Hygrometric determination of water activities,osmotic and activity coefficients of (NaCl + KCl)(aq) at T = 298.15 K

The purpose of this study is to present a model for the prediction of water activity in multicomponent aqueous solutions containing a common ion from available binary data. The hygrometric method has been used to measure relative humidities for the aqueous electrolyte mixture (NaCl  +  KCl)(aq) at total molalities ranging from 0.2 mol · kg ^− 1to saturation for different molal ratiosr of NaCl(aq) to KCl(aq) with r =  (0.2, 0.5, 1, 2, 3, and 4) at T =  298.15 K. The data obtained have been used to determine water activities and osmotic coefficients. The results show that the values of water activities and osmotic coefficients calculated with the proposed model are close to the experimental ones. This model is also compared with four other models (RS, Pitzer, RWR, and LS II) over the range of the studied total molalities. From the measurements, the activity coefficients of NaCl(aq) and KCl(aq) in the mixture have also been determined.     

Isopiestic Determination of the Osmotic and Activity Coefficients of Li2SO4(aq) at T=298.15 and 323.15 K, and Representation with an Extended Ion-Interaction (Pitzer) Model

Isopiestic vapor-pressure measurements were made for Li₂SO₄(aq) from 0.1069 to 2.8190 mol?kg^?1 at 298.15 K, and from 0.1148 to 2.7969 mol?kg^?1 at 323.15 K, with NaCl(aq) as the reference standard. Published thermodynamic data for this system were reviewed, recalculated for consistency, and critically assessed. The present results and the more reliable published results were used to evaluate the parameters of an extended version of Pitzer’s ion-interaction model with an ionic-strength dependent third-virial coefficient, as well as those of the standard Pitzer model, for the osmotic and activity coefficients at both temperatures. Published enthalpies of dilution at 298.15 K were also analyzed to yield the parameters of the ion-interaction models for the relative apparent molar enthalpies of dilution. The resulting models at 298.15 K are valid to the saturated solution molality of the thermodynamically stable phase Li₂SO₄?H₂O(cr). Solubilities of Li₂SO₄?H₂O(cr) at 298.15 K were assessed and the selected value of m(sat.)=3.13±0.04 mol?kg^?1 was used to evaluate the thermodynamic solubility product K _s(Li₂SO₄?H₂O, cr, 298.15 K) = (2.62±0.19) and a CODATA-compatible standard molar Gibbs energy of formation Δ_f G _m ^o (Li₂SO₄?H₂O, cr, 298.15 K) = ?(1564.6±0.5) kJ?mol^?1.     

Isopiestic determination of osmotic and activity coefficients of aqueous solutions of aliphatic polyols at 298.15 K

The osmotic coefficients of 1,2-butanediol (12BD), 1,3-butanediol (13BD), 1,4-butanediol (14BD), 2,3-butanediol (23BD), 1,2,4-butanetriol (124BT) and 1,2,3,4-butanetetrol (1234BT) in water were measured by the isopiestic method at 298.15 K. Experimental osmotic coefficients were used to calculate water activity, solute activity coefficients and the pairwise Gibbs energy coefficients for solute–solute interactions.     

Apparent molar heat capacities and apparent molar volumes ofY2(SO4)3(aq),La2(SO4)3(aq),Pr2(SO4)3(aq),Nd2(SO4)3(aq),Eu2(SO4)3(aq),Dy2(SO4)3(aq),Ho2(SO4)3(aq), andLu2(SO4)3(aq)atT = 298.15 K andp = 0.1 MPa

The apparent molar heat capacities C_{p, φ} ^∘ and apparent molar volumes V_φ ^∘ of Y₂(SO₄)₃(aq), La₂(SO₄)₃(aq), Pr₂(SO₄)₃(aq), Nd₂(SO₄)₃(aq), Eu₂(SO₄)₃(aq), Dy₂(SO₄)₃(aq), Ho₂(SO₄)₃(aq), and Lu₂(SO₄)₃(aq) were measured at T =  298.15 K and p =  0.1 MPa with a Sodev (Picker) flow microcalorimeter and a Sodev vibrating-tube densimeter, respectively. These measurements extend from lower molalities of m =  (0.005 to 0.018) mol ·kg ^− 1to m =  (0.025 to 0.434) mol ·kg ^− 1, where the upper molality limits are slightly below those of the saturated solutions. There are no previously published apparent molar heat capacities for these systems, and only limited apparent molar volume information. Considerable amounts of the R SO₄ ⁺ (aq) and R(SO₄)₂ ⁻ (aq) complexes are present, where R denotes a rare-earth, which complicates the interpretation of these thermodynamic quantities. Values of the ionic molar heat capacities and ionic molar volumes of these complexes at infinite dilution are derived from the experimental information, but the calculations are necessarily quite approximate because of the need to estimate ionic activity coefficients and other thermodynamic quantities. Nevertheless, the derived standard ionic molar properties for the various R SO₄ ⁺ (aq) and R(SO₄)₂ ⁻ (aq) complexes are probably realistic approximations to the actual values. Comparisons indicate that V_φ ^∘ {RSO₄ ⁺ , aq, 298.15K}  =  − (6  ±  4)cm³· mol ^− 1and V_φ ^∘ {R(SO₄)₂ ⁻ , aq, 298.15K}  =  (35  ±  3)cm³· mol ^− 1, with no significant variation with rare-earth. In contrast, values of C_{p, φ} ^∘ { RSO₄ ⁺ , aq, 298.15K } generally increase with the atomic number of the rare-earth, whereas C_{p, φ} ^∘ { R(SO₄)₂ ⁻ , aq, 298.15K } shows a less regular trend, although its values are always positive and tend to be larger for the heavier than for the light rare earths.     

Thermodynamic properties of {(NH4)2SO4(aq) + Li2SO4(aq)} and {(NH4)2SO 4(aq) + Na2SO4(aq)} at a temperature of 298.15 K

The water activities and osmotic coefficients of aqueous solutions of {(NH₄ )₂SO ₄ +  Li ₂SO ₄} and {(NH₄ )₂SO ₄ +  Na ₂SO ₄} have been determined at a temperature of 298.15 K with a hygrometric method, at molalities in the region 0.2 mol · kg ^− 1 to saturation of the solutes for different fractional ionic-strengthsy =  0.2, 0.5, and 0.8 of (NH ₄)₂SO ₄. The experimental results are compared with the predictions obtained from our extended compared additivity model, as well as the models reported by Zdanovskii, Stokes and Robinson, Pitzer, and Lietzke-Stoughton. From these measurements, parameters of Pitzers model have been determined. These were used to predict solute activity coefficients in the mixture and calculate the excess Gibbs function at total molalities for different y for these systems.     

Measurement and modeling of osmotic coefficients of binary mixtures (alcohol + 1,3-dimethylpyridinium methylsulfate) at T = 323.15 K

Measurement of osmotic coefficients of binary mixtures containing several primary and secondary alcohols (1-propanol, 2-propanol, 1-butanol, 2-butanol, and 1-pentanol) and the pyridinium-based ionic liquid 1,3-dimethylpyridinium methylsulfate were performed at T = 323.15 K using the vapor pressure osmometry technique, and from experimental data, vapor pressure, and activity coefficients were determined. The extended Pitzer model modified by Archer, and the NRTL model modified by Jaretun and Aly (MNRTL) were used to correlate the experimental osmotic coefficients, obtaining standard deviations lower than 0.017 and 0.054, respectively. From the parameters obtained with the extended Pitzer model modified by Archer, the mean molal activity coefficients and the excess Gibbs free energy for the studied binary mixtures were calculated. The effect of the cation is studied comparing the experimental results with those obtained for the ionic liquid 1,3-dimethylimidazolium methylsulfate.     

Vapour pressures,osmotic and activity coefficients for binary mixtures containing (1-ethylpyridinium ethylsulfate + several alcohols) at T = 323.15 K

Osmotic coefficients of binary mixtures containing several primary and secondary alcohols (1-propanol, 2-propanol, 1-butanol, 2-butanol, and 1-pentanol) and the pyridinium-based ionic liquid 1-ethylpyridinium ethylsulfate were determined at T = 323.15 K using the vapour pressure osmometry technique. From the experimental results, vapour pressure and activity coefficients can be determined. For the correlation of osmotic coefficients, the extended Pitzer model modified by Archer, and the modified NRTL (MNRTL) model were used, obtaining deviations lower than 0.017 and 0.047, respectively. The mean molal activity coefficients and the excess Gibbs free energy for the binary mixtures studied were determined from the parameters obtained with the extended Pitzer model modified by Archer.     

Thermodynamic study of (m1Cs2SeO4 + m2NiSeO4)(aq)wheremdenotes molality atT = 298.15 K

The isopiestic method has been used to determine the osmotic coefficients of the binary solutions Cs₂SeO₄(aq) at T =  298.15 K from (1.090 to 4.591)mol · kg ^− 1. The molalities m of (m₁Cs₂SeO₄ + m₂NiSeO₄)(aq) have been investigated by physicochemical analysis. The crystallization of a new double salt Cs₂SeO₄· NiSeO₄· 6H₂O has been established. The Pitzer ion-interaction model has been used for thermodynamic analysis of the results obtained. The thermodynamic data needed (binary and ternary parameters of ionic interaction, thermodynamic solubility products) have been calculated and the theoretical solubility isotherm has been plotted. The experimentally obtained and the calculated solubilities are in very good agreement. The standard molar Gibbs energy of the synthesis reaction Δ_rG_m^oof the double salt Cs₂SeO₄· NiSeO₄· 6H₂O from the corresponding simple salts Cs₂SeO₄and NiSeO₄· 6H₂O, as well as the standard molar Gibbs energy of formation Δ_rG_m^ohave been determined.     

Diffusion coefficients of nickel chloride in aqueous solutions of lactose at T = 298.15 K and T = 310.15 K

Binary mutual diffusion coefficients (interdiffusion coefficients) of nickel chloride in water at T = 298.15 K and T = 310.15 K, and at concentrations between (0.000 and 0.100) mol · dm^?3, using a Taylor dispersion method have been measured. These data are discussed on the basis of the Onsager–Fuoss and Pikal models. The equivalent conductance at infinitesimal concentration of the nickel ion in these solutions at T = 310.15 K has been estimated using these results. Through the same technique, ternary mutual diffusion coefficients (D₁₁, D₂₂, D₁₂, and D₂₁) for aqueous solutions containing NiCl₂ and lactose, at T = 298.15 K and T = 310.15 K, and at different carrier concentrations were also measured. These data permit us to have a better understanding of the structure of these systems and the thermodynamic behaviour of NiCl₂ in different media.     

Isopiestic determination of the osmotic and activity coefficients of aqueous Lu2(SO4)3 at 25°C

Osmotic coefficients have been measured for aqueous Lu₂(SO₄)₃ solutions from 0.12402 to 0.89631 mol-kg^–1 at 25°C by use of the isopiestic method; these measurements extend into the supersaturated molality region. Since there was a lack of activity data for Lu₂(SO₄)₃ solutions at lower molalities, they were approximated by equating them to results for La₂(SO₄)₃ from freezing temperature depression measurements. The combined osmotic coefficients were then used to derive mean molal activity coefficients for Lu₂(SO₄)₃ solutions. The osmotic coefficients decrease to 0.307 as their minimum value and the mean molal activity coefficients decrease to 0.0069. When these activities were combined with our previously reported solubility of 0.6260±0.0017 mol-kg^–1 for Lu₂(SO₄)₃·8H₂O, a thermodynamic solubility product of 2.3×10^–10 was obtained. This value yields the Gibbs energy of formation G _f ^° (Lu₂(SO₄)₃·8H₂O, cr)=–5518.9±16.4 kJ-mol^–1.     

Determination and modelling of osmotic coefficients and vapour pressures of binary systems 1- and 2-propanol with CnMimNTf2 ionic liquids (n = 2, 3, and 4) at T = 323.15 K

The osmotic and activity coefficients and vapour pressures of binary mixtures containing 1-propanol, or 2-propanol and imidazolium-based ionic liquids with bis(trifluoromethylsulfonyl)imide as anion (1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide, C₂MimNTf₂, 1-methyl-3-propylimidazolium bis(trifluoromethylsulfonyl)imide, C₃MimNTf₂, and 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide, C₄MimNTf₂) were determined at T = 323.15 K using the vapour pressure osmometry technique. The experimental osmotic coefficients were correlated using the extended Pitzer model modified by Archer and the MNRTL model, obtaining standard deviations lower than 0.033 and 0.064, respectively. The mean molal activity coefficients and the excess Gibbs free energy for the mixtures studied were calculated from the parameters of the extended Pitzer model modified by Archer. Besides the effect of the alkyl-chain of the cation, the effect of the anion can be assessed comparing the experimental results with those previously obtained for imidazolium ionic liquids with sulphate anions.     

Activities and osmotic coefficients of tropospheric aerosols: (NH4)2SO4(aq) and NaCl(aq)

The theory of multilayer adsorption for concentrated aqueous electrolytes developed by Ally and Braunstein (1998) is used to calculate the thermodynamic activities and osmotic coefficients of supersaturated solutions of (NH₄)₂SO₄(aq) and NaCl (aq) which are among man-made aerosols of atmospheric importance. The basis of the model is the postulate of Stokes and Robinson that concentrated aqueous electrolytes may be viewed as an irregular ionic lattice structure. Application to the electrolytes mentioned above is a special case of the generalized results which are proven (Ally and Braunstein, Braunstein and Ally) to be consistent with the Gibbs–Duhem equation. Calculated thermodynamic properties are compared against experimental data from isopiestic and electrodynamic balance (EDB) measurements.     

Thermodynamic properties of (NaCl + KCl + LiCl + H2O) at T = 298.15 K: Water activities,osmotic and activity coefficients

The water activities of aqueous electrolyte mixture (NaCl + KCl + LiCl + H₂O) were experimentally determined at T = 298.15 K by the hygrometric method at total ionic-strength from 0.4 mol · kg⁻¹ to 6 mol · kg⁻¹ for different ionic-strength fractions y of NaCl with y = 1/3, 1/2, and 2/3. The data allow the deduction of new osmotic coefficients. The results obtained were correlated by Pitzer’s model and Dinane’s mixing rules ECA I and ECA II for calculations of the water activity in mixed aqueous electrolytes. A new Dinane–Pitzer model is proposed for the calculation of osmotic coefficients in quaternary aqueous mixtures using the newly ternary and quaternary ionic mixing parameters of this studied system. The solute activity coefficients of component in the mixture are also determined for different ionic-strength fractions y of NaCl.     

Activity coefficients of CaCl2 in (serine or proline + water) mixtures at T = 298.15 K

Activity coefficients for the (CaCl₂ + amino acid + water) system were determined at a temperature of 298.15 K using ion-selective electrodes. The range of molalities of CaCl₂ is (0.01 to 0.20) mol · kg^?1, and that of amino acids is (0.10 to 0.40) mol · kg^?1. The activity coefficients obtained from the Debye–Hückel extended equation and the Pitzer equation are in good agreement with each other. Results show that the interactions between CaCl₂ and amino acid are controlled mainly by the electrostatic interactions (attraction). Gibbs free energy interaction parameters (g_EA) and salting constants (k_S) are positive, indicating that these amino acids are salted out by CaCl₂. These results are discussed based on group additivity model.     

Isopiestic measurement and solubility evaluation of the ternary system (CaCl2 + SrCl2 + H2O) at T = 298.15 K

Water activities in the ternary system (CaCl₂ + SrCl₂ + H₂O) and its sub-binary system (CaCl₂ + H₂O) at T = 298.15 K have been elaborately measured by an isopiestic method. The data of the measured water activity were used to justify the reliability of solubility isotherms reported in the literature by correlating them with a thermodynamic Pitzer–Simonson–Clegg (PSC) model. The model parameters for representing the thermodynamic properties of the (CaCl₂ + H₂O) system from (0 to 11) mol ⋅ kg⁻¹ at T = 298.15 K were determined, and the experimental water activity data in the ternary system were compared with those predicted by the parameters determined in the binary systems. Their agreement indicates that the PSC model parameters can reliably represent the properties of the ternary system. Under the assumption that the equilibrium solid phases are the pure solid phases (SrCl₂ ⋅ 6H₂O and CaCl₂ ⋅ 6H₂O)_(s) or the ideal solid solution consisting of CaCl₂ ⋅ 6H₂O_(s) and SrCl₂ ⋅ 6H₂O_(s), the solubility isotherms were predicted and compared with experimental data from the literature. It was found that the predicted solubility isotherm agrees with experimental data over the entire concentration range at T = 298.15 K under the second assumption described above; however, it does not under the first assumption. The modeling results reveal that the solid phase in equilibrium with the aqueous solution in the ternary system is an ideal solid solution consisting of SrCl₂ ⋅ 6H₂O_(s) and CaCl₂ ⋅ 6H₂O_(s). Based on the theoretical calculation, the possibility of the co-saturated points between SrCl₂ ⋅ 6H₂O_(s) and the solid solution (CaCl₂ ⋅ 6H₂O + SrCl₂ ⋅ 6H₂O)_(s) and between CaCl₂ ⋅ 6H₂O_(s) and the solid solution (CaCl₂ ⋅ 6H₂O + SrCl₂ ⋅ 6H₂O)_(s), which were reported by experimental researchers, has been discussed, and the Lippann diagram of this system has been presented.     

Isopiestic Measurement of the Osmotic Coefficients of Aqueous {xH 2 SO 4 + (1− x)Fe 2 (SO 4 ) 3 } Solutions at 298.15 and 323.15 K

This study measures the osmotic coefficients of {xH₂SO₄ + (1−x)Fe₂(SO₄)₃}(aq) solutions at 298.15 and 323.15 K that have ionic strengths as great as 19.3 mol,kg⁻¹, using the isopiestic method. Experiments utilized both aqueous NaCl and H₂SO₄ as reference solutions. Equilibrium values of the osmotic coefficient obtained using the two different reference solutions were in satisfactory internal agreement. The solutions follow generally the Zdanovskii empirical linear relationship and yield values of a _w for the Fe₂(SO₄)₃–H₂O binary system at 298.15 K that are in good agreement with recent work and are consistent with other M₂(SO₄)₃–H₂O binary systems.     

Density and activity of pertechnetic acid aqueous solutions at T = 298.15 K

The previous isopiestic investigations of HTcO₄ aqueous solutions at T = 298.15 K are believed to be unreliable, because of the formation of a ternary mixture at high molality. Consequently, published isopiestic molalities for aqueous HTcO₄ solutions at T = 298.15 K were completed and corrected. Binary data (variation of the osmotic coefficient and activity coefficient of the electrolyte in solution in the water) at T = 298.15 K for pertechnetic acid HTcO₄ were determined by direct water activity measurements. These measurements extend from molality m = 1.4 mol · kg⁻¹ to m = 8.32 mol · kg⁻¹. The variation of the osmotic coefficient of this acid in water is represented mathematically. Density variations at T = 298.15 K are also established and used to express the activity coefficient values on both the molar and molal concentration scale. The density law leads to the partial molar volume variations for aqueous HTcO₄ solutions at T = 298.15 K, which are compared with published data.     

Mutual Diffusion Coefficients and Refractive Index Increments of K2SO4(aq) at 298.15 K from Rayleigh Interferometry

Journal of Solution Chemistry - Isothermal mutual diffusion coefficients (interdiffusion coefficients) were measured for K2SO4(aq) at 298.15?±?0.005 K, at numerous...     

Hygrometric determination of the water activities and the osmotic and activity coefficients of (ammonium chloride + sodium chloride + water) atT = 298.15 K

The mixed aqueous electrolyte system of ammonium and sodium chlorides has been studied by the hygrometric method at the temperature 298.15 K. The relative humidities of this system were measured at total molalities from 0.3mol · kg ^− 1 to 6 mol · kg ^− 1for different ionic-strength fractions of NH ₄Cl with y =  (0.33, 0.50, and 0.67). The data obtained allow the deduction of new water activities and osmotic coefficients. The experimental results are compared with the predictions of the extended composed additivity model proposed in our previous work, the Robinson–Stokes, Reilly–Wood–Robinson, and Lietzke–Stoughton models. From these measurements, the new Pitzer mixing ionic parameters were determined and used to predict the solute activity coefficients in the mixture.