Conductance of tetraalkylammonium salts in 2-butanone from −45 to 25°C

Interactions of three types of tetraalkylammonium cations (tetrapropyltetrabutyl-and tri-isoamylbutyl- ammonium) with perchlorate and tetraphenylborate anions were studied by the conductivity method in 2-butanone from –45°C to 25°C. Conductance data obtained for diluted solutions (5×10^–5 – 2×10^–3 mol-dm^–3) were used to calculate the limiting molar conductivities and associationconstants. The conductance equation of Fuoss-Hsia including the Chen term and the chemical model assumption were applied. Limiting ion conductivities were calculated assuming equal limiting conductivities of the i-Am₃BuN⁺ and BPh ₄ ^– ions at all temperatures. Gibbs energies and entropies of ion pair formation, calculated from the dependence of association constants on temperature, are presented including the contributions due to short-range forces.     

Raman spectral study of the constitution and equilibria of nitric acid and d-nitric acid

From relative integrated intensity measurements of the symmetric stretching vibration of nitrate ion in nitric acid solutions (both HNO ₃ /H ₂ O and DNO ₃ /D ₂ O), the mass law concentration quotients, Q were obtained as functions of concentration. By extrapolation the limiting dissociation constants were estimated to be 24.4 and 15 respectively at 25°C. It is shown that this constant refers to a process in which the ion pair H ₃ O⁺ NO ₃ ^– is in equilibrium with the dispersed, solvated H ₃ O⁺ and NO ₃ ^– ions.     

Electron-pairing analysis from localization and delocalization indices in the framework of the atoms-in-molecules theory

This article presents an overview of recent advances in the study of electron pairing through the use of localization and delocalization indices obtained from double integration over atomic basins of the exchange–correlation density in the framework of the atoms-in-molecules theory. These localization and delocalization indices describe the intra- and interatomic distribution of the electron pairs in a molecule. The main results of the application of these second-order indices to the analysis of molecular structure and chemical reactivity are briefly reviewed. It is shown that localization and delocalization indices represent a powerful tool to describe the electron-pair structure of molecules, which, in turn, provides deeper insight into relevant chemical phenomena such as electron correlation effects and the formation of localized α, β electron pairs. Received: 8 April 2002 / Accepted: 26 June 2002 / Published online: 6 September 2002 Acknowledgements. Financial help was furnished by the Spanish DGES projects no. PB98-0457-C02-01 and BQU2002-04112-C02-02. J.P. thanks the Departament d'Universitats, Recerca i Societat de la Informació de la Generalitat de Catalunya for benefiting from a doctoral fellowship, no. 2000FI-00582. M.S. is indebted to the Departament d'Universitats, Recerca i Societat de la Informació of the Generalitat de Catalunya for financial support through the Distinguished University Research Promotion, 2001. We also thank the Centre de Supercomputació de Catalunya for providing us with computing facilities. Correspondence to: M. Solà e-mail: miquel.sola@udg.es     

Effect of the type of ion-pairing reagent in reversed-phase ion-pair chromatography

Summary The retention of positively and negatively charged and neutral solutes was studied in an aqueous phosphate buffer eluent, with constant inorganic-counterion concentration, on ODS-Hypersil stationary phase in the presence of various sulfonic acid ion-pairing reagents. The adsorption isotherms of the ion-pairing reagents d-camphor-10-sulfonic acid, sodium cyclohexylsulfamic acid and sodium alkylsulfonates (butyl-, hexyl- and octyl-) were determined by the breakthrough method.Dedicated to Professor J. F. K. Huber on the occasion of his 60th birthday.     

Effect of ion pairing on steady-state voltammetric limiting currents at microelectrodes Part I. Theoretical principles

Voltammetric studies in solutions of high resistivity are facilitated by the use of microelectrodes under steady-state conditions. Such solutions are encountered with solvents of low permittivity because of the very sparing solubility of electrolytes. Moreover, in such media the supporting electrolyte, as well as the electroactive ionic species, is usually extensively ion paired. Here we predict the limiting current that will flow in these circumstances, when a monovalent ion undergoes a one-electron transfer at a hemispherical microelectrode to form a neutral product. The ion pairing equilibria are assumed to be fast but all diffusion coefficients are treated as distinct. An analytical solution is elusive in the general case, but a simple numerical procedure allows the limiting current to be predicted for any combination of the system parameters. Several special cases are also discussed, some of which yield explicit formulae for the limiting current. In a companion paper, experimental data are compared with the theoretical predictions.     

Osmotic and activity coefficients of sodium chloride-sorbitol and potassium chloride-sorbitol solutions at 25°C

Osmotic and activity coefficients are reported for sorbitol over the range 1.8–11.1m with NaCl as the reference and 1.8–7.6m with KCl as the reference electrolyte. The osmotic coefficients over the range 0–3.7m are identical with those reported earlier by Robinson. It was found that the activity coefficients of sorbitol are uniformly about four percent lower than those of dextrose. Activity coefficients of trace quantities of NaCl in concentrated sorbitol solutions are about one-half of their value in pure NaCl solutions while the activity coefficients of trace quantities of sorbitol in concentrated NaCl solutions are about one-third of their value in pure sorbitol solutions. Potassium chloride lowers the activity coefficient of sorbitol less than does sodium chloride in solutions of similar water activity. Sorbitol lowers the activity coefficients of potassium chloride in concentrated solution but actually elevates them in dilute solutions.     

Fast solving of weighted pairing least-squares systems

This paper presents a generalization of the “weighted least-squares” (WLS), named “weighted pairing least-squares” (WPLS), which uses a rectangular weight matrix and is suitable for data alignment problems. Two fast solving methods, suitable for solving full rank systems as well as rank deficient systems, are studied. Computational experiments clearly show that the best method, in terms of speed, accuracy, and numerical stability, is based on a special {1, 2, 3}-inverse, whose computation reduces to a very simple generalization of the usual “Cholesky factorization-backward substitution” method for solving linear systems.     

{Omega}-Admissible Theory

Arakelov and Faltings developed an admissible theory on regulararithmetic surfaces by using Arakelov canonical volume formson the associated Riemann surfaces. Such volume forms are inducedfrom the associated Kähler forms of the flat metric onthe corresponding Jacobians. So this admissible theory is inthe nature of Euclidean geometry, and hence is not quite compatiblewith the moduli theory of Riemann surfaces. In this paper, wedevelop a general admissible theory for arithmetic surfaces(associated with stable curves) with respect to any volume form.In particular, we have a theory of arithmetic surfaces in thenature of hyperbolic geometry by using hyperbolic volume formson the associated Riemann surfaces. Our theory is proved tobe useful as well: we have a very natural Weil function on themoduli space of Riemann surfaces, and show that in order tosolve the arithmetic Bogomolov-Miyaoka-Yau inequality, it issufficient to give an estimation for Petersson norms of somemodular forms. 1991 Mathematics Subject Classification: 11G30,11G99, 14H15, 53C07, 58A99.     

An extension of the pairing theory between divergence-measure fields and BV functions

In this paper we introduce a nonlinear version of the notion of Anzellotti's pairing between divergence-measure vector fields and functions of bounded variation, motivated by possible applications to evolutionary quasilinear problems. As a consequence of our analysis, we prove a generalized Gauss–Green formula.