FULL PAPER Dissolution Modeling and Experimental Measurement of CaS–H2O Binary System Zekker, Ivar
Tenno, Toomas
Tomingas, Martin
Uiga, Kalev*
Institute of Chemistry, University of Tartu, 14A Ravila St., Tartu, 50411, Estonia
CaS formed during the retorting process of oil shale has a hazardous influence on surface water quality. Interaction of retorted oil shale with water generates highly alkaline leachate with a high content of sulfur due to the CaS component. A theoretical model describing the behavior of solid calcium sulfide in contact with water was developed. The model was consistent with the measurements showing change in dissolution behavior when solid CaS remained in the solution. Experimental measurements of pH and concentrations of ions were carried out in oxygen-free water at 25ºC using from 24.2–131.5 mg·L-1 (0.335–1.823 mM) CaS concentrations. Analysis of pH and concentrations of ions in the solution and calculations by the developed model showed that the solubility of CaS was estimated as 125.0 mg·L-1 (1.733 mM), and therefore the solubility product of CaS is 3.41·10ˉ10 (mol·Lˉ1)2 at a temperature of 25ºC.
Keywords: calcium sulfide (CaS); solubility product; the dissociation constants of H2S; chemical equilibrium
Introduction
Apart from technological synthesis, CaS is generated in the retorting process of oil shale containing pyrite and other sulfides.1–4 More than 50% of the initial sulfur in Estonian oil shale remains into the solid residue (called semi-coke) during the retorting process.5 Interaction of retorted shale with water generates highly alkaline leachate with a high content of sulfur due to different chemical reactions.6 Part of the sulfur is emitted into the atmosphere due to a gaseous * E-mail:
[email protected] Received (). Chin. J. Chem. 2011, 29, 1—X
© 2011 SIOC, CAS, Shanghai, & WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
1
FULL PAPER hydrogen sulfide generating atmospheric pollution. It is necessary to understand and to describe the interaction of CaS with H2O in order to solve the problem of hazardous semi-coke from the retorting process of oil shale. For the characterization of the behavior of calcium sulfide in water it is necessary to know the solubility or solubility product for CaS. There are only a few published data about the solubility of CaS because calcium sulfide is stable only in the dry, solid form. In aqueous solution CaS dissociates in water as follows: CaS Ca2+ + S2-
(1)
Interactions between CaS and water are not simple dissolution processes but a combination of more complex dissociation reactions. CaS solubility could be determined as ions concentrations in the state of equilibrium, where the solid phase was not retained, and the H2S influence on solubility minimized. Due to the complicated dissolution mechanism, different values have been found for the solubility of CaS. According to Perry and Green, calcium sulfide has solubility of less than 1 g·L-1 at 25 ºC.7 Riesenfeld and Feld8 studied the dissolution of pure CaS in distilled water and their measurements resulted in the solubility of CaS up to 0.212 g per 1L water at 20 °C. Similar values for the solubility of CaS (0.2 g per 1 kg water) are presented by Dean9 and the CRC handbook10. Solubility of CaS of 0.1 weight % has been presented by Licht11 and the value of 0.01 g per 100 cm3 solution at 15 °C was measured by Foerster and Kubel.12 It is difficult to determine the accurate solubility of metal sulfides because the solubility of the majority of metal sulfides is very low. The Ksp for heavy metal sulfides is commonly determined as follows13: Ksp= [Me2+] x [S2-]
(2)
Generally the Ksp has been determined from the experimental measurements using the values of acid dissociation constants. The values of the first and second acid dissociation constants (K1
FULL PAPER and K2, respectively) of H2S have been repeatedly determined by using a variety of techniques and their values have been summarized by different authors.14–17 Rao and Hepler15 presented a summary of the published values of the equilibrium constant Ka1 for the first ionization of dissolved H2S at different temperatures and their choice for the most suitable values was Ka1 = 1.02·10ˉ7 mol·L-1 at 25 °C. Presentation of the published values of the equilibrium constant Ka2 for the ionization of HSˉ confirmed very wide discrepancies between the results of different investigators (values of Ka2 ranged from 8·10ˉ18 mol·L-1 to 6.3·10ˉ13 mol·L-1 at room temperature (20–30 °C). They used Ka2 = 1.66·10ˉ14 mol·L-1 for their calculations and believed that the best overall interpretations of published results was consistent with Ka2 = 10ˉ13 mol·L-1 at 25 °C, however, further measurements are needed.15 Tsonopoulos et al.16 used a spectrophotometric method to measure the ionization constants of H2S, which resulted in pKa1= 7.045±0.019 at 25 °C. The dissociation constants of H2S determined by the sensitive amplified potentiometric Ag2S ISE method had values as follows: Ka1 = 8.91·10ˉ8 mol·L-1 and Ka2 = 10ˉ12 mol·L-1, respectively.16,17 Their Ka2 agreed with the published values, while the value of Ka2 agreed well with the earlier reported values (Ka2 = 10ˉ12–10ˉ13 mol·L-1), but it was about five orders of magnitude less than the values (Ka2 > 10ˉ17 mol·L-1) accepted by other authors.11 Sun et al.14 found the average Ka1 value to be 9.632·10ˉ8 mol·L-1 with the standard deviation of 1.955·10ˉ8 mol·L-1 at 25 °C (values ranged from 1.000·10ˉ8 to 1.096·10ˉ7 mol·L-1). The Ka2 values had a 7-orders-of-magnitude variation, ranging from 1.000·10ˉ19 mol·L-1 to 1.148·10ˉ12 mol·L-1, and they calculated the average value as Ka2 = 1.335·10ˉ13 mol·L-1 at room temperature (20−30°C). They also suggested that the use of K2 for calculating the concentrations of sulfide species and predicting solubility should be avoided due to the uncertainty of the available data.14 Licht11 declared a probable value of K2 = 5.01·10ˉ18 mol·L-1 through a comparison of the potentiometric results with the re-evaluated spectrophotometric results. Alternatively, the
FULL PAPER corrected values for metal sulfide solubility products might be directly determined from the free energy of the formation of an aqueous sulfide when combined with the most recent thermodynamic information relevant to each of the specific metal sulfides and Ksp = 7.94 10-7 (mol·L-1)2 was calculated for CaS.11 Possible reasons for a wide variation in the published values of the second dissociation constant of H2S (K2) can be the extremely low concentrations of S2ˉ at experimentally realistic values of pH and the tendency of bisulfide solutions to oxidize rapidly.18 The present investigation focused on two main areas. Firstly, development of a mathematical model of CaS dissolution to determine CaS solubility and to describe dissociation as well as the ions interaction mechanism both in the absence and in the presence of the solid phase. Secondly, the concentrations of ions and pH in the water solution of calcium sulfide of different concentrations were measured at the dynamic equilibrium state.
Theoretical model of CaS dissolution
CaS dissolution model was developed to give theoretical explanation of occurring chemical reactions during dissolution. Processes of the interaction of calcium sulfide (CaS) with water include the dissolution of CaS through its dissociation, water dissociation and reactions between sulfide (S2ˉ) or bisulfide (HSˉ) ions and proton (H+). For theoretical modeling, the absence of oxygen in water as well as the exchange of species between the gaseous and liquid phases of the system have not been taken into account. Solid calcium sulfide in contact with water dissociates into calcium (Ca2+) and sulfide (S2ˉ) ions. Sulfide anion forms two products with water, HSˉ and H2S, characterized by basicity constants Kb2 and Kb1, respectively: 2
[S ˉ] + H2O
HS OH [HSˉ] + [OHˉ], Kb2 = S
2
(3)
FULL PAPER [HSˉ] + H2O
[H2S] + [OHˉ], Kb1=
H 2S OH
HS
(4)
Previous two equations enable us to calculate sulfur species and OH- concentrations after knowing the values of Kb2 and Kb1. In order to describe quantitatively the solubility of CaS, the dissociation of H2O must be taken into account: 2H2O
[H3O+] + [OHˉ], Kw = [H3O+]×[OHˉ]
(5)
In sum, the system of solid CaS in equilibrium with water will contain, on a significant level, six different species in the water phase: Ca2+, S2ˉ, HSˉ, H2S, OHˉ and H3O+. The value of the particular equilibrium constant of the system is not influenced by other equilibriums in the solution, and a change in the concentration of one of the common species of the system leads to a change of concentrations of all conjugated components of the system in the state of equilibrium. A simplified scheme of the system of solid CaS in equilibrium with water is presented in Figure 1. CaS dissociates quickly in water and when its amounts are larger (e.g. in oversaturated CaS aqueous solutions), the solid phase influences the dissolution process by H2S feedback to S2ˉ, resulting in an increased concentration of OHˉ ions.
Figure 1
The scheme of the system of solid CaS in equilibrium with water.
FULL PAPER For calculating the concentrations of all six species present in the equilibrated system, it is necessary to derive six expressions and to solve them simultaneously. The expression of the massbalance for the system is presented as follows: [Ca2+] = [S2ˉ] + [HSˉ] + [H2S],
(6)
where [Ca2+], [S2ˉ], [HSˉ] and [H2S] are the equilibrium concentrations of the corresponding species of Ca2+, S2ˉ, HSˉ and H2S in the solution.
Three equations for equilibrium constants describing equilibriums of the sulfur-containing species and the autoprotolysis of water are taken into account for the set of balanced equations for all pertinent equilibriums. The second basicity constant, Kb2, is expressed as follows:
HS OH = K K S
Kb2 =
w
2
,
(7)
a2
where Ka2 is the second acidity constant of H2S. The first basicity constant, Kb1, is expressed as follows: Kb1 =
H 2S OH = K w
HS
K a1
,
(8)
where Ka1 is the first acidity constant of H2S.
The ion-product constant of water, Kw, is expressed as follows: Kw = [H3O+] × [OHˉ].
(9)
As the molar concentrations of positively- and negatively-charged ions in the solution are equal, the charge-balance equation for the system can be written as: 2 × [Ca2+] +2 [H3O+] = 2 × [S2ˉ] + [HSˉ] + [OHˉ]
(10)
Having five unknown concentrations of species in the equilibrium system ([S2ˉ], [HSˉ], [H2S], [OHˉ] and [H3O+]) and five independent algebraic relationships (equations 6–10), it becomes possible to solve the system of equations by one equation. The solution of the system of equations
FULL PAPER for determining five variables as a function of constants of Kw, Kb2, Kb2 and the concentration of Ca2+ ions for the equilibrium system of CaS–H2O becomes possible. Simplification of this quite a complicated system of equations should be made by an elimination of parameters, which are not substantial from the point of view of accuracy of the calculated concentrations. On the basis of the analysis of the mass-balance equation of the system in the region of pH = 7–12, we can conclude that the concentration of [S2ˉ] is significantly lower than the sum of [HSˉ] and [H2S]: [S2ˉ] [H3O+]
(15)
Due to the last assumption the charge-balance equation (13) could be presented as: 2 x [Ca2+] ≈ [HSˉ] + [OHˉ]
(16)
After elimination of the variables that do not have a significant influence on the accuracy of the results of the calculations of essential parameters of the equilibrium state, a simplified system of equations, describing the behavior of solid calcium sulfide in contact with water has been
FULL PAPER developed. Both the number of equations and number of unknowns ([HSˉ], [OHˉ], [H2S] has been reduced to three (equations 8, 12, 16).
Experimental measurements Materials and methods The experiments were carried out in air-tightly closed glass bottles with a volume of 1200 mL which were carefully washed and dried before each measurement. Distilled water (1 L) was purged with nitrogen (99.9% N2) for 20 minutes to remove oxygen (O2) and carbon dioxide (CO2). The purging of water and the following measurements were carried out at 25.0 (±0.2) °C in a thermostated water bath (Assistant 3180, Germany) on a magnetic stirrer at constant stirring speed. Removal of O2 and CO2 was necessary to avoid the oxidation of sulfide (bisulfide) ions and the sedimentation of calcium carbonate. The efficiency of oxygen removal was controlled by measurements of dissolved oxygen (DO) in water (oxygen-meter Marvet Junior MJ2000, Elke Sensor, Estonia) to achieve the absence of DO. The removal of CO2 was confirmed by the growth of pH from 5.68 to 7.00 during purging with nitrogen. pH of the mixture was measured with a pHmeter Jenway (Model 3510, UK) connected with special pH-electrodes for highly alkaline solutions (Jenway, UK), which were calibrated before each measurement at pH values of 7.00, 10.00 and 12.00 in buffer solutions (standard deviation of pH ±0.002 units). The pH electrode was tightly inserted in the cover of the measuring vessel. The pH of the solution in the process of the dissolution of CaS was recorded automatically after every three seconds using by software Dataway (Jenway, UK). The recording was finished when the pH of the solution stayed constant for at least three minutes. Solid calcium sulfide of analytical grade (99.9 %) (Alfa Aesar, Germany) was weighed by analytical balance (Scaltec SBC 31, Germany) just before its addition into water.
FULL PAPER Chemical analysis Concentration of the total sulfide (sum of dissolved H2S, HSˉ and S2ˉ) was determined iodometrically, where the excess of added iodine was titrated back with sodium tiosulfate [19, 20]. In comparison with titration, the concentration of bisulfide was determined by UV-Vis spectrometry.21,22 The Perkin Elmer (UK) Lambda 35 UV-Vis scanning spectrophotometer with an 10-mm quartz cell was used for absorbance measurements against distilled water as a blank. The characteristic peak of bisulfide ion appears clearly on the UV spectra (at 231 nm) and the intensity of the UV band is related to the concentration of the sulfide.22,23 The concentration of the bisulfide ions was practically determined by the calibration curve, prepared through preliminary measurements using sodium bisulfide. The received curve was linear within the studied range ([HS-] = 1–9 mg·L-1). Concentration of calcium was determined by a direct complexometric titration with ethylenediamine tetraacetate (EDTA).19 All solutions were prepared using analytical grade reagents and the determinations of ions were done immediately after the ending of the dissolution process. Each determination was made in three replicates at least and the mean value with the standard deviation was calculated.
Results and discussion The pH of the aqueous solution of CaS Dissociation of CaS during the dissolution process produces sulfide ions (S2-), which will bind protons from the water molecule generating equimolecular amounts of hydroxide ions (OH-) (equation 3). It means that a greater amount of added CaS has to generate a higher amount of OH-, which could be determined through a higher value of pH. Different amounts of solid CaS were added to 1 L of distilled water purged with nitrogen and the profiles for pH during the dissolution of CaS are presented in Figure 2.
FULL PAPER
Figure 2
The pH profiles during dissolution of CaS in water at 25 °C.
The results of the measurements showed (Figure 2) that the pH of the solution depended on the amount of added CaS and a greater amount of added CaS generated a faster growth of pH as well as a higher final pH. It is in conformity with the basis of our theoretical model. A longer time was required to reach the constant pH for the solution with a higher concentration of CaS although the initial rate of pH growth was higher. The profiles of pH values of the solution were used to determine the time required for the dissolution of added CaS at given conditions, and the constant pH was achieved in the system. Summary of the final constant pH values and the time required to reach the constant pH is presented in Table 1. The time required to reach the constant pH was proportional to the concentration of CaS from 24.2 (0.335 mM) up to 125.0 mg·L-1 (1.733 mM), but it was curved at higher concentrations of CaS, and the insoluble particles stayed in the solution during the experiment for a duration up to one hour.
Table 1 The pH values of the aqueous solution of CaS and time required to reach constant pH at 25 °C. Concentration
Final pH of
Time to reach
FULL PAPER of added CaS, mM 0.335 (±0.020) 0.554 (±0.049) 0.832 (±0.010) 1.123 (±0.010) 1.375 (±0.004) 1.386 (±0.094) 1.516 (±0.020) 1.650 (±0.013) 1.722 (±0.014) 1.733 (±0.006) 1.774 (±0.010) 1.823 (±0.010)
solution 10.600 (±0.02) 10.832 (±0.03) 10.963 (±0.01) 11.133 (±0.03) 11.170(±0.03) 11.172 (±0.04) 11.225 (±0.02) 11.250 (±0.003) 11.252 (±0.010) 11.260 (±0.011) 11.290 (±0.021) 11.314 (±0.014)
constant pH, sec 259 (± 30) 580 (± 60) 830 (± 120) 870 (±240) 940 (± 240) 1071 (± 300) 1100 (± 240) 1150 (± 30) 1189 (± 60) 1194 (± 120) 1330 (± 150) 1490 (± 120)
It is problematic to use the formation of precipitations in the solution for determining the moment of oversaturation. Assessment of oversaturation is difficult because precipitates of sparingly soluble metal sulfides consist of very small particles.24 Usually, metal sulfide colloids (1 nm–1µm of size) are formed in oversaturated conditions and tend to form larger particles and coagulate out of the solution.25 When the coagulation of a metal sulfide is likely to occur in oversaturated conditions, the difference between theoretically and experimentally estimated ions concentration makes it possible to determine salt solubility when the difference increases at a higher concentration of salt. Measured final pH values (in the range of pH 10.6–11.26) corresponding to the equilibrium state of the dissolution of CaS grew in proportion to an increasing amount of added salt (y = 0.0059x + 10.562, R² = 0.9365) as shown in Figure 2. A fairly sharp transition from the dissolved state of CaS to an insoluble state of the salt was observed between the CaS concentration of 125.0 (1.733 mM) to 131.5 mg·L-1 (1.823 mM) (registered pHs were in the region of 11.260–11.314). The measurements showed an increased growth of the final pH values in the more concentrated CaS solutions (over 1.774 mM) and the final concentration of [OH-] was 6.7 % higher than predicted by a relationship calculated through lower concentrations of CaS. It means that the corresponding concentration of CaS (1.733 mM)
FULL PAPER can generate saturation of CaS aqueous solution through short-term measurements. The determined amount of added CaS bringing along saturation was between the values of the published solubilities of CaS 212 mg·L-1 and 100.0 mg·L-1.8,12 For long-term measurements oversaturated solutions were prepared in order to study the formation and composition of precipitates of low solubility metal-sulfides. When 1.5 and 2.0 g CaS were dissolved in 1 L of water, the highest experimentally measured values of pH were 12.25 and 12.81, and the dissolution periods were 6 and 28 days, respectively. From the solutions containing 1.75 g·L-1 and 2.0 g·L-1 of CaS, 10.2 % and 11.7 % lower measured concentrations of calcium ([Ca2+]meas) than the calculated concentration ([Ca2+]theor) were determined, respectively. Ca(OH)2 formation can be the reason for a decreased [Ca2+]meas compared with [Ca2+]theor and the formation of insoluble particles due to the oversaturation of the CaS solution. A visible recognizable Ca(OH)2 formation was detected at pH>12; therefore, the measurements of [Ca2+] can be used for the prediction of CaS solubility. Inside of dumping fields of retorted oil shale, higher amounts of CaS can interact with water and a higher concentration of OH- is generating pH values up to 12.5 related to the solubility of Ca(OH)2. Measured pH values of leachate from a dumping site higher than pH=12.5 can be connected with the influence of different compounds of potassium, which were decomposed during the retorting process followed by a reaction with water.26 Alkaline leachate can absorb atmospheric CO2 and be diluted with rainwater and pH is lowered through it and the equilibrium of sulfide ions is shifted to a higher concentration of H2S, which can be emitted into the atmosphere causing odor problems.27
Concentration of ions Solubility can be practically determined through the analysis of ions in the solution. A weighed amount of solid CaS was added into 1 L of water and after the dissolution of added
FULL PAPER calcium sulfide, the concentration of ions in the aqueous phase was determined. [OH-] was calculated from the pH value, and the summary of results is presented in Table 2. The [Ca2+]theor/[OH-] ratio was calculated for characterizing the change of [OH-] in comparison with [Ca2+]theor at the different concentrations of dissolved salt, supposing added calcium occurs as ions in the solution.
Table 2 Amounts of added CaS into 1 L of water and concentrations of Ca2+, OH- and total sulfide- sulfur (Stot) CaS concentration, mM 0.335 (±0.020) 0.554 (±0.049) 0.832 (±0.010) 1.123 (±0.010) 1.375 (±0.004) 1.386 (±0.094) 1.516 (±0.020) 1.650 (±0.013) 1.722 (±0.014) 1.733 (±0.006) 1.774 (±0.010) 1.823 (±0.010) nd- not determined
Concentration of Ca2+, mM
Concentration of OH-, mM
Concentration of Stot, mM
nd nd 0.825 (±0.010) 1.112 (±0.003) 1.378 (±0.020) 1.384 (±0.010) 1.490 (±0.008) 1.652 (±0.010) 1.703 (±0.010) 1.719(±0.006) 1.744 (±0.060) 1.795 (±0.006)
0.398 (±0.019) 0.679 (±.049) 0.918 (±0.021) 1.358 (±0.097) 1.479 (±0.106) 1.486 (±0.143) 1.679 (±0.079) 1.778 (±0.012) 1.786 (±0.042) 1.820 (±0.047) 1.950 (±0.097) 2.061 (±0.068)
0.325 (±0.060) 0.546 (±0.020) 0.783 (±0.070) 1.100 (±0.020) 1.360 (±0.020) 1.372 (±0.050) 1.487 (±0.050) 1.587 (±0.100) 1.637 (±0.050) 1.696 (±0.050) 1.740 (±0.050) 1.760 (±0.050)
[Ca2+]theor/ [OH-] 0.84 0.82 0.91 0.83 0.93 0.93 0.90 0.93 0.96 0.95 0.91 0.88
Concentration of total dissolved sulfide-sulfur (Stot) is a sum of concentrations of three soluble forms of sulfur: H2Saq, HS- and S2-. Comparison of the measured [Ca2+] and [Stot] (Table 2) showed that [Ca2+]meas was higher in comparison with [Stot], but it was lower than [OH-]. The ratio of [Stot] to the measured [Ca2+] had the mean value of 0.972 (±0.02) and the ratio of the practically measured [Ca2+] to [OH-] had the mean value of 0.906 (±0.044) for 0.335–1.823 mM CaS aqueous solutions (relationships between [Ca2+] and [OH-], as shown in Figure 3).
FULL PAPER
Figure 3 Relationship between concentrations of measured and theoretically calculated [Ca2+] and [OH-] for CaS concentrations from 0.832 to 2.424 mM.
The concentrations of [Stot] and the measured [Ca2+] were very similar if more than a 1.774 mM CaS aqueous solution was composed (Table 2). The measurements showed that [OH-] exceeded [Stot] (Table 2) and the ratio of [OH-] to [Stot] had the mean value of 1.14 (±0.06) without a clear relationship to the added amount of CaS. The difference in their concentrations is connected with the autoprotolysis of water, and no difference was observed for over 1.733 mM CaS aqueous solutions. As the final values of pH in the solution stayed between 10.6 and 11.3 (Table 1), HSpredominated in the solution.28 [HS-] was measured spectrophotometrically and the results are presented in Table 3, and for comparison the theoretical concentration of HS- ([HS-]theor) was also calculated. The ratio between [HS-]meas and [HS-]theor (Table 3) showed increased values at higher [CaS]. It can be related to the emissions of gaseous H2S at lower pH values of the solutions
FULL PAPER prepared with lower amounts of CaS. For a 1.733 mM CaS aqueous solution [HS-]meas/[HS-]theor] = 0.977, and it was the moment when [HS-]meas was the nearest to the theoretical value among all results. For [CaS] under 1.733 mM the mean value of [HS-]meas/[HS-]theor] was 0.906 (±0.074). For [CaS] between 1.733-1.823 mM the mean value of [HS-]meas/[HS-]theor] was 0.970 (±0.009). [HS]meas reached equality with [S]tot in a 1.733 mM CaS aqueous solution – under 1.733 mM the mean [HS-]meas/[Stot] was 0.940 (±0.073) and above that concentration the mean [HS-]meas/[Stot] was 0.993 (±0.002). Table 3 Measured and calculated concentration of bisulfide ions ([HS-]meas, [HS-]theor) in solutions of CaS. CaS concentration, mM 0.554 (±0.049) 0.561 (±0.014) 0.638 (±0.012) 0.693 (±0.012) 1.303 (±0.016) 1.375 (±0.004) 1.386 (±0.094) 1.516 (±0.020) 1.733 (±0.006) 1.774 (±0.010) 1.823 (±0.010)
[HS-]meas, mM 0.453 (±0.05) 0.445 (±0.07) 0.533 (±0.05) 0.615 (±0.06) 1.247 (±0.03) 1.329 (±0.02) 1.330 (±0.06) 1.46 (±0.05) 1.694 (±0.01) 1.725 (±0.03) 1.750 (±0.05)
[HS-]theor, mM 0.554 0.561 0.638 0.693 1.303 1.375 1.386 1.516 1.733 1.774 1.823
[HS-]meas/ [HS-]theor 0.818 0.793 0.835 0.887 0.957 0.967 0.960 0.963 0.977 0.972 0.960
Although HS- is the predominant reduced sulfur compound in solutions at pH above 9, the occurrence of H2S and S2- is possible, but their practical measurement has certain problems and because of that concentrations of H2S and S2- were calculated using equations 3, 4, 7 and 8. Summary of the results is presented in Table 4.
Table 4 Calculated concentrations of sulfide ion and hydrogen sulfide in the solution of CaS. CaS concentration, mM
[S2-], 10-11 mM
[H2S], 110-11 mM
0.335 (±0.020) 0.554 (±0.049)
0.71 1.92
6.99 6.45
FULL PAPER 0.832 (±0.010) 1.123 (±0.010) 1.375 (±0.004) 1.386 (±0.094) 1.516 (±0.020) 1.650 (±0.013) 1.722 (±0.014) 1.733 (±0.006) 1.774 (±0.010) 1.823 (±0.010)
4.50 7.93 12.40 12.57 14.95 17.86 19.47 19.70 20.51 21.50
8.27 6.66 8.76 8.83 8.23 8.75 9.46 9.22 8.36 7.84
Concentration of H2S was calculated using the pKa1 value of 7.01, because it was the most frequently used for the calculations.16,29,30 The pKa2 value of 15.18 (Kb2=15.20 mol·L-1) used for S2- calculation was chosen on the basis of reliability and the scope of works by different authors. The Kb2 value was received by averaging the results of different researches, because there is still no good agreement about the value of the equilibrium constant for the ionization of HS-. The correlation between the measured concentrations of Ca2+ and OH- (Figure 3) was quite strong for CaS concentrations below 1.733 mM (y=1.0813x, R²=0.9389) as well as for those over 1.733 mM (y=2.8535x – 3.0647, R²=0.9932), but the slope describing the ratio of Ca2+meas to OHwas significantly higher when the concentration of CaS was over 1.733 mM. The presented values of the measured concentrations of calcium and hydroxide ions showed (Fig. 3) that the concentration of hydroxide ions (e. g. pH of the solution) was much higher in the CaS aqueous solutions with concentrations over 1.733 mM. It means that more protons were bound due to additional reactions between S2- (or HS-) and H+, and therefore more hydroxide ions appeared in the solution when larger amounts of CaS were added into water. The values of the ratios of Ca2+theor/OH- and had gradually increased from 0.820 to 0.950 (for Ca2+theor/OH-) or to 0.945 (for Ca2+meas/OH-) with the average [Ca2+]meas/[OH-] of 0.910 when [CaS] grew from 0.335 to 1.733 mM and the value of Ca2+meas/OH- decreased to 0.883 ±0.017 for 1.774 and 1.823 mM CaS aqueous solutions. It means that the CaS concentration of 1.733 mM in aqueous solutions can be estimated as the solubility of CaS for short-term measurements. Calcium
FULL PAPER ions are generated in the solution during the dissociation of solid CaS only, and therefore the measurement of [Ca2+] can be used to determine solubility of CaS.
Figure 4
Relationship between measured and theoretically calculated concentrations of Ca2+ for different CaS concentrations.
[Ca2+]meas decreased in the solution with a CaS salt concentration above 1.733 mM retained in when calcium was in the salt composition and remained in the solid phase (Figure 4). When in unsaturated solutions the ratio of [Ca2+]meas/[Ca2+]theor was rather large (mean value 0.994±0.006 mM), the ratio of [Ca2+]meas [Ca2+]theor for oversaturated CaS mixtures (1.733–1.823 mM) was less (mean value 0.984±0.001 mM). Saturation of CaS can be detected by the decreasing of value of the ratio of [Ca2+]meas/[Ca2+]theor at the concentration of 1.733 mM of CaS. Additional experiments were carried out to determine the ratio of [Ca2+]meas to [Ca2+]theor at higher concentrations of CaS. The ratio [Ca2+]meas/[Ca2+]theor had the mean value of 0.977 (±0.01 mM) for the suspensions with CaS concentrations of 1.823–2.424 mM (Figure 4). The inequality
FULL PAPER of the ratios of [Ca2+]meas and [Ca2+]theor for CaS concentrations over 1.733 mM compared with the CaS concentration range of 0.335 to 1.733 mM was almost 5-fold. It can be noted that the determinations of [Ca2+] were made just after the dissolving process terminated and the solution could not be supersaturated, because dissolution experiments were performed at room temperature (25º C) and the determination of ions was performed at the same temperature.
Solubility and dissolution rate of CaS The changes of OH- concentrations in the course of time were used to determine the rate of CaS dissolution. The process of dissolution was studied up to concentrations of [OH-] = 2.061 mM, which corresponds to the CaS concentration of 1.823 mM. Since [HS-]meas and [OH-] were determined at the end of the dissolution process and additionally pH was continuously measured during the experiment. The dissolution rates for CaS could be expressed as HS- – a major sulfide-sulfur species change of the measured concentration in time. Initial and average dissolution rates of CaS were calculated by [OH-] change in time. The relationship between [OH-] and [HS-] for CaS concentrations up to 1.733 mM (Table 5) showed that as many protons were bound by S2-, the same amount of bisulfide ions were formed during dissolution, and basically the same amounts of OH- remained in the solution. Higher [OH-] compared with [HS-]meas was detected at higher salt concentrations. The concentrations of H2S and S2- (Table 4) can be considered orders of magnitude lower than [HS-] and [OH-], thus by theory the initial and average rates of growth of [HS-] are proportional to the rate of growth of [OH-] during the dissolution of CaS. Slopes of concentration changes of HS- at the beginning of dissolution can be used for the determination of the initial rates of growth of [HS-]. The initial rates of growth of HS-
FULL PAPER concentrations increased steadily from 2.535·10-3 to 7.446·10-3 mM·s-1 (with R² = 0.968) when the concentrations of CaS aqueous solutions were from 0.554 to 1.733 mM, respectively. Besides, the initial rates of HS- were 8.9·10-3 and 10.274·10-3 mM·s-1 (with R² = 0.996) for CaS aqueous solutions with concentrations of 1.774 and 1.823 mM, respectively. It indicated that the behavior of CaS changed when the system reached concentrations of CaS higher than 1.733 mM; then these rates showed disproportional changes compared with the rates for lower concentrated solutions (Table 5). An average dissolution rate of CaS can be determined as a bisulfide concentration change in a time period responding to the duration of the dissolution process (Table 1). The CaS dissolution process was expected to be finished by reaching the steady pH of the solution and the dissolution rate was calculated by [HS-]meas and the pertinent values are presented in Table 5.
Table 5 Average and initial dissolution rates for different CaS concentrations.
CaS concentration, mmol·L-1 0.554 (±0.049) 0.832 (±0.010) 1.123 (±0.010) 1.375 (±0.004) 1.386 (±0.094) 1.733 (±0.006) 1.774 (±0.010) 1.823 (±0.010)
Initial dissolution rate, 10-3 mmol HS(mmol·L-1·s -1) 2.535 3.340 4.030 5.549 6.050 7.446 8.910 10.274
Average dissolution rate, 10-3 mmol HS(mmol·L-1·s -1) 0.781 0.890 1.020 1.242 1.327 1.419 1.297 1.174
The calculated values of the initial rate increased steadily with the growth of the added amount of solid CaS, but the calculated values of the average dissolution rate increased up to the concentration of 1.733 mM (Table 5), and the rate decreased when a higher amount of CaS was added into water. This can confirm the solubility of CaS as high as 125.0 mg·L-1 (1.733 mM). In addition to pH change during dissolution the solubility of CaS was estimated by breakpoints of concentration ratios for different reagent concentration ranges. When a 1.733 mM
FULL PAPER CaS aqueous solution was made, the following ratios reached their maximum values: [HS]meas/[HS-]theor] = 0.977 (Table 3), [HS-]meas/[Stot] = 0.999 (Tables 2 and 3). The calculated ratios of [Ca2+]meas/[OH-] were as high as 0.954 and 0.945 for concentrations of 1.733 and 1.722 mM CaS, respectively. These ratios reached their maximum values at the studied concentrations. The value of the ratio [HS-]meas/[Stot] = 0.999 emphasizes that nearly all sulfur is in the form of HS- at pH = 11.26. The mean calculated ratio of [HS-]meas/[Stot] was 0.940 at CaS concentrations below 1.733 mM, but above this concentration the mean value of the [HS-]meas/[Stot] ratio was 0.993, which implies proportionally higher H2S amounts for solutions with a lower CaS concentration and a higher concentration of S2- in oversaturated CaS aqueous solutions. The difference between the ratios of [HS-]meas/[Stot] for 1.733 mM CaS and above was not enough for determining the dissolution behavior change by this parameter. The ratios of [Ca2+]meas/[OH-] were 0.954 and 0.945 at the CaS concentrations of 1.722 mM and 1.733 mM, respectively. It showed that at determined CaS solubility (125.0 mg·L-1) or near to it these ratios reached their maximum values showing the state of saturation. Mean ratio [Ca2+]meas/[OH-] = 0.910 at the CaS concentrations below 1.733 mM was only 0.883 – above that concentration both of these ratios imply to undersaturated solutions. Comparison of the present value of CaS solubility (125.0 mg·L-1) with earlier published values showed that the determined value of solubility was between estimates published by different authors.8,9,12 The researches, who have been determined previously the solubility of CaS, did not take into account the time required to reach of equilibration and the respective pH of the system, as they mainly analyzed the composition of solution. The determined value of solubility for the CaS in present study accounted the pH of system and time period for the dissolution of CaS.
Solubility product of CaS
FULL PAPER Solubility product constants (Ksp) are used to describe saturated solutions of ionic compounds of relatively low solubility. The solubility product of a salt could be calculated from its solubility, or vice versa. It is necessary to know the concentrations of calcium and sulfide ions in order to calculate the solubility product for CaS. The concentration of Ca2+ has been measured practically, but the concentration of S2- was too low for exact experimental measurements and that is why it is necessary to calculate it. Concentration of S2- can be calculated from H2S second acid dissociation constant (Ka2) equation 3 as follows: S 2
HS OH
K b 2
The real value of the second dissociation constant for H2S (Kb2) is the major issue for the calculation, and that situation has been discussed by different authors.14,17,18 Thus, it was difficult to find the right value for Kb2 and because of that the concentration of S2- and the value of the solubility product of CaS were calculated by different values of Kb2 using experimentally measured concentrations of [Ca2+] = 1.719 mM, [HS-] = 1.694 mM and [OH-] = 1.820 mM (Table 6).
Table 6 Calculated concentration of S2- and Ksp(CaS) by different Kb2 at measured concentrations of [Ca2+]=1.719 mM, [HS-]=1.694 mM and [OH-]=1.820 mM. Kb2, mol·Lˉ1 3980 2510 1260 1000 20 15.5 83 72.4 0.603 0.0708 0.01
[S2-], mol·Lˉ1 7.74·10-10 1.23·10-9 2.45·10-9 3.08·10-9 1.55·10-7 1.99·10-7 3.71·10-7 4.26·10-6 5.12·10-6 4.35·10-5 3.08·10-4
Ksp(CaS), (mol·Lˉ1)2 1.33·10-12 2.11·10-12 4.21·10-12 5.30·10-12 2.66·10-10 3.42·10-10 6.37·10-10 7.32·10-9 8.80·10-9 7.49·10-8 5.30·10-7
Reference [31] [18] [32] [33] [34] [35] [36] [37] [38] [39] [17]
FULL PAPER Average 15.20
Average 2.03·10-7
Average 5.66·10-8
The published values of Kb2 varied significantly and their calculated average value resulted in 15.20 mol·Lˉ1 (Table 6). Solubility of CaS can be characterized by the solubility product (Ksp), which was calculated as a product of concentrations of ions in the saturated solution measured in the present study: Ksp (CaS) = [Ca2+] × [S2ˉ] = (1.719·10-3)(1.97·10-7) =3.39 x 10ˉ10 (mol·Lˉ1)2 The ion product (Ks) of the Ca2+, HSˉ, OHˉ ions in the saturated solution was calculated to check the validity of Ksp: Ks = [Ca2+]meas× [HSˉ]meas× [OHˉ] = (1.719·10ˉ3)(1.694·10ˉ3)(1.82·10ˉ3) = 5.30·10ˉ9 (mol·Lˉ1)3 The ion product describes the investigated system in the state when there is formed dynamic equilibrium between ions in the solution. The product depicts the main ion forms that dominate in the system. Instead, the solubility product indicates main ions concentrations in the system and rather a hypothetic situation without interactions between S2- and H+. The solubility product could also be calculated as a quotient of Ks to the second basicity constant (Kb2): Ksp = Ks/Kb2 = 5.30·10ˉ9/15.20 = 3.49·10ˉ10 (mol·Lˉ1)2 The received value is equal to an experimentally determined result and it supports the developed theoretical model. Determined CaS solubility product value of 3.49·10ˉ10 (mol·Lˉ1)2 was several orders of magnitude lower than the Ksp value of 7.943·10-7 (mol·L-1)2 published by Licht11. Using different published values of Kb2, the average value of the solubility product was calculated as 5.66·10-8 (mol·Lˉ1)2, which was one order of magnitude lower in comparison to the published value of 7.94 10-7 (mol·L-1)2.11
FULL PAPER
Conclusion The dissolution process of CaS was studied in oxygen-free water at a temperature of 25 ºC through measurements of pH in the solution, and the concentrations of generated ions were also determined. A theoretical model of CaS dissolution describing the dissociation of CaS and the equilibrium between the different forms of sulfide ions (S2ˉ, HS-) was developed. The time required to reach the constant pH was proportional to the amount of added CaS up to 125.0 mg·L-1 (1.733 mM), but it was disproportionate at the concentrations higher than this concentration. The growth of the measured final pH values (in the range of pH = 10.6 – 11.26) was proportional to an increasing amount of added salt (pH = 0.0059 + 10.562, R² = 0.9365). The increased growth of final pH values in the solutions with the CaS concentration above 1.733 mM indicated that the corresponding amount of salt (125.0 mg) can cause saturation of CaS aqueous solution throughout short-term measurements. The measurements showed that [OHˉ] exceeded [S]tot and the ratio of their concentrations had the mean value of 1.14 (±0.06) without a clear relationship to [CaS]. Calculation of the ratio of [S]tot and [Ca2+]meas resulted in the mean value of 0.972 (±0.02) and the ratio of [Ca2+]meas to [OHˉ] had the mean value of 0.906 (±0.044) at the concentration of CaS between 0.335 to 1.733 mM, but the concentrations of Stot and Ca2+ were similar if the salt concentration in the aqueous solution was higher than 1.774 mM. [HS-]meas reached equality with the concentration of [S]tot when a 1.733 mM CaS solution was prepared. The initial rates of the growth of HS- concentrations increased steadily when up to 1.733 mM CaS solutions were prepared, whereas the initial rate was disproportionate at a higher concentration of CaS, indicating the changed behavior of CaS when more concentrated solutions were composed. The calculated values of the average dissolution rate increased up to the CaS concentration of 1.733 mM and the rate decreased when higher amount of CaS was added into
FULL PAPER water, confirming the solubility of CaS as high as 1.733 mM. The values of the initial and average rates of dissoluted HS- were respectively 7.446·10-3 mM·s-1 and 1.419·10-3 mM·s-1 at the CaS concentration of 1.733 mM. The measurements resulted in the solubility of CaS as 1.733 mM (125.0 mg·Lˉ1), which was between the estimates published by different authors. Determined solubility product of CaS as 3.49·10ˉ10 (mol·Lˉ1)2 was several orders of magnitude lower than the published values.
Acknowledgements Financial support for this study was provided by the target-financed project No. SF0180135s08 of the Ministry of Education and Research of the Republic of Estonia.
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FULL PAPER Graphical abstract
The scheme of the system of solid CaS in equilibrium with water.
