Hydrogenium-bis-hydrogensulfate anions adjacent to [S₂O₇]²⁻ in Rb₃[S₂O₇][H(HSO₄)₂]: a structural evidence of the increasing acidity of polysulfuric acids with growing chain length

1 Introduction

Sulfuric acid is a strong acid whose first corresponding base HSO₄⁻ reacts still as an acid in aqueous medium. This behavior is reflected by the fact that there are by far more reports on sulfates containing the unprotonated anion SO₄²⁻ than on acidic sulfates displaying the monoprotonated anion HSO₄⁻ [1]. Table 1 summarizes the acidic sulfates of the alkali metals, in the first part – the H₂SO₄-rich sulfates – ordered by growing H₂SO₄ content and decreasing H₂O content, and in the second part – the SO₃-rich sulfates – ordered by growing SO₃ content and decreasing H₂SO₄ content. Theoretical calculations for the first members of the homologous series of polysulfuric acids H₂S_nO_3n+1 show that their acidity increases with growing chain length [26]. Thus, it is not surprising that even for disulfuric acid, H₂S₂O₇, nearly no hydrogen disulfates have been reported, whereas there are more than 50 well-characterized disulfates present in the literature. Just six hydrogen disulfates were obtained, more or less accidentally [27], [28], [29], [30], [31], [32], until we lately presented a systematic study on hydrogen disulfates with cations of low charge [24]. For the salts of trisulfuric acid, the monoprotonated anion was even completely unknown until we recently reported on the stabilization of the hydrogen trisulfate anion [HS₃O₁₀]⁻ in the crystal structures of Na[HS₃O₁₀], K[HS₃O₁₀], and Rb[HS₃O₁₀] [25]. With respect to the theoretical prediction that the acidity of polysulfuric acids increases with growing chain length, it can be assumed that in acidic compounds containing polysulfate anions of different chain lengths the shorter anion will be the protonated one. The structure of the recently reported K₂[S₂O₇][H₂SO₄] is an illustrative confirmation for this assumption [23]. It shows the disulfate anion adjacent to a molecule of coordinated sulfuric acid, and the structural data clearly prove that no protonation according to “K₂[HS₂O₇][HSO₄]” occurs. Following this line, the palladate Ba₂[Pd(HS₂O₇)₂(S₃O₁₀)₂] is another intriguing example [28]. Here the protonation of the disulfate anion is favored, in accordance with the low basicity of the [S₃O₁₀]²⁻ anion. The crystal structure of the now presented rubidium salt Rb₃[H(HSO₄)₂][S₂O₇] is not only another striking example for the assumptions on the acidity of polysulfuric acids, but it is also one of the very few examples exhibiting the hydrogenium-bis-hydrogensulfate anion [H(HSO₄)₂]⁻ that has been reported only twice, the first time by Werner et al. in the crystal structure of Li[H(HSO₄)₂](H₂SO₄)₂ [19] and the second time by our group in the structure of K₃[Pt₂(SO₄)₄H(HSO₄)₂] [33]. Furthermore, Rb₃[H(HSO₄)₂][S₂O₇] bridges the gap between acidic sulfates just containing A₂SO₄ (A: alkali metal), H₂SO₄, and H₂O in a certain ratio (Table 1, first part) and SO₃-rich acidic sulfates (Table 1, second part) as it is the SO₃-poorest acidic sulfate containing SO₃, A₂SO₄, and H₂SO₄.

2 Results and discussion

Rb₃[S₂O₇][H(HSO₄)₂] crystallizes in the monoclinic space group C2/c (no. 15) with four formula units per unit cell. The crystal structure exhibits two different anions with sulfur atoms on two crystallographically distinguishable positions (Fig. 1). The disulfate anion [S₂O₇]²⁻ is built up by the vertex connection of two crystallographically equivalent sulfate tetrahedra via the bridging oxygen atom O111 located on the Wyckoff position 4e with site symmetry 2. The S–O distances to the terminal oxygen atoms range between 143.27(7) and 145.67(7) pm, and the bond to the bridging oxygen atom O111 is elongated (163.14(4) pm).

Fig. 1:

Anions in the crystal structure of Rb₃[S₂O₇][H(HSO₄)₂]: the disulfate anion [S₂O₇]²⁻ and the hydrogenium-bis-hydrogensulfate anion [H(HSO₄)₂]⁻. For the hydrogen atom H23 (shown as light gray circles with hatched borders) an occupancy of 0.5 is found due to the location close to a center of symmetry. The displacement ellipsoids are drawn at a probability level of 85%. Bond length (pm): S1–O11 143.27(7), S1–O12 143.74(6), S1–O13 145.67(7), S1–O111 163.14(4), S2–O21 143.90(6), S2–O22 144.01(6), S2–O23 150.60(6), S2–O24 154.99(7).

The second sulfur atom is the center of a single sulfate tetrahedron which is formally protonated twice at the oxygen atoms O23 and O24 (Fig. 1, right). For H23, a chemical occupancy of 0.5 results due to the location of the hydrogen atom close to a center of inversion and for reasons of charge compensation. This is the same situation as in the crystal structure of Li[H(HSO₄)₂](H₂SO₄)₂ [19]. A difference Fourier map of the hydrogen bond is represented in Fig. 2, and the details of the hydrogen bonding system are given in Table 2. The difference Fourier map shows clearly the two crystallographically equivalent positions of the hydrogen atom close to the center of inversion and no blurred electron density as often observed for symmetrical hydrogen bonds [25], [34].

Fig. 2:

Difference Fourier map of the hydrogen bond O23···H23···O23 in the crystal structure of Rb₃[S₂O₇][H(HSO₄)₂].

Another indication for the formulation of a [H(HSO₄)₂]⁻ anion is the length of the respective S–O bond to the oxygen atom O23. With 150.60(6) pm it is just between the S–O distance to the fully protonated oxygen atom O24 (154.99(7) pm) and the terminal oxygen atoms O21 and O22 (143.90(6) pm, 144.01(6) pm). Thus, a single proton is found between two crystallographically equivalent HSO₄⁻ anions and the grade of protonation of the respective oxygen atoms (0 for O21, O22; 0.5 for O23; 1 for O24) is clearly reflected in the S–O bond lengths. The resulting hydrogen bond (donor acceptor distance: 247.1 pm) is strong according to the classification of Jeffrey and the anion can be described as a hydrogenium-bis-hydrogensulfate anion [H(HSO₄)₂]⁻ [35]. Via the hydrogen atom H24 of the fully protonated oxygen atom O24 a second moderately strong hydrogen bond is built to the oxygen atom O13 of the [S₂O₇]²⁻ unit (donor acceptor distance: 255.8 pm, Table 2) linking the anions to chains proceeding along [101] as shown in Fig. 3.

Fig. 3:

Unit cell of the crystal structure of Rb₃[S₂O₇][H(HSO₄)₂]. Disulfate anions are emphasized in light gray, and hydrogenium-bis-hydrogensulfate anions are shown in dark gray. Moderate hydrogen bonds are displayed as dashed lines, and the strong hydrogen bonds in the [H(HSO₄)₂]⁻ anion as solid lines. The hydrogen bonds link the anions to chains proceeding along [010].

Charge compensation is realized by Rb cations which are located on two crystallographically distinguishable sites. Rb1 is located on the Wyckoff position 8f with site symmetry 1, and Rb2 on the Wyckoff position 4e with site symmetry 2. Both [S₂O₇]²⁻ and [H(HSO₄)₂]⁻ anions are part of the coordination sphere of the cations. Rb1 is surrounded by 11 oxygen atoms belonging to three [S₂O₇]²⁻ units and three [H(HSO₄)₂]⁻ moieties (Fig. 4, left). Two disulfate anions function as bidentate ligands coordinated via an edge of one sulfate tetrahedron; the third attacks the cation in a monodentate way. The [H(HSO₄)₂]⁻ moieties coordinate to the cation bidentately, two via an edge of one [HSO₄]⁻ tetrahedron and one by one oxygen atom of each [HSO₄]⁻ unit. Rb2 is surrounded by 13 oxygen atoms belonging to two disulfate anions and four [H(HSO₄)₂]⁻ anions (Fig. 4, right). One disulfate anion attacks tridentately with the bridging oxygen atom O111 and one oxygen atom of each [SO₄]²⁻ moiety; the other one attacks with just one oxygen atom of each [SO₄]²⁻ tetrahedron. The [H(HSO₄]⁻ moieties coordinate bidentately via an edge of one [HSO₄]⁻ tetrahedron.

Fig. 4:

Coordination sphere of Rb1 (left) and Rb2 (right). Disulfate anions are emphasized in light gray, and hydrogenium-bis-hydrogensulfate anions are highlighted in dark gray.

The compound shows a ratio Rb₂[SO₄]:H₂SO₄:SO₃ of 1:1:0.67, and thereby it is the SO₃-poorest acidic sulfate that already shows an excess of SO₃. The next member of the SO₃-rich compounds is the double salt K₂[S₂O₇]·K[HSO₄] [20] (1:0.33:0.67) and the disulfate sulfuric acid adduct K₂[S₂O₇]·H₂SO₄ [23] (1:1:1) followed by the hydrogen polysulfates A[HS₂O₇] and A[HS₃O₁₀] (A=alkaline metal) with an even higher SO₃ content (A₂[SO₄]:H₂SO₄:SO₃ ratios of 1:1:2 and 1:1:4) [24], [25].

3 Conclusions

The scarcely communicated hydrogenium-bis-hydrogensulfate anion [H(HSO₄)₂]⁻ has been stabilized adjacent to a disulfate anion [S₂O₇]²⁻. In a difference Fourier map of the strong hydrogen bond, the two symmetry equivalent positions of the hydrogen atom close to the center of inversion are explicitly distinguishable and the grade of protonation of the oxygen atoms is reflected in the respective S–O bond lengths. Furthermore, the compound shows the poor basicity of the anion [S₂O₇]²⁻ as it remains unprotonated next to a strongly acidic species and thus confirms the assumption on the acidity of polysulfuric acid to increase with growing chain length.

4 Experimental section

Rb₃[S₂O₇][H(HSO₄)₂] was obtained from the reaction of commercial Rb₂[CO₃] (99.9%, Chempur, 150 mg, 0.6 mmol) with neat SO₃ in a torch-sealed glass ampoule. The remaining quantity of water in the starting material was sufficient to lead to an H-containing substance. Rb₂CO₃ was loaded into an ampoule. A 1000 mL three-necked flask was filled with P₄O₁₀ (20 g, 97%), and a dropping funnel filled with fuming sulfuric acid (1 mL, 65% SO₃) and the glass ampoule were connected. The ampoule was cooled with liquid nitrogen. The fuming sulfuric acid was dropped onto P₄O₁₀ within 5 min while heating the flask with a heat gun. The produced SO₃ condensed in the ampoule. The ampoule was torch sealed, placed into a tube furnace, and heated up to 100°C within 12 h. The temperature was maintained for 24 h and the furnace cooled down to room temperature within 120 h. Colorless extremely sensitive crystals were obtained. A small excess of SO₃ was removed by cooling the end of the ampoule not containing the crystals in liquid nitrogen before opening the ampoule. A suitable single crystal was selected under protecting oil with the help of a polarization microscope and transferred into the cool nitrogen stream of a single crystal diffractometer (BRUKER APEX II, graphite monochromator). Intensity data were collected and corrected using multiscan techniques. The structure solution was successful applying Direct Methods (Shelxs) [36]. Subsequent refinement with Shelxl yielded the complete crystal structure [36]. Anisotropic displacement parameters were introduced and a numerical absorption correction was applied to the reflection data. For the hydrogen atom H23, an occupancy of 0.5 was defined due to the location close to a center of inversion and for reasons of charge compensation. The other hydrogen atom H24 has been refined without restraints. Table 3 gives details of the data collection and crystallographic data. In Table 4, selected distances are summarized.

For the creation of the difference Fourier map, the structure was refined without refining the position of the hydrogen atom H23. The remaining electron density was plotted as a difference Fourier map using the program Olex2 [37].

Atomic positions and further details of the crystal structure investigation may be obtained from Fachinformationszentrum Karlsruhe, 76344 Eggenstein-Leopoldshafen, Germany (fax: +49-7247-808-666; e-mail: crysdata@fiz-karlsruhe.de, https://www.fiz-karlsruhe.de/en/leistungen/kristallographie/kristallstrukturdepot/anforderung-deponierter-datensaetze.html) on quoting the deposition number CSD-430319.