The apparent molal volumes of mixtures of 1:1 electrolytes in aqueous urea solutions: A test of Young's rule

The apparent molal volumes of sodium chloride, sodium bromide, potassium chloride, and potassium bromide were determined for each salt at 2.000m in 8.000m urea-in-water solvent systems at 25°C. In each instance, the volumes were larger than those observed for the same salts in pure water. The volume changes on mixing the six pairs of these salts were measured at a constant ionic strength of 2m in the same urea-water solvent. The results of this test suggest that Young's rule applies equally well in urea-water solvent systems as it does in pure water.     

The estimation of the thermodynamic properties of ternary alloys from binary data using the shortest distance composition path

A new composition path, X_i-X_j=constant, is suggested for the semi-empirical calculation of the thermodynamic properties of ternary ‘substitutional’ solutions from binary data, when the binary systems show deviations from the regular solution model. A comparison is made between the results obtained for integral and partial properties using this composition path and those calculated employing other composition paths suggested in literature. It appears that the best estimate of the ternary properties is obtained when binary data at compositions closest to the ternary composition are used.     

Experimental densities,dynamic viscosities and surface tensions of the ionic liquids series 1-ethyl-3-methylimidazolium acetate and dicyanamide and their binary and ternary mixtures with water and ethanol at T = (298.15 to 343.15 K)

In this paper, experimental densities and dynamic viscosities of 1-ethyl-3-methylimidazolium based ionic liquids (ILs) with the anions acetate and dicyanamide are presented in a wide temperature range (298.15 to 343.15 K) at atmospheric pressure. Surface tension of these ILs was measured at T = 298.15 K. The effect of water and/or ethanol compositions on densities and dynamic viscosities of these ILs are studied in binary and ternary mixtures. A quadratic mixing rule was used to correlate binary and ternary liquid densities. The Eyring–Patel–Teja model, which is recommended for polar and aqueous systems, is used to correlate dynamic viscosity data over the whole range of compositions and temperatures in binary and ternary mixtures. Temperature-dependent interaction parameters are introduced here to account for the changes of viscosities with temperature showing good agreements with experimental data.     

The speed of sound in mixtures of the major sea salts. A test of Young's rule for adiabatic PVT properties

The relative sound speed of mixtures of aqueous solutions of NaCl–MgSO₄ and MgCl₂–Na₂SO₄ at I=0.1 and 0.5m have been determined at 5, 15, and 25°C and pressures to 1000 bars. The resulting sound speeds, adiabatic and apparent molal compressibilities have been compared to results estimated from binary solutions using an additivity principle — Young's rule. The estimated sound speeds agree with the measured values for the NaCl–MgSO₄ system to ±0.15 m-sec^–1 and for the Na₂SO₄–MgCL₂ system to ±0.20 m-sec^–1. The deviations increase with increasing ionic strength (±0.08 m-sec^–1 at I=0.1 and ±0.25 m-sec^–1 at I=0.5 m).The sound speed of seawater have also been estimated from 0 to 40°C, 0.1 to 0.7 ionic strength and 0 to 1000 bars. The estimates were found to be in good agreement (±0.4 m-sec^–1) with the measured values.These results indicate that reasonable estimates of the adiabatic PVT properties of dilute mixtures of electrolyte solutions can be made using the additivity principle, without excess mixing terms.     

An inverse sum rule for isotopic frequencies

A rule relating to the square of the inverse harmonic frequencies of a set of isotopically substituted molecules is developed. The rule is

where Λⁱ_x. is the square of the Xth harmonic frequency of the ith isotopic species, and σⁱ is a weighting factor for the ith species, taken so that

for all a, where Mⁱ_a is the mass of the ath atom in the ith species. An upper bound for the residue (Res)_i can be evaluated from the frequencies of the ith species alone. If the rule is not satisfied, no harmonic force field is compatible with the set of assigned frequencies. The rule is applied to ethylene. The rule is most sensitive to the assignment of the low frequencies. The rule is shown to apply to the vibrations of crystals, including the lattice modes, and if the sum is taken over K = K' ≠ 0 modes, the residue→ 0.     

New mixing rule for predicting multi-component gas adsorption

The present work describes a predictive model for ascertaining the multi-component gas adsorption equilibria. The model utilizes special form of covolume-dependent (CVD) mixing which is combined with the generalized form of 2-D EOS. Four well known 2-D EOSs; van der Waals, Soave-Redlich-Kwong, Peng-Robinson, Eyring along with the modified CVD mixing rule were used to predict the total adsorption of several binary and ternary systems. Based on the concept of the CVD mixing rule, it was inspired that CVD mixing rule could be a binding bridge between the molecular size and the molecular interaction. To show this, the ratio of the classical mixing rule %AAD to the CVD mixing rule %AAD were plotted versus the difference of the collision or the Leonard-Jones diameters of the gas molecules in the mixtures. It shows that there is a criterion between the CVD and the classical mixing rules in terms of molecular size difference. It seems that, Δσ _LJ≈0.60 Å is the criterion. The CVD mixing rule is approximately predominant in the region of Δσ _LJ≥0.60 Å, whilst, region of Δσ _LJ≤0.60 Å is nearly governed by the classical mixing rule. All predictions by the new mixing rule and the classical mixing rule were compared with the experimental data from the case studies. The new form of the mixing rule is in good agreement with the experimental data even for the non-ideal systems; hence provides a powerful framework to predict multi-component gas adsorption.     

On the E1 partial wave sum rule and the WKB approximation

The electric dipole (E1) partial wave sum rule, relevant to Coulomb scattering, is derived semiclassically within the WKB theory. Limiting expressions are presented according to the values of the angular momentum l of the colliding particle, the Sommerfeld number and the adiabaticity parameter ξ = ν _? - ν _i. A comparison with the quantal results, of the WKB sum rule and the classical orbital integrals, shows that the WKB approximation is extremely accurate even in the case of light and/or fast particles (ν ? 1). An algorithm is presented for the calculation of the modified Bessel function of the second kind with imaginary argument K _iξ(x) and its derivative dK _iξ(x)/dx.     

Complexation study and spectrofluorometric determination of the binding constant for diquat and p-sulfonatocalix[4]arene

The interactions between diquat (DQ) and p-sulfonatocalix[4]arene (C4S) were studied in an aqueous solution as a function of the ionic strength. Evidence for the formation of a complex between DQ and C4S was obtained using fluorescence measurements, while the stoichiometry of the complex was confirmed as 1:1 for DQ/C4S using UV–vis spectroscopy. The ionic strength had no influence on the stoichiometry of the complex, but exerted a significant influence on the complexation constant, K_c, decreasing with an increase in the ionic strength. The thermodynamic complexation constant, K_c′, was computed as 5.25±1.11×10⁷ using the extended Debye–Hückel law. The rate constants for the heterogeneous electron transfer for the reduction of DQ at an electrode surface were evaluated as 0.150±0.010 cm s^?1 in the absence of C4S and 0.065±0.010 cm s^?1 when C4S was added to the solution in a 1:1 ratio.     

Densities and Conductivities of Aqueous N,N,N-Alkyloctyldimethylammonium Chloride at Different Temperatures

The simple equations for predictions of the density and conductivity of mixed electrolyte solutions were extended to the related properties of mixed ionic liquid solutions. The densities and conductivities were measured for the ternary solutions OOAC (N,N,N-dioctyldimethylammonium chloride) + OPAC (N,N,N-octylpentyldimethylammonium chloride) + H₂O, OOAC + N,N,N-octylbutyldimethylammonium chloride (OBAC) + H₂O, OPAC + OBAC + H₂O and their corresponding binary subsystems OOAC + H₂O, OPAC + H₂O, and OBAC + H₂O at (298.15, 303.15, and 308.15) K, respectively. The results were used to test the predictability of the extended equations. Comparison of the results shows that these simple equations can be used to predict the density and conductivity of the mixed ionic liquid solutions from the properties of their binary subsystems of equal ionic strength.     

Structural,elastic, electronic and thermal properties of the cubic perovskite-type BaSnO3

First-principles calculations are performed to investigate the structural, elastic, electronic and thermal properties of the cubic perovskite-type BaSnO₃. The ground-state properties are in agreement with experimental data. The independent elastic constants, C₁₁, C₁₂ and C₄₄, are calculated from direct computation of stresses generated by small strains. A linear pressure dependence of the elastic stiffnesses is found. From the theoretical elastic constants, we have computed the elastic wave velocities along [100], [110] and [111] directions. The shear modulus, Young's modulus, Poisson's ratio, Lamé’s coefficients, average sound velocity and Debye temperature are estimated in the framework of the Voigt-Reuss-Hill approximation for ideal polycrystalline BaSnO₃ aggregate. Using the sX-LDA for the exchange-correlation potential, the calculated indirect fundamental band gap value is in very good agreement with the measured one. The analysis of the site-projected l-decomposed density of states, charge transfer and charge density shows that the bonding is of ionic nature. Through the quasi-harmonic Debye model, in which the phononic effects are considered, the temperature effect on the lattice constant, bulk modulus, thermal expansion coefficient, heat capacity and Debye temperature is calculated.     

A local composition extension of the van der Waals mixing rule for PR cubic equation of state

New mixing rules (VWLC-I and II) capable of connecting van der Waals (VDW) to CEOS/A^E mixing rule models were developed. These models are able to incorporate the same multi-component mixture parameters obtained for the van der Waals and CEOS/A^E models simultaneously. The VWLC mixing rules directly incorporate local compositions into the cubic equations of state (CEOS). The energy parameters required for the local compositions are calculated from the CEOS parameters. The Peng–Robinson (PR) CEOS was used for this study. Binary interactions parameters were obtained by adjusting the vapor pressure of the binary mixture for several low and high-pressure systems. The predictive capabilities of the VWLC mixing rules were tested by vapor–liquid equilibria calculations for low and high-pressure multicomponent systems. The results were compared with the predictions of the VDW mixing rule and a Huron–Vidal (HV) kind of CEOS/A^E-NRTL mixing rule. The VWLC mixing rules are consistent models giving good results in a broad range of pressures and temperatures in binary and multicomponent mixtures. They compare favorably with the CEOS/A^E-NRTL mixing rule for low-pressure systems. In high-pressure ternary systems VWLC-I and II give good predictions, much better, in fact, than the CEOS/A^E-NRTL mixing rule.     

Determination of thermodynamic properties of aqueous mixtures of RbCl and Rb2SO4 by the EMF method at T=298.15 K

The thermodynamic properties, including activity coefficients, osmotic coefficients and excess Gibbs free energy for RbCl and Rb₂SO₄ aqueous mixtures at T=298.15 K and in 0.01 mol · kg⁻¹ to 5 mol · kg⁻¹ ionic strength, were determined by emf measurements. The Rb–ISE and Ag–AgCl electrodes used in this work were prepared in our laboratory and had a reasonably good Nernst response. The experimental data were fitted by using the Harned rule and Pitzer model. The Harned coefficients and the Pitzer binary and ternary interaction parameters for the system have been evaluated. The experimental results obey the Harned rule. The Pitzer model can be used to describe this aqueous system satisfactorily.     

Osmotic and Activity Coefficients of {yKCl+(1−y)MgCl2}(aq) at T=298.15 K

Isopiestic vapor-pressure measurements were made at the temperature 298.15 K for aqueous KCl + MgCl₂ solutions using KCl(aq) as the reference standard. The measurements for these ternary solutions were made at KCl ionic strength fractions of y=0.0, 0.1989, 0.3996, 0.5993, 0.7925 and 1.0 (with two additional sets at y=0.0, 0.2021, 0.3998, 0.6125, 0.8209 and 1.0) for the ionic strength range from 0.4014 to 6.2790 mol?kg^?1. Our results, and those from two previous isopiestic studies, were combined and used with previously determined parameters for KCl(aq) and those determined here for MgCl₂(aq) to evaluate mixing parameters for the Clegg-Pitzer-Brimblecombe model. These combined data were also used to determine the mixing parameters of the Scatchard model. Both sets of model parameters are valid for ionic strengths of I≤12.8 mol?kg^?1, where higher-order electrostatic effects have been included in the Clegg-Pitzer-Brimblecombe mixture model. The activity coefficients for KCl and MgCl₂ were calculated from these models and the results for KCl were compared to experimental data from Emf measurements. The Scatchard model interaction parameters were used for calculation of the excess Gibbs energy as a function of the ionic strength and ionic strength fraction of KCl. The Zdanovskii-Robinson-Stokes rule of linearity for mixing of isopiestic solutions was tested.     

Comparative crystal-chemical analysis of anhydrous salts My(TQ4)z (T = Si, Ge, P, As; Q = S, Se, Te) and binary compounds

Topological analysis and crystal-chemical classification of 67 compounds with tetrahedral anions with the general formula M_y(TQ₄)_z (T = Si, Ge, P, As; Q = S, Se, Te) have been carried out. These compounds are classified into 36 topological and 38 structure types. Cases of similarity of ternary anhydrous salts M_y(TQ₄)_z to binary compounds A_yX_z are revealed and discussed with the use of the TOPOS structural topological program package. Analysis of the topology and uniformity of ionic matrices shows that the matrices of chalcogenide ions and tetrahedral TQ ₄ ^y? anions play, as a rule, a leading structural role in M_y(TQ₄)_z compounds.     

Osmotic and activity coefficients of {yNaH2PO4+(1−y)Na2SO4}(aq) at the temperature 298.15 K

The osmotic coefficients of the mixed electrolyte solution {yNaH₂PO₄+(1−y)Na₂SO₄}(aq) have been measured by the isopiestic method, at the temperature T=298.15 K. The activity coefficients of NaH₂PO₄ and Na₂SO₄ were calculated by Scatchard's neutral-electrolyte method and by Pitzer and Kim's treatment for mixed-electrolyte solutions. The Scatchard interaction parameters are used for calculation of the excess Gibbs energy as a function of ionic strength and ionic-strength fraction of NaH₂PO₄. Also, the Zdanovskii's rule of linearity is tested.     

Auswahl von Phasensystemen in der Lösungs-, Adsorptions- und Ionenaustausch-Chromatographie

In contrast to GC selectivity in LC is determined by the composition of both the stationary as well as the mobile phase. Therefore the main problem in LC results in selecting an appropriate phase system for the given separation problem. The selectivity factorα _ijis defined as the ratio of the capacity factors k′ _i k′_jof two solutes, which corresponds to the ratio of their distribution coefficients ^c K _i, ^cK_j. In LLC α _ijis determined by the relative solubility of the solutes in the two immiscible phases, which were prepared from binary or ternary liquid-liquid-systems. Secondary effects on retention are caused by the support. Two variations exist (LLC, Reverse-Phase-LLC) which differ in whether the polar phase is used as stationary or mobile phase, resp. In LSC the same phase variation is possible. Using a polar support and an unpolar solvent α _ijis governed by the relative strength of interactions between the solute molecules and the surface of the support. In Reverse-Phase-LSC, however, using an unpolar support and a polar solvent, these interactions are very weak and α _ijis mainly determined by the solubility of the solutes in the mobile phase. In IEC α _ijdepends on a set of parameters such as the type of ion-exchange matrix, its pore structure and its degree of crosslinking, resp., the type, surface concentration and distribution of functional groups, the type of the eluent ion, its concentration, the ionic strength and pH-value of the eluent, the temperature. Different methods have been developed in order to calculate the distribution coefficients of solutes for a given phase system.     

Physical properties of the ternary mixture ethanol + water + 1-hexyl-3-methylimidazolium chloride at 298.15 K

In this work, densities and refractive indices of the ternary mixture ethanol?+?water?+?1-hexyl-3-methylimidazolium chloride ([C₆mim][Cl]) and of the binary systems containing the ionic liquids (ILs) have been measured at 298.15?K and atmospheric pressure. Excess molar volumes and changes of refractive indices on mixing were determined from experimental data. The binary data were correlated with the Redlich–Kister equation, while the Cibulka equation was applied for the ternary system.     

Excess Gibbs energies of the ternary system ethanol+N,N-dimethylformamide+cyclohexane at 298.15 K

Vapour–liquid equilibrium (VLE) for the ternary system ethanol (EtOH)+N,N-dimethylformamide (DMF)+cyclohexane (Cy) and for the relevant binary mixtures containing DMF have been determined at 298.15 K by headspace gas chromatographic analysis of the vapour phase directly withdrawn from an equilibrium apparatus. Measurements of liquid–liquid equilibria in both binary DMF+Cy and ternary mixtures have been also carried out. The binary VLE data have been described with different correlation equations. The capabilities of different models of either predicting or reproducing the ternary data have been compared. Excess Gibbs energies G^E as well as activity coefficients γ_i of components have been obtained and briefly discussed. While EtOH+DMF behaves almost ideally with slightly negative G^E-values, both EtOH+Cy and DMF+Cy exhibit large positive deviations. The G^Es of the ternary system are positive with the exception of a narrow region in dilute Cy. The excess entropy and the temperature dependence of G^E and γ_i have been calculated in the whole ternary domain from the known excess enthalpy and heat capacity. The predictions by different equations of the effect of temperature on the mutual solubilities of DMF and Cy as well as on the binodal curve of EtOH+DMF+Cy have been compared with experiment.     

Physical Properties of the Ternary Mixture Ethanol+Water+1-Butyl-3-Methylimidazolium Chloride at 298.15 K

In this work densities, refractive indices, speeds of sound and isentropic compressibilities of the ternary mixture ethanol+water+1-butyl-3-methylimidazolium chloride ([C₄mim][Cl]), and of the binary subsystems containing the ionic liquid, have been measured at 298.15 K and atmospheric pressure.