The formulation of the electron and proton balance equations for solving complicated equilibrium problems in redox titrations

 A plain, didactically convenient formulation of the electron balance and of the proton balance equations, suitable for complicated redox titration systems with redox, acid-base, precipitation and complexation side-reactions is discussed. Two typical examples, the standardisation of a permanganate solution by titration of iron(II), and the standardisation of a iodine solution by titration of sodium arsenite, are presented. Received: 30 January 1996/Accepted: 9 February 1996     

The formulation of the electron and proton balance equations for solving complicated equilibrium problems in redox titrations

 A plain, didactically convenient formulation of the electron balance and of the proton balance equations, suitable for complicated redox titration systems with redox, acid-base, precipitation and complexation side-reactions is discussed. Two typical examples, the standardisation of a permanganate solution by titration of iron(II), and the standardisation of a iodine solution by titration of sodium arsenite, are presented. Received: 30 January 1996/Accepted: 9 February 1996     

The necessary and sufficient conditions for chemical equilibrium

The article concerns a widely accepted but incorrect concept of conditions for chemical equilibrium. The authors present a mathematically rigorous derivation of the necessary and sufficient conditions for chemical equilibrium of systems of arbitrary complexity.     

Calculation techniques for solving non-isothermal kinetic problems

A calculation technique based on the SVD algorithm is suggested for solving non-isothermal kinetics problems. The uncertainties in the sought parameter values are obtained by superimposing random (Gauss) noise on experimental dependences.

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Zusammenfassung Ein auf dem SVD-Algorithmus beruhendes Rechenverfahren zur Lösung nichtisothermer kinetischer Probleme wir vorgeschlagen. Die Unbestimmtheit im Rauschparameterwert wurde in Abhängigkeit von den experimentellen Bedingungen durch die Überlagerung eines Random- (Gaußschen) Rauschens ermittelt.

     

Analysis of the informativity of kinetic measurements in solving inverse problems of chemical kinetics for multi-route reactions

Inverse problems of chemical kinetics that are solved in terms of a set of nonlinear ordinary differential, algebraic-differential, and algebraic equations corresponding to unsteady-state, steady-state, and equilibrium experimental conditions have been investigated. An algorithm has been devised for the analysis of the informativity of kinetic measurements in solving inverse problems of chemical kinetics for multi-route reactions.     

Validated computing approach for high-pressure chemical and multiphase equilibrium

For the computation of chemical and phase equilibrium at constant temperature and pressure, there have been proposed a wide variety of problem formulations and numerical solution procedures, involving both direct minimization of the Gibbs energy and the solution of equivalent nonlinear equation systems. Still, with very few exceptions, these methodologies may fail to solve the chemical and phase equilibrium problem correctly. Nevertheless, there are many existing solution methods that are extremely reliable in general and fail only occasionally. To take good advantage of this wealth of available techniques, we demonstrate here an approach in which such techniques can be combined with procedures that have the power to validate results that are correct, and to identify results that are incorrect. Furthermore, in the latter case, corrective feedback can be provided until a result that can be validated as correct is found. The validation procedure is deterministic, and provides a mathematical and computational guarantee that the global minimum in the Gibbs energy has been found. To demonstrate this validated computing approach to the chemical and phase equilibrium problem, we present several examples involving reactive and nonreactive components at high pressure, using cubic equation-of-state models.     

Semi-classical generalized Langevin equation for equilibrium and nonequilibrium molecular dynamics simulation

Molecular dynamics (MD) simulation based on Langevin equation has been widely used in the study of structural, thermal properties of matter in different phases. Normally, the atomic dynamics are described by classical equations of motion and the effect of the environment is taken into account through the fluctuating and frictional forces. Generally, the nuclear quantum effects and their coupling to other degrees of freedom are difficult to include in an efficient way. This could be a serious limitation on its application to the study of dynamical properties of materials made from light elements, in the presence of external driving electrical or thermal fields. One example of such system is single molecule dynamics on metal surface, an important system that has received intense study in surface science. In this review, we summarize recent effort in extending the Langevin MD to include nuclear quantum effect and their coupling to flowing electrical current. We discuss its applications in the study of adsorbate dynamics on metal surface, current-induced dynamics in molecular junctions, and quantum thermal transport between different reservoirs.     

A Numerical technique for solving carrier-mediated transport problems

A numerical technique and a computer program based on the method of orthogonal collocation on finite elements for solving steady state carrier-mediated transport problems is presented. The method is especially suitable in solving boundary layer type of problems as arise in carrier-mediated transport. The method uses an efficient LU decomposition of a blockdiagonal matrix. A residual criterion is used for the placement of elements which can be easily implemented using an interactive feature in the computer program. Numerical results for three different systems; a system with simple kinetics and equal diffusivities for carrier and its complex, a system with simple kinetics and unequal diffusivities and a system with complex kinetics and equal diffusivities, indicate that the method is very versatile and has very good convergence properties. The method can be used very easily for all these systems by making minor modifications to the computer program.     

Thermodynamic derivations of conditions for chemical equilibrium and of Onsager reciprocal relations for chemical reactors

For an isolated chemical reactor, we derive the conditions for chemical equilibrium in terms of either energy, volume, and amounts of constituents or temperature, pressure, and composition, with special emphasis on what is meant by temperature and chemical potentials as the system proceeds through nonequilibrium states towards stable chemical equilibrium. For nonequilibrium states, we give both analytical expressions and pictorial representations of the assumptions and implications underlying chemical dynamics models. In the vicinity of the chemical equilibrium state, we express the affinities of the chemical reactions, the reaction rates, and the rate of entropy generation as functions of the reaction coordinates and derive Onsager reciprocal relations without recourse to statistical fluctuations, time reversal, and the principle of microscopic reversibility.     

ESCA-Imaging used for problem solving in the chemical industry

Summary With a newly developed ESCA-experiment fast images with good lateral resolution are obtained. Examples from thin films on inorganic/ceramic-substrates (Langmuir-Blodgett, surfactants on ceramic) and on organic/polymeric-substrates (Pd-coating and polycarbonate, spin finish on polymer-fibres) as well as chemical changes of surfaces (oxidation of hair) are discussed. The simple analysis of electrically non-conducting samples represents an essential advantage of ESCA-Imaging.     

Correlation-function potential-harmonic and generalized Laguerre function method for directly solving Schrodinger equations of atoms

The potential-harmonic and generalized Laguerre function method (PHGLF) was modified into the correlation-function potential-harmonic and generalized Laguerre function method (CFPHGLF). The eigenenergies for 21S, 31S and 41S states of helium-like systems from the CFPHGLF are much more accurate than those from the previous PHGLF, but the eigenenergy for the 11S is not as good as that from the PHGLF method. The results indicate that the electron-nucleus cusp plays more important role than the electron-electron cusp and the cluster structure for the loosely bound excited states, and that the electron-electron cusp is absolutely essential for the tightly bound ground state.     

Generalized monotonically convergent algorithms for solving quantum optimal control problems

A wide range of cost functionals that describe the criteria for designing optimal pulses can be reduced to two basic functionals by the introduction of product spaces. We extend previous monotonically convergent algorithms to solve the generalized pulse design equations derived from those basic functionals. The new algorithms are proved to exhibit monotonic convergence. Numerical tests are implemented in four-level model systems employing stationary and/or nonstationary targets in the absence and/or presence of relaxation. Trajectory plots that conveniently present the global nature of the convergence behavior show that slow convergence may often be attributed to "trapping" and that relaxation processes may remove such unfavorable behavior.     

Theoretic quantum information entropies for the generalized hyperbolic potential

The Shannon entropy (S) and the Fisher Information (I) entropies are investigated for a generalized hyperbolic potential in position and momentum spaces. First, the Schrodinger equation is solved exactly using the Nikiforov-Uvarov-Functional Analysis method to obtain the energy spectra and the corresponding wave function. By Fourier transforming the position space wave function, the corresponding momentum wave function was obtained for the low-lying states corresponding to the ground and first excited states. The positions and momentum of Shannon entropy and Fisher Information entropies were calculated numerically. Finally, the Bialynicki-Birula and Mycielski and the Stam-Cramer-Rao inequalities for the Shannon entropy and Fisher Information entropies, respectively, were tested and were found to be satisfied for all cases considered.     

Applications of Haar basis method for solving some ill-posed inverse problems

In this paper a numerical method consists of combining Haar basis method and Tikhonov regularization method for solving some ill-posed inverse problems using noisy data is presented. By using a sensor located at a point inside the body and measuring the u(x, t) at a point x?=?a, 0?<?a?<?1, and applying Haar basis method to the inverse problem, we determine a stable numerical solution to this problem. Results show that an excellent estimation on the unknown functions of the inverse problem can be obtained within a couple of minutes CPU time at pentium IV-2.4?GHz PC.     

Flow injection analysis: A useful alternative for solving analytical problems

Summary In addition to its well-known advantages (e.g. ease of automation, high sample throughout and versatility, low sample and reagent consumption and analytical costs), flow injection analysis (FIA) offers the possibility of solving a number of specific analytical problems where poor sensitivity or selectivity, time-consuming preliminary steps, the use of HPLC in routine control for the analysis of a large number of samples, the determination of various analytes (multidetermination) or process monitoring in near-real time is involved.