Thermodynamic properties for Sm₂(MoO₄)₃ determined by calorimetric measurement and re-evaluation of heat capacities for elemental molybdenum: standard entropy, Néel temperature, solubility product

Abstract

The thermodynamic properties for Sm₂(MoO₄)₃ were investigated. Sm₂(MoO₄)₃ is the one of the yellow phase-related substances. Yellow phases are known as hygroscopic harmful phases in the nuclear fuel glasses. The standard molar entropy, $\Delta_{0}^{T} S_{\text{m}}^{^\circ }$, at 298.15 K of Sm₂(MoO₄)₃ was determined by measuring its isobaric heat capacities, $C_{{{p},{\text{m}}}}^{^\circ }$, from 2 K via the fitting functions including the Debye–Einstein formula and electronic as well as magnetic terms. The Néel temperature, T_N, was estimated by extrapolating the magnetic term in the fitting function. Its standard Gibbs energy of formation, $\Delta_{\text{f}} G_{\text{m}}^{^\circ }$, was determined by combining the obtained $\Delta_{0}^{T} S_{\text{m}}^{^\circ }$ datum with the reference datum of the standard enthalpy of formation,$\Delta_{\text{f}} H_{\text{m}}^{^\circ }$, where $\Delta_{0}^{T} S_{\text{m}}^{^\circ }$ at 298.15 K of the elemental molybdenum as the standard state was re-evaluated by re-reviewing the literature. The unknown standard Gibbs energy of solution, $\Delta_{\text{sln}} G_{\text{m}}^{^\circ }$, and the solubility product, K_s, at 298.15 K for Sm₂(MoO₄)₃ were predicted on the basis of the data obtained in this study and the reference datum of  MoO₄²⁻(aq) and Sm³⁺(aq). The thermodynamic values determined in the present study are as follows:

$$\Delta_{0}^{T} S_{\text{m}}^{^\circ } \left( {{\text{Sm}}_{2} \left( {{\text{MoO}}_{4} } \right)_{3} \left( {\text{cr}} \right), \, 298.15 {\text{K}}} \right)/\left( {{\text{J K}}^{ - 1} {\text{mol}}^{ - 1} } \right) = 400.14 \pm 4.00,$$

$$\Delta_{\text{f}} G_{\text{m}}^{^\circ } \left( {{\text{Sm}}_{2} \left( {{\text{MoO}}_{4} } \right)_{3} \left( {\text{cr}} \right), \, 298.15 {\text{K}}} \right)/\left( {{\text{kJ}}\;{\text{mol}}^{ - 1} } \right) = - 4048.71 \pm 4.45,$$

$$\Delta_{\text{sln}} G_{\text{m}}^{^\circ } \left( {{\text{Sm}}_{ 2} \left( {{\text{MoO}}_{ 4} } \right)_{ 3} \left( {\text{cr}} \right),\; 2 9 8. 1 5 {\text{K}}} \right)/\left( {{\text{kJ}}\;\left( {{\text{mol of MoO}}_{ 4}^{ 2- } \left( {\text{aq}} \right)} \right)^{ - 1} } \right) = 6 8. 5 6\pm 1. 8 8 ,$$

$$K_{\text{s}} \left( {\frac{1}{3} {\text{Sm}}_{2} \left( {{\text{MoO}}_{4} } \right)_{3} \left( {\text{aq}} \right),\;298.15{\text{K}}} \right) = 9.75 \times 10^{ - 13} \pm 1.95 \times 10^{ - 13} ,$$

$$T_{\text{N}} /{\text{K}} = 1. 30 \pm 0. 30,$$

$$\Delta_{0}^{T} S_{\text{m}}^{^\circ } \left( {{\text{Mo}}\left( {\text{cr}} \right), \, 298.15\,{\text{K}}} \right)/\left( {{\text{JK}}^{ - 1} {\text{mol}}^{ - 1} } \right) = 28.573 \pm 0.086.$$

These data are expected to be useful for geo-chemical simulation of diffusion of radioactive elements through underground water.

Graphical abstract