Thermodynamic Stability Areas of Polyvanadates of Alkaline Earth Metals

A thermodynamic method of the global Gibbs energy variation calculation for describing heterogeneous equilibria of transformations of calcium, strontium, and barium polyvanadates, that occur in systems MeO-V2O5-H2O, where Me is the alkaline earth element, has been developed and used. Its quintessence consists in the thermodynamic analysis of the real conditions of various processes on the basis of their total thermodynamic characteristics. On the basis of the selected thermodynamic data for involved species, the thermodynamic stability areas of solid polyvanadates towards the solution pH and vanadium and alkaline earth metal ion concentrations in heterogeneous mixtures have been established, taking into account the complex formation reactions in multicomponent heterogeneous systems. *e existing experimental data confirm the results on the thermodynamic stability of polyvanadates obtained in this paper.


Introduction
Polyvanadates obtained by solid-phase synthesis and subsequent study of their chemical properties in water-salt systems have a huge practical significance, because regardless of the type of source of raw materials, their processing includes stages of the synthesis of final products with desired properties (high or low solubility, etc.), with the transfer of vanadium in the solution and its subsequent precipitation.e abovementioned processes are associated with extremely complex chemical equilibria, the study of which would allow the development of technological basis of a number of combined productions: obtaining technical and pure vanadium pentoxide, vanadium catalysts, dyes, etc. [1,2].Up to 85-87% of the total amount of polyvanadates is used in ferrous metallurgy as highly efficient and habitually an indispensable alloying additive in the production of diverse steels.About 10-12% of polyvanadates is used in nonferrous metallurgy, mainly in the form of aluminum-vanadium alloys for alloying structural materials based on titanium, applied in space technology.Inorganic materials containing polyvanadates are used for production of optical quantum generators, ionic conductors, ferroelectrics, dielectrics, ceramics, etc. [1].
e demand for polyvanadates is projected to grow by seven percent a year till 2025 [2], thanks to the usage of vanadium-containing steels in both traditional areas and the implementation of new technologies for the manufacture of batteries [2].e concentrations of vanadium in surface waters caused by industrial wastes are small and, in general, are within the natural content (up to 65 μg/L) [3].Literature sources provide information on vanadium concentrations in surface waters of industrial wastes up to 2 mg/L [3].e chemistry of aqueous solutions of vanadium is complicated by the existence in solutions of numerous ions and polyions, the transition of which into an equilibrium state depends on the pH value and oxidation-reduction potentials in the systems, as well as its concentration and the content of other elements.us, the composition and stability of solid phases formed in the MeO-V 2 O 5 -H 2 O system, where Me is the alkaline earth element, exhibit complex functions of the chemical composition of solution, pH, etc. Experimentally, it has been demonstrated [4][5][6] that depending on the conditions in the MeO-V 2 O 5 -H 2 O system, different polyvanadates MeV 12 O 31 , MeV 6 O 16 , Me 3 V 10 O 28 , Me(VO 4 ) 2 , Me 2 V 2 O 7 , and Me 3 (VO 4 ) 2 can precipitate.For the compounds of Ca 2+ , Sr 2+ , and Ba 2+ the same authors determined the solubility products [4,5], taking into account the mutual transformation reactions of the vanadium (V) ionic species.
e coexistence areas of these polyvanadates were also calculated in the cited papers as a function of the solution pH and alkaline earth metal concentrations.At the same time, the reciprocal relationship between the solution composition and solid phases was established in the form of diagrams log ). is procedure is not always efficient.In particular, the solubility diagrams provide valuable information only if the solubility of solid phase is low.
In this paper, based on calculations of the global Gibbs energy variation of the dissolution-precipitation process of the polyvanadates of alkaline earth metals as a function of pH and total concentrations of vanadium and alkaline earth metals, their thermodynamic stability areas are determined.It has been proved that the value of global Gibbs energy variation under real conditions constitutes a more objective criterion for estimation of the stability areas of polyvanadates of alkaline earth metals than the solubility diagrams.

Theoretical Part
In a series of papers [6][7][8], it has been shown that as a strict criterion of solid-phase stability serves the value of the Gibbs energy variation of the solid-phase formation-dissolution process. is criterion will be applied for the determination of the thermodynamic stability areas of the alkaline earth metal polyvanadates.
e essence of the calculation method will be explained by a concrete example of equilibrium of calcium dodecavanadate with the saturated aqueous solution: e Gibbs energy variation under standard conditions is equal: where ΔG 0 f (i) is the standard Gibbs energy of formation of the i species.e ΔG 0 f (i) values used (kJ/mol) are recalculated from the selected equilibrium constants [4,5] and shown in Table 1.e ΔG 0 S (1) value cannot, however, serve as a characteristic of the thermodynamic stability of calcium dodecavanadate under real conditions.In the latter case, the equilibrium is described by the equation of reaction isotherm, which for Reaction (1) takes the following form: Note that the Gibbs energy variation in Reaction (1) strongly depends on the pH value.At the same time, Equation (3) cannot also serve as a characteristic of the thermodynamic stability of calcium dodecavanadate, because the vanadyl ion, in function of pH and C V , is subjected to complex chemical transformations in the solution (Table 2).
Obviously, in calculating ΔG S , all these equilibria must be taken into account.A rigorous thermodynamic analysis, developed in a series of papers [7,8], shows the global Gibbs energy variation of Reaction (1) under real conditions, considering the equilibria (Table 2), as described by the following equation: where α V is the coefficient that takes into account the contribution of the equilibria (Table 2), which is determined in the following way:

􏽨 􏽩
� VO 2 Analogous relations are valid for other vanadates.Under this approach, for −ΔG S > 0, the solid phase is thermodynamically unstable to dissolution according to Reaction (1) and vice versa; if −ΔG S < 0, the dissolution of the solid phase takes place.

Results and Discussion
Within the pH range where the solid phase (oxide) is thermodynamically unstable (dissolves), it is necessary to determine the areas of predominance of the soluble species in solution.In the presence of polynuclear species, it is necessary to calculate the partial molar fractions of the species as a function of pH and C V .e last ones for vanadium compounds (V), for example, are determined in the following way [7]: e results of calculating these functions for vanadium (V) compounds for C V � 1 × 10 −3 mol•L −1 as a function of pH are shown in Figure 1.Based on these results, it is easy to determine the thermodynamic stability of the species in the solution as a function of pH and C V .As one can see, in acidic media, within the pH range between 2.4 and 5.5, the species H 2 V 10 O 28 4− and HV 10 O 28 5− are dominant.In alkaline solutions, after pH > 8, the HVO 4 2− species prevail.e obtained data (Figure 1) correlate well with existing experimental evidences.It is well known that high-field NMR gives high-quality structural data and quantitative information about speciation and concentration of a large variety of species in aqueous solvents [9].Consequently, NMR 51 V spectroscopy measurements [10] confirm the speciation of vanadium (V) in aqueous vanadate solutions as a function of pH and vanadate concentrations.As seen in Figure 1, in alkaline solutions, tetrahedrally coordinated vanadates, metavanadate, and pyrovanadate are abundant.Decavanadate only forms when metavanadate is added to solutions of pH 3 or less.Acidification of metavanadate solutions to pH 4 or lower polymerizes all the oligomers to form V 10 .Readjusting the pH near to 8 produces a depolymerization of V 10 to form V 2 , V 4 , and V 5 , as it has been stated in [11][12][13].As the pH of metavanadate solutions increases, V 1 and V 2 become the predominant species [14].As reported Ralston et al. [15], in the basic pH (between 8 and 9) solution, V 4 O 12 4− and HVO 4 2− (or VO 3 (OH) 2− ) coexist.Orthovanadates VO 4 3− dominate at a solution pH greater than 13 [16].As highly basic solutions are acidified to pH values between 9 and 12, orthovanadate tetrahedral units can combine to form pyrovanadates V 2 O 7 4− , HV 2 O 7 3− , and HVO 4 2− , which are colorless [16].Continued acidification to pH values between 6 and 9 leads to the formation of colorless or yellow metavanadates V 4 O 12 4− , V 5 O 15 5− , H 3 VO 4 , and H 2 VO 4 − [16,17].Additional acidification to pH between 2 and 6 causes the coordination of vanadium to change from tetrahedral to octahedral.A combination of ten octahedral units forms the decavanadate ions V 10 O � 28 6− , HV 10 O � 28 5− , and HV 10 O � 28 5− , leading to orange or red solutions [16,17].
Table 2: Complex chemical transformations of the vanadyl ion in the solution at 295 ± 1 K [4,5].

Nr Equation of reaction log
Pervanadyl VO 2 + is yellow and dominates at dilute concentrations in strongly acidic solutions, at pH 1.0-2.5 (Figure 1).e calculated dependence of ΔG S on pH for C V � C Ca � 1 mol•L −1 for different calcium polyvanadates are shown in Figure 2.
e intersection points of the curves correspond to the boundaries of the stability areas of the respective salts.For two salts, e.g., 1 and 2, the Gibbs energy values in the given conditions are ΔG S (1) and ΔG S (2); in the case −ΔG S (1) < −ΔG S (2), salt 1 is thermodynamically more stable, and vice versa; for −ΔG S (1) > −ΔG S (2), salt 1 must transform into salt 2. In the case ΔG S (1) � ΔG S (2), equilibrium is established.In Figures 3-5, the ΔG S (pH) dependence for different calcium, strontium, and barium polyvanadates are displayed for several C V and C Me values.For simplicity, only the lower boundaries of the ΔG S values are shown.
As it is evident from Figures 2-5, the thermodynamic stability of polyvanadates towards each other strongly depends on pH and total alkaline earth metal and vanadium concentrations.e most insoluble compounds are barium polyvanadates in comparison with calcium and strontium ones.With decrease in the C V and C Me concentrations, the polyvanadates become thermodynamically unstable to dissolution.From Figures 3-5, one can see that alkaline earth metal polyvanadates are thermodynamically instable when C V � C Me ≤ 1 × 10 −3 mol•L −1 for all the examined pH values, excepting barium polyvanadates in very acidic solutions (pH < 3.3).e last fact is not reflected in the log C V � f(log[H + ]) and log C M � f(log[H + ]) diagrams, that is, the main priority of the criterion proposed in this paper for assessing the thermodynamic stability of alkaline earth metal polyvanadates.e existing experimental data [4,5,[18][19][20] confirm the results on the thermodynamic stability of polyvanadates obtained in this paper.
e effect of temperature on the thermodynamics stability of hydrocomplexes H i V j O n and solubility of polyvanadates for different temperatures are estimated on the basis of van't Hoff equation [7]: e appropriate values of the standard enthalpies ΔH can be found in handbooks available everywhere [21][22][23][24][25][26][27].Usually, it is supposed that T 1 � 298.15K and the temperature insignificantly influences the ΔH values within the investigated temperature interval.
Vanadium in inorganic media (a mixture of an inorganic acids and their salts) may form complexes with such anions such as SO 4 2− , Cl − etc.Note that the sulphate medium is important due to its industrial applications [28][29][30][31][32]. Schematically, if L -denotes the ligand, the reaction of complex formation may be written as follows: e thermodynamic equilibrium formation constant of VO 2 SO 4 − at 25 °C is equal to log K � 1.30 ± 0.02 [28].
Consequently, the VO 2 SO 4 − complexes may form in the presence of a large excess of ligand, C SO 4 − >> C V .e contribution of anions of aqueous electrolytes on the thermodynamics stability of soluble and insoluble species can be taken into account through the alpha coefficient, in the form described in Equation (6) [7,8].

Conclusions
4 Journal of Chemistry characteristics.On the basis of the selected thermodynamic data for involved soluble and insoluble species, the thermodynamic stability areas of solid polyvanadates towards the solution pH and vanadium and alkaline earth metal ion concentrations in heterogeneous mixtures have been established, taking into account the complex formation reactions in multicomponent heterogeneous systems.(iii) e calcium, strontium, and barium polyvanadates are dissolved for C V � C Me ≤ 1 × 10 −3 mol•L −1 for all the examined pH values.(iv) e thermodynamic stability of soluble species as function of pH and C V has been determined.(v) e obtained results, based on the thermodynamic analysis and graphical design of the calculated data, are in good agreement with the available experimental data.
(i) A thermodynamic method for calculating the global Gibbs energy variation for describing heterogeneous equilibria of transformations of polyvanadates of calcium, strontium, and barium, that occur in systems MeO-V 2 O 5 -H 2 O, where Me is the alkaline earth element, has been developed and applied.(ii) Its quintessence consists in the thermodynamic analysis of the real conditions of various processes on the basis of their total thermodynamic