Ind. Eng. Chem. Res. 1999, 38, 1149-1158
1149
Solubility of Sulfur Dioxide in Aqueous Solutions of Acetic Acid, Sodium Acetate, and Ammonium Acetate in the Temperature Range from 313 to 393 K at Pressures up to 3.3 MPa: Experimental Results and Comparison with Correlations/Predictions Jianzhong Xia, Bernd Rumpf, and Gerd Maurer* Lehrstuhl fu¨ r Technische Thermodynamik, Universita¨ t Kaiserslautern, D-67653 Kaiserslautern, Federal Republic of Germany
New experimental results for the solubility of sulfur dioxide in aqueous solutions of single solutes acetic acid, sodium acetate and ammonium acetate at temperatures from 313 to 393 K and total pressures up to 3.3 MPa are reported. Similar to the system sulfur dioxide-water, also in such systems with acetic acid and sodium or ammonium acetate a second (sulfur dioxide rich) liquid phase is observed at high sulfur dioxide concentrations. A model to describe the phase equilibrium is presented and calculated (i.e., predicted as well as correlated) phase equilibria are compared to the new experimental data. Introduction In many chemical plants, for example in coal gasification processes or desulfurization equipment, sour gas absorption columns and sour water strippers are used to remove weak electrolyte gases like sulfur dioxide, hydrogen cyanide, hydrogen sulfide or carbon dioxide from aqueous solutions. The basic design of such equipment requires physico-chemical models to describe the phase equilibrium as well as the caloric properties of such mixtures. Continuing earlier work on the solubility of sulfur dioxide in pure water (Rumpf and Maurer1) and in aqueous solutions of sodium and ammonium sulfate (Rumpf and Maurer2), this paper reports on experimental and theoretical work on the solubility of sulfur dioxide in aqueous solutions of single solutes acetic acid and sodium and ammonium acetate. Experimental Section The experimental equipment and procedure were basically the same as in previous investigations on the solubility of sulfur dioxide in pure water and in aqueous electrolyte solutions (Rumpf and Maurer1,2); therefore, only a few essential features are repeated here. In an experiment, a thermostated high pressure cell (volume, about 30 cm3; material, Hastelloy C4) equipped with two sapphire windows is partially filled with a known amount of the aqueous solvent. Next, a known amount of gas is added to the cell from a storage tank. More aqueous solvent is filled into the cell by means of a calibrated high-pressure displacer until the gas is completely dissolved in the liquid phase. The amount of solvent charged to the cell is only slightly above the minimum amount needed to dissolve the gas completely. After equilibration, very small amounts of the liquid mixture are withdrawn stepwise from the cell until the * To whom correspondence should be addressed. Telephone: +49 631 205 2410. Fax: +49 631 205 3835. E-mail:
[email protected].
first very small stable bubble appears. The pressure in the equilibrium state is the pressure needed to dissolve the charged amount of sulfur dioxide in the charged amount of solvent at the preset temperature. The mass of the charged gas (up to about 16.7 g) is determined by weighing with an uncertainty of (0.008 g. The volume of the aqueous solvent needed to dissolve the gas is determined by measuring the position of the high pressure displacer piston before and after each experiment. The mass of solvent is determined from the measured volume and the density of the aqueous solutions. Either the density is taken from the literature (Washburn3) or it was measured in the present work. The maximum relative uncertainty of the mass of the solvent charged to the cell is about 0.7%. The temperature is determined with two calibrated platinum resistance thermometers placed in the heating jacket of the cell with a maximum uncertainty of about (0.1 K. Three pressure transducers (WIKA GmbH, Klingenberg, Germany) with ranges of 0-0.6, 0-4, and 0-10 MPa were used to determine the solubility pressure. Before and after each series of measurements, the transducers were calibrated against a high precision pressure gauge (Desgranges & Huot, Aubervilliers, France). The maximum uncertainty in the pressure measurement is about 1 kPa in the pressure range from 0 to 0.5 MPa and 4 kPa at higher pressures. The aqueous solutions were prepared in a storage tank by dissolving known amounts of acetic acid or sodium and ammonium acetate in water. The relative uncertainty of the molality of these components in the aqueous solution is less than (0.1%. Substances. Sulfur dioxide (g99.98 mole %, from Messer-Griesheim, Ludwigshafen, Germany) was used without further purification. Acetic acid (g99.8 mass %), sodium acetate (g99 mass %), and ammonium acetate (g99 mass %) were purchased from Riedel de Hae¨n AG, Seelze, Germany, and further degassed and dried under vacuum. Water was deionized and further purified by vacuum distillation.
10.1021/ie980529t CCC: $18.00 © 1999 American Chemical Society Published on Web 02/13/1999
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Experimental Results System SO2-H2O-CH3COOH. The solubility of sulfur dioxide in aqueous solutions containing about 3 and 6 mol of acetic acid per kilogram of water was measured at 313, 333, 353, 373, and 393 K at total pressures of up to about 2.84 MPa. The maximum molality of sulfur dioxide was 16.6 mol/kg. The experimental results are given in Table 1. Figure 1 shows a comparison between the total pressures required to dissolve sulfur dioxide at 313 K in aqueous solutions of acetic acid and in pure water. The presence of acetic acid increases the solubility of sulfur dioxide. For example at 313 K, the pressure above an aqueous solution containing 4 mol of sulfur dioxide in 1 kg of water decreases from about 0.46 MPa to about 0.32 MPa when 3 mol of acetic acid are added to 1 kg of water. When sulfur dioxide is dissolved in large quantities in water, a second liquid, sulfur dioxide rich phase is observed. The presence of acetic acid has nearly no influence on the pressure of that three-phase liquidliquid-vapor equilibrium, but much more sulfur dioxide is required to induce that phase splitse.g. at 313 K, the addition of 3 mol of acetic acid to 1 kg of water increases the concentration of sulfur dioxide in the aqueous phase in three-phase equilibrium from about 5 mol to more than 9 mol/kg of water. Systems SO2-H2O-CH3COONa and SO2-H2OCH3COONH4. The solubility of sulfur dioxide in aqueous solutions of either sodium or ammonium acetate was also measured at temperatures between 313 and 393 K at pressures up to about 3.2 MPa, but only at a single salt molality of about 3 mol/kg of water. The experimental results are given in Tables 2 and 3. Some typical data are shown in Figure 2 together with the results for the solubility of sulfur dioxide in pure water at 313 K. The main difference between the solubility of sulfur dioxide in aqueous solutions of acetic acid and in aqueous solutions of the acetates is observed at low liquid phase sulfur dioxide concentrations where the overall amount of dissolved sulfur dioxide is smaller than the amount of dissolved acetates. Thus, dissolving sulfur dioxide in an aqueous solution of sodium or ammonium acetate at first requires only very small pressures. Obviously the stronger acid sulfur dioxide replaces the weaker acetic acid. Therefore, sulfur dioxide is dissolved in ionic form as sulfite and bisulfite ions while acetate ions are converted to acetic acid. When nearly all acetate ions have been converted to acetic acid, additional sulfur dioxide has to be dissolved in its (less soluble) nonionic form in an aqueous solution of sodium or ammonium bisulfite and acetic acid. While acetic acid causes an increase of the solubility of sulfur dioxide, the presence of sodium bisulfite reduces the solubility of (neutral) sulfur dioxide, whereas ammonium bisulfite has nearly no influence on the solubility of sulfur dioxide. This can be easily recognized when the amounts of “physically” dissolved sulfur dioxide in three-phase liquid-liquid-vapor equilibrium are compared. For example at 313 K, in three-phase equilibrium the molality of sulfur dioxide in water is about 5. It increases to about 9 in a 3 m aqueous solution of acetic acid. Adding three moles of sodium bisulfite per kilogram water to such an aqueous solution results in a decrease of the solubility of (neutral) sulfur dioxide to about 6 mol/kg of water. When the sodium ions are replaced by ammonium ions the solubility of (neutral) sulfur dioxide again increases to about 9 mol in 1 kg of
Table 1. Experimental Results for the Solubility of Sulfur Dioxide in Aqueous Solutions of Acetic Acid T, K
m j SO2, mol/kg
m j CH3COOH, mol/kg
10p, MPa
π
313.15 313.16 313.16 313.16 313.16 313.16 313.15 313.16
1.214 2.382 3.520 5.861 6.806 9.287 10.936 11.823
2.975 2.975 2.975 2.975 2.975 2.975 2.975 2.975
1.180 2.215 3.048 4.395 4.809 5.477 5.646 5.645
2 2 2 2 2 2 3 3
333.15 333.15 333.15 333.16 333.16 333.15 333.16 333.16 333.15
0.750 2.110 4.004 6.119 7.932 10.908 13.389 15.203 16.613
2.975 2.975 2.975 2.975 2.975 2.975 2.975 2.975 2.975
1.371 3.303 5.516 7.23 8.22 9.13 9.47 9.55 9.55
2 2 2 2 2 2 2 3 3
353.15 353.15 353.17 353.16 353.15 353.14 353.14 353.14
0.298 0.978 1.484 2.592 4.330 7.013 9.430 11.274
2.975 2.975 2.975 2.975 2.975 2.975 2.975 2.975
1.166 2.712 3.877 6.00 8.74 11.63 13.14 13.88
2 2 2 2 2 2 2 2
373.15 373.15 373.16 373.16 373.17 373.16 373.15
0.148 1.064 2.456 4.576 6.087 9.071 12.287
2.975 2.975 2.975 2.975 2.975 2.975 2.975
1.501 4.499 8.30 12.89 15.33 18.49 20.39
2 2 2 2 2 2 2
393.15 393.14 393.16 393.15 393.15 393.14 393.15 393.15 393.16 393.14
0 0.172 0.757 1.340 2.277 2.861 3.224 6.033 9.267 13.394
2.975 2.975 2.975 2.975 2.975 2.975 2.975 2.975 2.975 2.975
1.917 2.674 5.183 7.60 10.91 12.83 13.94 20.64 25.31 28.42
2 2 2 2 2 2 2 2 2 2
313.15 313.15 313.15 313.15 313.16 313.16 313.15
0.637 1.346 2.479 3.842 5.571 8.521 12.216
5.895 5.895 5.895 5.895 5.895 5.895 5.895
0.579 1.090 1.783 2.556 3.439 4.332 4.942
2 2 2 2 2 2 2
333.15 333.16 333.16 333.16 333.16 333.16 333.16
0.478 1.469 2.895 4.136 6.315 7.998 10.789
5.895 5.895 5.895 5.895 5.895 5.895 5.895
0.791 1.911 3.426 4.425 5.894 6.74 7.71
2 2 2 2 2 2 2
353.16 353.15 353.16 353.16 353.15 353.15 353.16
0.387 1.082 2.509 4.311 8.385 12.588 16.827
5.895 5.895 5.895 5.895 5.895 5.895 5.895
1.164 2.402 4.628 6.95 10.42 12.36 13.37
2 2 2 2 2 2 2
373.16 373.15 373.15 373.15 373.15 373.15 373.15
0.149 0.769 1.442 2.851 5.421 8.620 13.040
5.895 5.895 5.895 5.895 5.895 5.895 5.895
1.364 2.925 4.482 7.44 11.62 15.11 17.96
2 2 2 2 2 2 2
393.15 393.15 393.15 393.15 393.14 393.15 393.14 393.14
0 0.396 1.001 1.942 3.979 5.537 8.699 13.308
5.895 5.895 5.895 5.895 5.895 5.895 5.895 5.895
1.896 3.246 5.211 8.02 13.09 16.17 20.80 24.87
2 2 2 2 2 2 2 2
Ind. Eng. Chem. Res., Vol. 38, No. 3, 1999 1151 Table 2. Experimental Results for the Solubility of Sulfur Dioxide in Aqueous Solutions of Sodium Acetate
Figure 1. Total pressure in SO2-H2O-CH3COOH at T ) 313.15 K: (O, 0) experimental results, this work; (s) calculated results, this work; (- -) calculated results for the system SO2-H2O.
water. The pressure of the three-phase equilibrium is very little influenced by the presence of sodium or ammonium acetate. This again indicates that the second liquid phase is nearly pure sulfur dioxide. Modeling. Figure 3 shows a scheme of the model for the three-phase equilibrium in the system sulfur dioxidewater-(acetic acid or an acetate MAc). The model is an extension and modification of the thermodynamic framework developed by Edwards et al.4 for the solubility of ammonia and sour gases in water. It is assumed that sodium acetate as well as ammonium acetate are only present in the aqueous phase where they are completely dissociated. However, there are more species in that aqueous phase due to chemical reactions. The second (sulfur dioxide rich) liquid phase is treated as a binary liquid mixture of sulfur dioxide and water. The dimerization of acetic acid is only taken into account in the vapor phase. Chemical Equilibrium in the Aqueous Phase. Four chemical reactions are considered in the liquid phase:
SO2 + H2O h HSO3- + H+
(1)
HSO3- h SO32- + H+
(2)
+
H2O h H + OH
-
CH3COOH h H+ + CH3COO-
(3) (4)
The condition for chemical equilibrium for a reaction R in the aqueous phase is
KR(T) )
∏i aνi
i,R
(5)
The balance equation for the number of moles of a
T, K
m j SO2, mol/kg
m j CH3COONa, mol/kg
10p, MPa
π
313.15 313.15 313.16 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.16
2.281 2.932 3.448 3.986 4.198 4.636 5.117 5.986 7.892 9.225 9.719
3.001 3.001 3.001 3.001 3.001 3.001 3.001 3.001 3.001 3.001 3.001
0.159 0.201 0.743 1.401 1.713 2.161 2.744 3.532 4.931 5.426 5.426
2 2 2 2 2 2 2 2 2 3 3
333.15 333.15 333.15 333.16 333.16 333.17 333.16 333.15 333.16
2.826 3.026 3.490 4.942 6.707 7.854 8.974 9.561 10.079
3.001 3.001 3.001 3.001 3.001 3.001 3.001 3.001 3.001
0.427 0.582 1.426 4.134 6.74 8.01 8.90 9.29 9.30
2 2 2 2 2 2 2 3 3
353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.16 353.15 353.15
2.892 3.616 3.781 4.739 6.476 7.810 9.655 10.226 10.670 12.381
3.001 3.001 3.001 3.001 3.001 3.001 3.001 3.001 3.001 3.001
0.937 2.722 3.264 5.834 9.83 12.13 14.20 14.64 14.74 14.73
2 2 2 2 2 2 2 2 3 3
373.16 373.16 373.16 373.15 373.16 373.16 373.16 373.16 373.16
2.611 2.647 3.153 3.446 4.264 6.043 9.030 12.241 13.556
3.001 3.001 3.001 3.001 3.001 3.001 3.001 3.001 3.001
1.441 1.444 2.498 3.599 6.71 12.86 19.66 22.26 22.26
2 2 2 2 2 2 2 3 3
393.15 393.15 393.14 393.16 393.15 393.15 393.15 393.16 393.15 393.15
0 2.834 2.858 3.166 4.317 6.258 8.919 11.816 13.067 15.289
3.001 3.001 3.001 3.001 3.001 3.001 3.001 3.001 3.001 3.001
1.734 3.135 3.216 4.305 9.91 18.59 26.80 31.56 31.90 31.90
2 2 2 2 2 2 2 2 3 3
species i in the liquid phase is
n′i ) n ji +
νi,RξR ∑ R
(6)
where n j i is the overall number of moles of a component i, ξR is the extent of a reaction R and νi,R is the stoichiometric factor of a component i in an reaction R (νi,R > 0 for products and νi,R < 0 for educts). This set of equations can be solved in an iterative procedure to yield the true number of moles of each species present in the aqueous phase. Equilibrium constants for reactions 1 to 2 were obtained from Kawazuishi and Prausnitz5 (cf. Table 4), those for reaction 3 were taken from Bieling et al.6 (cf. Table 4), and for reaction 4 it was calculated from the Giauque functions for CH3COOH and CH3COO- as given by Brewer7 (cf. Appendix 1).
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Table 3. Experimental Results for the Solubility of Sulfur Dioxide in Aqueous Solutions of Ammonium Acetate T, K
m j SO2, mol/kg
m j CH3COOH4, mol/kg
10p, MPa
π
313.14 313.14 313.14 313.15 313.15 313.15 313.14 313.15 313.15 313.15 313.15 313.15
2.687 2.687 2.979 3.685 4.511 4.869 5.391 6.580 8.760 9.834 11.782 12.603
3.003 3.003 3.003 3.003 3.003 3.003 3.003 3.003 3.003 3.003 3.003 3.003
0.238 0.237 0.227 0.809 1.583 2.001 2.452 3.446 4.698 5.120 5.621 5.620
2 2 2 2 2 2 2 2 2 2 3 3
333.16 333.15 333.15 333.15 333.16 333.15 333.15 333.15
3.053 3.912 5.233 6.668 8.853 11.370 12.449 14.023
3.003 3.003 3.003 3.003 3.003 3.003 3.003 3.003
0.564 1.821 3.832 5.673 7.76 9.29 9.51 9.51
2 2 2 2 2 2 3 3
353.15 353.15 353.15 353.16 353.15 353.15 353.15 353.15 353.15
3.145 3.605 3.787 4.881 6.961 9.332 12.505 13.052 14.520
3.003 3.003 3.003 3.003 3.003 3.003 3.003 3.003 3.003
1.270 2.434 2.774 5.238 9.41 12.55 14.96 15.11 15.11
2 2 2 2 2 2 2 3 3
373.15 373.15 373.16 373.15 373.15 373.15 373.16 373.15 373.15 373.16 373.15
1.963 2.787 3.397 4.193 5.384 5.572 6.743 9.980 12.650 15.966 17.137
3.018 3.018 3.003 3.003 3.018 3.003 3.003 3.003 3.003 3.018 3.018
0.953 1.636 3.066 5.211 9.37 9.96 13.07 19.27 22.05 22.82 22.83
2 2 2 2 2 2 2 2 2 3 3
393.15 393.16 393.14 393.16 393.16 393.16 393.16 393.15 393.15 393.15
0 1.811 2.662 3.303 4.154 5.937 8.636 9.878 13.270 16.332
3.018 3.018 3.018 3.018 3.018 3.018 3.018 3.018 3.018 3.018
1.832 1.983 2.902 4.648 8.21 15.40 23.78 26.55 31.43 32.57
2 2 2 2 2 2 2 2 2 2
An extension of Pitzer’s model8 for the excess Gibbs energy of aqueous solutions containing strong electrolytes is applied to describe the activities of the solute species and water
GE RTnwMw
) f1(I) +
∑∑
(0) mimj[βi,j i*w j*w
+
(1) βi,j f2(I)]
Figure 3. VLLE and chemical reactions in the systems SO2CH3COOH-H2O and SO2-CH3COOM-H2O (M ) Na or NH4).
have to be known. The dielectric constant of pure water was taken from Bradley and Pitzer.9 The procedure to determine the binary and ternary interaction parameters will be explained below. Vapor-Liquid Equilibrium. The extended Raoult’s law is used to express the vapor-liquid equilibrium for water, while the extended Henry’s law is applied for expressing that equilibrium for sulfur dioxide and acetic acid. Solute concentration in the water-rich phase is expressed on a molality scale. s s pywφ′′′ w ) pwφw exp
+
∑ ∑ ∑ mimjmkτi,j,k
Figure 2. Total pressure in SO2-H2O-CH3COONa and SO2H2O-CH3COONH4 at T ) 313.15 K: (O, 0) experimental results, this work; (s) calculated results, this work; (- -) calculated results for the system SO2-H2O.
(7)
i*w j*w k*w
where f1 and f2 are functions of ionic strength I and (0) (1) βi,j , βi,j and τi,j,k are binary and ternary interaction parameters. The resulting expressions for the activity of a dissolved species and of water are summarized in Appendix 2. To apply eq 7, the dielectric constant of pure (0) (1) water and interaction parameters βi,j , βi,j , and τi,j,k
[
(m) s pyiφ′′′ i ) Hi,w (T, pw) exp
[
]
vw(p - psw) aw RT
]
(8)
∞ vi,w (p - psw) miγ(m) i RT i ) CH3COOH, SO2 (9)
Furthermore the dimerization of acetic acid in the vapor phase
2CH3COOH h (CH3COOH)2
Ind. Eng. Chem. Res., Vol. 38, No. 3, 1999 1153 Table 4. Equilibrium Constants for Chemical Reactions 1, 2, 3, and 4 (Kawazuishi and Prausnitz;5 Bieling et al.;6 Bu 1 ttner and Maurer10)
ln KR )
H+
SO2 + H2O h HSO3 + (1) HSO3- h SO32- + H+ (2) H2O h H+ + OH- (3) 2CH3COOH h (CH3COOH)2 (4)
+ BR ln(T/K) + CR(T/K) + DR
AR
BR
CR × 102
DR
26404.29 -5421.93 -13445.9 7928.7
160.3981 -4.6899 -22.4773 0
-27.5224 -4.98769 0 0
-924.6255 43.3136 140.932 -19.1001
reaction -
AR (T/K)
Table 5. Henry’s Constant for the Solubilities of Acetic Acid (Rumpf et al.11) and Sulfur Dioxide (Rumpf and Maurer1) in Pure Water (m) ln Hi,w (T,psw)/(MPa‚kg‚mol-1) ) Ai,w +
Bi,w (T/K)
+ Ci,w(T/K) + Di,w ln(T/K)
i
Ai,w
Bi,w
Ci,w
Di,w
SO2 CH3COOH
-154.827 52.9967
321.170 -8094.25
-0.0634 0
29.872 -6.41203
µ′i ) µ′′i
Table 6. Pure Component and Mixed Second Virial Coefficients and Partial Molar Volumes for SO2 at Infinite Dilution in Water T, K
BSO2,SO2, cm3/mol
BSO2,w, cm3/mol
∞ , vSO 2,w cm3/mol
313.15 333.15 353.15 373.15 393.15
-368 -315 -272 -238 -210
-1175 -817 -598 -456 -359
41.6 43.1 45.1 47.6 50.6
( ) cw
dw
(T/K)
i
aw
bw
cw
dw
H2O
-53.53
-39.29
647.3
4.3
is taken into account through the equilibrium constant:
K h p(T) )
y(CH3COOH)2φ′′′ (CH3COOH)2 pQ (yCH3COOHφ′′′ CH3COOH)
2
p
i ) SO2, H2O
(12)
For a solvent (i.e., water in the aqueous phase and sulfur dioxide in the second liquid phase) the reference state is the pure solvent. For a solute (i.e. sulfur dioxide in the aqueous phase and water in the second liquid phase) the reference state is a hypothetical solution at unit concentration of that solute in pure water with neglected interactions between the solute species. In the water-rich phase, the concentration scale is molality whereas for the sulfur dioxide rich phase, the mole fraction scale was chosen. Due to the lack of information it is assumed that the sulfur dioxide rich liquid phase (′′) behaves like an ideal mixture:
(10)
That equilibrium constant K h p was taken from Bu¨ttner and Maurer10scf. also Table 4. Henry’s constants for the solubility of sulfur dioxide and acetic acid in water were taken from Rumpf and Maurer1 and Rumpf et al.11scf. also Table 5. The method of Brelvi and O’Connell12 was used for estimating the partial molar volumescf. also Table 6. The influence of pressure on Henry’s constant for the solubility of acetic acid in water had to be neglected as no data for the partial molar volume of acetic acid in water at high dilution were available. The vapor pressure and molar volume of pure liquid water were taken from Saul and Wagner.13 The fugacity coefficients in the vapor phase were calculated using the virial equation of state truncated after the second virial coefficient. The second virial coefficient of water Bw,w was calculated from a correlation based on the values recommended by Dymond and Smith14scf. also Table 7. The second virial coefficient of pure sulfur dioxide BSO2,SO2 and the second virial coefficient for interactions between sulfur
(11)
The influence of pressure on the chemical potential µi is neglected. The chemical potential µi is split into two contributions representing the reference state chemical potential and the deviation from that reference state.
µi(T,concn) ) µQi (T) + RT ln ai(T,concn)
Table 7. Pure Component Second Virial Coefficient for Water
Bw,w/(cm3/mol) ) aw + bw
dioxide and water, Bw,SO2, were estimated following the recommendations by Hayden and O’Connell15scf. also Table 6. All other second virial coefficients were set to zero. Liquid-Liquid Equilibrium. As explained above, it is assumed that with the exception of water all other solute species are neglected in the sulfur dioxide rich liquid phase. Thus the condition of phase equilibrium between the coexisting aqueous and sulfur dioxide rich liquid phases at a given temperature results in
a′′w ) x′′w
(13)
a′′SO2 ) x′′SO2
(14)
Thus the phase equilibrium between the coexisting liquid phases can be expressed by
K(′′),(′) i
[
]
a′′i µQ,(′) - µQ,(′′) i i ) ) exp a′i RT
i ) SO2, H2O (15)
If a second liquid phase is present, equation 6 has to be modified to
ji + n′i ) n
νi,RξR - n′′i ∑ R
(16)
where the last term is the number of moles of component i in the sulfur dioxide rich phase. Details on the computational procedure to calculate the simultaneous chemical- and phase equilibria are given in Appendix 3. were calculated The distribution coefficients K(′′),(′) i from experimental results for the liquid-liquid equilib-
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equilibrium in the system SO2-H2O-CH3COOH. The influence of temperature on these three parameters was expressed by
Table 8. Distribution Coefficients of Sulfur Dioxide and Water in SO2-H2O
ln K(′′),(′) ) q1,i + i
q2,i (T/K)
i
q1,i
q2,i
SO2 H2O
-2.6542 3.9128
380 -1871.9
f(T) ) q1,i +
q2,i (T/K)
(18)
(T/K)
The resulting parameters are given in Table 9. The new experimental results for the pressure to dissolve sulfur dioxide in an aqueous solution of acetic acid are correlated with an average relative deviation of 2.3%. The maximum relative deviation is 8.7% (at T j SO2 ) 0.637 mol/ ) 313.15 K, m j CH3COOH ) 5.895 mol/kg, m kg, and p ) 58 kPa where the calculated pressure is too large by about 5 kPa). The model predicts the pressure at three-phase equilibrium (LLVE) with an average relative deviation of 0.75%. A typical comparison between the experimentally determined and calculated pressures is shown in Figure 4. SO2-H2O-CH3COONa. The thermodynamic framework presented before can also be used to calculate the pressure required to dissolve sulfur dioxide in an aqueous solution of sodium acetate. However, besides the parameters already given in the proceeding chapters, some more interaction parameters are needed. Binary and ternary parameters between sodium acetate species were taken from Kim and Frederick17scf. Table 10. Parameters β(0) for interactions between dissolved (0) sulfur dioxide and bisulfite ions (i.e. βSO -) were 2,HSO3 18 taken from Rumpf et al. and Rumpf and Maurer2 (cf. Table 9). Some preliminary calculations revealed that predictions for the total pressure are very sensitive to (0) the numbers for the binary parameters βSO + and 2,Na (0) βNa+,HSO3- as well as for the ternary parameter τSO2,Na+,HSO3-. Therefore, these parameters were fitted to the new experimental data for the total pressure above an aqueous solution of sulfur dioxide and sodium acetate. The influence of temperature on these param-
rium in the binary system water-sulfur dioxide by Van Berkum and Diepen.16 Experimental results for the concentration of sulfur dioxide in water were converted to the activities of water and sulfur dioxide using Pitzer’s model for the excess Gibbs energy of the aqueous phase (cf. eq 7) and taking into account only binary interactions between dissolved sulfur dioxide molecules. The corresponding binary interaction pa(0) ) was taken from Rumpf and Maurer1s rameter (βSO 2,SO2 cf. also Table 9. The resulting experimental data for the distribution coefficients were used to fit two parameters in
ln K(′′),(′) ) q1,i + i
q2,i
i ) SO2, H2O (17)
The resulting parameters q1,i and q2,i are given in Table 8. SO2-H2O-CH3COOH. To correlate the experimental vapor-liquid equilibrium results for the system SO2-H2O-CH3COOH, all interaction parameters for binary systems CH3COOH-H2O and SO2-H2O were taken from Rumpf et al.11 and Rumpf and Maurer1 (cf. Table 9), respectively. Due to the low concentrations of hydrogen-, hydroxide- and acetate ions, all interaction parameters between those species and sulfur dioxide were set to zero. The remaining parameters (0) , τSO2,SO2,HAc, and τSO2,HAc,HAc) were then fitted to (βSO 2,HAc the results for the total pressure of the vapor-liquid
Table 9. Interaction Parameters for Pitzer’s Equation for the Systems SO2-CH3COOH-H2O, SO2-CH3COONa-H2O, and SO2-CH3COONH4-H2O
f(T) ) q1,i +
parameter
q1,i
q2,i
+
q3,i (T/K)2
q3,i
Tmin
Tmax
31270
293
393
SO2-H2O
Rumpf and Maurer1
298
363
CH3COOH-H2O
Rumpf et al.11
313 308
373 368
SO2-NH3-H2O
Rumpf et al.18
313
373
-16.61 -2.6235 4.55719
313
393
SO2-H2O-CH3COOH
this work
0.0621
-7.78
313
393
SO2-H2O-Na2SO4
1.2876 -0.016836
-812.73 5.1473
313
393
SO2-H2O-CH3COONa
-137.92
(0) βSO 2,SO2
0.0934
(0) βHAc,HAc τHAc,HAc,HAc
-0.0576 0.00084
(0) βSO 2,HSO3 (0) βNH + 4 ,HSO3 (1) βNH + 4 ,HSO3 (0) βNH +,SO 24 3 (1) βNH + 24 ,SO3 τNH4+,NH4+,HSO3τNH4+,NH4+,SO32τSO2,NH4+,HSO3-
0.1044 -0.0662 0.1152 5.1357 11.301 -0.00036 -0.00477 -0.0007
-30.03 33.96 39.89 -2174.47 -5305.63
(0) βSO 2,HAc
-0.0174 0.00817 -0.01150
(0) βSO + 2,Na (0) βNa +,HSO 3 τSO2,Na+,HSO3-
τSO2,SO2,HAc τSO2,HAc,HAc
q2,i (T/K)
147951.9
subsystem
source
this work
Ind. Eng. Chem. Res., Vol. 38, No. 3, 1999 1155
Figure 4. Total pressure above SO2-CH3COOH-H2O: (O) experimental results, this work; (s) calculation, this work.
Figure 5. Total pressure above SO2-CH3COONa-H2O: (O) experimental results, this work; (s) calculation, this work.
Table 10. Ion Interaction Parameters for Aqueous Solutions of CH3COONa and CH3COONH4
f(T) ) q1,i +
salt i CH3COONa
CH3COONH4
parameter β(0)
q2,i (T/K)
q1,i
q2,i
β(1) Cφ
0.13723 0.34195 -0.00474
β(0) β(1) Cφ
-0.6638 -4.7117 0.0568
source Kim and Frederick17
119.11 Sing19 4671.08 -4.364 Figure 6. Predicted species distribution in the system SO2-H2OCH3COONa at 313.15 K and m j CH3COONa ) 3 mol/kg.
eters was taken into account by
f(T) ) q1,i +
q2,i (T/K)
+
q3,i (T/K)2
(19)
The parameters q1,i, q2,i, and q3,i are given in Table 9. Total pressures calculated with the model and that set of parameters agree with the experimental data given in Table 2 with an average relative deviation of 3.4%. The maximum deviations are observed at low sulfur j CH3COONa). For dioxide concentrations (i.e. when m j SO2 e m j CH3COONa = 1, the calcuexample, at 313 K and m j SO2/m lated total pressure is about 23 kPa while the measured pressure is about 20 kPa. The predicted pressures in three-phase equilibrium (LLVE) deviate from the experimental data by about 8%. Figure 5 shows the comparison between calculated and measured total pressures above an aqueous solution of sulfur dioxide and sodium acetate. As mentioned above the solubility of sulfur dioxide in aqueous solutions of sodium acetate is strongly influenced by the conversion of acetate ions to acetic acid which is accompanied by the conversion of neutral sulfur dioxide to bisulfite (and sulfite) ions. That behavior is shown in Figure 6, where the calculated molalities of those species in an aqueous, 3 m solution of sodium acetate are shown for 313 K as a function of the overall molality of dissolved sulfur dioxide. In accordance with the explanation given before, sulfur dioxide is dissolved as bisulfite (and also as sulfite) as long as there are acetate ions present. When all acetate is converted to acetic acid, i.e., at m j SO2/
m j CH3COONa > 1, more sulfur dioxide can only be dissolved physically, i.e. in neutral molecular form. SO2-H2O-CH3COONH4. The thermodynamic framework presented above requiressbesides the parameters already needed to describe the phase equilibrium in the system SO2-H2O-CH3COOH (cf. Table 9)ssome more interaction parameters. Binary and ternary parameters for interactions between ammonium and acetate ions were taken from Sing.19 They are given in Table 9. Binary and ternary interaction parameters between (0) (0) ammonium and bisulfite ions (βNH + -, βNH +,HSO -, 4 ,HSO3 4 3 and τNH4+,NH4+,HSO3-), between ammonium and sulfite (0) (0) ions (βNH + 2-, βNH +,SO 2- and τNH4+,NH4+,SO32-) and 4 ,SO3 4 3 between sulfur dioxide, bisulfite and ammonium ions (τSO2,NH4+,HSO3-) were taken from Rumpf et al.18 They are all given in Table 9. All those interaction parameters which are neither given in Table 9 nor in Table 10 were neglected, i.e. set to zero. Thus the model allows a prediction of the total pressure above aqueous solutions of sulfur dioxide and ammonium acetate. That comparison with the experimental results of the present work is shown in Figure 7. If one does not include the low pressure range into that comparison, i.e. the range j CH3COONH4 e 1, the relative deviation where m j SO2/m between predicted and measured total pressures is only j CH3COONH4 e 1, the uncertainty about 3.7%. When m j SO2/m of the experimental data for the pressure increases to about 5%. In that region the calculated total pressures deviate from the experimental data by about 10%. The
1156
Ind. Eng. Chem. Res., Vol. 38, No. 3, 1999
Figure 7. Total pressure above SO2-CH3COONH4-H2O: (O) experimental results, this work; (s) prediction, this work.
pressure at three-phase equilibrium (LLVE) is accurately predicted. The relative deviation is below 3%. Conclusions The solubility of sulfur dioxide in aqueous solutions of single solutes acetic acid, sodium acetate and ammonium acetate was measured at temperatures from about 313 to 393 K at total pressures up to about 3.3 MPa. The molalities were about 3 and 6 for acetic acid and about 3 for sodium acetate and ammonium acetate. The maximum overall molality of sulfur dioxide in the liquid phase was about 17 mol/kg. In some experiments that concentration was above the solubility limit for sulfur dioxide and therefore, a second, sulfur dioxide rich liquid phase was observed. A thermodynamic framework based on Pitzer’s model for the excess Gibbs energy of an aqueous solution of electrolytes was used to describe the vapor-liquid and liquid-liquid-vapor equilibrium. For the systems with acetic acid and sodium acetate, the new experimental data are correlated mostly within the experimental uncertainty. The set of parameters used to describe the phase equilibrium in those systems was extended by some parameters describing interactions between sulfur dioxide, ammonium, bisulfite, and sulfite ions. Therefore, it was possible to predict the pressure needed to dissolve sulfur dioxide in an aqueous solution of ammonium acetate. The predictions agree with the new experimental data mostly within the experimental uncertainty. Acknowledgment Financial support of this investigation by the government of the Federal Republic of Germany (BMFT Grant No. 0326558 C), BASF AG, Ludwigshafen, Germany, Bayer AG, Leverkusen, Germany, Degussa AG, Hanau, Germany, Hoechst AG, Frankfurt, Germany, Linde KCA, Dresden, Germany, and Lurgi AG, Frankfurt, Germany, is gratefully acknowledged. J.X. thanks the Deutsche Akademische Auslandsdienst (DAAD) for a scholarship. List of Symbols Ai,w...Di,w: coefficients for the temperature dependence of Henry’s constants
AR...DR: coefficients for the temperature dependence of equilibrium constants Aφ: Debye-Hu¨ckel parameter aw...dw: coefficients for the temperature dependence of second virial coefficients of water ai: activity of component i b: constant in modified Debye-Hu¨ckel expression Bi,j: second virial coefficient for interactions between species i and j Cφ: third virial coefficient in Pitzer’s equation D: relative dielectric constant of water e: charge of proton f: function for the temperature dependence of an interaction parameter f1, f2, f3: functions in Pitzer’s equation GE: excess Gibbs energy hi,f: standard enthalpy of formation of component i (m) Hi,w : Henry’s constant for the solubility of gas i in pure water (on a molality scale) I: ionic strength (on a molality scale) k: Boltzmann constant K(′′),(′) : distribution coefficient i KR: equilibrium constant for chemical reaction R (on molality scale) K h p: equilibrium constant for the dimerization of acetic acid in the vapor phase Mw: molar mass of water, kg/mol m j i: overall molality of component i mi: true molality of component i n j i: overall number of moles of component i ni: true number of moles of component i NA: Avogadro’s number p: total pressure pQ: standard pressure q1,i, q2,i, q3,i: coefficients for the temperature dependence of interaction parameters or distribution coefficients R: universal gas constant T: absolute temperature t: Celsius temperature v: partial molar volume xi: mole fraction of component i x: variable in Pitzer’s equation y: mole fraction in vapor zi: number of charges of component i Greek Letters R: constant in Pitzer’s equation β(0), β(1): binary interaction parameters in Pitzer’s equation γ(m): activity coefficient normalized to infinite dilution (on molality scale) 0: vacuum permittivity µi: chemical potential of component i νi,R: stoichiometric coefficient of component i in reaction R π: number of phases F: mass density τ: ternary interaction parameter in Pitzer’s equation φi: Giauque function of component i φ: fugacity coefficient ξR: extent of reaction R Subscripts f: formation HAc: acetic acid i, j, k: components i, j, k max: maximum min: minimum R: reaction R or reference w: water
Ind. Eng. Chem. Res., Vol. 38, No. 3, 1999 1157 Superscripts
I)
1
∑i mizi2
(29)
m: on molality scale s: saturation ∞: infinite dilution ′: liquid phase ′′: second liquid phase ′′′: gas phase Q: reference state
and b ) 1.2 (kg/mol)1/2. Aφ is the Debye-Hu¨ckel parameter for the osmotic coefficient
Appendix 1: Equilibrium Constant for the Dissociation of Acetic Acid in Water
The function f2 is defined as
Aφ )
Brewer7 reported numbers for the Giauque functions Q Q (T) - hi,f (298.15 K))/(RT) and standard φi ) -(µi,f Q for various substances. enthalpies of formation hi,f Standard thermodynamics yields the equilibrium constant for the dissociation of acetic acid:
ln K4 ) -φHAc + φH+ + φAc- +
(
)
Q Q hQHAc,f(298.15 K) - hH +,f(298.15 K) - hAc-,f(298.15) RT (20)
The following values as taken from Brewer were used:
2
(
Fw 1 2πNA 3 1000
-3
-8 3
9.1 × 10 t (22) φ H+ ) 0
(23)
Q The values for hi,f (298.15 K)/R:
hQHAc,f(298.15) R
) -58410 K
Q hAc -,f(298.15) ) -58454 K R
(24)
e2 4π0DkT
[
xI
) -Aφzi2 ln γ(m) i 2
∑ j*w
+
2 b
]
1 + bxI (1) 2 mj[β(0) + β ij ij f2(x)] - zi f3(x)
mjmkβ(1) ∑ ∑ jk + j*w k*w 3 ∑ ∑ mjmkτijk (32) j*w k*w
where f3 is defined as
[ (
) ]
1 x2 -x 1 1 + x + e 2 Ix2
f3(x) )
[
I1.5 ln aw ) Mw 2Aφ x 1+b I (1) -x mimj(β(0) ij + βij e ) -
∑∑ 2
Pitzer’s8 equation for the excess Gibbs energy of an aqueous, salt-containing system is
RTnwMw
) f1(K) +
β(0) i,j
(0) (1) mimj[βi,j + βi,j f2(x)] + ∑ ∑ i*w j*w
∑ ∑ ∑ mimjmkτi,j,k i*w j*w k*w
(27)
β(1) i,j
where and are binary and τi,j,k are ternary interaction parameters, respectively. The function f1(I) is a modified Debye-Hu¨ckel term
f1(I) ) -Aφ
4I ln(1 + bxI) b
where I is the ionic strength
(28)
(33)
The activity of water follows from the Gibbs-Duhem equation
(25)
(26)
(30)
(31)
i*w j*w
Appendix 2: Brief Outline of Pitzer’s Model
GE
1.5
ln(1 + bxI) +
∑ ∑ ∑ mimjmkτi,j,k - i*w ∑ mi
i*w j*w k*w Q hH +,f(298.15) )0K R
)
where x ) RxI. For the salts considered here, R ) 2.0 (kg/mol)1/2. Differentiation of eq 27 yields the activity coefficient of an dissolved species i:
-5 2
φAc- ) 10.42 + 1.64 × 10 t - 3.71 × 10 t +
0.5
2 [1 - (1 + x)e-x] x2
f2(x) )
φHAc ) 21.43 + 2.7 × 10-3t - 1.17 × 10-5t2 + 3.58 × 10-7t3 (21)
)(
]
(34)
For systems containing a single salt Mν+Xν-, the binary and ternary parameters involving two or more species of the same sign of charge are usually neglected. The ternary parameters τM,X,X, τM,M,X are usually reported as third virial coefficients Cφ for the osmotic coefficient. Instead of rewriting eqs 32 and 34 in terms of Cφ, the ternary parameter τM,X,X was set to zero and parameters τM,M,X were calculated from numbers reported for Cφ:
1 1:1 salt: τM,M,X ) Cφ 3 2:1 salt: τM,M,X )
x2 φ C 6
(35) (36)
Appendix 3: Details on the Calculation of the Simultaneous Phase and Chemical Equilibria To calculate the simultaneous phase- and chemical equilibria, we utilize a Gibbs energy minimization procedure. This we do as follows: For a system with two liquid phases, the Gibbs energy is
1158
Ind. Eng. Chem. Res., Vol. 38, No. 3, 1999
G)
∑i n′iµ′i + ∑i n′′iµ′′i
(37)
where n′i, n′′i and µ′i, µ′′i are the number of moles and the chemical potential of species i in the two liquid phases. As already mentioned, we assume that in the second, sulfur dioxide rich phase chemical reactions can be neglected. Assuming the overall number of moles of species i in the liquid phases to be given, combining eqs 16 and 37 results in
G)
ξR∑νi,Rµ′i + ∑n′′i(µ′′i - µ′i) ∑i nj iµ′i + ∑ R i i
(38)
Introducing the expressions for the chemical potentials of a species i into that equation leads to
G-
∑i nj iµQ(′) i RT
∑ ∑ R i
)
ξR ln KR + ∑i nj i ln a′i - ∑ R
νi,RξR ln a′i +
∑i
(
n′′i ln
a′′i a′i
)
- ln K(′′),(′) (39) i
Minimizing that function for a given temperature and given overall amounts n j i results in the extents of the chemical reactions ξR as well as the number of moles n′′i of each species i in the second liquid phase. In this work, a Nelder-Mead algorithm was chosen to solve the minimization problem. Literature Cited (1) Rumpf, B.; Maurer, G. Solubilities of hydrogen cyanide and sulfur dioxide in water at temperatures from 293.15 K to 413.15 K and pressures up to 2.5 MPa. Fluid Phase Equilib. 1992, 81, 241. (2) Rumpf, B.; Maurer, G. Solubility of sulfur dioxide in aqueous solutions of sodium- and ammonium sulfate at temperatures from 313.15 K to 393.15 K and pressures up to 3.5 MPa. Fluid Phase Equilib. 1993, 91, 113. (3) Washburn, E. W. International critical tables of numerical data. Physics, Chemistry and Technology; McGraw Hill: New York and London, 1928; Vol. III. (4) Edwards, T. J.; Maurer, G.; Newman, J.; Prausnitz, J. M. Thermodynamics of aqueous solutions containing volatile weak electrolytes. AIChE. J. 1978, 24, 966.
(5) Kawazuishi, K.; Prausnitz, J. M. Correlation of vapor liquid equilibria for the system ammonia-carbon dioxide-water. Ind. Eng. Chem. Res. 1982, 26, 1482. (6) Bieling, V.; Rumpf, B.; Strepp, F.; Maurer, G. An evolutionary optimization method for modeling the solubility of ammonia and carbon dioxide in water. Fluid Phase Equilib. 1989, 53, 251. (7) Brewer, L. Thermodynamic values for desulfurization processes. In Flue gas desulfurization; Hudson, J. L., Rochelle, G. T., Eds.; ACS Symposium Series 188; American Chemical Society: Washington, DC, 1982; p 1. (8) Pitzer, K. S. Thermodynamics of electrolytes. I. Theoretical basis and general equations. J. Phys. Chem. 1973, 77, 268. (9) Bradley, D. J.; Pitzer, K. S. Dielectric properties of water and Debye-Hu¨ckel parameters to 350 °C and 1 kbar. J. Phys. Chem. 1979, 83, 1599. (10) Bu¨ttner, R.; Maurer, G. Dimerisierung einiger organischer Sa¨uren in der Gasphase. Ber. Bunsen-Ges. Phys. Chem. 1983, 87, 877. (11) Rumpf, B.; Xia, J.; Maurer, G. Solubility of carbon dioxide in aqueous solutions containing acetic acid or sodium hydroxide in the temperature range from 313 to 433 K and total pressures up to 10 MPa. Ind. Chem. Eng. Res. 1998, 37, 2012. (12) Brelvi, S. W.; O’Connell, J. P. Corresponding states correlation for liquid compressibility and partial molal volumes of gases at infinite dilution in liquids. AIChE. J. 1972, 18, 1239. (13) Saul, A.; Wagner, W. International equations for the saturation properties of ordinary water substance. J. Phys. Chem. Ref. Data 1987, 16, 893. (14) Dymond, J. H.; Smith, E. B. The virial coefficients of pure gases and mixtures; Oxford University Press: Oxford, U.K., 1980. (15) Hayden, J. G.; O’Connell, J. P. A generalized method for predicting second virial coefficients. Ind. Eng. Chem. Proc. 1975, 14, 209. (16) Van Berkum, J. G.; Diepen, G. A. M. Phase equilibria in SO2 + H2O: the sulfur dioxide gas hydrate, two liquid phases, and the gas phase in the temperature range 273 to 400 K and at pressures up to 400 MPa. J. Chem. Thermodyn. 1979, 11, 317. (17) Kim, H. T.; Frederick, Jr. W. J. Evaluation of Pitzer Ion Interaction Parameters of Aqueous Electrolytes at 25 °C. 1. Single Salt Parameters. J. Chem. Eng. Data 1988, 33, 177. (18) Rumpf, B.; Weyrich, F.; Maurer, G. Simultaneous solubility of ammonia and sulfur dioxide in water at temperatures from 313.15 K to 373.15 K and pressures up to 2.2 MPa. Fluid Phase Equilib. 1993, 83, 253. (19) Sing, R. Untersuchungen zur Lo¨slichkeit von Ammoniak und sauren Gasen in Wasser und wa¨βrigen Lo¨sungen starker Elektrolyte. Ph.D. thesis, Universita¨t Kaiserslautern, Germany, 1998.
Received for review August 11, 1998 Revised manuscript received November 18, 1998 Accepted November 30, 1998 IE980529T
