Thermodynamic evaluation and optimization of the (Na2CO3 + Na2SO4 + Na2S + K2CO3 + K2SO4 + K2S) system

A critical evaluation of all phase diagram and thermodynamic data were performed for the solid and liquid phases of the (Na₂CO₃ + Na₂SO₄ + Na₂S + K₂CO₃ + K₂SO₄ + K₂S) system and optimized model parameters were obtained. The Modified Quasichemical Model in the Quadruplet Approximation was used for modelling the liquid phase. The model evaluates first- and second-nearest-neighbour short-range ordering, where the cations (Na⁺ and K⁺) are assumed to mix on a cationic sublattice, while anions $({\text{CO}}_3^{2-}\text{,}{\text{SO}}_4^{2-}\text{,}\text{and}{\text{S}}^{2-})$ are assumed to mix on an anionic sublattice. The Compound Energy Formalism was used for modelling the solid solutions of (Na, K)₂(CO₃, SO₄, S). The models can be used to predict the thermodynamic properties and phase equilibria in multicomponent heterogeneous systems. The experimental data from the literature were reproduced within experimental error limits.     

Phase relations in the system (chromium + rhodium + oxygen) and thermodynamic properties of CrRhO3

Phase relations in the system (chromium + rhodium + oxygen) at T = 1273 K have been determined by examination of equilibrated samples by optical and scanning electron microscopy, powder X-ray diffraction (XRD), and energy dispersive spectroscopy (EDS). Only one ternary oxide, CrRhO₃ with rhombohedral structure ($R\overline{3}$, a = 0.5031, and c = 1.3767 nm) has been identified. Alloys and the intermetallics along the (chromium + rhodium) binary were in equilibrium with Cr₂O₃. The thermodynamic properties of the CrRhO₃ have been determined in the temperature range (900 to 1300) K by using a solid-state electrochemical cell incorporating calcia-stabilized zirconia as the electrolyte. For the reaction,$\begin{array}{cc}\hfill & 1/2{\text{Cr}}_2{\text{O}}_3(\text{solid})+1/2{\text{Rh}}_2{\text{O}}_3(\text{solid})\to {\text{CrRhO}}_3(\text{solid})\text{,}\hfill \\ \hfill & \mathrm{\Delta }{G}^{°}\pm 140/(\text{J}·{\text{mol}}^{-1})=-31967+5.418(T/\text{K})\text{,}\hfill \end{array}$where Cr₂O₃ has the corundum structure and Rh₂O₃ has the orthorhombic structure. Thermodynamic properties of CrRhO₃ at T = 298.15 K have been evaluated. The compound decomposes on heating to a mixture of Cr₂O₃-rich sesquioxide solid solution, Rh, and O₂. The calculated decomposition temperatures are T = 1567 ± 5 K in pure O₂ and T = 1470 ± 5 K in air at a total pressure p^° = 0.1 MPa. The temperature-composition phase diagrams for the system (chromium + rhodium + oxygen) at different partial pressures of oxygen and an oxygen potential diagram at T = 1273 K are calculated from the thermodynamic information.     

Micellization behaviour and thermodynamic parameters of 12-2-12 gemini surfactant in (water + organic solvent) mixtures

The effect of organic solvents on micellization behaviour and thermodynamic parameters of a cationic gemini (dimeric) surfactant, C₁₂H₂₅(CH₃)₂N⁺–(CH₂)₂–N⁺(CH₃)₂C₁₂H₂₅·2Br^?, (12-2-12) was studied in aqueous solutions over the range of T = (293.15 to 323.15) K using the conductometric technique. Ethylene glycol (EG), dimethylsulfoxide (DMSO) and 1,4-dioxan (DO) were used as organic solvents with three different contents. The critical micelle concentration (cmc) and the degree of counter ion dissociation (α) of micelles in the water and in the (water + organic solvent) mixtures including 10%, 20%, and 30% solvent contents were determined. The standard Gibbs free energy $(\mathrm{\Delta }{G}_{\text{m}}^{°})$, enthalpy $(\mathrm{\Delta }{H}_{\text{m}}^{°})$ and entropy $(\mathrm{\Delta }{S}_{\text{m}}^{°})$ of micellization were estimated from the temperature dependence of the cmc values. It was observed that the critical micelle concentration of the gemini surfactant and the degree of counter ion dissociation of the micelle increased as the volume percentage of organic solvent, and temperature increased. The standard Gibbs free energy of micellization was found to be less negative with the increase in the organic solvent content and temperature.     

Standard state thermodynamic properties of aqueous sodium perrhenate using high dilution calorimetry up to 598.15 K

Standard state thermodynamic properties for aqueous sodium perrhenate at temperature in the range of (298.15 to 598.15) K and at p_sat were determined by high dilution solution calorimetry down to 10^?4 m. Standard state partial molar heat capacities, $C_{p\text{,}2}^{°}$, of aqueous sodium perrhenate calculated from present study are compared to literature values up to T = 398.15 K. The differences between $C_{p\text{,}2}^{°}$ of ${\text{ReO}}_4^{-}(\text{aq})$ and Cl^?(aq) at lower temperature is much greater than that due to their internal molecular motions. Consequently, the perrhenate ion appears to have an ionic incomplete primary hydration shell as compared to the chloride ion. The ${\text{ReO}}_4^{-}/{\text{Cl}}^{-}$ difference in thermodynamic functions has now been well defined up to T = 598.15 K for other important high temperature calculations.     

CsCu2Sc3Te6 and CsCuY2Te4: Two new quaternary cesium copper rare-earth metal tellurides

The two new quaternary cesium copper(I) rare-earth metal(III) tellurides CsCu₂Sc₃Te₆ and CsCuY₂Te₄ were prepared at 900 °C by reacting the elements copper, scandium or yttrium and tellurium together with CsBr as flux and cesium source for fourteen days in evacuated torch-sealed silica ampoules. Both compounds crystallize in space group C2/m of the monoclinic system with unit cells of the dimensions a = 1777.63(9), b = 414.20(2), c = 1033.51(5) pm, β = 113.032(4)° for CsCu₂Sc₃Te₆ (Z = 2) and a = 3741.90(19), b = 432.73(2), c = 2087.62(11) pm, β = 107.357(4)° for CsCuY₂Te₄ (Z = 12). The crystal structure of the scandium compound contains [CuTe₄]^7? tetrahedra, which are cis-edge connected in order to build up $\underset{\mathrm{\infty }}{1}\left\{{\left[{\text{CuTe}}_{1/1}^t{\text{Te}}_{3/3}^e\right]}^{3?}\right\}$ chains, and [ScTe₆]^9? octahedra, which share edges and vertices in forming corrugated $\underset{\mathrm{\infty }}{2}\left\{{\left[{\text{Sc}}_3{\text{Te}}_6\right]}^{3?}\right\}$ layers. These layers are separated from each other by [CuTe₄]^7? tetrahedra and Cs⁺ cations in trans-face bicapped square-prismatic Te^2? coordination (CN = 10). The yttrium compound has a three-dimensional structure as well built up of [CuTe₄]^7? tetrahedra and [YTe₆]^9? octahedra. All three crystallographically independent Cu⁺ cations reside in an individual infinite $\underset{\mathrm{\infty }}{1}\left\{{\left[{\text{CuTe}}_{2/1}^t{\text{Te}}_{2/2}^v\right]}^{5?}\right\}$ chain, in which each [CuTe₄]^7? tetrahedron shares two vertices with neighbouring ones. The anionic framework $\underset{\mathrm{\infty }}{3}\left\{{\left[{\text{Y}}_2{\text{Te}}_4\right]}^{2^{?}}\right\}$ and the copper-bearing $\underset{\mathrm{\infty }}{3}\left\{{\left[{\text{CuY}}_2{\text{Te}}_4\right]}^{?}\right\}$ one consist of sixteen-membered ring channels containing three different types of Cs⁺ cations (two in each channel) with bicapped trigonal prismatic (CN = 8) and monocapped cubic Te^2? coordination (CN = 9). Thus there is no isotypy with the KCuGd₂S₄-type structure, characteristic for the lighter chalcogens (e. g. ACuM₂Ch₄; A = K–Cs, M = La–Er, Ch = S and Se).     

Permittivity and density of the systems (monoglyme,diglyme, triglyme,or tetraglyme + n-heptane) at several temperatures

Relative permittivity and density on mixing at atmospheric pressure and temperatures from (288.15 to 308.15) K and atmospheric pressure have been measured over the entire composition range of mixing for {CH₃O(CH₂CH₂O)_mCH₃ with m = 1, 2, 3, 4 (also called monoglyme, diglyme, triglyme, or tetraglyme) + n-heptane}. The permittivity values were fitted as a function of the volume fraction and temperature to a logarithmic equation. The excess permittivity is calculated considering a definition that has been recently established in terms of the volume fraction. Excess molar volumes on mixing for the above systems have also been calculated. The density and excess molar volumes were fitted as a function of both mole fraction and temperature to a polynomial equation. The temperature dependence of derived magnitudes, $(?V_{\text{m}}^{\text{E}}/?T{)}_{P\text{,}x}$ and $(?H_{\text{m}}^{\text{E}}/?P{)}_{T\text{,}x}$, was computed, given their importance in the study of specific molecular interactions. The experimental values of permittivity have been compared to those estimated by usual models of literature and the results indicate that the predictions are better when the volume change on mixing is incorporated in calculations. From the values of permittivity and density on mixing the dipole moment for tetraglyme was calculated. The work concludes with an interpretation of the sign of excess permittivity and its behaviour with temperature and that of excess molar volume.     

Volumetric and viscometric properties of binary mixtures of {methyl tert-butyl ether (MTBE) + alcohol} at several temperatures and p = 0.1 MPa: Experimental results and application of the ERAS model

Densities and viscosities of binary mixtures of {methyl tert-butyl ether (MTBE) + methanol, or +ethanol, or +1-propanol, or +2-propanol, or +1-butanol, or +1-pentanol, or +1-hexanol} have been determined as a function of composition at several temperatures and atmospheric pressure. The temperatures studied were (293.15, 298.15, 303.15, and 308.15) K. The experimental results have been used to calculate the excess molar volume $(V_{\text{m}}^{\text{E}})$ and viscosity deviation (Δη). Both $V_{\text{m}}^{\text{E}}$ and Δη values were negative over the entire range of mole fraction for all temperatures and systems studied. Moreover, the $V_{\text{m}}^{\text{E}}$ values have been used to test the applicability of the Extended Real Associated Solution (ERAS) model.