Ind. Eng. Chem. Res. 1993,32, 2111-2117
2111
Solubility of Sulfur Dioxide at Low Partial Pressures in Dilute Sulfuric Acid Solutions V. M. H.Govindarao’ and K. V. Gopalakrishna Department of Chemical Engineering, Indian Institute of Science, Bangalore 560 012, India
Equilibrium of dissolution of sulfur dioxide a t ppm levels in aqueous solutions of dilute sulfuric acid is analyzed, and a general expression is derived relating the total concentration of sulfur dioxide in the liquid phase to the partial pressure of SO2 in the gas and to the concentration of sulfuric acid in the solution. The equation is simplified for zero and high concentrations of the acid. Experiments at high concentrations of sulfuric acid have enabled the direct determination of Henry’s constant and its dependency on temperature. Heat of dissolution is -31.47 kJ/mol. Experiments in the absence of sulfuric acid and the related simplified expression have led to the determination of the equilibrium constant of the hydrolysis of aqueous sulfur dioxide and its temperature dependency. The heat of hydrolysis is 15.69 kJ/mol. The model equation with these parameters predicts the experimental data of the present work as well as the reported data very well. Introduction Aqueous-phase oxidation of sulfur dioxide is an important method of controlling sulfur dioxide pollution, particularly from fossil-fuel-fired power plants. The oxidation leads to dilute sulfuric acid solutions. Presence of sulfuric acid in the solution is known to influence strongly the solubility of sulfur dioxide. At low concentrations of the acid,the solubility drops below that of water, while it is reported that at high concentrations it increases (Hayduk et al., 1988); at high concentrations, the roles of acid and water possibly reverse, acid becoming the solvent and water the solute (Hunger et al., 1990). There has been considerable interest in the solubility of SO2 because of its importance in both industrial and pollution control applications, and many reports have appeared on the subject. For example, Sherwood (1925), Johnstone and Leppla (19341,Beuschlein and Simenson (1940), Rabe and Harris (19631, Douabul and Riley (1979), Gerrard (1980), and Hunger et al. (1990) have reported data on solubility of sulfur dioxide in water. The gas solubility is expressed either by Henry’s law connecting the mole fraction (or molality) with the partial pressure or by Henry’s law in combination with the equilibrium of the reaction between dissolved SO2 and water. It has been reported by several investigators that in solution SO2 exists both in the molecular form and as an ionic species (formed by the hydrolysis of the dissolved sulfur dioxide). Data on the solubility in dilute sulfuric acid solutions are reported by Johnstone and Leppla (1934) and Hunger et al. (19901, and in concentrated solutions by Miles and Carson (1946) and Hayduk et al. (1988). Hunger et al. (1990) have empirically correlated the molality of the dissolved SO2 in the solution with the concentration of the sulfuric acid. A systematicstudy of the effect of sulfuric acid on the solubility has not been reported. A clear understanding of this effect and a knowledge of the concernedparameters are very vital not only in the analysis, design, and control of scrubber systems for flue gas desulfurization but also in the study of acid rain formation and related problems such as formation of smog and absorption of SO2 by bodies of water and by fauna and flora. Of relevance in these areas are low partial pressures of sulfur dioxide and dilute solutions of sulfuric acid. The purpose of the present work is to model rigorously the effect of sulfuric acid on the solubility of sulfur dioxide in such systems and to estimate experimentally the Henry’s law constant and the equilibrium constant of the hydrolysis 0888-5885/93/2632-2111$04.00/0
of S02. Specifically,the SO2 level in the inlet gas is varied from 190 to 1575 Pa, with sulfuric acid concentration in the range 0-2.815 moVkg of water and temperatures from 30 to 80 “C. Model for SO2 Dissolution. The following equations describe the equilibrium in SOzdilute H2S04 systems:
S02(aq)+ H 2 0
H+ + HSOf
(3)
(4)
H,SO, + H+ + HSO,
At the low partial pressures of SO2 and the temperatures of concern in the present work, Table 2 of Rabe and Harris (1963) showsthat the activity coefficientsare close tounity. The activity coefficients are therefore assumed to be unity in eqs 4 and 6. Also, the model neglects the dissociation of HSOS- into 503% because of the low pH values involved in the system under consideration, as was shown by Barrie (1978), Beilke and Gravenhorst (19781, and Hunger et al. (1990). In writing eqs 5 and 6, it is considered that the bisulfate ion (HS0.c) is fully ionized (Hartman and Coughlin, 1972; Hunger et al., 1990) since the concentrations of sulfuric acid of interest are low. Electroneutrality for the system requires that mH+
= mHSO,-
+ 2mso,Z-
(7)
In practice, it is usual and convenient to measure the molality of SOa(aq) and HSOs- together as S(1V) and the molality of undissociated HzS04 and Sod2- together as S(V1). Representing the molality of S(1V) by ma4 and that of S(V1) by ms6, we have 0 1993 American Chemical Society
2112 Ind. Eng. Chem. Res., Vol. 32, No. 9, 1993
msi = msO,(aq) + mnso,mS6
= mHfiO, + mSO,s
(8) (9)
Equations 2, 4, 6-8, and 9 can be combined to obtain the following expression relating the equilibrium mole fraction of the total SO2 in the solution to the partial pressure in the gas phase: e
II
Flow Meter
Y
where
R l k , Pyrogallol Absorbers
and For low values of ms4 (corresponding to low partial pressures of Sod and m s , such as the levels of interest in the present work, eq 12 reduces to Equation 10is solved numerically by the golden-section method (Rao, 1992). This method is an iterative procedure, where the initial range is established by taking l . l / H times the given Pso, as the lower bound and the corresponding estimated value of Na as the upper bound. The algorithm provides for shifting either boundary if a negative value is obtained for Ns4 in any iteration or if the current solution is very close to a boundary. Iterations are continued until the difference between successive estimates is within a desired level. It is seen from eq 10 that as the concentration of sulfuric acid increases Na decreases. The presence of sulfuric acid in the solution increases the hydrogen ion concentration, which results in shiftingthe equilibrium of reaction 3 to the left, that is, in suppressing the hydrolysis of the dissolved sulfur dioxide. At fairly high levels of sulfuric acid in the solution, the hydrolysis reaction may be neglected. Equation 10 now simplifies to
Ns4 H Nso2(aq) = PsO,/H, for high levels of ms6 (14) Equation 14 shows that the dissolution follows simple Henry's law and that the equilibrium relation between Pso, and Nso2caq) is independent of the concentration of sulfuric acid in the solution at high values of this concentration. Thus, for this condition eq 14 is the same as eq 2. Therefore, H of eq 14 is the Henry's constant for the dissolution of sulfur dioxide in water. Equation 14 suggests a direct and simple method for determining H, where SO2 is dissolved in sufficiently concentrated solutions of sulfuric acid. When there is no sulfuric acid in the solution, eq 10 reduces to KltPS02 112 , for ms6 = 0 (15) Ns4 7 Hmn,o where use is made of eq 13also. Once H is estimated from experiments with high concentration of sulfuric acid (by using eq 14) as suggested above, the equilibrium constant of the hydrolysis Kl' can be determined by conducting another experiment without sulfuric acid in the solution
(-)
Figure 1. Schematic of the experimental setup.
and by using eq 15. As discussed later, reported values of K2 are considered adequate, and therefore no separate effort is made to estimate this parameter in this work. Experimental Section Apparatus. Figure 1 gives a schematic of the apparatus used. The reactor is a 2.5 X 103 m3cylindrical glass vessel of 0.142-m inner diameter placed in a thermostated water bath. It is provided with an agitator which consists of a disk turbine-type perspex impeller of 0.071-mdiameter with six flat blades attached to a perspex shaft. The shaft is connected to a 0.25-hp direct current motor through an appropriate coupling. The reactor is also provided with a glass distributor and baffles, which are designed as per methods described by Nagata (1975). It is provided with a suitable lid that can be secured tightly to the vessel by means of a gasket and bolts and nuts. The stirrer can be maintained at any desired speed by controllingthe current to the armature of the motor. The lid is also provided with openings for the inlet and exit of the gas and for liquid sampling. The inlet tubing contains a three-way stopcock that facilitates diverting the inlet gas stream to the vent, when desired. Liquid samples are drawn by means of a syringe with a needle. Flow rates of sulfur dioxide and nitrogen are measured through suitably calibrated orifice-type flow meters. Nitrogen before passing through the system is bubbled through a series of columns containing alkaline pyrogallol solution to remove any traces of oxygen and through distilled water (maintained at the same temperature as the reactor) to saturate the inlet gas. The two gases are mixed to a desired proportion which is controlled by adjusting the respective flow rates before the gases are sent into the reactor. Sampling and Analysis. Sulfur dioxide content of the inlet and the exit gas streams is analyzed by bubbling the stream for a previously determined duration through
Ind. Eng. Chem. Res., Vol. 32,No. 9,1993 2113 an absorber containing known quantities of hydrogen peroxide. The amount of sulfuric acid formed is measured with a suitably calibrated conductivity analyzer. Measurements with synthetic samples have shown that SO2 at very low levels (around 100 Pa) can be estimated with an accuracy of about 98% and at higher levels (around 1600 Pa) with an accuracy of about 99.5% . The concentration of dissolved sulfur dioxide together with sulfurous acid in the solution is measured as total S(IV) by collecting a known volume of the solution into a known volume of standardized iodine solution and titrating the excessiodine with standardized fresh hypo solution. The maximum error (absolute) in the analysis is established to be about 0.5% by using synthetic samples of sodium sulfite. The concentration of sulfuric acid in the reactor is measured by titrating the sample against standard Borax solution with a mixed indicator of methylene blue and methyl red. The method can measure concentrations of the order of 10-4mol/kg of water at the lower level and with a maximum error (at this level) of about 0.5 9%;the error is much lower at higher levels. Materials. Sulfur dioxide was supplied by M/s. Industrial Gases and Equipments, New Delhi, and is of 99.8% purity. Nitrogen is supplied by M/s. Asiatic Industrial Gases Ltd., Bangalore, and is more than 99.5% pure. All other chemicals such as hydrogen peroxide, sulfuric acid, hypo, iodine, etc., are of analytical grade. Procedure. Concentration of sulfuric acid in the solution, partial pressure of SO2 in the inlet gas, and temperature are the three main factors investigated in the present studies. Their levels are selected as per the type of experiment and/or statistical design. In all the experiments, gas flow rate and agitator speed are set at 0.102 m3/h and 200 rpm, respectively (selected such that these factors do not affect the observed data). Before each run, dissolved gases in the solution are removed by boiling for about 2 h, and it is then allowed to cool to the temperature of the experiment while passing nitrogen continuously. When the solution reached the desired temperature, ita volume is noted from a calibrated chart pasted on the outside of the reactor. Flow rates of Nz and SO2 are then set at appropriate levels to obtain the desired SO2 partial pressure in the inlet gas. The inlet gas is let to the vent until its concentration has attained a steady value, as observed from the analysis of successivesamples. The gas is then let into the reactor. At regular intervals of about 10 min, the partial pressure in the exit gas is determined as discussed above. As this gas sampling is going on, a liquid sample (of about 2.0 mL) is drawn simultaneously,and its S(IV)concentration is determined volumetrically as already discussed. The experiment is allowed to run for about 3 h by which time the exit gas concentration would have attained a steady value. In the runs where H2S04 is used in the solution,ita concentration is measured both at the beginning and at the end of the experiment. The values are found to be the same, thus showing that there is no oxidation of SO2 during the dissolution. All the experiments are carried out at the local atmospheric pressure, which is 91.33 X lo3 Pa.
Results and Discussion The results obtained from the different experiments are shown in Figures 2 and 3 as plots of NU vs Psoz at several combinations of the operating variables, namely, rnm in the range 0-2.815 mol/kg of water, temperature 30-80 "C, and Psoai = 190 and 1575 Pa (partial pressure of SO2 in the inlet gas). Estimation of H. Experimentx are conducted at seven different levels of sulfuric acid concentration in the range
0
!n
0
6
7
X
2
4
2
0 50
0
100
150
i 0
P s o , , Pa
-
Curve Symbol
1 2 3 4 5 G
7 8 9 10
+ (K) (gmole/kg water)
@
* X
t 0
a 0 2.815
0 0
333
2.815 t Figure 2. Effect of sulfuric acid on solubility of sulfur dioxide at P w = 190 Pa; curve8 represent the model (eq 10).
8.2 X 10-4 to 2.815 mol/kg of water, at Psopi = 190 Pa, and at T = 303 K. The observed data are plotted as curves 2-8 in Figure 2. As seen from curves 6-8 of the graph, the slope of the equilibrium line becomes independent of the concentration of sulfuricacid as predicted by eq 14,beyond a concentration of 0.37 mol/kg of water. A similar conclusion is drawn from the data of Johnstone and Leppla (1934)and Hunger et al. (1990),as seen from curves 8-12 of Figure 4,where these reported data are compared with the predictions of the present model. In all further experiments (for determining H), a value of rnm = 2.815 mol/kg of water is employed, justifying the use of eq 14. To determine the effect of temperature and the inlet gas partial pressure on H, a two-level, two-factor experiment is designed statistically and conducted in random fashion with each run repeated once more. His estimated from the slope of the equilibrium line in each of the experiments. Table I gives the relevant data, and the estimated values of H are also included in column 3 of Table 111. The corresponding solubility data are plotted as curves 8 and 10 in Figure 2 and curves 5 and 7 in Figure 3, respectively. An analysis of variance with H as response (see Table 11) clearly indicates that the mean squares of the temperature stand out very significantly compared to those of Psozi and T X Pso~.The estimated value of the F-ratio for temperature effect is very high compared to the standard value (at 5% level of significance), while the values for Psozjand T X Psozi are very low. This means that only temperature has a very significant effect on H, while the effect of Psoi and its interaction with temperature are negligible. By the very nature of the estimation procedure, it is clear that H is independent of the
2114
Ind. Eng. Chem. Res., Vol. 32, No. 9, 1993
40
-i In
0
n 0
r
X
?
+
X
10,l1,12
f
i$
z
00
Pso, , Pa
Curve
I
Reference
Curve Symbol 1 2 3
o
x
t
4
*
5 G 7 8
@
0
a 0
T msg (K) (gmole/kg water) 303 318 333 353 303 318 333 353
0
0 0 0
2.815 2.815 2.815 2.815
1 2 3. 4 5 6 7 8 9
10 11 12 -
A ~
+
298 308 323 323 298 298 298 298 208 298 298 -
0 0 0 0 0.01 0.05 0.2 0.5 1.0 0.52 1.1
Jolinstone and Hunger et Johnstone and Johnstone and Hunger et Hunger et Huiiger et Hunger et Hunger et Hunger et Johnstone and Johnstone and
Leppla, 1934 al., 1990 Leppla, 1934 Leppla, 1934 al., 1990 al., 1990 al., 1990 al., 1990 al., 1990 al., 1990 Leppla, 1934 Leppla, 1934
Figure 4. Comparison of the present model with reported experimental data, curves represent the model (eq 10). Table I. Levels of the Variables and the Estimated Valuee of H in the Runs of 2' Factorial Design level of the factor lp plot of sl. no. T (K) Psoi (Pa) (Pa/molefraction) solubility data 190 5.72 curve 8 in Figure 2 1 303 2 333 190 15.54 curve 10 in Figure 2 4.82 curve 5 in Figure 3 3 303 1575 15.45 curve 7 in Figure 3 4 333 1575 a
Mean of the two repetitions.
Table 11. Analysis of Variance-Reeponse: from Column 4 of Table I) sumof degreesof factor squares freedom 1 209.0 temp, T partial pressure of SO2 0.48 1 in the inlet gas, P S O ~ 1 T X Pwi 0.32 1.01 4 error a
E X lo4 (Data
mean squares F-ratio0 209.0 829.36 0.48 1.92 0.32 0.25
1.29
Fsw (1,4)(from standard table) = 7.71.
than the experimental data. It is therefore concluded that eq 17 gives a better representation of the dependence of H on temperature in the entire range of 0-80 "C than the reported correlations. Estimation of K{. As discussed earlier, the equilibrium constant Kl' of the hydrolysis of SO2 is estimated by conducting the dissolution experiments in the absence of sulfuric acid, first as per a factorial design with temperature and partial pressure of SO2 in the inlet gas as the two factors and then at several temperatures. In each experiment, K1' is estimated from the slope of the plot of N N - Pso2/Hagainst (PsoJHmHp)'/2,as per eq 15. A typical plot is shown in Figure 6; plotted with the data from the
Ind. Eng. Chem. Res., Vol. 32,No. 9,1993 2115 Table 111. Estimated Values of Hand K'I Ha X 1O-a T (K) PSW (Pa) (Pdmole fraction) 303 190 5.72 303 1575 4.82 318 1575 7.73 333 190 15.54 333 1575 15.45 353 1575 30.66
x 109 (mol/ka) 10.8 11.22 7.49 5.88 5.98 4.67
-1
K1'b
v)
O F
X
a The experiments are conducted at mge = 2.815 mol/kg of water. The experiments are conducted at mge = 0.
40 0
-w
0 0
30
-
e,
E
-2 Q
I
\
.-
C
d
Z
U
I
3,\ 20
dPso,/(H
x 1 04,(kg/gmo1)0'5
x
Figure 6. Determination of K1' at 303 K (PSG = 190 Pa and mge = 0).
0
I
3.0
0 F
X
I
10
I 0 I
I
275
I
300
(I/T) Curve / Symbol Correlations curve 1 curve 2 curve 3 curve 4 Experimental Data
A 0
I
325
x
I
350
io5,
I
375
4 I
K-'
tT
2.5
-
$ E
2.0
-
No- 1.5
-
I
tT
-
Reference
X
eq 17 Beutier and Renon, 1978 Rabe and Harris, 1963 Edwards ct al., 1978
k
Johnstone and Leppla, 1934 Present work
I
.-
1.0
-
0.5
-
V."
I
250
I
275
I
300
I
325
I
350
I
375
Figure 5. Comparison of values of H predicted by eq 17 with the experimental data and with the predictionsof reported correlations.
experiment at 30 "C, Psozi = 190 Pa, and mS6 = 0,the corresponding solubilitydata are given in curve 1 of Figure 2. The estimated values of K1' are listed in column 4 of Table 111. Again, an analysis of variance from the data of the factorial experiments (not reported here) has clearly indicated that K1' is independent of the inlet gas composition but is strongly affected by the temperature. Considering van't Hoff equation-type dependency on temperature for KI' also and estimating the parameters by the least-squares method from the data at the four different temperatures (see Table 111),we have In K,' = -10.82 + 1911.23/T (18) Equation 18 predicts very closely, as seen from Figure 7,the present data as well as the reported data of Johnstone and Leppla (1934)in the entire range of temperatures studied. Also included in Figure 7 are the predictions of correlations reported by Rabe and Harris (1963)and Beutier and Renon (1978). It is seen that the correlation of Beutier and Renon (1978)fails to predict all the data, while that of Rabe and Harris (1963)predicts the data satisfactorily. The predictions of eq 18 and of the correlation of Rabe and Harris (1963)are even closer to each other at high temperatures. Rabe and Harris's (1963)
Curve / Symbol Correlations curve 1 curve 2 curve 3 Experirnrntal Data
A 0
Reference Beutier and Renon, 1978 Rabe and Harris, 1963 eq 18 Johnstone and Leppla, 1934 Present work
4 IO
2116 Ind. Eng. Chem. Res., Vol. 32, No. 9, 1993
2
0 0
10
20
30
40
ms6 x lo’, gmole/kg
I Curve 1 Symbol 1
T
1 P,,, I
50
water
Reference
untenable over the entire range of ms6, even for their own data. For high concentrations, say ms6 > 0.4 mol/kg of water, eq 14 is applicable. In eq 14, H i s the Henry’s law constant for dissolution of molecular SO2 in water. For ms6 = 0, eq 15 applies. From the available data in the literature (Hayduk et al., 1988), it appears that eq 10 or its approximate, eq 14, is applicable for concentrations of sulfuric acid up to about 37 mol/kg of water (the highest value used in the present work is 2.815 mol/kg of water). Beyond this range, the acid starts functioning as solvent, and the data (Figure 4 of Hayduk et al., 1988)suggest that the dissolution of sulfur dioxide still follows Henry’s law, but the proportionality constant now depends on the concentration of sulfuric acid (in addition to temperature). The constant is no longer equal to that corresponding to dissolution in water. The model (eq 10) and its associated assumptions are expected to be tested more severely at lower levels of the concentration of HzS04. The ability of eq 10 to predict satisfactorily the data at three different levels of the variable in this range (see curves 2-4 of Figure 2) is a further confirmation of the validity of the model. The plots of Figures 2 and 3 also clearly indicate that the solubility curves show a pronounced curvature at low levels of Pso, and low levels of sulfuric acid (see curves 1-3 of Figure 2 and 1-4 of Figure 3). This behavior is evidently due to the importance of the hydrolysis reaction of the dissolved sulfur dioxide in this region. Conclusions
Figure 8. Mole fraction of the total S(1V) in the solution against concentration of sulfuric acid; curves represent the model (eqlO).
sulfuric acid, are reported by several investigators (for example, Kerker, 1957; Pitzer et al., 1977; Hunger et al., 1990). They agree closely with each other and are quite reliable. Also, it is seen that Ns4 (in eq 10) is relatively insensitive to even large variations in K,; for example, a thousandfold variation in& from the reported values gives rise to only a 1 % change in Ns4. No separate experiments are therefore carried out to determine Kz; the following correlation of Pitzer et al. (1977) is employed for the estimation of Kz: In K, = -14.032
+ 2825.20/T
(19)
Equilibrium of SO2-Dilute H2S04 Systems. Equation 10, as pointed out earlier, is the generalized expression that is valid for all levels of the concentration of sulfuric acid in this system. Figures 2 and 3 give a comparison of the predictions of eq 10 (where values of H, KI’, and KZ estimated as described above are used) with the experimental data. The agreement is very close in the complete range of concentration of sulfuric acid (0-2.815 mol/kg of water) and temperature (30-80 “C)investigated. Figure 4 shows that eq 10 with the parameters estimated as above is able to predict the experimental data of Johnstone and Leppla (1934) and of Hunger et al. (1990) also very closely. Figure 8 gives a plot of Ns4 against ms6 from the data of the present work as well as the data of Hunger et al. (1990), where the curves represent the predictions of eq 10. The plots show a steep fall and a pronounced curvature at low concentrations of sulfuric acid. Ns4 approaches a constant value asymptotically as the concentration of sulfuric acid increases. Equation 10 is able to predict this behavior completely. Hunger et al. (1990)have correlated ms4as a linear function of ms6 with a negative slope which depends on temperature (see Table I of their paper). The plots of Figure 8 clearly show that such a relation is
The strong effect of dilute concentrations of sulfuric acid in solution on the dissolution of sulfur dioxide is analyzed in terms of the influence of the acid on the equilibrium concentration of the different ionic species. A general equation (eq 10) is derived based on Henry’s law and the equilibrium relations of the ions in the SOzdilute H2S04 system. The equation leads to simple expressions for high and zero levels of the acid concentration, which in turn respectively enable direct determination of the solubility constant H and the equilibrium constant Ki of the hydrolysis of SOz(aq). The parameters are strongly dependent only on the temperature and independent of the partial pressure of the inlet gas and acid concentration. Heat of dissolution of SO2 is found to be -31.47 kJ/mol and heat of hydrolysis to be 15.69 kJ/mol. This gives an overall heat of solubility of SO2 of -15.78 kJ/mol. Experiments show that the dissolution as well as the hydrolysisreaction may be considered to be instantaneous. The developed model (eq 10) predicts the experimental data as well as the reported data of Johnstone and Leppla (1934) and Hunger et al. (1990) very closely in the entire range of the variables of interest in the aqueous-phase oxidation of sulfur dioxide. The satisfactory prediction of the data by the model, particularly at low levels of concentration of sulfuric acid and high levels of temperature, further strengthens the validity of the model and its assumptions. The model should form the basis for estimating the equilibrium concentrations of SO2 in such oxidation systems and also in the interpretation of data where low levels of SO2 in the gas phase and dilute concentrations of sulfuric acid are involved, such as in acid rain formation. Nomenclature ad =
constant, defined in eq 16
aHIO
= activity of water
H = Henry’s law constant, Pa (mole fraction)-’
Ind. Eng. Chem. Res., Vol. 32, No. 9, 1993 2117 h H d = heat of dissolution of SOZ,kJ/mol K1 = equilibrium constant of hydrolysis of SOa(aq) K{ = equilibrium constant of hydrolysis of SOZ(aq),K~UHP K2 = equilibrium constant of dissociation of HzSO4, defined by eq 6 mH+= equilibrium concentration of H+ions, mol/kg of water mHSOs- = equilibrium concentration of HSOS- ions, mol/kg of water mH,o = molality of H20, mol/kg of water mHfi0, = equilibrium concentration of HzS04, moVkg of water m a = equilibrium concentration of S(IV), mol/kg of water m s = equilibrium concentration of S(VI), mol/kg of water ms?,ca!) = equilibrium concentration of sulfur dioxide in the liquid phase, mol/kg of water mso,s = equilibrium concentration of SO4” ions, mol/kg of water mt = defined by eq 12, moVkg of water Na = equilibrium concentration of S(IV), mole fraction Nsoz(q)= equilibrium concentration of SOz(aq),mole fraction PSO, = equilibrium partial pressure of SO2 in the exit gas, Pa Pso2i = partial pressure of SO2 in the inlet gas, Pa R = gas constant, 8.314 kJ/(kmol K) T = temperature, K W = defined by eq 11
Literature Cited Barrie, L. A. An Improved Model of Reversible S02-Washout by Rain. Atmos. Environ. 1978, 12, 407-412. Beilke, S.; Gravenhorst, G. Heterogeneous SOz-Oxidation in the Droplet Phase. Atmos Environ. 1978,12, 231-239. Beuschlein, W. L.; Simenson, L. 0. Solubility of Sulfur Dioxide in Water. J. Am. Chem. SOC.1940,62,610-612. Beutier, D.; Renon, H. Representation of NHa-H2S-H20, NHa-COr H20, and NHs-SO2-HzO Vapor-Liquid Equilibria. Znd. Eng. Chem. Process Des. Dev. 1978,17, 220-230. Douabul, A.; Riley, J. Solubility of Sulfur Dioxide in Distilled Water and Decarbonated Sea Water. J. Chem.Eng. Data 1979,24,274276.
Edwards, T. J.; Maurer, G.; Newman, J.; Prausnitz, J. M. VaporLiquid Quilibria in Multicomponent Aqueous Solutions of Volatile Weak Electrolytes. AlChE J. 1978,24, 966-976. Gerrard, W. Gas Solubilities-Widespread Applications; Pergamon Press: Oxford, 1980. Hartman, M.; Coughlin, R. W. Oxidation of SO2 in a Trickle Bed Reactor Packed with Carbon. Chem. Eng. Sci. 1972,27,867-880. Hayduk, W.; Asatani, H.; Lu, B. C. Y. Solubility of Sulfur Dioxide in Aqueous Sulfuric Acid Solutions. J.Chem.Eng. Data 1988,33, 606-509.
Hunger, T.; Lapicque, F.; Storck, A. Thermodynamic Equilibrium of Diluted SO2 Absorption into NazSO4 or HzSO4 Electrolyte Solutions. J. Chem. Eng. Data 1990,35,453-463. Johnstone, H. F.; Leppla, P. W. The Solubility of Sulfur Dioxide at Low Partial Pressures. The Ionization Constant and Heat of Ionization of Sulfurous Acid. J. Am. Chem. SOC.1934,56,22332238.
Kerker, M. The Ionization of Sulfuric Acid. J. Am. Chem.SOC.1967, 79,3664-3667.
Miles, F. D.; Carson,T. Solubilityof Sulfur Dioxide in Fuming Sulfuric Acid. J. Chem. SOC.1946,786-790. Nagata, S . Mixing Principles and Applications; Wiley: New York, 1975.
Pitzer, K. S.; Roy, R. N.; Silvester, L. F. Thermodynamics of Electrolytes. 7. Sulfuric Acid J.Am. Chem. SOC.1977,99,49304936.
Rabe, A. E.; Harris, J. F. Vapor Liquid Equilibrium Data for the Binary System, Sulfur Dioxide and Water. J. Chem. Eng. Data 1963,8,333-336.
Rao, S. S . Optimization-Theory and Applications; Wiley Eastern Ltd.: New Delhi, 1992. Sherwood,T. K. Solubilitiesof Sulfur Dioxide and Ammoniain Water. Ind. Eng. Chem. 1925,17,745-746. Received for review January 4, 1993 Accepted June 17, 1993. Abstract published in Advance ACS Abetructs, August 15, 1993.
