Adsorption standard deviations

The mobile phase was water in which the moderator alcohols were dissolved. It is seen that the linear relationship is completely validated and the data can provide the adsorption isotherms in the manner discussed. The mean surface area was found to be 199 m /g with a standard deviation between the different alcohols of 11 m /g. 

A method has been developed for differentiating hexavalent from trivalent chromium [33]. The metal is electrodeposited with mercury on pyrolytic graphite-coated tubular furnaces in the temperature range 1000-3000 °C, using a flow-through assembly. Both the hexa- and trivalent forms are deposited as the metal at pH 4.7 and a potential at -1.8 V against the standard calomel electrode, while at pH 4.7, but at -0.3 V, the hexavalent form is selectively reduced to the trivalent form and accumulated by adsorption. This method was applied to the analysis of chromium species in samples of different salinity, in conjunction with atomic absorption spectrophotometry. The limit of detection was 0.05 xg/l chromium and relative standard deviation from replicate measurements of 0.4 xg chromium (VI) was 13%. Matrix interference was largely overcome in this procedure. 

Van den Berg [131] used this technique to determine nanomolar levels of nitrate in seawater. Samples of seawater from the Menai Straits were filtered and nitrite present reacted with sulfanilamide and naphthyl-amine at pH 2.5. The pH was then adjusted to 8.4 with borate buffer, the solution de-aerated, and then subjected to absorptive cathodic stripping voltammetry. The concentration of dye was linearly related to the height of the reduction peak in the range 0.3-200 nM nitrate. The optimal concentrations of sulfanilamide and naphthyl-amine were 2 mM and 0.1 mM, respectively, at pH 2.5. The standard deviation of a determination of 4 nM nitrite was 2%. The detection was 0.3 nM for an adsorption time of 60 sec. The sensitivity of the method in seawater was the same as in fresh water. 

Lead(II) adsorbed on both columns was quantitatively eluted with ca. 6 bed volumes of 1 M nitric acid. In this work, 2 cylcles of the adsorption-elution operation were repeated at each flow rate. Then 16 cycles of the adsorption and elution operation were conducted for each column. In the case of FPS-f column, averaged recovery was 104% with standard deviation (sd) of 4 % (n = 16) and for the other column, averaged recovery 103% with sd of 4 %. Table 3 summarizes numerical data for results shown in Fig. 4. Breakthrough capacities at C/Co = 0.05 are 0.54 - 0.57 and 0.28 - 0.33 mmol/g for FPS-f and FP columns, respectively. Total uptake was 0.78 -0.83 mmol/g for FPS-f and 0.51 - 0.54 mmol/g for RF-f. During repeated adsorption-elution operations, no deterioration of both RFP-f and FP-f was observed. 

The standard deviation of the Gaussian zones expresses the extent of dispersion and corresponds to the width of the peak at 0.607 of the maximum height [24,25]. The total system variance (ofot) is affected by several parameters that lead to dispersion (Eq. 17.22). According to Lauer and McManigill [26] these include injection variance (of), longitudinal (axial) diffusion variance (of), radial thermal (temperature gradient) variance (of,), electroosmotic flow variance (of,), electrical field perturbation (electrodispersion) variance (of) and wall-adsorption variance (of ). Several authors [9,24,27-30] have described and investigated these individual variances further and have even identified additional sources of variance, like detection variance (erf,), and others... 

Lee and Chau [66] have discussed the development and certification of a sediment reference material for total polychlorobiphenyls. Alford Stevens et al. [49] in an inter-laboratory study on the determination of polychlorobiphenyls in environmentally contaminated sediments showed the mean relative standard deviation of measured polychlorobiphenyl concentrations was 34%, despite efforts to eliminate procedural variations. Eganhouse and Gosset [67] have discussed the sources and magnitude of bias associated with the determination of polychlorobiphenyls in environmental sediments. Heilman [30] studied the adsorption and desorption of polychlorobiphenyl on sediments. 

Figure 1. Proton adsorption-desorption heats ( 1 Standard Deviation or SD) as a function of pH for goethite at 10 g/L solid concentration in 0.05 M NaNO. All titrations were NaOH titrations starting from pH 4 followed by acid titrations back to pH 4.

Capillary coating can also stabilize the migration times and resolutions. This is in particular necessary in the case of peptide and protein analysis, because proteins tend to stick to capillary walls. Often low-concentration polyethylene oxide solutions are recommended as well as dynamic bilayer coating formed by a non-covalent adsorption of polybrene and polyvinylsulfonate (PVS). Due to the stability of the EOF, the variation of intra- and intercapillary migration time was less than 1% relative standard deviation (RSD) with basic analytes and peptides. 

It is obvious that the standard deviation for hematites is greater than that for goethites, mainly due to the greater variety of crystal faces. Al-for-Fe substitution did not directly influence the P adsorption for either synthetic goethites or hematites the surface area tends to increase with rising A1 incorporation and this, in turn, increases adsorption/unit weight (Ainsworth et al., 1985). 

The standard deviation has been determined as ct = j where v is the number of degrees of freedom in the fit. The parameters for the molecular interaction /3, the maximum adsorption Too, the equilibrium constant for adsorption of surfactant ions Ki, and the equilibrium constant for adsorption of counterions K2, are thus obtained. The non-linear equations for the Frumkin adsorption isotherm have been numerically solved by the bisection method. 

The rate parameters of importance in the multicomponent rate model are the mass transfer coefficients and surface diffusion coefficients for each solute species. For accurate description of the multicomponent rate kinetics, it is necessary that accurate values are used for these parameters. It was shown by Mathews and Weber (14), that a deviation of 20% in mass transfer coefficients can have significant effects on the predicted adsorption rate profiles. Several mass transfer correlation studies were examined for estimating the mass transfer coefficients (15, jL6,17,18,19). The correlation of Calderbank and Moo-Young (16) based on Kolmogaroff s theory of local isotropic turbulence has a standard deviation of 66%. The slip velocity method of Harriott (17) provides correlation with an average deviation of 39%. Brian and Hales (15) could not obtain super-imposable curves from heat and mass transfer studies, and the mass transfer data was not in agreement with that of Harriott for high Schmidt number values. 

The necessity of having two independent terms to describe the specific (or polar) interactions is relevant to the fact that most organic probes are amphoteric and may as well act as electron donors or electron acceptors, as seen in Table 9. In Table 9, it should be noted that LFERs for a general set of electron acceptors (or donors) which is the specific component of adsorption enthalpy may be closely related to LSERs of Kamlet-Taft, resulting in that the correlation coefficients are largely constant and the standard deviations are low, as below [119]... 

First, a typical power spectrum of capillary waves excited at the W/NB interface is shown in Figure 3.4a. The errors on the values of the capillary wave frequency were 0.1 kHz, obtained as the standard deviation of 10 repeated measurements. Capillary wave frequency dependence on CeHsONa is shown in Figure 3.4b. The frequency decreased significantly with increasing CeHsONa concentration. This indicated that interfacial tension was decreased by the interfacial adsorption of CeHsONa. 

It is useful to choose a solute which is really eluted by a size-exclusion process, without adsorption or any additional interaction phenomena which might modify the shape of the peak. The most trivial method is to analyze the shape of a low-MW pure substance. This is usually used to determine the number of theoretical plates, N = V,lcrf, where V, is the retention volume (volume at peak top) and a is the standard deviation, cr can be computed from the weighing of each data point of the peak or can be estimated from the width at 10% maximum height (cr = Wo,/4.3). 

The precision of the technique for seawater analysis as presented in the literature (i, 5) tends to be considerably better than we have observed here. The values obtained in other papers were for duplicate analysis of the same sample and were most likely extracted sequentially from the same bulk sample and analyzed one directly after the other. This was not the case here because the data analyzed in this paper were not generated specifically to analyze the ultimate precision of the technique. Line water samples run normally were as a rule interspersed throughout the test samples. A number of water samples would be drawn at the start of an experiment and stored unacidified in 4-1. polypropylene bottles. Over the course of up to 6 or 8 hr, extractions would be performed so that difiFerences in trace metal concentration might be expected between replicates run early and late in the experiments. This factor, which allows for significant adsorption and/or desorption of trace components, could readily explain our high standard deviations. We feel that this approach is valid to determine the precision of the technique in the field where non-optimum conditions often occur and where the factor of time between sampling and analysis is often an uncontrollable variable. It is likely that the actual precision of this technique in the field lies between those values calculated here and elsewhere (1,5). 

Reproducibility of the Raman intensity for the 1424 cm band of a particular dye at 10" M is summarized in Table 13.5. Relative standard deviations of five spectra of a given colloid solution as well as the relative standard deviation (rsd) for five different colloid solutions are listed. Significantly higher (rsd) was observed for different colloid solutions, implying that the particle agglomeration and analyte adsorption are quite sensitive to uncontrolled changes in conditions. The authors (61) concluded that preaggregation with poly-(L-lysine) yields quite reproducible intensities (rsd <5 per cent). 

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