Modeling spreading-pressure-dependent binary gas coadsorption equilibria using gravimetric data

The present work proposes an approach to building nonideal coadsorption models in a thermodynamically consistent fashion, including the effects of pressure and spreading pressure, from simple gravimetric measurements. This is an "inverse problem" of parameter determination from appropriate and limited experimental data.The approach relies on the nonideal adsorbed solution theory, which includes activity coefficients and their dependence on spreading pressure, and on an original form of the excess Gibbs energy of mixing. A fully analytical development leads to explicit relations between the infinite dilution activity coefficients and three sets of independent information: the parameters of this excess Gibbs function, the limiting slopes of measured binary gravimetric curves at two different total pressures, and the properties of the single-component isotherms. From there, the four parameters of the model may be determined quasi-analytically and uniquely. The method is exemplified with the coadsorption of CO(2) and CH(4) on activated carbon, and a heterogeneous set of data. On one hand, the total adsorbed mass of the two components is measured at 1 bar by "incremental gravimetry." On the other hand, data obtained from independent batch-type equilibration measurements at 2 bar allow a comparison of calculated and measured data for the individual component concentrations. It is emphasized, however, that only total adsorbed mass data are needed for application of the method.     

Densities and Apparent Molar Volumes of Aqueous NaNO3 Solutions at Temperatures from 292 to 573 K and at Pressures Up to 30 MPa

Densities of four aqueous NaNO₃ solutions (0.100, 0.303, 0.580, 0.892 mol-kg^–1 H₂O) have been measured in the liquid phase with a constant-volume piezometer immersed in a precision liquid thermostat. Measurements were made at ten isotherms between 292 and 573 K. The range of pressure was 0.1–30 MPa. The total uncertainty of density, pressure, temperature, and concentration measurements were estimated to be less than 0.06%, 0.05%, 10 mK, and 0.014%, respectively. Values of saturated densities were determined by extrapolating experimental P- data to the vapor pressure at fixed temperature and composition. Apparent molar volumes were derived using measured values of density for the solutions and for pure water. The apparent molar volumes were extrapolated to zero concentration to yield partial molar volumes at infinite dilution. The temperature, pressure, and concentration dependence of partial and apparent molar volumes were studied. The measured values of density and apparent and partial molar volume were compared with data reported in the literature.     

Disjoining Pressure of Thin Unfreezing Water Layers between the Pore Walls and Ice in Porous Bodies

Thickness h of unfreezing water layers formed between the ice column and the inner surface of thin molecularly smooth capillary (radius 1 m) was measured as a function of temperature (varying from –0.14 to –1°C) and external pressure (up to 8 MPa) by dilatometry. Disjoining pressure isotherms (h) were calculated on the basis of obtained data. The isotherms obtained give the same exponential dependence of onh, as the known isotherms for colloidal systems obtained using surface force apparatus and atomic force microscopy. The disjoining pressure arising in frozen bodies is balanced by the stresses in the skeleton of a porous body and can cause the local fracture of pore walls.     

Apparent molar volumes of aqueous calcium chloride to 250°C, 400 bars,and from molalities of 0.242 to 6.150

Relative densities of CaCl ₂ (aq) with 0.22ml(mol-kg^–1)6.150 were measured with vibrating- tube densimeters between 25 and 250°C and near 70 and 400 bars. Apparent molar volumes V calculated from the measured density differences were represented with the Pitzer ioninteraction treatment, with appropriate expressions chosen for the temperature and pressure dependence of the virial coefficients of the model. It was found that the partial molar volume at infinite dilution V ^o , and the second and third virial coefficients B ^V and C ^V , were necessary to represent V near the estimated experimental uncertainty. The ionic-strength dependent ^(1)v term in the B ^V coefficient was included in the fit. The representation for V has been integrated with respect to pressure to establish the pressure dependence of excess free energies over the temperature range studied. The volumetric data indicate that the logarithm of the mean ionic activity coefficient, ln ±(CaCl ₂ ), increases by a maximum of 0.3 at 400 bars, 250°C, and 6 mol-kg^–1 as compared with its value at saturation pressure.     

On the apparent molar volumes of nonelectrolytes in water

Apparent molar volumes of aqueous solutions of argon and xenon have been calculated using a previously developed comprehensive equation of state for nonelectrolyte systems. The equation consists of a virial expansion truncated after the fourth virial coefficient and a closed-form term approximating higher coefficients. Mixing rules are based on the composition dependence of virial coefficients, which is known from statistical mechanics. The equation accurately represents vapor-liquid and gas-gas equilibria for the Ar+H₂O and Xe+H₂O systems over wide ranges of pressure and temperature using two binary parameters. With the binary parameters determined from phase equilibrium data, the equation accurately predicts apparent molar volumes V in the near-critical and far-from-critical regions. Apart from reproducing experimental V data, the equation reveals remarkable maxima of V as a function of pressure and temperature in the near-critical region. The implications of this equation with respect to the Ar–H₂O potential are discussed via the second virial coefficient.     

P-Vm-x Properties of Water-Dimethylformamide Mixtures at 278.15 K and Pressures of up to 100 MPa

The compressibility coefficients k = (v ₀ - v)/v ₀ of water-dimethylformamide (DMF) binary mixtures in the entire composition range at 278.15 K and pressures of up to 100 MPa were measured with a constant-volume piesometer. From the measured densities at atmospheric pressure and the coefficients k, the following quantities were calculated: specific and molar volumes of water-DMF mixtures at the examined parameters of state, excess molar volumes, partial molar volumes of the components, and variation with external pressure of the excess Gibbs energy of the water-DMF system. At all the pressures, the dependence k = f(x) (where x is the mole fraction of DMF in the mixture) passes through a minimum at x 0.2. The composition dependence of the specific volume of water-DMF mixtures also shows extrema, and its shape depends on the pressure. The partial molar volume of water at infinite dilution in DMF slightly depends on pressure.     

Investigations of Molecular Interactions in Binary Mixtures of the Ionic Liquid [Emim][BF<Subscript>4</Subscript>] and <Emphasis Type="Italic">N</Emphasis>-Methylaniline at Temperatures from 293.15 to 323.15 K

Density (ρ) and speed of sound (u) values were measured for the binary mixture of 1-ethyl-3-methylimidazolium tetrafluoroborate ([Emim][BF₄]) and N-methylaniline over the entire range of mole fractions at temperatures from 293.15 to 323.15 K under atmospheric pressure. Using the basic experimental data, various acoustic and thermodynamic parameters were calculated and are discussed with regard to the molecular interactions in the binary systems. The partial molar volumes and partial molar isentropic compressibilities at infinite dilution have also been calculated. The excess values were fitted to Redlich–Kister polynomial equation to estimate the binary coefficients and standard deviation between the experimental and calculated values. Further, the molecular interactions in the binary mixture system are analyzed using the experimental FT-IR spectra recorded at room temperature.     

The predictive accuracy for estimating infinite dilution activity coefficients by γ∞-based UNIFAC

The predictive accuracy for estimating infinite dilution activity coefficients by a modification of the UNIFAC method wherein the group interaction parameters were based on only data (referred to as -based UNIFAC) has been studied. Estimates and measured values were compared for six prototypical solutes in a series of homologous n-alkanes, l-alcohols and alkanenitrile solvents. Despite the fact that the interaction parameters were derived using only data, this approach still gave serious errors due to several inherent problems in the original UNIFAC model. Its performance is sometimes even poorer than that of the original UNIFAC method. For example for nitromethane in alcohols and p-dioxane in nitriles values predicted by the -based UNIFAC are essentially zero. The large errors for these systems are most likely due to inaccurate interaction parameters in the -based UNIFAC method.     

Bestimmung der Aktivitätskoeffizienten im chromatographischen Modell „binärer Lösungen“

An explanation is given for the two possible ways of determination of the activity coefficients of solutes, when applying a new thermodynamic model of adsorption and partition chromatography, i. e. the binary solutions model.

     

On the Relation Between the Effective Resonance Energy and the Infinite Dilution Resonance Integral for (n,γ) Reactions

In this paper a possible relation between the effective resonance energy and the infinite dilution resonance integral of (n,) reactions is discussed. These two parameters are important data in thermal neutron activation analysis when using the single comparator method based on the Høgdahl convention. The values for these two parameters of more than one hundred (n,) reactions are considered, and the possibility of a — 2/3 power function is proposed.     

Time-dependent mixing and demixing processes in binary lipid monolayers studied by mixed and separate spreading using film pressure and film potential measurements

Using both spreading techniques — mixed spreading and separate spreading- and, simultaneously, film pressure and film potential measurements, the mixing behavior of the following five binary systems was investigated and compared: 1) system 1,2-dilauroyl-phosphatidylethanolamine/cholesterol; 2) system 1,2-dimyristoyl-phosphatidylethanolamine/cholesterol; 3) system 1,2-dipalmitoyl-phosphatidylethanolamine/cholesterol; 4) system Na-eicosyl sulphate/hexadecanol; 5) system phosphatidic acid/1,2-dimyristoyl-phosphatidylethanolamine.Analyzing the time and concentration dependence of the /a isotherms and v/a isotherms (^s = film pressure, v ^s potential,a=average area per molecule in mixed films in the monolayers) of the binary monolayers it can be concluded that the components of the binary systems 1–4 are complete miscible in the monolayers. On the other hand the components of the system 5 are probably partially miscible only.     

Sorption of Cations and Anions from a Binary Electrolyte at Uncharged Electrode Surface: Comparing the Monolayer and Two-Layer Adsorption Models

Equations for calculating coverage and decrease in the surface tension during co-adsorption of cations and anions (CA) on an uncharged interface from a binary electrolyte with concentration c are derived. The equations are valid if electric centers of CA are localized in two parallel layers. The vs. lnc curves, computed within this model and a model for co-adsorption in a common layer are compared. The vs. lnc curves, calculated within either model to an accuracy substantially exceeding experimental accuracy, may be formally described with an equation of the Frumkin isotherm for neutral molecules and a corresponding equation for . The link of effective parameters of the Frumkin isotherm with the adsorption parameters of mixed adsorption isotherms of CA depends on the model.     

Effect of Differences in the Orientation of Adsorbed Molecules and in the Magnitudes of Limiting Capacitances of the Inner Part on the Regularities of Coadsorption of Two Organic Substances

The Alekseev–Popov–Kolotyrkin model, complemented with a set of mixed Frumkin isotherms, is used to perform an analysis of joint adsorption of two neutral organic substances when there are substantial differences in (1) limiting potential drops _N1 and _N2 and (2) capacitances of the inner part at ₁ = 1 and ₂ = 1. It is shown that in the absence of a lateral interaction between coadsorbed species and at a certain ratio between their concentrations, in either case there exists a region of potentials where the set of isotherms has three solutions. The stability of these solutions is characterized and the curves of the differential capacitance (equilibrium and nonequilibrium) and the interfacial tension are calculated. A general analysis of the set of isotherms in the region of physically reasonable values of adsorption parameters is conducted.     

Dielectric constants of acetonitrile, γ-butyrolactone,propylene carbonate,and 1,2-dimethoxyethane as a function of pressure and temperature

The dielectric constants of 1,2-dimethoxyethane, acetonitrile, -butyrolactone, and propylene carbonate were determined from capacitance measurements extrapolated to infinite frequency; ln are reported as a function of pressure up to 80 MPa at 15, 25, 35, 45°C and as a function of temperature in the range 10 to 50°C at 0.10133 MPa. The variation of ln with temperature or pressure can be expressed by a second order polynomial expression. The isothermal compressibilities of the solvents were determined at 25°C from sound velocities, densities, and heat capacities. A simple correlation can be established between ln /P and for most aprotic solvent.     

Solid-Phase Surface Adsorption in Ag–Au|F–, H2O and Ag–Au|ClO–4, H2O Systems: Allowing for the Solid-Solution Nonideality

Integral and differential (with respect to the composition) isotherms of changes in the interfacial free energy (_m– ), the charge density q, and the surface composition X _Au of alloys equilibrated with an aqueous surface-inactive electrolyte are obtained in terms of a finite-thickness interfacial layer, with use of concentration dependences of activity coefficients of components of a polycrystalline binary alloy. Using ac measurements of the double-layer parameters, it is stated that the surface-active component in the Ag–Au|F^–, H₂O and Ag–Au|ClO^– ₄, H₂O systems at 298 K is gold. The Ag–Au solid solution shows negative deviations from Raoult's law, except for the compositions X _Au 0.04 and X _Au 0.80, where the solid solution properties approach those of an ideal solution.     

Powder dilution as a new method of elimination of interelement effects in energy-dispersive X-ray fluorescence analysis

Summary If the concentration of elements with Z>22 (Ti) is to be determined in mineral samples and if the concentration of any of these elements is greater than 1%, the sample is diluted by grinding it together with an appropriate amount of quartz powder in an agate mortar mill. The diluted sample is measured in powdered form in a spectro-cup at practically infinite thickness by energy-dispersive X-ray fluorescence; the counting rates are corrected by means of the Compton scattering peak and evaluated by use of calibration curves obtained by measuring standards on the basis of silica gel. The applicability of this method is established by measuring the concentrations of 12 elements with Z>22 in 14 mineral samples of varying composition.We thank the Bundesministerium für Forschung und Technologie for financial support and the Uranerzbergbau GmbH, Bonn, for supplying the mineral samples.     

Vapor‐Liquid Phase Equilibria for Carbon Dioxide+Isopentanol Binary System at Elevated Pressure

High‐pressure vapor‐liquid phase equilibrium data for carbon dioxide+isopentanol were measured at temperatures of 313.2, 323.1, 333.5 and 343.4 K in the pressure range of 4.64 to 12.71 MPa in a variable‐volume high‐pressure visual cell. The experimental data were well correlated with Peng‐Robinson equation of state (PR‐EOS) together with van der Waals‐2 two‐parameter mixing rule, and the binary interaction parameters were obtained. Henry coefficients and partial molar volumes of CO₂ at infinite dilution were estimated based on Krichevsky‐Kasarnovsky equation, and Henry coefficients increase with increasing temperature, however, partial molar volumes of CO₂ at infinite dilution are negative and the magnitudes decrease with temperature.     

Standard partial molar volumes of alcohols in aqueous dodecyltrimethylammonium bromide solutions

Density measurements of water-dodecyltrimethylammonium bromide (DTAB)-alcohol ternary systems as a function of alcohol and surfactant concentrations were carried out at 25°C. The alcohols were propanol (PrOH), 2-propanol (2-PrOH) and hexanol (HexOH). The apparent molar volume V_,R of alcohols have been calculated and the standard (infinite dilution) partial molar volumes of alcohols V _R at each surfactant concentration were obtained by means of a least squares fit of V_,R vs. the alcohol concentration. The V _R vs. surfactant concentration curves have been rationalized in terms of the partial molar volume of alcohol in the aqueous V _f and the micellar V _b phases and the distribution constant of alcohol between the aqueous and the micellar phases K. The V _b values for PrOH and HexOH together with those of butanol and pentanol previously reported satisfy the additivity rule giving a methylene group contribution of 16.7 cm³-mol^–1 which is identical to that reported in the literature from the study of pure liquid alcohols. No difference between V _b for PrOH and 2-PrOH has been found. From density data of water-alcohol and water-surfactant binary systems and of water-surfactant-alcohol ternary system, the apparent molar volume of the surfactant in the water-alcohol mixed solvent V_,S have been calculated as a function of the surfactant concentration and of the mixed solvent composition. The effect of the alkyl chain length of the alcohols and the effect of isomerization of the alcohols on the V_,S vs. surfactant concentration trends have been analyzed.     

Sedimentation equilibrium of suspensions of colloidal particles at finite concentrations

Equilibrium concentration profiles of non-dilute colloidal suspensions are calculated by means of the Carnahan-Starling expression for the osmotic compressibility of hard sphere liquids. The profiles depend on the average volume fraction of the suspension, , and on the field interaction parameter, ₀ (reciprocal of the Péclet number at infinite dilution). Profiles are computed for values of and ₀ typical of those encountered in sedimentation field-flow fractionation experiments. It is found that, in most cases, the volume fraction at the depletion wall is negligibly small and that the volume fraction at the accumulation wall ₀, depends on the ratio <>₀/₀ only. An inflexion point is found in the concentration profile if ₀ is larger than 0.13 whatever the value of ₀.