Goodbye to S2− in aqueous solution

P. M. May*a, D. Batkaa, G. Heftera, E. Königsbergera and D. Rowlandab
aChemistry, School of Engineering and Information Technology, Murdoch University, Murdoch, WA 6150, Australia. E-mail:; Tel: +61 8 9360 6068
bFluid Science and Resources Division, University of Western Australia, Crawley, WA 6009, Australia

Received 9th January 2018 , Accepted 30th January 2018

First published on 30th January 2018

New Raman spectra of Na2S dissolved in hyper-concentrated NaOH(aq) and CsOH(aq) cast serious doubt on the widely-assumed existence of S2−(aq). To avoid conceptual and practical problems with sulfide equilibria in numerous applications, S2−(aq) should be expunged from the chemical literature. Thermodynamic databases involving sulfide minerals also need careful revision.

A simple chemical problem that defies the best that modern instrumentation can provide is rare nowadays. A widespread, ongoing misadventure in science is even rarer. However, both have happened over the assumed existence of the chemical species S2−(aq). This species appears in respected inorganic chemistry treatises,1–4 reference works,5–9 introductory textbooks,10–15 innumerable research papers (ESI), and many widely-used thermodynamic databases. It is a pillar in classroom teaching of elementary solubility equilibria and it is commonly invoked in analytical, environmental and hydrometallurgical investigations (ESI). Yet the presence of significant amounts of S2− in aqueous solution was ruled out over 30 years ago.16 New Raman spectroscopic measurements presented below cast serious doubt on the formation of any S2−(aq) whatsoever. While it is impossible to prove that a chemical species never exists, we demonstrate that there is no credible experimental evidence to support the existence of S2−(aq) even when conditions are most favourable. Adopting the proposition that S2−(aq) does not exist would eliminate a great deal of confusion in the literature and counteract the ruinous effects on thermodynamic modelling of aquatic sulfide systems caused by previous interpretations. Significant benefits from improved understanding can thus be expected in a variety of environmental and industrial applications.

The most influential works to date on hydrogen sulfide deprotonation at high pH are those of Giggenbach17 and Meyer et al.18 Both show conclusively that there is no significant formation of S2−(aq) at [NaOH(aq)] ≲ 5 M (where the square brackets denote concentration and M is the concentration unit mol L−1). These observations are in accord with the value of pK0a2 ≥ 17 which these investigators derive for the presumed second acid dissociation constant of H2S(aq):

HS ⇌ S2− + H+K0a2 = {S2−}·{H+}/{HS}
pK0a2 = −log10(K0a2) (1)
image file: c8cc00187a-t1.tif(1a)
where braces, {[thin space (1/6-em)]}, represent activities and image file: c8cc00187a-t2.tif is the corresponding conditional equilibrium constant (when the activity coefficients are constant). At higher [NaOH(aq)], where significant formation of S2−(aq) might be expected, the data in both of these papers are equivocal. Giggenbach,17 using UV-absorption spectroscopy, proposed a lower limit of pK0a2 = 17.1 ± 0.2 from a shoulder attributed to S2− on the intense HS absorbance band centred at 260 nm. Tellingly, however, even in saturated NaOH(aq) solutions (ca. 23 M), the equilibrium (eqn (2)) could not be forced so far to the right that the HS signal disappeared completely.
HS + OH ⇌ S2− + H2O
K0b = {S2−}·{H2O}/{HS}·{OH} (2)
Meyer et al.18 employed Raman spectroscopy to calculate pK0a2 using the H–S stretching mode at ∼2600 cm−1. The intensity of this mode started to decrease at about 8.9 M NaOH and reached ca. 50% in 16.9 M NaOH. From a limited analysis of their measurements Meyer et al. selected pK0a2 = 17 ± 1, in accord with Giggenbach's estimate. Relevantly, both Giggenbach and Meyer et al. relied on numerical fitting processes to compare simulated and measured data even though it is clear from their accompanying figures that the effect being quantified falls worryingly close to some limiting experimental conditions.

The above conclusions appear to be supported by the work of Licht et al.19,20 who reported values of pK0a2 in good agreement with the spectroscopic estimates: 17.6 ± 0.3 from pH measurements with a glass electrode19 and 17.0 ± 0.3 from differential density measurements.20 Unfortunately, given the well-known limitations21 of even the best glass electrodes at pH > 12 and the general inapplicability of density measurements to the quantification of chemical speciation, little reliance can be placed on these results.

Usually such good agreement among independent investigators, using different techniques, would be considered as strong evidence for the existence of a proposed chemical species. In this case, however, there is a simpler and more compelling explanation. Hyper-alkaline metal hydroxide solutions are radically different from their dilute counterparts,22,23 which is not being properly taken into account. At the molecular level, the interactions between water-depleted ions become determined by packing and other structural factors, rather than the electrostatic forces that dominate in more dilute electrolyte solutions. Such effects render the notion of a related pK0a2 meaningless because there is no reasonable way to extrapolate the activity of a chemical species in [NaOH(aq)] > 10 M back to infinite dilution. The idea that this can be done even approximately is fallacious. The conceivable effects of ion interactions in concentrated electrolyte solutions are non-trivial24,25 and far beyond any current theoretical treatment. To be fair, Giggenbach17 and Meyer et al.18 carried out high quality work and they were well aware of the limitations of their methods, pointedly expressing doubts over the physical significance of their pK0a2 estimates. Regrettably, their concerns have largely been ignored.

Appropriate analytical probes for sulfide species, particularly in chemically-aggressive hyper-alkaline solutions, are almost non-existent. There is none at present that can be used to observe S2−(aq) directly so numerical fitting had to be employed in all of the above studies. However, much has been learned about the dangers of such fitting procedures in recent years.25,26 Co-incidences arising from physical artefacts and/or misinterpretations can occur all too easily. For example, take the earlier erroneous agreement (pK0a2 ≈ 14) between Ellis and Golding27 and Widmer and Schwarzenbach28 (ESI). Changes in bulk properties such as density, viscosity, refractive index and water activity, as well as impurity co-factors,29 may well obscure, or be mistaken for, changes in chemical speciation. Unless HS deprotonation is believed a priori, there are other possible interpretations of the experimental observations in high [OH].

Great improvements have been made in Raman spectroscopy technology since the study of Meyer et al.18 Nevertheless, our experimental findings are similar to those reported by them for the same NaOH(aq) medium: at room temperature (ca. 22 °C) the intensity of the HS band (Fig. 1) drops significantly only when [NaOH] ≥ 7 mol kg−1. Moreover, the intensity remains at >50%, even at [NaOH] ≈ 20 mol kg−1. Adjustment of band intensity using ClO4(aq) as an internal standard made little difference, further confirming the reliability of these observations.

image file: c8cc00187a-f1.tif
Fig. 1 Variation of the Raman intensity (in normalised units) of the HS(aq) mode at ∼2600 cm−1 with the molal concentration of NaOH(aq), also showing three simple fits as described in the text and ESI. The only adjusted parameters were image file: c8cc00187a-t3.tif for HS–H+ = S2−; pK′(NaS) = 16.8 for HS + Na+–H+ = NaS; and pK′(NaHS) = 1.7 for HS + Na+ = NaHS0.

While the variation of the intensity of the H–S mode with [NaOH] superficially resembles that expected from a simple deprotonation equilibrium (eqn (2)), it is quantitatively inconsistent with such a reaction. The data are inherently difficult to interpret because in these highly concentrated solutions {H2O} will decrease in parallel with any supposed change in [HS]. Nevertheless, three simple simulations using the ESTA package (ESI), each with one (conditional) equilibrium constant as an adjusted variable, suggests that the formation of NaS(aq) matches the observed data better (green line) than would the formation of either S2−(aq) (red line) or NaHS0(aq) (dashed black line).

An even more instructive result was obtained from analogous measurements in CsOH(aq). The Raman intensity, adjusted using SO42−(aq) as the internal standard (CsClO4(s) is sparingly soluble), showed no decrease at all (Fig. 2) up to the approximate solubility limit of CsOH(s).

image file: c8cc00187a-f2.tif
Fig. 2 Raman spectra at 1 ≲ [CsOH(aq)]/(mol kg−1) ≲ 11 (increasing from bottom to top) at ∼22 °C. Inset shows the invariance of the Raman intensity of the HS(aq) mode at ∼2600 cm−1 over the entire range of CsOH concentration.

The displacement of H+ from HS(aq) by Na+ in concentrated NaOH(aq) is consistent with all this evidence. Eqn (3) is therefore more pertinent than eqn (2), although even this would still be an over-simplification (ignoring the possible weak binding of HS and OH by Na+, for example). We note, in particular, that there is no spectral signal to confirm NaS(aq).

HS + OH + Na+ ⇌ NaS + H2O (3)
Importantly, however, if HS deprotonation occurs in NaOH(aq) it is unequivocally due to the presence Na+ as is evident from a comparison of Fig. 1 and 2 (inset). Values of image file: c8cc00187a-t4.tif obtained from measurements in NaOH(aq) thus refer to a medium in which the critical effect is dominated by strong Na+ interactions and, as such, cannot be characterised by any method currently available. Every connection between a putative S2− species in concentrated NaOH(aq) and other sulfide species in aqueous solution is therefore refuted.

There is not just this inability to extrapolate to infinite dilution (i.e., by appropriately defining activity coefficients in concentrated solutions), on top of the chaotic history of reported pK0a2 values (ESI). Even more compellingly, there is no practical difference between the above experimental estimates of 17, the OECD Nuclear Energy Agency recommendation30 of 19 or any other even-higher (order of magnitude) value. In other words, there is no relationship between independent and dependent observations. Sustaining the present situation by adding and then subtracting the same pK0a2 value is purely artificial.

We specifically do not depend here on any fundamental explanation for the difference found between NaOH(aq) and CsOH(aq) other than to note that structural causes (such as changes in hydration and packing) are likely, permitting a stronger interaction of S2− with Na+(aq) than Cs+(aq). A valuable conclusion can nonetheless be drawn with confidence: it is implausible to suggest that S2−(aq) forms via equilibrium (2) in NaOH(aq) but not in CsOH(aq). Hydroxide alone is evidently insufficient. Such reasoning, on the other hand, is not proof: S2−(aq) might exist in ‘regular aqueous solutions’ at negligibly low concentrations, even if it were of no practical interest (ESI). The issue is not just philosophical. It also has widespread tangible consequences.

A better understanding of equilibria in sulfide solutions can only be achieved by a major shift in thinking and practice in all relevant fields of chemical research and teaching, as required (ESI) by our ‘null hypothesis’: the sulfide anion, S2−, does not exist in aqueous solution. Previous attempts to deprecate this species have failed spectacularly. Just emphasising that pK0a2 is uncertain and/or that S2−(aq) is unimportant, as Myers did,16 will not suffice. The species S2−(aq) should no longer be tolerated (unless and until there is solid evidence to the contrary). It is easy enough to avoid by writing the reaction equations differently (ESI).

Our findings have significant ramifications, most notably for thermodynamic databases in which reliable older data of many chemical reactions become inconsistent with more-recent estimates based on differing values of pKa2. Errors so arising tend to become embedded in derived thermodynamic parameters in ways that are not easy to reverse (ESI). All thermodynamic calculations of sulfide solutions, even under acidic conditions, must therefore be treated with more-than-usual caution.31 Note, for instance, the major differences in Gibbs energies of formation for H2S(aq) between recent evaluations,32,33 and when compared with traditional values. Modellers can ensure that these confounding knock-on effects are minimised by working only with well-characterised equilibria established between chemical species at realistic concentrations. Experimentalists can help by proving the existence of putative chemical species beyond reasonable doubt. As shown above, no experimental investigation of S2−(aq) to date has met this critical standard. The sorry caravan of confusion over pK0a2 will roll on until S2−(aq) is comprehensively banished by the chemical community.

Conflicts of interest

There are no conflicts to declare.

Notes and references

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Electronic supplementary information (ESI) available. See DOI: 10.1039/c8cc00187a
Our experiments were performed as part of AMIRA (Australian Mineral Industries Research Association) project P507D supported by Alcoa World Alumina, BHP Billiton/Worsley Alumina, Hydro Aluminium Metal Products, and Rio Tinto Alcan. The Raman facility was purchased with funding from an Australian Research Council LIEF grant (LE120100112). We thank Professor Eric F. May (University of Western Australia) for helpful comments. We also acknowledge an anonymous referee who points out “…another argument also contradicting the existence of sulfide dianion in a low-water content environment like a concentrated sodium hydroxide solution where at best 2–3 water molecules solvate the individual ionic species. Hydrated sulfate dianion, for instance, fragments when stripped of the water molecules, so that low-hydrated sulfate (less than 2–3 water molecules attached) does not exist in the gas phase. By the same token sulfide dianion would undergo a Coulomb explosion thereby diminishing its charge density.”

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