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.     

Application of Restrictive Primitive SAFT Coupled with Different Hard-Sphere Equations to Model Mean Ionic Activity Coefficients of Electrolyte Solutions

In this work, the primitive SAFT equation of state along with three different hard-sphere equations was used to correlate and predict mean ionic activity coefficients of aqueous electrolyte solutions. The mean ionic activity coefficient of aqueous electrolyte solutions was considered as the contribution of hard-sphere and dispersion effects. The Mansoori (M), Wang-Khoshkbarchi-Vera (WKV) and Ghotbi-Vera (GV) hard-sphere equations were applied in correlating the mean ionic activity coefficient of electrolyte solutions. The comparison among above indicated equations was shown. First, vapor pressure and densities of water in the temperature range of 373.15 to 423.15 K was regressed by SAFT equation of state. In the restrictive primitive mean spherical model, ions were hard spheres without any chain structure. Neither association effects were considered in this study. Clearly, in common used five SAFT parameters were decreased to three, which were calculated by using the experimental mean ionic activity coefficients of electrolyte solutions. The comparison among three hard-sphere equations of state approved that Ghotbi-Vera hard-sphere model (GV) correlated the experimental data accurately than the others; two hard-sphere models. The mean ionic activity coefficients of some electrolyte solutions were being predicted by taking the advantage of the regressed values surely, in a wide range of molality.     

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.     

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.     

Hydration of nonelectrolytes in binary aqueous solutions

Literature data on the thermodynamic properties of binary aqueous solutions of nonelectrolytes that show negative deviations from Raoult’s law due largely to the contribution of the hydration of the solute are briefly surveyed. Attention is focused on simulating the thermodynamic properties of solutions using equations of the cluster model. It is shown that the model is based on the assumption that there exists a distribution of stoichiometric hydrates over hydration numbers. In terms of the theory of ideal associated solutions, the equations for activity coefficients, osmotic coefficients, vapor pressure, and excess thermodynamic functions (volume, Gibbs energy, enthalpy, entropy) are obtained in analytical form. Basic parameters in the equations are the hydration numbers of the nonelectrolyte (the mathematical expectation of the distribution of hydrates) and the dispersions of the distribution. It is concluded that the model equations adequately describe the thermodynamic properties of a wide range of nonelectrolytes partly or completely soluble in water.     

Activities of Individual Ions From Infinite Dilution to Saturated Solutions

A new procedure, which provides a closer approximation for the junction potentials than the Henderson equation, is tested to reduce new emf data for the chloride ion in CsCl solutions and previously measured data for individual ions in aqueous solutions of KCl, NaCl, and NaBr. The liquid junction potential is calculated from numerical integration of its basic equation without assuming constant mobility or using concentrations instead of activities. The mean ionic activity coefficients of the salts, obtained from the activity coefficients of the individual ions, show good agreement with values reported in the literature. The activity coefficients of the individual chloride ion at 25°C in aqueous solutions of CsCl up to 3 molal and in KCl solutions were measured using a chloride ion-selective electrode. It has been confirmed that the activity of the chloride ion is equal to the activity of the cation in CsCl solutions and, contrary to the prediction of hydration theory, it is higher than the activity of the cation in aqueous KCl solutions. The New Hydration Theory has been developed to overcome the shortcomings of the older hydration theory and has been used to smooth the experimental activity coefficients of the individual ions in aqueous solutions and to extrapolate them up to the saturated solution.     

Expressions for the Activity Coefficients and Osmotic Coefficients of Solutions of Electrolytes and Nonelectrolytes Based on the Hydration Model of Zavitsas

In two papers Zavitsas described a model for the thermodynamic properties of aqueous solutions of a single electrolyte or nonelectrolyte (Zavitsas, J Phys Chem B 105:7805–7817, 2001; J Solution Chem 39:301–317, 2010) in which he assumed that part of the water is so strongly bound to the solute that it can be considered as part of it, and thus only the remaining unbound water is considered to be the solvent. He showed that when the usual water mole fraction was replaced by the resulting mole fraction of unbound water, obtained by optimizing an effective hydration number, basically linear relations were obtained to fairly high molalities for the freezing temperature lowering, boiling temperature elevation, and the water activity/vapor pressure of water. However, Zavitsas only considered the properties of the solvent, not the solute. In this paper we derive the corresponding expressions for the activity coefficient of the solute for the usual molality scale based on 1 kg of water, for the modified molality scale based on 1 kg of unbound water, for the mole fraction scale based on the total number of moles of water, and for the modified mole fraction scale based on the number of moles of unbound water. These equations show that if the hydration number is larger than the stoichiometric ionization number of the electrolyte, then all four types of mean activity coefficients are predicted to always be >1 (nearly all hydration numbers reported by Zavitsas for electrolyte solutions are greater than the corresponding ionization numbers), which directly conflicts with extensive experimental and theoretical evidence that the mean activity coefficients of electrolytes in aqueous solutions always initially decrease below unity. In contrast, for nonelectrolyte solutions, the hydration model of Zavitsas gives more realistic values of the activity coefficients.     

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.     

Some Structural and Thermodynamic Aspects of Solvation of Single Ions. 2. Salt Effects in Aqueous Solutions of 1–1 Electrolytes

The ionic coefficients of the pair interionic interaction in aqueous solutions of 1–1 electrolytes at 298 K were determined from the real activity coefficients of single-charged single ions using the McMillan–Mayer formalism. Analysis of the results of calculations revealed that salt effects are stronger in the case of cations. The weakening of cation hydration (increased negative hydration) and the strengthening of anion hydration (increased positive hydration) enhance the mutual salting of cations and anions. It is shown that the structural effects of hydration produce a strong effect on the interionic interaction in solutions.     

甘氨酸在尿素、甲脲及二甲脲水溶液中的体积性质

用精密数字密度计测定了甘氨酸在不同质量分数的尿素、甲脲和二甲脲水溶液中的密度,计算了甘氨酸的极限偏摩尔体积、迁移偏摩尔体积、理论水化数和体积作用系数,讨论了溶剂组成变化对甘氨酸迁移偏摩尔体积和理论水化数的影响.结果表明,甘氨酸与尿素及烷脲分子间的相互作用主要以1:1的形式为主.尿素、甲脲、二甲脲分子与氨基酸荷电中心的直接相互作用,削弱了两性离子带电中心对周围水分子的电致收缩效应,造成了理论水化数随溶液浓度的增加而减小.     

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.     

Precise twin ebulliometry

A simple twin ebulliometer is described that makes it possible to achieve a standard error of about 45 μdeg in measuring the difference between the boiling temperatures of two aqueous solutions in the vicinity of 760 torr. Sodium chloride is recommended as a reference electrolyte in aqueous twin ebulliometry, and precise information is given on the concentration dependence of the osmotic and mean ionic activity coefficients of aqueous solutions of sodium chloride over the range 0–l m A quick and simple procedure is described for using this information to evaluate the osmotic coefficients of other solutions by twin ebulliomet-y, and is applied to an investigation of the osmotic and mean ionic activity coefficients of aqueous solutions of lithium chloride at 100°C The potentiahties of twin ebulliometry are Judged to be superior to those of cryoscopy and comparable with those of thermoelectric vapor-pressure osmometry.     

Apparent Molar Volume and Apparent Molar Expansibility of Lithium,Sodium, Potassium,and Tetramethylammonium Cyclohexylsulfamate in Aqueous Solution

Summary. The apparent molar volume of lithium, sodium, potassium, and tetramethylammonium cyclohexylsulfamate was determined from the density data of their aqueous solutions at 293.15, 298.15, 303.15, 313.15, and 323.15 K. The apparent molar expansibility was calculated from the apparent molar volume at various temperatures. The limiting apparent molar volume and apparent molar expansibility were evaluated and divided into their ionic components. The partial molar ionic expansibilities were discussed in terms of the hydration of the ion in solution, as well as in terms of the hydration effects on the solute as a whole. From the partial molar expansibility of the solute at infinite dilution the partial molar expansibility of the hydration shell was deduced. The coefficients of thermal expansion of the investigated solutions at 298.15 K were calculated and are presented graphically. The density of the investigated solutions can be adequately represented by an equation derived by Root.     

Apparent Molar Volume and Apparent Molar Expansibility of Lithium, Sodium, Potassium, and Tetramethylammonium Cyclohexylsulfamate in Aqueous Solution

The apparent molar volume of lithium, sodium, potassium, and tetramethylammonium cyclohexylsulfamate was determined from the density data of their aqueous solutions at 293.15, 298.15, 303.15, 313.15, and 323.15 K. The apparent molar expansibility was calculated from the apparent molar volume at various temperatures. The limiting apparent molar volume and apparent molar expansibility were evaluated and divided into their ionic components. The partial molar ionic expansibilities were discussed in terms of the hydration of the ion in solution, as well as in terms of the hydration effects on the solute as a whole. From the partial molar expansibility of the solute at infinite dilution the partial molar expansibility of the hydration shell was deduced. The coefficients of thermal expansion of the investigated solutions at 298.15 K were calculated and are presented graphically. The density of the investigated solutions can be adequately represented by an equation derived by Root.     

An equation of state for electrolyte solutions by a combination of low-density expansion of non-primitive mean spherical approximation and statistical associating fluid theory

A two-parameter equation of state (EOS) for electrolyte solutions is developed. The equation is in terms of Helmholtz free energy and incorporated with our previous results of the low-density expansion of non-primitive mean spherical approximation (MSA). The concentration dependent dielectric constant is thus inherently included in the model. The statistical associating fluid theory (SAFT) is introduced to represent the association interactions, including the solvent–solvent and ion–solvent. The EOS is tested for 15 aqueous alkali halide solutions at ambient condition. The equation can represent simultaneously the mean ionic activity coefficients, the osmotic coefficients and densities in a good accuracy up to saturated concentration. The comparisons with EOSs published earlier in the literature are carried out. The limitations of the model are also discussed.     

Structural parameters of aqueous solutions of potassium fluoride under hydrothermal conditions

The structural parameters of aqueous KF solutions with concentrations of 10 and 20 wt % in the temperature range 473–623 K (p 18.7–24.6 MPa), obtained by the method of integral equations, are presented and compared with the structural parameters under standard conditions. Regularities of the structure formation of the systems under hydrothermal conditions, connected with ionic hydration and association, are elucidated. It is established that within the studied temperature range the number of contact associates in the solutions is stabilized, implying the possibility of formation of crystallization centers.     

The unusual importance of activity coefficients for micelle solutions illustrated by an osmometry study of aqueous sodium decanoate and aqueous sodium decanoate + sodium chloride solutions

Freezing-point and vapor-pressure osmometry data are reported for aqueous sodium decanoate (NaD) solutions and aqueous NaD + NaCl solutions. The derived osmotic coefficients are analyzed with a mass-action model based on the micelle formation reaction qNa(+) + nD(-) = (Na(q)D(n))(q-n) and Guggenheim equations for the micelle and ionic activity coefficients. Stoichiometric activity coefficients of the NaD and NaCl components and the equilibrium constant for micelle formation are evaluated. Illustrating the remarkable but not widely appreciated nonideal behavior of ionic surfactant solutions, the micelle activity coefficient drops to astonishingly low values, below 10(-7) (relative to unity for ideal solutions). The activity coefficients of the Na(+) and D(-) ions, raised to large powers of q and n, reduce calculated extents of micelle formation by up to 15 orders of magnitude. Activity coefficients, frequently omitted from the Gibbs equation, are found to increase the calculated surface excess concentration of NaD by up to an order of magnitude. Inflection points in the extent of micelle formation, used to calculate critical micelle concentration (cmc) lowering caused by added salt, provide unexpected thermodynamic evidence for the elusive second cmc.     

甘氨酸、L-丙氨酸和L-丝氨酸在尿素水溶液中的体积性质

蛋白质的折叠与解折叠、稳定性、变性行为和酶的活性等都受到环境中其它各种物质影响.作为蛋白质模型分子,氨基酸在混合溶液中的热力学研究近年来引起了广泛重视.尿素在生物体系中的独特地位主要表现在:它是水结构的破坏者,同时又是许多球状蛋白的变性剂.然而,尿素对球状蛋白的变性作用尚未达成共识.