In situ determination of polysulfides in alkaline hydrogen sulfide solutions

Accepted Manuscript In situ determination of polysulfides in alkaline hydrogen sulfide solutions Franky E. Bedoya-Lora, Anna Hankin, Geoff H. Kelsall PII:

S0013-4686(19)30807-2

DOI:

https://doi.org/10.1016/j.electacta.2019.04.119

Reference:

EA 34067

To appear in:

Electrochimica Acta

Received Date: 28 January 2019 Revised Date:

17 April 2019

Accepted Date: 18 April 2019

Please cite this article as: F.E. Bedoya-Lora, A. Hankin, G.H. Kelsall, In situ determination of polysulfides in alkaline hydrogen sulfide solutions, Electrochimica Acta (2019), doi: https:// doi.org/10.1016/j.electacta.2019.04.119. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT In situ determination of polysulfides in alkaline hydrogen sulfide solutions Franky E. Bedoya-Lora*, Anna Hankin and Geoff H. Kelsall# Departments of Chemical Engineering, Imperial College London, London, SW7 2AZ, UK Abstract

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A method was developed to determine low concentrations of polysulfide ions (Sn2- expressed as zero-valent sulfur) in situ and in the presence of high concentrations (0.5 mol dm-3) of hydrogen sulfide ions, HS-, at pH 14. UV-visible spectrophotometry was used to determine

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absorbances at 295 and 420 nm using an immersion probe, designed for highly corrosive environments. Three absorbance trends were found, corresponding to three concentration

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ranges of zero-valent sulfur: low (0 – 1.2 × 10-3 mol dm-3), medium (1.2 – 3.6 × 10-3 mol dm) and high (3.6 – 10 × 10-3 mol dm-3). The non-linear dependence of absorbance on

concentration over the range studied was due to disproportionation of polysulfides. Determination of these species is well known to be problematic at low concentrations due to

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the effects of adventitious oxygen in solution, meta-stability and speciation of polysulfide species: S22- – S82-. Oxygen concentrations must be minimised in the inert gas used to deoxygenate sulfide solutions and for the same reason, their contact with atmospheric oxygen

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should be minimised. During potentiostatic oxidation of alkaline solutions containing HS-

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ions in the anolyte of electrochemical reactors incorporating cation-permeable membranes, temporal changes in anolyte absorbance and charge were used to estimate polysulfide concentrations. Charge yields for sulfide to polysulfide oxidation were close to unity, confirming the utility of the technique developed. Molar attenuation coefficients of the predominant polysulfide ions S32- at 420 nm and S42- at 295 nm were also estimated as 289 and 3609 dm3 mol-1 cm-1, respectively, and comparable to values of (190, 206) and (3420, 3690) dm3 mol-1 cm-1 reported previously.

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ACCEPTED MANUSCRIPT Keywords: hydrogen sulfide; polysulfide; sulfide speciation * Corresponding author E-mail address: [email protected] (F.E. Bedoya-Lora).

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ACCEPTED MANUSCRIPT 1.

Introduction

Attempts to determine concentrations of polysulfide ions, Sn2-, and the speciation of sulfur compounds in aqueous solutions was first reported in 1822 [1]. Polysulfides are involved in a wide range of applications and energy-related systems in which fast kinetics, reversibility and

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low thermodynamic energy barriers are required, such as aqueous [2, 3] and non-aqueous [3] lithium-sulfur batteries, and, more recently, hydrogen production combined with aqueous hydrogen sulfide waste treatment driven by solar energy [4-6]. Sulfide and polysulfide

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speciation are also of major importance in the Kraft pulp industry for processes involved in delignification of wood [7, 8]. Polysulfides are known to be intermediate and meta-stable

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species in the oxidation mechanism of hydrogen sulfide ions, HS-, to elemental sulfur and sulfoxy species, such as sulfate (SO42-), sulfite (SO32-) and thiosulfate (S2O32-) ions [9]. Numerous ex situ techniques have been developed aiming to quantify individual polysulfide ions, including polarography, potentiometric titration, UV and infrared spectrophotometry

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[10], iodometric and acidimetric methods [11]. In situ UV spectroscopy has also been reported to quantify total polysufide ion concentration expressed as the ratio between total zero-valent sulfur to hydrogen sulfide ion [7]. These techniques require high concentrations

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of zero-valent sulfur with respect to dissolved sulfur (Na2S:S0 > 1:0.1), when tetra- and penta-sulfides are the predominant and most (meta-)stable species. Cyclic voltammetry can

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also be used to quantify organic polysulfides (R-Sn-R) at concentrations as low as 5 to 6 × 10mol dm-3 [12]. A novel method involving several stages of enrichment coupled with HPLC-

UV analysis is the most recent development for analysing polysulfide ions at concentrations down to 10-9 mol dm-3 [13]. From all these methods, UV spectrophotometry has been the most popular and extensively used to study polysulfide solutions in alkaline aqueous solutions [1, 10, 14, 15]. However, its use to quantify individual polysulfides is limited and relatively high ratios of zero-valent sulfur to dissolved sulfur are required to obtain a linear

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ACCEPTED MANUSCRIPT response. A thorough literature review of the available techniques for polysulfide determinations and a summary of equilibrium properties has been reported [16]. Recently, there has been an increased interest in the analysis of sulfidic waters due to the biological implications in the sulfur cycle [17] and metabolic and enzymatic processes involving

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polysulfide speciation in living cells [18]. Despite research across the wide range of applications and environments in which polysulfides are important, there is still no consensus on the longest polysulfide chain (Sn2-) and their speciation is still debated [18]. Giggenbach

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[19] and Licht [20] reported n < 5 for highly alkaline (pH > 12) and concentrated hydrogen sulfide ([HS-] > 0.1 mol dm-3) solutions; DFT methods have been used to calculate the UV-

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vis absorption energies for polysulfides with n < 6 [21], while sulfur chain lengths up to n = 8 (S82-) have been reported [17] for pH < 12 and [HS-] < 0.01 mol dm-3. Our application used (photo-) electrochemical reactors to effect oxidation of concentrated alkaline aqueous hydrogen sulphide ions by photo-generated holes to polysulfides, coupled to

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water reduction to hydrogen by photo-generated electrons [5]. More details of such photoassisted hydrogen sulfide splitting, why charge yields for hydrogen sulfide ion conversion to

in [22].

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polysulfides ions needed to be measured and the implications of such processes, are reported

The objective of what is described below was to develop a method to measure those initially

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low concentrations of polysulfide ions (ca. 10-3 mol dm-3), expressed as zero-valent sulfur, using an immersion probe coupled to a UV-visible spectrophotometer. In situ and real-time quantification of polysulfide ion concentrations is critical to assessing the reactor performance for hydrogen production by aqueous hydrogen sulfide splitting [22]. 2.

Polysulfide speciation

2.1. Polysulfide concentrations at equilibrium

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ACCEPTED MANUSCRIPT Equilibrium polysulfide speciation was predicted as a function of dissolved zero-valent sulfur, ‘S’, following a mass balance based on reports by Licht [14, 20], Giggenbach [1, 19] and Helz [17]. Full details of these calculations and comparison of the models can be found in the ESI, Fig. S10 – S13 and Table S2. The numerical model by Licht (Fig. S12) was not

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able to converge for small concentrations of zero-valent sulfur (< 0.001 mol dm-3) due to the complexity and non-linear behaviour of the equilibria. Hence, we simplified the model by assuming constant concentrations of OH- and HS- ions. The validity of this assumption was

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confirmed with the full mass balance, in which the predicted pH (14.158 – 14.160), ionic strength (2.003 – 2.005) and HS- concentration (0.4987 – 0.4943 mol dm-3) remained

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relatively constant for zero-valent sulfur concentrations between 0.001 and 0.01 mol dm-3. This behaviour was also evident experimentally after measuring pHs of polysulfide ion solutions

with

different

concentrations.

Furthermore,

the

calculated

equilibrium

concentrations of penta-sulfide ions were found to be several orders of magnitude lower in

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the presence of high concentrations of HS- and OH-, as predicted by reaction (1), in which [HS-] × [OH-] displace the equilibrium to lower polysulfide activities / concentrations: 



(n − 2)S + HS + OH ⇔ (n − 1)S( ) + H O

(1)

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Hence, under these conditions, concentrations of higher polysulfides (Sn>52-) are negligible.

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Fig. 1 shows the predicted concentrations assuming a constant product of [HS-] × [OH-]. S32ions were the predominant species for [‘S’] > 0.0005 mol dm-3, whereas S22- ions predominated for even lower [‘S’]; S42- ions became the main species only at concentrations > 0.1 mol dm-3 (not shown in figure). These predictions were supported by experimental data, in which S42- ions accounted for up to 90% of the zero-valent sulfur at 1 mol dm-3 of added elemental sulfur [23]. Polysulfides of order n > 5 have been proposed theoretically [21] and more recently, experimental proof was reported of such species in natural ground waters [13, 16] . However, 5

ACCEPTED MANUSCRIPT polysulfides with n > 5 should not be stable due to the limited aqueous solubility of zerovalent sulfur [10, 24]. For this reason, the study of their disproportionation has focused on polysulfides with 2 ≤ n ≤ 5. More importantly, Fig. 1 also shows how S42- ion concentrations are predicted not to increase linearly as a function of zero-valent sulfur concentrations. This

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behaviour was reported first by Pringle for higher concentrations [10], but implies that UVvisible absorbance peaks related to S42- ions would not be expected to increase linearly with concentration. S22- ions disproportionate rapidly with increasing sulfur at very low

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concentrations, also causing deviations from linear behaviour.

Table 1 summarises the molar attenuation coefficients, ελ, of polysulfides with characteristic

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peak absorbances at ca. 300, 360 and 420 nm [1, 20], whereas solutions of 1 mol dm-3 NaOH absorb only at wavelengths < 200 nm and 260 nm when Na2S is added [15, 25], typical of sulfide compounds (< 280 nm). However, S22- ions are known to have an additional absorbance peak at 360 nm, to which S42- and S52- ions also contribute with their higher

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attenuation coefficients, in contrast to S32- ions which absorb at ca. 420 nm. Hence, it was expected that any absorbance at ca. 420 nm was due exclusively to S32- ions, while S42- ions had a higher absorbance at 300 nm, assuming that the concentration of S52- ions was

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negligible. Consequently, any deviation from linearity at 300 nm could be associated with the

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disproportionation of S42- ions, specifically for concentrations between 0.001 and 0.006 mol dm-3, as evident in Fig. 1.

2.2. Effect of electrode potentials on polysulfide concentrations Increasing electrode potentials control both the oxidation kinetics of the polysulfide / hydrogen sulfide ion couple: S + nH O + 2(n − 1)e ⟺ nHS + nOH

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(2)

ACCEPTED MANUSCRIPT and the speciation of polysulfide ions, with mean sulfur oxidation states of -1 (S22-) to -0.25 (S82-). At higher potentials, further oxidation to zero-valent sulfur can occur by the overall reaction: ′  + H O + 2e ⟺ HS + OH

(3)

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Reduction and oxidation of water in alkaline aqueous solution, with hydrogen and oxygen as products respectively, can also take place at the electrode surface: 2H O + 2e ⇔ H + 2OH

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O + 2H O + 4e ⇔ 4OH

(4) (5)

Using critically reviewed thermodynamic data [26], the potential-pH diagram in Fig. 2 was

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computed for a (meta-stable) S – H2O system from which sulfoxide species were excluded [5], because, though more thermodynamically stable than polysulfide ions, their rates of oxidative formation from sulphide ions are limited by relatively large activation energies. Elemental sulfur ‘S’ was predicted to be the stable form of sulfur at pH 14 and potentials >

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0.53 vs. RHE. Based on previous reports [26, 27], Fig. 3 shows the effect of electrode potential on activities of polysulfide ions for pH 14, 298 K and dissolved sulfur activity of 0.5. As shown in the ESI, these results were computed after solving numerically the

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equilibrium equations for the electrochemical reactions, represented by Nernst equations, and homogeneous chemical equilibria of hydrogen sulfide ions in alkaline conditions [26]. Fig. 3

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predicts that for electrode potentials > 0.45 V vs. RHE, S52- ions become the predominant polysulfide ions, formed by reaction (2). In our case, the oxidation was driven by photogenerated holes at a photo-anode, from which they were expected to diffuse towards the bulk of the solution, being reduced progressively by the fast homogeneous reaction (1) by HS- ions to lower polysulfides, and ultimately equilibrating with species in the bulk solution. Using other published thermodynamic data [16, 28], the effect of electrode potential on polysulfide speciation was predicted for higher polysulfides (Sn2- for 2 < n < 8), and their

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ACCEPTED MANUSCRIPT corresponding protonated (HSn-) and diprotonated forms (H2Sn0), Fig. S10 and S11 in the ESI. Concentrations of such protonated species in highly alkaline electrolyte solutions were predicted to be negligible, as expected from their pKa values. The predicted behaviour is very sensitive to the source of the thermodynamic data, which can be dissimilar even for the same

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authors [16, 28]. Potential-pH diagrams (Fig. S10 and S11) were constructed using both sets of thermodynamic data showing disagreement on the equilibrium lines and order of oxidation/reduction of polysulfide ions. The model also predicted that at sufficiently high

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electrode potentials (> 0.55 V vs. RHE), S62- ions, or even higher polysulfides, could predominate, but were also expected to be reduced by the fast homogeneous reaction (1) and

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to equilibrate to lower polysulfides in the bulk solution.

Fig. 3 predicts that, depending on the electrode potential, oxidation of HS- ions would have produced high concentrations of Sn2- ions near the anode by reaction (2), so given the high molar absorption coefficient of these species, increasing absorption at 300 nm was expected,

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as reported previously [5] and below. Elemental sulfur was also expected to be formed at the anode by reaction (3) at applied potentials > 0.53 V vs. RHE, followed by reaction (6) with

solution.

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non-adsorbed ‘S’, causing homogeneous reduction to Sn2- ions by HS- ions in the bulk



n S  + HS + OH ⟺ S + H O

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(6)

2.3. Decomposition of polysulfide ions to sulfoxides Oxygen ingress into the electrolyte solution potentially can result in the oxidation of the added zero-valent sulfur and hydrogen sulfide ions to form sulfate, sulfite and thiosulfate according to reactions (7) to (11), as predicted thermodynamically [9]: 2HS + O ⟺ 2S + 2OH

(7)

2HS + 2O ⟺ S O

 + H O

(8)

2HS + 3O + 2OH ⟺ 2SO

 + 2H O

(9)

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ACCEPTED MANUSCRIPT HS + 2O + OH ⟺ SO

 + H O

(10)

Polysulfide ions are intermediates in the above reactions and can be oxidised faster than hydrogen sulfide in presence of oxygen, by reactions such as [29]: 2S + 3O ⟺ S O

 + (n − 2)S

(11)

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Yellow polysulfide solutions usually become fully decolourised in the presence of oxygen over 1 to 9 days [29]. However, this is sufficiently fast to affect concentrations of polysulfide ions due to their decomposition during experiments and calibrations, which usually lasted a

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day. Early studies on polysulfide ions found that elemental sulfur can also react directly with hydroxide species in absence of oxygen and at room temperature to form thiosulfate and

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polysulfides [30]:

(2n + 2)S + 6OH ⟺ 2S + S O

 + 3H O

(12)

Likewise, decolouration of polysulfide solutions has also been proposed to be promoted by temperature, accelerating their conversion to thiosulfate ions in alkaline conditions [14, 31]. (13)

S + 3OH ⟺ S O

 + 3HS

(14)

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S + 8OH + H O ⟺ S O

 + 10HS

Fig. 4 shows an E-pH diagram for which, unlike Fig. 2, sulfoxy species other than

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sulfate(VI) were included in the calculation. This predicts that under alkaline conditions and

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relatively low electrode potentials, SO32- and S2O32- ions may form as metastable species, sulfate ions being the thermodynamically stable species under those conditions. However, hydrogen sulfide oxidation to polysulfide ions is faster than to sulfoxy species, presumably as activation energies of the latter reactions are greater than of those for polysulfide formation. The consequences of the decomposition of polysulfides was observed experimentally, when de-aerated solutions were sonicated without temperature control, reaching ca. 60 °C, they turned completely transparent, and in some cases typical absorbance peaks disappeared completely. The lower the concentration of zero-valent sulfur and higher the concentration of 9

ACCEPTED MANUSCRIPT hydroxide ions, the faster the decomposition of polysulfides to thiosulfate and the lower the temperature required to drive the reaction(s). For example, it took 1 hour to decompose half of the amount of zero-valent sulfur in an equimolar solution of S42--S32- ions at 100 °C and pH 14 [31], 31 days at 60 °C and 5400 days at 20 °C [20]. A recent extensive study of

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polysulfide disproportionation found that at 25 °C and in absence of oxygen, there was minimal decomposition after 50 days [14]. Hence, even at lower concentrations, it is reasonable to believe that at room temperature, the polysulfide decomposition can be

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disregarded.

It is essential to minimise the ingress of oxygen to minimise rates of decomposition reactions

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(7) to (14), driven by oxygen and temperature at high pH, as well as ensuring a fresh source of sulfur. This is contrary to what was recommended in a recent report [15]; solutions prepared in a typical laboratory atmosphere exhibited similar behaviour to that of a solution prepared with de-aerated water in a controlled nitrogen environment. However, no details

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were given for the purity of nitrogen, which, as will be reported in the results section, can influence the polysulfide decomposition rates even at trace levels of oxygen. 3.

Experimental

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All solutions were prepared in distilled water purged for more than one hour with zero grade

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nitrogen (99.998% and oxygen impurity removed, BOC Ltd.) to remove residual dissolved oxygen. Once solutions were prepared, contact with air was minimised by purging with nitrogen at times when the container had to be opened. 1 mol dm-3 NaOH (97%, SigmaAldrich, UK) and 0.5 mol dm-3 Na2S (Na2S·9H2O ≥99.99%, Sigma-Aldrich, UK) were prepared as the blank solution; typically, 1 dm3 of solution was needed for a single calibration curve. Polysulfide solutions were prepared by adding elemental sulfur (99.998%, Sigma-Aldrich, UK), which was weighted (A&D Weighing GH-252 Delta Range) rapidly in atmospheric

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ACCEPTED MANUSCRIPT conditions and added to prepared stock solutions of 0.1 dm3: 1.5 × 10-2 mol dm-3 (48.09 ± 0.03 mg) for low concentration and 3 × 10-2 mol dm-3 (96.18 ± 0.03 mg) for medium and high concentrations. The formation of polysulfide ions from elemental sulfur in alkaline aqueous solutions follows reaction (6) [19].

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Stock solutions were closed and sonicated for 1 h until sulfur was dissolved completely. Heating of the solution was prevented by changing the sonicator (SW 6H, Sonno Swiss) bath every 15 min or by using ice to keep the bath cooled. The effect of sonication on hydrogen

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sulfide solution was tested and found not to be significant if solutions were kept at room temperature, as shown in Fig. S1 in the ESI. Solutions at different concentration (0.3 – 10 ×

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10-3 mol dm-3) were prepared by diluting stock solution in 0.05 dm3 of blank solution, and left closed for more than 15 h until polysulfide species reached equilibrium, as shown in Fig. S2 and S3 in the ESI.

Absorbance spectra were measured using a reflective immersion probe (AIFDP-7UV200-

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2VAR-PK8, Anglia Instruments) made of PEEK with an aperture of 5 mm (10 mm optical path) and a wavelength range of 200 – 1100 nm. The probe was connected to a deuterium arc lamp (8453 UV-Vis SP, Agilent). Absorbance spectra were recorded with a UV-vis

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spectrometer (Black-Comet CXR-25, StellarNet) using an integration time of 0.8 s between

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270 and 900 nm. Three measurements were recorded and averaged for each data point. Fig. 5 shows a schematic of the equipment for determination of polysulfide ion concentrations. Synthetic polysulfide solutions were produced by HS- oxidation, reaction (2), in two electrochemical reactors, each with two compartments separated by a cation-permeable membrane (PTFE reinforced Nafion® 424, DuPont Inc.). The smaller, bench-scale reactor comprised an anolyte and catholyte compartment of 0.1 dm3 (PVC body) each with an SnIVdoped hematite photo-anode supported on a titanium sheet and electro-active area of 1.8 × 105

m2; constant potential electrolyses over 23 h and 50 h resulted in current density – time data

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ACCEPTED MANUSCRIPT to correlate with polysulfide formation rates. An up-scaled and gas-tight reactor with an anolyte volume of 0.8 dm3 (PVDF body) utilising electrodes with geometrical areas of 0.01 m2 had a greater electrode area : solution volume ratio, so greater rates of polysulfide formation could be achieved. However, large electrodes (> 0.01 m2) result in inhomogeneous

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potential and current density distributions over photo-electrode surfaces, decreasing the performance of photo-electrochemical reactors. This can be mitigated by perforating electrodes, thereby decreasing ionic current path lengths between cathode an anode [32].

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Hence, 0.01 m2 planar and perforated (perforations of ca. 3 mm × 1.5 mm, spaced 5.8 mm horizontally and 2 mm vertically apart) SnIV-doped hematite anodes were used and compared

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in this study. In both reactors, bench and up-scaled, platinised titanium mesh (Expanded Metal Company) acted as a counter electrode and a home-made 0.5 mol dm-3 Na2S|Ag2S|Ag as pseudo-reference electrode (0.170 V vs. RHE at pH = 14). Blank solutions (1 mol dm-3 NaOH and 0.5 mol dm-3 Na2S) were used as anolyte and 1 mol dm-3 NaOH as catholyte.

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Rates of cross-over of Sn2- and HS- ions between compartments was decreased effectively by the membrane, so no time dependence of catholyte absorbance was determined over extended periods. A potentiostat/galvanostat (Autolab PGSTAT 30) was used to record current-time

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data at an applied potential of 1.15 V vs. RHE at the anode, over 25 h for the bench-scale

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reactor and at a fixed cell potential difference of 1.226 V for 15 h for the up-scaled reactor. Hematite photo-anodes for hydrogen sulfide splitting [5] were characterised in the benchscale reactor, to enable spatial distributions of current densities to be minimised and ensure a controlled potential at the anode vs. a Ag2S|Ag reference electrode. Subsequently, zero-valent sulfur and hydrogen fluxes were determined to assess the performances of such systems in a scaled-up reactor, which was usually operated in the absence of a reference electrode, but at a fixed cell potential difference.

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ACCEPTED MANUSCRIPT Spectra were recorded typically every 1 or 5 minutes in the anolyte, and current densities recorded every 10 seconds. Zero grade nitrogen was bubbled into the anolyte at all times, which prevented the ingress of oxygen and maintained a well-stirred electrolyte. Hydrogen flux densities generated at the cathode were measured with a gas flow meter

Charge yields,

Φ"# ,

were computed as the fraction of the flux density of the reaction products

of interest and the total current density (j) passed: %& '(')*

=

+& ν,,& .

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Φ"# = %

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(MilliGascounter MGC-1, Ritter). The time to reach steady state was typically 3 to 8 hours.

%'(')*

(15)

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where /" is the flux density of the species 0, ν#," is the charge number for reaction 0,

123245 is the total current density at the electrode and 6 is the Faraday constant, 96485.33 C mol-1.

Results and discussion

4.1. Calibrations curves

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4.

The characteristic three absorption peaks at 295 nm, 360 nm and 420 nm were observed in

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polysulfide solutions prepared as reported above. Fig. 6 shows typical spectra of polysulfide solutions at different concentrations of zero-valent sulfur. The peak at 295 nm had a

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characteristic higher absorbance, followed by a less-defined peak at 360 nm. The shoulder at 420 nm exhibited a lower absorbance as expected, and was possibly associated to S32- ions, according to the values presented in Table 1. However, this peak appeared peculiarly only for [‘S’] > 4 × 10-3 mol dm-3. This could be explained by the appearance of polysulfide ions which became predominant at about this concentration. However, according to the predictions of disproportionation shown in

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ACCEPTED MANUSCRIPT Fig. 1, S32- ions predominated at concentrations > 0.5 × 10-3 mol dm-3. This is an indication that predictions at such low [‘S’] could be misleading and a revision of the equilibrium constants is recommended, as also was suggested recently by Safyan [15]. No features were evident at wavelengths > 520 nm.

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Fig. 7 shows the calibration at three different ranges: low, medium and high. The first two calibration curves used the absorbance peak at 295 nm and the latter at 420 nm. Due to the low signal in the low concentration range, the determination coefficient, R2 = 0.992, was

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relatively low for a calibration curve not forced through zero (R2 > 0.999). Nevertheless, a linear behaviour was evident, assumed to be associated with S32- ions. S22- ions did not absorb

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at this wavelength and S42- and S52- ions were predicted to be present at low concentrations, according to

Fig. 1. The calibration at medium range showed a clear non-linear behaviour, which could be

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associated with the non-linear increase in concentrations of the highly absorbing S42- ions. The calibration curve was fitted to an exponential function. Lastly, the calibration curve for the high concentration range was again linear at 420 nm, but with a distinct offset towards

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higher concentrations. As described previously, this might have been due to a wrongly

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assigned absorptivity peak, predicted to be S32-ions, instead of possibly higher polysulfide ions with n > 3. However, for calibration purposes, the curve was still useful to determine the concentration of zero-valent sulfur in the solution. Calibrations were also performed using an inferior grade of nitrogen, the small traces of impurities in which can affect calibrations significantly. Oxygen, even in small amounts, would partially oxidise the elemental sulfur and polysulfides to sulfoxy species; thus, lower absorbances were observed in all peaks, as shown comparatively in Fig. S4 for different calibration curves and Fig. S5 in ESI for solutions with added sulfoxy species. Following an

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ACCEPTED MANUSCRIPT opposite trend and after prolonged and excessive exposure to oxygen (e.g. bubbling air), elemental sulfur and intermediated polysulfides were formed directly from the hydrogen sulfide ion present in blank solution, and higher absorbances were observed over time, as shown in Fig. S6 in ESI.

oxidation of HS- at the anode. 4.2. Estimation of molar attenuation coefficient

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Table 2 shows the calibration functions used for the estimation of ‘S’ rate evolution after

In order to confirm the molar attenuation coefficients, ε , reported by other authors, an

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λ

estimation of these parameters was attempted using the spectra and predictions of polysulfide

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disproportionation. The absorbance at 420 nm was used exclusively for the quantification of ε for S32- ions, which were predicted to be the only species absorbing at that wavelength. λ

After assuming a negligible concentration of S52- ions and that S22- ions did not absorb at 295 nm, ε was estimated for S32- and S42- ions for this wavelength. Table 3 summarises and λ

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compares these estimations with the values reported by Licht [20] and Giggenbach [1]. Molar attenuation coefficients at 295 nm for S42- ions and at 420 nm for S32- ions were similar to the values reported in the literature, but that of S32- ions was significantly lower at 295 nm. As

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shown in the inset of Fig. 8, this might be due to an over-estimation of the concentration of

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S42- ions in the disproportionation models. The non-linear behaviour should be more pronounced in order to fit the experimental data. This might be the case only if at low [‘S’] the disproportionation of S42- ions, or even higher polysulfides, had a more abrupt increase in concentration compared to lower polysulfides. The incongruities found between our data and those from the literature are an indication that the equilibrium constants and molar attenuation coefficients of polysulfides, especially at low [‘S’], should be revised. Deconvolution of spectra for a wider range of concentrations, including OH- and HS- species, are required; this requires more meticulous studies, as 15

ACCEPTED MANUSCRIPT described previously [1, 10, 20], but was beyond the scope of this investigation. Despite the indication of unsuitability and uncertainty of these parameters, calibration curves were fitted as a function of zero-valent sulfur and were still considered valid for estimating its content in

4.3. Validation via electrochemical generation of polysulfides

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polysulfide solutions, as shown in the next section.

Fig. 9 and Fig. 10 show the time dependences of current densities and zero-valent sulfur concentrations, for the bench-scale and up-scaled reactors, respectively. In the bench-scale

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reactor, current densities were constant after stability was achieved, usually after ≥ 5 hours. The initial transient state arises for two inter-related reasons: (i) newly oxidised polysulfides

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near the surface of the electrode are usually of high order (n = 5), as predicted in Fig. 3. The reduction of these species by HS- via reaction (1) in the bulk of the electrolyte, did not happen instantaneously, so equilibration time was required. (ii) Elemental sulfur was deposited on the electrode surface by electrochemical reaction (3) or indirectly by oxygen

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evolution by reaction (5), followed by its consumption by reaction (7). The area covered by elemental sulfur increased with time, until these reactions occurred at similar rates to sulfur and higher polysulfide reduction by HS- ions via reactions (6) and (1), respectively.

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In the bench-scale reactor, there was a steady increase of polysulfide concentrations, expressed here as zero-valent sulfur. The rate of polysulfide generation was then extracted

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from the slope as 78′S  9/7; and used to estimate the charge yield, equation (15), i.e. the fraction of charge effectively transferred in the polysulfide (2) and hydrogen evolution (4) reactions. For these estimations, the transfer of 2 electrons was assumed to produce zerovalent sulfur from HS- ions by reaction (3). In fact, the ratio of electron to HS- ion reactant stoichiometries, 2(n-1) : n, is always < 2 when polysulfides are formed directly at anodes, according to reaction (2). However, given that the reported concentrations and calibrations

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ACCEPTED MANUSCRIPT are expressed as zero-valent sulfur, the speciation issue can be circumvented while still being consistent. In the case of the up-scaled reactor, the perforated electrode did not show a stable current density even after 8 hours. This was due to polysulfide ions accumulating within the

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perforations, from which mass transport rates were restricted geometrically, and that polysulfide ions oxidise faster than hydrogen sulfide ions [29, 33]. Then alternatively, charge yields were calculated from current integration and absorbance increase between two given

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times. As in the case of the bench-scale reactor, polysulfides were produced with a steady rate after 8 hours of operation. The absorbance spectra for the four cases are presented in the

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ESI, Fig. S7 - S9. Hydrogen fluxes were also measured, and charge yields for hydrogen evolution were estimated, assuming the measured gas was pure hydrogen and that the cationpermeable membrane precluded cross-over of Sn2- or HS- ions to the catholyte. Fig. 11 shows the temporal trends in charge yields for polysulfide formation at the anode by

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reaction (2) and hydrogen evolution at the cathode by reaction (4). Charge yields for hydrogen evolution were less than unity, sometimes decreasing to values < 0.8, probably due to gas leaks in the reactor over the course of longer term experiments. On the other hand,

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charge yields for polysulfide formation were very close to unity and their deviation could be

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explained by the uncertainty of the measurements and calibrations. This uncertainty ought to be computed in future studies with a larger number of samples and different rates of polysulfide oxidation by reverse reaction (2). Table 4 summarises averaged charge yields for polysulfide formation in the electrochemical reactor. All estimations were very close to unity, reflecting the quality of the calibration, from which to determine, in situ and uninterruptedly, the rate of polysulfide evolution in electrochemical reactors for hydrogen sulfide oxidation.

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Conclusions

A methodology was developed for the quantification of polysulfide concentrations, expressed as zero-valent sulfur, via UV-visible spectrophotometry, and with the advantage of being able to measure low concentrations of polysulfides in situ and uninterruptedly. Charge yields close

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to unity confirmed the effectiveness of the technique developed. Absorptions at 295 and 420 nm were used to build calibration curves at polysulfide concentrations between 0 and 0.01 mol dm-3 zero-valent sulfur. Three ranges of concentrations were necessary due to the non-

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linear absorption behaviour due to changes in polysulfide speciation. This was confirmed by predicted polysulfide concentrations using equilibrium constants and molar absorption

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coefficients. Nevertheless, these parameters should be revised, as the only available data can be traced to dated studies. The effect of oxygen depletion and the purity of nitrogen (or any inert gas) used to de-aerate the solutions was critical to avoid adventitious formation of

Acknowledgments

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sulfoxy species by homogeneous oxidation of HS- and Sn2- ions (reactions (7) to (11)).

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The authors thank the UK Engineering and Physical Sciences Research Council for a post-

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doctoral research associateship for AH, and COLCIENCIAS scholarship 568 for PhD studies abroad for FB.

References

[1] W. Giggenbach, Optical spectra and equilibrium distribution of polysulfide ions in aqueous solution at 20.deg, Inorganic Chemistry, 11 (1972) 1201-1207. [2] N. Li, Z. Weng, Y. Wang, F. Li, H.-M. Cheng, H. Zhou, An aqueous dissolved polysulfide cathode for lithium-sulfur batteries, Energy & Environmental Science, 7 (2014) 3307-3312.

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ACCEPTED MANUSCRIPT [3] C. Dillard, A. Singh, V. Kalra, Polysulfide Speciation and Electrolyte Interactions in Lithium–Sulfur Batteries with in Situ Infrared Spectroelectrochemistry, The Journal of Physical Chemistry C, 122 (2018) 18195-18203. [4] X. Zong, J. Han, B. Seger, H. Chen, G. Lu, C. Li, L. Wang, An Integrated Photoelectrochemical–Chemical Loop for Solar-Driven Overall Splitting of Hydrogen Sulfide, Angewandte Chemie, 126 (2014) 4488-4492.

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[5] F. Bedoya-Lora, A. Hankin, G.H. Kelsall, Photo-electrochemical hydrogen sulfide splitting using SnIV-doped hematite photo-anodes, Electrochemistry Communications, 68 (2016) 19-22.

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[6] X. Zong, H. Chen, B. Seger, T. Pedersen, M.S. Dargusch, E.W. McFarland, C. Li, L. Wang, Selective production of hydrogen peroxide and oxidation of hydrogen sulfide in an unbiased solar photoelectrochemical cell, Energy & Environmental Science, 7 (2014) 33473351.

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[7] L.-G. Danielsson, S. Chai, M. Behm, L. Renberg, UV characterization of sulphidepolysulphide solutions and its application for process monitoring in the electrochemical production of polysulphides, Journal of Pulp and Paper Science (JPPS), 22 (1996) J187J191. [8] M. Behm, D. Simonsson, Graphite as anode material for the electrochemical production of polysulfide ions in white liquor, Journal of Applied Electrochemistry, 29 (1999) 521-524.

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[9] W.E. Kleinjan, A.d. Keizer, A.J.H. Janssen, Kinetics of the chemical oxidation of polysulfide anions in aqueous solution, Water Research, 39 (2005) 4093-4100. [10] D.L. Pringle, The nature of the polysulfide anion, in: Chemistry, Iowa State University, 1967.

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[11] G. Schwarzenbach, A. Fischer, Die Acidität der Sulfane und die Zusammensetzung wässeriger Polysulfidlösungen, Helvetica Chimica Acta, 43 (1960) 1365-1390.

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[12] G. Le Guillanton, Q.T. Do, D. Elothmani, Determination of Mixtures of Polysulfides by Cyclic Voltammetry, Journal of The Electrochemical Society, 143 (1996) L223-L225. [13] A. Kamyshny, I. Ekeltchik, J. Gun, O. Lev, Method for the Determination of Inorganic Polysulfide Distribution in Aquatic Systems, Analytical Chemistry, 78 (2006) 2631-2639. [14] S. Licht, J. Davis, Disproportionation of Aqueous Sulfur and Sulfide:  Kinetics of Polysulfide Decomposition, The Journal of Physical Chemistry B, 101 (1997) 2540-2545. [15] S.A. Khan, UV-ATR Spectroscopy Study of the Speciation in Aqueous Polysulfide Electrolyte Solutions, International Journal of Electrochemical Science, 7 (2012) 561 - 568. [16] A. Kamyshny, A. Goifman, J. Gun, D. Rizkov, O. Lev, Equilibrium Distribution of Polysulfide Ions in Aqueous Solutions at 25 ºC:  A New Approach for the Study of Polysulfides' Equilibria, Environmental Science & Technology, 38 (2004) 6633-6644. 19

ACCEPTED MANUSCRIPT [17] G.R. Helz, Activity of zero-valent sulfur in sulfidic natural waters, Geochemical Transactions, 15 (2014) 13.

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[18] V. Bogdándi, T. Ida, T.R. Sutton, C. Bianco, T. Ditrói, G. Koster, H.A. Henthorn, M. Minnion, J.P. Toscano, A. van der Vliet, M.D. Pluth, M. Feelisch, J.M. Fukuto, T. Akaike, P. Nagy, Speciation of reactive sulfur species and their reactions with alkylating agents: do we have any clue about what is present inside the cell?, British Journal of Pharmacology, 176 (2018) 646-670. [19] W.F. Giggenbach, Equilibriums involving polysulfide ions in aqueous sulfide solutions up to 240.deg, Inorganic Chemistry, 13 (1974) 1724-1730.

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[20] S. Licht, G. Hodes, J. Manassen, Numerical analysis of aqueous polysulfide solutions and its application to cadmium chalcogenide/polysulfide photoelectrochemical solar cells, Inorganic Chemistry, 25 (1986) 2486-2489.

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[21] J.A. Tossell, Calculation of the visible-UV absorption spectra of hydrogen sulfide, bisulfide, polysulfides, and As and Sb sulfides, in aqueous solution, Geochemical Transactions, 4 (2003) 28-33. [22] F.E. Bedoya-Lora, A. Hankin, G.H. Kelsall, Solar-driven hydrogen sulfide splitting using SnIV-doped hematite photo-anodes, Electrochim. Acta, (2019), under review.

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[23] P. Lessner, J. Winnick, F.R. McLarnon, E.J. Cairns, Kinetics of Aqueous Polysulfide Solutions: II . Electrochemical Measurement of the Rates of Coupled Electrochemical and Chemical Reactions by the Potential Step Method, Journal of The Electrochemical Society, 133 (1986) 2517-2522. [24] R.H. Arntson, F.W. Dickson, G. Tunell, Saturation Curves of Orthorhombic Sulfur in the System S-Na2S-H2O at 25 and 50 ºC, Science, 128 (1958) 716.

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[25] X.S. Chai, J. Li, J.Y. Zhu, Simultaneous and rapid analysis of hydroxide, sulfide, and carbonate in kraft liquors by attenuated total reflection UV spectroscopy, Journal of pulp and paper science, 28 (2002) 105-109.

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[26] G.H. Kelsall, I. Thompson, Redox chemistry of H2S oxidation by the British Gas Stretford Process. Part I: Thermodynamics of sulphur-water systems at 298 K, Journal of Applied Electrochemistry, 23 (1993) 279-286. [27] G.H. Kelsall, I. Thompson, Redox chemistry of H2S oxidation by the British Gas Stretford Process. Part. II: Electrochemical behaviour of aqueous hydrosulphide (HS-) solutions, Journal of Applied Electrochemistry, 23 (1993) 287-295. [28] A. Kamyshny, J. Gun, D. Rizkov, T. Voitsekovski, O. Lev, Equilibrium Distribution of Polysulfide Ions in Aqueous Solutions at Different Temperatures by Rapid Single Phase Derivatization, Environmental Science & Technology, 41 (2007) 2395-2400. [29] R. Steudel, G. Holdt, R. Nagorka, On the Autoxidation of Aqueous Sodium Polysulfide [1], in: Zeitschrift für Naturforschung B, 1986, pp. 1519. [30] T.G. Pearson, P.L. Robinson, CLXXXIX.-The polysulphides of the alkali metals. Part I. Sodium (i), Journal of the Chemical Society (Resumed), (1930) 1473-1497. 20

ACCEPTED MANUSCRIPT [31] W.F. Giggenbach, Kinetics of the polysulfide-thiosulfate disproportionation up to 240.deg, Inorganic Chemistry, 13 (1974) 1730-1733. [32] A. Hankin, F.E. Bedoya-Lora, C.K. Ong, J.C. Alexander, F. Petter, G.H. Kelsall, From millimetres to metres: the critical role of current density distributions in photoelectrochemical reactor design, Energy & Environmental Science, 10 (2017) 346-360.

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[33] M. Behm, D. Simonsson, Electrochemical production of polysulfides and sodium hydroxide from white liquor: Part II: Electrolysis in a laboratory scale flow cell, Journal of Applied Electrochemistry, 27 (1997) 519-528.

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ACCEPTED MANUSCRIPT Figure captions

Fig. 1. Predicted (top) concentration and (bottom) molar fraction of Sn2- as a function of zero-

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valent sulfur in 1 mol dm-3 NaOH and 0.5 mol dm-3 Na2S, pH 14, 298 K.

Fig. 2. Potential-pH diagram for a meta-stable S-H2O system with sulfoxides excluded; total

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dissolved sulfur activity 0.5, 298 K and 0.1 MPa [5].

pH 14, 298 K and 0.1 MPa.

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Fig. 3. Effect of electrode potential on polysulfide distribution; dissolved sulfur activity 0.5,

Fig. 4. Potential-pH diagram for a S-H2O system excluding sulfate(VI) species 0.01, 298 K

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and 0.1 MPa.

Fig. 5. Equipment for polysulfide determination as zero-valent sulfur in alkaline solution

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using an immersion probe and UV-vis spectrophotometer.

Fig. 6. Typical absorbance spectra of different polysulfide solutions expressed as zero- valent

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sulfur content in 1 mol dm-3 NaOH and 0.5 mol dm-3 Na2S.

Fig. 7. Calibration curves of polysulfide solutions for different ranges of concentrations in 1 mol dm-3 NaOH and 0.5 mol dm-3 Na2S. (a) Linear regression for low range at 295 nm (b) exponential regression for medium range at 295 nm, affected by polysulfide disproportionation, and (c) linear regression for high range at 420 nm.

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Fig. 9. Time dependences of polysulfide concentrations expressed as zero-valent sulfur in 1 mol dm-3 NaOH and 0.5 mol dm-3 Na2S after HS- oxidation in an 0.1 dm-3 electrochemical reactor, (top) short and (bottom) long term current densities for two different anode samples.

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Electrode potential of 1.15 vs. RHE.

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Fig. 10. Time dependences of polysulfide concentrations expressed as zero-valent sulfur in 1 mol dm-3 NaOH and 0.5 mol dm-3 Na2S after HS- oxidation in an 0.8 dm-3 electrochemical reactor for two different electrodes (planar and perforated) and applied cell potential

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difference of 1.226 V.

Fig. 11. Time dependences of charge yields of polysulfide formation expressed as zero-valent sulfur in 1 mol dm-3 NaOH and 0.5 mol dm-3 Na2S after HS- oxidation and hydrogen in an

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0.8 dm3 electrochemical reactor for two different electrodes (planar and perforated) and

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applied cell potential difference of 1.226 V.

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ACCEPTED MANUSCRIPT Table captions Table 1. Estimated molar attenuation coefficients of polysulfides ions in aqueous solution.

Table 2. Calibration curve parameters for different ranges of polysulfide concentration

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expressed as zero-valent sulfur in 1 mol dm-3 NaOH and 0.5 mol dm-3 Na2S.

Table 3. Molar attenuation coefficient of S32- and S42- ions in aqueous solution derived from

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experimental data reported here compared to values reported in the literature.

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and (bottom) averaged currents.

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Table 4. Summary of charge yields obtained by (top) charge integration of current densities

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ACCEPTED MANUSCRIPT Table 1. Estimated molar attenuation coefficients of polysulfides ions in aqueous solution. Wavelength / nm S22S32-

358 303 417 303 368 299 375

S42S52-

Licht [13]

ελ / dm3 mol-1 cm-1 850 2280 190 3420 960 8000 2560

Wavelength / nm 358 302 429 302 372 296 377

ελ / dm3 mol-1 cm-1 990 2600 206 3690 1140 6800 1800

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Giggenbach [1]

Table 2. Calibration curve parameters for different ranges of polysulfide concentration expressed as zero-valent sulfur in 1 mol dm-3 NaOH and 0.5 mol dm-3 Na2S. Calibration curve
mol dm = ((absorbance))

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295 295 420

1.646 × 10  + 1.683 × 10 1.061 × 10 ln() + 4.398 × 10 1.165 × 10"  + 3.761 × 10

0.973 0.995 0.992

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Wavelength / nm

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Range / × 10-3 mol dm-3 0 – 1.2 1.2 - 3.6 3.6 - 10

Table 3. Molar attenuation coefficient of S32- and S42- ions in aqueous solution derived from experimental data reported here compared to values reported in the literature. Polysulfide

S42-

ελ / dm3 mol-1 cm-1 This work Giggenbach [1] 157 2280 289 190 3609 3420

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S32-

Wavelength / nm 295 420 295

Licht [13] 2600 206 3690

Charge yield results by current integration over time Calibration range Time range Integrated current Moles ‘S’ / × 10-3 mol dm-3 /h /C / × 10-3 mol 0 – 1.2 2 – 23 12.09 0.06518 1.2 – 3.6 14 – 54 30.65 0.1718 3.6 – 10 8 – 15 978.5 5.130 3.6 – 10 8 – 15 1685 8.323

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Reactor / dm3 0.1 0.1 0.8 0.8

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Table 4. Summary of charge yields obtained by charge integration of current densities and time-averaged currents. Charge yield 1.040 1.082 1.012 0.953

Charge yield results by averaged currents over a given time range under stable conditions Reactor Calibration range Time range Average current Molar rate ‘S’ Charge yield / dm3 / × 10-3 mol dm-3 /h / mA / × 10-9 mol s-1 0.1 0 – 1.2 2 - 23 0.1599 ± 0.012 0.8078 0.975 ± 0.071 0.1 1.2 – 3.6 14 - 54 0.2138 ±0.019 1.180 1.065 ± 0.087 0.8 3.6 – 10 8 - 15 38.82 ± 2.39 207.2 1.030 ± 0.113 0.8 3.6 – 10 8 - 15 67.33 ± 18.28 344.2 0.986 ± 0.346

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