Heat capacities,third-law entropies and thermodynamic functions of the geometrically frustrated antiferromagnetic spinels GeCo2O4 and GeNi2O4 from T=(0 to 400) K

The molar heat capacities of GeCo₂O₄ and GeNi₂O₄, two geometrically frustrated spinels, have been measured in the temperature range from T=(0.5 to 400) K. Anomalies associated with magnetic ordering occur in the heat capacities of both compounds. The transition in GeCo₂O₄ occurs at T=20.6 K while two peaks are found in the heat capacity of GeNi₂O₄, both within the narrow temperature range between 11.4<(T/K)<12.2. Thermodynamic functions have been generated from smoothed fits of the experimental results. At T=298.15 K the standard molar heat capacities are (143.44 ± 0.14) J · K⁻¹ · mol⁻¹ for GeCo₂O₄ and (130.76 ± 0.13) J · K⁻¹ · mol⁻¹ for GeNi₂O₄. The standard molar entropies at T=298.15 K for GeCo₂O₄ and GeNi₂O₄ are (149.20 ± 0.60) J · K⁻¹ · mol⁻¹ and (131.80 ± 0.53) J · K⁻¹ · mol⁻¹ respectively. Above 100 K, the heat capacity of the cobalt compound is significantly higher than that of the nickel compound. The excess heat capacity can be reasonably modeled by the assumption of a Schottky contribution arising from the thermal excitation of electronic states associated with the CO²⁺ ion in a cubic crystal field. The splittings obtained, 230 cm⁻¹ for the four-fold-degenerate first excited state and 610 cm⁻¹ for the six-fold degenerate second excited state, are significantly lower than those observed in pure CoO.     

A calorimetric and thermodynamic investigation of A2[(UO2)2(MoO4)O2] compounds with A = K and Rb and calculated phase relations in the system (K2MoO4 + UO3 + H2O)

A calorimetric and thermodynamic investigation of two alkali-metal uranyl molybdates with general composition A₂[(UO₂)₂(MoO₄)O₂], where A = K and Rb, was performed. Both phases were synthesized by solid-state sintering of a mixture of potassium or rubidium nitrate, molybdenum (VI) oxide and gamma-uranium (VI) oxide at high temperatures. The synthetic products were characterised by X-ray powder diffraction and X-ray fluorescence methods. The enthalpy of formation of K₂[(UO₂)₂(MoO₄)O₂] was determined using HF-solution calorimetry giving Δ_fH° (T = 298 K, K₂[(UO₂)₂(MoO₄)O₂], cr) = −(4018 ± 8) kJ · mol⁻¹. The low-temperature heat capacity, С_р°, was measured using adiabatic calorimetry from T = (7 to 335) K for K₂[(UO₂)₂(MoO₄)O₂] and from T = (7 to 326) K for Rb₂[(UO₂)₂(MoO₄)O₂]. Using these С_р° values, the third law entropy at T = 298.15 K, S°, is calculated as (374 ± 1) J · K⁻¹ · mol⁻¹ for K₂[(UO₂)₂(MoO₄)O₂] and (390 ± 1) J · K⁻¹ · mol⁻¹ for Rb₂[(UO₂)₂(MoO₄)O₂]. These new experimental results, together with literature data, are used to calculate the Gibbs energy of formation, Δ_fG°, for both phases giving: Δ_fG° (T = 298 K, K₂[(UO₂)₂(MoO₄)O₂], cr) = (−3747 ± 8) kJ · mol⁻¹ and Δ_fG° (T = 298 K, Rb₂[(UO₂)₂(MoO₄)], cr) = −3736 ± 5 kJ · mol⁻¹. Smoothed С_р°(Т) values between 0 K and 320 K are presented, along with values for S° and the functions [H°(T) − H°(0)] and [G°(T) − H°(0)], for both phases. The stability behaviour of various solid phases and solution complexes in the (K₂MoO₄ + UO₃ + H₂O) system with and without CO₂ at T = 298 K was investigated by thermodynamic model calculations using the Gibbs energy minimisation approach.     

Thermodynamic properties of Na2Ti6O13 and Na2Ti3O7: electrochemical and calorimetric determination

Standard values of Gibbs free energy, entropy, and enthalpy of Na₂Ti₆O₁₃ and Na₂Ti₃O₇ were determined by evaluating emf-measurements of thermodynamically defined solid state electrochemical cells based on a Na–β″-alumina electrolyte. The central part of the anodic half cell consisted of Na₂CO₃, while two appropriate coexisting phases of the ternary system Na–Ti–O are used as cathodic materials. The cell was placed in an atmosphere containing CO₂ and O₂. By combining the results of emf-measurements in the temperature range of 573⩽T/K⩽1023 and of adiabatic calorimetric measurements of the heat capacities in the low-temperature region 15⩽T/K⩽300, the thermodynamic data were determined for a wide temperature range of 15⩽T/K⩽1100. The standard molar enthalpy of formation and standard molar entropy at T=298.15 K as determined by emf-measurements are Δ_fH_m⁰=(−6277.9±6.5) kJ · mol⁻¹ and S_m⁰=(404.6±5.3) J · mol⁻¹ · K⁻¹ for Na₂Ti₆O₁₃ and Δ_fH_m⁰=(−3459.2±3.8) kJ · mol⁻¹ and S_m⁰=(227.8±3.7) J · mol⁻¹ · K⁻¹ for Na₂Ti₃O₇. The standard molar entropy at T=298.15 K obtained from low-temperature calorimetry is S_m⁰=399.7 J · mol⁻¹ · K⁻¹ and S_m⁰=229.4 J · mol⁻¹ · K⁻¹ for Na₂Ti₆O₁₃ and Na₂Ti₃O₇, respectively. The phase widths with respect to Na₂O content were studied by using a Na₂O-titration technique.     

Heat capacity and thermodynamic properties of germanium disulfide at temperatures from T = (2 to 1240) K

The heat capacity of polycrystalline germanium disulfide α-GeS₂ has been measured by relaxation calorimetry, adiabatic calorimetry, DSC and heat flux calorimetry from T = (2 to 1240) K. Values of the molar heat capacity, standard molar entropy and standard molar enthalpy are 66.191 J · K^?1 · mol^?1, 87.935 J · K^?1 · mol^?1 and 12.642 kJ · mol^?1. The temperature of fusion and its enthalpy change are 1116 K and 23 kJ · mol^?1, respectively. The thermodynamic functions of α-GeS₂ were calculated over the range (0 ? T/K ? 1250).     

Thermodynamic properties of calcium titanates: CaTiO3, Ca4Ti3O10, and Ca3Ti2O7

The chemical potentials of CaO in two-phase fields (TiO₂ + CaTiO₃), (CaTiO₃ + Ca₄Ti₃O₁₀), and (Ca₄Ti₃O₁₀ + Ca₃Ti₂O₇) of the pseudo-binary system (CaO + TiO₂) have been measured in the temperature range (900 to 1250) K, relative to pure CaO as the reference state, using solid-state galvanic cells incorporating single crystal CaF₂ as the solid electrolyte. The cells were operated under pure oxygen at ambient pressure. The standard Gibbs free energies of formation of calcium titanates, CaTiO₃, Ca₄Ti₃O₁₀, and Ca₃Ti₂O₇, from their component binary oxides were derived from the reversible e.m.f.s. The results can be summarised by the following equations: CaO(solid) + TiO₂(solid) → CaTiO₃(solid), ΔG° ± 85/(J · mol^?1) = ?80,140 ? 6.302(T/K); 4CaO(solid) + 3TiO₂(solid) → Ca₄Ti₃O₁₀(solid), ΔG° ± 275/(J · mol^?1) = ?243,473 ? 25.758(T/K); 3CaO(solid) + 2TiO₂(solid) → Ca₃Ti₂O₇(solid), ΔG° ± 185/(J · mol^?1) = ?164,217 ? 16.838(T/K).The reference state for solid TiO₂ is the rutile form. The results of this study are in good agreement with thermodynamic data for CaTiO₃ reported in the literature. For Ca₄Ti₃O₁₀ Gibbs free energy of formation obtained in this study differs significantly from that reported by Taylor and Schmalzried at T = 873 K. For Ca₃Ti₂O₇ experimental measurements are not available in the literature for direct comparison with the results obtained in this study. Nevertheless, the standard entropy for Ca₃Ti₂O₇ at T = 298.15 K estimated from the results of this study using the Neumann–Koop rule is in fair agreement with the value obtained from low-temperature heat capacity measurements.     

Heat capacities,third-law entropies and thermodynamic functions of the negative thermal expansion material Zn2GeO4 from T=(0 to 400) K

The molar heat capacity of Zn₂GeO₄, a material which exhibits negative thermal expansion below ambient temperatures, has been measured in the temperature range 0.5⩽(T/K)⩽400. At T=298.15 K, the standard molar heat capacity is (131.86 ± 0.26) J · K⁻¹ · mol⁻¹. Thermodynamic functions have been generated from smoothed fits of the experimental results. The standard molar entropy at T=298.15 K is (145.12 ± 0.29) J · K⁻¹ · mol⁻¹. The existence of low-energy modes is supported by the excess heat capacity in Zn₂GeO₄ compared to the sums of the constituent binary oxides.     

Thermodynamics of Cr2O3, FeCr2O4, ZnCr2O4, and CoCr2O4

High-temperature heat capacity measurements were obtained for Cr₂O₃, FeCr₂O₄, ZnCr₂O₄, and CoCr₂O₄ using a differential scanning calorimeter. These data were combined with previously available, overlapping heat capacity data at temperatures up to 400 K and fitted to 5-parameter Maier–Kelley C_p(T) equations. Expressions for molar entropy were then derived by suitable integration of the Maier–Kelley equations in combination with recent S^∘(298) evaluations. Finally, a database of high-temperature equilibrium measurements on the formation of these oxides was constructed and critically evaluated. Gibbs free energies of Cr₂O₃, FeCr₂O₄, and CoCr₂O₄ were referenced by averaging the most reliable results at reference temperatures of (1100, 1400, and 1373) K, respectively, while Gibbs free energies for ZnCr₂O₄ were referenced to the results of Jacob [K.T. Jacob, Thermochim. Acta 15 (1976) 79–87] at T = 1100 K. Thermodynamic extrapolations from the high-temperature reference points to T = 298.15 K by application of the heat capacity correlations gave Δ_fG^∘(298) = (−1049.96, −1339.40, −1428.35, and −1326.75) kJ · mol⁻¹ for Cr₂O₃, FeCr₂O₄, ZnCr₂O₄, and CoCr₂O₄, respectively.     

The role of the double bond position in hydroboration using HBBr2 · SMe2, HBCl2 · SMe2 and H2BBr · SMe2: A detailed kinetic and mechanistic study

Hydroboration reactions of 4-octene with HBBr₂ · SMe₂, HBCl₂ · SMe₂ and H₂BBr · SMe₂ in CH₂Cl₂ were studied as function of concentration and temperature and compared with those of 1-octene. On average, hydroboration with dihaloborane proceeded 16 times slower for 4-octene than for 1-octene. In the case of the reactions with the monohaloborane, this factor is halved. This can be explained by the difference in the relative rates of dissociates of Me₂S from the dihaloborane and a monohaloborane complex, respectively. The reactions involving H₂BBr · SMe₂ also exhibited a k_?2 value, an indication of the presence of a parallel reaction, most likely a rearrangement process facilitating isomerization by way of a π-complex. The moderate ΔH^≠ values accompanied by small ΔS^≠ values (94 ± 4 kJ mol^?1, ?3 ± 13 J K^?1 mol^?1 for HBBr₂ · SMe₂; 93 ± 1 kJ mol^?1, ?17 ± 4 J K^?1 mol^?1 for HBCl₂ · SMe₂ and in the case of H₂BBr · SMe₂, 90 ± 13 kJ mol^?1, +12 ± 44 J K^?1 mol^?1 and 83 ± 13 kJ mol^?1, ?24 ± 45 J K^?1 mol^?1, respectively, for the k₂ and k_?2 processes) imply a process that is dissociatively dominated, with the overall mode of activation being interchange dissociative (I_d).     

(Liquid + solid) metastable equilibria in quinary system Li2CO3 + Na2CO3 + K2CO3 + Li2B4O7 + Na2B4O7 + K2B4O7 + H2O at T=288 K for Zhabuye salt lake

An experimental study on metastable equilibria at T=288 K in the quinary system Li₂CO₃ + Na₂CO₃ + K₂CO₃ + Li₂B₄O₇ + Na₂B₄O₇ + K₂B₄O₇ + H₂O was done by isothermal evaporation method. Metastable equilibrium solubilities and densities of the solution were determined experimentally. According to the experimental data, the metastable equilibrium phase diagram under the condition saturated with Li₂CO₃ was plotted, in which there are four invariant points; nine univariant curves; six fields of crystallization: K₂CO₃ · 3/2H₂O, K₂B₄O₇ · 5H₂O, Li₂B₂O₄ · 16H₂O, Na₂B₂O₄ · 8H₂O, Na₂CO₃ · 10H₂O, NaKCO₃ · 6H₂O. Some differences were found between the stable phase diagram at T=298 K and the metastable one at T=288 K.     

Heat capacity and enthalpy of fusion of pyrimethanil laurate (C24H37N3O2)

Low-temperature heat capacities of pyrimethanil laurate (C₂₄H₃₇N₃O₂) were precisely measured with an automated adiabatic calorimeter over the temperature range between T = 78 K and T = 340 K. The sample was observed to melt at (321.52 ± 0.04) K. The molar enthalpy and entropy of fusion as well as the chemical purity of the compound were determined to be (67244 ± 11) J · mol⁻¹, (209.28 ± 0.02) J · mol⁻¹ · K⁻¹, (0.9943 ± 0.0004) mass fraction, respectively. The extrapolated melting temperature for the absolutely pure compound obtained from fractional melting experiments was (322.264 ± 0.006) K.     

Potential energy surface and rate constant of the inversion substitution reactions CH3X + O2 → CH3O2• + X• (X = SH,NO2)

The temperature dependence of the rate constant of the inversion substitution reactions CH₃X + O₂ → CH₃O₂^? + X^? (X = SH, NO₂), can be expressed as k = 6.8 × 10^–12(T/1000)^1.49exp(–62816 cal mol^–1/RT) cm³ s^–1 (X = SH) and k = 6.8 × 10^–12(T/1000)^1.26 × × exp(–61319 cal mol^–1/RT) cm³ s^–1 (X = NO₂), as found with the use of high-level quantum chemical methods and the transition state theory.     

The solubility measurements of sodium dicarboxylate salts; sodium oxalate,malonate, succinate,glutarate, and adipate in water from T = (279.15 to 358.15) K

The solubility measurements of sodium dicarboxylate salts; sodium oxalate, malonate, succinate, glutarate, and adipate in water at temperatures from (278.15 to 358.15 K) were determined. The molar enthalpies of solution at T = 298.15 K were derived: Δ_solH_m (m = 2.11 mol · kg^?1) = 13.86 kJ · mol^?1 for sodium oxalate; Δ_solH_m (m = 3.99 mol · kg^?1) = 14.83 kJ · mol^?1 for sodium malonate; Δ_solH_m (m = 2.45 mol · kg^?1) = 14.83 kJ · mol^?1 for sodium succinate; Δ_solH_m (m = 4.53 mol · kg^?1) = 16.55 kJ · mol^?1 for sodium glutarate, and Δ_solH_m (m = 3.52 mol · kg^?1) = 15.70 kJ · mol^?1 for sodium adipate. The solubility value exhibits a prominent odd–even effect with respect to terms with odd number of sodium dicarboxylate carbon numbers showing much higher solubility. This odd–even effect may have implications for the relative abundance of these compounds in industrial applications and also in the atmospheric aerosols.     

Thermodynamic characterization of NiAl

Thermodynamic properties of the high-stability intermetallic compound nickel aluminide, NiAl, have been determined from mass-spectrometric, weight-loss effusion, and calorimetric measurements, using samples from a single preparation with a composition determined to be Ni_0.986Al_1.014. Per mole of NiAl molecules, the specific heat capacity at room temperature of 298 K is 48.54 J · K^?1 · mol^?1, with a linear temperature dependence of +0.0104 J · K^?2 · mol^?1. At the same temperature, the enthalpy of formation is ?133.7 kJ · mol^?1, the entropy is about 53.8 J · K^?1 · mol^?1 and the enthalpy difference between room temperature and absolute zero is 7.97 kJ · mol^?1. The Gibbs free-energy is ?130.2 kJ · mol^?1 at T = 298 K, with a linear temperature dependence of +5.04 J · K^?1 · mol^?1. The Debye temperature is 452 K, while the electronic density-of-states at the Fermi-level is about 0.29 states per eV-atom. The NiAl⁺ ions were observed in the high-temperature mass spectra. Pressures for the gas at these temperatures were estimated and used with the results of quantum-mechanical calculations of total energy, specific heat, and entropy to calculate free-energy functions for the gas. These and additional results are compared with other measurements and discussed in terms of current theories of the electronic and structural properties of the compound.     

Thermodynamic study of the system (LiCl + CaCl2 + H2O)

Solubility isotherms of the ternary system (LiCl + CaCl₂ + H₂O) were elaborately determined at T = (283.15 and 323.15) K. Several thermodynamic models were applied to represent the thermodynamic properties of this system. By comparing the predicted and experimental water activities in the ternary system, an empirical modified BET model was selected to represent the thermodynamic properties of this system. The solubility data determined in this work at T = (283.15 and 323.15) K, as well as those from the literature at other temperatures, were used for the model parameterization. A complete phase diagram of the ternary system was predicted over the temperature range from (273.15 to 323.15) K. Subsequently, the Gibbs free energy of formation of the solid phases CaCl₂ · 4 H₂O_(s), CaCl₂ · 2 H₂O_(s), LiCl · 2H₂O_(s), and LiCl · CaCl₂ · 5H₂O_(s) was estimated and compared with the literature data.     

Apparent molar volumes and apparent molar heat capacities of aqueous tetrahydrofuran,dimethyl sulfoxide, 1,4-dioxane,and 1,2-dimethoxyethane at temperatures from 278.15 K to 393.15 K and at the pressure 0.35 MPa

We determined apparent molar volumes V_? at 278.15 ? (T/K) ? 368.15 and apparent molar heat capacities C_p,? at 278.15 ? (T/K) ? 393.15 at p = 0.35 MPa for aqueous solutions of tetrahydrofuran at m from (0.016 to 2.5) mol · kg^?1, dimethyl sulfoxide at m from (0.02 to 3.0) mol · kg^?1, 1,4-dioxane at m from (0.015 to 2.0) mol · kg^?1, and 1,2-dimethoxyethane at m from (0.01 to 2.0) mol · kg^?1. Values of V_? were determined from densities measured with a vibrating-tube densimeter, and values of C_p,? were determined with a twin fixed-cell, differential, temperature-scanning calorimeter. Empirical functions of m and T for each compound were fitted to our V_? and C_p,? results.     

Isopiestic determination of the osmotic and activity coefficients of Rb 2SO4 (aq) and Cs 2SO 4(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 Rb ₂SO ₄(aq) from molalitym =  (0.16886 to 1.5679 )mol · kg ^− 1atT =  298.15 K and from m =  (0.32902 to 1.2282 )mol · kg ^− 1at T =  323.15 K, and for Cs ₂SO₄ (aq) from m =  (0.11213 to 3.10815 )mol · kg ^− 1at T =  298.15 K and fromm =  (0.11872 to 3.5095 )mol · kg ^− 1atT =  323.15 K, with NaCl(aq) as the reference standard. Published thermodynamic information for these systems were reviewed and the isopiestic equilibrium molalities and dilution enthalpies were critically assessed and recalculated in a consistent manner. Values of the four parameters of an extended version of Pitzer`s model for osmotic and activity coefficients with an ionic-strength dependent third virial coefficient were evaluated for both systems at both temperatures, as were those of the usual three-parameter Pitzer model. Similarly, parameters of Pitzer`s model for the relative apparent molar enthalpies of dilution were evaluated at T =  298.15 K for both Rb ₂SO ₄(aq) and Cs ₂SO ₄(aq) for the more restricted range of m⩽ 0.101 mol · kg ^− 1. Values of the thermodynamic solubility product K_s(Rb₂ SO ₄, cr, 298.15 K )  =  (0.1392  ±  0.0154) and the CODATA compatible standard molar Gibbs free energy of formationΔ_fG_m^o (Rb ₂SO ₄, cr, 298.15 K )  =  − (1316.91  ±  0.59)kJ · mol ^− 1, standard molar enthalpy of formationΔ_fH_m^o (Rb ₂SO ₄, cr, 298.15 K )  =  − (1435.07  ±  0.60)kJ · mol ^− 1, and standard molar entropy S _m^o(Rb₂ SO ₄, cr, 298.15 K )  =  (199.60  ±  2.88)J · K ^− 1· mol ^− 1were derived. A sample of one of the lots of Rb ₂SO ₄(s) used for part of our isopiestic measurements was analyzed by ion chromatography, and was found to be contaminated with potassium and cesium in amounts that significantly exceeded the claims of the supplier. In contrast, analysis by ion chromatography of a lot of Cs ₂SO ₄(s) used for some of our experiments showed it was highly pure.     

(Solid + liquid) isothermal evaporation phase equilibria in the aqueous ternary system (Li2SO4 + MgSO4 + H2O) at T = 308.15 K

The solubility and the density in the aqueous ternary system (Li₂SO₄ + MgSO₄ + H₂O) at T = 308.15 K were determined by the isothermal evaporation. Our experimental results permitted the construction of the phase diagram and the plot of density against composition. It was found that there is one eutectic point for (Li₂SO₄ · H₂O + MgSO₄ · 7H₂O), two univariant curves, and two crystallization regions corresponding to lithium sulphate monohydrate (Li₂SO₄ · H₂O) and epsomite (MgSO₄ · 7H₂O). The system belongs to a simple co-saturated type, and neither double salts nor solid solution was found. Based on the Pitzer ion-interaction model and its extended HW models of aqueous electrolyte solution, the solubility of the ternary system at T = 308.15 K has been calculated. The predicted solubility agrees well with the experimental values.     

The low-temperature heat capacity and standard entropy of synthetic huttonite ThSiO4

The low-temperature heat capacity of synthetic huttonite ThSiO₄ has been measured from T = (2 to 300) K. The sample was synthesised successfully from SiO₂ and ThO₂ by solid-state reaction at T = 1873 K at atmospheric pressure. From the calorimetric results, the value for the standard entropy $S_{\text{m}}^{°}$ (ThSiO₄, huttonite, 298.15 K) = (104.3 ± 2.0) J · K^?1 · mol^?1 has been obtained. This value indicates that the entropy of reaction from SiO₂ and ThO₂ is negative, giving a positive entropy term (?T · Δ_rS) of the Gibbs free energy of reaction. The implications of this finding are discussed extensively.