Thermodynamics of electrolyte mixtures. Enthalpy and the effect of temperature on the activity coefficient

The temperature dependence of the parameters for symmetrical mixing of ions of the same sign in the virial-coefficient (Pitzer) system are evaluated from literature data on heats of mixing in the presence of a common ion for 20 systems. The higher-order limiting law for symmetrical mixing is used in the form of an expression for the ionic strength dependence of the binary mixing parameter. Heats of mixing of the MX-NYtype (without common ion) are calculated for eight systems from these parameters and found to be in excellent agreement with experimental values. Since pure-electrolyte parameters are required for the non-common-ion calculations, these are calculated as needed from recently published data.     

Activity Coefficient Prediction for Binary and Ternary Aqueous Electrolyte Solutions at Different Temperatures and Concentrations

The mean spherical approximation (MSA) model, coupled with two hard sphere models, was used to predict the activity coefficients of mixtures of electrolyte solutions at different temperatures and concentrations. The models, namely the Ghotbi-Vera-MSA (GV-MSA) and Mansoori et al.-MSA (BMCSL-MSA), were directly used without introducing any new adjustable parameters for mixing of electrolyte solutions. In the correlation step, the anion diameters were considered to be constant, whereas the cation diameters were considered to be concentration dependent. The adjustable parameters were determined by fitting the models to the experimental mean ionic activity coefficients for single aqueous electrolytes at fixed temperature. The results showed that the studied models predict accurately the activity coefficients for single electrolyte aqueous solutions at different temperatures. In the systems of binary aqueous electrolyte solutions with a common anion, the GV-MSA model has slightly better accuracy in predicting the activity coefficients. Also, it was observed that the GV-MSA model can more accurately predict the activity coefficients for ternary electrolyte solutions with a common anion, especially at higher concentrations.     

Heats of Mixing of Aqueous Solutions of Alkali Metal Salts of Substituted Benzenesulfonic Acids

The enthalpy change on mixing aqueous solutions of substituted benzene sulfonic acids and their salts, with salts having a common cation or anion, were measured at constant total ionic strength and at 25°C. The results are qualitatively interpreted in terms of solute–water structural properties and the ion size effect. The heat effects of mixing solutions having common anions obey the sign rule of Young and Smith. In anion–common cation mixings at concentration of 0.5 mol-kg^–1 only exothermic heat effects were observed, whose magnitude increase with the increasing difference in size of the mixed anions. The magnitude of the mixing effect increased with the salt concentration in cation–common anion mixing processes, In anion–common cation mixings the enthalpy of mixing changes sign from negative to positive, indicating a predominantly endothermic effect as concentration increases.     

Liquid phase behavior of ionic liquids with alcohols: experimental studies and modeling

Ionic liquids (ILs) have been suggested as potential "green" solvents to replace volatile organic solvents in reaction and separation processes due to their negligible vapor pressure. To develop ILs for these applications, it is important to gain a fundamental understanding of the factors that control the phase behavior of ionic liquids with other liquids. In this work, we continue our study of the effect of chemical and structural factors on the phase behavior of ionic liquids with alcohols, focusing on pyridinium ILs for comparison to imidazolium ILs from our previous studies. The impact of different alcohol and IL characteristics, including alcohol chain length, cation alkyl chain length, anion, different substituent groups on the pyridinium cation, and type of cation (pyridinium vs imidazolium) will be discussed. In general, the same type of behavior is observed for pyridinium and imidazolium ILs, with all systems studied exhibiting upper critical solution temperature behavior. The impacts of alcohol chain length, cation chain length, and anion, are the same for pyridinium ILs as those observed previously for imidazolium ILs. However, the effect of cation type on the phase behavior is dependent on the strength of the cation-anion interaction. Additionally, all systems from this study and our previous work for imidazolium ILs were modeled using the nonrandom two-liquid (NRTL) equation using two different approaches for determining the adjustable parameters. For all systems, the NRTL equation with binary interaction parameters with a linear temperature dependence provided a good fit of the experimental data.     

Heats of Mixing of Mixed Solvent Solutions of Alkali Metal Salts of Substituted Benzenesulfonic Acids

The enthalpy change on mixing solutions of methyl-substituted benzenesulfonic acids and their salts, with salts having a common cation or anion, at constant ionic strength in mixtures of 1,4-dioxane with water, were measured at 25°C. The heat effects of mixing solutions having a common anion increase almost linearly with the reciprocal value of the dielectric constant of the solvent. The heat effects of mixing solutions having a common cation, which are all negative in water-rich solutions, become endothermic after a certain value of the dielectric constant is passed. The results are discussed in terms of the solute-solvent structural properties. This revised version was published online in July 2006 with corrections to the Cover Date.     

Activity coefficients for the system NaCl+Na2SO4+H2O at various temperatures. Application of Pitzer's equations

The mean activity coefficients of NaCl in the system NaCl+Na₂SO₄+H₂O at various compositions were determined in the temperature range 5–45°C from the emf of potentiometric cells. By processing the results using Pitzer's equations the mixing parameters describing the non-ideal behavior of electrolytes were calculated. The temperature coefficients of the mixing parameters were determined and found not to be significant. The mixing parameters and temperature coefficients calculated for the binary mixture can be used to describe the behavior of multicomponent systems containing NaCl and Na₂SO₄, and eventually sea water.     

The influence of cation, anion and temperature on the liquid-liquid equilibrium of some pentanols-water system

Liquid-liquid equilibrium (LLE) measurements for aqueous systems containing some pentanols and sodium, or potassium nitrate have been performed experimentally at 25 °C and atmospheric pressure. The pentanols are: 1-pentanol (1P), 2-pentanol (2P), 3-pentanol (3P), 2-methyl-1-butanol (3M1B) and 2-methyl-2-butanol (2M2B). The obtained data have been modeled using an extended UNIQUAC activity coefficient model. The influence of the cation, the anion and the temperature on the liquid-liquid equilibrium, are illustrated by applying the Setschenow equation on the studied systems and on other systems from literature. The results show that the influence of sodium salts is higher than that of potassium salts with the same anion and the same alcohol. On the other hand, the influence of the nitrate and bromide salts is lower than that of chloride salts with the same cation and the same alcohol. Linearity of Setschenow relation indicates that the influence of the given salts on the liquid-liquid equilibrium in the systems under study, are additive. The effect of temperature on the phase behavior is that the mutual solubilities of both liquids, in the presence of salt, decrease with temperature.     

Transport properties in two pyrrolidinium-based protic ionic liquids as determined by conductivity,viscosity and NMR self-diffusion measurements

Conductivity and viscosity measurements of pyrrolidinium hydrogen sulfate, [Pyrr][HSO₄], and pyrrolidinium trifluoroacetate [Pyrr][CF₃COO] were performed at various temperatures over a wide temperature range (i.e., from T = 273 K to 353 K). The results were utilized in the Stokes–Einstein equation to investigate the proton conductivity in both PILs. The self-diffusion coefficients (D) of the cation and anion species in both studied PILs were independently determined in the same temperature range by observing ¹H and ¹⁹F nuclei with the pulsed-field gradient spin-echo NMR technique. With regard to the mechanism of self-diffusion, based on the values of the coefficients, a relatively large difference was observed between the two ionic liquids (ILs). Independently of the temperature, the D values indicated that the diffusion of both ions was similar, signifying that they were tightly bound together as ion pairs. Nevertheless, mobile protons attached to nitrogen atoms exhibited D values five times higher than those of the pyrrolidinium cation or hydrogenosulfate anion in [Pyrr][HSO₄], and twofold those in the case of [Pyrr][CF₃CO₂]. In order to comment d.c. conductivities results, the self-diffusion coefficients determined by PGSE NMR were converted into charge diffusivity D by means of the Nernst–Einstein equation. In a similar way, a viscosity-related diffusivity D was calculated with the aid of the Stokes–Einstein equation. The temperature-independent cation transference number and the effective hydrodynamic radius were also deduced from these equations. Such parameters play an important role in charge and mass transports in ILs. Moreover, proton conduction follows a combination of Grotthuss- and vehicle-type mechanisms, which confirms that Brønsted acid–base ionic liquid systems are good candidates as proton conductors in fuel cells or supercapacitor electrolyte devices operating under anhydrous conditions at elevated temperatures.     

Vapor-liquid equilibria for the system water + tert.-pentanol at 4 temperatures

Precise isothermal vapor-liquid equilibrium data at 10, 30, 55 and 70°C for the system water + tert.-pentanol were measured using a computer-operated differential static apparatus. Activity coefficients at infinite dilution were derived from the experimental P − x data in the dilute region using a flexible Legendre polynomial, and the vapor-liquid-liquid locus was derived directly from the P − x data near the liquid-liquid phase boundary. Heteroazeotropic points were measured directly by distillation using a rotating band column. Furthermore the UNIQUAC and the NRTL models were used to correlate the experimental P − x data and to derive the azeotropic data.

Experimental H^E data were taken from literature and used together with the experimental P − x data to simultaneously fit temperature dependent interaction parameters for UNIQUAC and NRTL. The parameters were used to predict the azeotropic composition over a large temperature range. The results were compared with those of a simple analytical thermodynamic equation using only the pure component vapor pressure data, heats of mixing in the heterogeneous region and the azeotropic composition at one temperature.

Heats of mixing were measured at 140°C with the help of a flow calorimeter in order to determine the slope of H^E vs. x₁ in the heterogeneous region. The H^E data were used to check the reliability of the G^E model parameters and the equation to calculate the temperature dependence of the heteroazeotropic composition.     

Thermodynamic modeling of CO2 solubility in ionic liquid with heterosegmented statistical associating fluid theory

Heterosegmented statistical associating fluid theory is used to represent the CO₂ solubility in ionic liquids. As in our previous work, ionic liquid molecule is divided into several groups representing the alkyls, cation head, and anion. The cation of ionic liquid is modeled as a chain molecule that consists of one spherical segment representing the cation head and groups of segments of different types representing different substituents (alkyls). The anion of ionic liquid is modeled as a spherical segment of different type. To account for the electrostatic/polar interaction between the cation and anion, the spherical segments representing cation head and anion each have one association site, which can only cross associate. Carbon dioxide is modeled as a molecule with three association sites, two sites of type O and one site of type C, where sites of the same type do not associate with each other. The parameters of CO₂ are obtained from the fitting of the density and the saturation vapor pressure of CO₂. For the CO₂-ionic liquid systems, cross association between site of type C in CO₂ and another association site in anion is allowed to occur to account for the Lewis acid–base interaction. The parameters for cross association interactions and the binary interaction parameters used to adjust the dispersive interactions between unlike segments are obtained from the fitting of the available CO₂ solubility in ionic liquids. The model is found to well represent the CO₂ solubility in the imidazolium ionic liquids from 283 to 415 K and up to 200 bar.     

Thermodynamic properties of the system NH4NO3 + (NH4)2SO4 + H2O at 298.15 K

In this investigation, the mixed aqueous electrolyte system of nitrate and sulfate with common ammonium cation has been studied with the hygrometric method at the temperature 298.15 K. The water activities of the system [yNH₄NO₃ + (1 − y)(NH₄)₂SO₄](aq) are measured at total molalities from 0.4 mol kg⁻¹ up to saturation for different ionic-strength fractions y of NH₄NO₃ with y = 0.2, 0.5 and 0.8. The obtained data allow the deduction of osmotic coefficients. The experimental results are compared with the predictions of the Zdanovskii–Stokes–Robinson (ZSR), Leitzke and Stoughton (LSII), Kusik and Meissner (KM), and Pitzer models. From these measurements, new Pitzer mixing ionic parameters are determined and used to predict the solute activity coefficients in the mixture. The obtained results are used to calculate the excess Gibbs energy at total molalities for different ionic-strength fractions y.     

Activity of components of melts of binary systems with a common anion

The model of regular solutions and the data on the enthalpy of mixing for binary systems with a common anion were used to calculate the activities of the components of the systems LiF-KF, NaI-CsI, NaCl-RbCl, and NaCl-SrCl₂.     

Interactions of DL-serine and L-serine with NaCl and KCl in aqueous solutions

The activity coefficients at 25‡C of DL-serine and L-serine in aqueous solutions of NaCl and KC1 were measured. This study examines the effect of the nature of the cation of the electrolyte on the activity coefficients of the optical-isomers of serine in aqueous solutions for molality of serine up to 0.4 and molality of electrolyte up to 1. An electrochemical cell with two ion-selective electrodes, a cation, and an anion ion selective electrode,vs. a double-junction reference electrode was used to measure the activity coefficients of the electrolyte and the results were converted to the activity coefficients of serine in the aqueous electrolyte solution. The comparison of the results obtained for DL- and L-serine indicates that the two optical isomers have identical interactions with electrolytes in aqueous solutions and that for this amino acid the effect of the cation of the electrolyte is not significant. Comparison of these results with previous measurements for DL-alanine in aqueous solutions of the same electrolytes show the notable effect of the backbone of the amino acid.     

Thermodynamics of mixtures formed by polycyclic aromatic hydrocarbons with long chain alkanes

Thermodynamic properties of polycyclic aromatic hydrocarbons (PAH) and long chain alkanes determine the phase behaviour of heavy petroleum fractions. Studying thermodynamic excess functions of these systems is difficult and consequently experimental data available in the literature are scarce. Enthalpies of mixing of 13 PAH-alkane systems at temperature above the melting point of both components are reported in this paper. Morever, 13 solid-liquid equilibria of the same family of systems are presented. Experimental results were correlated using S.S.F. model (Rogalski and Malanowski, 1977). Several regularities observed in the liquid-solid phase diagrams of the systems studied are discussed     

Modeling the solubility behavior of CO(2), H(2), and Xe in [C(n)-mim][Tf(2)N] ionic liquids

We present here a new model for the imidazolium-based ionic liquids (ILs) with the bis(trifluoromethylsulfonyl)imide anion [Tf(2)N](-) in the context of the soft-SAFT EoS. The model is used to predict the solubility of several compounds in these ILs, and results are compared to available experimental data. Since in the soft-SAFT EoS an associating site is used to represent a short-range and highly directional attractive force among molecules, we have used this feature to mimic the main interactions between the anion and the cation for the alkylimidazolium-[Tf(2)N] ILs. The members of the alkylimidazolium-[Tf(2)N] family are modeled as Lennard-Jones chains with three associating sites in each molecule (one "A" site and two "B" sites). An "A" site represents the nitrogen atom interactions with the cation, and a "B" site represents the delocalized charge due the oxygen molecules on the anion. Each type of associating site is identically defined, but only AB interactions between different IL molecules are allowed. Model parameters for the ionic liquids were estimated with experimental density data from different authors, following a similar approach taken in our previous work [Andreu and Vega, J. Phys. Chem. C 2007, 111, 16028]. The new set of parameters was used to study the solubility behavior of hydrogen, carbon dioxide, and xenon in these ILs over a wide range of temperature and pressure. It has been observed that no binary parameters are needed to correlate the solubility of hydrogen in [C(6)-mim][Tf(2)N] at different temperatures, and predictions up to 100 MPa are presented here. The model is able to correlate with very good agreement the experimental data for the systems [C(n)-mim][Tf(2)N] + CO(2) with only one temperature-independent mixture parameter, while two temperature-independent mixture parameters are needed to correlate the experimental solubility data for the systems IL + Xe, attaining an excellent agreement in a wide range of temperatures. The work presented here reinforces previous results, proving that a reasonable simple model for the IL within the framework of soft-SAFT is able to describe the physical absorption of different gases in ILs with good accuracy, in spite of the most complex nature of the anion, without the need of further parameters or terms. In addition, since these parameters do not depend on the particular conditions at which they were fitted, soft-SAFT is used then to analyze the solubility dependence of these gases in ILs, according to the anion nature and the alkyl chain length of the imidazolium cation by the use of the models developed within this approach.     

Volumetric and compressibility behaviour of ionic liquid, 1-n-butyl-3-methylimidazolium hexafluorophosphate and tetrabutylammonium hexafluorophosphate in organic solvents at T = 298.15 K

Density and speed of sound measurements have been made on the systems containing the ionic liquid 1-n-butyl-3-methylimidazolium hexafluorophosphate ([BMIM][PF₆]) and some organic solvents having a wide range of dielectric constants. Similar studies have been carried out for tetrabutylammonium hexafluorophosphate ([TBA][PF₆]), which has common anion ([PF₆]⁻) with the studied ionic liquid. For the systems investigated, the apparent molar volumes and apparent molar isentropic compressibilities were determined and fitted to the Redlich–Mayer and the Pitzer equations from which the corresponding limiting values were obtained. These limiting values were used to obtain some information about ion–solvent interactions. Furthermore, using the ionic limiting apparent volume values for [TBA]⁺ from the literature and limiting apparent molar volume for the ionic liquid and [TBA][PF₆] obtained in this work, the ionic limiting apparent molar volume values for the cation [BMIM]⁺ in different organic solvents were also estimated.     

New parametrization method for dissipative particle dynamics

We introduce an improved method of parametrizing the Groot-Warren version of dissipative particle dynamics (DPD) by exploiting a correspondence between DPD and Scatchard-Hildebrand regular solution theory. The new parametrization scheme widens the realm of applicability of DPD by first removing the restriction of equal repulsive interactions between like beads, and second, by relating all conservative interactions between beads directly to cohesive energy densities. We establish the correspondence by deriving an expression for the Helmoltz free energy of mixing, obtaining a heat of mixing which is exactly the same form as that for a regular mixture (quadratic in the volume fraction) and an entropy of mixing which reduces to the ideal entropy of mixing for equal molar volumes. We equate the conservative interaction parameters in the DPD force law to the cohesive energy densities of the pure fluids, providing an alternative method of calculating the self-interaction parameters as well as a route to the cross interaction parameter. We validate the new parametrization by modeling the binary system SnI(4)SiCl(4), which displays liquid-liquid coexistence below an upper critical solution temperature around 140 degrees C. A series of DPD simulations were conducted at a set of temperatures ranging from 0 degrees C to above the experimental upper critical solution temperature using conservative parameters based on extrapolated experimental data. These simulations can be regarded as being equivalent to a quench from a high temperature to a lower one at constant volume. Our simulations recover the expected phase behavior ranging from solid-liquid coexistence to liquid-liquid coexistence and eventually leading to a homogeneous single phase system. The results yield a binodal curve in close agreement with the one predicted using regular solution theory, but, significantly, in closer agreement with actual solubility measurements.     

Geometrical preferences of the crotyl anion,radical and cation

ab initio MO calculations have been performed on the cis and trans isomers of the crotyl cation, free radical and anion in each of two orientations of the Me rotor about the allylic framework. In agreement with available experimental data, both the crotyl cation and free radical prefer trans skeletal geometries. On the other hand, the cis isomer of the crotyl anion is found to be more stable than the trans, the same preference as has been noted for alkali metal allyl organometallics in solution, but opposite to that recently reported for the free (gas phase) anion. The Me groups are predicted to eclipse the partial double bond for the trans isomers of all three systems and for the cis cation. These results are rationalized with the aid of perturbation MO theory.     

Transport of alkali halides through a liquid organic membrane containing a ditopic salt-binding receptor

A ditopic receptor is shown to have an impressive ability to recognize and extract the ion pairs of various alkali halides into organic solution. X-ray diffraction analysis indicates that the salts are bound in the solid state as contact ion pairs. Transport experiments, using a supported liquid membrane and high salt concentration in the source phase, show that the ditopic receptor can transport alkali halide salts up to 10-fold faster than a monotopic cation or anion receptor and 2-fold faster than a binary mixture of cation and anion receptors. All transport systems exhibit the same qualitative order of ion selectivity; that is, for a constant anion, the cation selectivity order is K+ > Na+ > Li+, and for a constant cation, the anion transport selectivity order is I- > Br- > Cl-. The data suggest that with a ditopic receptor, the polarity of the receptor-salt complex can be lowered if the salt is bound as an associated ion pair, which leads to a faster diffusion through the membrane and a higher maximal flux.     

Transference numbers for KCl in 10 weight % ethanol-water at 25°C

Cation and anion transference numbers are reported for KCl in a 10 wt. % ethanol-water mixture at 25°C and at concentrations from 0.02 to 0.1 mole/liter^–1. The moving-boundary method employing the standard optical detector was used. The sum of the cation and anion transference numbers was within 0.02% of unity, and the limiting cation value ofT _o ⁺ (KCl)=0.5017 verifies the earlier data of Fratiello and Kay.