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.     

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.     

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.     

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 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.     

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.     

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.     

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.     

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.     

The molar enthalpies of solution and vapour pressures of saturated aqueous solutions of some cesium salts

Vapour pressures of water over saturated solutions of cesium chloride, cesium bromide, cesium nitrate, cesium sulfate, cesium formate, and cesium oxalate were determined as a function of temperature. These vapour pressures were used to evaluate the water activities, osmotic coefficients and molar enthalpies of vapourization. Molar enthalpies of solution of cesium chloride, Δ_solH_m(T = 295.73 K; m = 0.0622 mol · kg⁻¹) = (17.83 ± 0.50) kJ · mol⁻¹; cesium bromide, Δ_solH_m(T = 293.99 K; m = 0.0238 mol · kg⁻¹) = (26.91 ± 0.59) kJ · mol⁻¹; cesium nitrate, Δ_solH_m(T = 294.68 K; m = 0.0258 mol · kg⁻¹) = (37.1 ± 2.3) kJ · mol⁻¹; cesium sulfate, Δ_solH_m(T = 296.43 K; m = 0.0284 mol · kg⁻¹) = (16.94 ± 0.43) kJ · mol⁻¹; cesium formate, Δ_solH_m(T = 295.64 K; m = 0.0283 mol · kg⁻¹) = (11.10 ± 0.26) kJ · mol⁻¹ and Δ_solH_m(T = 292.64 K; m = 0.0577 mol · kg⁻¹) = (11.56 ± 0.56) kJ · mol⁻¹; and cesium oxalate, Δ_solH_m(T = 291.34 K; m = 0.0143 mol · kg⁻¹) = (22.07 ± 0.16) kJ · mol⁻¹ were determined calorimetrically. The purity of the chemicals was generally greater than 0.99 mass fraction, except for HCOOCs and (COOCs)₂ where purities were approximately 0.95 and 0.97 mass fraction, respectively. The uncertainties are one standard deviations.     

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.     

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.     

Solubilities of l-glutamic acid, 3-nitrobenzoic acid,p-toluic acid,calcium-l-lactate,calcium gluconate,magnesium-dl-aspartate,and magnesium-l-lactate in water

Solubilities of l -glutamic acid, 3-nitrobenzoic acid, p -toluic acid, calcium-l -lactate, calcium gluconate, magnesium- dl -aspartate, and magnesium- l -lactate in water were determined in the temperature range 278 K to 343 K. The apparent molar enthalpies of solution at T =  298.15 K as derived from these solubilities areΔ_solH_m (l -glutamic acid,m_sat =  0.0565 mol · kg ^− 1)  =  30.2 kJ · mol ^− 1,Δ_solH_m (3-nitrobenzoic acid, m =  0.0188 mol · kg ^− 1)  =  28.1 kJ · mol ^− 1, Δ_solH_m( p - toluic acid, m =  0.00267 mol · kg ^− 1)  =  23.9 kJ · mol ^− 1,Δ_solH_m (calcium- l -lactate tetrahydrate,m =  0.2902 mol · kg ^− 1)  =  25.8 kJ · mol ^− 1,Δ_solH_m (calcium gluconate, m =  0.0806 mol · kg ^− 1)  =  22.1 kJ · mol ^− 1, Δ_solH_m(magnesium-dl -aspartate tetrahydrate, m =  0.1469 mol · kg ^− 1)  =  11.5 kJ · mol ^− 1, andΔ_solH_m (magnesium- l -lactate trihydrate,m =  0.3462 mol · kg ^− 1)  =  3.81 kJ · mol ^− 1.     

The enthalpy of dilution and thermodynamics of Na2CO3(aq) and NaHCO3(aq) fromT = 298 K toT = 523.15 K and pressure of 40 MPa

Molar enthalpies of dilution Δ_dilH_mofNa₂CO₃(aq) were measured from molality m =  1.45 mol · kg ^− 1to m =  0.008 mol · kg ^− 1at seven temperatures from T =  298 K toT =  523 K at the pressure p =  7 MPa, and at four temperatures fromT =  371 K to T =  523 K at the pressurep =  40 MPa. Molar enthalpies of dilutionΔ_dilH_m of NaHCO₃(aq) were measured fromm =  0.98 mol · kg ^− 1tom =  0.007 mol · kg ^− 1at the same temperatures and pressures. Hydrolysis and ionization equilibria contribute substantially to the measured enthalpies under many of the conditions of this study. Explicit consideration of these reactions, using thermodynamic quantities from previous studies, facilitates a quantitative representation of apparent molar enthalpies, activity coefficients, and osmotic coefficients with the Pitzer ion-interaction treatment over the ranges of temperature, pressure, and molality of the experiments.     

Thermodynamics of the oxidation–reduction reaction {2 glutathionered(aq) + NADPox(aq)=glutathioneox(aq) + NADPred(aq)}

Microcalorimetry, spectrophotometry, and high-performance liquid chromatography (h.p.l.c.) have been used to conduct a thermodynamic investigation of the glutathione reductase catalyzed reaction {2 glutathione_red(aq) + NADP_ox(aq)=glutathione_ox(aq) + NADP_red(aq)}. The reaction involves the breaking of a disulfide bond and is of particular importance because of the role glutathione_red plays in the repair of enzymes. The measured values of the apparent equilibrium constant K^′ for this reaction ranged from 0.5 to 69 and were measured over a range of temperature (288.15 K to 303.15 K), pH (6.58 to 8.68), and ionic strength I_m (0.091 mol · kg⁻¹ to 0.90 mol · kg⁻¹). The results of the equilibrium and calorimetric measurements were analyzed in terms of a chemical equilibrium model that accounts for the multiplicity of ionic states of the reactants and products. These calculations led to values of thermodynamic quantities at T=298.15 K and I_m=0 for a chemical reference reaction that involves specific ionic forms. Thus, for the reaction {2 glutathione_red⁻(aq) + NADP_ox³⁻(aq)=glutathione_ox²⁻(aq) + NADP_red⁴⁻(aq) + H⁺(aq)}, the equilibrium constant K=(6.5±4.4)·10⁻¹¹, the standard molar enthalpy of reaction Δ_rH^o_m=(6.9±3.0) kJ · mol⁻¹, the standard molar Gibbs free energy change Δ_rG^o_m=(58.1±1.7) kJ · mol⁻¹, and the standard molar entropy change Δ_rS^o_m=−(172±12) J · K⁻¹ · mol⁻¹. Under approximately physiological conditions (T=311.15 K, pH=7.0, and I_m=0.25 mol · kg⁻¹ the apparent equilibrium constant K^′≈0.013. The results of the several studies of this reaction from the literature have also been examined and analyzed using the chemical equilibrium model. It was found that much of the literature is in agreement with the results of this study. Use of our results together with a value from the literature for the standard electromotive force E^o for the NADP redox reaction leads to E^o=0.166 V (T=298.15 K and I=0) for the glutathione redox reaction {glutathione_ox²⁻(aq) + 2 H⁺(aq) + 2 e⁻=2 glutathione_red⁻(aq)}. The thermodynamic results obtained in this study also permit the calculation of the standard apparent electromotive force E^′o for the biochemical redox reaction {glutathione_ox(aq) + 2 e⁻=2 glutathione_red(aq)} over a wide range of temperature, pH, and ionic strength. At T=298.15 K, I=0.25 mol · kg⁻¹, and pH=7.0, the calculated value of E^′o is −0.265 V.     

Thermodynamic properties of two zinc borates: 3ZnO·3B2O3·3.5H2O and 6ZnO·5B2O3·3H2O

Two pure zinc borates with microporous structure 3ZnO·3B₂O₃·3.5H₂O and 6ZnO·5B₂O₃·3H₂O have been synthesized and characterized by XRD, FT-IR, TG techniques and chemical analysis. The molar enthalpies of solution of 3ZnO·3B₂O₃·3.5H₂O(s) and 6ZnO·5B₂O₃·3H₂O(s) in 1 mol · dm⁻³ HCl(aq) were measured by microcalorimeter at T = 298.15 K, respectively. The molar enthalpies of solution of ZnO(s) in the mixture solvent of 2.00 cm³ of 1 mol · dm⁻³ HCl(aq) in which 5.30 mg of H₃BO₃ were added were also measured. With the incorporation of the previously determined enthalpy of solution of H₃BO₃(s) in 1 mol · dm⁻³ HCl(aq), together with the use of the standard molar enthalpies of formation for ZnO(s), H₃BO₃(s), and H₂O(l), the standard molar enthalpies of formation of −(6115.3 ± 5.0) kJ · mol⁻¹ for 3ZnO·3B₂O₃·3.5H₂O and −(9606.6 ± 8.5) kJ · mol⁻¹ for 6ZnO·5B₂O₃·3H₂O at T = 298.15 K were obtained on the basis of the appropriate thermochemical cycles.     

The vapour pressures of saturated aqueous solutions of magnesium,calcium, nickel and zinc acetates and molar enthalpies of solution of magnesium,calcium, zinc and lead acetates

Vapour pressures of water over saturated solutions of magnesium, calcium, nickel and zinc acetates were determined as a function of temperature. The vapour pressures served to evaluate the water activities, osmotic coefficients and molar enthalpies of vaporization. Molar enthalpies of solution of magnesium acetate tetrahydrate,Δ_solH_m (T =  294.71K ;m =  0.01 mol · kg ^− 1)  =  − (15.65  ±  0.97)kJ · mol ^− 1; calcium acetate,Δ_solH_m (T =  297.18K ;m =  0.01 mol · kg ^− 1)  =  − (28.15  ±  0.28)kJ · mol ^− 1; zinc acetate dihydrate,Δ_solH_m (T =  297.36K ;m =  0.01 mol · kg ^− 1)  =  − (22.49  ±  0.90)kJ · mol ^− 1and lead acetate trihydrate,Δ_solH_m (T =  297.36K ;m =  0.0086 mol · kg ^− 1)  =  (22.46  ±  0.94)kJ · mol ^− 1, were determined calorimetrically.     

The estimation of the heat capacity of NpO2

The heat capacity C_{p, m}of NpO₂was estimated for temperatures between 300 K and 1400 K. The C_{p, m}was evaluated as a sum of three terms, phonon vibration C_{ph, m}, dilation C_{d, m}, and Schottky specific heat C_{s, m}. The C_{ph, m}and C_d,mwere calculated using the Debye temperature, Grüneisen constant and thermal expansion data obtained by high-temperature X-ray diffractometry. The coefficient of the linear thermal expansion (l.t.e.) for NpO₂was given as a polynomial function up to T =  1573 K. The estimated C_p,mwas compared with that of previous studies. The present result at T =  300 K was 66.87 J · K ^− 1· mol ^− 1, which agreed well with previous results, 66.22 J · K ^− 1· mol ^− 1, measured by using calorimetry. The thermodynamic functions were given as a function of temperature.