The Gibbs free energy of formation and heat capacity of β-Rh₂o₃ and MgRh₂O₄, the MgO-Rh-O phase diagram, and constraints on the stability of Mg₂Rh⁴⁺O₄

The oxygen potentials of the reactions 4/3Rh + O₂ = 2/3β-Rh₂O₃ and 2/3MgO + 4/3Rh + O₂ = 2/3MgRh³⁺₂O₄ were measured using electrochemical cells of the type Pt, metal + oxide |CSZ|YDT (air), Pt. Relative to a reference pressure of 1 bar we find μ_O2(β-Rh2O3) (±63 J·mol^-1) = -278500 + 283.8T - 11.69T ln T (860 K < T < 1355 K) and μ_O2(MgRh2O4) (±110 J·mol^-1) = -297314 + 369.405T - 23.3338T ln T (940 K < T < 1495 K). The constant pressure heat capacities of β-Rh₂O₃ and MgRh₂O₄ were measured with a differential scanning calorimeter operated in step heating mode between 360 K and 1065 K. Best fits to the data (in J·mol^-1·K^-1 with an uncertainty of ±2 J·mol^-1·K^-1) give C_p(β-Rh₂O₃) = 123.6 + 0.0141T - 208.8T^-0.5 - 2312000T^-2 and C_p(MgRh₂O₄) = 174.0 + 0.014T - 4297000T^-2 A third law analysis showed satisfactory internal consistency of the Gibbs free energy of formation and heat capacity data of β-Rh₂O₃, but with a much lower value for S_{298.15,β-Rh2O3} (71.5 ± 1.5 J·mol^-1·K^-1 compared with 106.27 J·mol^-1·K^-1; Barin, 1989). This is attributed to the new C_p(β-Rh₂O₃) data that are significantly different from the original measurements of Wöhler and Jochum (1933) and the adjusted values of Barin (1989). Spinels prepared in the MgO-Rh-O system are solid solutions between MgRh³⁺₂O₄ and Mg₂Rh⁴⁺O₄ and the interpretation of the data for μ_O2(MgRh2O4) requires an understanding of phase relationships in the MgO-Rh-O system. From an isothermal projection of oxygen potentials onto the Mg-Rh binary at 1373 K, the mol fraction MgRh³⁺₂O₄ in spinel (X_MgRh2O4) in equilibrium with MgO and Rh at 1373 K was estimated to be about 0.92. (i.e., X_Mg2RhO4 ≈ 0.08). This provides a calibration point for determining the temperature dependence of a^spinel_MgRh2O4 in MgRh³⁺₂O₄-Mg₂Rh⁴⁺O ₄ solid solutions. A third-law analysis showed that, once corrected for a^spinel_MgRh2O4, our data for μ_O2(MgRh2O4) and C_p(MgRh₂O₄) are fully consistent. The calculated value for S_{298.15,MgRh2O4} is 105.75 ± 2 J·mol^-1·K^-1. This is in reasonable agreement with the assumption of additive oxide entropies (S_{298.15,MgRh2O4} ≈ 98.4 J·mol^-1·K^-1), using our new value of S_{298.15,β-Rh2O3}. We, therefore, conclude that our data for β-Rh₂O₃ and MgRh³⁺₂O₄ are internally consistent. From the third-law analysis it is also possible to determine the activity of Mg₂Rh⁴⁺O₄, in MgRh³⁺₂O₄-Mg₂Rh⁴⁺O ₄ solid solutions (a^spinel_Mg2RhO4) as a function of temperature. The data for a^spinel_Mg2RhO4 may be combined with the emf measurements for the spinel + MgO + Rh assemblage to evaluate the Gibbs free energy of formation of Mg₂Rh⁴⁺O₄: Δ_fG^o_Mg2RhO4,T (±6000 J·mol^-1) = -100076.3 + 100.0T (1008 < T < 1495 K) We conclude that Mg₂Rh⁴⁺O₄ is an important component in rhodate spinels at high temperatures, thus extending the stability field of spinel in the MgO-Rh-O system.