Thermodynamic properties, low-temperature heat-capacity anomalies, and single-crystal X-ray refinement of hydronium jarosite, (H₃ O)Fe₃(SO₄)₂(OH)₆

Crystals of hydronium jarosite were synthesized by hydrothermal treatment of Fe(III)-SO₄ solutions. Single-crystal XRD refinement with R₁ = 0.0232 for the unique observed reflections ( F_o > 4σ_F and wR₂ = 0.0451 for all data gave a = 7.3559(8) Å, c = 17.019(3) Å, V^o = 160.11(4) cm³, and fractional positions for all atoms except the H in the H₃O groups. The chemical composition of this sample is described by the formula (H₃O) _0.91Fe_2.91(SO₄)₂[(OH) _5.64(H₂O)_0.18]. The enthalpy of formation (ΔH^o_f) is -3694.5 ± 4.6 kJ mol^-1, calculated from acid (5.0 N HCl) solution calorimetry data for hydronium jarosite, γ-FeOOH, MgO, H₂O, and α-MgSO₄. The entropy at standard temperature and pressure (S^o is 438.9 ± 0.7 J mol^-1 K^-1, calculated from adiabatic and semi-adiabatic calorimetry data. The heat capacity (C_p) data between 273 and 400 K were fitted to a Maier-Kelley polynomial C_p(T in K) = 280.6 + 0.6149T - 3199700T^-2. The Gibbs free energy of formation is - 3162.2 ± 4.6 kJ mol^-1. Speciation and activity calculations for Fe(III) - SO₄ solutions show that these new thermodynamic data reproduce the results of solubility experiments with hydronium jarosite. A spin-glass freezing transition was manifested as a broad anomaly in the C_p data, and as a broad maximum in the zero-field-cooled magnetic susceptibility data at 16.5 K. Another anomaly in C_p, below 0.7 K, has been tentatively attributed to spin cluster tunneling. A set of thermodynamic values for an ideal composition end member (H₃O)Fe₃(SO₄)₂(OH) ₆ was estimated ΔG^o_f = -3226.4 ± 4.6 kJ mol^-1, ΔH^o_f = -3770.2 ± 4.6 kJ mol^-1, S^o = 448.2 ± 0.7 J mol^-1 K^-1, C_p(T in K) = 287.2 + 0.6281T-3286000T^-2 (between 273 and 400 K).