Activity coefficients of adsorbed mixtures

Experimental and simulated data for adsorption of gas mixtures on energetically heterogeneous surfaces like activated carbon and zeolites exhibit negative deviations from ideality. The deviations are large in some cases, with activity coefficients at infinite dilution equal to 0.1 or less. Similar molecules form ideal mixtures, but molecules of different size or polarity are nonideal. Equations for bulk liquid mixtures (Wilson, Margules, etc.) do not apply to isobars for adsorbed mixtures. A two-constant equation for activity coefficients as a function of composition and spreading pressure is in good agreement with theory, simulation, and experiment.     

GCA-EoS: A SAFT group contribution model—Extension to mixtures containing aromatic hydrocarbons and associating compounds

GCA-EoS is the first equation of state that takes into account association using a SAFT-like group contribution term. It has been recently upgraded to deal simultaneously with multiple associating and solvating groups. In this work a review of applications and parameters revisions are presented and the GCA-EoS extension to aromatic hydrocarbons is discussed. These compounds are important in different industrial fields (textile, fine chemicals, pharmaceutical, petrochemicals, materials, etc.). Moreover, compounds like phenol play a major role not only in several polymers syntheses but also in biomass processing mixtures. Specifically, the extension to systems containing aromatic hydrocarbons (BETX and alkylbenzenes), water and alkanols is discussed.     

Activity coefficients of concentrated strong and weak electrolytes by a hydration equilibrium and group contribution model

A new speciation-based group contribution model for activity coefficients is proposed to estimate the equilibrium properties of aqueous solutions containing electrolytes. The chemical part of the model accounts for the hydration equilibrium of water and ions with the formation of ion n-water complexes in a single stage process; the hydration number n and the hydration equilibrium constant K are the two independent parameters in this part. The physical part of the model is the UNIFAC group contribution model for short-range interactions. Each ion is considered as a group. Long-range interactions are accounted for by a Pitzer contribution (Debye–Hückel theory). The model is compared with experimental data at 25 °C including water activity, osmotic coefficients, activity coefficients, and pH of binary diluted and concentrated electrolyte solutions (up to 20 mol kg⁻¹ for NaOH, 16 mol kg⁻¹ for HCl, etc.).     

Activity coefficients of binary methanol alcohol mixtures from cluster weighting

The hydrogen bond network of different small alcohols is investigated via cluster analysis. Methanol/alcohol mixtures are studied with increasing chain length and branching of the molecule. Those changes can play an important role in different fields, including solvent and metal extraction. The extended tight binding method GFN2-xTB allows the evaluation and geometry optimization of thousands of clusters built via a genetic algorithm. Interaction energies and geometries are evaluated and discussed for the neat systems. Thermodynamic properties, such as vaporization enthalpies and activity coefficients, are calculated with the binary quantum cluster equilibrium (bQCE) approach using our in-house code Peacemaker 2.8. Combined distribution functions of the distances against the angles of the hydrogen bonds are evaluated for neat and mixed clusters and weighted by the equilibrium populations achieved from bQCE calculations.     

Activity coefficients for NaCl in ethanol-water mixtures at 25°C

Activity coefficient values for NaCl in ethanol-water mixtures containing 20, 40, 60, 70, 80 and 90 weight % ethanol are calculated from the emf for the galvanic cell $$Na - glass|NaCl(m), H_2 O (100 - Y), EtOH(Y), AgCl|Ag$$ in which the weight % of the corresponding solvent is indicated in parenthesis. The results obtained are analyzed by using different theoretical models. Chemical models which take into account the presence of ion pairs in solutions of high ethanol content are also used. There is good agreement between the results obtained from all the models.     

Activity coefficients of electrolytes in binary mixtures calculated using total molal quantities

Activity coefficients in binary mixed electrolytes are expressed in terms of the parameters from total molal quantities. Two versions of the calculations are presented and compared with the methods of Pitzer and Scatchard. For each method interrelations among the various parameters are examined. The system being tested is HCl+CoCl₂+H₂O at 25°C, for which new experimental data at low ionic strengths are included.     

Application of the disquac group contribution model to binary liquid organic mixtures

The DISQUAC group contribution method for correlating and predicting the thermodynamic properties of liquid mixtures (phase diagrams and related excess functions, Gibbs energy and enthalpy) is reviewed. Examples are given of its application to recently investigated mixtures, including linear or cyclic ketones, mono- or polychloroalkanes, cycloalkanes and n-a1kanes.     

Prediction of global vapor-liquid equilibria for mixtures containing polar and associating components with improved renormalization group theory

Our recently improved renormalization group (RG) theory is further reformulated within the context of density functional theory. To improve the theory for polar and associating fluids, an explicit and complete expression of the theory is derived in which the density fluctuation is expanded up to the third-order term instead of the original second-order term. A new predictive equation of state based on the first-order mean spherical approximation statistical associating fluid theory (FMSA-SAFT) and the newly improved RG theory is proposed for systems containing polar and associating fluids. The calculated results for both pure fluids and mixtures are in good agreement with experimental data both inside and outside the critical region. This work demonstrates that the RG theory incorporated with the solution of FMSA is a promising route for accurately describing the global phase behavior of complex fluids and mixtures.     

Activity and osmotic coefficients oft-butylammonium chloride; Activity coefficients of HCl in mixtures with tris hydrochloride ort-butylammonium chloride at 25°C

In an earlier study, the activity coefficients of aqueous mixtures of HCl with the hydrochlorides of tris(hydroxymethyl)aminomethane (Tris) ort-butylamine (t-B) were determined at ionic strengths of 0.1, 0.5, and 1.0 mol-kg^–1. The work has been extended to ionic strengths of 2.0 and 3.0 through emf measurements with hydrogen and AgCl/Ag electrodes at 25°C. The results are considered in terms of Harned's rule and the Pitzer and Rush-Johnson-Scatchard treatments of activity coefficients in electrolyte mixtures. In order to compare ionic interaction parameters in the two systems, the activity coefficients and osmotic coefficients of t-butylammonium chloride at molalities up to saturation (7.14 mol-kg^–1) were determined by the gravimetric isopiestic method with solutions of NaCl as reference. The behavior for both systems can be accounted for satisfactorily in terms of binary (H⁺–N⁺) and ternary (H⁺–N⁺–Cl^–) interactions, where N⁺ is either Tris·H⁺ or t-B·H⁺.     

Virial coefficients and inversion curve of simple and associating fluids

Free energy simulation method is applied to calculate the virial coefficients of square-well (SW) fluids of variable well-width and square-well based dimer forming associating fluids. In this approach, Monte Carlo sampling is performed on a number of molecules equal to the order of integral, and configurations are weighted according to the absolute value of the integrand. An umbrella-sampling average yields the value of the cluster integral in reference to a known integral. By using this technique, we determine the virial coefficients up to B₆ for SW fluid with variable potential range from λ = 1.25 to λ = 3.0 and model associating fluids with different association strengths: ?_af = 0.0, 8.0, 16.0 and 22.0. These calculated values for SW fluids are in good agreement with the literature. We examine these coefficients in the context of the virial equation of state (VEOS) of SW fluids. VEOS up to B₄ or up to B₆ describes the PVT behavior along the saturated vapor line better than the series that includes B₅. We used these coefficients to find the critical properties of SW fluids and compared with the literature values. Boyle temperature is also determined and is found to increase with the increase in the well-extent and associating strength. We also report Joule–Thomson inversion curve for Lennard–Jones fluid and SW fluids using different truncated VEOS and compared with that predicted from established EOS.     

Bulk and interfacial wetting behavior of binary mixtures induced by associating between unlike-pair molecules

The statistical associating fluid theory of Wertheim is applied to describe binary mixtures with associating between unlike-pair molecules. The phase behavior of this binary mixture would fall into five different types (I, II, III, V, and VI) of the classification scheme of van Konynenburg and Scott by varying the associating strength and the energy parameters. Both interfacial wetting behavior and wetting transitions are carefully examined in all the vapor-liquid-liquid (gamma-beta-alpha) three-phase-coexisting regions of the binary mixtures. The global wetting behavior and wetting transitions are delineated by scanning the parameter space. In certain regions, the middle beta phase exhibits interfacial phase transitions sequentially, nonwetting --> partial-wetting --> nonwetting, at the interface separating lower alpha and upper gamma phases along with increasing temperature.     

Ionization coefficients in gas mixtures

We have tested the application of the common $E/N$ (E—electric field, N—gas number density) or Wieland approximation [Van Brunt, R.J., 1987. Common parametrizations of electron transport, collision cross section, and dielectric strength data for binary gas mixtures. J. Appl. Phys. 61 (5), 1773–1787.] and the common mean energy (CME) combination of the data for pure gases to obtain ionization coefficients for mixtures. Test calculations were made for $\mathrm{Ar}–{\mathrm{CH}}_4$, $\mathrm{Ar}–{\mathrm{N}}_2$, He–Xe and ${\mathrm{CH}}_4–{\mathrm{N}}_2$ mixtures. Standard combination procedure gives poor results in general, due to the fact that the electron energy distribution is considerably different in mixtures and in individual gases at the same values of $E/N$. The CME method may be used for mixtures of gases with ionization coefficients that do not differ by more than two orders of magnitude which is better than any other technique that was proposed [Marić, D., Radmilović-Rađenović, M., Petrović, Z.Lj., 2005. On parametrization and mixture laws for electron ionization coefficients. Eur. Phys. J. D 35, 313–321.].     

Activity coefficients in aqueous mixtures of hydrochloric acid and lanthanum chloride at 25°C

Activity coefficients of hydrochloric acid in aqueous solutions of lanthanum chloride were determined by an emf method at 25°C over an ionic strength range 0.05–3 mol-kg^–1. Harned's rule was obeyed within experimental error by the acid in all the mixtures. However, the fit with Pitzer's equations was not as good as the Harned rule fit, even though the effects of higher-order electrostatic terms were considered. Activity coefficients for the salt in the mixtures were derived using the Pitzer equations and fitted to the Harned equation, whereupon Harned's rule was found to be valid for the salt up to an ionic strength of 0.3 mol-kg^–1 only.     

Activity coefficients of NaF in aqueous mixtures with ɛ-increasing co-solvent: formamide–water mixtures at 298.15 K

The electromotive force E, of the cell containing the ion-selective electrodes Na-ISE | NaF(m), formamide (Y), H₂O(100 − Y) | F-ISE has been measured at 298.15 K as a percentage of the weight of the amide in the mixed solvent. The percentage (Y) was varied from 0 to 90% in 10-unit steps, and the molality of the electrolyte (m) from approximately 0.005 to saturation. The corresponding standard electromotive forces, E⁰ (molal scale), were determined using traditional methods of extrapolation (Debye–Hückel and Pitzer equations). The results obtained by application of both equations show experimental errors of the same sort as those for this type of measurements. Once the E⁰ was obtained, we determined the mean ionic activity coefficients for NaF, the transfer free energy from water to the water–formamide mixture, and the NaF primary hydration number. The variation of these parameters, with the composition of this ɛ-increasing solvent, is discussed in comparison with that previously obtained for the ɛ-decreasing methanol–water and ethanol–water systems, in terms of both ion–solvent and ion–ion interactions and of the effect of the medium dielectric constant change.     

Activity coefficients and excess Gibbs’ free energy of some binary mixtures formed by p-cresol at 95.23 kPa

Bubble point temperatures at 95.23 kPa, over the entire composition range are measured for the binary mixtures formed by p-cresol with 1,2-dichloroethane, 1,1,2,2-tetrachloroethane trichloroethylene, tetrachloroethylene, and o- , m- , and p-xylenes, making use of a Swietoslawski-type ebulliometer. Liquid phase mole fraction (x₁) versus bubble point temperature (T) measurements are found to be well represented by the Wilson model. The optimum Wilson parameters are used to calculate the vapor phase composition, activity coefficients, and excess Gibbs free energy. The results are discussed.     

Modelling of phase equilibria for associating mixtures using an equation of state

In the present work, the group contribution with association equation of state (GCA-EoS) is extended to represent phase equilibria in mixtures containing acids, esters, and ketones, with water, alcohols, and any number of inert components. Association effects are represented by a group-contribution approach. Self- and cross-association between the associating groups present in these mixtures are considered. The GCA-EoS model is compared to the group-contribution method MHV2, which does not take into account explicitly association effects. The results obtained with the GCA-EoS model are, in general, more accurate when compared to the ones achieved by the MHV2 equation with less number of parameters. Model predictions are presented for binary self- and cross-associating mixtures.     

Activity coefficients and excess Gibbs’ energies of the binary mixtures formed by 2-cyanopyrazine with some chloroaliphatics at 95.5 kPa

Bubble points at a pressure of 95.5?kPa, over the entire composition range are measured for the binary mixtures formed by 2-cyanopyrazine with: 1,2-dichloroethane, 1,1,2,2-tetrachloroethane, trichloroethylene and tetrachloroethylene making use of a Swietoslawski type ebulliometer. The liquid phase composition versus temperature measurements are found to be well represented by the Wilson model. Computed values of the activity coefficients and excess Gibbs’ energies are also presented along with the phase equilibrium data.