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.     

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.     

Thermodynamic properties of CaTiF5(s)

Calcium titanofluoride CaTiF₅(s) was prepared by solid-state reaction of CaF₂(s) with TiF₃(s) and characterized by X-ray diffraction method. The standard molar isobaric heat capacity $(C_{p\text{,m}}^{\circ })$ of CaTiF₅(s) was determined by a power compensated differential scanning calorimeter in the temperature from 230 K to 710 K. A solid-state galvanic cell with CaF₂ as electrolyte was used to determine the standard molar Gibbs energy of formation $({\mathrm{\Delta }}_{\text{f}}{G}_{\text{m}}^{\circ })$ of CaTiF₅ in the temperature range from 803 K to 1005 K. The galvanic cell can be depicted as:$(-)\text{Pt,}{\text{O}}_2(\text{g,}101.325\text{kPa})/\{\text{CaO(s)}+{\text{CaF}}_2(\text{s})\}//{\text{CaF}}_2//\{{\text{CaTiF}}_5(\text{s})+{\text{CaTiO}}_3(\text{s})\}/{\text{O}}_2(\text{g,}101.325\text{kPa})\text{,Pt}(+)$The second law analysis of present data were carried out to derive the standard entropy $S_{\text{m}}^{\circ }(298.15\text{K})$ and the enthalpy of formation ${\mathrm{\Delta }}_{\text{f}}{H}_{\text{m}}^{\circ }(298.15\text{K})$ and the values derived are 68.7 J · K⁻¹ · mol⁻¹ and −2848.4 kJ · mol⁻¹, respectively.     

Thermodynamic evaluation and optimization of the (NaCl + Na2SO4 + Na2CO3 + KCl + K2SO4 + K2CO3) system

A complete, critical evaluation of all phase diagrams and thermodynamic data was performed for all condensed phases of the (NaCl + Na₂SO₄ + Na₂CO₃ + KCl + K₂SO₄ + K₂CO₃) system, and optimized parameters for the thermodynamic solution models 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 order, where the cations (Na⁺ and K⁺) were assumed to mix on a cationic sublattice, while anions $({\text{CO}}_3^{2-}\text{,}{\text{SO}}_4^{2-}\text{,}\text{and}{\text{Cl}}^{-})$ were assumed to mix on an anionic sublattice. The thermodynamic properties of the solid solutions of (Na,K)₂(SO₄,CO₃) were modelled using the Compound Energy Formalism, and (Na,K)Cl was modelled using a substitutional model in previous studies. Phase transitions in the common-cation ternary systems (NaCl + Na₂SO₄ + Na₂CO₃) and (KCl + K₂SO₄ + K₂CO₃) were studied experimentally using d.s.c./t.g.a. The experimental results were used as input for evaluating the phase equilibrium in the common-cation ternary systems. The models can be used to predict the thermodynamic properties and phase equilibria in multicomponent heterogeneous systems. The experimental data from the literature are reproduced within experimental error limits.     

A thermodynamic study of ketoreductase-catalyzed reactions 4. Reduction of 2-substituted cyclohexanones in n-hexane

The equilibrium constants K for the ketoreductase-catalyzed reduction reactions (2-substituted cyclohexanone + 2-propanol = cis- and trans-2-substituted cyclohexanol + acetone) have been measured in n-hexane as solvent. The 2-substituted cyclohexanones included in this study are: 2-methylcyclohexanone, 2-phenylcyclohexanone, and 2-benzylcyclohexanone. The equilibrium constants K for the reactions with 2-methylcyclohexanone were measured over the range T = 288.15 to 308.05 K. The thermodynamic quantities at T = 298.15 K are: K = (2.13 ± 0.06); ${\mathrm{\Delta }}_{\text{r}}{G}_{\text{m}}^{\circ }=-(1.87\pm 0.06)\text{kJ}·{\text{mol}}^{-1}$; ${\mathrm{\Delta }}_{\text{r}}{H}_{\text{m}}^{\circ }=-(6.56\pm 2.68)\text{kJ}·{\text{mol}}^{-1}$; and ${\mathrm{\Delta }}_{\text{r}}{S}_{\text{m}}^{\circ }=-(15.7\pm 9.2)\text{J}·{\text{K}}^{-1}·{\text{mol}}^{-1}$ for the reaction involving cis-2-methylcyclohexanol, and K = (10.7 ± 0.2); ${\mathrm{\Delta }}_{\text{r}}{G}_{\text{m}}^{\circ }=-(5.87\pm 0.04)\text{kJ}·{\text{mol}}^{-1}$; ${\mathrm{\Delta }}_{\text{r}}{H}_{\text{m}}^{\circ }=-(2.54\pm 1.8)\text{kJ}·{\text{mol}}^{-1}$; and ${\mathrm{\Delta }}_{\text{r}}{S}_{\text{m}}^{\circ }=(11.2\pm 6.4)\text{J}·{\text{K}}^{-1}·{\text{mol}}^{-1}$ for the reaction involving trans-2-methylcyclohexanol. The standard molar Gibbs free energy changes ${\mathrm{\Delta }}_{\text{r}}{G}_{\text{m}}^{\circ }$ for the reactions (trans-2-substituted cyclohexanol = cis-2-substituted cyclohexanol) in n-hexane have also been calculated and compared with the literature data that pertain to reactions in the gas phase and at higher temperatures. Experiments carried out with a chiral column demonstrated that the enzymatic reduction of 2-phenylcyclohexanone catalyzed by the ketoreductase used in this study is not stereoselective.     

Standard values of fugacity for sulfur which are self-consistent with the low-pressure phase diagram

A method for calculating the fugacity of pure sulfur in the α-solid, β-solid and liquid phase regions has been reported for application to industrial equilibrium conditions, e.g., high-pressure solubility of sulfur in sour gas. The fugacity calculations are self-consistent with the low-pressure phase diagram. As recently discussed by Ferreira and Lobo [1], empirical fitting of the experimental data does not yield consistent behaviour for the low-pressure phase diagram of elemental sulfur. In particular, there is a discrepancy between the vapour pressure of β-solid (monoclinic) and liquid sulfur at the fusion temperature. We have provided an alternative semi-empirical approach which allows one to calculate values of the fugacity at conditions removed from the conditions of the pure sulfur phase transitions. For our approach, we have forced the liquid vapour pressure to equal the β-solid vapour pressure at the β-l-g triple point corresponding to the ‘natural’ fusion temperature for β-solid. Many studies show a higher ‘observed’ fusion temperature for elemental sulfur. The non-reversible conditions for ‘observed’ fusion conditions for elemental sulfur result from a kinetically hindered melt which causes some thermodynamic measurements to be related to a metastable S₈ liquid. We have measured the ‘natural’ fusion temperature, $T_{\mathit{fus}}^{\mathrm{\beta }}(\text{exp.})=(388.5\pm 0.2)\text{K}$ at p = 89.9 kPa, which is consistent with literature fusion data at higher-pressures. Using our semi-empirical approach, we have used or found the following conditions for the low-pressure sulfur phase diagram: T^α-β-g = 368.39 K, p^α-β-g = 0.4868 Pa, T^β-l-g = 388.326 K, p^β-l-g = 2.4437 Pa, $T_{\mathit{fus}}^{\mathrm{\beta }\text{-l}}(101.325\text{kPa})=388.348\text{K}$, T^α-β-l = 419.06 K, and p^α-β-l = 124,360 kPa.