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 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.     

Thermochemistry of the biochemical reaction: { pyrophosphate(aq) + H2O(l) = 2 phosphate(aq)}

Calorimetric enthalpies of reaction have been measured for the overall biochemical reaction{pyrophosphate(aq)  +  H₂O(l)  =  2phosphate (aq)} . The reaction was catalyzed by alkaline phosphatase and, to simplify the thermochemistry, was carried out in the absence of Mg ^2 + (aq). Measurements were performed with phosphate buffer ( pH  =  7.19 and 7.94), PIPES buffer ( pH  =  7.13), and HEPES buffer ( pH  =  7.86). The results of these measurements were analyzed by using an equilibrium model. These calculations lead to the standard molar enthalpy changeΔ_rH_m^o =  − (17.3  ±  0.6)kJ·mol ^− 1 (temperature T =  298.15 K and ionic strengthI =  0) for the reference reaction{HP₂O₇^3 − (aq)  +  H₂O(l)  =  2HPO₄^2 − (aq)  +  H ⁺ (aq)} . Values of the apparent equilibrium constantK^′ for the overall biochemical reaction from the literature were also analyzed by using the equilibrium model in order to obtain what is believed to be a reliable value for the equilibrium constantK =  4.7 · 10 ^− 4 for the reference reaction. The values ofK and Δ_rH_m^o for the reference reaction have been used together with values from the CODATA tables to calculate standard molar formation properties for the pyrophosphate species.     

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.     

Buffer standards for the physiological pH of N-[2-hydroxy-1,1-bis(hydroxymethyl)ethyl]glycine (TRICINE) from T = (278.15 to 328.15) K

The pH values of two buffer solutions without NaCl and seven buffer solutions with added NaCl, having ionic strengths (I = 0.16 mol · kg⁻¹) similar to those of physiological fluids, have been evaluated at 12 temperatures from T = (278.15 to 328.15) K by way of the extended form of the Debye–Hückel equation of the Bates–Guggenheim convention. The residual liquid junction potentials (δE_j) between the buffer solutions of TRICINE and saturated KCl solution of the calomel electrode at T = (298.15 and 310.15) K have been estimated by measurement with a flowing junction cell. For the buffer solutions with the molality of TRICINE(m₁) = 0.06 mol · kg⁻¹, NaTRICINE(m₂) = 0.02 mol · kg⁻¹, and NaCl(m₃) = 0.14 mol · kg⁻¹, the pH values at T = 310.15 K obtained from the extended Debye–Hückel equation and the inclusion of the liquid junction correction are 7.342 and 7.342, respectively. These are in excellent agreement. The zwitterionic buffer TRICINE is recommended as a secondary pH standard in the region for clinical application.     

Calorimetric investigation of mixing enthalpy of liquid (Co + Cu + Zr) alloys at T = 1873 K

The enthalpies of mixing of liquid (Co + Cu + Zr) alloys have been determined using the high-temperature isoperibolic calorimeter. The measurements have been performed along three sections (x_Co/x_Cu = 3/1, 1/1, 1/3) with x_Zr = 0 to 0.55 at T = 1873 K. Over the investigated composition range, the partial mixing enthalpies of zirconium are negative. The limiting partial enthalpies of mixing of undercooled liquid zirconium in liquid (Co + Cu) alloys are (−138 ± 18) kJ · mol⁻¹ (the section x_Co/x_Cu = 3/1), (−155 ± 10) kJ · mol⁻¹ (the section x_Co/x_Cu = 1/1), and (−130 ± 22) kJ · mol⁻¹ (the section x_Co/x_Cu = 1/3). The integral mixing enthalpies are sign-changing. The isenthalpic curves have been plotted on the Gibbs triangle. The main features of the composition dependence of the integral mixing enthalpy of liquid ternary alloys are defined by the pair (Co + Zr) and (Cu + Zr) interactions.     

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.     

Speeds of sound in {(1 − x)CH4 + xN2} with x = (0.10001, 0.19999, and 0.5422) at temperatures between 170 K and 400 K and pressures up to 30 MPa

The speed of sound in {(1 − x)CH₄ + xN₂} has been measured with a spherical acoustic resonator. Two mixtures with x = (0.10001 and 0.19999) were studied along isotherms at temperatures between 220 K and 400 K with pressures up to 20 MPa; a few additional measurements at p = (25 and 30) MPa are also reported. A third mixture with x = 0.5422 was studied along pseudo-isochores at amount-of-substance densities between 0.2 mol · dm⁻³ and 5 mol · dm⁻³. Corrections for molecular vibrational relaxation are discussed in detail and relaxation times are reported. The overall uncertainty of the measured speeds of sound is estimated to be not worse than ±0.02%, except for those measurements in the mixture with x = 0.5422 that lie along the pseduo-isochore at the highest amount-of-substance density. The results have been compared with the predictions of several equations of state used for natural gas systems.     

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.     

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.     

Equilibrium solubility of carbon dioxide in the amine solvent system of (triethanolamine + piperazine + water)

In this study, a new set of data for the equilibrium solubility of carbon dioxide in the amine solvent system that consists of triethanolamine (TEA), piperazine (PZ), and water is presented. Equilibrium solubility values were obtained at T = (313.2, 333.2, and 353.2) K and pressures up to 153 kPa using the vapour-recirculation equilibrium cell. The TEA concentrations in the considered ternary (solvent) mixture were (2 and 3) kmol · m^?3 and those of PZ’s were (0.5, 1.0, and 1.5) kmol · m^?3. The solubility data (CO₂ loading in the amine solution) obtained were correlated as a function of CO₂ partial pressure, system temperature, and amine composition via the modified Kent–Eisenberg model. Results showed that the model applied is generally satisfactory in representing the CO₂ absorption into mixed aqueous solutions of TEA and PZ.     

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.     

Thermodynamic properties of (NaCl + KCl + LiCl + H2O) at T = 298.15 K: Water activities,osmotic and activity coefficients

The water activities of aqueous electrolyte mixture (NaCl + KCl + LiCl + H₂O) were experimentally determined at T = 298.15 K by the hygrometric method at total ionic-strength from 0.4 mol · kg⁻¹ to 6 mol · kg⁻¹ for different ionic-strength fractions y of NaCl with y = 1/3, 1/2, and 2/3. The data allow the deduction of new osmotic coefficients. The results obtained were correlated by Pitzer’s model and Dinane’s mixing rules ECA I and ECA II for calculations of the water activity in mixed aqueous electrolytes. A new Dinane–Pitzer model is proposed for the calculation of osmotic coefficients in quaternary aqueous mixtures using the newly ternary and quaternary ionic mixing parameters of this studied system. The solute activity coefficients of component in the mixture are also determined for different ionic-strength fractions y of NaCl.     

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.     

Thermodynamics of ion pairs in mixed solvents. I. The standard association constant of the ion pair [ MgSO4]oin { 0.03226 CO(NH2)2 + 0.96774 H2O}

The standard potential of the (Ag, AgCl) electrode E^o, the standard second ionization constant of sulfuric acid K₂, and the standard association constant of the ion pair [MgSO₄]^o, K in {0.03226CO(NH₂)₂ +  0.96774 H₂O } at five temperatures from 278.15 K to 318.15 K were determined from precise e.m.f. measurements of different cells without liquid junction. The dependence of p K on temperature T is expressed by the empirical equation pK =  6.617  −  777.9 · (K / T)  −  0.02001 · (T / K). The other thermodynamic functions of the association process were also calculated and show that the driving force for the process is the entropy of association.     

Measuring and validation for isothermal solubility data of solid 2-(3,4-Dimethoxyphenyl)-5,6,7,8-tetramethoxychromen-4-one (nobiletin) in supercritical carbon dioxide

Isothermal solubility of 2-(3,4-Dimethoxyphenyl)-5,6,7,8-tetramethoxychromen-4-one (nobiletin) in supercritical carbon dioxide at temperatures of (313, 323 and 333) K and pressures from (18 to 31) MPa was measured using an analytic-recirculation methodology, with direct determination of the molar composition of the carbon dioxide-rich phase by using high performance liquid chromatography. Results indicated that the range of the measured solubility of nobiletin was from 107 · 10⁻⁶ mol · mol⁻¹ at T = 333 K and 18.35 MPa to 182 · 10⁻⁶ mol · mol⁻¹ at T = 333 K and 31.40 MPa, with a temperature crossover around 18 MPa. The validation of the experimental solubility data was carried out by using three approaches, namely, estimation of combined expanded uncertainty for each solubility data point from experimental parameters values (⩽77 · 10⁻⁶ mol · mol⁻¹); thermodynamic consistency, verified utilizing a test adapted from tools based on Gibbs–Duhem equation and solubility modelling results; and, self-consistency, proved by correlating the solubility data with a semi-empirical model as a function of temperature, pressure and pure CO₂ density.     

Isopiestic study of (calcium chloride + water) and (calcium chloride + magnesium chloride + water) atT = 313.15 K

The osmotic coefficients of aqueous calcium chloride solutions were experimentally determined atT =  313.15 K by the isopiestic method. Magnesium chloride served as the isopiestic standard for the calculation of osmotic coefficients. The molality range covered in this study correspond to about 0.1mol · kg ^− 1to 3.0mol · kg ^− 1. In addition, the osmotic coefficients of aqueous mixtures of calcium chloride and magnesium chloride were determined over the range of ionic strength levels of about 0.1mol · kg ^− 1to 9mol · kg ^− 1and at various mole fractions. The results obtained were correlated by the Pitzer equation.     

Excess molar enthalpies for (benzonitrile + an aromatic hydrocarbon) atT = 298.15 K

The excess molar enthalpies of (benzonitrile  +  benzene, or methylbenzene, or 1,2-dimethylbenzene, or 1,3-dimethylbenzene, or 1,4-dimethylbenzene, or 1,3,5-trimethylbenzene, or ethylbenzene) have been determined at T =  298.15 K. The excess molar enthalpies range from  − 10 J · mol ^− 1for methylbenzene to 130 J · mol ^− 1for 1,3,5-trimethylbenzene. The Redlich–Kister equation, the NRTL, and UNIQUAC models were used to correlate the data. The results indicate a relatively strong association between benzonitrile and each of the aromatic compounds, decreasing with increasing methyl substitution on the benzene moiety.