A strong law of large numbers for generalized random sets from the viewpoint of empirical processes

In this article we prove a strong law of large numbers for Borel measurable nonseparably valued random elements in the case of generalized random sets.

     

Differential pulse polarographic determination of trace amounts of vanadium and molybdenum in various standard alloys and environmental samples after preconcentration of their morpholine-4-carbodithioates on microcrystalline naphthalene or morpholine-4-dithiocarbamate cetyltrimethyl-ammonium bromide-naphthalene adsorbent

A highly selective, sensitive, and fairly rapid and economical differential pulse polarographic (DPP) method has been reported for the determination of trace amounts of vanadium and molybdenum in standard alloys and various environmental samples. The morpholine-4-carbodithioates of these metals were retained (>99% recovery) quantitatively on microcrystalline naphthalene in the pH range 4.5-6.9 for vanadium and 1.5-4.5 for molybdenum. These metals were determined by DPP after desorption with 10 ml of 1 M HCl. Vanadium and molybdenum may also be preconcentrated by passing their aqueous solutions under similar conditions on morpholine-4-dithiocarbamate CTMAB-naphthalene adsorbent packed in a column at a flow rate of 1-5 ml min(-1) and determined similarly. The detection limits are 0.20 ppm for vanadium and 0.04 ppm for molybdenum at minimum instrumental settings (signal to noise ratio=2). The linearity is maintained in the following concentration ranges, vanadium 0.50-10.0 and molybdenum 0.10-9.0 ppm, with a correlation factor of 0.9996 (confidence interval of 95%, slopes 0.0196 and 0.01497 muA mug(-1), intercepts 3.65x10(-3) and -1.92x10(-3) respectively) and relative standard deviation of 1.1% in the microcrystalline method, while in the column method, the linearity is maintained in the concentration ranges, 0.50-6.5 for vanadium and 0.10-5.5 ppm for molybdenum with correlation factor of 0.9994 (with confidence interval of 95%, slopes 0.0194, 0.015 muA mug(-1), intercepts 3.60x10(-3) and -1.90x10(-3) respectively) and relative standard deviation of 1.4%. Various parameters such as the effect of pH, reagent, naphthalene and CTMAB concentrations, volume of aqueous phase and interference of a large number of metal ions on the estimation of vanadium and molybdenum have been studied in detail to optimize the conditions for their voltammetric determination at trace level in various standard alloys and environmental samples.     

Column preconcentration of trace manganese with the ion pair of 2-nitroso-1-naphthol-4-sulfonic acid tetradecyldimethylbenzyl-ammonium chloride supported on naphthalene and determination by derivative spectrophotometry

A column preconcentration method has been developed for the determination of trace amounts of manganese by preconcentration on 2-nitroso-1-naphthol-4-sulfonic acid (nitroso-S)-tetradecyldimethylbenzylammonium (TDBA) naphthalene as an adsorbent using a simple funnel tipped glass tube. Manganese reacts with nitroso-S to form a water soluble brown colored chelate anion. The chelate anion forms a water insoluble Mn-Nitroso-S-TDBA ion pair on naphthalene packed in a column in the pH range 9.6-10.5 at a flow rate of 1-2 ml/min. The solid mass consisting of manganese complex and naphthalene is dissolved in 5 ml of dimethylformamide (DMF) and the metal determined by second derivative spectrophotometry. The calibration curve is linear in the concentration range 0.25-35.0 micrograms of Mn in 5 ml of the final DMF solution. Eight replicate determinations of 25 micrograms of standard manganese solution give a mean peak height of 4.0 with a correlation coefficient of 0.9995 and relative standard deviation of +/- 1.1%. The sensitivity was calculated to be 0.502(d2 A/d lambda 2)/microgram ml-1 from the slope of the calibration curve. The detection limit was 0.020 microgram ml-1 for manganese at the minimum instrumental settings (signal to noise ratio = 2). Various parameters effecting the method such as the effect of pH, volume of aqueous phase and interference of a number of metal ions on the determination of manganese have been evaluated to optimize the conditions for its determination in standard alloys and biological samples.     

Simultaneous determination of lead and cadmium in various environmental and biological samples by differential pulse polarography after adsorption of their morpholine-4-carbodithioates onto microcrystalline naphthalene or morpholine-4-dithiocarbamate-CTMAB-naphthalene adsorbent

A highly selective, sensitive and rapid differential pulse polarographic method (DPP) has been developed for the simultaneous estimation of trace amounts of lead and cadmium in standard alloys, biological and environmental samples. The morpholine-4-carbodithioates of the samples were absorbed on microcrystalline naphthalene in the pH range of 5-10 for lead and 3.4-11 for cadmium. The metal complexes were desorbed with 10 ml of 1M HCl and determined simultaneously with a differential pulse polarograph. These metals can alternatively be quantitatively adsorbed on morpholine-4-dithiocarbamate-cetyltrimethylammonium bromide-naphthalene adsorbent packed in a column and determined similarly. The detection limits are 0.14 ppm for Pb and 0.014 ppm for Cd at minimum instrumental settings (signal-to-noise ratio = 2). The linearity is maintained in the concentration ranges of Pb, 0.7-15 ppm and Cd, 0.07-10 ppm with a correlation factor of 0.9997 and relative standard deviations of 0.95 and 0.81%, respectively. Various parameters such as the effect of pH, volume of aqueous phase, and interference of a number of metal ions on the estimation of lead and cadmium have been studied in detail to optimize the conditions for their simultaneous estimation in various biological and environmental samples.     

Column chromatographic preconcentration of palladium with dimethyl glyoxime and acenaphthenequinone dioxime on naphthalene

A solid material consisting of dimethyl glyoxime (DMG), acenaphthenequinone dioxime (ANDO) or DMG-ANDO on naphthalene provides a very convenient, rapid and economical method for the preconcentration of palladium in synthetic samples. Pd-DMG, Pd-ANDO and Pd-DMG-ANDO are quantitatively retained on naphthalene in the column in the pH ranges 2.2–4.4, 1.8–5.6 and 1.7–6.8, respectively. The solid mixture consisting of the metal complex together with naphthalene is stripped from the column with 5 ml of dimethylformamide (DMF)-n-butylamine and the absorbance is measured at 247.6 nm with an atomic absorption spectrometer. Calibration graphs are linear over the palladium concentration range 5–25 μg per 5 ml of the final solution for all the three complexes. Ten replicate determinations of a sample solution containing 10 μg of palladium gave mean absorbances of 0.180, 0.225 and 0.230 with relative standard deviations of 1.8, 1.7 and 1.6% using the reagents DMg, ANDO and DMG-ANDO, respectively. The sensitivity of the method is better than the direct atomic absorption spectrometric determination of palladium. It is highest in case of the mixed ligands, i.e., DMG-ANDO (0.038 μg ml^?1 for 1% absorption). The method can be applied to the trace determination of palladium in complex materials.     

N-Methylethylxanthocarbamate as an Analytical Reagent: Differential Pulse Polarographic Determination of Cadmium in Standard Alloys, Biological and Environmental Samples after Adsorption of its Complex on Microcrystalline Naphthalene

N-methylethylxanthocarbamate has been used as an analytical reagent for the determination of trace amounts of cadmium in standard alloys, biological, and environmental samples. The reagent has been found to form a water insoluble complex with cadmium. It is quantitatively adsorbed over microcrystalline naphthalene in the pH range 2.5 to 12.0. The metal complex is desorbed with HCl and cadmium determined with a differential pulse polarograph. The detection limit is 0.05 ppm (signal-to-noise ratio = 2) and the linearity is maintained in the concentration range 0.2–25 g/ml, with correlation coefficient of 0.9995 and a relative standard deviation of ±0.81%. Characterization of the electroactive process includes an examination of the degree of reversibility. Various parameters, such as the effect of pH, reagent concentration, amount of naphthalene, volume of aqueous phase, and the interference of a large number of metal ions on the determination of cadmium, have been studied in detail to optimize the conditions for its determination in various complex materials.     

Solvolytic behaviour and the solubilities of various inorganic compounds, lewis acids and bases in fused monobromo acetic acid solvent system—II

Solubilities and the solvolytic behaviour of various inorganic compounds, Lewis acids and bases in fused monobromoacetic acid at 60 ± 0.5°C are discussed. Ionic compounds are fairly soluble, iodides and thiocyanates being comparatively more soluble than chlorides and bromides. Tetraalkyl ammonium halides are highly soluble in this solvent. Conductometric and spectroscopic studies of various Lewis acids and bases in fused monobromoacetic acid indicate their solvolytic behaviour and their subsequent ionization. The solvolyses products BBr₃·CH₂BrCOOH and SbCl₅·CH₂BrCOOH have been observed to be the strongest Bronsted acids. Auto-ionization of this solvent has been supported by acid/base titrations.     

Ethylene- ando-phenylenediamine-N,N′-bis(dimethylmethylenephosphonic) acids as complexing agents

Summary Ethylene- ando-phenylene-diamine-N, N-bis(dimethylmethylenephosphonic) acids form polymeric complexes of general formula M₂L · xH₂O (M = Mn^II, Co^II, Ni^II, Cu^II, Zn^II, Cd^II or Pb^II; x=2 or 4). These have octahedral geometry and are polymeric, according to i.r. (far and near) and electronic spectral data and magnetic moment and thermogravimetric studies. The ligands are thought to be tetradentate for each metal atom, coordination taking place through phosphoryl oxygen and amino-group nitrogen.     

Preconcentration of trace cobalt with the ion pair of 2-(5-bromo-2-pyridylazo)-5-diethylaminophenol and tetraphenylborate onto microcrystalline naphthalene or column method and its determination by derivative spectrophotometry

Cobalt-2-(5-bromo-2-pyridylazo)-5-diethylaminophenol (5-Br-PADAP)-tetraphenylborate ion associated complex is quantitatively adsorbed on microcrystalline naphthalene in the pH range 3.5-9.5 from a fairly large volume of the aqueous samples (preconcentration factor ~30). After filtration, the solid mass consisting of the cobalt complex and naphthalene was dissolved with 5 ml of dimethylformamide (DMF) and the metal determined by first-derivative spectrophotometry. The cobalt-5-Br-PADAP complex can alternatively be quantitatively retained on ammonium tetraphenylborate-naphthalene adsorbent filled in a column (preconcentration factor 120) in the same pH range and determined similarly. The detection limit is 30 ppb (signal-to-noise ratio=2) and the calibration curve is linear over 0.3-8.0 mug of cobalt in 5 ml of the final DMF solution. Eight replicate determinations of 1.0 mug of cobalt gave a mean peak height of 0.208 (at 611.5 nm) with a relative standard deviation of 1.2%. The sensitivity of the method is 1.04 (dA/dnm) ml mug(-1) found from the slope of the calibration curve. The interference of a large number of anions and cations on the determination of cobalt has been studied and the optimized conditions developed were utilized for its trace determination in various standard alloys and biological samples.