The dependence of the osmotic coefficient on the composition of multicomponent solutions

The thermodynamic theory of binary aqueous solutions of electrolytes taking into account the electrostatic interaction of ions and their hydration and association was extended to multicomponent solutions. Equations for calculating the osmotic coefficient of multicomponent solutions from parameter estimates (hydration and association numbers under standard conditions) determined for the corresponding binary subsystems were substantiated. Interval parameter estimates were used to calculate the osmotic coefficients for several three-five-component aqueous solutions containing both nonelectrolytes and electrolytes. A comparison of the results with the literature data showed that cross interactions between components could be ignored for the multicomponent solutions studied.     

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.).     

Thermodynamic studies of ionic interactions in aqueous solutions of imidazolium-based ionic liquids [Emim][Br] and [Bmim][Cl

Experimental measurements of density at different temperatures ranging from 293.15 to 313.15 K, the speed of sound and osmotic coefficients at 298.15 K for aqueous solution of 1-ethyl-3-methylimidazolium bromide ([Emim][Br]), and osmotic coefficients at 298.15 K for aqueous solutions of 1-butyl-3-methylimidazolium chloride ([Bmim][Cl]) in the dilute concentration region are taken. The data are used to obtain compressibilities, expansivity, apparent and limiting molar properties, internal pressure, activity, and activity coefficients for [Emim][Br] in aqueous solutions. Experimental activity coefficient data are compared with that obtained from Debye-Hückel and Pitzer models. The activity data are further used to obtain the hydration number and the osmotic second virial coefficients of ionic liquids. Partial molar entropies of [Bmim][Cl] are also obtained using the free-energy and enthalpy data. The distance of the closest approach of ions is estimated using the activity data for ILs in aqueous solutions and is compared with that of X-ray data analysis in the solid phase. The measured data show that the concentration dependence for aqueous solutions of [Emim][Br] can be accounted for in terms of the hydrophobic hydration of ions and that this IL exhibits Coulombic interactions as well as hydrophobic hydration for both the cations and anions. The small hydration numbers for the studied ILs indicate that the low charge density of cations and their hydrophobic nature is responsible for the formation of the water-structure-enforced ion pairs.     

Temperature and Concentration Dependence of the Electrical Conductance,Diffusion, and Kinetics Parameters of the Ions in Aqueous Solutions of Sulfuric Acid,Selenic Acid,and Potassium Tellurate

The temperature and concentration dependences of the electrical conductance of aqueous solutions of sulfuric acid, selenic acid, and potassium tellurate were studied. The coefficients of the corresponding empirical equations were determined, and the values of equivalent conductances of the anions were evaluated at infinite dilution at the experimental temperatures. The values of the coefficients in the Fuoss and Onsager equation were evaluated for the three electrolytes at 298 K. The values of the molecular and ionic coefficients of self-diffusion at infinite dilution were calculated in the temperature range 288–318 K. The change of the translational energy Δ E∘_tr. of water molecules in the ionic hydration sphere was determined. The number of water molecules participating in the ionic hydration sphere at 298 K and the changes of Gibbs free energy, enthalpy, and entropy of activation of ionic conductance were calculated. The results obtained were interpreted according to the Samoylov’s theory of positive and negative hydration of ions. The differences observed in the temperature dependences of the mentioned parameters were explained in terms of the different radii and hydration numbers of the ions.     

Calculating the thermodynamic properties of aqueous solutions of alkali metal carboxylates

A modified Robinson-Stokes equation with terms that consider the formation of ionic hydrates and associates is used to describe thermodynamic properties of aqueous solutions of electrolytes. The model is used to describe data on the osmotic coefficients of aqueous solutions of alkali metal carboxylates, and to calculate the mean ionic activity coefficients of salts and excess Gibbs energies. The key contributions from ionic hydration and association to the nonideality of solutions is determined by analyzing the contributions of various factors. Relations that connect the hydration numbers of electrolytes with the parameters of the Pitzer-Mayorga equation and a modified Hückel equation are developed.     

Dependences of the osmotic coefficients of aqueous calcium chloride solutions on concentration at different temperatures

A model that considers the contributions from hydration, ion association, and electrostatic interactions to the nonideality of 2?1 electrolyte solutions is substantiated. The parameters of the model’s equations are the mean ion hydration number, the spread of the distribution of hydrated ion stoichiometric coefficients in the standard state, and the number of association. The model is successfully used to describe literature experimental data on the concentration dependence of osmotic coefficients of aqueous CaCl₂ solutions at temperatures ranging from 0 to 100°C. The modeling of the above systems shows that as the temperature rises, the hydration number falls slightly, the distribution of the hydration number broadens, and the ion paring of the salt rises by the first degree.     

A new model for the activity coefficients of individual ions in aqueous electrolyte solutions

In this study, the individual ion activity coefficient in an aqueous solution is modeled with a new model. This model contains two physical significant ionic parameters regarding the ionic solvation and the closest distance of approach between ions in a solution. The present model was evaluated by the estimation of the individual activity coefficients of the ions of thirty electrolytes in aqueous solutions. The results showed that this model suitably predicts the individual ion activity coefficients in aqueous two-electrolyte solutions consisting of the binary pairs of electrolytes of NaCl, KCl, KBr and CaCl₂ in a temperature range from 298.15 to 243.15 K. The results by this model were compared to the literature values. The average absolute relative deviations of vapor pressures showed acceptable agreement between experimental data and the results of this model.     

Numerical calculation of the Onsager transport coefficients for isothermal binary electrolytes

The Ebeling-Falkenhagen diffusion equations are applied to calculate the Onsager transport coefficients as well as the electrical conductances, transference numbers, and mutual diffusion coefficients for isothermal binary electrolytes. For this purpose the hierarchy of diffusion equations is closed on the level of the binary distribution functions by the superposition approximation. The resulting system of common differential equations is solved by numerical methods. Hydrodynamic interactions are taken into account up to first order. Some results are given for symmetrically charged binary electrolytes with hard-core ions (restricted primitive interaction model). The model parameters (Bjerrum parameter and Debye screening length) are chosen to represent strong electrolytes up to the molar region.     

Ionic Concentrations and Hydration Numbers of “Supporting Electrolytes”

Eight decades ago, Peter Zuman was born when the first polarograms of aqueous “supporting electrolytes” had just been recorded. Around that period, the pioneering idea of partial dissociation due to Arrhenius was unfortunately replaced by that of ‘complete dissociation’ and empirical ‘mean ionic activities’. Over the next decades, as the theory of electrolytes became too complicated to be meaningful, it became clear that the earlier ideas of partial dissociation and hydration were correct. Here, it is shown that solution properties of electrolytes can be explained quantitatively using simple mathematical expressions involving concentrations and volumes of ions and ion‐pairs and hydration numbers. Five tables of degrees of dissociation and hydration numbers of many strong electrolytes are provided in the Appendix.     

Theory for the determination of activity coefficients of strong electrolytes with regard to concentration dependence of hydration numbers

A new theory of electrolyte solutions is discussed which, as opposed to the Debye–Huckel method valid for relatively small concentrations only, enables one to describe the thermodynamic properties of electrolyte solutions over a wide range of state parameters. The novelty of the proposed theory is that it takes into account the dependence of hydration numbers upon concentration, the fact that failed to attract much attention before. The applicability of the theory to the calculation of activity coefficients of some electrolytes (LiCl, NaCl, KCl, RbCl, and CsCl) is demonstrated. A method is proposed for the determination of the thermodynamic parameters of solvation of separate ions.     

Quantitative analysis of physical factors that determine the behavior of activity coefficients of electrolytes

The development of theoretical ideas on the cause and the mechanism of the change of activity coefficients is the main aim of the investigation. The model describing the interaction of hydrated ions in electrolytes is proposed. In the model the electrostatic forces between ions and change of the energy of the hydrate shell in the process of ion convergence determine ions distribution in solution. The significant factor is the dependence of dielectric permittivity on the concentration of the electrolyte and on the distance to ion. The statistical approach developed allows one to calculate the influence of principal physical factors and, on this basis, to explain the nature of curves describing the activity coefficients. The results of simulation have been tested on a large number of experimental data.     

Volumetric,Viscosity and Self-Diffusion Coefficient Studies of [18-Crown-6:M]A Complexed Species in Water at 298.15 K

Density and viscosity measurements were made for aqueous solutions of electrolytes containing 18-crown-6 (18C6) at 298.15 K. A method is proposed to extract the volumetric and viscosity data of the [18C6:M]A complexed species in aqueous solutions from ternary mixtures using the thermodynamic equilibrium constant values at 298.15 K. The apparent molar volume of the [18C6:M]A complexed species have been estimated for these binary solutions. Further, the viscosity data thus obtained were subjected to analysis using the Jones-Dole equation to get viscosity A- and B-coefficients of complexed ions in water. The hydration number and molecular radius of the hydrated complexes in water have been estimated. It was observed that hydration of the complexed ion is strongly influenced by the charge density of the metal ions in the complexed state. The self-diffusion coefficient and correlation time values for the complexes in water were calculated using viscosity data, which indicated that diffusion of complexed species was faster than that of the host ligand 18C6 (D_3d structural entity) in water at 298.15 K. It was suggested that the ionic radii estimated in this work for large hydrophobic cations can be of use in studying electrostatic and hydrophobic interactions especially in aqueous solutions.     

Influence of ion properties on the equilibrium and transport properties of electrolyte solutions

Strong electrolytes are described in the framework of the primitive model in which the solvent is regarded as a dielectric continuum, using the mean spherical approximation. The analytical solution of the equilibrium and transport properties is dependent on the ions' diameters and valencies. For hydrated or nonspherical ions, an effective diameter must be fitted. A sensitivity study of the osmotic coefficient and the transport coefficients is performed on theoretical 1-1, 2-1, and 3-1 electrolytes, up to a total ion concentration of 2 mol/L.     

Diffusion coefficients of lithium chloride and potassium chloride in hydrogel membranes derived from acrylamide

Diffusion of non-associated electrolytes (potassium chloride and lithium chloride) in concentrated aqueous solutions (0.1-1.0 mol dm⁻³) has been studied in hydrogels derived from acrylamide and methyl methacrylate to study the mechanism of electrolyte transport. The preparation of two gels with different monomer ratio compositions resulted in obtaining membranes of substantially different hydrophilic character with polymer fractions of 0.3 and 0.5.Cukier hydrodynamic model was applied to explain the dependence of the diffusion coefficients of KCl and LiCl on the electrolyte concentration in hydrogel obtained experimentally. It was shown that the increase of the diffusion coefficients is accompanied with a decrease of the mean distance of approach of the ions. This can be explained by the formation of ion-pairs, resulting in a further contribution to diffusion once there is a decrease in the hydrodynamic resistance of the medium to the diffusing particles. Parameters, which characterise such a behaviour quantitatively, are different for different electrolytes and depend on water content in the gel.     

Structural and dynamic properties of concentrated alkali halide solutions: a molecular dynamics simulation study

The physicochemical properties of alkali halide solutions have long been attributed to the collective interactions between ions and water molecules in the solution, yet the structure of water in these systems and its effect on the equilibrium and dynamic properties of these systems are not clearly understood. Here, we present a systematic view of water structure in concentrated alkali halide solutions using molecular dynamics simulations. The results of the simulations show that the size of univalent ions in the solution has a significant effect on the dynamics of ions and other transport properties such as the viscosity that are correlated with the structural properties of water in aqueous ionic solution. Small cations (e.g., Li+) form electrostatically stabilized hydrophilic hydration shells that are different from the hydration shells of large ions (e.g., Cs+) which behave more like neutral hydrophobic particles, encapsulated by hydrogen-bonded hydration cages. The properties of solutions with different types of ion solvation change in different ways as the ion concentration increases. Examples of this are the diffusion coefficients of the ions and the viscosities of solutions. In this paper we use molecular dynamics (MD) simulations to study the changes in the equilibrium and transport properties of LiCl, RbCl, and CsI solutions at concentrations from 0.22 to 3.97 M.     

The inevitable accumulation of large ions and neutral molecules near hydrophobic surfaces and small ions near hydrophilic ones

The present contribution offers a unified explanation to three central phenomena in physical chemistry of interfaces in contact with aqueous solution: (1) Accumulation of large anions at the air/water interface. (2) Accumulation of neutral gas molecules near hydrophobic surfaces and the resulting hydrophobic interaction between two such surfaces, and (3) The Hofmeister effect, namely, the enhanced propensity of small ions to hydrophilic surfaces and large ions to hydrophobic surfaces. The common thread linking these phenomena is the free energy balance between ion or molecule hydration in solution and the cost of localizing these objects at the water-surface interface. Comparing the results of an abstract lattice-gas model to force spectroscopy data collected by AFM we reveal the underlying principles and demonstrate their universality.     

Effective interaction potentials for alkali and alkaline earth metal ions in SPC/E water and prediction of mean ion activity coefficients

The potential of mean force (PMF) acting between two simple ions surrounded by SPC/E water have been determined by molecular dynamics (MD) simulations using a spherical cavity approach. Such effective ion-ion potentials were obtained for Me-Me, Me-Cl-, and Cl(-)-Cl- pairs, where Me is a Li+, Na+, K+, Mg2+, Ca2+, Sr2+, and Ba2+ cation. The ionic sizes estimated from the effective potentials are not pairwise additive, a feature in the frequently used primitive model for electrolytes. The effective potentials were used in Monte Carlo (MC) simulations with implicit water to calculate mean ion activity coefficients of LiCl, NaCl, KCl, MgCl2, CaCl2, SrCl2, and BaCl2. Predicted activities were compared with experimental ones in the electrolyte concentration range 0.1-1 M. A qualitative agreement for LiCl and a satisfactory agreement for NaCl were found, whereas the predictions for KCl by two K+ models were less coherent. In the case of alkaline earth metal ions, all experimental activities were successfully reproduced at c = 0.1 M. However, at higher concentrations, similar deviations occurred for all divalent cations, suggesting that the dependence of the permittivity on the salt concentration and the polarization deficiency arising from the ordering of water molecules in the ion hydration shells are important in such systems.     

Intradiffusion coefficients for perchlorate ions in zinc perchlorate and zinc chloride solutions at 25°C: Comparing transport properties of zinc chloride and zinc perchlorate systems

Intradiffusion coefficients for³⁶ClO ₄ ^– have been measured in solutions of zinc perchlorate of concentration 0.1 to 3 mol dm^–3 at 25°C by the diaphragm cell technique. In addition, intradiffusion coefficients for perchlorate ions in zinc chloride solutions have been measured over a concentration range at 25°C. The results confirm previous work on the effect of complexation on diffusion in zinc chloride solutions above a salt concentration of 0.1M. The present data, together with literature data for diffusion coefficients of the other species present in the zinc perchlorate electrolyte system, have enabled a simple analysis of the hydration around the zinc ions to be carried out. This indicates that the water diffusion data are consistent with the zinc ions having an effective hydration sphere of 11 (±2) water molecules. This is in keeping with values obtained for other simple divalent electrolytes using the same model. The model is extended here to allow analysis of water diffusion in zinc chloride solutions taking into account the presence of complexed chloro-zinc species. The experimental data are consistent with the effective hydration of the chloro-zinc complexes being independent of the number of chloride ligands and equal to 18±3 over a concentration range of 0 tol mol-dm^–3. This postulate is discussed in terms of its consequences on the water ligand dynamics for the complex equilibria.