ABSTRACT

Thermochemical data for solution at 25°C and 1 atm (ΔG_s°, ΔH_s° and ΔS_s°) of fully isomorphous LnES₃·9H₂O (ES = C₂H₅SO₄^-) and partly isomorphous LnCl₃·nH₂O (n = 7 for La-Pr and n = 6 for Nd-Lu) are discussed, because they provide important clues to understand the tetrad effects in REE patterns of geochemical samples. All the differences in ΔH_s°, ΔG_s° and ΔS_s° between LnCl₃·6H₂O and LnES₃·9H₂O show convex tetrad effects, and they correspond to ΔH_r, ΔG_r and ΔS_r for the reaction series: LnCl₃·6H₂O (c) + 3(ES^-)(aq) + 3H₂O(l) = LnES₃·9H₂O(c) + 3Cl^-(aq). The convex tetrad effects are explained by the refined spin-pairing energy theory (RSPET) and thermodynamic principles: LnES₃·9H₂O have larger Racah (E¹ and E³) parameters than LnCl₃·6H₂O by about 0.5% and 1%, respectively. The differences in E¹ and E³ relate to minute but significant differences in dissociation energies for bondings of Ln³⁺ ions with ligands, and then to ΔH_r and the vibrational entropy differences of ΔS_r(vib). They emerge as convex tetrad effects in ΔH_r and ΔS_r. A similar tetrad effect is seen in ΔG_r, because ΔH_r dominates in ΔG_r = ΔH_r - TΔS_r for the low temperature reactions. Each series variation of ΔH_s°, ΔG_s° or ΔS_s° for LnES₃·9H₂O or LnCl₃·6H₂O consists of (i) a tetrad effect due to the differences in Racah parameters between Ln³⁺(aq) and each isomorphous Ln(III) hydrate series, (ii) an irregularity caused by the hydration change of light Ln³⁺(aq) from nonahydrate to octahydrate with going from La to Tb, and (iii) the smooth residual variation. Concave tetrad effects are seen in ΔH_s°, ΔG_s° and ΔS_s° for heavy LnES₃·9H₂O, but no such variations in those for heavy LnCl₃·6H₂O. This means the Racah parameters decreasing in the order: LnES₃·9H₂O > LnCl₃·6H₂O ≈ Ln³⁺(aq, octahydrate). The RSPET makes it possible to determine the irregularity due to the hydration change of light Ln³⁺(aq) from ΔH_s°, ΔG_s° or ΔS_s° for the two isomorphous Ln(III) hydrate series. The irregularity is the thermodynamic parameter (ΔH_h^∗, ΔS_h^∗ or ΔG_h^∗) for the stabilization of real light Ln³⁺(aq) relative to octahydrate Ln³⁺(aq).