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 studies on the saturated systems {H2O + BaCl2(sat) + NaCl + NH4Cl} and {H2O + BaCl2(sat) + mannitol(sat) + NaCl + NH4Cl} at the temperature 298.15 K: Comparison with the ideal-like solution model

Isopiestic measurements have been carried out at the temperature 298.15 K for two saturated aqueous solutions: {H₂O + BaCl₂(sat) + NaCl + NH₄Cl} saturated with barium chloride and {H₂O + BaCl₂(sat) + mannitol(sat) + NaCl + NH₄Cl} saturated with barium chloride and mannitol. Taking sodium chloride (aq) as reference solutions, osmotic coefficients of the aqueous solutions were determined. The experimental results are well represented by the ideal-like solution model.     

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.     

Hygrometric determination of water activities,osmotic and activity coefficients of (NaCl + KCl)(aq) at T = 298.15 K

The purpose of this study is to present a model for the prediction of water activity in multicomponent aqueous solutions containing a common ion from available binary data. The hygrometric method has been used to measure relative humidities for the aqueous electrolyte mixture (NaCl  +  KCl)(aq) at total molalities ranging from 0.2 mol · kg ^− 1to saturation for different molal ratiosr of NaCl(aq) to KCl(aq) with r =  (0.2, 0.5, 1, 2, 3, and 4) at T =  298.15 K. The data obtained have been used to determine water activities and osmotic coefficients. The results show that the values of water activities and osmotic coefficients calculated with the proposed model are close to the experimental ones. This model is also compared with four other models (RS, Pitzer, RWR, and LS II) over the range of the studied total molalities. From the measurements, the activity coefficients of NaCl(aq) and KCl(aq) in the mixture have also been determined.     

Activity coefficients of CaCl2 in (maltose + water) and (lactose + water) mixtures at 298.15 K

Activity coefficients of CaCl₂ in disaccharide {(maltose, lactose) + water} mixtures at 298.15 K were determined by cell potentials. The molalities of CaCl₂ ranged from about 0.01 mol · kg^?1 to 0.20 mol · kg^?1, the mass fractions of maltose from 0.05 to 0.25, and those of lactose from 0.025 to 0.125. The cell potentials were analyzed by using the Debye–Hückel extended equation and the Pitzer equation. The activity coefficients obtained from the two theoretical models are in good agreement with each other. Gibbs free energy interaction parameters (g_ES) and salting constants (k_S) were also obtained. These were discussed in terms of the stereo-chemistry of saccharide molecules and the structural interaction model.     

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.     

Thermodynamic evaluation and optimization of the (NaNO3 + KNO3 + Na2SO4 + K2SO4) system

A complete critical evaluation of all available phase diagram and thermodynamic data has been performed for all condensed phases of the (NaNO₃ + KNO₃ + Na₂SO₄ + K₂SO₄) ternary reciprocal system, and optimised model parameters have been found. The model parameters obtained for the four binary common-ion subsystems (i.e. (NaNO₃ + Na₂SO₄), (KNO₃ + K₂SO₄), (NaNO₃ + KNO₃) and (Na₂SO₄ + K₂SO₄)) are used to predict thermodynamic properties and phase equilibria for the entire system. The Modified Quasichemical Model in the Quadruplet Approximation for short-range ordering was used for the molten salt phase, and the Compound Energy Formalism was used for the various solid solutions.     

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.     

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.     

Thermodynamics of the ternary systems: (water + glycine,l-alanine and l-serine + di-ammonium hydrogen citrate) from volumetric,compressibility, and (vapour + liquid) equilibria measurements

The apparent molar volumes and isentropic compressibility of glycine, l-alanine and l-serine in water and in aqueous solutions of (0.500 and 1.00) mol · kg^?1 di-ammonium hydrogen citrate {(NH₄)₂HCit} and those of (NH₄)₂HCit in water have been obtained over the (288.15 to 313.15) K temperature range at 5 K intervals at atmospheric pressure from measurements of density and ultrasonic velocity. The apparent molar volume and isentropic compressibility values at infinite dilution of the investigated amino acids have been obtained and their variations with temperature and their transfer properties from water to aqueous solutions of (NH₄)₂HCit have also been obtained. The results have been interpreted in terms of the hydration of the amino acids. In the second part of this work, water activity measurements by the isopiestic method have been carried out on the aqueous solutions of {glycine + (NH₄)₂HCit}, {alanine + (NH₄)₂HCit}, and {serine + (NH₄)₂HCit} at T = 298.15 K at atmospheric pressure. From these measurements, values of vapour pressure, osmotic coefficient, activity coefficient and Gibbs free energy were obtained. The effect of the type of amino acids on the (vapour + liquid) equilibrium of the systems investigated has been studied. The experimental water activities have been correlated successfully with the segment-based local composition Wilson model. Furthermore, the thermodynamic behaviour of the ternary solutions investigated has been studied by using the semi-ideal hydration model and the linear concentration relations have been tested by comparing with the isopiestic measurements for the studied systems at T = 298.15 K.     

Thermodynamic study of (m1Cs2SeO4 + m2NiSeO4)(aq)wheremdenotes molality atT = 298.15 K

The isopiestic method has been used to determine the osmotic coefficients of the binary solutions Cs₂SeO₄(aq) at T =  298.15 K from (1.090 to 4.591)mol · kg ^− 1. The molalities m of (m₁Cs₂SeO₄ + m₂NiSeO₄)(aq) have been investigated by physicochemical analysis. The crystallization of a new double salt Cs₂SeO₄· NiSeO₄· 6H₂O has been established. The Pitzer ion-interaction model has been used for thermodynamic analysis of the results obtained. The thermodynamic data needed (binary and ternary parameters of ionic interaction, thermodynamic solubility products) have been calculated and the theoretical solubility isotherm has been plotted. The experimentally obtained and the calculated solubilities are in very good agreement. The standard molar Gibbs energy of the synthesis reaction Δ_rG_m^oof the double salt Cs₂SeO₄· NiSeO₄· 6H₂O from the corresponding simple salts Cs₂SeO₄and NiSeO₄· 6H₂O, as well as the standard molar Gibbs energy of formation Δ_rG_m^ohave been determined.     

Activity coefficients of CaCl2 in (serine or proline + water) mixtures at T = 298.15 K

Activity coefficients for the (CaCl₂ + amino acid + water) system were determined at a temperature of 298.15 K using ion-selective electrodes. The range of molalities of CaCl₂ is (0.01 to 0.20) mol · kg^?1, and that of amino acids is (0.10 to 0.40) mol · kg^?1. The activity coefficients obtained from the Debye–Hückel extended equation and the Pitzer equation are in good agreement with each other. Results show that the interactions between CaCl₂ and amino acid are controlled mainly by the electrostatic interactions (attraction). Gibbs free energy interaction parameters (g_EA) and salting constants (k_S) are positive, indicating that these amino acids are salted out by CaCl₂. These results are discussed based on group additivity model.     

Thermodynamic evaluation and optimization of the (NaCl + Na2SO4 + Na2CO3 + KCl + K2SO4 + K2CO3) system

A complete, critical evaluation of all phase diagrams and thermodynamic data was performed for all condensed phases of the (NaCl + Na₂SO₄ + Na₂CO₃ + KCl + K₂SO₄ + K₂CO₃) system, and optimized parameters for the thermodynamic solution models were obtained. The Modified Quasichemical Model in the Quadruplet Approximation was used for modelling the liquid phase. The model evaluates first- and second-nearest-neighbour short-range order, where the cations (Na⁺ and K⁺) were assumed to mix on a cationic sublattice, while anions $({\text{CO}}_3^{2-}\text{,}{\text{SO}}_4^{2-}\text{,}\text{and}{\text{Cl}}^{-})$ were assumed to mix on an anionic sublattice. The thermodynamic properties of the solid solutions of (Na,K)₂(SO₄,CO₃) were modelled using the Compound Energy Formalism, and (Na,K)Cl was modelled using a substitutional model in previous studies. Phase transitions in the common-cation ternary systems (NaCl + Na₂SO₄ + Na₂CO₃) and (KCl + K₂SO₄ + K₂CO₃) were studied experimentally using d.s.c./t.g.a. The experimental results were used as input for evaluating the phase equilibrium in the common-cation ternary systems. The models can be used to predict the thermodynamic properties and phase equilibria in multicomponent heterogeneous systems. The experimental data from the literature are reproduced within experimental error limits.     

High-pressure (vapour + liquid) equilibria for ternary systems composed by {(E)-2-hexenal or hexanal + carbon dioxide + water}: Partition coefficient measurement

A new apparatus based on a static–analytic method assembled in this work was utilised to perform high-pressure (vapour + liquid) equilibria measurements of aqueous ternary systems. This work includes values of isothermal partition coefficients between CO₂ and water of two apple aroma constituents, (E)-2-hexenal and hexanal. Additionally, this work reports new experimental (vapour + liquid) equilibria measurements for the ternary systems (CO₂ + (E)-2-hexenal + water) and (CO₂ + hexanal + water), at fixed liquid phase composition (600 mg · kg⁻¹), at temperatures of (313, 323 and 333) K and at pressures from (8 to 19) MPa. Vapour liquid interphase was checked and monitored visually for all the systems studied in this work. No liquid immiscibility was observed at the composition, temperatures and pressures studied. In order to suggest reasonable operation conditions for fractionation of aromas with dense carbon dioxide, partition coefficients of the aroma compounds between CO₂ and water along with their separation factors from water were calculated. Partition coefficients of (E)-2-hexenal between CO₂ and water were in the range of (6 to 91) and where found to be near six times higher than those of hexanal (9 to 17). Very high separation factors from water were observed (∼10⁴) especially for (E)-2-hexenal. The highest separation factor, for both compounds, was found at a temperature of 313 K and pressures from (12 to 14) MPa.     

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.     

Hygrometric determination of the water activities and the osmotic and activity coefficients of (ammonium chloride + sodium chloride + water) atT = 298.15 K

The mixed aqueous electrolyte system of ammonium and sodium chlorides has been studied by the hygrometric method at the temperature 298.15 K. The relative humidities of this system were measured at total molalities from 0.3mol · kg ^− 1 to 6 mol · kg ^− 1for different ionic-strength fractions of NH ₄Cl with y =  (0.33, 0.50, and 0.67). The data obtained allow the deduction of new water activities and osmotic coefficients. The experimental results are compared with the predictions of the extended composed additivity model proposed in our previous work, the Robinson–Stokes, Reilly–Wood–Robinson, and Lietzke–Stoughton models. From these measurements, the new Pitzer mixing ionic parameters were determined and used to predict the solute activity coefficients in the mixture.     

(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.     

Quaternary liquid–liquid equilibria for systems of {(water + methanol or ethanol) + m-xylene + n-dodecane}

Liquid–liquid equilibrium (LLE) data were determined for the quaternary systems of {(water + methanol or ethanol) + m-xylene + n-dodecane} at three temperatures 298.15, 303.15 and 313.15 K and atmospheric pressure. The composition of liquid phases at equilibrium was determined by gas–liquid chromatography and the results were correlated with the UNIQUAC and NRTL activity coefficient models. The partition coefficients and the selectivity factor of the solvent are calculated and compared. The phase diagrams for the quaternary systems including both the experimental and correlated tie lines are presented.     

Thermodynamic properties of the system NH4NO3–KNO3–H2O at 298.15 K

The water activity and osmotic coefficients of the system {y NH₄NO₃+(1-y) KNO₃}(aq) has been measured at total molalities from 0.2 mol kg⁻¹ to about saturation of one of the solutes for different ionic-strength fractions y of NH₄NO₃ with y=0.2, 0.5 and 0.8 at the temperature 298.15 K using the hygrometric method. The obtained data allow the deduction of the thermodynamic parameters. From these measurements, new Pitzer ionic mixing parameters are determined and used to predict the solute activity coefficients in the mixture. The results obtained are used to calculate the excess Gibbs energy at total molalities for different ionic-strength fractions of NH₄NO₃.