Thermodynamics of formation of double salts M2SO4 · M′SO4 · 6H2O and M2SeO4 · M′SeO4 · 6H2O where M denotes Rb,or Cs and M′ denote Co,Ni, or Zn

This paper describes a chemical model that calculates (solid + liquid) equilibria in the (m₁Rb₂SO₄ + m₂CoSO₄)(aq), (m₁Rb₂SeO₄ + m₂CoSeO₄)(aq), (m₁Rb₂SO₄ + m₂NiSO₄)(aq), (m₁Rb₂SO₄ + m₂ZnSO₄)(aq), (m₁Rb₂SeO₄ + m₂ZnSeO₄)(aq), (m₁Cs₂SO₄ + m₂CoSO₄)(aq), (m₁Cs₂SeO₄ + m₂CoSeO₄)(aq), (m₁Cs₂SO₄ + m₂NiSO₄)(aq), (m₁Cs₂SeO₄ + m₂NiSeO₄)(aq), (m₁Cs₂SO₄ + m₂ZnSO₄)(aq), and (m₁Cs₂SeO₄ + m₂ZnSeO₄)(aq) systems, where m denotes molality at the temperature T=298.15 K. The Pitzer ion-interaction model has been used for thermodynamic analysis of the experimental osmotic and solubility data presented in the literature. The thermodynamic functions needed (binary and ternary parameters of ionic interaction, thermodynamic solubility products) have been calculated and the theoretical solubility isotherm has been plotted. The mixing parameters {θ(MN) and ψ(MNX)} have been chosen on the basis of the compositions of saturated ternary solutions and data on the binary solubility of the sulfate M₂SO₄. M^′SO₄ · 6H₂O double salts in water. To validate the mixing solutions model two different approaches have been used in evaluation of the ternary parameters: (I) preserving the same value of the binary mixing θ(MN) for the corresponding chloride, bromide, sulfate, and selenate systems with the same cations, and (II) with constant θ(MN) value (set equal to −0.05) for the all 11 sulfate and selenate systems. Very good agreement between experimentally determined and model predicted solubilities has been found. Important thermodynamic characteristics (thermodynamic solubility products, standard molar Gibbs free energy of formation) of the solid phases (simple salts, six sulfate – M₂SO₄ · M^′SO₄ · 6H₂O, and five selenate – M₂SeO₄ · M^′SeO₄ · 6H₂O – double salts) crystallizing in the systems under consideration are determined.     

Pitzer ion-interaction parameters for Fe(II) and Fe(III) in the quinary {Na + K + Mg + Cl + SO4 + H2O} system at T=298.15 K

This paper describes a chemical model that calculates (solid + liquid) equilibria in the {m₁FeCl₂ + m₂FeCl₃}(aq), {m₁FeSO₄ + m₂Fe₂(SO₄)₃}(aq), {m₁NaCl + m₂FeCl₃}(aq), {m₁Na₂SO₄ + m₂FeSO₄}(aq), {m₁NaCl + m₂FeCl₂}(aq), {m₁KCl + m₂FeCl₃}(aq), {m₁K₂SO₄ + m₂Fe₂(SO₄)₃}(aq), {m₁KCl + m₂FeCl₂}(aq), {m₁K₂SO₄ + m₂FeSO₄}(aq), and {m₁MgCl₂ + m₂FeCl₂}(aq) systems, where m denotes molality at T=298.15 K. The Pitzer ion-interaction model has been used for thermodynamic analysis of the experimental activity data in binary FeCl₂(aq) and FeCl₃(aq) solutions, and ternary solubility data, presented in the literature. The thermodynamic functions needed (binary and ternary parameters of ionic interaction, thermodynamic solubility products) have been calculated and the theoretical solubility isotherms have been plotted. The mixed solution model parameters {θ(MN) and ψ(MNX)} have been chosen on the basis of the compositions of saturated ternary solutions and data on the pure water solubility of the K₂SO₄ · FeSO₄ · 6H₂O double salt. The standard chemical potentials of four ferrous {FeCl₂ · 4H₂O, Na₂SO₄ · FeSO₄ · 4H₂O, K₂SO₄ · FeSO₄ · 6H₂O, and MgCl₂ · FeCl₂ · 8H₂O} and three ferric {FeCl₃ · 6H₂O, 2KCl · FeCl₃ · H₂O, and 2K₂SO₄ · Fe₂(SO₄)₃ · 14H₂O} solid phases have been determined. Comparison of solubility predictions with experimental data not used in model parameterization is given. The component activities of the saturated {m₁MgSO₄ + m₂FeSO₄}(aq) and in the mixed crystalline phase were determined and the change of the molar Gibbs free energy of mixing Δ_mixG^∘_m(s) of crystals was determined as a function of the solid phase composition. It is established that at T=298.15 K the mixed (Mg,Fe)SO₄ · 7H₂O and (Fe,Mg)SO₄ · 7H₂O crystals show small positive deviations from the ideal mixed crystals. Limitations of the {Fe(II) + Fe(III)} model due to data insufficiencies are discussed.     

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.     

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.     

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.     

(Liquid + solid) metastable equilibria in quinary system Li2CO3 + Na2CO3 + K2CO3 + Li2B4O7 + Na2B4O7 + K2B4O7 + H2O at T=288 K for Zhabuye salt lake

An experimental study on metastable equilibria at T=288 K in the quinary system Li₂CO₃ + Na₂CO₃ + K₂CO₃ + Li₂B₄O₇ + Na₂B₄O₇ + K₂B₄O₇ + H₂O was done by isothermal evaporation method. Metastable equilibrium solubilities and densities of the solution were determined experimentally. According to the experimental data, the metastable equilibrium phase diagram under the condition saturated with Li₂CO₃ was plotted, in which there are four invariant points; nine univariant curves; six fields of crystallization: K₂CO₃ · 3/2H₂O, K₂B₄O₇ · 5H₂O, Li₂B₂O₄ · 16H₂O, Na₂B₂O₄ · 8H₂O, Na₂CO₃ · 10H₂O, NaKCO₃ · 6H₂O. Some differences were found between the stable phase diagram at T=298 K and the metastable one at T=288 K.     

Thermodynamic properties of multicomponent electrolyte solutions in mixed solvents {HCl + NaCl-tert-C4H9OH + H2O} at (278.15 to 318.15) K

The thermodynamic properties of (HCl (m_A) + NaCl (m_B)-tert-C₄H₉OH + H₂O) system were studied by means of e.m.f. measurements in the cell without liquid junction at constant total ionic strength I=1.00 mol · kg⁻¹ from 278.15 K to 318.15 K. The standard electrode potential of Ag–AgCl and activity coefficient of HCl in the mixed solvents have been determined. The results show that the activity coefficient of HCl in HCl–NaCl solution still obeys Harned’s Rule and the logarithm of HCl activity coefficient, lgγ_A, is a linear function reciprocal of temperature at constant composition of the mixture. The standard transfer Gibbs free energy of HCl was calculated.     

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 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.     

Study of bromide salts solubility in the (m1NaBr + m2MgBr2)(aq) system at T = 323.15 K. Thermodynamic model of solution behavior and (solid + liquid) equilibria in the (Na + K + Mg + Br + H2O) system to high concentration and temperature

The bromide minerals solubility in the mixed system (m₁NaBr + m₂MgBr₂)(aq) have been investigated at T = 323.15 K by the physico-chemical analysis method. The equilibrium crystallization of NaBr·2H₂O(cr), NaBr(cr), and MgBr₂·6H₂O(cr) has been established. The solubility-measurements results obtained have been combined with all other experimental equilibrium solubility data available in literature at T = (273.15 and 298.15) K to construct a chemical model that calculates (solid + liquid) equilibria in the mixed system (m₁NaBr + m₂MgBr₂)(aq). The solubility modeling approach based on fundamental Pitzer specific interaction equations is employed. The model gives a very good agreement with bromide salts equilibrium solubility data. Temperature extrapolation of the mixed system model provides reasonable mineral solubility at high temperature (up to 100 °C). This model expands the previously published temperature variable sodium–potassium–bromide and potassium–magnesium–bromide models by evaluating sodium–magnesium mixing parameters. The resulting model for quaternary system (Na + K + Mg + Br + H₂O) is validated by comparing solubility predictions with those given in literature, and not used in the parameterization process. Limitations of the mixed solution models due to data insufficiencies at high temperature are discussed.     

Apparent molar heat capacities and apparent molar volumes ofY2(SO4)3(aq),La2(SO4)3(aq),Pr2(SO4)3(aq),Nd2(SO4)3(aq),Eu2(SO4)3(aq),Dy2(SO4)3(aq),Ho2(SO4)3(aq), andLu2(SO4)3(aq)atT = 298.15 K andp = 0.1 MPa

The apparent molar heat capacities C_{p, φ} ^∘ and apparent molar volumes V_φ ^∘ of Y₂(SO₄)₃(aq), La₂(SO₄)₃(aq), Pr₂(SO₄)₃(aq), Nd₂(SO₄)₃(aq), Eu₂(SO₄)₃(aq), Dy₂(SO₄)₃(aq), Ho₂(SO₄)₃(aq), and Lu₂(SO₄)₃(aq) were measured at T =  298.15 K and p =  0.1 MPa with a Sodev (Picker) flow microcalorimeter and a Sodev vibrating-tube densimeter, respectively. These measurements extend from lower molalities of m =  (0.005 to 0.018) mol ·kg ^− 1to m =  (0.025 to 0.434) mol ·kg ^− 1, where the upper molality limits are slightly below those of the saturated solutions. There are no previously published apparent molar heat capacities for these systems, and only limited apparent molar volume information. Considerable amounts of the R SO₄ ⁺ (aq) and R(SO₄)₂ ⁻ (aq) complexes are present, where R denotes a rare-earth, which complicates the interpretation of these thermodynamic quantities. Values of the ionic molar heat capacities and ionic molar volumes of these complexes at infinite dilution are derived from the experimental information, but the calculations are necessarily quite approximate because of the need to estimate ionic activity coefficients and other thermodynamic quantities. Nevertheless, the derived standard ionic molar properties for the various R SO₄ ⁺ (aq) and R(SO₄)₂ ⁻ (aq) complexes are probably realistic approximations to the actual values. Comparisons indicate that V_φ ^∘ {RSO₄ ⁺ , aq, 298.15K}  =  − (6  ±  4)cm³· mol ^− 1and V_φ ^∘ {R(SO₄)₂ ⁻ , aq, 298.15K}  =  (35  ±  3)cm³· mol ^− 1, with no significant variation with rare-earth. In contrast, values of C_{p, φ} ^∘ { RSO₄ ⁺ , aq, 298.15K } generally increase with the atomic number of the rare-earth, whereas C_{p, φ} ^∘ { R(SO₄)₂ ⁻ , aq, 298.15K } shows a less regular trend, although its values are always positive and tend to be larger for the heavier than for the light rare earths.     

Thermodynamic study of the mixed system (CsCl + CaCl2 + H2O) by EMF Measurements at T = 298.15 K

This work reports the results of a thermodynamic investigation of the ternary mixed-electrolyte system (CsCl + CaCl₂ + H₂O). The activity coefficients of this mixed aqueous electrolyte system have been studied with the electromotive force measurement (EMF) of the cell: Cs ion-selective electrode (ISE)|CsCl(m_A), CaCl₂(m_B), H₂O|Ag/AgCl at T = 298.15 K and over total ionic strengths from (0.01 to 1.50) mol · kg^?1 for different ionic strength fractions y_B of CaCl₂ with y_B = (0, 0.2, 0.4, 0.6, and 0.8). The cesium ion-selective electrode (Cs-ISE) and the Ag/AgCl electrode used in this work were made in our laboratory and had a good Nernst response. The experimental results obey the Harned rule, and the Pitzer model can be used to describe this ternary system satisfactorily. The osmotic coefficients, excess Gibbs free energies and activities of water of the mixtures were also calculated.     

(Solid + liquid) isothermal evaporation phase equilibria in the aqueous ternary system (Li2SO4 + MgSO4 + H2O) at T = 308.15 K

The solubility and the density in the aqueous ternary system (Li₂SO₄ + MgSO₄ + H₂O) at T = 308.15 K were determined by the isothermal evaporation. Our experimental results permitted the construction of the phase diagram and the plot of density against composition. It was found that there is one eutectic point for (Li₂SO₄ · H₂O + MgSO₄ · 7H₂O), two univariant curves, and two crystallization regions corresponding to lithium sulphate monohydrate (Li₂SO₄ · H₂O) and epsomite (MgSO₄ · 7H₂O). The system belongs to a simple co-saturated type, and neither double salts nor solid solution was found. Based on the Pitzer ion-interaction model and its extended HW models of aqueous electrolyte solution, the solubility of the ternary system at T = 308.15 K has been calculated. The predicted solubility agrees well with the experimental values.     

(Solid + solute) phase equilibria in aqueous solution. XIII. Thermodynamic properties of hydrozincite and predominance diagrams for (Zn2 + + H2O + CO2)

The thermodynamic properties ofZn₅(OH)₆(CO₃)₂ , hydrozincite, have been determined by performing solubility and d.s.c. measurements. The solubility constant in aqueous NaClO₄media has been measured at temperatures ranging from 288.15 K to 338.15 K at constant ionic strength (I =  1.00 mol · kg ^− 1). Additionally, the dependence of the solubility constant on the ionic strength has been investigated up to I =  3.00 mol · kg ^− 1NaClO₄at T =  298.15 K. The standard molar heat capacity C_{p, m}^ofunction fromT =  318.15 K to T =  418.15 K, as well as the heat of decomposition of hydrozincite, have been obtained from d.s.c. measurements. All experimental results have been simultaneously evaluated by means of the optimization routine of ChemSage yielding an internally consistent set of thermodynamic data (T =  298.15 K): solubility constant log ^* K_{ps 0}⁰ =  (9.0  ±  0.1), standard molar Gibbs energy of formationΔ_fG_m^o {Zn₅(OH)₆(CO₃)₂ }  =  ( − 3164.6  ±  3.0)kJ · mol ^− 1, standard molar enthalpy of formation Δ_fH_m^o{Zn₅(OH)₆(CO₃)₂ }  =  ( − 3584  ±  15)kJ · mol ^− 1, standard molar entropy S_m^o{Zn₅(OH)₆(CO₃)₂ }  =  (436  ±  50)J · mol ^− 1· K ^− 1and C_p,m^o / (J · mol ^− 1· K ^− 1)  =  (119  ±  11)  +  (0.834  ±  0.033)T / K. A three-dimensional predominance diagram is introduced which allows a comprehensive thermodynamic interpretation of phase relations in(Zn^2 +  +  H₂O  +  CO₂) . The axes of this phase diagram correspond to the potential quantities: temperature, partial pressure of carbon dioxide and pH of the aqueous solution. Moreover, it is shown how the stoichiometric composition{n(CO₃) / n(Zn)} of the solid compoundsZnCO₃ and Zn₅(OH)₆(CO₃)₂can be checked by thermodynamically analysing the measured solubility data.     

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 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 hydrolysis reactions of adenosine 3′,5′-(cyclic)phosphate(aq) and phosphoenolpyruvate(aq); the standard molar formation properties of 3′,5′-(cyclic)phosphate(aq) and phosphoenolpyruvate(aq)

Molar calorimetric enthalpy changes Δ_rH_m(cal) have been measured for the biochemical reactions {cAMP(aq) + H₂O(l)=AMP(aq)} and {PEP(aq) + H₂O(l)=pyruvate(aq) + phosphate(aq)}. The reactions were catalyzed, respectively, by phosphodiesterase 3^′,5^′-cyclic nucleotide and by alkaline phosphatase. The results were analyzed by using a chemical equilibrium model to obtain values of standard molar enthalpies of reaction Δ_rH_m^∘ for the respective reference reactions {cAMP⁻(aq) + H₂O(l)=HAMP⁻(aq)} and {PEP³⁻(aq) + H₂O(l)=pyruvate⁻(aq) + HPO²⁻₄(aq)}. Literature values of the apparent equilibrium constants K^′ for the reactions {ATP(aq)=cAMP(aq) + pyrophosphate(aq)}, {ATP(aq) + pyruvate(aq)=ADP(aq) + PEP(aq)}, and {ATP(aq) + pyruvate(aq) + phosphate(aq)=AMP(aq) + PEP(aq) + pyrophosphate(aq)} were also analyzed by using the chemical equilibrium model. These calculations yielded values of the equilibrium constants K and standard molar Gibbs free energy changes Δ_rG_m^∘ for ionic reference reactions that correspond to the overall biochemical reactions. Combination of the standard molar reaction property values (K, Δ_rH_m^∘, and Δ_rG_m^∘) with the standard molar formation properties of the AMP, ADP, ATP, pyrophosphate, and pyruvate species led to values of the standard molar enthalpy Δ_fH_m^∘ and Gibbs free energy of formation Δ_fG_m^∘ and the standard partial molar entropy S_m^∘ of the cAMP and PEP species. The thermochemical network appears to be reasonably well reinforced and thus lends some confidence to the accuracy of the calculated property values of the variety of species involved in the several reactions considered herein.     

The role of the double bond position in hydroboration using HBBr2 · SMe2, HBCl2 · SMe2 and H2BBr · SMe2: A detailed kinetic and mechanistic study

Hydroboration reactions of 4-octene with HBBr₂ · SMe₂, HBCl₂ · SMe₂ and H₂BBr · SMe₂ in CH₂Cl₂ were studied as function of concentration and temperature and compared with those of 1-octene. On average, hydroboration with dihaloborane proceeded 16 times slower for 4-octene than for 1-octene. In the case of the reactions with the monohaloborane, this factor is halved. This can be explained by the difference in the relative rates of dissociates of Me₂S from the dihaloborane and a monohaloborane complex, respectively. The reactions involving H₂BBr · SMe₂ also exhibited a k_?2 value, an indication of the presence of a parallel reaction, most likely a rearrangement process facilitating isomerization by way of a π-complex. The moderate ΔH^≠ values accompanied by small ΔS^≠ values (94 ± 4 kJ mol^?1, ?3 ± 13 J K^?1 mol^?1 for HBBr₂ · SMe₂; 93 ± 1 kJ mol^?1, ?17 ± 4 J K^?1 mol^?1 for HBCl₂ · SMe₂ and in the case of H₂BBr · SMe₂, 90 ± 13 kJ mol^?1, +12 ± 44 J K^?1 mol^?1 and 83 ± 13 kJ mol^?1, ?24 ± 45 J K^?1 mol^?1, respectively, for the k₂ and k_?2 processes) imply a process that is dissociatively dominated, with the overall mode of activation being interchange dissociative (I_d).