Energetics of Al₁₃ Keggin cluster compounds

Abstract

The ϵ-Al₁₃ Keggin aluminum hydroxide clusters are essential models in establishing molecular pathways for geochemical reactions. Enthalpies of formation are reported for two salts of aluminum centered ϵ-Keggin clusters, Al₁₃ selenate, (Na(AlO₄)Al₁₂(OH)₂₄(SeO₄)₄•12H₂O) and Al₁₃ sulfate, (NaAlO₄Al₁₂(OH)₂₄(SO₄)₄•12H₂O). The measured enthalpies of solution, ΔH_sol, at 28 °C in 5 N HCl for the ε-Al₁₃ selenate and sulfate are −924.57 (± 3.83) and −944.30 ( ± 5.66) kJ·mol^-1, respectively. The enthalpies of formation from the elements, ΔH_f,el, for Al₁₃ selenate and sulfate are −19,656.35 ( ± 67.30) kJ·mol^-1, and −20,892.39 ( ± 70.01) kJ·mol^-1, respectively. In addition, ΔH_f,el for sodium selenate decahydrate was calculated using data from high temperature oxide melt solution calorimetry measurements: −4,006.39 ( ± 11.91) kJ·mol^-1. The formation of both ε-Al₁₃ Keggin cluster compounds is exothermic from oxide-based components but energetically unfavorable with respect to a gibbsite-based assemblage. To understand the relative affinity of the ϵ-Keggin clusters for selenate and sulfate, the enthalpy associated with two S-Se exchange reactions was calculated. In the solid state, selenium is favored in the Al₁₃ compound relative to the binary chalcogenate, while in 5 N HCl, sulfur is energetically favored in the cluster compound compared to the aqueous solution. This contribution represents the first thermodynamic study of ε-Al₁₃ cluster compounds and establishes a method for other such molecules, including the substituted versions that have been created for kinetic studies. Underscoring the importance of ε-Al₁₃ clusters in natural and anthropogenic systems, these data provide conclusive thermodynamic evidence that the Al₁₃ Keggin cluster is a crucial intermediate species in the formation pathway from aqueous aluminum monomers to aluminum hydroxide precipitates.

Few subjects are more central to geochemistry and materials science than aluminum hydrolysis chemistry. From a geochemist’s perspective, aluminum hydrolysis products are key to mineral paragenesis and watershed chemistry. In addition, nanometer-size aluminum hydroxide molecules, including Al₁₃ ϵ-Keggin clusters, are critical to both experiment and simulation to detail possible reaction pathways at the solid–water interface (1). Aluminum clusters form complexes with a variety of reactive components including clay particles, natural organic matter, viruses, bacteria, and spores and thus are of interest to the environmental community for applications in water treatment and contaminant remediation technologies (2). Such clusters have also been used in a wide variety of industrial and consumer applications (3) and, because of their unique size and reactivity, they are effective as clay pillars (4) and catalysts (5).

At near-neutral and higher pH, the dominant multimeric aluminum complex in aqueous systems is the large polycation, [Al₁₂(AlO₄)(OH)₂₄(H₂O)₁₂]⁷⁺, which forms quickly via Al³⁺ hydrolysis and is a precursor to solid flocs (6). It consists of a central tetrahedrally coordinated AlO₄ moiety, enveloped by a sheath of 12 edge-shared AlO₆ units in four sets of three linked trimers. The most familiar form of this molecule, referred to as ε-Al₁₃, has a structure identical to the ϵ-isomer of the Baker–Figgis–Keggin structures (7–9). This isomer has edge-shared trimeric capping groups organized around a central tetrahedral AlO₄ site that is inert. Under favorable conditions, other isomers and larger clusters can be synthesized by hydrothermal reaction or by slow aging at room temperature (10).

Because high-purity crystals form when sulfate or selenate anions are added to cluster-containing solutions, the sulfate and selenate Al₁₃ Keggins have been widely studied, beginning with Johansson’s work decades ago (11). In addition, these salts can be back-extracted into an aqueous solution in the presence of aqueous BaCl₂ to release the ions , [M = Al(III), Ga(III), and Ge(IV)] (12), thus affording a wider range of experimental studies to be conducted on both the solid and solution phases.

The selenate or sulfate salts of these ε-Al₁₃ clusters crystallize with either monoclinic or cubic symmetry depending on the synthesis conditions (1, 13–15). However, if pH is carefully controlled and the crystals are given several days to grow, the pure cubic phase is readily obtainable (16).

Kinetic studies of these molecules have raised questions that can only be answered with detailed thermodynamic data. It is generally assumed that these clusters are an intermediate in the hydrolysis of aqueous aluminum species leading to eventual precipitation of aluminum hydroxides (e.g., gibbsite), but at present there are no thermodynamic data to test this hypothesis. Moreover, kinetic studies have raised speculation that strain affects the reactivity of the [Al₁₂(AlO₄)(OH)₂₄(H₂O)₁₂]⁷⁺ molecule relative to species containing other central tetrahedral ions [e.g., Ga(III) or Ge (IV)] (1). Such strain is likely to be evident in the enthalpies of formation, but again no data are currently available. Thus, the goal of this study is to obtain thermodynamic data, specifically enthalpies of solution, enthalpies of formation from the elements, and enthalpies of formation from oxide- and hydroxide-based assemblages, for two ε-Al₁₃ Keggin cluster compounds, Al₁₃ selenate (Na(AlO₄)Al₁₂(OH)₂₄(SeO₄)₄•12H₂O) and sulfate (Na(AlO₄)Al₁₂(OH)₂₄(SO₄)₄•12H₂O). These thermochemical quantities are necessary for understanding the formation and transformation pathways of such materials and are the start for a library of thermochemical data on substituted versions of nanometric aluminum clusters of different sizes and compositions. Thus we have synthesized and characterized the Al₁₃ sulfate and selenate crystalline materials and measured their enthalpies of solution in 5 N HCl.

These calorimetric data and those for auxiliary calorimetric reference materials are used in thermochemical cycles (see Tables S1 and S2) to calculate enthalpies of formation from oxides and elements and enthalpies of other reactions relevant to the formation and transformation of these clusters (Table 1).

Table 1.

Enthalpies of reactions involving ε-Al₁₃ Keggin sulfate and selenate cluster compounds at 298 K unless noted otherwise

Dissolution in 5 N HCl at 301 K [1]

Formation from calorimetric reference materials [2]

Formation from elements [3]

Formation from oxides [4]

Formation from sodium aluminate, corundum, sulfuric or selenic acid, and water [5]

Decomposition to gibbsite [6]

Exchange of S and Se between solid and aqueous solution (5 N HCl) [7]

All values in kJ/mol; xl = crystal, l = liquid, g = gas, sol = solution of ionic species in 5 N HCl.

References: Enthalpies of formation from the elements for all reactants are from ref. 25.

Results

Synthesis and Characterization.

The synthesis was straightforward using methods described later in the paper. The thermograms for ε-Al₁₃ selenate and sulfate Keggin crystals are in very good agreement with earlier studies (14). The DSC profile features two distinct endothermic events centered near 100 °C and 460 °C, both of which are due to water expulsion resulting in the loss of approximately 12 water and 24 hydroxyl equivalents, respectively (14). Above 460 °C the sulfate and selenate anions decompose. At sufficiently high temperature (e.g., above 900 °C) the final product is predominantly Al₂O₃ (14). The powder XRD pattern for the selenate Keggin is in excellent agreement with the published powder diffraction file (PDF) # 76-1750 (11). Although no PDF was available for the sulfate, very good agreement was observed between the XRD pattern in this study and that reported by Wang and Muhammed (14). Single crystal patterns for the selenate crystals are consistent with the powder diffraction results and the ²⁷Al-MAS-NMR. No extraneous peaks were observed in either the selenate or sulfate powder XRD patterns or in the ²⁷Al-NMR. To avoid impurities at less than a few percent, which would be difficult to rule out based only upon NMR or XRD, only well-faceted single crystals were selected for calorimetric study.

Solution Calorimetry.

Enthalpies of solution of ε-Al₁₃ selenate and sulfate cluster compounds and of relevant auxiliary compounds were measured in 5 N HCl at room temperature. To calculate enthalpies of formation of the cluster compounds (see Tables S1 and S2), the enthalpies of formation of the sodium sulfate and selenate must be known. This value is well established for sodium sulfate (17) but, in the case of sodium selenate decahydrate, we considered it prudent to verify the accuracy of the enthalpy of formation from the elements from Selinova and Sazykina (18), because that paper provided limited experimental and analytical detail. Therefore, we calculated ΔH_f,el for Na₂SeO₄·10H₂O from the newly measured enthalpy of formation from the oxides using high temperature oxide melt solution calorimetry. Because this reagent dehydrates rapidly (in minutes), care was taken to quantify the rate of dehydration with isothermal TG analysis. In addition, the sodium selenate decahydrate was dropped immediately into the calorimeter as agglomerated crystals rather than as pellets made from powdered sample to ensure consistency with respect to hydration. The associated thermochemical cycles and data are reported in Table S3. The resulting enthalpy of formation from Na₂O, SeO₂, O₂ and H₂O is −504.89 ( ± 11.12) kJ·mol^-1, and that from the elements is −4,006.39 ( ± 11.91) kJ·mol^-1. Selinova and Sazykina (18) reported ΔH_f,el = -4,003.67 kJ·mol^-1 but did not include any uncertainty in their measurements. This new value was used in thermochemical cycles to calculate, from acid solution calorimetric data, the enthalpy of formation of the Al₁₃ selenate compound.

Enthalpies of solution in 5 N HCl were measured for both ε-Al₁₃ selenate and sulfate compounds as well as for all auxiliary calorimetric reference materials (AlCl₃·6H₂O, NaOH, Na₂SeO₄·10H₂O, Na₂SO₄, and NaCl), and all individual data are reported in Tables S4 and S5, respectively. This concentration (5 N HCl) proved to be effective for rapid and complete dissolution of the Al₁₃ Keggin crystals; and to be consistent, the same conditions were required for all the other materials.

The ΔH_sol data, together with ΔH_f,el literature data for all materials except Na₂SeO₄·10H₂O, for which the newly measured enthalpy of formation was used, were applied to the appropriate thermochemical cycles (see Tables S1 and S2) in the following stepwise manner. From all of the enthalpy of solution data (ΔH₁-ΔH₆ in Tables S1 and S2), a reaction from the calorimetric reference materials and the associated enthalpy, ΔH₇, was obtained. Combining ΔH₇ and enthalpies of formation from the elements for all the calorimetric reference materials (ΔH₈-ΔH₁₂ in Tables S1 and S2) yielded ΔH_f,el for the appropriate Keggin compound. Finally, using ΔH_f,el, additional enthalpies for various environmentally relevant reactions were obtained. These enthalpies of solution, formation, and transformation reactions of the ε-Al₁₃ Keggin cluster compounds are summarized in Table 1.

Discussion

Several points are evident in the thermochemical data. First, the enthalpy of solution of both the sulfate and selenate compound in 5 N HCl is strongly exothermic, with only a small difference between the two (Eq. 1 in Table 1). The dissolution reaction in acid can be written as (X = S or Se):

It has a strongly negative enthalpy that cannot be counteracted by any plausible entropy term, so the calorimetric data support the instability of the Keggin clusters in acidic environments. As pH increases, the reaction will become less favorable and the Keggin will be formed.

Because the enthalpy of hydration for the sulfate anion (-1,035 kJ·mol^-1) is also more exothermic than that of selenate (-900 kJ·mol^-1) (19), the measured ΔH_sol values for the clusters suggest a stronger interaction between sulfate and water than between selenate and water. This is most clearly evident in the difference in enthalpies of solution represented by an exchange reaction between S and Se in the solid and in aqueous solution (Eq. 7 in Table 1). Because the exchange reaction involving the production of the selenate crystal and the sulfate aqueous molecule is exothermic, sulfate is favored in solution (and selenate in the cluster solid phase), but only by a small enthalpy difference of about -20 kJ. The smaller difference observed in the calorimetric experiments relative to the calculated hydration energies may suggest that some hydration of the sulfate and selenate anions also occurs in the Keggin.

Both clusters also exhibit exothermic enthalpies of formation from reactions involving their respective calorimetric reference materials (Eq. 2 in Table 1) but the sulfate Keggin formation is more exothermic. Correspondingly, the sulfate Keggin also shows a more negative enthalpy of formation from the elements (ΔH_f,el) than the selenate (Eq. 3 in Table 1). These data are in accord with trends observed for other selenate and sulfate compounds. When compared directly, ceteris paribus, sulfates typically exhibit more exothermic enthalpies of formation. A comparison of the enthalpies of formation from the elements and from the oxides for various selenate and sulfate solid phases is summarized in Table 2.

Table 2.

Comparison of enthalpies of formation from elements (ΔH_f,el) and enthalpies of formation from oxides (ΔH_r-ox) for various selenate and sulfate solids

SeO4/SO4 solid	ΔHf,el	ΔHf-ox
Na2SeO4	−1066.5 (±0.4) (17)	−426.2 (±3.3)
Na2SO4	−1387.8 (±0.4) (16)	−577.3 (±2.6)
K2SeO4	−1121.3 (±?) (26)	−533.5 (±4.7)
K2SO4	−1437.7 (±0.5)(27)	−679.7 (±4.3)
Al2(SeO4)3	−2870.64 (±?) (28)	−518.38 (±4.3)
Al2(SO4)3	−3441.8 (±1.8) (29)	−579.0 (±2.3)
Ga2(SeO4)3	−2227.14 (±?) (30)	−461.48 (±4.0)
Ga2(SO4)3	−3161.39 (±?) (30)	−885.19 (±3.8)

To further monitor the energetics of the selenate and sulfate Keggins relative to simpler compounds, enthalpies of formation from the oxides, ΔH_f,ox, were calculated for the selenate and sulfate Keggins relative to Al₂O₃, Na₂O, Se/SO₂, H₂O, and O₂ (Eq. 4 in Table 1), and relative to NaAlO₂, Al₂O₃, H₂Se/SO₄, and H₂O (Eq. 5 in Table 1). Consistent with ΔH_f,el data, these reactions are also exothermic, and in all cases the ε-Al₁₃ sulfate Keggin is correspondingly more favorable than the selenate.

Due to its sluggish dissolution, the common aluminum hydroxide mineral, gibbsite (γ-Al(OH)₃, was avoided as a reference material in this study. Instead, the energetics of gibbsite–Keggin reactions (Eq. 6, Table 1) were calculated in the following manner. Because the enthalpies of formation from the elements are known, and the enthalpies of solution for all of pertinent calorimetric reference materials except gibbsite have been measured in this study, the enthalpy of solution for γ-Al(OH)₃ in 5 N HCl was calculated using the following equation:

This value, together with the corresponding ΔH_sol for the Keggin compounds and pertinent reference materials, was used to calculate the decomposition of the Keggins to gibbsite (γ-Al(OH)₃, Reaction 6): -620.02 ± 56.91 kJ/mol and -891.57 ± 56.91 kJ/mol for the sulfate and selenate Keggin compounds, respectively.

It is noteworthy that the cluster compounds are energetically significantly unstable relative to gibbsite (Eq. 6). Though the entropy changes, ΔS°, for these reactions are not known, it is likely that the relative entropic contributions to the free energies of these reactions are small in magnitude when no gas phases are involved. Thus it is not surprising that, given sufficient time, these cluster compounds dissociate in solution and precipitate a gibbsite-like layered phase (6). Indeed, the calorimetric data unequivocally prove the metastability of the cluster compounds.

That both the selenate and sulfate Keggin crystals are energetically unstable with respect to gibbsite-bearing assemblages strongly supports the hypothesis that these cluster materials are transitory intermediate species (6) that can only form within a small pH range. They form an intermediate state in a complex energy landscape going from aqueous solution to precipitated aluminum oxyhydroxides. Moreover, although the pathway of formation of the Al₁₃ polyoxocation is not well understood, most workers hypothesize that it is formed via the Al dimer and/or trimer; however, the latter molecule has not yet been isolated. Further research is needed in this area: We are currently conducting thermodynamic investigations to monitor the pathway of formation from monomer to aqueous cluster. In any case, the Al₁₃ Keggin polyoxocation forms at slightly acidic pH, and, upon an increase in pH, the molecules condense into a gel, due to deprotonation of the associated water groups, making a familar floc that has been reported in streams. The floc in turn will transform to gibbsite or bayerite (6).

Finally, these thermochemical measurements are best placed in the context of the larger series of similar molecules and in relation to the kinetic information about reactivities. Near-surface geologic environments, with high aluminum content in feldspars, micas, and clays, undergo extensive reworking of aluminum chemistry as dissolution, transport, and precipitation take place. Aluminum nanoclusters are almost certainly involved in these transformations, and both aqueous cluster molecules and solid phases are tractable simple systems for understanding the molecular processes occurring at the mineral–solution interface.

Isostructural gallium(III)- and germanium(IV)-centered versions of these Keggin clusters can be made by substitution into the central tetrahedral site (1). Although the oxygens immediately bonded to this central metal are inert to isotopic exchange, this single-atom substitution dramatically affects the reactivities of all other bridging oxygens in the structures. The rates of isotopic substitution vary by a factor well over 10⁷ upon the simple substitution of Ga(III) and Ge(IV) for the central Al(III) in the Al₁₃ Keggin polyoxocation (12). The extraordinary sensitivity of the rates to simple substitution is attributed to differences in the extent that a key metastable intermediate forms; this intermediate is a dimer-like structure and requires dissociation of bonds to the inert M(O)₄ site (20) and is thus quite sensitive to small changes in bonding.

These kinetic studies also showed that the Al-centered version, the ε-Al₁₃ molecule, has anomalously high activation energies for isotopic exchange at one set of structural oxygens when compared to the other Ga(III)- and Ge(IV)-centered versions. The activation energies double to approximately 200 kJ·mol^-1, suggesting that the ε-Al₁₃ molecule is strained (21). Documentation of such strain will require calorimetric examination of the Ga(III)- and Ge(IV)-centered versions of ϵ-Keggin structure, and perhaps also examination of the energetics of the double-bridged Al₂(μ₂-OH)₂ dimeric structure, which exists as both sulfate and selenate salts (20). The present results suggest that such experiments should be relatively straightforward.

The goal of both this thermochemical study and the kinetic research is to establish a robust set of rules relating structure to reactivity for Earth-abundant materials. These aluminum hydroxide clusters thus are surrogates for the wider classes of aluminosilicate minerals, for which molecular experiments are difficult. Direct thermochemical documentation of such strain of the ε-Al₁₃ molecule, implied from the isotope-exchange rates, would establish the first strong link between structure and reactivity for these aluminum hydroxide molecules. It would represent an enormous advance in organizing the kinetics of simple hydrolytic reactions in geochemical systems. The present study, which establishes the experimental methodology and provides first data for the Al₁₃ Keggins, paves the way for such future studies.

Materials and Methods

Chemicals and Solution Preparation.

All chemicals were reagent grade or higher. Deionized water (DI, 18 MΩ) was used in the preparation of all solutions. Solution and suspension pH were measured with a ThermoElectron Corp. Orion 4 Star pH meter equipped with a Ross combination pH electrode (Orion Model 8102). Prior to each use, the pH electrode was calibrated with NIST standards.

ϵ-Al₁₃ Keggin Selenate and Sulfate Synthesis.

The ε-Al₁₃ selenate and sulfate crystals were synthesized according to the modified method of ref. 11. Briefly, 2.0 M NaOH was added dropwise into 100 mL of 0.3 M AlCl₃·6H₂O to achieve an OH/Al ratio of ca. 2.25 while stirring at 60 °C (± 0.1) in a jacketed borosilicate reaction vessel. Initial flocculation was immediately noticeable upon addition of base. However, after approximately 12 hr the floc dissolved. The solution was allowed to cool and vacuum-filtered through 0.2 μm Gelman Science filters into an Erlenmeyer flask. The solution was subsequently diluted by a factor of 15 with DI water into separate 1,000 mL beakers and covered with watch glasses. A solution of 1.0 M Na₂SeO₄·10H₂O (or Na₂SO₄) was added dropwise to attain a 25∶1 SeO₄ (or SO₄) to Al ratio. Immediate precipitation was observed. Suspensions were allowed to settle and equilibrate for 4 d, at which time tetrahedral shaped crystals of Al₁₃ selenate (or sulfate) were noticeable at the bottom and along the walls of the beakers. Solutions were vacuum filtered through Whatman filters and the crystals rinsed with DI water, allowed to dry and stored in a borosilicate vials for analysis. Under a microscope, large (up to approximately 1 mm) tetrahedral shaped crystals were observed.

NMR Studies.

The recipe for making the ε-Al₁₃ selenate and sulfate salts is well accepted and effective (22). The identity of the salts was determined both by X-ray structural determination and by both solid- and solution-state ²⁷Al-NMR spectroscopy. The ²⁷Al-NMR solution-state spectroscopy was performed on solutions extracted from batches of crystals to yield the AlO₄Al₁₂(OH)₂₄(H₂O)⁷⁺(aq) ions. Purity was also confirmed from solid-state spectra collected on a Chemagnetics CMX-400 NMR spectrometer at 104.3 MHz. Samples of powder were spun at 15–17.2 kHz in sealed 4.0 mm (o.d.) ZrO₂ rotors. The ²⁷Al-MAS-NMR spectra were taken with single-pulse excitation with 0.5–1.0 μs pulses and a 0.1 s pulse delay. The solution-state ²⁷Al-NMR spectra were collected on a Bruker Avance spectrometer that is based on an 11.7 T magnet (ν_o = 130.3 MHz for ²⁷Al) fitted with a 10-mm broadband probe. Depending upon the sample, 300–1,200 acquisitions on the solutions were required to establish adequate signal-to-noise ratio with 1 s relaxation delays, and the number of acquisitions was typically 80,000 for the MAS-NMR spectra.

X-ray Powder Diffraction (XRD).

XRD measurements were performed on powdered samples of ε-Al₁₃ selenate and sulfate crystals mounted on a zero-background quartz slide at room temperature using a Bruker D8 Advance diffractometer with the following parameters: rotating stage; copper source (Kα; 1.5418 Å); 40 keV, 40 mA, Kβ filter: LynxEye detector solid-state detector; continuous mode: 0.02 d/ min; 2θ range: 5–70. The diffractograms were produced using supporting MDI Data Scan 4 and Jade 8 software packages. The identity of the crystalline selenate product was confirmed by comparison to the X-ray data of Johansson (11) and Parker et al. (23).

Thermal Analysis.

Thermogravimetric (TG) and differential scanning calorimetry (DSC) analyses were conducted using a Setaram Setsys Evolution instrument. The TG balance was calibrated with a known reference mass and the DSC was calibrated with standard samples of tin, aluminum, silver, and gold. Platinum crucibles were used on both sample and reference sides, and the Al₁₃ crystals were analyzed under a stream of 20 mL/ min of argon. Approximately 5 mg of solid was used at a scan rate of 10 °C/ min and a temperature range of 25 °C to 800 °C.

Acid Solution Calorimetry.

The enthalpy of solution (ΔH_sol) for ε-Al₁₃ selenate and sulfate crystals was obtained using a Setaram C80 Calvet type microcalorimeter with 5 N HCl aqueous solutions and an experimental temperature of 28 °C (28.0001 ± 0.0005 °C). The calorimeter was calibrated using the enthalpy of fusion of indium and by measuring the heat of solution of KCl (National Institute of Standards and Technology, Standard Reference Material # 1655) which, prior to analysis, was oven-dried overnight at 500 °C.

The C80 calorimeter consists of a sample cell and a reference cell. Inside the sample cell a small amount of analyte (typically 2–3 mg of crystals) was placed in a small polyproplylene cup above 5 g (5.00–0.01 g) of aqueous solution inside a Teflon container. The reference cell consists of an empty polypropylene cup also initially suspended above 5 g of aqueous solution inside a Teflon container. After thermal equilibrium was attained, evidenced by a stable baseline established after a minimum of 4 h, the sample and the reference cups were simultaneously submerged into respective solutions and the heat effects were recorded. Complete dissolution of all of the samples was verified by observing a complete return to a stable baseline and by visually inspecting the sample containers after the completion of each individual run.

Because several of the reagents in this study rapidly reacted with atmospheric water, a different setup was used. With this technique, the samples were not equilibrated above the solution for 4 h. Instead, after thermal equilibrium was attained, typically pellets (approximately 3 mg) of powdered sample were dropped directly into the calorimeter. For AlCl₃·6H₂O, Na₂(SeO₄)·10H₂O, Na₂SO₄, and NaOH, better reproducibility was observed with this latter approach. For NaCl, the enthalpy of solution data from both techniques were statistically indistinguishable.

For NaOH, an additional precaution was necessary, that is, quickly and firmly adhering NaOH (approximately 3 mg) to a small piece of platinum metal before dropping the sample into the calorimeter. This method ensured that NaOH did not stick to any other surfaces (e.g., silica dropping tube) and that it dropped directly to the bottom of the 5 N HCl solution.

High Temperature Oxide Melt Solution Calorimetry.

To obtain the enthalpy of formation of sodium selenate decahydrate, high temperature calorimetric measurements were conducted on a custom built Tian-Calvet microcalorimeter. Details of the instrumental techniques are provided elsewhere (24). In brief, pelletized samples (approximately 5 mg) were dropped from room temperature into a melt of sodium molybdate (3Na₂O·4MoO₃) at 976 K inside platinum crucibles. The calorimeter was calibrated prior to analysis with a standard reference of α-Al₂O₃ (Alfa Aesar, 99.9997 wt % metal basis). Upon rapid and complete dissolution of the sample, the enthalpy of drop solution ΔH_ds, was measured and used to calculate the enthalpy of formation from the elements, ΔH_f,el, and enthalpy of formation from the oxides, ΔH_f,ox, for sodium selenate decahydrate.