Prediction of the Stability of Tutton Salts Using the Simple Salt Approximation

Abstract

The simple salt approximation (SSA) for lattice energies is used to rationalize the composition of Tutton salts with the formula A₂M(SO₄)₂(H₂O)₆, where A is a monovalent cation, usually K⁺, and M is a divalent cation, usually a transition metal cation such as Cu²⁺. These salts have become increasingly advantageous due to their heat exchange and optical properties, as well as providing vehicles for the study of the Jahn–Teller effect. The SSA suggests that the solubility of a double salt will be about the same as, or slightly lower than, that of the constituent simple salts when the simple salts have similar solubilities. This generalization has been used to rationalize the stability of the double salts synthesized and reported herein using standard procedures (mixing of simple salt constituents followed by slow evaporation). As expected, the hexa-coordination of water was obtained only with small divalent cations. Of particular interest is the absence of Tutton salts containing small alkali metal cations, specifically Li⁺ and Na⁺, an observation that is seemingly inconsistent with the large lattice energies that these ions should confer on the double salts and the similar solubilities of their salts to those of the transition metal sulfate. Although analytical data appeared to provide evidence for Tutton salts when M = Li⁺, the PXRD patterns of the synthesized compounds clearly showed mixtures of the simple-salt-starting reagents. We conclude that inability to synthesize a Tutton salt using small alkali metal cations is predominantly due to the lower-than-expected lattice energies of these compounds and consequent greater solubilities than their simple salt constituents. Moreover, we can attribute this instability to the extensive hydrogen-bonding present in the Tutton structure, which produces long monovalent sulfate distances and weaker-than-supposed lattice energies. However, it is also true that both the heat of hydration of the Li⁺ ion and its entropy of hydration also conspire to provide greater solubility.

1. Introduction

1.1. Composition of Tutton Salts

Named for the British crystallographer Alfred Edward Howard Tutton, Tutton salts are double salts, with the general formula A₂M(SO₄)₂(H₂O)₆, whose “constituent” simple salts contain both monovalent (A) and hexahydrate divalent (M) cations [1,2]. Their relatively easy synthesis from solutions containing simple salt reactants, namely A₂SO₄ and MSO₄, along with the low-temperature removal of water of hydration, suggest their use as heat exchangers [3]. Their optical properties have led to the development of ultraviolet light filters [4]. Moreover, their existence in extra-planetary conditions has been suggested [5,6], and they are an ideal system for the study of the Jahn–Teller effect, along with simple spin systems [7]. These double salts have been discovered in evaporate deposits, fumaroles, geysers, and ore tailings, and are members of the picromerite group of minerals [8,9].

In addition to Tutton salts, in the picromerite group of minerals, many other salts have been synthesized; compounds with the monovalent cations NH₄, K, Rb, Cs, and Tl, along with the divalent cations Mg, V, Cr, Mn, Fe, Co, Ni, Cu, and Zn, have been reported [9,10]. These compounds are prepared by mixing saturated aqueous solutions of the simple salt constituents followed by slow evaporation of the mother liquor until crystallization produces platelets of the monoclinic crystals. The majority of synthetic salts contain sulfate or selenate anions, but Tutton salts are also known to include other anions such as fluorophosphate [10], tetrafluoroberyllate [11], and hydrogen phosphate [12]. Although the lighter alkali metal cations are present in double salts such as krohnkite (Na₂Cu(SO₄)₂·2H₂O) and bloedite (Na₂Mg(SO₄)₂·4H₂O), they appear not to form salts with the Tutton salt stoichiometry—that is, with hexa-coordination of water at the divalent cation—[3] but they have been reported to form mixed-monovalent-cation Tutton salts [13,14].

The most distinctive feature of Tutton salts is the octahedral coordination of divalent cations with water molecules (Figure 1), which is not expected for the transition metals.

Tutton salts containing Mg²⁺—which, unlike the transition metal cations, does not have low-lying d-orbitals—also have octahedral aqua coordination, suggesting that the primary stabilizing force for this coordination may be ion–dipole interactions, as evidenced by the small ionic radii of both Mg²⁺ and the transition metals (ionic radii: Mg²⁺ 72 pm; Cu²⁺ 73 pm).

1.2. Stability

The successful formation of a Tutton salt depends on the solubility of the resultant Tutton double salt relative to the solubilities of the simple salt reactants. Although the solubilities of many simple salts are known, the same is not true for double salts, such as Tutton salts. Fortunately, solubilities are generally related to the lattice energy of the salt and the heats of hydration of its ions. The heats of hydration of the ions are generally known, and the lattice energies can be estimated [15] by methods that are relatively simple to apply.

For Tutton salts, the simple salt approximation [15,16,17,18] is particularly appropriate. This approximation assumes that the lattice energy of a double salt is equal to the sum of the lattice energies of the two simple salt constituents. For example, as seen in Equation (1), for the double salt A₂M(SO₄)_2(s), the lattice energy, LE, is assumed to be

LE (A₂M(SO₄)_2(s)) = LE (A₂SO_4(s)) + LE(MSO_4(s))

(1)

This approximation assumes that interactions in a double salt are similar to those in the “constituent” simple salts., This assumption is borne out by the average 2% difference between lattice enthalpies calculated by this approximation and those obtained from heat of formation temperatures using the Born–Haber cycle [16]. This approximation allows for the derivation of a series of generalizations about the solubilities of double salts relative to their simple salt “constituents”:

“When two simple salt constituents have the same or similar solubilities, the solubility of the double salt can be expected to be similar to or slightly less than the solubility of the simple salts. When the simple salts have different solubilities, the solubility of the double salt will fall between the solubilities of the two simple salts” [16].

For example, the similar solubilities of Na₂SO4 and CuSO₄ (2.0 and 1.3 moles/L) would suggest that these simple salts could form a double salt with the stoichiometry of Na₂Cu(SO₄)₂. In fact, the mineral krohnkite (Na₂Cu(SO₄)₂(H₂O)₂) has this stoichiometry, but does not have the hexa-coordination of water at the divalent cation, which is necessary for the Tutton classification. On the other hand, the formation of a double salt between Na₂SO₄ and BaSO₄ (solubilities of 2.0 and 1 × 10⁻⁵ moles/L, respectively [19]) is unlikely because of the very large difference in solubilities of the simple salts.

Indeed, the stability of Tutton salts is based on the very similar solubilities of the simple salts used in the preparation of the target Tutton salt. For example, the simple salt constituents of cyanochroite, K₂Cu(SO₄)₂(H₂O)₆, are K₂SO₄ and CuSO₄, which have molar solubilities of 0.6 and 1.3 mol/L, respectively [19]. These similar simple salt solubilities lead to the formation of a Tutton double salt with a solubility that allows it to be produced by evaporation from a mixture of the simple salts.

Our objective in this work is to use the simple salt approximation as a predictor of the ease of formation of Tutton salts and as a means to understand the factors that control their stability. To this end, we have attempted the preparation of both known and unknown salts that might possess the Tutton stoichiometry.

2. Materials and Methods

2.1. Synthesis

All double salts were prepared by mixing saturated solutions of the simple salt “constituents” in a one-to-one mole ratio. The simple salt solutions were prepared using ACS reagent-grade reactants with purities above 97% in quantities sufficient to prepare 0.01 mole of the double salt. The simple salt reagents were dissolved in the amount of water required to reach their solubility limit (

Table 1. Molar solubilities of selected sulfates, at 20 °C, unless specified otherwise [19].

	Compound	Hydrate	Solubility at 20 °C (mol/L)
Group 1	Li2SO4	monohydrate	3.5
	Na2SO4	anhydrous 1	2.0
	K2SO4	anhydrous	0.64
	Rb2SO4	anhydrous 2	1.4
	Cs2SO4	anhydrous	4.9
	(NH4)2SO4	anhydrous	5.6
Group 2	MgSO4	anhydrous	2.9
	CaSO4	anhydrous	1.5 × 10−2
	SrSO4	anhydrous	7.5 × 10−4
	BaSO4	anhydrous	1.3 × 10−5
Group 14	SnSO4	anhydrous 2	1.5
	PbSO4	anhydrous 2	1.3 × 10−3
Transition Metals	CuSO4	anhydrous	1.3
	NiSO4	anhydrous	4.2
	CoSO4	anhydrous	2.4
	MnSO4	anhydrous	4.2

¹ Anhydrous at 25 °C. ² Solubilities estimated at 0 °C.

), producing saturated solutions. For most reagents (except for Li₂SO₄ which was prepared at 20 °C due to its inverse solubility with water temperature), saturation was attained by gentle heating to 50–60 °C and magnetic stirring. The two solutions were then combined with continued heating and stirring for about 10 min. After the mixed salt solution cooled to room temperature, it was transferred to a recrystallizing dish and allowed to sit undisturbed until crystals formed. The amount of time required for the crystallization depended on the double salt and the extent of evaporation from the mixed solutions, but for most salts, 1–4 days were required. To slow crystallization to approximately one week, the recrystallizing dish was covered almost completely with a watch glass or parafilm. The thin aqueous mother liquor remaining after crystallization was used to wash the crystals, which were then removed either by tweezer or by filtration (either by gravity or suction). The crystals were dried at room temperature on a piece of filter paper, and, after one day, they were stored in a vial. The mother liquor was allowed to undergo further evaporation in order to generate another batch of crystals. In some cases, several successive batches of crystals were obtained to determine possible changes in structures with concentration change.

2.2. Characterization

Double salts were characterized by X-ray diffraction using a PANalytical X’pert PRO Multipurpose diffractometer Theta-Theta System with CuΚα radiation (λ = 1.54060 Å) over a 2θ range of 5.99–90.00° with a step size of 0.0167°. The results were analyzed using the PANalytical program X’Pert Highscore Plus. The samples were scanned with five repetitions at a current of 40 mA and a voltage of 45 kV. Using the PANalytical HighScore Plus software (version 5.0), the five scans were summed and compared with peak patterns (PXRD Fit Score, max 100 for perfect agreement with literature) from the ICDD database to determine the identity of the Tutton salts.

Elemental analyses were obtained from Galbraith Laboratory (TN) and by in-house gravimetric analyses for copper (II), cobalt (II), sulfate, and water. Divalent cation analyses by Galbraith were determined by ICP-OES, sulfate by ion chromatography, and H₂O by Karl Fischer analysis. Uncertainties were generally 5%.

In-house copper (II) and cobalt (II) analyses were obtained by precipitation of the hydroxide using 0.1 M NaOH after the removal and analysis of sulfate by precipitation of SrSO₄. The precipitated hydroxide was then converted to the oxide by ignition. The analysis of H₂O was performed by dehydration in a Bunsen flame. The uncertainties for the in-house analyses were 5%.

3. Results

A variety of double salts were prepared. that includes transition metal Tutton salts, where A = NH₄, K, Rb, Cs and M = Fe, Co, Ni, Cu, Zn (

Table 2. Transition metal Tutton salts, A₂M(H₂O)₆(SO₄)₂, and the main group salts, A₂M(H₂O)_x(SO₄)₂, where x ≠ 6. Search-match analyses were performed using HighScore Plus. Goodness-of-fit scores and corresponding PDF references included.

	A+	M2+	Empirical Formula from the Literature	PXRD Fit Score	PDF Number
Tutton Salts	K	Cu	K2Cu(H2O)6(SO4)2	81	98-017-1288
		Co	K2Co(H2O)6(SO4)2	78	00-021-0632
		Mg	K2Mg(H2O)6(SO4)2	78	01-074-1064
		Zn	K2Zn(H2O)6(SO4)2	75	98-016-2318
		Fe	K2Fe(H2O)6(SO4)2	76	98-017-2062
		Ni	K2Ni(H2O)6(SO4)2	78	98-016-2316
	NH4	Cu	(NH4)2Cu(H2O)6(SO4)2	61	01-072-1658
		Co	(NH4)2Co(H2O)6(SO4)2	65	01-071-2155
	Rb	Cu	Rb2Cu(H2O)6(SO4)2	70	00-061-0646
	Cs	Cu	Cs2Cu(H2O)6(SO4)2	84	98-024-9345
Main Group	K	Ca	K2Ca(H2O)(SO4)2	70	01-075-9128
		Sn	K2Sn(SO4)2	77	00-026-0924
	Na	Cu	Na2Cu(H2O)2(SO4)2	69	98-001-5434
		Co	Na2Co(H2O)4(SO4)2	70	01-074-7115

), along with the main group salts, where A = Na, and K and M = Ca, Sr, Sn(II). In Table 2, we include a sample of the compounds prepared, all of which were identified by PXRD. Only the literature reference for the PXRD pattern that showed the best agreement is reported.

4. Discussion

According to the data reported in Table 2, it appears that the double salt A₂M(SO₄)₂ can be obtained if the solubilities of the simple salts differ by no more than a factor of 100. The only example of this large variation in solubility of the simple salts is K₂Ca(SO₄)₂(H₂O), as shown in Table 2. It must be emphasized that this difference in experimental solubilities is dependent on temperature, concentration, and the nature of the anion. The success of the aqueous preparation of transition metal Tutton salts, as shown in Table 2, can be rationalized by the simple salt tenet that the target Tutton salt can be obtained at the expense of the simple salt reactants when the solubilities of the simple salts are similar (within less than a factor of about 10) and when the divalent cation achieves hexa-hydration. It is important to recognize that the sulfate and selenate salts of both the monovalent cation (usually K⁺) and the transition metals are quite soluble, but this is not necessarily the case with other anions.

The attempted preparation of sulfate Tutton salts, in which the divalent cation is a main group +2 cation, is often hindered by the low solubility of the main group sulfate. For example, SrSO₄ has a molar solubility more than a thousand times lower than that of K₂SO₄, and it is likely that the hypothetical double salt K₂Sr(SO₄)₂(H₂O)_x would be more soluble than SrSO₄, and therefore difficult to prepare (the product of the addition of the two simple salts would simply be SrSO₄). Moreover, if the double salt K₂Sr(SO₄)₂ did exist, it would likely not have the hexa-coordination of the Tutton structure: the Sr²⁺ cation has a significantly larger radius (1.2 Å) than that of Mg²⁺ (0.72 Å), which does form a Tutton structure. The same analysis suggests that while some double salts with the A₂MX₂ stoichiometry containing a main group divalent cation should be synthetically feasible, they would be unlikely to contain the Tutton hexa-coordination. This is illustrated in Table 2 by the potassium sulfate candidates K₂Ca(SO₄)₂(H₂O) and K₂Sn(SO₄)₂, which do not have hexa-coordination of water, presumably as a result of the size of the divalent cation (Ca, 1.0 Å, and Sn, 1.2 Å).

The similarities of the solubilities of all of the alkali sulfates to those of the transition metal divalent cation sulfates suggest that any of the alkali metals could be incorporated into a Tutton salt. However, our attempted preparation of both lithium and sodium Tutton salts indicates that, even with extensive fractional crystallization, the Tutton structure could not be obtained. For example, in our attempt to prepare Li₂Cu(SO₄)₂(H₂O)₆ using Li₂SO₄ and CuSO₄, the products obtained after three crystallizations were mainly CuSO₄ in the first crystallization, and primarily Li₂SO₄(H₂O) in the second and third crystallizations. Similarly, attempts at the preparation of the Co analog, Li₂Co(SO₄)₂(H₂O)₆, the Mg analog, Li₂Mg(SO₄)₂(H₂O)₆, and the mixed Tutton salt, Li₂Cu_xCo_y(H₂O)₆(SO₄)₂, all resulted in mixtures of the simple salts. Figure 2 shows an expansion of the PXRD pattern for a fraction of the attempted synthesis of Li₂Mg(SO₄)₂(H₂O)₆ that has elemental analyses somewhat similar to (but with differences greater than the 5% experimental error) the theoretical values for the lithium salt with the experimental formula of Li_2.45Mg(SO₄)_2.75(H₂O)_6.33. A representative pattern of the attempted synthesis of Li₂Cu_xCo_y(H₂O)₆(SO₄)₂ is shown in Figure 3, and indicates that this fraction is a mixture of the simple salts used in its preparation.

We were also not able to incorporate a significant amount of lithium or sodium ions along with the potassium ions, as indicated in the literature [13].

Table 3. Elemental composition of mixed Tutton salts with small radii ions of lithium and sodium as determined by Galbraith Laboratories.

	Formula	K+ (%)	A+ (%) 1	B+ (%) 2	SO42− (%)	H2O (%)
Theory	KLiCu(H2O)6(SO4)2	9.54	1.69	15.5	46.9	26.4
Exp.	K1.70Li0.013Cu(H2O)5.01(SO4)1.56	18.6	0.0245	14.9	40.6	22.4
Theory	KLiNi(H2O)6(SO4)2	9.66	1.71	14.5	47.4	26.7
Exp.	K2.09Li0.0128Ni(H2O)4.30(SO4)1.89	19.2	0.0209	13.8	42.6	18.2
Theory	KNaCu(H2O)6(SO4)2	9.18	5.40	15.5	45.1	25.4
Exp.	K1.70Na0.0138Cu(H2O)5.00(SO4)1.58	18.4	0.0882	17.6	42.0	25.0
Theory	KNaNi(H2O)6(SO4)2	9.29	5.46	13.9	45.6	25.7
Exp.	K1.98Na0.0131Cu(H2O)4.97(SO4)1.91	18.5	0.072	14.0	43.9	21.4

¹ Either lithium or sodium. ² Either divalent copper or nickel.

reports the percentages of lithium or sodium with potassium for divalent cations of copper and nickel.

Considering that the SSA predicts that the double salt product resulting from the mixing of two simple salts with similar solubilities will be a slightly less-soluble product. Moreover, the lack of incorporation of the two smallest alkali metal salts in a Tutton salt is surprising. For example, the mixing of Li₂SO₄, with a solubility of 3.2 moles/L, and CoSO₄, with a solubility of 2.4 moles/L, would surely be expected to produce Li₂Co(SO₄)₂(H₂O)₆. Since the products of the attempted preparations of lithium Tutton salts were the simple salt “constituents” rather than a double salt, it seems likely that the target double salt is more soluble than expected. In terms of the SSA, we can say that the lattice energy of the double salt is lower than expected. There are several rationalizations for the apparent lower stability of Tutton salts containing small monovalent ions:

(a)

The lattice energy produced by the small monovalent cation may not be large enough to produce a sufficiently insoluble Tutton salt. In addition to increasing the lattice energy of the Tutton salt, the small size of the monovalent cation also increases the heat of hydration of the cations, thereby increasing the solubility of the Tutton salt. For lithium sulfate in particular, the solubility decreases with temperature due to its exothermic dissolution, which occurs when the heat of hydration of the ions in dissolution exceeds the lattice energy of the crystal.

(b)

The small size of the monovalent cation and stronger hydration can also lead to lower entropy in the dissolved salt (greater ∆S for dissolution) and greater solubility of the salt.

(c)

The structure of a Tutton salt has been shown to involve extensive hydrogen bonding [20] that creates a more open structure with larger cation–anion distances than might be expected [9,21]. These greater distances would have the effect of decreasing the lattice energy and thus increasing the solubility of the salt.

Given what appears to be the importance of the size of the monoatomic cation, we have also explored Tutton salts with monovalent cations sizes larger than that of K⁺. In addition to Rb⁺ and Cs⁺ (see Table 3), ammonium sulfate has a higher solubility (5.6 mole/L) than even Cs₂SO₄, and the ammonium ion is a frequently used monovalent cation source in the preparation of Tutton salts [19]. A more complex manifestation of differences in solubility is encountered in the formation of the tetrahydrate rather than the Tutton hexahydrate of manganese (II), the most soluble of the transition metal sulfates. The mixing of saturated solutions of MnSO₄ with K₂SO₄ produced K₂Mn(SO₄)₂(H₂O)₄ in our hands, as well as in the hands of Hertweck et al. [22]. Indeed, in all but 2 of the 12 reports of hexahydrate manganese (II) Tutton salts, the ammonium ion is the monovalent cation. The two outliers contain either thallium (I) [23] or mixed divalent cations [24,25]. Like (NH₄)₂SO₄, Cs₂SO₄ also has a higher solubility than K₂SO₄, and we have used it to prepare a manganese hexahydrate Tutton salt (see Section 2).

The SSA also applies to the preparation of Tutton salts with other anions. The synthesis of potassium copper hydrogen phosphate K₂Cu(HPO₄)₂(H₂O)₆ has been reported, but our repeated attempts to prepare this compound using the treatment of H₃PO₄ with KOH and Cu(OH)₂ have produced only copper phosphate [12]. It is likely that the hydrogen phosphates of the transition metal cations are less soluble than CaHPO₄, which has a measured solubility of 1 × 10⁻³ moles/L [19]. The concentration of the HPO₄²⁻ anion also depends on the pH of the solution; if the solution is more basic than ca. pH = 9, the main anionic species will be phosphate, which forms very insoluble compounds with many cations. Thus, attempts to prepare Tutton salts containing, for example, K⁺, Cu²⁺, and the anion HPO₄²⁻, are likely to produce the relatively insoluble hydrogen phosphate CuHPO₄, or the more insoluble phosphate Cu₃(PO₄)₂.

5. Conclusions

The simple salt approximation provides a relative measure to predict solubility based on the known solubilities of simple salt constituents. For instance, it suggests that double salts prepared from K₂SO₄ and CaSO₄ are likely to be less soluble than salts prepared from K₂SO₄ and CuSO₄ because of the greater solubility of CuSO₄ than CaSO₄. Applying this reasoning to Tutton salts, their formation is primarily governed by the solubilities of the reactant simple salts and the ability of the divalent cation to interact strongly in octahedral coordination with water molecules. The first-row transition metal divalent cations form sulfates and selenates with appropriate solubilities for their interaction with monovalent, usually alkali metal, sulfates, whose cations are larger than Na⁺. Divalent sulfates from the main group, such as those from alkaline earth metals (except Mg), and the Group 14 cations, for example, Sn²⁺, have cations with lower charge densities and lower Lewis acidities, which cannot form octahedral coordination with water molecules. The simple salt approximation of the lattice energy of double salts is usually, but not always, within about 4% of the experimental lattice energy obtained from the experimental heats of formation and the Born–Haber cycle. There are, however, exceptions that may be the result of structural and/or energetic differences between the interactions of ions in simple salts and those in double salts, or from differences in the entropies of dissolution of Tutton salts relative to those of the simple salts. We suggest that the instability of the lithium and sodium Tutton salts is a result of lower-than-expected lattice energies in the lithium and sodium Tutton salts, relative to those energies of the simple salts. These differences are proposed as being due to the predominance of hydrogen bonding in the Tutton structure.