Ind. Eng. Chem. Res. 1998, 37, 1167-1172
1167
Solubility of Sulfur Dioxide in Sulfuric Acid of High Concentration Qinglin Zhang, Hui Wang, Ivo G. Dalla Lana, and Karl T. Chuang* Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta T6G 2G6, Canada
The solubility of sulfur dioxide (SO2) in concentrated aqueous sulfuric acid (60-96 wt %) was measured at different SO2 partial pressures and at temperatures of 298, 383, and 393 K. A correlation is derived relating the SO2 solubility in aqueous sulfuric acid solution with different SO2 partial pressures. Further simplifications for high concentrations of the sulfuric acid solution allow the direct determination of a Henry’s law constant and its dependence on temperature using the measured solubility data and the correlation. A comparison of the correlation with limited literature data is also presented. The correlation well represents both the experimental data of this work and the data reported in the literature. The overall heats of solution of SO2 in 79.01 and 95.91 wt % sulfuric acid solutions were also estimated using a van’t Hoff type dependence of Henry’s law constant on temperature. Introduction Sulfur dioxide (SO2) is frequently encountered when recovering metals from sulfide ores, in sulfuric acid production, in the combustion of sulfur-containing fossil fuels, and during sulfur recovery from hydrogen sulfide. It is possible to analyze SO2 recovery by gas-liquid absorption in an appropriate solvent providing solubility properties are available. In our work, we needed to establish material balances for sulfur in the two phases of the gas-liquid system, SO2-concentrated sulfuric acid. However, a comprehensive survey of the literature indicated very limited information on solubility of SO2 in sulfuric acid of concentration from 60 to 96 wt % at temperatures >373 K. Of the available properties, the majority deal with SO2 solubility at 101.3 kPa and 353 K or lower temperatures (Miles et al., 1920 and 1946; Lopatto et al., 1934; Johnstone et al., 1934; Hayduk et al., 1988). Although various studies have been carried out on SO2 solubility in pure water (Edwards et al., 1975 and 1978; Rumpf and Maurer, 1992) or in dilute sulfuric acid of concentrations of 22 wt %. Because our sulfuric acid concentration of interest is in the range 65-98 wt %, the concentration of molecular SO2 in sulfuric acid solution, mSO2, may be approximated by its solubility in sulfuric acid, (mSO2); that is:
mSO2 = mSO2
(17)
Based on this assumption (eq 17), the activities of ionized species in sulfuric acid are no longer needed for the calculation of the concentration of the molecular solute, SO2. In this paper, the assumption (eq 17) was used in the interpretation of sulfuric acid concentrations >65 wt %. The concentration of dissolved molecular SO2 is taken equal to the solubility of SO2 in concentrated sulfuric acid. The latter was measured experimentally. Combining eqs 13, 14, 15, and 17, we obtain:
ln PSO2 +
BP ) ln H + ln mSO2 + 2βSO2-SO2mSO2 RT (18)
At relatively low SO2 pressures and high temperatures, φSO2 approaches unity, enabling eq 18 to be further simplified to:
ln PSO2 ) ln H + ln mSO2 + 2βSO2-SO2mSO2 (19) The Henry’s law constant defined in eq 18 or 19, H, can be estimated using the experimental solubility data of SO2 at different sulfuric acid concentrations and temperatures. Experimental Section
(16)
The total concentration of SO2 dissolved in the aqueous sulfuric acid solution, [i.e., the solubility of SO2 (mSO2)] is determined experimentally. However, to correlate the solubility of SO2 at different SO2 partial pressure using eq 13, the solubility of molecular form, SO2 (mSO2), has to be determined based on the equilibrium eqs 6-10 and mass and charge balance eqs 11 and 12 in the liquid phase. Additionally, activity coefficients for the different species in the liquid phase are also required for the determination of solubility of molecular form SO2 (mSO2). In high concentration sulfuric acid solutions, the dissolved SO2 was shown to be present mostly in its molecular rather than ionic form (Gold and Tye, 1950). Govindarao and Gopalakrishna (1993) further showed that ionization of SO2 becomes negligible at sulfuric acid
Materials. The SO2 (>99.9%) was purchased from Linde, N2 (prepurified) was purchased from Praxair Canada Inc., and sulfuric acid (>96 wt %) was supplied by Anachemia Canada Inc. Sulfuric acid of a specific concentration was prepared by adding the concentrated acid solution to distilled water, and the concentration was determined by titration using a standard 0.1 N NaOH solution (Fisher Scientific Ltd.). SO2 Solubility Measurements. A diagram of the apparatus used for solubility measurements is shown in Figure 1. Two vessels were used: a stainless steel gas reservoir of 334 cm3, and a solubility cell made of Pyrex glass with an internal magnetic stirrer and a volume of 122 cm3. A Heiss pressure gauge ((0.5 kPa) was used to measure the pressures in both the reservoir and the solubility cell. The temperature in the solubility cell was controlled with an OMRON digital temperature
Ind. Eng. Chem. Res., Vol. 37, No. 3, 1998 1169 Table 1. Solubility of Pure SO2 in H2SO4 Solution H2SO4 concentration, wt %
SO2 partial pressure, kPa
SO2 solubility, mmol/kg H2SO4
79.01 79.01 79.01 79.01 79.01
95.72 128.4 152.8 167.0 179.1
325.6 441.6 535.5 598.8 658.1
79.01 79.01 79.01 79.01
142.8 173.8 190.6 199.9
72.02 84.56 95.50 108.5
65.71 65.71 65.71 65.71
64.34 86.84 113.5 115.4
42.81 61.25 75.47 88.13
79.01 79.01 79.01 79.01
131.0 206.0 231.3 254.6
87.72 87.72 87.72 87.72
157.9 202.5 228.8 258.2
H2SO4 concentration, wt %
SO2 partial pressure, kPa
SO2 solubility, mmol/kg H2SO4
95.91 95.91 95.91 95.91 95.91
110.4 117.5 128.7 138.8 153.0
476.4 511.7 563.6 621.9 700.5
95.91 95.91 95.91 95.91
147.1 177.4 205.0 240.5
100.7 124.0 144.6 171.3
75.19 75.19 75.19
142.9 155.0 166.2
79.70 86.88 95.16
51.72 87.06 99.25 113.4
84.37 84.37 84.37 84.37 84.37
68.60 109.4 129.7 151.0 168.2
32.81 50.16 61.56 73.91 86.41
100.8 131.1 139.3 160.9
95.91 95.91 95.91 95.91
184.3 202.6 228.9 248.2
99.53 110.6 130.5 140.6
at 298 K
at 383 K
at 393 K
controller. Stainless steel tubing of 1/8 in. o.d. was used for all connections. Compared with the volume of the gas phase in the solubility cell, the volume of the tubing was negligible. The measurement procedure involved accurately weighing the solubility cell and magnetic stirrer before and after charging the cell with ∼70 g of acid. The accurate weight of sulfuric acid of the desired concentration is obtained by subtracting the weight of the cell and the stirrer from the total weight including the acid. The total volume of the cell and the connecting tubes was predetermined by filling the sealed cell with water. The volume of acid charged was determined based on the weight and density for a particular acid concentration and temperature. The volume of gas phase at equilibrium was then obtained by subtracting the acid volume from the total volume. The acid was deaerated for a few minutes, with a nitrogen purge, under reduced pressure and with stirring. The amount of acid evaporated was considered to be negligible because of the very low vapor pressure of concentrated sulfuric acid. Before the SO2 gas was transferred from the reservoir to the solubility cell, the initial pressure and temperature in both the reservoir and the cell were recorded. The temperature of the cell was raised to a predetermined level. The SO2 gas was then introduced from the reservoir to the desired pressure in the cell by adjusting the needle valve. When the stirrer was turned on, the rate of solution of SO2 gas into the concentrated acid in the cell was initially very high requiring that additional gas be introduced to reach/maintain the desired pressure. When the pressure in the cell became constant, the final pressure readings in both the reservoir and the solubility cell were recorded after an elapsed time of at least 1 h to ensure equilibrium conditions. At equilibrium, the gas-phase compositions were analyzed with a GOW MAC gas chromatograph (GC) equipped with a 2-meter long 1/8 in. o.d. stainless steel column packed with Poropak Q (-100+120 mesh). A thermal conductivity detector (TCD) was used, with the
column temperature kept at 333 K and the detector temperature at 408 K. The GC was calibrated using standard gas mixtures of SO2 and N2 supplied by Praxair Canada Inc. The pressure of SO2 was then calculated based on the analysis and the total pressure in the cell. The mass of SO2 remaining in the gas phase was estimated with the equation of state for an ideal gas. The amount of SO2 transferred from the reservoir to the solubility cell was calculated from the pressure decrease in the reservoir. The solubility of SO2 in sulfuric acid could then be obtained by subtracting the SO2 remaining in the cell as gas phase from the total amount of SO2 gas transferred to the cell from the reservoir. An isotherm of SO2 solubility in aqueous sulfuric acid as a function of partial pressure of SO2 can be measured by gradually increasing the cell pressure and recording the pressure changes in both the reservoir and the solubility cell at equilibrium. Although it was possible to complete all of the measurements simply by successive increases in gas pressure over an initial acid charge, each measurement was repeated with fresh acid (prepared in a large batch) to avoid possible accumulation of experimental errors when the pressure change in the reservoir was very small. Results and Discussion Experiments were conducted with pure SO2 at different partial pressures and at temperatures of 298, 383, and 393 K. The results obtained from different experiments are shown in Table 1. Estimation of Henry’s Law Constant, H. The Henry’s law constant, H, can be determined with eq 18 or 19 combined with eqs 14 and 16. The mean values of H and their mean square of variance are shown in Table 2 for different sulfuric acid concentrations and different temperatures. For comparison, the solubility data for pure SO2 reported by Hayduk et al. (1988) were also used to calculate H for 97 wt % sulfuric acid at 298
1170 Ind. Eng. Chem. Res., Vol. 37, No. 3, 1998 Table 2. Estimated Henry’s Law Constant temperature, K
H2SO4 concentration, wt %
298 298 298
79.01 95.91 97.00
0.2882 ( 0.02a 0.2310 ( 0.01 0.2032 ( 0.01
0.2955 ( 0.01a 0.2360 ( 0.01 0.2102 ( 0.01b
383 383
79.01 95.91
1.988 ( 0.08 1.456 ( 0.02
2.012 ( 0.08 1.475 ( 0.01
398 398 398 398 398 398
65.71 75.19 79.01 84.37 87.72 95.91
1.469 ( 0.08 1.795 ( 0.02 2.290 ( 0.09 2.088 ( 0.07 1.605 ( 0.06 1.836 ( 0.09
1.482 ( 0.09 1.813 ( 0.02 2.327 ( 0.09 2.105 ( 0.07 1.628 ( 0.06 1.861 ( 0.09
a
H, mPa (kg H2SO4 solution)/mol by eq 18 by eq 19
Mean square of variance. b Taken from Hayduk et al., 1988.
K. As Table 2 shows, H depends strongly on the temperature. The Henry’s law constant, H, is also a complicated function of acid concentration. At 393 K, H increases with sulfuric acid concentration and reaches a maximum at an acid concentration of ∼79 wt %; further increase in acid concentration results in a decrease in H. This complicated dependence of SO2 solubility on acid concentration has been observed by many researchers and was summarized by Hayduk et al. (1988). The small mean square of variance indicates that either eq 18 or 19 well represent the relationship between SO2 partial pressure and its solubility in concentrated sulfuric acid solution. For process design purposes, H may be estimated from correlation (eq 18) or based on a single experimental solubility measurement at a particular acid concentration and temperature (eq 19). With H values determined, the dependence of SO2 solubility in a specific acid concentration on SO2 partial pressure can be calculated using either eq 18 or 19. For a given partial pressure of SO2, PSO2, the solubility of SO2, mSO2, can be calculated directly using eq 19. To calculate the dependence of the solubility of SO2, mSO2, on its partial pressure using eq 18, a numerical iteration procedure has to be used because the total pressure, P, is the sum of SO2 partial pressure, PSO2, and the vapor pressure of the sulfuric acid solution. Because eq 18 cannot be solved analytically for PSO2 versus mSO2, a FORTRAN program was developed to solve eq 18 numerically. The computer program involves an iterative procedure where eq 18 is changed into the general form of F(PSO2, mSO2) ) 0, and the iteration is continued until the value of F becomes < 10-5. Comparisons of the calculated SO2 solubility using either correlation 18 or 19 with the experimentally measured solubility data are shown in Figures 2-4. Evidently, both correlations represent the experimental data well (Figures 2-4). As shown in Figure 4, the solubility of SO2 decreases with increase in acid concentration and reaches a minimum at ∼79 wt % sulfuric acid. The calculated solubility values using either eq 18 or 19 overlapped in the experimental range of interest, confirming the validities of these correlations. The results also indicate that the assumption of ideal gas behavior for SO2 is valid at the low partial pressures and high temperatures used in the experiments. An additional comparison of the reported data with the calculated solubilities was also done using eq 19 to avoid the unnecessary iteration procedures. Figure 5 shows that these calculated solubility values agree well with the experimental data.
Figure 2. Solubility of pure SO2 in sulfuric acid solution at 298 K. Key: (9) 79.01 wt % H2SO4; (b) 95.91 wt % H2SO4; (2) 97.00 wt % H2SO4 (Hayduk et al., 1988). Dashed line: calculated with eq 19; dotted line: calculated with eq 18.
Figure 3. Solubility of pure SO2 in sulfuric acid solution at 383 K. Key: (b) 95.91 wt % H2SO4; (O) 79.01 wt % H2SO4. Dashed line: calculated with eq 19; dotted line: calculated with eq 18.
Figure 4. Solubility of pure SO2 in sulfuric acid solution at 393 K. Key: (O) 95.91 wt % H2SO4; (b) 87.72 wt % H2SO4; (9) 84.37 wt % H2SO4; (0) 79.01 wt % H2SO4; (2) 75.19 wt % H2SO4; (1) 65.71 wt % H2SO4. Dashed line: calculated with eq 19; dotted line: calculated with eq 18.
Estimation of the Overall Heat of Solution. As reported previously by Govindarao and Gopalakrishna (1993), Henry’s law constant, H, exhibits a van’t Hoff equation-type dependency on temperature; that is:
Ind. Eng. Chem. Res., Vol. 37, No. 3, 1998 1171
Figure 5. Comparison of the model with reported experimental data by Lopatto et al. (1934). Key: (b) 66.71 wt % H2SO4 at 303 K; (9) 66.71 wt % H2SO4 at 313 K; (2) 70.74 wt % H2SO4 at 303 K; (1) 70.74 wt % H2SO4 at 323 K. Dashed lines: calculated with eq 19.
ln H ) ln as -
∆Hs RT
(20)
Then, the heat of solution, ∆Hs, can be determined by plotting ln H versus 1/T. The values of H for particular sulfuric acid concentrations and different temperatures are used to estimate the least-squares value of the parameters as and ∆Hs in eq 20. Figure 6 shows excellent linearity (with squared regression coefficient (r2) > 0.999) for the sulfuric acid concentrations of 79.01 and 95.91 wt %. The data reported by Lopatto et al. (1934) were also used to estimate the heat of solution at acid concentrations of 66.71 and 70.74 wt %. Table 3 shows the overall heat of solution of SO2 estimated with eq 20 for different acid concentrations and temperature ranges. For the solution of SO2 in water, Johnstone and Leppla (1934) reported an estimated heat of absorption of 26.08 kJ/mol for the following reaction;
SO2 (gas) S SO2 (aqueous)
(21)
If we consider that the solution of SO2 in high concentration acid involves only the reaction in eq 20 (i.e., no dissociation or hydrolysis occurs), then the heat of solution in a concentrated sulfuric acid solution should approximate the heat of absorption estimated by Johnstone and Leppla (1934). Our values, 20.87 and 20.95 kJ/mol for 79.01 and 95.91 wt % acid solutions, respectively, are in the range of the value of 26.08 kJ/ mol reported by Johnstone and Leppla (1934). This agreement further supports the assumption of little or no dissociation of SO2 occurring in sulfuric acid of high concentrations. It has been shown that the presence of sulfuric acid in the solution increases the hydrogen ion concentration, which suppresses the hydrolysis of dissolved SO2. The hydrolysis of SO2 may be neglected even at acid concentration of 22 wt % (Govindarao and Gopalakrishna 1993). This assumption of negligible hydrolysis or dissociation of SO2 led to the simpler correlations developed in our study. This assumption presumably is even more valid at the much higher acid concentrations (65-96 wt %) used in this study, compared with its verification at 22 wt % by Govindarao and Gopalakrishna (1993). The good agreement of the calcu-
Figure 6. Estimation of SO2 heat of solution in sulfuric acid. Key: (b,O) 79.01 wt % H2SO4 with H obtained with eqs 18 and 19, respectively, and ∆Hs ) 20.87 kJ/mol ; (9,0) 95.91 wt % H2SO4 with H obtained with eq 18 and 19, respectively, and ∆Hs ) 20.95 kJ/mol; (2) 66.71 wt % H2SO4, with H obtained with eq 19, and ∆Hs ) 19.70 kJ/mol; (1) 70.74 wt % H2SO4, with H obtained with eq 19, and ∆Hs ) 22.61 kJ/mol. Table 3. Estimated Overall Heat of Solution of SO2 sulfuric acid, wt %
temperature, K
∆Hs, kJ/mol
22.0
303-353
-15.78
66.71 70.74 79.01 95.91
303-313 303-323 298-393 298-393
-19.70 -22.61 -20.87 -20.95
reference Govindarao and Gopalakrishna (1993) Lopatto et al. (1934) Lopatto et al. (1934) this work this work
lated solubility using our correlations with the experimental data follows. The main attribute of our simplified correlation (eq 19) is that it contains no adjustable parameters, which enables the evaluation of the solubility of SO2 in sulfuric acid at different partial pressures of SO2 from one experimentally determined value of SO2 solubility at the desired sulfuric acid concentration and temperature. Conclusions The SO2 solubility in concentrated aqueous sulfuric acid solution was measured at temperatures of 298, 383, and 393 K and at different SO2 partial pressures. A relatively simple correlation is presented that describes the solubility of SO2 in sulfuric acid. The good agreement between the calculated solubility value and the experimental data reported in the present study and also in the literature further strengthens the validity of the correlation and its assumptions. The correlation should be useful for predictions of the equilibrium solubility of SO2 in high concentration sulfuric acid under various process conditions. Acknowledgment The authors acknowledge the financial support from the Natural Sciences and Engineering Research Council of Canada. The fruitful discussions with Prof. A. Mather of the University of Alberta are much appreciated. Nomenclature as ) constant, defined in eq 20
1172 Ind. Eng. Chem. Res., Vol. 37, No. 3, 1998 B ) the second virial coefficient of SO2 at a specified temperature H ) Henry’s law constant, (kPa) (kg-solvent) (mol)-1 ∆Hs ) heat of solution of SO2 in sulfuric acid, kJ/mol Ki ) the dissociation equilibrium constant for dissociation reaction i mj ) the concentration of the species j (molecule, cation, or anion) in sulfuric acid solution, mole/(kg-sulfuric acid solution) mSO2 ) solubility of SO2 in sulfuric acid solution, mol/(kgsulfuric acid solution) P ) the total gas pressure in the solubility cell, kPa PSO2 ) the partial pressure of SO2 over sulfuric acid of given concentration, kPa T ) absolute temperature, K R ) gas constant, 8.314 J/(mol K) Greek βSO2-SO2 ) the specific interaction parameter for SO2 molecules γj ) the activity coefficient of the species j in sulfuric acid solution φSO2 ) the fugacity coefficient of SO2 Subscripts i ) dissociation reaction as defined by eq i, i ) 1-5 j ) species, H2O, H2SO4, H2SO3, SO2,H+, OH-, HSO3-, HSO4-, SO32s ) solution
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Received for review September 2, 1997 Revised manuscript received November 26, 1997 Accepted December 1, 1997 IE9706119
