Standard Molar Gibbs Energy Research Articles

Thermodynamic studies on [formula omitted](s)

The Standard molar Gibbs energies of formation of Sr 3 Zr 2 O 7 (s) have been determined for the first time by measuring Sr(g) pressures over the three phase {x 1 Sr 4 Zr 3 O 10( s)+x 2 Sr 3 Zr 2 O 7( s)+(1−x 1−x 2) Zr 1−x O x( s)} using a Knudsen effusion mass-loss technique employing a Sartorius micro-balance model 4410. The values of the mole fractions x 1 and x 2 in the three phase mixture are 0.3795 and 0.5391, respectively. The Δ f G 0 m ( Sr 3 Zr 2 O 7, s,T) has been calculated and is given by: Δ f G 0 m ( Sr 3 Zr 2 O 7, s,T)/( kJ· mol −1)={−4229+0.7357(T/ K)}±15, where (1349 K⩽T/ K⩽1466). The Δ f H 0 m ( Sr 3 Zr 2 O 7 ,s,298.15 K) value has been calculated from the Δ f G 0 m ( Sr 3 Zr 2 O 7 ,s, T), and molar heat capacities of Sr(s,l), Zr(s), and O 2 (g) from the literature using the values of Sr 4 Zr 3 O 10 (s) from our previous work. The resulting value is −(4186±38) kJ· mol −1 . A corresponding value of Δ f H 0 m ( Sr 3 Zr 2 O 7, s,298.15 K)=−(4163±42) kJ· mol −1 has also been calculated using the third law. In this method, Φ 0 m =( Δ T 0S 0 m − Δ T 298.15 K H 0 m /T) values for Sr 4 Zr 3 O 10 (s), Sr(g), Zr 0.72 O 0.26 (s), Sr 3 Zr 2 O 7 (s), and Sr(g) pressure over the three phase system have been used for the calculation of Δ f H 0 m ( Sr 3 Zr 2 O 7, s,298.15 K) at each experimental temperature.

Thermodynamic study of aqueous rubidium and cobalt selenate system at the temperature 298.15 K

The isopiestic method has been used to determine the osmotic coefficients of the binary solutions Rb 2SeO 4(aq) at the temperature T=298.15 K from (1.072 to 5.200) mol·kg −1. The molalities m of ( m 1Rb 2SeO 4+ m 2CoSeO 4)(aq) have been investigated by the physicochemical analysis method. The crystallization of a new double salt Rb 2SeO 4·CoSeO 4·6H 2O has been established. This double salt crystallizes in a monoclinic crystal system, space group P2 1/ a, a=0.9281(2) nm , b=1.2422(2) nm , c=0.6276(9) nm , β=105.70 (2)° , and V=0.6966(2) nm 3 . The double salt is isostructural with Rb 2SeO 4·ZnSeO 4·6H 2O. T.g. and d.t.a measurements indicate that the double salt loses the crystallization water in two steps in the temperature interval from 393.15 K to 523.15 K. The Pitzer ion-interaction model has been used in the thermodynamic analysis of the experimental osmotic and solubility data obtained. The thermodynamic parameters 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 r G 0 m of the double salt Rb 2SeO 4·CoSeO 4·6H 2O from the corresponding simple salts Rb 2SeO 4 and CoSeO 4·6H 2O, as well as the standard molar Gibbs energy of formation Δ f G 0 m have been determined.

Systems Ln–Fe–O ( Ln=Eu, Gd): thermodynamic properties of ternary oxides using solid-state electrochemical cells

The standard molar Gibbs energies of formation of LnFeO 3(s) and Ln 3Fe 5O 12(s) where Ln=Eu and Gd have been determined using solid-state electrochemical technique employing different solid electrolytes. The reversible e.m.f.s of the following solid-state electrochemical cells have been measured in the temperature range from 1050 to 1255 K. Cell (I): (−)Pt / { LnFeO 3(s)+ Ln 2O 3(s)+Fe(s)} // YDT/CSZ // {Fe(s)+Fe 0.95O(s)} / Pt(+); Cell (II): (−)Pt/{Fe(s)+Fe 0.95O(s)}//CSZ//{ LnFeO 3(s)+ Ln 3Fe 5O 12(s)+Fe 3O 4(s)}/Pt(+); Cell (III): (−)Pt/{ LnFeO 3(s)+ Ln 3Fe 5O 12(s)+Fe 3O 4(s)}//YSZ//{Ni(s)+NiO(s)}/Pt(+); and Cell(IV):(−)Pt/{Fe(s)+Fe 0.95O(s)}//YDT/CSZ//{ LnFeO 3(s)+ Ln 3Fe 5O 12(s)+Fe 3O 4(s)}/Pt(+). The oxygen chemical potentials corresponding to the three-phase equilibria involving the ternary oxides have been computed from the e.m.f. data. The standard Gibbs energies of formation of solid EuFeO 3, Eu 3Fe 5O 12, GdFeO 3 and Gd 3Fe 5O 12 calculated by the least-squares regression analysis of the data obtained in the present study are given by Δ f G° m (EuFeO 3, s) /kJ mol −1 (± 3.2)=−1265.5+0.2687( T/K) (1050 ⩽ T/K ⩽ 1570), Δ f G° m (Eu 3Fe 5O 12, s)/kJ mol −1 (± 3.5)=−4626.2+1.0474( T/K) (1050 ⩽ T/K ⩽ 1255), Δ f G° m (GdFeO 3, s) /kJ mol −1 (± 3.2)=−1342.5+0.2539( T/K) (1050 ⩽ T/K ⩽ 1570), and Δ f G° m (Gd 3Fe 5O 12, s)/kJ·mol −1 (± 3.5)=−4856.0+1.0021( T/K) (1050 ⩽ T/K ⩽ 1255). The uncertainty estimates for Δ f G° m include the standard deviation in the e.m.f. and uncertainty in the data taken from the literature. Based on the thermodynamic information, oxygen potential diagrams for the systems Eu–Fe–O and Gd–Fe–O and chemical potential diagrams for the system Gd–Fe–O were computed at 1250 K.

System Dy—Fe—O: Thermodynamic Properties of Ternary Oxides Using Calvet Calorimetry and Solid‐State Electrochemical Cell

AbstractFor Abstract see ChemInform Abstract in Full Text.

Standard Molar Gibbs Energy of Formation of Ba3Te2O9(s) by Transpiration Technique.

Abstract The standard molar Gibbs energy of formation of barium tellurite, Ba 3 Te 2 O 9 (s), was determined by the transpiration technique using pure oxygen as the carrier gas in the temperature range from 1119 to 1280 K. The condensate was exclusively identified as TeO 2 (s) by chemical analysis. Chemical analysis of the residue left in the alumina boat after the transpiration experiments confirmed the coexistence of BaO(s) with Ba 3 Te 2 O 9 (s) during the vaporization reaction. The incongruent vaporization reaction could be established as: Ba 3 Te 2 O 9 (s)=3BaO(s)+2TeO 2 (g)+O 2 (g). From the quantitative chemical analysis of the condensed TeO 2 (s), the vapor pressure of TeO 2 (g) over pure Ba 3 Te 2 O 9 (s) was calculated. The equilibrium constant for the incongruent vaporization reaction at each temperature has been calculated from the vapor pressure data and is fitted to an expression: ln K (±1.0)=11.32–55518.6·( K /T) . The Gibbs energy of formation of Ba 3 Te 2 O 9 (s) was computed from the above data and the values of Δ f G° m for BaO(s) and TeO 2 (g) taken from the literature and are given by: {Δ f G ° m (Ba 3 Te 2 O 9 , s, T )±3.0}/(kJ mol −1 )=−2296.8+0.4302·( T /K).

Thermodynamics of the reduction of NADP with 2-propanol catalyzed by an NADP-dependent alcohol dehydrogenase

The apparent equilibrium constant of the biochemical reaction, 2-propanol + NADP ox=acetone + NADP red, was determined at I=0.25 M over a wide range of pH (5.63 to 8.02) and temperature (5 to 40 °C). The reaction was catalyzed by an NADP-dependent alcohol dehydrogenase. The results were used to calculate thermodynamic quantities for the chemical (ionic) reference reaction: 2-propanol + NADP ox 3−=acetone + NADP red 4−+H +. The thermodynamic quantities for this reference reaction are as follows: equilibrium constant K=(5.98±0.46)×10 −10; standard molar Gibbs energy change Δ r G 0=(52.65±0.19) kJ mol −1 ; standard molar enthalpy change Δ r H 0=(38.9±0.6) kJ mol −1 ; and standard molar entropy change Δ r S 0=−(46.1±2.2) J K −1 mol −1 . All of these results pertain to 25 °C (298.15 K) and I=0. The results also lead, in conjunction with tabulated thermodynamic quantities, to the standard electromotive force E 0=−0.140 V for the reduction of NADP ox 3− to NADP red 4−.

Solubility of 1-butene in water and in a medium for cultivation of a bacterial strain

Solubility measurements of 1-butene in water, from 20 to 50°C and at atmospheric pressure, were carried out using a Ben-Naim/Baer-type apparatus. The experimental results have a precision of about ±0.3%. Using accurate thermodynamic relations, the Ostwald coefficients at the experimental conditions and at infinite dilution, the mole fractions of the dissolved gas at the gas partial pressure of 101.325 kPa and the Henry coefficients at the water vapor pressure were calculated. The mole fraction of dissolved gas were fitted to the Clarke, Glew, and Weiss equation and thermodynamic quantities, standard molar Gibbs energy, entropy, and enthalpy changes, for the process of transferring the 1-butene molecules from the gaseous to the water phase, were computed. Moreover, solubility measurements of 1-butene in an aqueous medium for the cultivation of Xanthobacter Py2 in the same temperature range were also performed at atmospheric pressure. These solubility data are approximately 2.6% lower than those observed in pure water.

Thermodynamics of the lipase-catalyzed transesterification of 1-phenyl-1-alkanols and butyl acetate in organic solvents

The thermodynamics of the lipase-catalyzed transesterification reactions of butyl acetate and 1-phenyl-1-alkanols from C 1 to C 4 have been studied in organic solvents. Equilibrium measurements of the reactions with benzyl alcohol and ( R)-(+)-1-phenyl ethanol were carried out in n-hexane, acetonitrile, 2-butanone, tert-butyl methyl ether, carbon tetrachloride and neat (no solvent added) at 298.15 K. The average value for the equilibrium constant and the standard molar Gibbs energy change Δ r G° m in these solvents for the reaction with benzyl alcohol (C 1) are 0.29 and 3.1 kJ mol −1, respectively; for the reaction with ( R)-(+)-1-phenyl ethanol (C 2) the respective values are 0.11 and 5.4 kJ mol −1. The difference of 2.3 kJ mol −1 in the values of Δ r G° m between the C 1 and C 2 alkanols is attributed to increased steric hindrance associated with the additional methyl group in ( R)-(+)-1-phenyl ethanol. In addition, the temperature dependence of the equilibrium constants for the reactions with C 1 and C 2 alkanols were also studied in n-hexane. The standard molar Gibbs energy Δ r G° m, enthalpy Δ r H° m, and entropy Δ r S° m changes at 298.15 K have been calculated from these results. It is seen that the temperature variation of the values of the equilibrium constants is small and that the values of Δ r H° m are zero within experimental error. The equilibrium constants for the reactions involving ( R)-(+)-1-phenyl-1-propanol (C 3) and ( R)-(+)-1-phenyl-1-butanol (C 4) were measured in n-hexane only and the values are both 0.11. The fact that the values of the equilibrium constants for the reactions involving C 2–C 4 are constant is consistent with the view that no additional steric hindrance is caused by adding more than one methylene group to the ( R)-(+)-1-phenyl-1-alkanol reactant.

System DyFeO: thermodynamic properties of ternary oxides using Calvet calorimetry and solid-state electrochemical cell

The enthalpy increments and the standard molar Gibbs energies of formation of DyFeO 3(s) and Dy 3Fe 5O 12(s) have been measured using a Calvet micro-calorimeter and a solid oxide galvanic cell, respectively. A co-operative phase transition, related to anti-ferromagnetic to paramagnetic transformation, is apparent from the heat capacity data for DyFeO 3 at ∼648 K. A similar type of phase transition has been observed for Dy 3Fe 5O 12 at ∼560 K which is related to ferrimagnetic to paramagnetic transformation. Enthalpy increment data for DyFeO 3(s) and Dy 3Fe 5O 12(s), except in the vicinity of the second-order transition, can be represented by the following polynomial expressions: {H 0 m (T)−H 0 m (298.15 K)} ( J mol −1) (±1.1%)=−52754+142.9×(T ( K))+2.48×10 −3×(T ( K)) 2+2.951×10 6×(T ( K)) −1;(298.15⩽ T ( K)⩽1000) for DyFeO 3(s), and {H 0 m (T)−H 0 m (298.15 K)} ( J mol −1) (±1.2%)=−191048+545.0×(T ( K))+2.0×10 −5×(T ( K)) 2+8.513×10 6×(T ( K)) −1;(298.15⩽T ( K)⩽1000) for Dy 3Fe 5O 12(s). The reversible emfs of the solid-state electrochemical cells: (−)Pt/{DyFeO 3(s) + Dy 2O 3(s) + Fe(s)}//YDT/CSZ//{Fe(s) + Fe 0.95O(s)}/Pt(+) and (−)Pt/{Fe(s) + Fe 0.95O(s)}//CSZ//{DyFeO 3(s) + Dy 3Fe 5O 12(s) + Fe 3O 4(s)}/Pt(+), were measured in the temperature range from 1021 to 1250 K and 1035 to 1250 K, respectively. The standard Gibbs energies of formation of solid DyFeO 3 and Dy 3Fe 5O 12 calculated by the least squares regression analysis of the data obtained in the present study, and data for Fe 0.95O and Dy 2O 3 from the literature, are given by: Δ f G 0 m ( DyFeO 3, s) ( kJ mol −1) (±3.2)=−1339.9+0.2473×(T ( K));(1021⩽T ( K)⩽1548) and Δ f G 0 m ( Dy 3 Fe 5 O 12, s) ( kJ mol −1) (±3.5)=−4850.4+0.9846×(T ( K));(1035⩽T ( K)⩽1250). The uncertainty estimates for Δ f G 0 m include the standard deviation in the emf and uncertainty in the data taken from the literature. Based on the thermodynamic information, oxygen potential diagram and chemical potential diagrams for the system DyFeO were developed at 1250 K.

Thermodynamic study of quaternary systems with participation of ammonium and sodium alums and chromium alums

The Pitzer ion-interaction model has been used for thermodynamic simulation of the ternary NaCl-NH 4Cl-H 2O, NaBr-NH 4Br-H 2O, Na 2SO 4-(NH 4) 2SO 4-H 2O, NiSO 4-Al 2(SO 4) 3-H 2O, and CuSO 4-Al 2(SO 4) 3-H 2O systems at T=298.15 K. The mixing parameters have been chosen on the basis of the compositions of saturated ternary solutions taking into account the unsymmetrical mixing terms E θ and E θ′. The sodium-ammonium systems have been simulated simultaneously with a view to preserving a constant value of the binary θ Na, NH 4 mixing parameter. It was established that the zero values of θ M, Me and ψ M, Me, SO 4 describe the properties of the ternary aqueous mixtures of 2-2 and 3-2 electrolytes with a sufficient accuracy. Important thermodynamic characteristics (thermodynamic solubility product, standard molar Gibbs energy of formation) of the solid phases (simple and double salts) crystallizing in the systems under consideration are determined. The calculated thermodynamic functions have been used for a thermodynamic study of the quaternary Na 2SO 4-(NH 4) 2SO 4-Cr 2(SO 4) 3-H 2O, and Na 2SO 4-NiSO 4-Al 2(SO 4) 3-H 2O systems. Good agreement between experimentally determined and calculated solubilities has been found.

Determination of the standard molar Gibbs energy of formation of lanthanum zirconate by a galvanic cell involving lanthanum β-alumina electrolyte

The standard molar Gibbs energy of formation of La 2Zr 2O 7from La2 O 3and ZrO 2has been determined in the temperature range 1073 K to 1273 K by the e.m.f. measurements. The solid-state galvanic cell involving lanthanum β -alumina electrolyte was applied. The average values of the standard enthalpy and the standard entropy in the temperature range covered by the e.m.f. measurements have also been estimated. The results have been compared with those obtained by other authors.

Thermodynamic study of aqueous sodium and potassium chloride and chromate systems at the temperature 298.15 K

The solubilities of ( m1NaCl +m2Na2 CrO 4)(aq) and ( m1KCl +m2 K 2CrO 4)(aq) where m denotes molality have been investigated at the temperature T= 298.15 K by the physico-chemical analysis method. Only the crystallization of the simple salts NaCl, Na 2CrO 4·4H 2O, KCl, and K 2CrO 4have been established. The ternary solutions have been simulated thermodynamically at T= 298.15 K using the Pitzer model. The necessary thermodynamic parameters (binary and ternary ion-interaction parameters, thermodynamic solubility products) have been calculated and the theoretical solubility isotherms plotted. A very good agreement is found between calculated and experimental solubility isotherms. The standard molar Gibbs energies of formationΔrGmo of solid phases crystallizing in the systems under consideration have been estimated from theory.

Aqueous solubility diagrams for cementitious waste stabilization systems. 4. A carbonation model for Zn-doped calcium silicate hydrate by Gibbs energy minimization.

A thermodynamic Gibbs energy minimization (GEM) solid solution-aqueous solution (SSAS) equilibrium model was used to determine the solubility of Zn from calcium silicate hydrate (CSH) phases doped with 0, 0.1, 1, 5, and 10% Zn at a unity (Ca+Zn)/Si molar ratio. Both the stoichiometry and standard molar Gibbs energy (G(o)298) of the Zn-bearing end-member in the ideal ternary Zn-bearing calcium silicate hydrate (CZSH) solid solution were determined by a "dual-thermodynamic" (GEM-DT) estimation technique. The SSAS model reproduces a complex sequence of reactions suggested to occur in a long-term weathering scenario of cementitious waste forms at subsurface repository conditions. The GEM model of CZSH leaching at several Zn loadings and solid/water (s/w) ratios in a C02-free system showed that, upon complete dissolution of portlandite and calcium zincate phases at decreasing s/w < 0.01 mol x kg(H2O)(-1), the total dissolved concentrations Si(aq), Ca(aq), and Zn(aq) are controlled by a CZSH solid solution of changing composition, with a trough-like Znaq drop by 2-3 orders of magnitude. Carbonation was simulated in another GEM model run series by CO2 titration of the system with initial s/w approximately 0.9 mol/kg(H2O). Formation of (Ca,Zn)-CO3 nonideal solid solution was predicted already at early reaction stage in the presence of both portlandite and calcium zincate hydrate phases. Upon their disappearance, pH, Zn(aq), C(aq), and fCO2 were predicted to change due to the incongruent dissolution of two concurrent CZSH-I and CZSH-II solid solutions, until the total re-partitioning of Ca and Zn into a carbonate solid solution coexisting with amorphous silica at fCO2 > 0.1 bar. Along this solid-phase transition, dissolved Zn(aq) concentrations follow a highly nonlinear trend. The model results predict that at low to moderate Zn loading (< or = 1% per mole Si), CZSH-type compounds can efficiently immobilize Zn in the near field of a cement-stabilized waste repository.

Standard molar Gibbs energy of formation of Ba 3Te 2O 9(s) by transpiration technique

The standard molar Gibbs energy of formation of barium tellurite, Ba 3Te 2O 9(s), was determined by the transpiration technique using pure oxygen as the carrier gas in the temperature range from 1119 to 1280 K. The condensate was exclusively identified as TeO 2(s) by chemical analysis. Chemical analysis of the residue left in the alumina boat after the transpiration experiments confirmed the coexistence of BaO(s) with Ba 3Te 2O 9(s) during the vaporization reaction. The incongruent vaporization reaction could be established as: Ba 3Te 2O 9(s)=3BaO(s)+2TeO 2(g)+O 2(g). From the quantitative chemical analysis of the condensed TeO 2(s), the vapor pressure of TeO 2(g) over pure Ba 3Te 2O 9(s) was calculated. The equilibrium constant for the incongruent vaporization reaction at each temperature has been calculated from the vapor pressure data and is fitted to an expression: ln K (±1.0)=11.32–55518.6·( K/T) . The Gibbs energy of formation of Ba 3Te 2O 9(s) was computed from the above data and the values of Δ fG° m for BaO(s) and TeO 2(g) taken from the literature and are given by: {Δ f G° m (Ba 3Te 2O 9, s, T)±3.0}/(kJ mol −1)=−2296.8+0.4302·( T/K).

Thermodynamic Quantities for the Ionization Reactions of Buffers

This review contains selected values of thermodynamic quantities for the aqueous ionization reactions of 64 buffers, many of which are used in biological research. Since the aim is to be able to predict values of the ionization constant at temperatures not too far from ambient, the thermodynamic quantities which are tabulated are the pK, standard molar Gibbs energy ΔrG∘, standard molar enthalpy ΔrH°, and standard molar heat capacity change ΔrCp∘ for each of the ionization reactions at the temperature T=298.15 K and the pressure p=0.1 MPa. The standard state is the hypothetical ideal solution of unit molality. The chemical name(s) and CAS registry number, structure, empirical formula, and molecular weight are given for each buffer considered herein. The selection of the values of the thermodynamic quantities for each buffer is discussed.

Thermodynamic properties of BaTeO 3(s)

The standard molar Gibbs energy of formation of barium tellurite, BaTeO 3(s), was determined by the transpiration technique using pure oxygen as the carrier gas in the temperature range 1133 K to 1260 K. The condensate was exclusively identified as TeO 2(s) by chemical analysis. From a quantitative chemical analysis of the condensed TeO 2(s), the vapour pressure of TeO 2(g) over pure BaTeO 3(s) was calculated and is given by ln{ p(TeO 2, g) /kPa ±0.1} = 18.64 − 30863.2 · (K/T). The Gibbs energy of formation of BaTeO 3(s) was computed from the values of ln{ p(TeO 2, g) /kPa} and the values of ΔfGmofor BaO(s) and TeO 2(g) taken from the literature and is given by { ΔfGmo(BaTeO 3, s, T) /kJ · mol −1± 1.0} =−856.5 + 0.2067 · (T/K).The enthalpy increments of BaTeO 3(s) were measured using a high-temperature Calvet micro-calorimeter in the temperature range 304 K to 1000 K. Enthalpy increment values are represented by a polynomial of the form { Ho(T)−Ho(298.15 K)}/(J · mol−1) =−39 190+118.96·(T/K)+4.235·10−3·(T/K)2+9.975·105·(K/T), with an accuracy of ±0.4 per cent over the interval (304 ⩽T/K⩽ 1000).

Thermodynamics of formation of ammonium, sodium and potassium alums and chromium alums

The Pitzer ion-interaction model has been used for thermodynamic simulation of the binary Cr 2(SO4) 3H2O, KCr(SO4) 2H2O, and ternary (NH 4) 2SO 4Al 2(SO 4) 3H 2O, Na 2SO 4Al 2(SO 4) 3H 2O, K 2SO 4Al 2(SO 4) 3H 2O, (NH 4) 2SO 4Cr 2(SO 4) 3H 2O, Na 2SO 4Cr 2(SO 4) 3H 2O, and K 2SO 4Cr 2(SO 4) 3H 2O systems at T=298.15 K. The optimum values of the binary parameters of ionic interactions for chromium solutions have been calculated using osmotic data for unsaturated binary solutions. The mixing parameters have been chosen on the basis of the compositions of saturated ternary solutions and data on the binary solubility of the alums and chromium alums in water. Good agreement between experimentally determined and calculated solubilities has been found. Important thermodynamic characteristics (thermodynamic solubility product, standard molar Gibbs energy of formation) of the solid phases (simple and double salts) crystallizing in the systems under consideration are determined.

Solid-Solute Phase Equilibria in Aqueous Solutions XVII [I]. Solubility and Thermodynamic Data of Nickel(II) Hydroxide

The solubility of nickel(II) hydroxide (theophrastite) in water was determined as a function of temperature and ionic strength by the pH variation method. In each experiment the inert electrolyte medium was made up with sodium perchlorate. The experimental data were thermodynamically analyzed, and the standard solubility constant was extrapolated to zero ionic strength with the specific ion-interaction equation. Furthermore, the standard molar Gibbs energy and the enthalpy of formation for theophrastite, β-Ni(OH)2, were evaluated. For all calculations, ChemSage and its optimizer routine were used.

Thermodynamic Studies on NdFeO3(s)

The enthalpy increments and the standard molar Gibbs energy of formation of NdFeO3(s) have been measured using a high-temperature Calvet microcalorimeter and a solid oxide galvanic cell, respectively. A λ-type transition, related to magnetic order–disorder transformation (antiferromagnetic to paramagnetic), is apparent from the heat capacity data at ∼687 K. Enthalpy increments, except in the vicinity of transition, can be represented by a polynomial expression: {H°m(T)−H°m(298.15 K)}/J·mol−1 (±0.7%)=−53625.6+146.0(T/K) +1.150×10−4(T/K)2 +3.007×106(T/K)−1; (298.15≤T/K ≤1000). The heat capacity, the first differential of {H°m(T)−H°m(298.15 K)} with respect to temperature, is given by Cop, m/J·K−1·mol−1=146.0+2.30×10−4(T/K)−3.007×106(T/K)−2. The reversible emf's of the cell, (−) Pt/{NdFeO3(s) +Nd2O3(s)+Fe(s)}//YDT/CSZ//{Fe(s)‘FeO’(s)}/Pt(+), were measured in the temperature range from 1004 to 1208 K. It can be represented within experimental error by a linear equation: E/V:(0.1418±0.0003)−(3.890±0.023)×10−5(T/K). The Gibbs energy of formation of solid NdFeO3 calculated by the least-squares regression analysis of the data obtained in the present study, and data for Fe0.95O and Nd2O3 from the literature, is given by ΔfG°m(NdFeO3, s)/kJ·mol−1(±2.0)=−1345.9+0.2542(T/K); (1000≤T/K ≤1650). The error in ΔfG°m(NdFeO3, s, T) includes the standard deviation in emf and the uncertainty in the data taken from the literature. Values of ΔfH°m(NdFeO3, s, 298.15 K) and S°m(NdFeO3, s, 298.15 K) calculated by the second law method are −1362.5 (±6) kJ·mol−1 and 123.9 (±2.5) J·K−1·mol−1, respectively. Based on the thermodynamic information, an oxygen potential diagram for the system Nd–Fe–O was developed at 1350 K.

Thermodynamic study of the KMgAlClSO 4H 2O system at the temperature 298.15 K

The Pitzer ion-interaction model has been used for thermodynamic simulation of the binary AlCl 3H 2O, Al 2(SO4) 3H2O, ternary KClAlCl 3H 2O, K 2SO 4Al 2(SO 4) 3H 2O, MgCl 2AlCl 3H 2O, MgSO 4Al 2(SO 4) 3H 2O, and the quaternary KClMgCl 2AlCl 3H 2O systems at T=298.15 K. The optimum values of the binary parameters of ionic interactions for aluminum solutions have been calculated using activity data up to saturation of solutions. The ternary parameters have been chosen on the basis of the compositions of saturated ternary solutions taking into account the unsymmetrical mixing terms. Good agreement between experimentally determined and calculated solubilities has been found. Important thermodynamic characteristics (thermodynamic solubility product, standard molar Gibbs energy of formation) of the solid phases (simple and double salts) crystallizing in the systems under consideration are determined.