior to the concentration-dependent distribution method in that it requires less sample preparation for radioactivity measurements and fewer measurements. On the other hand, the calibration curvK of the sub- and super-equivalence method are generally steeper than those of the concentration-dependent distribution method, which would favor the latter. 

An alternative calibration curve approach for nonquantitative reactions is to determine the distribution coefficient by a concentration-dependent distribution method [2], [75], which is a variant of the radioreagent method (Section 8.5.1). 

Methods of concentration-dependent distribution (CDD) utilizing reactions where products of unstable composition are formed, but in which the extent of reaction is determined by the corresponding equilibrium constant or reaction time. 

Concentration-dependent distribution (CDD) is based on the utilization of a calibration graph that shows the dependence of the distribution ratio of the substance to be determined in a two-phase system on the total concentration of the substance [2], [32], [87], [92], [95], [96]. Characteristic features of the method of CDD are as follows ... 

Finally, when the reactions are of different order and of different activation energies, we must combine the methods of Chapters. 7, 8, and 9. Jackson et al. (1971) treat a particular system of this type and find that the optimum policy requires adjusting only one of the two factors, temperature or concentration, while keeping the other at its extreme. Which factor to adjust depends on whether the change in product distribution is more temperature dependent or concentration dependent. It would be interesting to know whether this finding represents a general conclusion. 

Note that is not necessarily constant with varying p,. In fact, evaluation of the air-water equilibrium distribution ratio as a function ofp, is one of the methods that can be used to assess the concentration dependence of y-w of an organic compound, regardless whether the compound is a gas, liquid, or solid at the temperature considered (see below). 

In the MIP literature the most widespread method for establishing the selectivity of an MIP for its template against an interferent has been to determine by HPLC the corresponding a value. In the section on MIP HPLC we have shown, however, that the k values determined in MIP HPLC depend on the injected sample concentration. Therefore they do not provide a distribution ratio. Indeed, the distribution ratio is obviously concentration dependent when the isotherm is not linear. It is not self-evident but it has been shown [35] that the ratio of the apparent k values (as determined from the peak maximum positions) for two compounds with nonlinear isotherms is not a constant and such an a value is not suitable to quantitate the separation selectivity. 

Modeling of H F contactors is in most papers based on a simple diffusion resistance in series approach. In many systems with reactive extractants (carriers) it could be of importance to take into account the kinetics of extraction and stripping reactions that can influence the overall transport rate, as discussed in refs. [30,46], A simple shortcut method for the design and simulation of two-phase HF contactors in MBSE and MBSS with the concentration dependent overall mass-transfer and distribution coefficients taking into account also reaction kinetics in L/L interfaces has been suggested [47]. 

Laws regulating toxic substances in various countries are designed to assess and control risk of chemicals to man and his environment. Science can contribute in two areas to this assessment firstly in the area of toxicology and secondly in the area of chemical exposure. The available concentration ( environmental exposure concentration ) depends on the fate of chemical compounds in the environment and thus their distribution and reaction behaviour in the environment. One very important contribution of Environmental Chemistry to the above mentioned toxic substances laws is to develop laboratory test methods, or mathematical correlations and models that predict the environ-... 

Peskin [49] used the Galerkin finite-element method to compute current distribution and shape change for electrodeposition into rectangular cavities. A concentration-dependent overpotential expression including both forward and reserve rate terms was used, and a stagnant diffusion layer was assumed. An adaptive finite-element meshing scheme was used to redefine the problem geometry after each time step. 

Distribution methods for determining [M] depend on knowing the distribution coefficient for the metal ion or the ligand between two immiscible solvents. Thus free ammonia in equilibrium with the ammine complex of a metal can be determined from the ammonia concentration of a chloroform layer in equilibrium with the aqueous solution. 

Chemical relaxation methods [52] show evidence of a distribution of relaxation frequencies rather than a single one as found with classic ion detergents [193]. Thus, in agreement with the above conclusions, NaC and NaDC apparently self-associate over a whole range of concentrations and not at some critical micellar concentration. Further, the relaxation frequencies are strongly concentration dependent, suggesting that the distribution of aggregate sizes is wide and shifts upwards as bile salt concentration is increased [52]. 

The surface excess obtained by the second-harmonic generation in the concentration range below the CMC, however, changes with concentration in contradiction to the usual interpretation of surface tension data. Moreover, the absolute values of the adsorption determined by two experimental methods differ by one order of magnitude. These discrepancies were explained by means of the concept of a depth-dependent distribution of surfactant molecules [66]. Different distributions can lead to identical adsorption values. The surface excess determined by the second-harmonic generation can be attributed only to the very top layer, whereas the values obtained from surface tension techniques are apparently more sensitive to the near-surface layer. 

Difficulties arise when the concentration of an element is below the detection limit (DL). It is often standard practice to report these data simply as

generally depends on the amount of data below the detection hmit, the size of the data set, and the probability distribution of the measurements. When the number of < DL observations is small, replacing them with a constant is generally satisfactory (Clarke, 1998). The values that are commonly used to replace the < DL values are 0, DL, or DL/2. Distributional methods such as the marginal maximum likelihood estimation (Chung, 1993) or more robust techniques (Helsel, 1990) are often required when a large number of < DL observations are present. 

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