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,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.     

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 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.     

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.     

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.     

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.     

Low-temperature thermal properties of 2,2-dimethyl-1,3-propanediol and its deuterated analogues

Heat capacities of 2,2-dimethyl-1,3-propanediol(CH₃)₂C(CH₂OH)₂ were measured in the temperature range between T =  13 K and T =  350 K using an adiabatic calorimeter. The compound underwent a first-order phase transition at T =  (314.5  ±  0.1) K. The enthalpy and the entropy of transition were (12.52  ±  0.02)kJ · mol ^− 1and (39.81  ±  0.08)J · K ^− 1· mol ^− 1, respectively. Measurement of the fusion peak by d.s.c. showed that the purity of the sample was 0.9999 mass fraction and the entropy of fusion was 9.9 J · K ^− 1· mol ^− 1. Another first-order phase transition was observed at T =  (60.4  ±  0.1) K with the associated entropy change of (2.93  ±  0.05)J · K ^− 1· mol ^− 1. Heat capacities of two deuterated samples,(CH₃)₂C(CH₂OD)₂ and(CD₃)₂C(CD₂OD)₂ , were also measured and the results were compared with those on the natural compound. Possible mechanisms of the transition have been discussed from the isotope effects on the thermodynamic quantities associated with the transition. Standard thermodynamic functions of the compounds are tabulated.     

Crystal structures and magnetic properties of complexes of M(NO3)2; M = MnII,CoII, NiII,and CuII,with pyridine ligands carrying an aminoxyl radical

Four complexes of M(NO₃)₂(4NOPy-OMe)₂, (4NOPy-OMe = 4-(N-tert-butyloxylamino)-2-(methoxymethylenyl)pyridine, and M = Mn^II, 1; Co^II, 2; Ni^II, 3; Cu^II, 4), were prepared and fully characterized. X-ray single crystal analysis reveals that four complexes are isostructural. The molecular structures are distorted octahedral in which the methoxy oxygen atoms coordinate to the metal ion by trans-configuration while the pyridyl nitrogen atoms and the nitrate oxygen atoms coordinate by cis-configuration. The magnetic properties of all complexes were investigated by SQUID magneto/susceptometry. Temperature dependence of the molar magnetic susceptibilities in the temperature range of 2–300 K indicated that the magnetic coupling between aminoxyl radicals and metal ion was antiferromagnetic in the complex 1 and were ferromagnetic in the complexes 2–4. The quantitative analysis based on the spin Hamiltonian, H = −2J(S₁S_M + S_MS₂) yielded the best fit as J/k_B = −13.4 ± 0.1 K, g = 1.94 ± 0.002, and θ = −0.78 ± 0.02 K for the complex 1, J/k_B = 48.7 ± 2.1 K, g = 2.07 ± 0.02, and θ = −2.83 ± 0.41 K for the complex 3 (the data in the temperature range 300–50 K were used), and J/k_B = 57.0 ± 1.2 K, g = 2.002 ± 0.004, and θ = −9.8 ± 0.1 K for the complex 4.     

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.     

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.     

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.     

Determination of Henry’s constant using a photoacoustic sensor

We present a simple method for measuring Henry’s constant k_Hof ethanol using photoacoustic spectroscopy. At T =  298.1 K the measured value fork_H is (0.877  ±  0.039)kPa · kg · mol ^− 1. Our data show that Henry’s law is valid at ethanol molalities between 0.1mol · kg ^− 1 and 1.4 mol · kg ^− 1. The temperature dependence of Henry’s constant was carefully examined by measuring the ethanol vapour pressure of six different aqueous solutions between T =  273.1 K and T =  298.1 K. By analysing the gas phase concentration and applying Henry’s law, an ethanol molality of 0.864 mol · kg ^− 1in the liquid phase can be measured with an error of  ± 0.038mol · kg ^− 1. The detection limit of the photoacoustic sensor is a gaseous ethanol pressure of 10 ^− 3kPa. Ethanol molality changes as low as 1.10 ^− 3mol · kg ^− 1can be measured.     

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.     

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.     

Effective scrap iron particles (SIP) pre-treatment for complete mineralization of benzidine based azo dye effluent

This study proposed that hybrid scrap cast iron particles (SIP)-aerobic biodegradation technology could enhance the biodegradability of toxic wastewater. SIP cleaved the azo linkages of Direct Green1 dye to form benzidine, 4-aminophenol, aniline and 1,2,7-triamino-8-hydroxynapthalene-3,6-disulfonic acid. SIP-mediated dye reduction was effective at wide pH range; however, kinetic analysis revealed fastest pseudo-first order dye reduction rate at acidic pH 3 (k_d = 0.549 min⁻¹) followed by pH 9 (k_d = 0.383 min⁻¹) and pH 7 (k_d = 0.318 min⁻¹). The daughter aromatic amines produced were partially adsorbed onto the SIP surface and maximally at neutral pH. The adsorption process followed pseudo-second order adsorption kinetics and Langmuir isotherm. Benzidine was adsorbed more than 4-aminophenol and aniline. BOD₅ of the SIP-treated effluent increased from 0.93 to 12 mg/L showing improved biodegradability. The daughter amines were rapidly mineralized in the aerobic bioreactor within 6 h. Cost-effective SIP pre-treatment could accelerate mineralization and detoxification of recalcitrant wastewater.     

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.     

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.