The Gibbs free energy of formation and heat capacity of β-Rh 2O 3 and MgRh 2O 4, the MgORhO phase diagram, and constraints on the stability of Mg 2Rh 4+O 4

Abstract

The oxygen potentials of the reactions 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 O 2(β − Rh 2O 3 (±63 J · mol −1) = −278500 + 283.8T − 11.69T ln T (860 K < T < 1355 K) and μ O 2( MgRh 2O 4 (±63 J · mol −1) = 297314 + 369.405T − 23.3338T ln T (940 K < T < 1495 K) . The constant pressure heat capacities of β-Rh 2O 3 and MgRh 2O 4 were measured with a differential scanning calorimeter operated in step heating mode between 360 K and I065 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− Rh 2O 3) = 123.6 + 0.0141T − 208.8T −0.5 − 2312000T −2 and C p (MgRh 2O 4) = 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-Rh 2O 3, but with a much lower value for S 298.15, β-Rh 2O 3 (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-Rh 2O 3) 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 MgRh 2 3+O 4 and Mg 2Rh 4+O 4 and the interpretation of the data for μ O 2(MgRh 2O 4) 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 MgRh 2 3+O 4 in spinel ( X MgRh 2O 4 ) in equilibrium with MgO and Rh at 1373 K was estimated to be about 0.92. (i.e., X Mg 2RhO 4 ≈ 0.08). This provides a calibration point for determining the temperature dependence of a MgRh 2O 4 spinel in MgRh 2 3+O 4-Mg 2Rh 4+O 4 solid solutions. A third-law analysis showed that, once corrected for a MgRh 2O 4 spinel, our data for μ O 2(MgRh 2O 4) and C p(MgRh 2O 4) are fully consistent. The calculated value for S 298.15, β-Rh 2O 4 is 105.75 ± 2 J · mol −1 · K −1 . This is in reasonable agreement with the assumption of additive oxide entropies ( S 298.15,MgRh 2O 4≈ 98.4 · J · mol −1 · K −1, using our new value of S 298.15, β-Rh 2O 3 . We, therefore, conclude that our data for β-Rh 2O 3 and MgRh 2 3+O 4 are internally consistent. From the third-law analysis it is also possible to determine the activity of Mg 2Rh 4+O 4, in MgRh 2 3+O 4-Mg 2Rh 4+O 4 solid solutions ( a Mg 2RhO 4 spinel) as a function of temperature. The data for a Mg 2RhO 4 spinel may be combined with the emf measurements for the spinel + MgO + Rh assemblage to evaluate the Gibbs free energy of formation of Mg 2Rh 4+O 4: δ fG O Mg 2RhO 4,T (±6000 J · mol −1) = −100076.3 + 100.0T (1008 < T < 1495 K) We conclude that Mg 2Rh 4+O 4 is an important component in rhodate spinels at high temperatures, thus extending the stability field of spinel in the MgORhO system.