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.     

The heat capacities and thermodynamic properties of NiAl2O4 and CoAl2O4 measured by adiabatic calorimetry from T = (4 to 400) K

The low-temperature heat capacity of NiAl₂O₄ and CoAl₂O₄ was measured between T = (4 and 400) K and thermodynamic functions were derived from the results. The measured heat-capacity curves show sharp anomalies peaking at around T = 7.5 K for NiAl₂O₄ and at T = 9 K for CoAl₂O₄. The exact cause of these anomalies is unknown. From our results, we suggest a standard entropy for NiAl₂O₄ at T = 298.15 K of (97.1 ± 0.2) J · mol^?1 · K^?1 and for CoAl₂O₄ of (100.3 ± 0.2) J · mol^?1 · K^?1.     

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.     

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.     

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.     

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.     

Low-temperature heat capacity and standard molar enthalpy of formation of 9-fluorenemethanol (C14H12O)

Low-temperature heat capacities of the 9-fluorenemethanol (C₁₄H₁₂O) have been precisely measured with a small sample automatic adiabatic calorimeter over the temperature range between T=78 K and T=390 K. The solid–liquid phase transition of the compound has been observed to be T_fus=(376.567±0.012) K from the heat-capacity measurements. The molar enthalpy and entropy of the melting of the substance were determined to be Δ_fusH_m=(26.273±0.013) kJ · mol⁻¹ and Δ_fusS_m=(69.770±0.035) J · K⁻¹ · mol⁻¹. The experimental values of molar heat capacities in solid and liquid regions have been fitted to two polynomial equations by the least squares method. The constant-volume energy and standard molar enthalpy of combustion of the compound have been determined, Δ_cU(C₁₄H₁₂O, s)=−(7125.56 ± 4.62) kJ · mol⁻¹ and Δ_cH_m^∘(C₁₄H₁₂O, s)=−(7131.76 ± 4.62) kJ · mol⁻¹, by means of a homemade precision oxygen-bomb combustion calorimeter at T=(298.15±0.001) K. The standard molar enthalpy of formation of the compound has been derived, Δ_fH_m^∘(C₁₄H₁₂O,s)=−(92.36 ± 0.97) kJ · mol⁻¹, from the standard molar enthalpy of combustion of the compound in combination with other auxiliary thermodynamic quantities through a Hess thermochemical cycle.     

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).     

Determination of thermodynamic properties of Na2S using solid-state EMF measurements

To obtain reliable thermodynamic data for Na₂S(s), solid-state EMF measurements of the cell Pd(s)|O₂(g)|Na₂S(s), Na₂SO₄(s)|YSZ| Fe(s), FeO(s)|O₂(g)_ref| Pd(s) were carried out in the temperature range 870 < T/K < 1000 with yttria stabilized zirconia as the solid electrolyte. The measured EMF values were fitted according to the equation E_fit/V (±0.00047) = 0.63650 − 0.00584732(T/K) + 0.00073190(T/K) ln (T/K). From the experimental results and the available literature data on Na₂SO₄(s), the equilibrium constant of formation for Na₂S(s) was determined to be lg K_f(Na₂S(s)) (±0.05) = 216.28 − 4750(T/K)⁻¹ − 28.28878 ln (T/K). Gibbs energy of formation for Na₂S(s) was obtained as Δ_fG^∘(Na₂S(s))/(kJ · mol⁻¹) (±1.0) = 90.9 − 4.1407(T/K) + 0.5415849(T/K) ln (T/K). By applying third law analysis of the experimental data, the standard enthalpy of formation of Na₂S(s) was evaluated to be Δ_fH^∘(Na₂S(s), 298.15 K)/(kJ · mol⁻¹) (±1.0) = −369.0. Using the literature data for C_p and the calculated Δ_fH^∘, the standard entropy was evaluated to S^∘(Na₂S(s), 298.15 K)/(J · mol⁻¹ · K⁻¹) (±2.0) = 97.0.     

High-temperature calorimetry of zirconia: Heat capacity and thermodynamics of the monoclinic–tetragonal phase transition

The high-temperature heat capacity of zirconia was directly measured by differential scanning calorimetry between T = (1050 and 1700) K and derived from the heat content measured by transposed temperature drop calorimetry between T = (970 and 1770) K, including the monoclinic–tetragonal (m–t) phase transition region. The enthalpy and entropy of the m–t phase transition are (5.43 ± 0.31) kJ · mol⁻¹ and (3.69 ± 0.21) J · K⁻¹ · mol⁻¹, respectively. Values of thermodynamic functions are provided from room temperature to 2000 K.     

Low temperature heat capacity of bulk and nanophase ZnO and Zn1−xCoxO wurtzite phases

The low temperature heat capacity of the ZnO–CoO solid solution system was measured from 2 to 300 K using the heat capacity option of a Quantum Design Physical Property Measurement System (PPMS). The thermodynamic functions in this temperature range were derived by curve fitting. The standard entropies of bulk ZnO and bulk ZnO–CoO (wurtzite, 18 mol% CoO) at T = 298.15 K were calculated to be (43.1 ± 0.4) J · mol⁻¹ · K⁻¹ and (45.2 ± 0.5) J · mol⁻¹ · K⁻¹, respectively. The surface entropy of ZnO was evaluated to be (0.02 ± 0.01) mJ · K⁻¹ · m⁻², which is essentially zero. No sharp magnetic transitions were observed in the solid solution samples. The nanophase solid solution, 12 mol% CoO, appears to bind H₂O on its surface more strongly than ZnO.     

Molar heat capacity and thermodynamic properties of 1-cyclohexene-1,2-dicarboxylic anhydride [C8H8O3]

The molar heat capacity C_p,m of 1-cyclohexene-1,2-dicarboxylic anhydride was measured in the temperature range from T=(80 to 360) K with a small sample automated adiabatic calorimeter. The melting point T_m, the molar enthalpy Δ_fusH_m and the entropy Δ_fusS_m of fusion for the compound were determined to be (343.46 ± 0.24) K, (11.88 ± 0.02) kJ · mol⁻¹ and (34.60 ± 0.06) J · K⁻¹ · mol⁻¹, respectively. The thermodynamic functions [H_(T)−H_(298.15)] and [S_(T)−S_(298.15)] were derived in the temperature range from T=(80 to 360) K with temperature interval of 5 K. The mass fraction purity of the sample used in the adiabatic calorimetric study was determined to be 0.9928 by using the fractional melting technique. The thermal stability of the compound was investigated by differential scanning calorimeter (DSC) and thermogravimetric (TG) technique, and the process of the mass-loss of the sample was due to the evaporation, instead of its thermal decomposition.     

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.     

Standard Gibbs energy of formation of platinic acid H2Pt(OH) 6in the crystalline state

Heat capacity of platinic acid, hydrogen hexahydroxyplatinate(IV)H₂Pt(OH)₆ , was measured from T =  7 K toT =  310 K by means of adiabatic calorimetry. The standard entropy and the standard Gibbs energy of formation of platinic acid in the crystalline state were determined to be 176.5  ±  3.6 J · K ^− 1· mol ^− 1and  − 988.8  ±  3.8 kJ · mol ^− 1, respectively.     

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.     

Heat capacity and thermodynamic properties of 2,4-dichlorobenzaldehyde (C7H4Cl2O)

Heat capacities of 2,4-dichlorobenzaldehyde have been measured with a high-precision automatic adiabatic calorimeter over the temperature range from (79 to 371) K. The melting temperature, molar enthalpy, and entropy of fusion were determined by the heat capacity measurements to be (347.24 ± 0.13) K, (20468 ± 19) J · mol⁻¹, and (58.94 ± 0.04) J · K⁻¹ · mol⁻¹, respectively. The melting temperatures for the sample and the absolutely pure compound have been obtained from fractional melting experiments to be (347.230 and 347.619) K, respectively, and the chemical purity of the sample was calculated to be 0.9921 mol fraction according to the Van't Hoff equation. Moreover, the solid-to-liquid phase transition of the substance was further investigated by using DSC technique. The results obtained from the heat capacity measurements were in agreement with those from the DSC analysis.     

The thermodynamic properties of DyBr3(s) and DyI3(s) from T=5 K to their melting temperatures

Low-temperature calorimetric measurements have been performed on DyBr₃(s) in the temperature range (5.5 to 420 K ) and on DyI₃(s) from T=4 K to T=420 K. The data reveal enhanced heat capacities below T=10 K, consisting of a magnetic and an electronic contribution. From the experimental data on DyBr₃(s) a C⁰_p,m (298.15 K) of (102.2±0.2) J·K⁻¹·mol⁻¹ and a value for {S⁰_m (298.15 K) − S⁰_m (5.5 K)} of (205.5±0.5) J·K⁻¹·mol⁻¹, have been obtained. For DyI₃(s), {S⁰_m (298.15 K) − S⁰_m (4 K)} and C⁰_p,m (298.15 K) have been determined as (226.9±0.5) J·K⁻¹·mol⁻¹ and (103.4±0.2) J·K⁻¹·mol⁻¹, respectively. The values for {S⁰_m (5.5 K) − S⁰_m (0)} for DyBr₃(s) and {S⁰_m (4 K) − S⁰_m (0)} for DyI₃(s) have been calculated, giving S⁰_m (298.15 K)=(212.3±0.9) J·K⁻¹·mol⁻¹ in case of DyBr₃(s) and S⁰_m (298.15 K) =(233.1±0.7) J·K⁻¹·mol⁻¹ for DyI₃(s). The high-temperature enthalpy increment has been measured for DyBr₃(s) in the temperature range (525 to 799 K) and for DyI₃(s) in the temperature range (525 to 627 K). From the results obtained and enthalpies of formation from the literature, thermodynamic functions for DyBr₃(s) and DyI₃(s) have been calculated from T→0 to their melting temperatures at 1151.0 K and 1251.5 K, respectively.