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.     

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.     

Thermodynamic study on complex of neodymium with glycine

Neodymium complex with glycine, Nd(Gly)₂Cl₃·3H₂O, was synthesized and characterized by IR spectra. The thermal stability of the complex was tested through TG and DTG and a possible mechanism of thermal decomposition was proposed. The heat capacities of the complex were measured by using an automated adiabatic calorimeter over the temperature range from T = (80 to 380) K, the thermodynamic functions, [H_T − H_298.15] and [S_T − S_298.15], were calculated based on the heat capacity measurements. Two (solid + solid) phase transitions in the ranges of T = (170 to 247) K were observed with the peak temperatures of 184.896 K and 231.217, respectively. The standard molar enthalpy of formation of [Nd(Gly)₂Cl₃·3H₂O] was determined to be (−3081.3 ± 1.1) kJ · mol⁻¹ in terms of an isoperibol solution-reaction calorimeter.     

Thermochemistry of some barium compounds

The molar enthalpies of reaction of metallic barium with 0.047 mol·dm⁻³ HClO₄ as well as the molar enthalpies of dissolution of BaCl₂ in 1.01 mol·dm⁻³ HCl and in water have been measured at T=298.15 K in a sealed swinging calorimeter with an isothermal jacket. From these results the standard molar enthalpy of formation of the barium ion in an aqueous solution at infinite dilution, as well as the enthalpies of formation of barium chloride and barium perchlorate, are calculated to be: Δ_fH⁰_m(Ba²⁺,aq)=−(535.83±1.25) kJ · mol⁻¹; Δ_fH⁰_m(BaCl₂,cr)=−(855.66±1.28) kJ · mol⁻¹; and Δ_fH⁰_m(BaClO₄,cr)=−(796.26±1.35) kJ · mol⁻¹. The results obtained are discussed and compared with previous experimental values.     

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.     

Determination of the standard enthalpy of formation of paratungstate A ion

Enthalpy changes for the reaction of HCl(aq) withNa₂WO₄ (aq) were measured at T =  298.15 K in a HT-1000 calorimeter. The standard enthalpy of reaction for the formation ofW₇O₂₄^6 −  (aq) was calculated on the basis of the experimental results, Δ_rH_m^o(298.15K )  =  − (320.7  ±  1.0)kJ · mol ^− 1. Combining this with the values from the literature led to the standard enthalpy of formation of W₇O₂₄^6 − (aq),Δ_fH_m^o (298.15 K)  =  − 6689.8 kJ · mol ^− 1.     

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.     

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.     

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 standard molar enthalpy of sublimation ofη5-bis-pentamethylcyclopentadienyl iron measured with an electrically calibrated vacuum-drop sublimation microcalorimetric apparatus

A heat-flow Calvet microcalorimeter was adapted for the measurement of sublimation enthalpies by the vacuum-drop method, with samples of masses in the range 1 mg to 5 mg. The electrically calibrated apparatus was tested by determining the enthalpies of sublimation of benzoic acid and ferrocene, at T =  298.15 K. The obtained results, Δ_cr^gH_m^o(C₇H₆O₂)  =  (88.3  ±  0.5)kJ · mol ^− 1and Δ_cr^gH_m^o(C₁₀H₁₀Fe) =  (73.3  ±  0.1)kJ · mol ^− 1, are in excellent agreement with the corresponding values recommended in the literature. Subsequent application of the apparatus to the determination of the enthalpy of sublimation of η⁵-bis-pentamethylcyclopentadyenyl iron, at T =  298.15 K, led to Δ_cr^gH_m^o(C₂₀H₃₀Fe)  =  (96.8  ±  0.6)kJ · mol ^− 1.     

The thermodynamics of formation,molar heat capacity,and thermodynamic functions ofZrTiO4(cr)

As part of an ongoing study of titanate-based ceramic materials for the disposal of surplus weapons-grade plutonium, we report thermodynamic properties of a sample ofzirconium titanate (ZrTiO₄) quenched from a high-temperature synthesis. The standard enthalpy of formationΔ_fH_m^o was obtained by using high-temperature oxide-melt solution calorimetry. The molar heat capacity C_{p, m}was measured fromT =  13 K to T =  400 K in an adiabatic calorimeter and extrapolated toT =  1800 K by using an equation fitted to the low-temperature results. The results atT =  298.15 K areΔ_fH_m^o =  − (2024.1  ±  4.5)kJ · mol ^− 1,Δ₀^TS_m^o =  (116.71  ±  0.31 )J · K ^− 1· mol ^− 1, andΔ_fG_m^o =  − (1915.8  ±  4.5 )kJ · mol ^− 1; the molar entropy includes a contribution of 2 R ln2 to account for the random mixing of Zr^4 + and Ti^4 + on a four-fold crystallographic site. Values for the standard molar Gibbs energies and enthalpies of formation of ZrTiO_4,Δ_fG_m^oandΔ_fH_m^o , and for the free energies and enthalpies for the reaction to form ZrTiO₄(cr) from ZrO₂(cr) and TiO₂(cr), are tabulated over the temperature interval, 0 ⩽(T / K)⩽ 1800. From these results, we conclude that ZrTiO₄is not stable with respect to (ZrO₂ +  TiO₂) at T =  298.15 K, but becomes so at T =  (1250  ±  150) K.     

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.     

Micro-combustion calorimetry employing a Calvet heat flux calorimeter

Two micro-combustion bombs developed from a high pressure stainless steel vessel have been adapted to a Setaram C80 Calvet calorimeter. The constant of each micro-bomb was determined by combustions with benzoic acid NIST 39j, giving for the micro-combustion bomb in the measurement sensor k_m=(1.01112±0.00054) and for the micro-combustion bomb in the reference sensor k_r=(1.00646±0.00059) which means an uncertainty of less than 0.06 per cent for calibration. The experimental methodology to get results of combustion energy of organic compounds with a precision also better than 0.06 per cent is described by applying this micro-combustion device to the measurement of the enthalpy of combustion of the succinic acid, giving Δ_cH^∘_m(cr, T=298.15 K)=−(1492.89 ± 0.77) kJ · mol⁻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 capacities and derived thermodynamic properties of lithium,sodium, and potassium disilicates from T = (5 to 350) K in both vitreous and crystalline states

Cryogenic heat capacities determined by equilibrium adiabatic calorimetry from T = (6 to 350) K on Li, Na, and K disilicates in both crystalline and vitreous phases are adjusted to end member composition and the vitreous/crystal difference ascertained. The thermophysical properties of these and related phases are estimated, compared, and updated. The values at T = 298.15 K of {S^∘(T) − S^∘(0)}/R for stoichiometric compositions of alkali disilicate (M₂O · 2SiO₂): vitreous, crystal: Li, 16.30, 14.65; Na, 20.67, 19.47; and K, 23.26, 23.00. Entropy differences confirm greater disorder in the vitreous compounds compared with the crystalline compounds. The entropy data also show that disorder increases with decreasing atomic mass of the alkali ion.     

Synthesis,structure and thermochemical study of a cobalt energetic coordination compound incorporating 3,5-diamino-1,2,4-triazole and pyridine-2,6-dicarboxylic acid

An energetic coordination compound [Co₂(C₂H₅N₅)₂(C₇H₃NO₄)₂(H₂O)₂]·2H₂O (Hdatrz(C₂H₅N₅) = 3,5-diamino-1,2,4-triazole, H₂pda(C₇H₅NO₄) = pyridine-2,6-dicarboxylic acid) has been synthesized and characterized by elemental analysis, chemical analysis, IR spectroscopy, single-crystal X-ray diffraction and thermal analysis. X-ray diffraction analysis confirmed that the compound possessed a di-nuclear unit and featured a 3D super-molecular structure. Furthermore, a reasonable thermochemical cycle was designed based on the preparation reaction of the compound and the standard molar enthalpy of dissolution of reactants and products was measured by the RD496-2000 calorimeter. Finally, the standard molar enthalpy of formation of the compound was determined to be −(2475.0 ± 3.1) kJ · mol⁻¹ in accordance with Hess’s law. In addition, the specific heat capacity of the compound at T = 298.15 K was determined to be (1.13 ± 0.02) J · K⁻¹ · g⁻¹ by RD496-2000 calorimeter.     

Apparent molar volumes and apparent molar heat capacities of aqueous KI,HIO3, NaIO3, and KIO3 at temperatures from 278.15 K to 393.15 K and at the pressure 0.35 MPa

We determined apparent molar volumes V_? at 298.15 ? (T/K) ? 368.15 and apparent molar heat capacities C_p,? at 298.15 ? (T/K) ? 393.15 for aqueous solutions of HIO₃ at molalities m from (0.015 to 1.0) mol · kg^?1, and of aqueous KIO₃ at molalities m from (0.01 to 0.2) mol · kg^?1 at p = 0.35 MPa. We also determined V_? at the same p and at 298.15 ? (T/K) ? 368.15 for aqueous solutions of KI at m from (0.015 to 7.5) mol · kg^?1. We determined C_p,? at the same p and at 298.15 ? (T/K) ? 393.15 for aqueous solutions of KI at m from (0.015 to 5.5) mol · kg^?1, and for aqueous solutions of NaIO₃ at m from (0.02 to 0.15) 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 were fitted to our results for each compound. Values of K_a, Δ_rH_m, and Δ_rC_p,m for the proton ionization reaction of aqueous HIO₃ are calculated and discussed.     

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.     

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.