Conditional equilibrium constants in multicomponent heterogeneous adsorption: The conditional affinity spectrum

The concept of conditional stability constant is extended to the competitive binding of small molecules to heterogeneous surfaces or macromolecules via the introduction of the conditional affinity spectrum (CAS). The CAS describes the distribution of effective binding energies experienced by one complexing agent at a fixed concentration of the rest. We show that, when the multicomponent system can be described in terms of an underlying affinity spectrum [integral equation (IE) approach], the system can always be characterized by means of a CAS. The thermodynamic properties of the CAS and its dependence on the concentration of the rest of components are discussed. In the context of metal/proton competition, analytical expressions for the mean (conditional average affinity) and the variance (conditional heterogeneity) of the CAS as functions of pH are reported and their physical interpretation discussed. Furthermore, we show that the dependence of the CAS variance on pH allows for the analytical determination of the correlation coefficient between the binding energies of the metal and the proton. Nonideal competitive adsorption isotherm and Frumkin isotherms are used to illustrate the results of this work. Finally, the possibility of using CAS when the IE approach does not apply (for instance, when multidentate binding is present) is explored. © 2006 American Institute of Physics.

Determination of the complexing capacity of synthetic and real wine for Zn using Absence of Gradients and Nerstian Equilibrium Stripping technique

The complexing capacity of synthetic (0.011 M tartrate in 13.5% ethanol) and real wine (Raimat Abadia) in titrations with added total Zn concentrations up to 0.03 M has been determined following the free Zn concentrations with AGNES (absence of gradients and Nernstian equilibrium stripping) technique. A correction to find the preconcentration factor or gain (Y1) really applied at each one of the ionic strengths reached due to Zn additions along the titration has been applied. The standard implementation of AGNES to real wine led to the observation of two anomalous behaviors: (a) an increasingly negative current in the deposition stage (labeled as “HER” effect) and (b) a minimum in the currents of the stripping stage plot (labeled as the “dip” effect). A practical strategy to apply AGNES avoiding the dip effect has been developed to quantify properly free Zn concentrations. The van den Berg–Ružic–Lee linearization method (assuming the existence of just 1:1 complexes) has been adapted to consider the dilution effect and the ionic strength changes. Aggregated stability constants and total ligand concentrations have been calculated from synthetic and wine titration data. The found complexing capacity in the studied wine (cT,L = 0.0179 ± 0.0007 M) indicates the contribution of ligands other than tartrate (which is confirmed to be the main one).

Coarse-graining and thermodynamics in far-from-equilibrium systems

Lying at the core of statistical physics is the need to reduce the number of degrees of freedom in a system. Coarse-graining is a frequently-used procedure to bridge molecular modeling with experiments. In equilibrium systems, this task can be readily performed; however in systems outside equilibrium, a possible lack of equilibration of the eliminated degrees of freedom may lead to incomplete or even misleading descriptions. Here, we present some examples showing how an improper coarse-graining procedure may result in linear approaches to nonlinear processes, miscalculations of activation rates and violations of the fluctuation-dissipation theorem.

Equilibrium of the simultaneous etherification ofisobutene and isoamylenes with ethanol inliquid-phase

The simultaneous etherification of isobutene and isoamylenes with ethanol has been studied using macroreticu-lar acid ion-exchange resins as catalyst. Most of the experiments were carried out over Amberlyst-35. In addition,Amberlyst-15 and Purolite CT-275 were also tested. Chemical equilibrium of four chemical reactions was studied:ethyl tert-butyl ether formation, tert-amyl ethyl ether formation from isoamylenes (2-methyl-1-butene and 2-methyl-2-butene) and isomerization reaction between both isoamylenes. Equilibrium data were obtained in a batchwisestirred tank reactor operated at 2.0 MPa and within the temperature range from 323 to 353 K. Experimental molarstandard enthalpy and entropy changes of reaction were determined for each reaction. From these data, the molarenthalpy change of formation of ethyl tert-butyl ether and tert-amyl ethyl ether were estimated. Besides, the chemical equilibrium between both diisobutene dimers, 2,4,4-trimethyl-1-pentene and 2,4,4-trimethyl-2-pentene, wasevaluated. A good agreement between thermodynamic results for the simultaneous etherification carried out in thiswork and those obtained for the isolated ethyl tert-butyl ether and tert-amyl ethyl ether systems was obtained.

General Equilibrium Analysis. A Century after Walras

2010 marks the hundredth anniversary of the death of Léon Walras, the brilliant originator and first formaliser of general equilibrium theory - one of the pillars of modern economic theory. In advancing much derided practical solutions Walras also displayed more concern for the problems of living in a second best world than is common in modern pure theories of the invisible hand, efficient market hypothesis, DSGE macroeconomics or the thinking of some contemporary free market admirers all based on general equilibrium theory. This book brings contributions from the likes of Kenneth Arrow, Alan Kirman, Richard Posner, Amartya Sen and Robert Solow to share their thoughts and reflections on the theoretical heritage of Léon Walras. Some authors reminisce on the part they played in the development of modern general economics theory; others reflect on the crucial part played by general equilibrium in the development of macroeconomics, microeconomics, growth theory, welfare economics and the theory of justice; others still complain about the wrong path economic theory took under the influence of post 1945 developments in general equilibrium theory.

General Equilibrium Long-Run Determinants for Spanish FDI: A Spatial Panel Data Approach

While general equilibrium theories of trade stress the role of third-country effects, little work has been done in the empirical foreign direct investment (FDI) literature to test such spatial linkages. This paper aims to provide further insights into long-run determinants of Spanish FDI by considering not only bilateral but also spatially weighted third-country determinants. The few studies carried out so far have focused on FDI flows in a limited number of countries. However, Spanish FDI outflows have risen dramatically since 1995 and today account for a substantial part of global FDI. Therefore, we estimate recently developed Spatial Panel Data models by Maximum Likelihood (ML) procedures for Spanish outflows (1993-2004) to top-50 host countries. After controlling for unobservable effects, we find that spatial interdependence matters and provide evidence consistent with New Economic Geography (NEG) theories of agglomeration, mainly due to complex (vertical) FDI motivations. Spatial Error Models estimations also provide illuminating results regarding the transmission mechanism of shocks.

The Role of Surfactant Properties of Extractants in Hydrometallurgical LiquidLiquid Extraction Processes

The amphiphilic nature of metal extractants causes the formation of micelles and other microscopic aggregates when in contact with water and an organic diluent. These phenomena and their effects on metal extraction were studied using carboxylic acid (Versatic 10) and organophosphorus acid (Cyanex 272) based extractants. Special emphasis was laid on the study of phase behaviour in a pre neutralisation stage when the extractant is transformed to a sodium or ammonium salt form. The pre neutralised extractants were used to extract nickel and to separate cobalt and nickel. Phase diagrams corresponding to the pre neutralisation stage in a metal extraction process were determined. The maximal solubilisation of the components in the system water(NH3)/extractant/isooctane takes place when the molar ratio between the ammonia salt form and the free form of the extractant is 0.5 for the carboxylic acid and 1 for the organophosphorus acid extractant. These values correspond to the complex stoichiometry of NH4A•HA and NIi4A, respectively. When such a solution is contacted with water a microemulsion is formed. If the aqueous phase contains also metal ions (e.g. Ni²+), complexation will take place on the microscopic interface of the micellar aggregates. Experimental evidence showing that the initial stage of nickel extraction with pre neutralised Versatic 10 is a fast pseudohomogeneous reaction was obtained. About 90% of the metal were extracted in the first 15 s after the initial contact. For nickel extraction with pre neutralised Versatic 10 it was found that the highest metal loading and the lowest residual ammonia and water contents in the organic phase are achieved when the feeds are balanced so that the stoichiometry is 2NH4+(org) = Nit2+(aq). In the case of Co/Ni separation using pre neutralised Cyanex 272 the highest separation is achieved when the Co/extractant molar ratio in the feeds is 1 : 4 and at the same time the optimal degree of neutralisation of the Cyanex 272 is about 50%. The adsorption of the extractants on solid surfaces may cause accumulation of solid fine particles at the interface between the aqueous and organic phases in metal extraction processes. Copper extraction processes are known to suffer of this problem. Experiments were carried out using model silica and mica particles. It was found that high copper loading, aromacity of the diluent, modification agents and the presence of aqueous phase decrease the adsorption of the hydroxyoxime on silica surfaces.

Essential factors for control of the equilibrium in the reversible rearrangement of M3N@Ih-C80 fulleropyrrolidines: Exohedral functional groups versus endohedral metal clusters

The effects of exohedral moieties and endohedral metal clusters on the isomerization of M3N@Ih-C80 products from the Prato reaction through [1,5]-sigmatropic rearrangement were systematically investigated by using three types of fulleropyrrolidine derivatives and four different endohedral metal clusters. As a result, all types of derivatives provided the same ratios of the isomers for a given trimetallic nitride template (TNT) as the thermodynamic products, thus indicating that the size of the endohedral metal clusters inside C80 was the single essential factor in determining the equilibrium between the [6,6]-isomer (kinetic product) and the [5,6]-isomer. In all the derivatives, the [6,6]- and [5,6]-Prato adducts with larger metal clusters, such as Y3N and Gd3N, were equally stable, which is in good agreement with DFT calculations. The reaction rate of the rearrangement was dependent on both the substituent of exohedral functional groups and the endohedral metal-cluster size. Further DFT calculations and 13C NMR spectroscopic studies were employed to rationalize the equilibrium in the rearrangement between the [6,6]- and [5,6]-fulleropyrrolidines

Analytical investigation of the atmospheric radiation limits in semigray atmospheres in radiative equilibrium

We model the wavelength-dependent absorption of atmospheric gases by assuming constant mass absorption coefficients in finite-width spectral bands. Such a semigray atmosphere is analytically solved by a discrete ordinate method. The general solution is analyzed for a water vapor saturated atmosphere that also contains a carbon dioxide-like absorbing gas in the infrared. A multiple stable equilibrium with a relative upper limit in the outgoing long-wave radiation is found. Differing from previous radiative–convective models, we find that the amount of carbon dioxide strongly modifies the value of this relative upper limit. This result is also obtained in a gray (i.e., equal absorption of radiation at all infrared wavelengths) water vapor saturated atmosphere. The destabilizing effect of carbon dioxide implies that massive carbon dioxide atmospheres are more likely to reach a runaway greenhouse state than thin carbon dioxide ones

Influence of the temperature and type of salt on the phase equilibrium of peg 1500 + potassium phosphate and peg 1500 + sodium citrate aqueous two-phase systems

The present work analyzed the effect of the temperature and type of salt on the phase equilibrium of aqueous two-phase systems (ATPS) formed by poly (ethylene glycol) (PEG) 1500 + potassium phosphate, from (278.15 to 318.15) K, and PEG 1500 + sodium citrate, from (278.15 to 298.15) K. The rise of the temperature normally increased the slope of the tie line (STL). With respect to the influence of the type of salt, sodium citrate showed better capability to induce phase separation, when compared to potassium phosphate.

Equilibrium studies of 2,2'-(5-bromo-6-methylpyrimidine-2,4-diyl)bis(azanediyl)dipropanoic acid with some transition-metal ions in aqueous solution

The stability constants of the 1:1 complexes formed between M2+ (M2+: Mn2+, Ni2+, Cu2+, or Cd2+) and BMADA2- (BMADA: 2,2'-(5-bromo-6-methylpyrimidine-2,4 diyl)bis(azanediyl)dipropanoic acid) were determined by potentiometric pH titration in aqueous solution (I = 0.1 mol L-1, NaNO3, 25 °C). The stability of the binary M - BMADA complexes is determined by the basicity of the carboxyl or amino groups. All the stability constants reported in this work exhibit the usual trend, and the order obtained was Mn2+< Ni2+ < Cu2+ > Cd2+. The observed stability order for BMADA approximately follows the Irving - Williams sequence. In the M - BMADA complexes, the M ion is able to form a macrochelate via the pyrimidine group of BMADA.