Multiple additions method

Gran plot A commonly employed multiple-addition method, used to correct for unknown amounts of contaminant and for dilution errors (see Section 4.3.2). 

Cx = (CsFo//xF3)(1-10- ) = Ac (1-10- ) (ASM). (5.20) The double and multiple addition methods are introduced in an attempt further to improve the measuring precision, because with three or more experimental potential values the slope value S need not be knowa Under the same assumptions and with the same symbols as above, provided the same volumes are always added, it holds for the nth addition of the determinand standard solution that... 

Double addition methods do not significantly improve the precision of the determination and thus multiple addition methods should be preferred. 

In potentiometry with ISEs, however, the second Gran method [46] has found especially wide use, not only in titrations, but also in multiple addition methods in general. In these methods, the concentration of the test substance is plotted against the volume of the titrant or of the standard solution and thus the curve is linearized. The end-point in the titration or the determinand concentration in a multiple addition method is found as the intercept of the straight line with the volume axis. Linearization is attained by taking the antilogarithm of the Nernst equation ... 

In the Gran linearization of a multiple addition method, (5.21) is rearranged to give... 

Fig. 5.3. The use of the Gran method in the multiple addition method. For explanation see the text.

In the method of standard additions, a known amount of a standard solution of analyte is added to one portion of the sample. The responses before and after the addition are measured and used to obtain the analyte concentration. Alternatively, multiple additions are made to several portions of the sample. The standard additions method assumes a linear response. This should always be confirmed or the multiple additions method used to check linearity. 

We use the method of standard additions when it is difficult or impossible to duplicate the sample matrix. In general, the sample is spiked with a known amount or amounts of a standard solution of the analyte. In the single-point standard addition method, two portions of the sample are taken. One portion is measured as usual, but a known amount of standard analyte solution is added to the second portion. The responses for the two portions are then used to calculate the unknown concentration, assuming a linear relationship between response and analyte concentration (see Example 8-8). In the multiple additions method, additions of known amounts of standard analyte solution are made to several portions of the sample, and a multiple additions cahbration eurve is obtained. The multiple additions method gives some... 

The method of standard additions is quite powerful when used properly. First, there must be a good blank measurement so that extraneous species do not contribute to the analytical response. Second, the calibration curve for the analyte must be linear in the sample matrix. The multiple additions method provides a check on this assumption. A significant disadvantage of the multiple additions method is the extra time required for making the additions and measurements. The major benefit... 

The standard addition method can take several forms as discussed in Section 8C-3 the single-point method was described in Example 8-8. The multiple additions method is often chosen for photometric or spectrophotometric analyses, and this method will be described here. This technique involves adding several increments of a standard solution to sample aliquots of the same size. Each solution is then diluted to a fixed volume before measuring its absorbance. When the amount of sample is limited, standard additions can be carried out by successive addition of increments of the standard to a single measured aliquot of the unknown. The measurements are made on the original solution and after each addition of standard analyte. This procedure is often more convenient for voltammetry. 

The single-addition method is somewhat dangerous because it presumes a linear relationship and provides no check of this assumption. The multiple-addition method ai leasi gives a check on the linearity supposition. 

In the case of multiple additions. If there are more levels to be added, the first two levels are added using the graph and then the third is added to the resultant using the same method. 

Known concentrations of Sn solutions were spiked Into acid digested samples of Ps. 244 which had been exposed to 10 ppm solutions of Bu Sn (x = 0,1,2,3). Atomic absorption analysis of these samples allowed for the calculation of the amount of tin accumulated on the cell by the method of multiple additions Q6). 

Alkane physisorption on ZSM-22 can be described using an additivity method accounting for the number of carbon atoms inside and outside the ZSM-22 micropores [22]. Linear alkanes can fully enter the micropores while branched alkanes can only enter the pore mouths. Multiple physisorption modes exist at the pore mouths where branched alkanes can enter the pore mouth with each of their straight ends . 

In Section 8.2.8 we have discussed the standard addition method as a means to quantitate an analyte in the presence of unknown matrix effects cf. Section 13.9). While the matrix effect is corrected for, the presence of other emalytes may still interfere with the analysis. The method can be generalized, however, to the simultaneous analysis of p analytes. Multiple standard additions are applied in order to determine the analytes of interest using many q > p) analytical sensors. It... 

Packed column SFC and CE are both able to make inroads into the application area served by HPLC, but from opposite extremes of polarity and with little overlap. CE is likely to be more efficient and faster, but mostly applicable to very polar molecules and ions. SFC qualifies as a more reproducible, trace technique, with greater selectivity and multiple detection options. HPLC and CE have been compared [365], Owing to their orthogonality, CZE and SFC are worth developing, not in competition or as an alternative to HPLC, but as an additional method in order to augment the information obtained from the analysis. With the broad scope of possible eluents and stationary phases, HPLC has fewer constraints than SFC and CZE. The parameters influencing selectivity may be used as a guide to optimisation (Table 4.44). 

The use of the particle-beam interface for introduction of samples into a mass spectrometer (PB-MS), without chromatographic separation, was shown by Bonilla [55] to be a useful method for analysis of semi-volatile and nonvolatile additives in PC and PC/PBT blends. The method uses the full power of mass spectrometry to identify multiple additives in a single matrix. The usefulness, speed and simplicity of this approach were illustrated for AOs, UVAs, FRs, slip agents and other additives. 

Walters [24] examined the effect of chloride on the use of bromide and iodide solid state membrane electrodes, and he calculated selectivity constants. Multiple linear regression analysis was used to determine the concentrations of bromide, fluorine, and iodide in geothermal brines, and indicated high interferences at high salt concentrations. The standard curve method was preferred to the multiple standard addition method because of ... 

The multiple standard addition method is time-consuming although it usually yields superior results to those of the other methods outlined in Table 3.3. 

In addition techniques, the test substance concentration is determined from the difference in the ISE potentials obtained before and after a change in the sample solution concentration. The main advantage Ues in the fact that the whole measurement is carried out in the presence of the sample matrix, so that results with satisfactory accuracy and precision can be obtained even if a substantial portion of the test substance is complexed. Several addition techniques can be used, namely, single, double or multiple known addition methods, in which the sample concentration is increased by additions of a test substance standard solution single, double or multiple known subtraction methods, in which the sample concentration is decreased by additions of a standard solution of a substance that reacts stoichiometrically with the determinand and analyte addition and subtraction methods, in which the sample is added to a test substance solution or to a reagent solution. 

Potentiometric titration is actually a form of the multiple known subtraction method. The main advantage of titration procedures, similar to multiple addition techniques in general, is the improved precision, especially at high determinand concentrations. ISEs are suitable for end-point indication in all combination titrations (acid-base, precipitation, complexometric), provided that either the titrand or the titrant is sensed by an ISE. If both the titrant and the titrand are electro-inactive, an electrometric indicator must be added (for example Fe ion can be titrated with EDTA using the fluoride ISE when a small amount of fluoride is added to the sample solution [126]). 

Volume additivity methods generally do not take into account crystal packing efficiency or molecular conformation effects and thus will afford identical calculated densities for positional and conformational isomers and for compounds that possess different multiples of the same functional group composition. As an example, a volume additivity calculation predicts that l,3,5-trinitro-l,3,5-triazacyclohex-ane (RDX), l,3,5,7-tetranitro-l,3,-5,7-tetraazacyclooctane (a-HMX), and /3-HMX all will possess the same crystal density, 1.783 g/cm [32]. In fact, the experimentally observed densities of these three compounds differ markedly (i.e., 1.806 [33], 1.839 [34], and 1.902 [35], respectively). 

Refluxing benzene solutions of Cjq in the presence of a 20-fold excess of BujSnH leads to hydrostannylation (Scheme 6.15) [73]. Multiple additions can also take place. To maximize the yield of the monoadduct CgoHSnBuj (24), the time dependence of the reaction was followed quantitatively by HPLC. After about 4 h, the concentration of the monoadduct 24 reaches its maximum. Compound 24 can be isolated by preparative HPLC on a Cjg-reversed-phase stationary phase with CHCI3-CH3CN (60 40, v/v) as eluent. The structure of C5oHSnBu3 (24) was determined by NMR spectroscopy and other methods, showing that a 1,2-addition takes place regio-selectively (Scheme 6.15) [73]. 

This study demonstrates the use of multiple-core methods to obtain whole-basin sediment fluxes from a suite of lakes and the application of these data to questions of atmospheric metal deposition. Multiple-core data can be economically produced by integrating longer core sections and reducing the number stratigraphic units for analysis. As few as three 210Pb analyses per core can yield a modern accumulation rate additional samples provide more historical detail. 

Fifolt [ 130] reported this chemical shift additivity method for fluorobenzenes in two deuterated solvents d6 acetone and d6 dimethyl sulfoxide (DMSO) Close correlations between experimental and calculated fluorine chemical shifts were seen for 50 compounds Data presented in Table 18 result from measurements in deuterochloroform as (he solvent [56] Fluorine chemical shifts calculated by this additivity method can be used to predict approximate values for any substituted benzene with one or more fluorines and any combination of the substituents, to differentiate structural isomers of multisubstituted fluorobenzenes [fluoromtrotoluenes (6, 7, and 8) in example 1, Table 19], and to assign chemical shifts of multiple fluorines in the same compound [2,5 difluoroamline (9) in example 2, Table 19] Calculated chemical shifts can be in error by more than 5 ppm (upfield) in some highly fluonnated systems, especially when one fluonne is ortho to two other fluorines Still, the calculated values can be informative even in these cases [2,3,4,6-tetrafluorobromobenzene (10) in example 3, Table 19]... 

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