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Ind. Eng. Chem. Res. 1999, 38, 3812-3816
Kinetic and Mechanistic Study of Reaction between Sulfide and Sulfite in Aqueous Solution Tung Siu and Charles Q. Jia* Department of Chemical Engineering and Applied Chemistry, University of Toronto, Ontario, Canada M5S 3E5
The reaction between sulfide and sulfite in neutral to weak alkaline aqueous solutions was studied by following thiosulfate and sulfite concentrations using ion chromatography. The thiosulfate formation rate from the reaction 2HS- + 4HSO3- f 3S2O32- + 3H2O at pH 8 to 9 was found to be d[S2O32-]/dt ) kA[HS-][HSO3-]2, where kA ) 1.1 × 1012 exp(-48000/RT) M-2 s-1. A mechanism for this reaction has been proposed with disulfite (S2O52-) and HSO2intermediates. The measured rate of sulfite disappearance was higher than that calculated from the stoichiometry of the above reaction. This phenomenon is attributed to other reactions, that consume sulfite and form other sulfur compounds such as polythionates, polysulfides, and elemental sulfur. These reactions were treated as a single reaction, whose rate was found to be (-d[HSO3-]/dt)B ) kB[H+]-0.6[HS-]0.7[HSO3-]1.5, where kB ) 5 × 10-5 M-0.6 s-1 at 20 °C. A kinetic model was established on the basis of the kinetic data obtained in this and a previous work. The experimental data at pH 7 agreed with the model prediction in a satisfactory manner. The biphasic behavior of thiosulfate is considered to be critical in developing a new sulfur-producing flue gas desulfurization (SP-FGD) process based on sulfur dioxide absorption using sodium sulfide solution. Introduction To remove sulfur-containing gases from flue gases and convert them into elemental sulfur, a number of processes have been developed during the past 10 years. Many of them1-3 are based on the Claus reaction
SO2 + 2H2S f 3S + 2H2O
(1)
Depending on the phase in which the reaction proceeds, these processes are categorized into “dry” or “wet” processes. The main advantage shared by “wet” methods is the high efficiency in sulfur gas removal. The wet Claus reaction, however, has an extremely complicated mechanism, which includes numerous sulfur compounds, such as thiosulfate, polythionates, polysulfides, and elemental sulfur. The limited knowledge of the mechanism of the wet Claus reaction represents a major obstacle to the improvement of existing technologies and to the development of new processes. A wet sulfur-producing flue gas desulfurization (SPFGD) process, which is based on sulfur dioxide absorption using aqueous sulfide solution, is being developed in this group, for flue gases of high strength such as those generated by nonferrous metal smelters.3 Although we have proven the feasibility of the process and provided qualitative explanations for the behavior of the sulfide-sulfite system, the lack of kinetic and mechanistic information on the corresponding inorganic sulfur chemistry poses great difficulties in quantitative description of the system behavior. The magnitude of generation of a specific product in the aqueous sulfide-sulfite system is dependent on the pH and the ratio of reactants as well. In neutral to alkaline solutions (pH g 7) and when sulfide is the * Corresponding author. E-mail:
[email protected]. Telephone: +1-(416)946-3097. Fax: +1-(416)978-8605.
limiting reagent, thiosulfate is the prevailing product.4,5 Heunisch6 analyzed the stoichiometry of the reaction between sulfite and sulfide in an aqueous phase at room temperature and suggested the following equation for thiosulfate formation:
2HS- + 4HSO3- f 3S2O32- + 3H2O
(2)
Elemental sulfur is formed predominantly from the sulfite-sulfide system in acidic solutions with sulfide present in sufficient excess.7,8 The reaction between thiosulfate (from reaction 2) and sulfide is one of the pathways of elemental sulfur formation
2H2S(aq) + S2O32- + 2H+ f 4S(s) + 3H2O
(3)
Kundo et al.9 showed that reaction 3 is the controlling step of the sulfur-forming Claus reaction in aqueous solutions. Kinetic studies of reaction 3 have been done by Pai and Kundo10 and in this group as well.11 When surplus sulfite is available at acidic pH’s, elemental sulfur, thiosulfate, and polythionates can be found in the sulfite-sulfide system. A striking example is the Wackenroder’s liquid, a mixture of H2S and excess SO2 in an aqueous phase, which was studied by many researchers.12,13 The polythionates were considered to be formed by reaction between thiosulfate and sulfite:14
4HSO3- + S2O32- + 2H+ f 2S3O62- + 3H2O (4) Acting as both a stable product and a precursor for elemental sulfur and polythionates formation, thiosulfate appears to be the key compound in the sulfitesulfide system. The current investigation is to quantify the rate of the reaction between sulfide and sulfite in aqueous solutions under controlled pH, temperature,
10.1021/ie990254x CCC: $18.00 © 1999 American Chemical Society Published on Web 09/08/1999
Ind. Eng. Chem. Res., Vol. 38, No. 10, 1999 3813
and ionic strength. Combining with our previous knowledge of the sulfide-thiosulfate system,11 it is hoped that a better understanding of the sulfide-sulfite-thiosulfate system can be afforded. Experimental Section Reactions between sodium sulfide and sodium sulfite were conducted in a glass reactor, thermostated using an RTE-8 circulating water bath (NESLAB Instruments Inc.), and buffered with a mixture of 0.1 M KH2PO4 (pH ) 4.39) and 0.05 M Borax (pH ) 9.26) solutions. The ionic strength was controlled by adding solid NaCl to the reaction solutions. The reacting system was closed to prevent emission and oxidation of H2S by oxygen in air. All chemicals were reagent grade and used as received without further purification. A saturated stock solution of Na2S (2.412 M) was prepared and diluted to desired concentrations before each kinetic experiment. Because of its unstability, fresh sodium sulfite solutions were prepared just before used, and the concentrations were calculated by weight. Thiosulfate concentrations were followed during the reaction in the same way as described previously.11 After analyzing for thiosulfate, excess iodine solution (ca. 0.5 M) was added to the sample solutions to oxidize sulfite to sulfate. The latter was analyzed using ion chromatography. A Dionex DX 500 ion chromatography system, equipped with an ED40 conductivity detector, was used to determine thiosulfate and sulfate concentrations. The thiosulfate calibration curve obtained in the previous work11 was used. A linear response curve (r2 ) 0.9973) was acquired for sulfate in the concentration range 56.3-704 µM. The six-sample relative standard deviation (RSD) of the sulfate measurements was determined to be 0.3%. Results and Discussion The pH of reaction between sulfide and sulfite was first controlled at 8 to 9 to prevent the side reaction between sulfide and thiosulfate. According to our previous study11 as well as Battaglia and Miller’s,14 the reaction between sulfite and thiosulfate is unfavorable at this pH. Thus thiosulfate formation is isolated under this condition and the kinetic data so obtained were used in the modeling. This restraint was later removed when the reaction was studied at pH 7 to compare experimental data with the model prediction. Initial Rate Method. Generally a rate equation can be written as r ) -dCA/dt ) kCAa, where CA is the concentration of species A. During the first few percent of reaction, CA may be considered as a constant, CA,0, and the initial rate is obtained from the slope of the CA-t plot at t ) 0. Thus, the rate equation at t ) 0 is
-(dCA/dt)t)0 ) r0 ) k(CA,0)a
(5)
or most usefully in the log-log form
log r0 ) a log CA,0 + log k
(5′)
Therefore, by measuring r0 at several values of CA,0, the log-log plot yields the reaction order. This method also works if the rate equation includes the concentrations
Table 1. Initial Thiosulfate Formation Rate and Calculated Rate Constants kA′ at Various Total Sulfide (CNa2S) and Sulfite (CNa2SO3) Concentrations (I ) 0.20 M and T ) 20 °C) pH
CNa2S (mM)
CNa2SO3 (mM)
d[S2O32-]/dt (×10-8 M s-1)
k A′ (×103 M-2 s-1)
9.00 9.00 9.00 9.00 9.00 8.50 8.50 8.50 8.50 8.50 8.00 8.00 8.00 8.00 8.00
2.41 2.41 2.41 6.03 9.65 2.41 2.41 2.41 1.21 6.03 1.21 1.21 1.21 2.41 6.03
0.793 1.08 2.38 2.38 2.38 0.397 0.635 1.59 0.635 0.635 1.59 0.793 0.476 0.793 0.793
0.176(8)a 0.34(3) 1.54(8) 4.1(2) 6.3(4) 0.452(5) 1.06(2) 7.7(2) 0.533(6) 3.0(1) 22.8(4) 6.3(3) 2.00(5) 11.8(3) 27(1)
3.7(2) 3.8(3) 3.6(2) 3.8(2) 3.6(2) 4.17(5) 3.8(1) 4.3(1) 3.83(4) 4.3(2) 3.52(6) 3.9(2) 3.4(1) 3.7(1) 3.5(1)
a The number in parentheses represents the standard deviation of the last digit of the value.
Table 2. Reaction Orders With Respect to Sulfide (a) and Sulfite (b) in Thiosulfate Formation (I ) 0.20 M and T ) 20 °C) pH
a
b
9.00 8.50 8.00
1.03(2)a 0.92(2) 0.93(1)
1.9(1) 2.06(7) 2.01(4)
a The number in parentheses represents the standard deviation of the last digit of the value.
of other reactants, provided their concentrations are held constant throughout the series of measurements.15 In the current kinetic study of reaction between sulfide and sulfite, the initial rate method was applied. The reactions were allowed to proceed to less than 10%, during which six data points for each reaction were collected. The concentration-time curves were subject to the conventional linear regression, and the slopes from the regression were taken as the initial rates. Kinetics and Mechanism of Thiosulfate Formation. The thiosulfate formation rate of reaction 2 can be expressed as
d[S2O32-]/dt ) kA[HS-]a[HSO3-]b[H+]c
(6)
The initial rates of thiosulfate formation were measured with various sulfide and sulfite concentrations under controlled pH, ionic strength, and temperature. The results are presented in Table 1. HS- and HSO3concentrations, [HS-] and [HSO3-], were calculated from the total sulfide and sulfite concentrations, CNa2S and CNa2SO3, respectively, using equilibrium constants. The orders with respect to [HS-] and [HSO3-], that is, a and b, were calculated and listed in Table 2, along with the standard deviations. It is evident from Table 2 that reaction 2 is first order with respect to sulfide and second order with respect to sulfite. The rate constant kA′ ) kA[H+]c can therefore be determined by
kA′ ) (d[S2O32-]/dt)[HS-]-1[HSO3-]-2
(7)
The calculated rate constants kA′ are also listed in Table 1. The log kA′ versus pH plot gave a slope of 0.008 (kB′ ) kB[H+]-0.008), and therefore the rate constants kA′ can
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Table 3. Calculated Rate Constants of Reaction 2 at Different Temperatures (pH ) 9.00 and I ) 0.20 M) T (K)
kA (×103 M-2 s-1)
273 283 293 303 313
0.91(2)a 1.84(6) 3.8(3) 6.1(4) 14(1)
d[S2O32-]/dt )
a The number in parentheses represents the standard deviation of the last digit of the value.
Table 4. Activation Parameters of Reaction 2 (pH ) 9.00 and I ) 0.20 M) Ea (kJ mol-1)
∆Hq (kJ mol-1)
∆Sq (J K-1 mol-1)
A (M-2 s-1)
48(2)a
45(2)
-22(1)
1.1(3) × 1012
a
2k1k2[HSO3-]2[HS-] k-1 + k2[HS-]
(14)
The assumption of k-1 . k2[HS-] will regenerate the observed rate law where kA ) 2K1k2. Thus k2 can be calculated to be 2.6 × 104 M-1 s-1, using the results by Betts and Voss.18 Under the current experimental conditions, [HS-] is on the order of 10-3 M and the validity of the above assumption is ensured. The rate-limiting step in the mechanism (reaction 12) is a bimolecular neucleophilic displacement (SN2) reaction at the disulfite (I) sulfur-sulfur bond. An empirical correlation has been found, by Davis et al.,19 between the activation energy of the SN2 reaction and the length of the sulfur-sulfur bond being attacked:
The number in parentheses represents the standard deviation of the last digit of the value.
Ea ) C‚rSS-3
be considered as pH independent; that is, kA ) kA′. The averaged kA value is calculated to be 3.8(3) × 103 M-2 s-1. The activation parameters of reaction 2 were determined by conducting the reaction in the temperature range 0-40 °C. The calculated rate constants are listed in Table 3, and the activation parameters from the Arrhenius and Eyring plots
where rSS is the sulfur-sulfur bond length (in angstroms) and C is a constant characteristic of the neucleophile. For HS- the C value was calculated to be 130 kcal mol-1.20 Using a sulfur-sulfur bond length of 0.221 nm in disulfite,17 the activation energy for reaction 12 is calculated to be 50.3 kJ mol-1, which coincides with the experimental result of 48 kJ mol-1. Kinetics of Other Reactions between Sulfite and Sulfide. The sulfite consumption rates were also monitored as described in the Experimental Section. It was found that the overall rate of sulfite consumption is always higher than that calculated from the stoichiometry of reaction 2. This observation implies the existence of other reactions between sulfite and sulfide which lead to possible products of polythionates, polysulfides, and elemental sulfur. No attempt has been made in this work to identify these products, and these reactions were treated as a single reaction:
ln k ) ln A - Ea/RT
(8)
ln(k/T) ) ln(kB/h) + ∆Sq/R - ∆Hq/RT
(9)
are listed in Table 4. The negative entropy of activation suggests a bimolecular reaction in the rate-determining step.15 The ionic strength (I) effect was studied in the range 0.20-1.0 M, at pH 9 and 20 °C. The rate constants at the ionic strengths 0.20, 0.50, and 1.0 M are determined to be 3.8(3) × 103, 11.2(6) × 103, and 37.1(7) × 103 M-2 s-1, respectively. The plot according to eq 10 gives a slope ZAZB of 1.8, which indicates that two charged reactants are involved in the rate-determining step.16
log k ) log k0 + 2ZAZBAI
1/2
(10)
The following mechanism is proposed for thiosulfate formation, on the basis of the kinetic information:
2HSO32- S -O3S-SO2- (I) + H2O fast, K1 ) k1/k-1 (11) -
O3S-SO2- + HS- f S2O32- + HSO2- (II) slow, k2
2HSO2- (II) f S2O32- + H2O fast, k3
(12) (13)
Compound I has been known by a number of names, including metabisulfite and pyrosulfite. The name disulfite is more appropriate than the others, since the X-ray crystallography showed the molecule contains no S-O-S bridge.17 Betts and Voss18 studied reaction 11 and reported k1 and k-1 values of 700 M-1 s-1 and 104 s-1, respectively. Applying the steady-state approximation to both intermediates I and II, the thiosulfate formation can be expressed as
HS- + HSO3- f “P”
(15)
(16)
The sulfite consumption rate from “reaction” 16 can be written as
(-d[HSO3-]/dt)B ) kB[HS-]a′[HSO3-]b′[H+]c′
(17)
The total sulfite consumption rate, which was measured experimentally, is therefore
-d[HSO3-]/dt ) (-d[HSO3-]/dt)B + /3(-d[S2O32-]/dt) (18)
4
where the factor 4/3 is introduced according to stoichiometry of reaction 2. The initial rates of sulfite disappearance for “reaction” 16 are calculated as per eq 18 and listed in Table 5. The reaction orders a′ and b′ were determined and are tabulated in Table 6. While the a′ values are quite consistent, the order of HSO3- is pH dependent, ranging from 1.4 to 1.7. The averaged value of b′, that is, 1.5, was chosen, and the rate constants kB′ ) kB[H+]c′ are calculated according to
kB′ ) (-d[HSO3-]/dt)B[HS-]-0.7[HSO3-]-1.5
(19)
The kB′ values are also listed in Table 5. The plot of log kB′ versus pH gives a c′ value of - 0.6(1). The averaged kB is calculated to be 5(1) × 10-5 M-0.6 s-1.
Ind. Eng. Chem. Res., Vol. 38, No. 10, 1999 3815 Table 5. Initial Sulfite Consumption Rates of “Reaction” 16 and Calculated Rate Constants kB′ at Various Total Sulfide (CNa2S) and Sulfite (CNa2SO3) Concentrations (I ) 0.20 M and T ) 20 °C) pH
CNa2S (mM)
CNa2SO3 (mM)
(-d[HSO3-]/dt)B (×10-8 M s-1)
kB′ (M-1.2 s-1)
9.00 9.00 9.00 9.00 9.00 8.50 8.50 8.50 8.50 8.50 8.00 8.00 8.00 8.00 8.00
2.41 2.41 2.41 6.03 9.65 2.41 2.41 2.41 1.21 6.03 1.21 1.21 1.21 2.41 6.03
0.793 1.08 2.38 2.38 2.38 0.397 0.635 1.59 0.635 0.635 1.59 0.793 0.476 0.793 0.793
0.78(6) a 1.4(1) 4.1(2) 9.2(7) 11(1) 1.26(6) 2.5(1) 8.8(5) 1.6(1) 5.4(3) 8.6(6) 3.2(2) 1.1(1) 4.7(5) 9.3(5)
10(1) 11(1) 10(1) 12(1) 10(1) 8.8(5) 8.6(3) 7.6(5) 8.9(6) 9.8(6) 2.7(2) 2.8(2) 2.1(2) 2.6(3) 2.7(2)
Figure 1. Theoretical prediction (solid line) and experimental data (b) of thiosulfate concentrations in the reaction of sulfide and sulfite (pH ) 7.00, I ) 0.20 M, and T ) 20 °C).
a The number in parentheses represents the standard deviation of the last digit of the value.
Table 6. Reaction Orders with Respect to Sulfide (a′) and Sulfite (b′) for “Reaction” 16 (I ) 0.20 M and T ) 20 °C) pH
a′
b′
9.00 8.50 8.00
0.7(1)a 0.7(1) 0.67(5)
1.5(2) 1.39(4) 1.7(2)
a The number in parentheses represents the standard deviation of the last digit of the value.
Overall Behavior of the Sulfide-Sulfite-Thiosulfate System. By combining the kinetic information obtained above and in previous work,11 the behavior of the sulfide-sulfite-thiosulfate system can be described by the following set of equations:
d[S2O32-]/dt ) kA[HS-][HSO3-]2 - kC[H2S][S2O32-] (20)
Figure 2. Theoretical prediction (solid line) and experimental data (b) of sulfite concentrations in the reaction of sulfide and sulfite (pH ) 7.00, I ) 0.20 M, and T ) 20 °C).
-d[HSO3-]/dt ) kB[HS-]0.7[HSO3-]1.5[H+]-0.6 +
concentrations. It is evident that the experimental data agree well with the model prediction. Although the identity and quantity of product(s) “P” were not determined in this work, the extent of reaction 16 can be estimated from the present kinetic model. Under the above experimental conditions, for example, reaction 16 contributes about 10% to the overall reaction that consumes sulfite. Further works on this “other” reaction would be of great interest.
4
-
- 2
/3kA[HS ][HSO3 ] (21)
where the kC term is for reaction 3 and determined previously. Theoretically, the time dependence of the sulfide species is necessary to solve these equations and may be calculated from the mass balance. An alternative way, however, is to experimentally use a sufficient excess of sulfide so that the terms [HS-] and [H2S] in the above equations are considered as invariant and included in the rate constants. Such an experiment was conducted at pH 7.00, ionic strength 0.20 M, and T ) 20 °C with a total sodium sulfide concentration of 0.0121 M and an initial sodium sulfite concentration of 7.94 × 10-4 M. Equations 20 and 21 are now converted into
dCThio/dt ) 8.7(CNa2SO3)2 - (2.7 × 10-4)Cthio
(20′)
-dCNa2SO3/dt ) 12(CNa2SO3)2 + 0.011(CNa2SO3)1.5 (21′) where Cthio and CNa2SO3 are thiosulfate and sulfite concentrations, respectively. The model prediction curves of Cthio and CNa2SO3 are shown in Figures 1 and 2, respectively, along with the experimentally determined
Conclusions A systematic kinetic study of the aqueous sulfidesulfite system has been performed. By combining with our previous results, a mathematical model has been set up to describe the behavior of the sulfide-sulfitethiosulfate system. Experimental data at pH 7 coincided with the model prediction in a satisfactory manner. The biphasic behavior of thiosulfate, that is, its rapid formation and slow consumption, is indicated by both the modeling and experimental data. This provides an explanation of thiosulfate accumulation in the sulfidesulfite system, which was observed by various researchers.21-24 An immediate application of the above kinetic information is in the development of a new SP-FGD process.3,11 The findings in this study are potentially applicable in other air pollution control processes, for
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example, H2S emission control, where sulfide and/or sulfite are involved. Acknowledgment The financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC) is gratefully acknowledged. Literature Cited (1) Sulfur Dioxide Abatement; INCO Ltd., Manitoba Division: Thompson, Manitoba, Canada, 1990; Appendix C. (2) Olper, M.; Maccagni, M. Removal of SO2 from Flue Gas and Recovery of Elemental Sulfur. European Patent EP728,698, 1996. (3) Liu, J. H.; Siu, T.; Jia, C. Q. Reduction of SO2 to Elemental Sulfur with Aqueous Na2S at Low Temperatures. Submitted for publication in Environ. Sci. Technol. (4) Foerster, F.; Mommsen, E. T. Chem. Ber. 1924, 57, 258. (5) Urban, P. Removal of H2S from a Gas Stream Containing H2S and CO2. U.S. Patent 3,859,414, 1975. (6) Heunisch, G. W. Inorg. Chem. 1977, 16 (6), 1411. (7) Riesenfeld, E. H.; Feld, G. W. Z. Anorg. Allg. Chem. 1921, 119, 225. (8) von Deines, O.; Grassmann, H. Z. Anorg. Allg. Chem. 1934, 220, 337. (9) Kundo, N. N.; Pai, Z. P.; Gutova, E. A. Zh. Prikl. Khim. 1987, 60 (8), 1702. (10) Pai, Z. P.; Kundo, N. N. Zh. Prikl. Khim. 1989, 62 (4), 780. (11) Siu, T.; Jia, C. Q. Ind. Eng. Chem. Res. 1999, 38, 1306.
(12) Blasius, E.; Burmeister, W. Z. Anorg. Allg. Chem. 1959, 268, 1. (13) Stamm, H.; Becke-Goehring, M.; Schmidt, M. Angew. Chem. 1960, 72, 34. (14) Battaglia, C. J.; Miller, W. J. Photogr. Sci. Eng. 1968, 12 (1), 46. (15) Connors, K. A. Chemical Kinetics: The Study of Reaction Rates in Solutions; VCH Publishers: New York, 1990. (16) Laidler, K. J. Chemical Kinetics; Harper & Row: New York, 1987. (17) Lindquist, I.; Morsell, M. Acta Crystallogr. 1957, 10, 406. (18) Betts, R. H.; Voss, R. H. Can. J. Chem. 1970, 48, 2035. (19) Davis, R. E.; Louis, J. B.; Cohen, A. J. Am. Chem. Soc. 1966, 88 (1), 1. (20) Ciuffarin, E.; Pryor, W. A. J. Am. Chem. Soc. 1964, 86, 3621. (21) Foerster, F.; Janitzki, J. Z. Anorg. Allg. Chem. 1931, 200, 23. (22) Muller, E.; Mehlhorn, I. K. Angew. Chem. 1934, 47 (9), 134. (23) Strong, H. W.; Radway, J. E.; Cook, H. A. Cyclical Process for Recovery of Elemental Sulfur from Waste Gases. U.S. Patent 3,784,680, 1974. (24) Talonen, T. T.; Poijarvi, J. T. I. Method for Removing Sulfur in Elemental Form from Gases Containing Sulfur Dioxide or Sulfur Dioxide and Hydrogen Sulfide. U.S. Patent 4,937,057, 1990.
Received for review April 9, 1999 Accepted July 17, 1999 IE990254X
