Colorimetric determination of molybdenum using sodium diethyldithiocarbamidate as reagent

Summary A method for the photometric estimation of molybdenum(V) by extraction of the complex formed with NaDDTC in 5 N HCl solution is discussed. The reduction of Mo(VI) to Mo(V) is achieved with hydrazine sulphate. The colour intensity of the chloroform extract of the complex is measured at 450 nm. Beer's law is obeyed up to 500 g/25 ml of molybdenum.

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Zusammenfassung Zur photometrischen Molybdänbestimmung wird der Komplex mit Diäthyldithiocarbamidat verwendet, der in 5 N salzsaurer Lösung gebildet und mit Chloroform extrahiert wird. Mo(VI) wird mit Hydrazinsulfat zur fünfwertigen Stufe reduziert. Die Messung erfolgt bei 450 nm; das Beersche Gesetz ist bis zu 500 g Mo/25 ml erfüllt.

     

On the order of the error function of the square-full integers

LetL(x) denote the number of square full integers ≤x. By a square-full integer, we mean a positive integer all of whose prime factors have multiplicity at least two. It is well known that $$\left. {L(x)} \right| \sim \frac{{\zeta ({3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-\nulldelimiterspace} 2})}}{{\zeta (3)}}x^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} + \frac{{\zeta ({2 \mathord{\left/ {\vphantom {2 3}} \right. \kern-\nulldelimiterspace} 3})}}{{\zeta (2)}}x^{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}} ,$$ where ζ(s) denotes the Riemann Zeta function. Let Δ(x) denote the error function in the asymptotic formula forL(x). On the basis of the Riemann hypothesis (R.H.), it is known that \(\Delta (x) = O(x^{\tfrac{{13}}{{81}} + \varepsilon } )\) for every ε>0. In this paper, we prove the following results on the assumption of R.H.: (1) $$\frac{1}{x}\int\limits_1^x {\Delta (t)dt} = O(x^{\tfrac{1}{{12}} + \varepsilon } ),$$ (2) $$\int\limits_1^x {\frac{{\Delta (t)}}{t}\log } ^{v - 1} \left( {\frac{x}{t}} \right) = O(x^{\tfrac{1}{{12}} + \varepsilon } )$$ for any integer ν≥1. In fact, we prove some general results and deduce the above from them. On the basis of (1) and (2) above, we conjecture that \(\Delta (x) = O(x^{{1 \mathord{\left/ {\vphantom {1 {12}}} \right. \kern-0em} {12}} + \varepsilon } )\) under the assumption of R.H.     

Existence theorems for optimization problems concerning hyperbolic partial differential equations

Existence theorems are given for optimal control problems with partial integro-differential equations of hyperbolic type. A variety of conditions are given depending on whether (i) the cost functional is in the Lagrange form or Mayer form, (ii) the controls vary in a fixed compact set or variable but closed sets, (iii) the required solutions are generalized or usual, (iv) the defining equations are nonlinear or linear in the state variable or linear in the control, (v) the trajectories belong to the usual Sobolev classW _p ² ,p>1, or the special Sobolev classW _p ^* , 1?p?∞. Several examples are given to illustrate the above cases. Necessary conditions for some of these problems have been discussed in an earlier paper.     

Hexavalent Chromium-Thioacetamide Redox System Initiated Polymerization of Acrylonitrile

Polymerization of acrylonitrile initiated by the Cr⁶⁺/thioacetamide redox system was studied in nitrogen atmosphere in the temperature range 35–45°C. The rate of polymerization and the rate of Cr⁶⁺ ion disappearance were measured. The effect of certain water-miscible organic solvents, neutral electrolytes, and complexing agents on the rate of polymerization was investigated. Chromic acid alone did not initiate the polymerization under deaerated and undeaerated conditions. Depending on the results obtained, a suitable kinetic scheme was proposed and various rate parameters were evaluated.     

Development of Polar Organic Mode Chromatographic Method by Polysaccharide-Based Immobilized Chiral Selector and Validation for the Determination of the Enantiopurity of Novel Mineralocorticoid Receptor Antagonist Atropisomer–Esaxerenone

Esaxerenone is a new nonsteroidal mineralocorticoid receptor antagonist utilized to treat high blood pressure. Chemically, esaxerenone is a pyrrole derivative consisting of hindered rotation, which results in stereoisomers named atropisomers. Currently, no methods exist for the separation and quantification of these atropisomers. A new and accurate chiral liquid chromatographic technique was developed and validated to estimate the enantiomeric purity of esaxerenone. Polar organic chiral separation was carried out on an immobilized amylose-based chiral stationary phase (Chiralpak IG) with methanol:acetonitrile:diethylamine (9:1:0.1, v/v/v) mixture as a mobile phase. The total runtime was 15 min, and the resolution (R_s) between the atropisomers was more than 3.0. The detection and quantification thresholds for the R-atropisomer were found to be 0.03 and 0.1 µg mL^?1, respectively, for a test concentration of esaxerenone (1000 µg mL^?1). Over the range from the limit of quantification to 0.3 percent, the method's linearity for the R-atropisomer was excellent (R²?>?0.999). The R-atropisomer recovery varied from 95 to 102%, confirming the method’s good accuracy. For a 48-h research period, the chemical was shown to be stable.

     

Application of p-N,N-dimethylphenylenediamine dihydrochloride for the determination of some diuretics

A spectrophotometric method is described for the determination of acetazolamide, frusemide, polythiazide, benzthiazide, hydrochlorothiazide, hydroflumethiazide, trichlormethiazide and amiloride hydrochloride (AML) either in pure form or in pharmaceutical formulations. The method is based on the reaction with p-N,N-dimethylphenylenediamine dihydrochloride and chloramine-T, to give a coloured product having maximum absorbance at 660 nm (for AML) or at 540 nm for the others, and reproducible within +/- 1.0%.