The utilization of galvanic cells using Caβ″-Alumina solid electrolytes in a thermodynamic investigation of the CaO- AI2O3 system

Caβ″-alumina solid electrolytes have been used in calcium concentration electrochemical cells to determine the standard free energies of formation of the calcium aluminates, from their constituent oxides, in the temperature ranges specified: (1) CaO(s) + 6Al₂O₃(s) → CaO6Al₂0₃(s) ΔG° =-4270.9 - 9.4r(K)(±200)cal = -17869.4 - 39.3T (±840)J; 1100 to 1500 K. (2) CaO(s) + 2Al₂O₃(s) → CaO.2Al₂O₃(s) ΔG° = -3087.1 - 6.39HK) (±300)cal = -12916.4 -26.74T (±1260)J; 1100 to 1500 K. (3) CaO(s) + Al₂O₃(s)→ CaO-Al₂O₃(s) ΔG° = -3612.1 -4.35T(K) (±200)cal = -15113.0 - 18.2r(±840)J; 1050 to 1500 K. (4) 3CaO(s) + Al₂O₃(s) → 3CaO-Al₂O₃(s) ΔG° = -1868.7 - 7.05T(K)(±200)cal = -7818.6 - 29.57(±840)J; 1050 to 1320 K.     

On the Gibbs energy of formation of wustite

Gibbs energy change for the reactionxFe_(s) + 1/2O_2(g) = Fe _x O_(s) has been redetermined using the galvanic cell (−) Fe_(s), Fe _x O_(s)∥ZrO₂ − CaO∥NiO_(s), Ni_(s)(+) in the temperature range 866 to 1340 K. The results are at variance with earlier works in that they reflect the transformations occurring in the iron phase. The Gibbs energy function is represented by two nonlinear equations,viz., ΔG° (866 to 1184 K) = −251480 − 18.100T + 10.187T lnT ± 210 J/mol and ΔG° (1184 to 1340 K) = −286248 + 181.419T - 13.858T lnT ± 210 J/mol. Formerly Research Assistant at the Department of Theoretical Metallurgy, The Royal Institute of Technology, Stockholm     

Equilibrium phase relations and thermodynamics of the Cr-0 system in the temperature range of 1500 °C to 1825 °C

Phase relations and thermodynamic properties of the Cr-O system were studied at temperatures from 1500 °C to 1825 °C. In addition to Cr and Cr₂O₂, a third crystalline phase was found to be stable in the temperature range from 1650 °C to 1705 °C. The atomic ratio of oxygen to chromium of this phase, which decomposes upon cooling to form Cr and Cr₂O₃, was determined as 1.33 + 0.02, in good agreement with the formula Cr₃O₄. Temperatures and phase assem blages for invariant equilibria of the Cr-O system were determined as follows: Cr₂O₃ + Cr + Cr₃O₄, 1650 °C ± 2 °C; Cr₃O₄ + Cr + liquid oxide, 1665 °C ± 2 °C; and Cr₃O₄ + Cr₂O₃ + liquid oxide, 1705 °C ± 3 °C. The composition of the liquid oxide phase at the eutectic temperature of 1665 °C was found to be close to CrO. Relations between oxygen pressure and temperature for the univariant equilibria of the Cr-O system were established by equilibrating Cr and/or Cr₂O₃ starting materials in H₂-CO₂ mixtures of known oxygen potentials at temper atures from 1500 ΔC to 1825 °C. From this information, the standard free-energy changes (ΔGΔ) for various reactions were calculated as follows: 2Cr (s) + 3/2O₂ = Cr₂O₃ (s): ΔG ° = -1,092,442 + 237.94T Joules, 1773 to 1923 K; 3Cr (s) + 2O₂ = Cr₂O₄ (s): ΔG ° =-1,355,198 + 264.64T Joules, 1923 to 1938 K; and Cr (s) + l/2O₂ = CrO (1): ΔG ° =-334,218 + 63.81T Joules, 1938 to 2023 K. Formerly Graduate Research Assistant, The Pennsylvania State University Formerly Professor     

Gibbs energies of formation of intermetallic phases in the systems Pt-Mg,Pt-Ca,and Pt-Ba and some applications

The standard Gibbs energies of formation of platinum-rich intermetallic compounds in the systems Pt-Mg, Pt-Ca, and Pt-Ba have been measured in the temperature range of 950 to 1200 K using solid-state galvanic cells based on MgF2, CaF2, and BaF2 as solid electrolytes. The results are summarized by the following equations: ΔG° (MgPt₇) = −256,100 + 16.5T (±2000) J/mol ΔG° (MgPt₃) = −217,400 + 10.7T (±2000) J/mol ΔG° (CaPt₅) = −297,500 + 13.0T (±5000) J/mol ΔG° (Ca₂Pt₇) = −551,800 + 22.3T (±5000) J/mol ΔG° (CaPt₂) = −245,400 + 9.3T (±5000) J/mol ΔG° (BaPt₅) = −238,700 + 8.1T (±4000) J/mol ΔG° (BaPt₂) = −197,300 + 4.0T (±4000) J/mol where solid platinum and liquid alkaline earth metals are selected as the standard states. The relatively large error estimates reflect the uncertainties in the auxiliary thermodynamic data used in the calculation. Because of the strong interaction between platinum and alkaline earth metals, it is possible to reduce oxides of Group ILA metals by hydrogen at high temperature in the presence of platinum. The alkaline earth metals can be recovered from the resulting intermetallic compounds by distillation, regenerating platinum for recycling. The platinum-slag-gas equilibration technique for the study of the activities of FeO, MnO, or Cr₂O₃ in slags containing MgO, CaO, or BaO is feasible provided oxygen partial pressure in the gas is maintained above that corresponding to the coexistence of Fe and “FeO.” Formerly Professor and Chairman, Department of Metallurgy, Indian Institute of Science Formerly Visiting Scientist, Department of Metallurgy, Indian Institute of Science     

Determination of standard free energies of formation of Ca3P2 and Ca2Sn at high temperatures

The standard free energies of formation of calcium phosphide and calcium stannide were determined by a chemical equilibration technique, yielding the following results: 3Ca(1) + P₂(g) = Ca₃P₂(s) ΔG° = −653,460(±7110) + 144.01(±4.98)T (J/mol)1000 °C to 1300 °C2Ca(1) + Sn(1) = Ca₂Sn(s) ΔG° = −353,970(±1670) + 79.28(±1.26)T (J/mol)1000 °C to 1300 °C 1120 °C The experimental data to express the thermodynamics for removal of phosphorus and tin from molten iron by calcium based slags by other investigators were discussed in terms of the activity co-efficients of Ca₃P₂ and Ca₂Sn in slag melts by using the present results described above.     

Determination of standard free energies of formation of Ca3P2 and Ca2Sn at high temperatures

The standard free energies of formation of calcium phosphide and calcium stannide were determined by a chemical equilibration technique, yielding the following results: 3Ca(1) + P₂(g) = Ca₃P₂(s) ΔG° = −653,460(±7110) + 144.01(±4.98)T (J/mol)1000 °C to 1300 °C2Ca(1) + Sn(1) = Ca₂Sn(s) ΔG° = −353,970(±1670) + 79.28(±1.26)T (J/mol)1000 °C to 1300 °C 1120 °C The experimental data to express the thermodynamics for removal of phosphorus and tin from molten iron by calcium based slags by other investigators were discussed in terms of the activity co-efficients of Ca₃P₂ and Ca₂Sn in slag melts by using the present results described above.     

Activities of oxygen in liquid Bi,Sn, and Ge from electrochemical measurements

Modified coulometric titrations on the galvanic cell: O in liquid Bi, Sn or Ge/ZrO₂( + CaO)/Air, Pt, were performed to determine the oxygen activities in liquid bismuth and tin at 973, 1073 and 1173 and in liquid germanium at 1233 and 1373 K. The standard Gibbs energy of solution of oxygen in liquid bismuth, tin and germanium for 1/2 O₂ (1 atm) →O (1 at. pct) were determined respectively to be ΔG° (in Bi) = −24450 + 3.42T (±200), cal· g-atom⁻¹ = − 102310 + 14.29T (±900), J·g-atom⁻¹, ΔG° (in Sn) = −42140 + 4.90T (±350), cal· g-aton⁻¹ = −176300 + 20.52T (± 1500), J-g-atom⁻¹, ΔG° (inGe) = −42310 + 5.31 7 (±300), cal·g-atom⁻¹ = −177020 + 22.21T(± 1300), J· g-atom⁻¹, where the reference state for dissolved oxygen was an infinitely dilute solution. It was reconfirmed that the modified coulometric titration method proposed previously by two of the present authors produced far more reliable results than those reported by other investigators. TOYOKAZU SANO, formerly a Graduate Student, Osaka University     

Stability of chromium (III) sulfate in atmospheres containing oxygen and sulfur

The stability of chromium (III) sulfate in the temperature range from 880 to 1040 K was determined by employing a dynamic gas-solid equilibration technique. The solid chromium sulfate was equilibrated in a gas stream of controlled SO₃ potential. Thermogravimetric and differential thermal analyses were used to follow the decomposition of chromium sulfate. Over the temperature range studied, the change in the Gibbs’ free energy of formation of chromium sulfate Cr₂O₃(s) + 3SO₃(g) → Cr₂(SO₄)₃(s) can be expressed as ΔG⁰ = •143,078 + 129.6T (±300) cal mole^•1 ΔG⁰ = •598,350 + 542T (±1250) J mole^•1. X-ray diffraction analysis indicated that the decomposition product was crystalline Cr₂O₃ and that the mutual solubility between Cr₂(SO₄)₃ and Cr₂O₃ was negligible. Over the temperature range investigated, the decomposition pressures were significantly high so that chromium sulfate is not expected to form on commercial alloys containing chromium when exposed to gaseous environments containing oxygen and sulfur (such as those encountered in coal gasification).     

The Decomposition equilibria of platinum di- and mono-chlorides by the simultaneous torque-knudsen technique

The decomposition equilibria of platinum dichloride have been found to consist of two decomposition steps, with chlorine molecules being the vapor species for both steps. An intermediate metastable PtCl solid is formed in the first step in addition to platinum metal and chlorine molecules. The platinum dichloride decomposes incongruently, the stepwise decomposition being PtCl₂ → PtCl → Pt. The PtCl₂ decomposition reactions consist of PtCl₂(s) = PtCl (metastables) + 1/2 Cl₂ (g) and PtCl₂(s) = Pt(s) + Cl₂ (g). The sum of the third lawΔH _{D, 298} K for the above two reactions is 214.637 ± 1.963 kJ/mole, in very good agreement with the second law ΔH_{D, 298 K} = 215.107 ± 13.062 kJ/mole. The second decomposition step is given by the reaction 2PtCl (metastables) = 2Pt(s) + Cl₂ (g) with a third law ΔH_{D, 298 K} = 127.356 ± 0.791 kJ/mole, in excellent agreement with the second law ΔH_{D, 298 K} = 127.509 ± 6.154 kJ/mole. The calculated heat of formation of PtCl₂ is -139 ± 2 kJ/mole and that of PtCl is -63 ± 1 kJ/mole. Formerly Graduate Assistant. Formerly Undergraduate Research Helper,     

Determination of standard gibbs energies of formation of MgO,SrO, and BaO

The standard Gibbs energy of formation of MgO was determined from the measurement of the ΔG° for the reaction ; by equilibrating Mg and Nb with a magnesia crucible and is expressed as follows: Mg(l)+ l/2O₂(g) = MgO(s) ΔG° = −657,000(±5000) + 141(±13)T [J/mol] (973 to 1323 K) The standard Gibbs energies of formation of SrO and BaO were determined by equilibrating silver and MO(M: Sr, and Ba) in a graphite crucible on the basis of the reactionM(in Ag) + CO (g) = MO (s) + C (s), yielding the following results:

High-temperature thermodynamic properties of the vanadium carbides V2C and VC0.73 determined using a galvanic cell technique

The standard free energies of formation of V₂C and VC_0.73 have been obtained from electromotive force (emf) measurements on the following galvanic cells with BaF₂-BaC₂ solid solutions as the electrolyte: Ta, Ta₂CBaF₂-BaC₂V, V₂ (850 to 1200K) (D) VC_0.73, V₂C BaF₂-BaC₂ Cr, Cr₂₃C₆ (850 to HOOK) (E) VC_0.73, V₂C BaF₂-BaC₂ Mo, Mo₂C (890 to 1247 K) (F) Combining the results of this study with previous work1151 and those of Kukarniet al., ^[19.25] the following equations for ΔG_f° of V₂C and VC_0.73 have been determined: From cell (D), ΔG_v2c°(±1263) = -152,824(±9200) + 5.45(±0.27)7 Joule for the reaction 2V + C = V₂C. From cell (E), ΔG_{vc 0.73}°(±662) = -96,790.8(±6511.7) + 7.0(±0.3)r Joule/g * atom V From cell (F), ΔG_{vc 0.73}°(±665) = -97,000(±4606) + 6.79(±0.78)J Joule/g * atom V for the reaction V + 0.73C = VC_0.73.     

Activities of oxygen in liquid copper and silver from electrochemical measurements

Modified coulometric titrations on the galvanic cell:O in liquid Cu or Ag / ZrO₂( + CaO) / Air, Pt, were performed to determine precisely the oxygen activities in liquid copper and silver in the range of relatively low oxygen concentration. The present experimental results were remarkably reproducible in comparison with the published data. The standard Gibbs energies of solution of oxygen in liquid copper and liquid silver for 1/2 O₂(l atm) → O(l at. pct) were determined respectively to be ΔG° (in Cu) = −18040 −0.03 T(K) (± 120) cal · g-atom−1 = −75500 −0.12 T(K)(± 500) J · g-atom−1, ΔG°(inAg)= -3860+ 1.56 T(K) (±90) cal · g-atom−1 = −16140 + 6.52 T(K)(±380) J · g-atom−1 where the reference state for dissolved oxygen was an infinitely dilute solution. The present value of the partial entropy of oxygen dissolved in liquid copper differs significantly from that suggested by many investigators. Further, the present equation for liquid copper has been found to be consistent with a correlation proposed previously by the present authors. The equation for liquid silver is in good agreement with the published ones.     

Activities of chromium in molten copper at dilute concentrations by solid-state electrochemical cell

In order to obtain the activities of chromium in molten copper at dilute concentrations (<0.008 chromium mole fractions), liquid copper was brought to equilibrium with molten CaCl₂ + Cr₂O₃ slag saturated with Cr₂O₃ (s), at temperatures between 1423 and 1573 K, and the equilibrium oxygen partial pressures were measured by means of solid-oxide galvanic cells of the type Mo/Mo + MoO₂/ZrO₂(MgO)/(Cu + Cr))alloy + Cr₂O₃ + (CaCl₂ + Cr₂O₃)_slag/Mo. The free energy changes for the dissolution of solid chromium in molten copper at infinite dilution referred to 1 wt pct were determined as Cr (s) = Cr(1 wt pct, in Cu) and ΔG° = + 97,000 + 73.3(T/K) ± 2,000 J mol⁻¹.     

Determination of the standard gibbs energies of formation of Ca3As2, Ca3Sb2, and Ca3Bi2

The standard Gibbs energies of formation of Ca₃As₂, Ca₃Sb₂, and Ca₃Bi₂ were determined by a chemical equilibration technique yielding the following results: 3Ca(1)+2As(1)=Ca₃As₂ (s) ΔG°=−723,800+172.8T (±23,700)(J/mol) 1273 to 1573 K 3Ca(1)+2Sb(1)=Ca₃Sb₂(s) ΔG°=−726,300+159.3T(±24,600) (J/mol) 1273 to 1573K 3Ca(1)+2Bi(1)=Ca₃Bi₂(s) ΔG°=−696,400+195.6T(±23,200) (J/mol) 1148 to 1323 K The thermodynamic data for removal of arsenic, antimony, and bismuth by other experimental investigations were discussed in terms of the activity coefficients of these compounds in slags. The stabilities of these compounds were also discussed by using the critical oxygen partial pressures calculated from the above equations. D.J. MIN, formerly Graduate Student, Department of Metallurgy, The University of Tokyo, Bunkyo-ku, Tokyo 113, Japan     

High-temperature thermodynamic stability of ditantalum carbide (Ta2C)

The CO(g) pressure in equilibrium with a Ta₂C-Ta₂O₅-Ta mixture has been measured at temperatures between 1740 and 1900 K using the torsion-effusion technique. From the equilibrium data, the following equation for ΔG°₂ of Ta₂C has been obtained: ΔG°₂ (±300) = −47,000 (±2200) +.IT From the enthalpy term in the ΔG°f equation, a value of —47.9 (±2.3) kcal/mole has been calculated for ΔH°₂₉₈ of Ta₂C which is in good agreement with several calorimetric results. This paper is based upon a thesis submitted by A. D. KULKARNI in partial fulfillment of the requirements of the degree of Doctor of Philosophy at the University of Pennsylvania.     

Determination of the standard gibbs energies of formation of Ba3P2 and Ba3(PO4)2

The standard Gibbs energies of formation of barium phosphide and barium orthophosphate were determined by a chemical equilibration technique yielding the following results: 3Ba(1)+P₂(g)=Ba₃P₂ (s) ΔG°=−732,000+156.1T(±12,800) (J/mol) 3BaO (s)+P₂(g)+5/2O₂(g)=Ba₃(PO₄)₂(s) ΔG°=−2,523,000+580.0T(±16,600) (J/mol) The stability and the thermodynamic behavior of barium compounds as reaction products of dephosphorization of steel were discussed in terms of the oxygen partial pressure and the activity coefficient of Ba_1.5P in molten Ba saturated with CaO. D.J. MIN, formerly Graduate Student, Department of Metallurgy, The University of Tokyo, Bunkyo-ku, Tokyo 113, Japan     

Solubility and activity of oxygen in liquid germanium and germanium-copper alloys

The solubility of oxygen in liquid germanium in the temperature range 1233 to 1397 K, and in liquid germanium-copper alloys at 1373 K, in equilibrium with GeO₂ has been measured by the phase equilibration technique. The solubility of oxygen in pure germanium is given by the relation log(at. pct 0)=-6470/T + 4.24 (±0.07). The standard free energy of solution of oxygen in liquid germanium is calculated from the saturation solubility, and recently measured values for the free energy of formation of GeO₂, assuming that oxygen obeys Sievert’s law up to the saturation limit. For the reaction, 1/2 O₂(g)→O_Ge ΔG° = -39,000 + 3.21T (±500) cal = -163,200 + 13.43T (±2100) J. where the standard state for dissolved oxygen is that which makes the value of activity equal to the concentration (in at. pct), in the limit, as concentration approaches zero. The effect of copper on the activity of oxygen dissolved in liquid germanium is found to be in good agreement with that predicted by a quasichemical model in which each oxygen was assumed to be bonded to four metal atoms and the nearest neighbor metal atoms to an oxygen atom are assumed to lose approximately half of their metallic bonds. On leave at the Department of Metallurgy and Materials Science, University of Toronto, when this investigation was undertaken.     

Calorimetrically measured enthalpies for the reaction of Hf with H(D) 2 (g)

The enthalpy for the direct reaction of H₂ (g) with Hf has been measured by calorimetry for the first time at both moderate, 334 K, and elevated, 919 K, temperatures. The enthalpy for the reaction: 1/2 H₂ (g) + 1/(b - a)HfH_a(α) → 1/(b - a)HfH_b(δ) is -70 ± 2.0 kJ/mol H at 334 K over a range of H contents from (H/Hf) = 0.5 to 1.5 with similar values found for D. The quantities α and δ are the coexisting phases anda andb are the corresponding (H/ Hf) ratios, respectively. The magnitude of the enthalpy decreases from (H/Hf) = 0 to 0.5 and is then stable from 0.5 to 1.7. The value of ΔH°_f (HfH_1.5) = -107.5 kJ/mol and ΔH°_f (HfH_2.0) = -142.0 kJ/mol. In the elevated temperature range, calorimetric and equilibrium hydrogen pressure were determined over the range of H contents from 0 to 1.6. The enthalpy for the plateau reaction is -74.5 kJ/mol H and after the two-phase region, |ΔH_H| increases with the increase of (H/Hf) passing through a maximum at about (H/Hf) = 1.3. Formerly Graduate Student, Department of Chemistry, University of Vermont     

Thermodynamic properties of Ni-S melts between 700° and 1100°c

The vapor pressure of sulfur over Ni-S melts of various compositions was calculated from the equilibrium weight of the melt in gas streams of known H₂S-H₂ composition. The Gibbs-Duhem equation was used to calculate the activity of nickel and other thermodynamic properties. For the reaction: 3Ni(S) + S₂(g) ⇌ Ni₃S₂(l) the suggested free energy rslationship is: ΔG° = -57,910 + 15.89T (800° to 1100°C). The Calculations were extrapolated to predict that for the reaction: Ni(s) + 1/2S₂(g) ⇌ NiS(l), ΔG° = -26.730 + 10.5T (1000° to 1100°C)     

The thermodynamics of volatilization of chromic oxide: Part I. the species CrO3 and CrO2 OH

A study has been made, using the transpiration technique, of the volatility of chromic oxide in oxygen-argon and oxygen-water vapor-argon mixtures in the approximate temperature range 1300 to 1585° . Volatilization is shown to occur by the reactions r₂O₃(s) + 3/2O₂ (g) =₃(g) and Cr₂O₃(s) + O₂ (g) + H₂O(g) = 2CrO₂OH(g). The standard Gibbs free energy changes are given byAG ⁰ = 472,800 (±6200) - 118.5 (±3.6) andAG ⁰ = 428,200 (±9400) — 119.4 (±5.6)TJ, respectively, where the reference state for the gases is one standard atmosphere.