1306
Ind. Eng. Chem. Res. 1999, 38, 1306-1309
Kinetics of Reaction of Sulfide with Thiosulfate in Aqueous Solution Tung Siu and Charles Q. Jia* Department of Chemical Engineering and Applied Chemistry, University of Toronto, Ontario, Canada M5S 3E5
The kinetics of the reaction 2H2S(aq) + S2O32- + 2H+ f 1/2S8(s) + 3H2O has been investigated at 0-40 °C in the pH interval from 5 to 7. The rate law was found to be r ) -d[S2O32-]/dt ) k[H2S][S2O32-], where k ) 8 × 1011 exp(-74 300/RT) M-1 s-1. Thermodynamic calculation shows that the reaction is unfavorable at pH g 8, which is confirmed by the experimental observation. The ionic strength effect on the reaction also has been studied. The mechanism postulated to account for the observed rate law involves the formation and subsequent reactions of an intermediate H2S3O32-. 2HS- + 4HSO3- f 3S2O32- + 3H2O
Introduction Sulfur dioxide (SO2) in flue gases is detrimental to the well being of ecosystems if discharged. Removing SO2 from flue gases and converting it into useful products in an economically viable way are important and challenging tasks. Because it is easier to handle and transport, elemental sulfur is a desirable byproduct of flue gas desulfurization (FGD) processes for some SO2 producers, particularly for those in remote areas. The corresponding processes are referred to as the sulfurproducing flue gas desulfurization (SP-FGD). Aiming at the development of an auspicious SP-FGD process, Liu et al. (1998) studied SO2 absorption using sodium sulfide solution and found that simultaneous SO2 absorption and elemental sulfur production can be achieved at low temperatures (near 0 °C). Two types of reactions, namely, acid-base and redox reactions, occur in the Na2S(aq)-SO2(g) system. The acid-base reactions are necessary for providing a favorable pH environment for the sulfur-forming redox reactions that may be summarized by the following equation:
2HS- + HSO3- + 3H+ f 3S(S) + 3H2O
(1)
On the other hand, the acid-base reactions also compete with the redox reactions for sulfides by hydrolyzing S2- and HS- ions to produce aqueous H2S, which can escape to the gaseous phase. This loss of H2S into gaseous phase was significant even at 0 °C (about 20% of initial Na2S). Clearly, the rate of sulfur-forming redox reactions has to be increased in order to improve the yield of elemental sulfur. To do so, a better understanding of the kinetics of redox reactions in aqueous phase is essential. Previous investigations (Muller and Mehlhorn, 1934; Heunisch, 1977; Talonen and Poijarvi, 1990) showed that thiosulfate tends to accumulate in MS-SO2 (M ) Na, Ca) reaction systems. Heunisch (1977) analyzed the stoichiometry of the reaction between sulfite and bisulfide in aqueous phase at room temperature and suggested the following equation for thiosulfate formation: * E-mail:
[email protected]. Telephone: +1-(416)946-3097. Fax: +1-(416)978-8605.
(2)
It was observed that the formation of thiosulfate was enhanced at lower pHs. Studying an SO2-Na2S(aq) system, Talonen and Poijarvi (1990) reported the formation of thiosulfate and its dependency on the solution acidity. It is known that the reaction between sulfide and thiosulfate produces elemental sulfur through
2H2S(aq) + S2O32- + 2H+ f 1/2S8(s) + 3H2O (3) The accumulation of thiosulfate, as mentioned above, indicates that the conversion of thiosulfate to elemental sulfur is a relatively slow step in the overall process of sulfur production. This was confirmed by a study of Kundo et al. (1987), who showed that the reduction of thiosulfate by hydrogen sulfide (reaction 3) is the controlling step of the sulfur-forming Claus reaction in aqueous solutions. The same group (Pai and Kundo, 1989) later conducted a kinetic study of reaction 3 with a catalyst. The gaseous phase content of H2S was followed and converted to aqueous concentration [H2S], which implies that the rate of transfer of H2S from the gaseous to aqueous phase is much faster than the rate of consumption of aqueous H2S by thiosulfate. No attempt was made by the authors to justify this implication. The rate law of reaction 3 was reported as
W ) k[S2O32-]1.5[H2S]n[H+]m
(4)
where W is the reaction rate in terms of a decrease of aqueous H2S concentration. When partial pressure of H2S, PH2S > 0.02 MPa, n ) 0.2, and when PH2S < 0.02 MPa, n ) 1. When pH < 5.0, m ) 1, and m ) 0 when pH > 5.0. Under reaction conditions of PH2S > 0.02 MPa, pH < 5.0, and T ) 40-70 °C, these authors expressed the rate constant k as
k ) (83.3 ( 6.5) exp(-62000/RT) M-1.7 s-1
(5)
For bimolecular reactions in aqueous solutions, the frequency factor is typically in the range of 1011-1012 M-1 s-1 (Moelwyn-Hughes, 1947). The extremely small frequency factor (83.3 M-1.7 s-1) reported in the study
10.1021/ie980537+ CCC: $18.00 © 1999 American Chemical Society Published on Web 02/17/1999
Ind. Eng. Chem. Res., Vol. 38, No. 4, 1999 1307
is indeed dubious and is probably a result of the omission of a multiplier by mistake. We believe that a better understanding of the kinetics of thiosulfate reduction by sulfide is essential to further promotion of elemental sulfur yield in the aqueous phase. The current investigation is a study of the homogeneous reaction of sodium sulfide and sodium thiosulfate in aqueous solution under controlled pH, temperature, and ionic strength. The pseudo-order technique has been utilized by keeping sulfide concentration in large excess and following the thiosulfate concentration. Experimental Section Apparatus. A 250 mL single-neck round-bottom glass flask was used as the reactor for all of the aqueous reactions conducted. The reactor was thermostated ((1.0 °C) using an RTE-8 circulating water bath (NESLAB Instruments Inc.). The reacting system was closed to prevent emission and oxidation of H2S by oxygen in air. Reagents and Preparation of Solutions. All chemicals were reagent grade and used as received without further purification. Solutions were prepared with deionized distilled water, which was deaerated by bubbling nitrogen gas (BOC, > 99.999 vol %) through it for about 30 min just before using. A saturated stock solution of Na2S was prepared with Na2S‚9H2O crystals (BDH Inc., 98.0-103.0%) and standardized using iodometric titration. The concentration of this stock solution was 2.412 M. Standard thiosulfate solutions for ion chromatography calibration were prepared using Na2S2O3‚5H2O crystals (ACP Chemicals, 99.5-101.0%) and standardized iodometrically (Kolthoff and Belcher, 1947). A 0.05 M ZnCl2 solution was prepared by weighing out 3.4 g of zinc chloride powder (Aldrich, 98+%) and dissolving it in 500 mL of water. Buffer solutions with pH 5-8 were prepared by mixing 0.1 M KH2PO4 (13.62 g/L, pH ) 4.39) and 0.05 M Borax (19.40 g/L Na2B4O7‚10H2O, pH ) 9.26) solutions (Lange’s, 1985). The mixed buffer solutions were used to dilute stock Na2S solution or to prepare sodium thiosulfate solution for reactions. The reacting solutions thus prepared had a calculated ionic strength of 0.10 M. For reactions at higher pH and higher ionic strength, 0.10 M NaOH solution and solid NaCl were used to maintain pH and ionic strength. Stock solutions of 180 mM Na2CO3/170 mM NaHCO3 were prepared by dissolving 19.08 g of Na2CO3 (BDH, 99.9%, dried at 250 °C for 0.5 h) and 14.28 g of NaHCO3 (ACP, 99.7-100.3%) in 1 L deionized-distilled water (boiled and cooled before use). Fresh solutions for ion chromatography elution were prepared just before use by diluting the above solution 100 fold. Procedures and Analytical Methods. Reactions between thiosulfate and sulfide were conducted in the above-mentioned reactor. Na2S (100 mL) and Na2S2O3 solutions (100 mL) were kept in a water bath at reacting temperature for 30-60 min and then mixed in the reactor. During the reaction, 5.00 mL aliquots of the reacting solution were pipetted from the reactor and injected immediately into test tubes containing 2.00 mL or more of 0.05 M ZnCl2 solutions to precipitate sulfide. When reactions were conducted at high pH (7-11), 1.00 mL of 0.01 M HCl solutions were mixed with each of the ZnCl2 solutions to prevent formation of Zn(OH)2 precipitates. The resulting solutions, after the addition
of reacting solutions, had pH around 6. Under these conditions, the concentrations of free sulfide in solution were calculated as lower than 10-10 M, and reaction between sulfide and thiosulfate was considered to be stopped. These solutions were then filtered using syringe filter units with 0.22 µm pore size poly(tetrafluoroethylene) (PTFE) membranes. The filtrates were used for ion chromatography analyses. A Dionex DX 500 ion chromatography system was used to determine thiosulfate concentration. The IC system was equipped with a GD40 gradient pump and an ED40 conductivity detector integrated with an anion self-regenerating suppressor. A Dionex IonPac AS4ASC column (4 × 50 mm) was used to separate thiosulfate ions which were detected by the conductivity detector. Sodium carbonate/bicarbonate (1.8/1.7 mM) eluent with an isocratic flow rate of 3.0 mL/min was used. The chromatography system was interfaced to a Digital Pentium166 PC by using an Analogue to Digital Conversion (ADC) board. The Star Chromatography Workstation v. 4.51 software package provided by Varian was used to collect and analyze the data. The thiosulfate calibration curve was obtained using standard sodium thiosulfate solutions with concentrations ranged from 3.7 to 190 µM. A linear response curve was obtained with a slope of 5.19(2) × 104 counts/µM and a correlation coefficient (r2) of 0.9998. A six-sample relative standard deviation of thiosulfate measurement was determined to be 0.7%. The pH values were measured using an Orion 520A pH meter with automatic temperature compensation. The pH electrode which was specially designed for aqueous solutions containing sulfide or heavy metal ions was supplied by Cole-Parmer. Results and Discussion The Pseudo-Order Condition. It is important to ensure that aqueous sulfide concentration is in sufficient excess and does not change significantly during the reaction with thiosulfate. The sulfide species distribute in both aqueous and gaseous phases, and the mass constraint is imposed by the nominal concentration of Na2S, Cs:
Cs ) [H2S(aq)] + [HS-] + [S2-] + nH2S,g/Vaq (6) where nH2S,g is amount of H2S in gaseous phase and Vaq is the volume of reacting solution. The reacting system was closed during the course of reaction except for sampling, and the loss of H2S from gaseous phase is considered to be negligible. Under the condition of pH 5-7, [S2-] can be ignored, and the aqueous H2S concentration can be calculated as
[H2S(aq)] ) Cs(1 + K1/[H+] + g)-1
(7)
where K1 is the first acidic dissociation constant of H2S. The dimensionless correction term, g, which can be expressed as
h aq g ) HV h g/RTV
(8)
h aq represents the gaseous partition of sulfide. V h g and V are the average gaseous and aqueous volumes of the reacting system; H (in J/mol) is the Henry’s law constant of H2S, which is calculated from H2S solubility data (Lange’s, 1985); R is the gas constant and T is the
1308 Ind. Eng. Chem. Res., Vol. 38, No. 4, 1999 Table 1. Pseudo-First-Order Rate Constants kobsd Determined at 20 °C pH 5.00
5.50 6.00
6.50 7.00
Table 2. Calculated Second-Order Rate Constants, k, at Various pHs and T ) 20 °C
[H2S]0, mM
kobsd, 10-5 s-1
pH
k, M-1 s-1
0.877 1.10 2.19 5.48 8.77 1.08 2.15 5.38 1.02 2.03 5.07 8.11 10.2 0.861 1.71 4.29 2.89 4.62 5.79 11.5
3.7(1)a
5.00 5.50 6.00 6.50 7.00
0.0446(4)a 0.0447(2) 0.0454(9) 0.0458(3) 0.0447(6)
4.82(5) 9.6(5) 24.9(5) 39(1) 4.8(1) 9.8(1) 24.0(6) 4.8(2) 9.7(2) 25.1(4) 37(1) 45(1) 3.89(6) 8.0(1) 19.6(4) 12.6(3) 21(1) 27(1) 50.7(8)
a The numbers in parentheses represent the standard deviations at the last digits of k values.
Table 3. Calculated Second-Order Rate Constants at Different Temperatures
absolute temperature. The highest fraction of H2S in gas phase is calculated to be 13% under experimental conditions. Because the total sulfide concentration was kept at least 10-fold in excess over thiosulfate, the pseudo-order condition was maintained in aqueous phase. Reaction Orders with Respect to Thiosulfate. The thiosulfate concentrations were followed using ion chromatography as mentioned above. The reaction order with respect to thiosulfate was estimated using Wilkinson’s relation (Wilkinson, 1961):
(9)
where p ) 1 - [S2O32-]/[S2O32-]0 is the fraction reacted and n is the reaction order with respect to thiosulfate. The plot of t/p vs t gives a slope of n/2. Data obtained at different pH values (ranging from 5 to 7) and sulfide concentrations were analyzed, and the values of n was found to be 1.04-1.11, indicating first-order kinetics with respect to thiosulfate. Pseudo-First-Order Rate Constant kobsd. The integrated rate law thus can be written as
ln[S2O32-]0/[S2O32-] ) kobsdt
k, M-1 s-1
273 283 293 303 313
0.0050(1)a 0.0167(4) 0.045(1) 0.131(2) 0.33(1)
a The numbers in parentheses represent the standard deviations at the last digits of k values.
a The averaged values of three measurements are reported. The numbers in parentheses represent the standard deviations at the last digits of kobsd values.
t nt 1 ) + p 2 k[S2O32-]n-1 0
T, K
(10)
By plotting ln([S2O32-]0/[S2O32-]) vs t, the pseudo-firstorder rate constant kobsd can be obtained. For various hydrogen sulfide concentrations and pHs, the results are listed in Table 1. Second-Order Rate Constant k. The reaction order with respect to H2S was obtained using the relation
kobsd ) k[H2S]0m
(11)
log kobsd ) log k + m log [H2S]0
(12)
or
where [H2S]0 is the initial hydrogen sulfide concentration and considered to be invariant during the course of reaction. The plots according to eq 12 for reactions
Table 4. Activation Parameters of the Reaction (pH ) 6.00 and I ) 0.10 M) Ea, kJ mol-1
∆Hq, kJ mol-1
∆Sq, J K-1 mol-1
A, M-1 s-1
74.3(7)a
71.9(8)
-24.6(4)
8(2) × 1011
a
The numbers in parentheses represent the standard deviations at the last digits.
conducted at pH 5-7 gave m values of 1.01-1.03. Therefore, it can be concluded that the reaction is firstorder with respect to hydrogen sulfide. The calculated second-order rate constants at various pHs are listed in Table 2. Effects of pH. It is obvious, from Table 2, that the rate constants k fluctuate only slightly over a 100-fold hydrogen ion concentration range (pH 5-7). This leads to the conclusion that the reaction is zeroth-order with respect to H+. The rate constant k at 20 °C was thus calculated as the averaged k value, i.e., k ) 0.045(1) M-1 s-1. For reactions at pH 8.0, 9.3, and 11, there was no significant change in thiosulfate concentrations over a period of 8 h. This was explained by the calculated redox potential for reaction 2, which shows the reaction is thermodynamically unfavorable at pH higher than 7.6 under the experimental conditions. Effects of Temperature. Reactions were conducted at different temperatures (273-313 K), and the secondorder rate constants k are listed in Table 3. The energy of activation (Ea), enthalpy of activation (∆Hq), entropy of activation (∆Sq), and frequency factor (A) were obtained from the Arrhenius and Eyring plots:
ln k ) ln A - Ea/RT
(13)
ln(k/T) ) ln(kB/h) + ∆Sq/R - ∆Hq/RT
(14)
where kB is Boltzmanns constant and h is Planck’s constant. The activation parameters are presented in Table 4. The negative entropy of activation (∆Sq) indicates a bimolecular mechanism in the rate-determining step (Connors, 1990), where two reactant particles are converted to a single transition-state particle, with a loss of disorder of the system. Effect of Ionic Strength. Variations of ionic strength (I ) 0.10-1.0 M) caused by adding sodium chloride to the reacting solutions affected the reaction rate only
Ind. Eng. Chem. Res., Vol. 38, No. 4, 1999 1309 Table 5. Ionic Strength Effect on Second-Order Rate Constant (pH ) 6.00 and T ) 20 °C) ionic strength, M
k, M-1 s-1
0.10 0.50 1.0
0.045(1)a 0.042(2) 0.039(2)
a The numbers in parentheses represent the standard deviations at the last digits of k values.
slightly. The second-order constants at different ionic strengths are listed in Table 5. For a bimolecular reaction, the relationship between rate constant and ionic strength can be expressed as (Laidler, 1987)
log k ) log k0 + 2ZAZBAI1/2
Acknowledgment The authors are grateful for the financial support from the Natural Science and Engineering Research Council of Canada.
(15)
where ZA and ZB are charges of the reactants, A is the Debye-Huckel constant, and k0 is the rate constant extrapolated to zero ionic strength. The plot of log k against 2AI1/2 gives a slope ZAZB of 0.09, which suggests that a neutral molecule is involved in the ratedetermining step of the reaction (Laidler, 1987). The deviation of ZAZB from zero can be attributed to the simplification in eq 15, where the limiting DebyeHuckel law is used. Proposed Mechanism of the Reaction. A mechanism that fits both the observed rate law and stoichiometry is postulated in the following sequence:
S2O32- + H2S f H2S3O32- (slow)
temperature (273-313 K) and ionic strength (0.10-1.0 M). The observed rate law is first-order in both [H2S] and [S2O32-] and independent of [H+]. The value of entropy of activation and observed ionic strength effect provide supportive clues in the postulation of a reaction mechanism. In accordance with these observations, H2S3O32- is proposed as the intermediate in the ratedetermining step.
(16)
H2S3O32- + H+ f H2O + HS3O2- (fast)
(17)
HS3O2- + H2S f H3S4O2- (fast)
(18)
H3S4O2- + H+ f H2O + H2S4O (fast)
(19)
2H2S4O f 2H2O + S8 (fast)
(20)
where eq 16 is rate determining. Dividing eq 20 by 2 and adding up the mechanistic equations leads to the stoichiometry, eq 3. Future studies will be of interest to probe for the intermediate H2S3O32-, if it can be generated in significant quantity. Another related intermediate, S4O2-, was proposed by Licht and Davis (1997) in their study of polysulfide decomposition, which is also pending identification. Conclusions The reaction between sulfide and thiosulfate in aqueous solution was investigated for a range of pH (5-7),
Literature Cited Connors, K. A. Chemical Kinetics: The Study of Reaction Rates in Solution; VCH Publishers: New York, 1990. Heunisch, G. W. Stiochiometry of the Reaction of Sulfites with Hydrogen Sulfide. Inorg. Chem. 1977, 16 (6), 1411. Kolthoff, I. M.; Belcher, R. Titration Methods: Oxidation-Reduction Reactions; Volumetric Analysis. Vol. III; Interscience Publishers: New York, 1947. Kundo, N. N.; Pai, Z. P.; Gutova, E. A. Study of Liquid-Phase Reduction of the Products of Sulfur Dioxide Absorption. Zh. Prikl. Khim. 1987, 60 (8), 1702. Laidler, K. J. Chemical Kinetics; Harper & Row: New York, 1987. Lange’s Handbook of Chemistry; Dean, J. A., Ed.; McGraw-Hill: New York, 1985. Licht, S.; Davis, J. Disproportionation of Aqueous Sulfur and Sulfide: Kinetics of Polysulfide Decomposition. J. Phys. Chem. B 1997, 101, 2540. Liu, J. H.; Siu, T.; Jia, C. Q. Behavior of Na2S(aq)-SO2(g) System at Low Temperatures. 1998, submitted to Environ. Sci. Technol. for publishing. Moelwyn-Hughes, E. A. The Kinetics of Reactions in Solution, 2nd ed.; Oxford University Press: London, 1947; Chapter III. Muller, E.; Mehlhorn, I. K. Potentiometric Investigation of the Formation of Thiosulfate from Alkali Sulfide and Sulfuric Acid. Angew. Chem. 1934, 47 (9), 134. Pai, Z. P.; Kundo, N. N. Kinetics of Catalytic Reduction of Ammonium Thiosulfate by Hydrogen Sulfide in Aqueous Solutions. Zh. Prikl. Khim. 1989, 62 (4), 780. 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 (Cl. C01b17/05), Jan. 26 1990. Wilkinson, R. W. A Simple Method for the Determination of Reaction Velocity Constants and Orders of Reaction. Chem. Ind. 1961, 2, 1395.
Received for review August 13, 1998 Revised manuscript received November 30, 1998 Accepted December 28, 1998 IE980537+
