Concentration ratio method

Assuming eutectic batch melting, the variation in concentration of a trace element of the melt, Q, is given by (Shaw, 1970)  

For element a (highly incompatible) and b (not-so-highly incompatible), their concentrations in the melt and are given by  

Let the degree of partial melting increase from stage 1 to stage 2. Using Eq. (7.5) for two different degrees of partial melting, Fj and F2, the 

Similarly, using Eq. (7.6) the enrichment ratio gb for the less incompatible element is defined by  

The calculated F, and F for batch melting may yield fairly reliable results for primary magmas formed at low degrees of partial melting (Maaloe, 1994). 

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Electrical discharges are affected by a number of serious matrix interferences associated with the way that the sample is vaporized into the discharge as well as various chemical and physical interactions within the discharges. Spectral interferences are as serious as for ICP-OES. These interferences can be mitigated, in part, by the use of internal standards and the concentration ratio method. However, these approaches are not as successful as with the ICP because the latter has fewer interferences and better precision. Internal standards have to be chosen with great care because they must behave in the same way as the analyte. This is not trivial because the physicochemical interference problems that occur in these atom cells vary greatly from element to element and sample to sample. 

In the slope-ratio method two sets of solutions are prepared. The first set consists of a constant amount of metal and a variable amount of ligand, chosen such that the total concentration of metal, Cm, is much greater than the total concentration of ligand. Cl- Under these conditions we may assume that essentially all the ligand is complexed. The concentration of a metal-ligand complex of the general... 

This experiment describes the use of FIA for determining the stoichiometry of the Fe +-o-phenanthroline complex using the method of continuous variations and the mole-ratio method. Directions are also provided for determining the stoichiometry of the oxidation of ascorbic acid by dichromate and for determining the rate constant for the reaction at different pH levels and different concentration ratios of the reactants. 

The most widely used method for fitting a straight line to integrated rate equations is by linear least-squares regression. These equations have only two variables, namely, a concentration or concentration ratio and a time, but we will develop a more general relationship for use later in the book. 

The method of evaluation of the rate constants for this reaction scheme will depend upon the type of analytical information available. This depends in part upon the nature of the reaction, but it also depends upon the contemporary state of analytical chemistry. Up to the middle of the 20th century, titrimetry was a widely applied means of studying reaction kinetics. Titrimetric analysis is not highly sensitive, nor is it very selective, but it is accurate and has the considerable advantage of providing absolute concentrations. When used to study the A —> B — C system in which the same substance is either produced or consumed in each step (e.g., the hydrolysis of a diamide or a diester), titration results yield a quantity F = Cb + 2cc- Swain devised a technique, called the time-ratio method, to evaluate the rate... 

They concluded, thereby, that Ag2Te formation is governed by the initial amount of silver deposit. It is worth noting that the present method, involving dilute electrolytic baths of the compound precursors, deviates from the typical, initially proposed by Panicker et al., method of employing high concentration ratios of the metal to the chalcogen precursor. 

Anderson and Bonner made the first detailed kinetic study on the exchange using the isotopic method ( Cr) and a separation method based on the conversion of Cr(II) into Cr(IIl) oxalate and an ion-exchange treatment. To prevent oxidation of Cr(II) during exchange a hydrogen atmosphere was maintained over the reaction mixture. The rate law found to be obeyed for the concentration ratio range Cr(III)/Cr(II) of between 3.3 x 10 and 2.0 in perchlorate media was... 

Transfer constants for regulators may be determined by application of the previously discussed molecular weight method, which depends on the use of Eq. (42). The concentration ratio [S]/[M] is assumed to be constant in this method, hence the conversion must be kept very low, unless C5 is near unity. For transfer constants greater than about five, impractically low conversions are required. A second method - depends on determination of the amount of regulator reacting. The rate of reaction of regulator is given by... 

The reason for this confusing situation is that all efficacy data are depending from the test method used to find the effective time - concentration ratio of the disinfectant. 

Effective diffusivities for these ions in equimolar concentration ratio and with various inert electrolytes, have been determined by several methods (see Table III). The mobility products obtained from capillary cell (stagnant diffusion) and rotating-disk measurements are in fairly good agreement. 

In order to apply the zero-point method, it is necessary to know the value of the frequency at which the rectification voltage tends to zero. The experimental determination of the zero-point frequency has some practical difficulties, because over a small frequency range, the rectification signal is indistinguishable. Hence, the zero-point frequencies have been determined by extrapolating plots of EJ V versus w 1/2 for those redox concentration ratios which intercept the abscissa (i.e., when AE = 0). 

For the more general case of arbitrary rate constants, the analysis is more complex. Various approximate techniques that are applicable to the analysis of reactions 5.4.1 and 5.4.2 have been described in the literature, and Frost and Pearson s text (11) treats some of these. One useful general approach to this problem is that of Frost and Schwemer (12-13). It may be regarded as an extension of the time-ratio method discussed in Section 5.3.2. The analysis is predicated on a specific choice of initial reactant concentrations. One uses equivalent amounts of reactants A and B (A0 = 2B0) instead of equi-molal quantities. 

Keeping the concentration ratio of H20 and CO in the simulation model constant (according to the Thiele modulus see Equation 12.21) leads to equal concentration profiles of H2, as shown in Figure 12.4, and consequently to equal effectiveness factors for both methods (Thiele modulus and simulation). In fact, the concentrations of H2, CO, and H20 change inside the pore, as considered in the simulation. Therefore, the results obtained by the software used represent reality best. 

The experimental approaches are similar to those for solubility, i.e., employing shake flask or generator-column techniques. Concentrations in both the water and octanol phases may be determined after equilibration. Both phases can then be analyzed by the instrumental methods discussed above and the partition coefficient is calculated from the concentration ratio Q/Cw. This is actually the ratio of solute concentration in octanol saturated with water to that in water saturated with octanol. 

Based on the analytical figures of merit of the methods in Table 1, the best precision and selectivity are accomplished by using the decay rate rather than the formation rate or conventional CL-measured parameters such as the peak height or area under the CL curve. Table 2 gives the selectivity factor, expressed as decay-rate and peak-height tolerated concentration ratio, for the CL determination of hydrogen peroxide using SF-CLS. As can be seen, the selectivity factor was quite favorable in most instances. 

The [S]cr value depends on the nature of the catalyst, its surface area per unit of weight, the ratio of the rates of hydroperoxide decomposition into free radicals and molecular products, hydrocarbon and dioxygen concentrations, the method of catalyst preparation, and the chemical treatment of the surface. 

There have recently been significant advances in the technique of carbon 14 measurements, which have permitted the determination of the concentration ratio C14/C12 in samples of small size. Two developments have occurred the first is an entirely new mass-spectrometric separation of Cl4 and Cl2 ions and their subsequent estimation by counting [1-8]1, while the second is simply the extension of conventional proportional counter operation to very small size carbon samples [9]. The first method is very fast, precise, and capable of treating samples of even submilligram size, but requires an expensive installation. The second method is slow (counting times of two months or more are necessary), can probably be made sufficiently precise to handle most problems, works down to sample sizes of 10 mg carbon, and is relatively inexpensive, especially to install in already-existing radiocarbon laboratories. 

The quantity and quality of experimental information determined by the new techniques call for the use of comprehensive data treatment and evaluation methods. In earlier literature, quite often kinetic studies were simplified by using pseudo-first-order conditions, the steady-state approach or initial rate methods. In some cases, these simplifications were fully justified but sometimes the approximations led to distorted results. Autoxidation reactions are particularly vulnerable to this problem because of strong kinetic coupling between the individual steps and feed-back reactions. It was demonstrated in many cases, that these reactions are very sensitive to the conditions applied and their kinetic profiles and stoichiometries may be significantly altered by changing the pH, the absolute concentrations and concentration ratios of the reactants, and also by the presence of trace amounts of impurities which may act either as catalysts and/or inhibitors. 

Galceran, J., Cecilia, J., Salvador, J., Monne, J., Torrent, M., Companys, E., Puy, J., Garces, J. L. and Mas, F. (1999). Voltammetric currents for any ligand-to-metal concentration ratio in fully labile metal-macromolecular complexation. Easy computations, analytical properties of the currents and a graphical method to estimate the stability constant, J. Electroanal. Chem., 472, 42-52. 

The quantitative analysis of pharmaceutical substances may be achieved by emperical-ratio method either by plotting percentage transmittance against wavelength or by plotting the log T1 o/T1 against concentration as illustrated in Figure 22.4. 

When the fluorescence spectra of the probe shifts on protonation, two emission wavelengths with opposite proton-sensitive response are chosen to give a pH-dependent emission intensity ratio. In this ratio method a number of ion-independent factors that affect the signal intensity like photobleaching, variations in probe concentration, and illumination instability are eliminated. 

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