Solubility of calcium molybdate in aqueous solutions at 573 K and thermodynamics of monomer hydrolysis of Mo(VI) at elevated temperatures

Abstract

This study presents new experimental results on solubility of synthetic crystalline calcium molybdate, CaMoO₄(cr), at 573 K and pressure ~ 10 MPa in aqueous solutions of HCl (10⁻⁴–0.02 m), HClO₄ (10⁻⁴–0.03 m), NaCl (0–3.82 m) and NaClO₄ (0.10–1.61 m). In addition, the thermodynamic analysis of literature and own data allowed recommendations of the equilibrium constants, $\log_{10} {{K}}^{\text {o}}$, of the reactions H⁺ + MoO₄ ²⁻ = HMoO₄ ⁻, MoO₃(cr) + OH⁻ = HMoO₄ ⁻, MoO₃(cr) + H₂O(l) = H₂MoO₄(aq), and 2H⁺ + MoO₄ ²⁻ = H₂MoO₄(aq) at temperatures 273–623 K and the saturated water vapor pressure, P _s. Knowledge of the thermodynamic properties of the molybdate ion, MoO₄ ²⁻ (this work), Ca²⁺, and of calcium molybdate CaMoO₄(cr) allowed calculating the values of the solubility product of this phase at temperatures 273–623 K and P _s. The thermodynamic modeling of solubility of CaMoO₄(cr) at 573 K and P _s in studied aqueous solutions (HCl, HClO₄, NaCl, and NaClO₄) showed that all our experimental data can be reproduced using the same set of species, which includes only the molybdate ion, MoO₄ ²⁻, and products of its hydrolysis, HMoO₄ ⁻ and H₂MoO₄(aq). Although the formation of ion pairs involving Na⁺ and the molybdate and hydrogenmolybdate ions at high temperatures appears likely due to the fall of the dielectric constant of water, the current data do not support the formation of such forms of Mo(VI), at least they are never the dominating species at conditions of presented experiments. The increase of temperature leads to the expansion of the predominance field of the hydrogenmolybdate ion HMoO₄ ⁻ and of H₂MoO₄(aq) and the decrease of the relative share of MoO₄ ²⁻.

Graphical abstract

Appendix: Temperature dependence of the second ionization constant of H2SO4 at the saturated water vapor pressure

Thermodynamic properties of ions SO₄ ²⁻ and HSO₄ ⁻ at 298.15 K, 0.1 MPa are known with high precision, see Table 10. From there, for reaction (A1)

Table 10 Thermodynamic properties of reactants/products of reaction (A1)

$${\text{H}}^{ + } + {\text{SO}}_{ 4}^{ 2- } = {\text{HSO}}_{ 4}^{ - }$$

(A1)

one calculates at 298.15 K $\Delta_{\text{r}} H_{\text{m}}^{\text{o}}$ = 22.44 kJ mol⁻¹, $\Delta_{\text{r}} S_{\text{m}}^{\text{o}}$ = 113.2 J K⁻¹ mol⁻¹, $\Delta_{\text{r}} C_{{p , {\text{m}}}}^{\text{o}}$ = 258 J K⁻¹ mol⁻¹. Literature values of equilibrium constants of reaction (A1) at the saturated water pressure (P _s), given in Table 11, have been used to find parameters of Eq. (A2):

Table 11 Studies of the second ionization constant of H₂SO₄, which results have been used to derive the parameters of Eq. (A2) at the saturated water pressure

$$\log_{10} K^{\text{o}} = 1. 5 7 90 \times 10^{ 4} /T - 6 9 8. 6 3 + 1 2 8. 7 9 {\text{ln}}T - 0. 3 3 6 6 7T + 1. 60 20 \times 10^{ - 4} T^{ 2}$$

(A2)

The relation (A2) was constrained in such a way to exactly reproduce the values of the thermodynamic functions of reaction (A1) at 298.15 K.

Values of equilibrium constants of reaction (A1) at temperatures above 373 K have been determined in a number of studies, see Table 11. Studies of $K^{\text{o}}$ based on measurements of solubility of sulfates [70, 71] have not been accepted, because they provide lower values of the second ionization constant of H₂SO₄ at highest temperatures, presumably due to difficulties of interpretation of experimental results. Values of $K^{\text{o}}$ at temperatures 473 and 573 K reported in [72] are significantly (up to 1.7 log₁₀ units) larger than the values reported by the same research group in an earlier study [73], and the earlier results [73] were rejected. In cases, where measurements have been performed at pressures exceeding the saturated water vapor pressure, values of $\log_{10} K^{\text{o}}$ have been extrapolated to P _s using the dependence of $\log_{10} K^{\text{o}}$ on the water density recommended in [57], see their Eqs. (27) and (28). When necessary, values of equilibrium constants have been recalculated to the molality concentration scale.

Experimental and calculated values of $\log_{10} K^{\text{o}}$ are shown in Fig. 19. Smoothed values of $\log_{10} K^{\text{o}}$ and thermodynamic functions of reaction (A1) at temperatures 273.15–623.15 K are given in Table 12.

Fig. 19

Experimental (symbols) and calculated (the curve) values of $\log_{10} K^{\text{o}}$ of reaction (A1)

Table 12 Calculated thermodynamic quantities for reaction (A1) along the liquid–vapor saturation curve of water