Internally consistent thermodynamic data for magnesium sulfate hydrates

Experimental studies on the stability of several Mg-sulfate hydrates including epsomite (MgSO₄·7H₂O), hexahydrite (MgSO₄·6H₂O), starkeyite (MgSO₄·4H₂O), and kieserite (MgSO₄·H₂O) as a function of temperature and relative humidity are in poor agreement with calculations based on thermodynamic properties of these substances taken from the literature. Therefore, we synthesized four different MgSO₄ hydrates and measured their enthalpies of formation by solution calorimetry at T = 298.15 K. The resulting enthalpies of formation from the elements are:

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Δ_fH⁰₂₉₈ (epsomite) = −3387.7 ± 1.3 kJmol⁻¹

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Δ_fH⁰₂₉₈ (hexahydrite) = −3088.1 ± 1.1 kJmol⁻¹

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Δ_fH⁰₂₉₈ (sanderite, MgSO₄·2H₂O) = −1894.9 ± 1.3 kJmol⁻¹

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Δ_fH⁰₂₉₈ (kieserite) = −1612.4 ± 1.3 kJmol⁻¹

Using mathematical programming (MAP) techniques, standard thermodynamic values consistent both with our calorimetric data and previously published humidity brackets could be derived:

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Epsomite: Δ_fH⁰₂₉₈ = −3388.7 kJmol⁻¹, S⁰₂₉₈ = 371.3 Jmol⁻¹ K⁻¹, Δ_fG⁰₂₉₈ = −2871.0 kJmol⁻¹

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Hexahydrite: Δ_fH⁰₂₉₈ = −3087.3 kJmol⁻¹, S⁰₂₉₈ = 348.5 Jmol⁻¹ K⁻¹, Δ_fG⁰₂₉₈ = −2632.3 kJmol⁻¹

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Starkeyite: Δ_fH⁰₂₉₈ = −2496.1 kJmol⁻¹, S⁰₂₉₈ = 259.9 Jmol⁻¹ K⁻¹, Δ_fG⁰₂₉₈ = −2153.8 kJmol⁻¹

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Kieserite: Δ_fH⁰₂₉₈ = −1611.5 kJmol⁻¹, S⁰₂₉₈ = 126.0 Jmol⁻¹ K⁻¹, Δ_fG⁰₂₉₈ = −1437.9 kJmol⁻¹

Additionally, heat capacity measurements and standard entropy determinations of several magnesium sulfate hydrate minerals from the literature are analyzed and judged against estimates obtained from a linear combination of the heat capacities of MgSO₄ and hexagonal ice. The results of the MAP analysis are compared to these estimates to conclude that heat capacity and entropy correlate well with the number of waters of hydration. However, even the good correlation is not good enough to capture the fine variations in these properties. Consequently, their experimental measurement is inevitable if reliable thermodynamic data are sought. Our MAP thermodynamic data show that epsomite, hexahydrite, and kieserite have stability fields in the T-%RH space. Starkeyite is metastable. Although no MAP data could have been derived for pentahydrite (MgSO₄·5H₂O) and sanderite, their transient existence suggest that both of them are metastable as well.