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.     

Theory of swelling of a crosslinked substance in equilibrium with a pure solvent in various phases. Part II: The variation of the pressure

A theory of swelling is presented which describes the equilibrium swelling of a body in a solvent in its various states. The pressure dependence of the pressure-concentration swelling curves is treated for the swelling agent occurring in the liquid, crystalline or vapor phase. The slopes of the pressureconcentration swelling curves are dependent on the differential volume of dilution of the solvent and, additionally, on the volume changes of vaporization, crystallization, and sublimation of the solvent corresponding to the state of the swelling agent. At the melting and boiling pressure of the swelling agent the swelling curves change their slopes with a discontinuity, which is most distinct at the evaporation transition. By measurements of the slopes of the swelling curves at the transition pressure the derivative ₁/w₁ at constant temperature and pressure, which is the change of the chemical potential of the solvent with its weight fraction, is obtained. Thus, a further equation is given to test statistical theories at the transition pressures. Simultaneous variations of the swelling with changes of temperature are also treated.     

Some remarks on the solubility of gases in liquid long-chainn-alkanes andn-alkan-1-ols

The Ostwald coefficients L_2,1 of He, Ne, Ar, Kr, Xe, N₂, O₂, CH₄ CF₄ and SF₆ dissolved in several homologous_n-alkanes,_n-C₁H₂₁₊₂, 6l16, andn-alkan-1-ols,n-C₁H₂₁₊₁OH, 1l11, were recently measured at 298.15 K and atmospheric pressure with a modified Ben-Naim/Baer apparatus. Altogether, 201 gas/liquid systems were investigated. For about half of these systems, both pressure control and measurement of the volume of gas dissolved in a given volume of solvent were achieved with a microprocessor. This improved medium-precision instrument (0.5% in most cases) combines easy handling with fully automated data retrieval, and is totallymercury-free. In this communication, the salient points of data reduction are presented, with the focus on the estimation of several important auxiliary quantities such as second virial coefficients and partial molar volumes at infinite dilution. The effect of the chain lengthl of then-alkane or then-alkan-1-ol upon solubility is demonstrated, and some correlations betweenL _2,1, or the derived Henry fugacitiesH _2,1, and appropriate molecular and/or bulk properties of the gases and the solvents are discussed.     

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.     

Gas chromatography on a self-associating component of a binary phase. Retention model by formal analogy with conductance of electrolytes in dilute solution

Summary The dependence of specific retention by a binary stationary phase in GC can be expressed as the sum of the products of the specific retention of the pure components times their respective volume fractions. In this study, however, one component has a site, which is not only mainly responsible for the selectivity, but also participates in strong self-association. This requires introduction of a concentration-dependent factor (^x) in the corresponding term of the equation correlating Vg _mix ^x with x. In the GC resolution of N-trifluoroacetyl-amino acid isopropyl esters on a binary phase, N-lauroyl-L-amino t-butyl amide-squalane, data for the values of ^x were obtained.Adapting a previously developed LC retention model to the above GC data, an equation was derived for the dependence of ^x on the weight fraction (x) of the selector, namely ^x=1/x. This relationship permits calculation of retention volumes on the binary phase for a given x, as well as corresponding resolution coefficients of enantiomeric amino acid derivatives with generally excellent agreement with experiment. The chirality of the system is not relevant to application of the equation.     

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.     

Estimation of solubility and interaction parameters in binary liquid mixtures by reversed-flow gas chroamtography

Summary A new method, called reversed-flow gas chromatography, is presented for the measurement of the gaseous equilibrium concentrations of all the components under study, both in the pure state and in binary liquid mixtures. From the equilibrium concentrations, activities, activity coefficients and volume fraction activity coefficients were determined. Using various empirical equations relating activity with the molecular interactions between the components of a binary liquid mixture, the solubility parameters of ethanol, 1-propanol, acetone and methylethylketone in water were calculated. The total interaction parameters and the partial contributions of the dispersion, orientation and residue forces on the van der Waals attraction between the organic compounds and water were also computed. The variation of the interaction parameters with the composition of organic component in the binary mixture was investigated. The successful application of reversed-flow gas chromatography to the estimation of polymer solubility parameters is also reported. Finally, the solubility parameters found by the present method are compared with those determined by other techniques or calculated theoretically.     

Substantiation of the method of an “ideal adsorption solution” for calculating the adsorption of binary vapor mixtures from the individual isotherms

Conclusions Substantiation was offered for the method of an ideal adsorption solution, which was proposed by Myers and Prausnitz to calculate the adsorption equilibrium of binary vapor mixtures with a solid adsorbent from the individual isotherms, for the particular case of adsorption systems for which is fulfilled the condition of an affinity of the adsorption isotherms of the vapor mixtures at a constant composition of the adsorption solution, and the condition of the additivity of the affinity coefficient of such a solution.Translated from Izvestiya Akademii Nauk SSSR, Seriya, Khimicheskaya, No. 1, pp. 171–173, January, 1972.     

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.     

An automatic gravimetric titrator and its use for the potentiometric determination of uranium by the Davies and Gray method

Summary Construction and mode of operation of an automatic gravimetric titrator are described. Center of the system is a Titroprint E 475 which was modified on a few points. The titrant is added by use of two automatically controllable motor burettes as a main volume, and then in steps of 0.01 ml. The losses of weight of the reservoir vessel are correspondingly recorded by an electronic balance. The measured data are obtained on a punched tape and allow evaluations of the analysis as gravimetric and volumetric titration by use of two Basic computer programs. When the system was used for the potentiometric determination of uranium a relative standard deviation of 0.48 (gravimetric and volumetric) and relative deviations from the nominal value of –0.41 (gravimetric) and –0.79 (volumetric) were obtained as mean values for 14 groups of 5–6 samples.

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Ein automatischer gravimetrischer Titrator und seine Anwendung für die potentiometrische Bestimmung von Uran nach Davies und Gray

Zusammenfassung Es werden Aufbau und Betriebsweise eines automatischen gravimetrischen Titrators beschrieben, dessen Hauptkomponente ein in mehreren Punkten modifizierter Titroprint E 475 ist. Das Titrationsmittel wird mit zwei elektronisch steuerbaren Motorbüretten grob- bzw. feindosiert, wobei eine elektronische Waage die entsprechenden Gewichtsverluste des Reservoirgefäßes registriert. Die auf Lochstreifen ausgegebenen Meßdaten lassen Auswertungen der Analyse als gravimetrische und volumetrische Titration über entsprechende Basic-Computerprogramme zu. Bei Benutzung des Systems für die potentiometrische Bestimmung von Uran wurden für Gruppen von 5–6 Proben mittlere relative Standardabweichungen von 0,48 (gravimetrisch und volumetrisch) sowie mittlere relative Abweichungen vom Sollwert von –0,41 (gravimetrisch) bzw. –0,79 (volumetrisch) erhalten.

     

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.

     

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.     

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.     

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.     

Pure and mixed monolayers of poly-L-methionine and poly-γy-methyl-L-glutamate with 1,2 dioleyl-L-α-phosphatidylcholine at air-water interface

Monolayers of poly-L-methionine (PM) and poly--methyl-L-glutamate (PMG), spread at an air-water interface, exhibit a high compressibility plateau region at 10 dyn/cm and 18 dyn/cm in their respective-A curves. This behaviour is related to a-helical conformation of the polypeptide molecules in the said interface.Comparative studies of the areas per residue observed in the spreading isotherms, with the areas calculated from molecular models, indicate that the polypeptide molecules should be associated in parallel, forming islets of at least 5-helix chains.Mixed monolayers corresponding to the poly-L-methionine (PM)-1,2 dioleyl-L--phosphatidylcholine (DOPC) and poly--methyl-L-glutamate (PMG)-1,2 dioleyl-L--phosphatidylcholine (DOPC) systems, follow, in every case, the additivity rule for monolayer composition, any indicating that its components are insoluble in the surface mixture. In the case of mixed monolayers of PM-DOPC, a certain degree of compatibility is possible among its components, as a modulation of the plateau region is observed in the spreading isotherms, while for the PMG-DOPC system the plateau region appears at the same surface pressure value as the isotherm corresponding to pure PMG polypeptide.Instituto de Química-Física Rocasolano, C.S.I.C. Madrid -6, España