Aplicação de métodos quimiométricos na especiação de Cr(VI) em solução aquosa

The equilibria, the spectra and the identities of the species of Cr(VI) that are present in aqueous solution have long been an active subject of discussion in the literature. In this paper, three different chemometric methodologies are applied to sets of UV/Visible spectra of aqueous Cr(VI) solutions, in order to solve a chemical system where there is no available information concerning the composition of the samples nor spectral information about the pure species. Imbrie Q-mode factor analysis, followed by varimax rotation and Imbrie oblique projection, were used to estimate the composition of Cr(VI) equilibrium solutions and, by combining these results with the k-matrix method, to obtain the pure spectra of the species. Evolving factor analysis and self modeling curve resolution were used to confirm the number of the species and the resolution of the system, respectively. Sets of 3.3×10-4 and 3.3×10-5 mol L-1 Cr(VI) solutions, respectively, were analyzed in the pH range from 1 to 12. Two factors were identified, which were related to the chromate ion (CrO4(2-)) and bichromate ion (HCrO4-). The pK of the equilibrium was estimated as 5.8.

A new method for analysing the equilibrium and time-dependent behaviour of Markovian models

Many large-scale stochastic systems, such as telecommunications networks, can be modelled using a continuous-time Markov chain. However, it is frequently the case that a satisfactory analysis of their time-dependent, or even equilibrium, behaviour is impossible. In this paper, we propose a new method of analyzing Markovian models, whereby the existing transition structure is replaced by a more amenable one. Using rates of transition given by the equilibrium expected rates of the corresponding transitions of the original chain, we are able to approximate its behaviour. We present two formulations of the idea of expected rates. The first provides a method for analysing time-dependent behaviour, while the second provides a highly accurate means of analysing equilibrium behaviour. We shall illustrate our approach with reference to a variety of models, giving particular attention to queueing and loss networks. (C) 2003 Elsevier Ltd. All rights reserved.

A quimiometria nos cursos de graduação em química: proposta do uso da análise multivariada na determinação de pkª

An experiment was proposed applying the Chemometric approach of Multivariate Analysis for inclusion in undergraduate Chemistry courses to promote and expand the use of this analytical-statistical tool. The experiment entails the determination of the acid dissociation constant of dyes via UV-Vis electronic spectrophotometry. The dyes used show from simple equilibrium to very complex systems involving up to four protolytic species with high spectral overlap. The Chemometric methodology was more efficient than univariate methods. For use in classes, it is up to the teacher to decide which systems should be utilized given the time constraints and laboratory conditions.

Solvatochromism in Binary Mixtures: First Report on a Solvation Free Energy Relationship between Solvent Exchange Equilibrium Constants and the Properties of the Medium

We have employed UV-vis spectroscopy in order to investigate details of the solvation of six solvatochromic indicators, hereafter designated as ""probes"", namely, 2,6-diphenyl-4-(2,4,6-triphenylpyridinium-1-yl) phenolate (RB); 4-[(E)-2-(1-methylpyridinium-4-yl)ethenyl] phenolate, MePM; 1-methylquinolinium-8-olate, QB; 2-bromo-4-[(E)-2-(1-methylpyridinium-4-yl)ethenyl] phenolate, MePMBr, 2,6-dichloro-4-(2,4,6-triphenylpyridinium-1-yl) phenolate (WB); and 2,6-dibromo-4-[(E)-2-(1-methylpyridinium-4-yl)ethenyl] phenolate, MePMBr,, respectively. These can be divided into three pairs, each includes two probes of similar pK(a) in water and different lipophilicity. Solvation has been studied in binary mixtures, BMs, of water, W, with 12 protic organic solvents, S, including mono- and bifunctional alcohols (2-alkoxyethanoles, unsaturated and chlorinated alcohols). Each medium was treated as a mixture of S, W, and a complex solvent, S-W, formed by hydrogen bonding. Values of lambda(max) (of the probe intramolecular charge transfer) were converted into empirical polarity scales, E(T)(probe) in kcal/mol, whose values were correlated with the effective mole fraction of water in the medium, chi w(effective). This correlation furnished three equilibrium constants for the exchange of solvents in the probe solvation shell; phi(W/S) (W substitutes S): phi(S-W/W) (S-W substitutes W), and phi(S-W/S) (S-W substitutes S), respectively. The values of these constants depend on the physicochemical properties of the probe and the medium. We tested, for the first time, the applicability of a new solvation free energy relationship: phi = constant + a alpha(BM) + b beta(BM) + s(pi*(BM) + d delta) + p log P(BM), where a, b, s, and p are regression coefficients alpha(BM), beta(BM), and pi*(BM) are solvatochromic parameters of the BM, delta is a correction term for pi*, and log P is an empirical scale of lipophilicity. Correlations were carried out with two-, three-, and four-medium descriptors. In all cases, three descriptors gave satisfactory correlations; use of four parameters gave only a marginal increase of the goodness of fit. For phi(W/S), the most important descriptor was found to be the lipophilicity of the medium; for phi(S-W/W) and phi(S-W/S), solvent basicity is either statistically relevant or is the most important descriptor. These responses are different from those of E(T)(probe) of many solvatochromic indicators in pure solvents, where the importance of solvent basicity is usually marginal, and can be neglected.

THE EQUILIBRIUM CONSTANT FOR THE GLYCINE SYNTHASE REACTION (ONE-CARBON, METABOLISM, FOLATE)

The equilibrium constant (K(,c)) under physiological conditions (38(DEGREES)C, 0.25 M ionic strength (I), pH 7.0) for the glycine synthase (GS) reaction (E C 2.1.2.1.0) (Equation 1) has been determined. (UNFORMATTED TABLE FOLLOWS)^ 5,10-CH(,2)-H(,4)Folate NADH NH (,4)+ CO(,2) ^ K(,c) = Eq. 1^ H(,4)Folate NAD('+) GLY ^(TABLE ENDS)^ The enzymatic instability of the GS enzyme complex itself has made it necessary to determine the overall K(,c) from the product of constants for the partial reactions of GS determined separately under the same conditions. The partial reactions are the H(,4)Folate-formaldehyde (CH(,2)(OH)(,2)) condensation reaction (Reaction 1) the K(,c) for which has been reported by this laboratory (3.0 x 10('4)), the lipoate (LipS(,2)) dehydrogenase reaction (LipDH) (Reaction 2) and the Gly-Lip^ decarboxylase reaction (Reaction 3) forming reduced lipoate (Lip(SH)(,2)), NH(,4)('+), CO(,2) and CH(,2)(OH)(,2.) (UNFORMATTED TABLE FOLLOWS)(,)^ H(,4)Fote + CH(,2)(OH)(,2) 5,10-CH(,2)-H(,4)Folate (1)^ Lip(SH)(,2) + NAD('+) LipS(,2) + NADH + H('+) (2)^ H('+) + Gly + LipS(,2) Lip(SH)(,2) + NH(,4)('+) CO(,2) + CH(,2)(OH)(,2) (3)^(TABLE ENDS)^ In this work the K(,c) for Reactions 2 and 3 are reported.^ The K(,c)' for the LipDH reaction described by other authors was reported with unexplainable conclusions regarding the pH depend- ence for the reaction. These conclusions would imply otherwise unexpected acid dissociation constants for reduced and oxidized lipoate. The pK(,a)',s for these compounds have been determined to resolve discrepancy. The conclusions are as follows: (1) The K(,c) for the LipDH reaction is 2.08 x 10('-8); (2) The pK(,a)',s for Lip(SH)(,2) are 4.77(-COOH), 9.91(-SH), 11.59(-SH); for LipS(,2) the carboxyl pK(,a)' is 4.77; (3) Contrary to previous literature, the log K(,c)' for the LipDH reaction is a linear function of the pH, a conclusion supported by the values for the dissociation constants.^ The K(,c) for Reaction 3 is the product of constants for Reactions 4-7. (UNFORMATTED TABLE FOLLOWS)^ LipSHSCH(,2)OH + H(,2)O Lip(SH)(,2) + CH(,2)(OH)(,2) (4)^ H(,2)O + LipSHSCH(,2)NH(,3)('+) LipSHSCH(,2)OH + NH(,4)('+) (5)^ LipSHSCH(,2)NH(,2) + H('+) LipSHSCH(,2)NH(,3)('+) (6)^ Gly + LipS(,2) LipSHSCH(,2)NH(,2) + CO(,2) (7)^(TABLE ENDS)^ Reactions 4-6 are non-enzymatic reactions whose constants were determined spectrophotometrically. Reaction 7 was catalyzed by the partially purified P-protein of GS with equilibrium approached from both directions. The value for K(,c) for this reaction is 8.15 x 10('-3). The combined K(,c) for Reactions 4-7 or Reaction 3 is 2.4 M.^ The overall K(,c) for the GS reaction determined by combination of values for Reactions 1-3 is 1.56 x 10('-3). ^

Corrección del deslizamiento de una ladera en la autovia A-4. PK. 340 en el término municipal de Marmolejo, Jaén mediante pantalla de pilotes y sistemas de drenaje

En este proyecto se describe el cálculo y diseño de una serie de medidas correctoras propuestas a raíz de un deslizamiento de ladera que tuvo lugar en noviembre de 2010 y afectó a parte de la calzada de la autovía A-4 en el P.K. 340 entre Córdoba y Jaén; principalmente en la ejecución de una pantalla de pilotes como elemento estructural de estabilización y contención del terreno, por medio del método de equilibrio límite y cálculo del módulo de reacción o coeficiente de balasto horizontal, a través del empleo de los programas Slope/W y RIDO respectivamente. ABSTRACT This project describes the calculation and design of a series of proposed corrective measures following a landslide of which took place in November 2010 and hit part of the road A-4 on the P.K. 340 between Cordoba and Jaen, mainly in the execution of a pile wall as a structural element of stabilization and containment of the terrain, through the limit equilibrium method and calculating the reaction module or horizontal ballast coefficient, through employment of the Slope/W and RIDO programs respectively.

Rumor Propagation Model: An Equilibrium Study

Compartmental epidemiological models have been developed since the 1920s and successfully applied to study the propagation of infectious diseases. Besides, due to their structure, in the 1960s an interesting version of these models was developed to clarify some aspects of rumor propagation, considering that spreading an infectious disease or disseminating information is analogous phenomena. Here, in an analogy with the SIR (Susceptible-Infected-Removed) epidemiological model, the ISS (Ignorant-Spreader-Stifler) rumor spreading model is studied. By using concepts from the Dynamical Systems Theory, stability of equilibrium points is established, according to propagation parameters and initial conditions. Some numerical experiments are conducted in order to validate the model.

The non-equilibrium nature of culinary evolution

Food is an essential part of civilization, with a scope that ranges from the biological to the economic and cultural levels. Here, we study the statistics of ingredients and recipes taken from Brazilian, British, French and Medieval cookery books. We find universal distributions with scale invariant behaviour. We propose a copy-mutate process to model culinary evolution that fits our empirical data very well. We find a cultural 'founder effect' produced by the non-equilibrium dynamics of the model. Both the invariant and idiosyncratic aspects of culture are accounted for by our model, which may have applications in other kinds of evolutionary processes.

Phase Equilibrium and Optimization Tools: Application for Enhanced Structured Lipids for Foods

Solid-liquid phase equilibrium modeling of triacylglycerol mixtures is essential for lipids design. Considering the alpha polymorphism and liquid phase as ideal, the Margules 2-suffix excess Gibbs energy model with predictive binary parameter correlations describes the non ideal beta and beta` solid polymorphs. Solving by direct optimization of the Gibbs free energy enables one to predict from a bulk mixture composition the phases composition at a given temperature and thus the SFC curve, the melting profile and the Differential Scanning Calorimetry (DSC) curve that are related to end-user lipid properties. Phase diagram, SFC and DSC curve experimental data are qualitatively and quantitatively well predicted for the binary mixture 1,3-dipalmitoyl-2-oleoyl-sn-glycerol (POP) and 1,2,3-tripalmitoyl-sn-glycerol (PPP), the ternary mixture 1,3-dimyristoyl-2-palmitoyl-sn-glycerol (MPM), 1,2-distearoyl-3-oleoyl-sn-glycerol (SSO) and 1,2,3-trioleoyl-sn-glycerol (OOO), for palm oil and cocoa butter. Then, addition to palm oil of Medium-Long-Medium type structured lipids is evaluated, using caprylic acid as medium chain and long chain fatty acids (EPA-eicosapentaenoic acid, DHA-docosahexaenoic acid, gamma-linolenic-octadecatrienoic acid and AA-arachidonic acid), as sn-2 substitutes. EPA, DHA and AA increase the melting range on both the fusion and crystallization side. gamma-linolenic shifts the melting range upwards. This predictive tool is useful for the pre-screening of lipids matching desired properties set a priori.

Liquid-Liquid Equilibrium of Aqueous Two-Phase Systems Containing Some Synthetic Polyelectrolytes and Polyethylene Glycol

Experimental results are presented for the liquid-liquid equilibrium of aqueous two-phase systems containing a synthetic polyelectrolyte (polysodium acrylate, polysodium methacrylate, and polysodium ethylene sulfonate) and polyethylene glycol at (298.2 and 323.2) K. A total of 40 phase diagrams were obtained, comprising data both of the binodal curve (obtained through cloud-point measurements) and of equilibrium compositions. The influences of temperature, the nature of the polyelectrolyte monomer unit, and the chain length of both types of polymers are analyzed and discussed.

Influence of Plasma Protein Binding on Pharmacodynamics: Estimation of In Vivo Receptor Affinities of beta Blockers Using a New Mechanism-Based PK-PD Modelling Approach

The objective of this investigation was to examine in a systematic manner the influence of plasma protein binding on in vivo pharmacodynamics. Comparative pharmacokinetic-pharmacodynamic studies with four beta blockers were performed in conscious rats, using heart rate under isoprenaline-induced tachycardia as a pharmacodynamic endpoint. A recently proposed mechanism-based agonist-antagonist interaction model was used to obtain in vivo estimates of receptor affinities (K(B),(vivo)). These values were compared with in vitro affinities (K(B),(vitro)) on the basis of both total and free drug concentrations. For the total drug concentrations, the K(B),(vivo) estimates were 26, 13, 6.5 and 0.89 nM for S(-)-atenolol, S(-)-propranolol, S(-)-metoprolol and timolol. The K(B),(vivo) estimates on the basis of the free concentrations were 25, 2.0, 5.2 and 0.56 nM, respectively. The K(B),(vivo)-K(B),(vitro) correlation for total drug concentrations clearly deviated from the line of identity, especially for the most highly bound drug S(-)-propranolol (ratio K(B),(vivo)/K(B),(vitro) similar to 6.8). For the free drug, the correlation approximated the line of identity. Using this model, for beta-blockers the free plasma concentration appears to be the best predictor of in vivo pharmacodynamics. (C) 2008 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 98:3816-3828, 2009

The Equilibrium Flux Method for the calculation of flows with non-equilbrium chemical reactions

The Equilibrium Flux Method [1] is a kinetic theory based finite volume method for calculating the flow of a compressible ideal gas. It is shown here that, in effect, the method solves the Euler equations with added pseudo-dissipative terms and that it is a natural upwinding scheme. The method can be easily modified so that the flow of a chemically reacting gas mixture can be calculated. Results from the method for a one-dimensional non-equilibrium reacting flow are shown to agree well with a conventional continuum solution. Results are also presented for the calculation of a plane two-dimensional flow, at hypersonic speed, of a dissociating gas around a blunt-nosed body.

Non-Equilibrium Reaction Rates in the Macroscopic Chemistry Method for DSMC Calculations

The Direct Simulation Monte Carlo (DSMC) method is used to simulate the flow of rarefied gases. In the Macroscopic Chemistry Method (MCM) for DSMC, chemical reaction rates calculated from local macroscopic flow properties are enforced in each cell. Unlike the standard total collision energy (TCE) chemistry model for DSMC, the new method is not restricted to an Arrhenius form of the reaction rate coefficient, nor is it restricted to a collision cross-section which yields a simple power-law viscosity. For reaction rates of interest in aerospace applications, chemically reacting collisions are generally infrequent events and, as such, local equilibrium conditions are established before a significant number of chemical reactions occur. Hence, the reaction rates which have been used in MCM have been calculated from the reaction rate data which are expected to be correct only for conditions of thermal equilibrium. Here we consider artificially high reaction rates so that the fraction of reacting collisions is not small and propose a simple method of estimating the rates of chemical reactions which can be used in the Macroscopic Chemistry Method in both equilibrium and non-equilibrium conditions. Two tests are presented: (1) The dissociation rates under conditions of thermal non-equilibrium are determined from a zero-dimensional Monte-Carlo sampling procedure which simulates ‘intra-modal’ non-equilibrium; that is, equilibrium distributions in each of the translational, rotational and vibrational modes but with different temperatures for each mode; (2) The 2-D hypersonic flow of molecular oxygen over a vertical plate at Mach 30 is calculated. In both cases the new method produces results in close agreement with those given by the standard TCE model in the same highly nonequilibrium conditions. We conclude that the general method of estimating the non-equilibrium reaction rate is a simple means by which information contained within non-equilibrium distribution functions predicted by the DSMC method can be included in the Macroscopic Chemistry Method.