Buffer standards for the physiological pH of the zwitterionic compound of 3-(N-morpholino)propanesulfonic acid (MOPS) from T = (278.15 to 328.15) K

This paper reports the pH values of five NaCl-free buffer solutions and 11 buffer compositions containing NaCl at I = 0.16 mol · kg⁻¹. Conventional pa_H values are reported for 16 buffer solutions with and without NaCl salt. The operational pH values have been calculated for five buffer solutions and are recommended as pH standards at T = (298.15 and 310.15) K after correcting the liquid junction potentials. For buffer solutions with the composition m₁ = 0.04 mol · kg⁻¹, m₂ = 0.08 mol · kg⁻¹, m₃ = 0.08 mol · kg⁻¹ at I = 0.16 mol · kg⁻¹, the pH at 310.15 K is 7.269, which is close to 7.407, the pH of blood serum. It is recommended as a pH standard for biological specimens.     

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.     

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.     

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.     

The solubility measurements of sodium dicarboxylate salts; sodium oxalate,malonate, succinate,glutarate, and adipate in water from T = (279.15 to 358.15) K

The solubility measurements of sodium dicarboxylate salts; sodium oxalate, malonate, succinate, glutarate, and adipate in water at temperatures from (278.15 to 358.15 K) were determined. The molar enthalpies of solution at T = 298.15 K were derived: Δ_solH_m (m = 2.11 mol · kg^?1) = 13.86 kJ · mol^?1 for sodium oxalate; Δ_solH_m (m = 3.99 mol · kg^?1) = 14.83 kJ · mol^?1 for sodium malonate; Δ_solH_m (m = 2.45 mol · kg^?1) = 14.83 kJ · mol^?1 for sodium succinate; Δ_solH_m (m = 4.53 mol · kg^?1) = 16.55 kJ · mol^?1 for sodium glutarate, and Δ_solH_m (m = 3.52 mol · kg^?1) = 15.70 kJ · mol^?1 for sodium adipate. The solubility value exhibits a prominent odd–even effect with respect to terms with odd number of sodium dicarboxylate carbon numbers showing much higher solubility. This odd–even effect may have implications for the relative abundance of these compounds in industrial applications and also in the atmospheric aerosols.     

(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 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.     

Apparent molar volumes and apparent molar heat capacities of aqueous magnesium nitrate,strontium nitrate,and manganese nitrate at temperatures from 278.15 K to 393.15 K and at the pressure 0.35 MPa

Apparent molar volumes V_ϕ and apparent molar heat capacities C_p,ϕ were determined at the pressure 0.35 MPa for aqueous solutions of magnesium nitrate Mg(NO₃)₂ at molalities m = (0.02 to 1.0) mol · kg⁻¹, strontium nitrate Sr(NO₃)₂ at m = (0.05 to 3.0) mol · kg⁻¹, and manganese nitrate Mn(NO₃)₂ at m = (0.01 to 0.5) mol · kg⁻¹. Our V_ϕ values were calculated from solution densities obtained at T = (278.15 to 368.15) K using a vibrating-tube densimeter, and our C_p,ϕ values were calculated from solution heat capacities obtained at T = (278.15 to 393.15) K using a twin fixed-cell, differential, temperature-scanning calorimeter. Empirical functions of m and T were fitted to our results, and standard state partial molar volumes and heat capacities were obtained over the ranges of T investigated.     

Diffusion coefficients of nickel chloride in aqueous solutions of lactose at T = 298.15 K and T = 310.15 K

Binary mutual diffusion coefficients (interdiffusion coefficients) of nickel chloride in water at T = 298.15 K and T = 310.15 K, and at concentrations between (0.000 and 0.100) mol · dm^?3, using a Taylor dispersion method have been measured. These data are discussed on the basis of the Onsager–Fuoss and Pikal models. The equivalent conductance at infinitesimal concentration of the nickel ion in these solutions at T = 310.15 K has been estimated using these results. Through the same technique, ternary mutual diffusion coefficients (D₁₁, D₂₂, D₁₂, and D₂₁) for aqueous solutions containing NiCl₂ and lactose, at T = 298.15 K and T = 310.15 K, and at different carrier concentrations were also measured. These data permit us to have a better understanding of the structure of these systems and the thermodynamic behaviour of NiCl₂ in different media.     

Solubilities of l-glutamic acid, 3-nitrobenzoic acid,p-toluic acid,calcium-l-lactate,calcium gluconate,magnesium-dl-aspartate,and magnesium-l-lactate in water

Solubilities of l -glutamic acid, 3-nitrobenzoic acid, p -toluic acid, calcium-l -lactate, calcium gluconate, magnesium- dl -aspartate, and magnesium- l -lactate in water were determined in the temperature range 278 K to 343 K. The apparent molar enthalpies of solution at T =  298.15 K as derived from these solubilities areΔ_solH_m (l -glutamic acid,m_sat =  0.0565 mol · kg ^− 1)  =  30.2 kJ · mol ^− 1,Δ_solH_m (3-nitrobenzoic acid, m =  0.0188 mol · kg ^− 1)  =  28.1 kJ · mol ^− 1, Δ_solH_m( p - toluic acid, m =  0.00267 mol · kg ^− 1)  =  23.9 kJ · mol ^− 1,Δ_solH_m (calcium- l -lactate tetrahydrate,m =  0.2902 mol · kg ^− 1)  =  25.8 kJ · mol ^− 1,Δ_solH_m (calcium gluconate, m =  0.0806 mol · kg ^− 1)  =  22.1 kJ · mol ^− 1, Δ_solH_m(magnesium-dl -aspartate tetrahydrate, m =  0.1469 mol · kg ^− 1)  =  11.5 kJ · mol ^− 1, andΔ_solH_m (magnesium- l -lactate trihydrate,m =  0.3462 mol · kg ^− 1)  =  3.81 kJ · mol ^− 1.     

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.     

Density and activity of pertechnetic acid aqueous solutions at T = 298.15 K

The previous isopiestic investigations of HTcO₄ aqueous solutions at T = 298.15 K are believed to be unreliable, because of the formation of a ternary mixture at high molality. Consequently, published isopiestic molalities for aqueous HTcO₄ solutions at T = 298.15 K were completed and corrected. Binary data (variation of the osmotic coefficient and activity coefficient of the electrolyte in solution in the water) at T = 298.15 K for pertechnetic acid HTcO₄ were determined by direct water activity measurements. These measurements extend from molality m = 1.4 mol · kg⁻¹ to m = 8.32 mol · kg⁻¹. The variation of the osmotic coefficient of this acid in water is represented mathematically. Density variations at T = 298.15 K are also established and used to express the activity coefficient values on both the molar and molal concentration scale. The density law leads to the partial molar volume variations for aqueous HTcO₄ solutions at T = 298.15 K, which are compared with published data.     

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.     

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.     

Apparent molar volumes and apparent molar heat capacities of aqueous urea, 1,1-dimethylurea,and N,N′-dimethylurea at temperatures from (278.15 to 348.15) K and at the pressure 0.35 MPa

Apparent molar volumes V_ϕ and apparent molar heat capacities C_p,ϕ were determined for aqueous solutions of urea, 1,1-dimethylurea, and N,N′-dimethylurea. Measurements were made at molalities m = (0.02 to 6.0) mol · kg⁻¹ for urea, at m = (0.01 to 1.6) mol · kg⁻¹ for 1,1-dimethylurea, and at m = (0.01 to 8.0) mol · kg⁻¹ for N,N′-dimethylurea. Experimental temperatures ranged from (278.15 to 318.15) K for both urea and 1,1-dimethylurea, and from (278.15 to 348.15) K for N,N′-dimethylurea. All measurements were conducted at the pressure p = 0.35 MPa. Density measurements obtained with a vibrating-tube densimeter were used to calculate V_ϕ values. Heat capacity measurements obtained with a twin fixed-cell differential temperature-scanning calorimeter were used to calculate C_p,ϕ values. Functions of m and T were fitted to the results and were compared with the literature values. The “structure making/structure breaking” aspects of urea in water are discussed. Comparisons are made between the different urea compounds, and the effects of the methyl-group additions are outlined.     

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.     

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.     

Dependence of enthalpic pairwise self-interactions on ionic strength: Some 2-deoxy and N-acetyl monosaccharides in aqueous NaCl solutions at T = 298.15 K

The dilution enthalpies of four derivatives of monosaccharides, namely 2-deoxy-d-glucose (2-DGlu), N-acetyl-d-glucosamine (GluNAc), 2-deoxy-d-galactose (2-DGal) and N-acetyl-d-galactosamine (GalNAc), in aqueous NaCl solutions of various molalities (b = 0–3.0 mol · kg⁻¹) have been determined respectively at T = 298.15 K by isothermal titration calorimetry (MicroCal ITC200). The corresponding values of enthalpic pairwise self-interaction coefficients (h₂) have been calculated according to the McMillan–Mayer theory. It was found that across the range studied of ionic strength (I) or molality (b = I), the h₂ coefficients are all positive, in the order h₂ (GluNAc) > h₂ (GalNAc) > h₂ (2-DGlu) > h₂ (2-DGal), and decrease gradually after increasing first up to a maximum at b ≈ 1.5 mol · kg⁻¹. The effects of ionic strength (I) on the trends of h₂ have been discussed from the point of view of complex (solute + solute) and (solute + solvent) interactions in solutions.     

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.