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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
253
Fluid Phase Equrlzbria, 83 (1993) 253-260 Elsevier Science Publishers B.V., Amsterdam
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 B. Rumpf, F. Weyrich and G. Maurer’ Lehrstuhl fiir Technische Thermodynamik, Universitat D-6750 Kaiserslautern, Federal Republic of Germany
Keywords: gas solubility in liquids, weak electrolytes, data, phase equilibria in complex mixtures
Kaiserslautern
sulfur dioxide, ammonia, water, experiments,
ABSTRACT The simultaneous solubility of ammonia and sulfur dioxide in water was measured by a synthetic method in the temperature range from 313.15 K to 373.15 K at two overall molalities of ammonia zz 3 mol/kg and IfiN& x 6 mol/kg) and pressures up to 2.2 MPa corresponding to a maximum (fiNIf, overall molality of SOs of about 10 mol/kg. Pitzer’s semiempirical approach is used to correlate the new data. Results are reported and compared with literature data and correlations.
INTRODUCTION In many chemical plants, for example in coal gasification processes or desulfurization equipment, aqueous solutions of weak electrolyte gases have to be processed. The basic design of such equipment requires information on phase equilibrium. Experimental data for the simultaneous solubility of the weak base ammonia and acid gases like carbon dioxide, sulfur dioxide or hydrogen cyanide in most cases are restricted to small ranges of temperature and composition. Therefore, physico-chemical models for the involved complex equilibria cannot be tested or improved. As part of an ongoing project dealing with experimental and theoretical work on the solubility of weak electrolyte gases in aqueous phases, this contribution reports on experimental results for the simultaneous solubility of ammonia and sulfur dioxide in water. From the new data, interaction parameters for an adapted Pitzer model were determined.
EXPERIMENTAL The apparatus for measuring the solubility of a gas in aqueous solutions is a modification of the equipment presented in a recent publication on the solubility of hydrogen cyanide and sulfur dioxide in water (Rumpf and Maurer, 1992). In an experiment, a thermostated high pressure optical cell (material: Hastelloy C) is partially filled with a known amount of the ammoniacal solution. At next, a known amount of sulfur dioxide is added. More aqueous solvent is filled into the cell by a calibrated high pressure displacer until the gas is completely dissolved. The pressure in the cell is reduced stepwise by withdrawing very small amounts of the liquid mixture until the first stable bubble appears. The mass of the gas (about 0.7 to 14 g) charged into the cell is determined by weighing with an uncertainty of f 0.008 g. The volume of the ammoniacal solution filled into the cell was determined by measuring the position of the high pressure displacer piston before and after each experiment. The mass of the ammoniacal solution charged into the cell is determined with an relative uncertainty of about 0.9 %. ‘Author to whom correspondence
03783812/93/$06.00
should be addressed
01993 Elsevier Science Publishers B.V. All rights reserved
254
The temperature was determined with two calibrated platinum resistance thermometers placed in the heating jacket of the cell with an uncertainty of about f 0.1 K. Pressure transducers with ranges of 0.25, 0.6 and 2.5 MPa were used to determine the solubility pressure. Before and after each series of measurements, the transducers were calibrated against a pressure gauge. The maximum uncertainty in the pressure measurement as determined from the calibration is 0.6 kPa at pressures up to 0.6 MPa and 11 kPa at higher pressures. The ammoniacal solutions were prepared in a storage tank. The overall amounts of ammonia and water f&led into the storage tank were determined by weighing. Corrections for the masses of ammonia and water present in the gas phase have been applied, The combined uncert~nty in determining the molality of ammonia (resulting from uncertainties in determining the mass of the components as well as in determining the composition and the volume of the vapor phase) does not exceed 610-” % 3 mol/kg) and l.lO-’ mol/kg (h,v~~ x 6 mol/kg) (for details see Rumpf, 1992). mol/kg (%H,
SUBSTANCES High grade sulfur dioxide (2 99.98 mass per cent) and ammonia (2 99.999 moles per cent) were purchased from Messer Griesheim, Ludwigshafen and used without further purification. Water was deionized and further purified by vacuum distillation.
RESULTS The experimental results for the simultaneous solubility of ammonia and sulfur dioxide in water at temperatures between 313.15 and 373.15 K are given in table 1. Two overall modalities of ammonia 2: 3 mol/kg, mN& x 6 mol/kg) were investigated at total pressures up to 2.2 MPa corre(%HJ sponding to a maximum overall molality of sulfur dioxide of about 10 mol/kg. The concentration range was limited by the appearance of a second, sulfur dioxide rich phase at sulfur dioxide molalities somewhat higher than those reported in table 1. Some of the results are plotted in fig. 1. The addition of sulfur dioxide to an ammoniacal solution at fixed temperature and overall molality of ammonia results in a decrease in total pressure as both gases are dissolved chemically. When nearly all ammonia present in the liquid phase is converted into ionic form, a rapid increase in the total pressure is observed. Increasing the overall amount of ammonia in the liquid phase at mole ratios O< tiso,/rizN~~ SO.5 results in an increase in total pressure. The opposite behaviour is observed for fisoz/Ifi~~a 21. Due to the strong chemical reactions, a decrease in the total pressure below the vapor pressure of pure water at the same temperature is observed at mole ratios 0.5< fi~o,/fi~~,
MODELING Fig. 2 shows a scheme of the model applied to correlate the new data. The model is a modification of the thermodynamic framework developed by Edwards et al. (1978). Due to the chemical reactions, the liquid phase contains ammonia and sulfur dioxide not only in molecular but also in ionic form. To calculate the true molalities of the species present in the hquid phase, the condition for chemical equilibrium yields the following expression for the thermodynamic equilibrium constant of reaction R:
(1) The following balance equations the liquid phase were applied:
for the overall amounts of ammonia and sulfur dioxide present in
Table
T
1: Exp. results for the simultaneous
mNH,
313.18 313.20 313.19 313.18 313.16 313.18 313.10 313.06
%OL
mol/kg
K
T P
T
MPa
K
of ammonia
G-L mol/ kg
3.192
0.000
0.0182
353.10
3.193
3.192 3.192
3.306 3.717
0.0232 0.0799
353.12 353.10
3.193 3.193
3.192 3.191 3.191
4.601 5.647 6.806 0.000 6.245
0.1968 0.3269 0.4534 0.0305 0.0341
353.10 353.11 353.11 353.12
3.193 3.193 3.192 3.193 3.192
3.705 4.974
6.085 6.085 6.085
6.960 7.468
0.1318 0.1860
313.11 313.12
6.085 6.085 6.085
7.643 8.748
0.2076 0.3408
333.09 333.12
3.194 3.193
0.000 0.702
313.15 313.11
solubility
353.11 353.09
0.000 0.556 1.183 1.908 2.ri.59 3.4’13
and sulfur dioxide in water
P
T
MPa
K
LYTL mol/kg
I P
MPa
0.1838
0.0944
373.06
3.191
0.000
0.0809 0.0683
372.98 373.07 373.01 373.09 373.06 373.09 373.09
3.190 3.191
0.000
3.191 3.191 3.191 3.191 3.191
2.720 3.184
0.0945 0.1140
373.08 373.08
3.191 3.191
4.019 4.620
0.5509 0.859
0.0459 0.0467 0.1365 0.2400
0.586 1.199 1.741 2.437
0.1841 0.1603 0.1274 0.1028 0.0954
353.11 353.10 353.10
3.193 3.193
4.990 5.506
0.689 0.695 0.865
3.192 3.192
5.997 7.693
1.006 1.443
372.99 373.19
3.190 3.190
5.720 7.450
1.379 2.045
353.09 353.15
6.083 6.082
0.1405 0.1346
372.88 372.88
6.086 6.086
0.2640 0.2489
333.12
3.193
1.407
0.0433 0.0373 0.0254
353.15
6.082
0.000 0.434 1.194
0.1183
372.86
6.086
0.000 0.648 0.713
333.11 333.12
3.193 3.193
2.462 3.030
0.0214 0.0214
353.15 353.15
6.082 6.082
2.116 2.764
0.0883 0.0601
372.88 372.90
6.086 6.086
1.548 2.028
0.2470 0.2077 0.1779
333.12 333.11 333.12
3.193 3.193 3.193
333.11 333.11 333.11 333.13
3.193 3.193 3.193 3.193
3.567 3.580 4.034 5.379 6.051 7.457 7.797
0.1133 0.1203 0.2236 0.5144
353.14 353.16 353.15 353.15 353.15 353.16 353.09
6.081 6.081 6.081 6.081 6.081 6.081 6.082
3.583 4.849 5.718 6.838 7.496 8.219 8.734
0.0434 0.0412 0.0469 0.3380 0.5785 0.831
372.93 372.94 372.92 372.87
2.675 3.297 3.837 5.125 5.814 6.220 6.757
0.1331 0.1072 0.0931 0.0950 0.0933 0.1978 0.4789
333.18 333.16
6.084 6.084 6.084 6.084
353.09 353.10
6.082 6.082
9.550 10.522
372.99 373.06 373.03 372.94 373.05
6.086 6.086 6.086 6.086 6.086 6.080 6.081 6.086 6.079
0.4934 1.020
373.03 373.13
6.080 6.079
6.770 7.734 8.724 10.182
333.17 333.18 333.18 333.18 333.19 333.18 333.17 The
6.083 6.084 6.084 6.084 6.083
(small)
0.646 0.890 0.945 0.0682 0.0602
0.000 0.941 1.953 6.306 6.587
1.005 1.254 1.542
0.0448 0.0752 0.1378 0.3220
7.349 7.861 8.483 9.537
0.4259 0.5631 0.771
decrease in the number of moles of water was calculated
amount of oxygen
from a balance for the total
present in the liquid phase:
1000 - nHSO; - ns@72, = MW
- nOH-
(4)
The charge balance yields nH+ $ n,H$
= nHso;
The total
pressure
P.Yw-ip’,:
=P;.&.e-v(
+ 2 ’ nsOg-
+ nOH-
.
and the vapor phase composition
(4 P. Yz . cp:’ = 4,” CT, P3
(5) were caiculated
using the equations
W(P-P:)).xW.y,
(f-3
R.T . f=P(
i=NHs,
SO*.
(7)
256
Figure I: Experimental results for the simultaneous sotubility water. oq l : experimental results, this work. correlation.
of ammonia and sulfur dioxide in
The caiCulation requires the knowledge of the temperature dependent equilibrium constants Kr-K4, the activity coefficients of all species present in the liquid phase, Henry’s constants H!‘J) for ammonia and sulfur dioxide in pure water, the vapor pressure, molar volume and dielectric constant of water as well as information on the vapor phase nonideality and the partial molar volumes of the dissolved gases. The equilibrium constant for reaction Kr was taken from Bieling et al. (1989), those for reactions 2 and 3 from Kawazuishi and Prausnitz ( 1988) wh ereas the equilibrium constant for the autoprotolysis of water was obtained from Edwards et al. (1978). Henry’s constants for ammonia and sulfur dioxide were obtained from Bieling et al. (1989) and Rumpf and Maurer (1992), respectively. The dielectric constant of pure water was taken from Bradley and Pitzer (1979). The vapor pressure and the molar volume of water were taken from Saul and Wagner (1987)., A truncated virial equation of state was used to calculate the fugacity coefficients. Pure component second virial coefhcients BNH~.NH~and EL,, were calculated from a correlation based on the data recommended by Dymond and Smith (1980). The second virial coefficient B soz,so2 and the mixed virial coefficients were taken from Hayden and O’Connell (1975). There exist few methods to calculate activity coefficients of both ionic and molecular solutes in concentrated electrolyte solutions. A well established method is
257
vapor sos
NHs
t
t
t
I
I
I
NHs
YOs
Hz0
NHs + Hz0 = NH: SOz + Hz0
Hz0
*
+ OH-
(1)
+ H+
(2)
= HSO;
= SO;-
HSO,
+ H+
(3)
H+ + OH-
(4) liquid
Figure the Pitzer
2: VLE and chemical
model
(Pitzer,
1973) as adapted
1000. GE = Jr(l)
R.T.n,.M,
reactions
+ C
’
in the ammonia-sulfur
by Edwards
m, (P!,:’ +
m,
”
Hz0
dioxide-water
system
et al. (1978):
P!,:’h(J))
W#W
+ C
ma. mJ
mk ’ T,J,k .
(8)
w.k#w
As seven dissolved species are considered in the liquid phase, that equation in principle requires 56 binary interaction parameters fi!,;‘, @,$) and 84 ternary param eters r,,+ where only four parameters $0) ) may be obtained from the binary subsystems. But (P(O) NH3,NHJr S02,so2, rNH~.NH~.NHa, TSo~So,,So~ this large number of unknown parameters may be reduced drastically by the following approximations: In the concentration range investigated, it seems to be reasonable to neglect all interaction parameters between two or more ionic species of the same sign of charge. As the concentrations of H+ and OH- are rather small in comparison to other species, all interaction parameters between those and other solute species are set to zero. Furthermore, molecular ammonia and sulfur dioxide are not simultaneously present in the liquid phase (cf. fig. 2), therefore, all parameters describing interactions between
those
species
are neglected.
The parameter
&kZ,NH3
was obtained
from a correlation
based on literature data for the solubility of ammonia in water whereas the parameter &~Z,so2 was taken from Rumpf and Maurer (1992) (cf. table 2). Further considerations (cf. Rumpf, 1992) s h owed that the following equations may be used to describe the interactions between the dissolved gases and the salts NH4HS0s, (NHd)sSOs:
B,t$,
rG.MX,MX=
r G,G,MX where showed
/3,$,+ v-
= v+
=
vt
u+
TG,G,M +
G is either that
TG,M,M
(9)
@, +
u-
2 u+ ’
V-
~G,M,,,’
+
V’
(10)
TG,X,X
(11)
rG,G,X
SOz or NHs and
M,X is either
NH:,HSO,
or NH:,SOi-.
A sensitivity
study
the parameters B$La,(NH,)lso,: B&,NH,HS~~~ ~NH~.NH~,(NH,)~so~, r NH~,(NH,)~sO~,(NH,)~SO~ and FS02,NH,HS03,NH,WS03 is sufficrent to correlate the new data within the experimental uncertainty. The temperature dependence of the binary interaction parameters was taken into account whereas it was neglected for the ternary parameters. The binary and ternary parameters were simultaneously fitted to the new results for the total pressure. The resulting numbers are given in table 2. Furthermore, table 2 re orts numbers for the temperature dependence of the P so2-, /$k+ HSO-, /$$+ soz-, rNH:,NH:,HSO; ionic interaction parameters /3$+ HSO-, pcH+ and rNH+ NH+ sozpart%
,‘,kss:res
including
which above
were deter&ed3from solutions
containing
data
;eportec!
ammonia
‘by johnstoye
and sulfur
dioxide
(51935) for the total (0.51
%so,/~fi~~,
and 51).
258 Table 2: Interaction dioxide in water
parameters
for describing
the simultaneous
solubility
of ammonia and sulfur
T,‘,/Ii
-0.00477
‘NH;,NH;,SO:-
-
273.15
473.15
293.15
393.15
313.15
373.15
308.15
368.15
-
Again, the influence of temperature on the ternary parameters was neglected whereas it was taken into account for the binary parameters. The combined set of parameters correlates the new data with an average relative deviation of only 2.6 % (I & I:;“=14 %, 1G II”- -4.8 kPa at T=313.06 I< and p=34.1 kPa). Table 3 reports relative and absolute deviations between the correlation of the present work and literature data. All of these authors (most of the data were reported more than thirty years ago) report partial pressures of sulfur dioxide in the order of about 10 kPa, therefore larger relative deviations Table 3: Comparison
of literature
data with the correlation
of the present work Source of data
323
14
2.0
-
37.3
-
303-323
24
14.7
-
51
-
303-368
103
13.0
228
36.3
8.6
12.5
-
-
0.01
-
0.8 2.4
0.34
1.2
Newall (1955) Sedov (1957)
1.5
Szarawara (1961)
259
are observed. But the absolute deviations are mostly less than 1 kPa. The numbers for psoz given by Berdyanskaya are mostly larger than those calculated from the correlation of the present work. The opposite behaviour is observed for the data given by Sedov (1957) and Szarawara (1961) whereas the data given by Jackson (1955), Johnstone (1955) and Newall (1955) show no systematic deviations.
CONCLUSIONS The simultaneous solubility of ammonia and sulfur dioxide in water was determined by a synthetic method at temperatures 313.15
ACKNOWLEDGEMENT Financial support of this investigation by the government of the Federal Republic (BMFT Grant No. 0326558 A), BASF AG, L u d wi‘g s h a f en and Lurgi AG, Frankfurt acknowledged.
LIST OF SYMBOLS coefficients a, b, c
B(o)
Cfs GE H(“) 1.w I KR
M m, m, n, n, N P PZ R T V X
z, Greek letters /$O), /j(i) V IY iJ+, vrf,,R 7
for temperature dependence of interaction parameters “observable” combination of binary interaction parameters activity of component i functions of ionic strength in Pitzers equation excess Gibbs energy
Henry’s constant of component i in water (on molality scale) ionic strength (=f . C, m, zf) equilibrium constant for chemical reaction R molar mass overall molality of component i true molality of component i overall number of moles of component i true number of moles of component i number of data points total pressure partial pressure of component i universal gas constant temperature partial molar volume mole fraction number of charges of component i binary interaction parameters fugacity coefficient “observable” combination of ternary interaction parameters activity coefficient number of cations and anions in salt MX stoichiometric coefficient of component i in reaction R ternary interaction parameter
of Germany is gratefully
260
Subscripts abs cal exp G i,j, k MX R rel w
Superscripts max min
absolute calculated experimental
S
tot *
gas component i, j, k Salt MX reaction R relative water
Definition of average absolute deviation: Definition of average relative deviation:
maximum minimum saturation total normalized to infinite dilution
1& laba=k . ~~=, 1pk,eol- pk,erp1 ) G Ire,= k Cr=‘=,1pktc~:~~~1
REFERENCES Berdyanskaya, R. A., Golyand, S. M. and Chertkov, B. A. , 1959. On the partial pressure of SOz over ammonium sulfite-bisulfite solutions. Zh. Prikl. Khim., 37: 1930-1936. Bieling, V., Rumpf, B., Strepp, F. and Maurer, G. , 1989. An evolutionary optimization method for modeling the solubility of ammonia and carbon dioxide in aqueous solutions. Fluid Phase Equilibria, 53: 251-259. Bradley, D. J. and Pitzer, K. S. , 1979. Dielectric properties of water and Debye-Hiickel parameters to 350% and 1 kbar. J. Phys. Chem., 83: 1599-1603. Brelvi, S. W. and O’Connell, J. P. , 1972. Corresponding states correlations for liquid compressibility and partial molal volumes of gases at infinite dilution in liquids. AIChE-J., 18: 1239-1243. Dymond, J. H. and Smith, E. B. University Press.
, 1980. The virial coefficients of pure gases and mixtures.
Oxford
Edwards, T. J., Maurer, G., Newman, J. and Prausnitz, J. M. , 1978. Vapor-liquid equilibria in multicomponent aqueous solutions of volatile weak electrolytes. AIChE-J., 24: 966-976. Hayden, J. G. and O’Connell, J. P. cients. Ind. Eng. Chem. Proc. Jackson, Johnstone,
A. and Solbett, H. F.
J. M.
, 1975. A generalized method for predicting second virial coeffiDev., 14: 209-216.
, 1955. As cited by: Berdyanskaya et al., 1959.
, 1935. Recovery of sulfur dioxide from waste gases. Ind. Eng. Chem., 27: 587-593.
Kawazuishi, K. and Prausnitz, J. M. , 1988. Correlation of vapor liquid equilibria ammonia-carbon dioxide-water. Ind. Eng. Chem. Res., 26: 1482-1485. Newall, H. E.
for the system
, 1955. As cited by: Berdyanskaya et al., 1959.
Pitzer, K. S. , 1973. Thermodynamics Phys. Chem., 77: 268-277.
of electrolytes.
I. Theoretical
basis and general equations.
J.
Rumpf, B. and Maurer, G. , 1992. Solubility 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. Submitted to Fluid Phase Equilibria. Rumpf, B. , 1992. Untersuchungen zur Lijslichkeit reagierender Gase in Wasser und salzhaltigen wiilrigen Liisungen. Dissertation, Universitit Kaiserslautern. Saul, A. and Wagner, W. , 1987. International equations for the saturation water substance. J. Phys. Chem. Ref. Data, 16: 893-901. Sedov, N. V.
properties
of ordinary
, 1957. As cited by: Berdyanskaya et al., 1959.
Szarawara, J. , 1961. Studies on statics of the system: HsO-NHs-SO,. “solution-gas phase”. Chem. Stosowana, 3: 395-425.
II. Diphase equilibrium
Fluid Phase Equrlzbria, 83 (1993) 253-260 Elsevier Science Publishers B.V., Amsterdam
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 B. Rumpf, F. Weyrich and G. Maurer’ Lehrstuhl fiir Technische Thermodynamik, Universitat D-6750 Kaiserslautern, Federal Republic of Germany
Keywords: gas solubility in liquids, weak electrolytes, data, phase equilibria in complex mixtures
Kaiserslautern
sulfur dioxide, ammonia, water, experiments,
ABSTRACT The simultaneous solubility of ammonia and sulfur dioxide in water was measured by a synthetic method in the temperature range from 313.15 K to 373.15 K at two overall molalities of ammonia zz 3 mol/kg and IfiN& x 6 mol/kg) and pressures up to 2.2 MPa corresponding to a maximum (fiNIf, overall molality of SOs of about 10 mol/kg. Pitzer’s semiempirical approach is used to correlate the new data. Results are reported and compared with literature data and correlations.
INTRODUCTION In many chemical plants, for example in coal gasification processes or desulfurization equipment, aqueous solutions of weak electrolyte gases have to be processed. The basic design of such equipment requires information on phase equilibrium. Experimental data for the simultaneous solubility of the weak base ammonia and acid gases like carbon dioxide, sulfur dioxide or hydrogen cyanide in most cases are restricted to small ranges of temperature and composition. Therefore, physico-chemical models for the involved complex equilibria cannot be tested or improved. As part of an ongoing project dealing with experimental and theoretical work on the solubility of weak electrolyte gases in aqueous phases, this contribution reports on experimental results for the simultaneous solubility of ammonia and sulfur dioxide in water. From the new data, interaction parameters for an adapted Pitzer model were determined.
EXPERIMENTAL The apparatus for measuring the solubility of a gas in aqueous solutions is a modification of the equipment presented in a recent publication on the solubility of hydrogen cyanide and sulfur dioxide in water (Rumpf and Maurer, 1992). In an experiment, a thermostated high pressure optical cell (material: Hastelloy C) is partially filled with a known amount of the ammoniacal solution. At next, a known amount of sulfur dioxide is added. More aqueous solvent is filled into the cell by a calibrated high pressure displacer until the gas is completely dissolved. The pressure in the cell is reduced stepwise by withdrawing very small amounts of the liquid mixture until the first stable bubble appears. The mass of the gas (about 0.7 to 14 g) charged into the cell is determined by weighing with an uncertainty of f 0.008 g. The volume of the ammoniacal solution filled into the cell was determined by measuring the position of the high pressure displacer piston before and after each experiment. The mass of the ammoniacal solution charged into the cell is determined with an relative uncertainty of about 0.9 %. ‘Author to whom correspondence
03783812/93/$06.00
should be addressed
01993 Elsevier Science Publishers B.V. All rights reserved
254
The temperature was determined with two calibrated platinum resistance thermometers placed in the heating jacket of the cell with an uncertainty of about f 0.1 K. Pressure transducers with ranges of 0.25, 0.6 and 2.5 MPa were used to determine the solubility pressure. Before and after each series of measurements, the transducers were calibrated against a pressure gauge. The maximum uncertainty in the pressure measurement as determined from the calibration is 0.6 kPa at pressures up to 0.6 MPa and 11 kPa at higher pressures. The ammoniacal solutions were prepared in a storage tank. The overall amounts of ammonia and water f&led into the storage tank were determined by weighing. Corrections for the masses of ammonia and water present in the gas phase have been applied, The combined uncert~nty in determining the molality of ammonia (resulting from uncertainties in determining the mass of the components as well as in determining the composition and the volume of the vapor phase) does not exceed 610-” % 3 mol/kg) and l.lO-’ mol/kg (h,v~~ x 6 mol/kg) (for details see Rumpf, 1992). mol/kg (%H,
SUBSTANCES High grade sulfur dioxide (2 99.98 mass per cent) and ammonia (2 99.999 moles per cent) were purchased from Messer Griesheim, Ludwigshafen and used without further purification. Water was deionized and further purified by vacuum distillation.
RESULTS The experimental results for the simultaneous solubility of ammonia and sulfur dioxide in water at temperatures between 313.15 and 373.15 K are given in table 1. Two overall modalities of ammonia 2: 3 mol/kg, mN& x 6 mol/kg) were investigated at total pressures up to 2.2 MPa corre(%HJ sponding to a maximum overall molality of sulfur dioxide of about 10 mol/kg. The concentration range was limited by the appearance of a second, sulfur dioxide rich phase at sulfur dioxide molalities somewhat higher than those reported in table 1. Some of the results are plotted in fig. 1. The addition of sulfur dioxide to an ammoniacal solution at fixed temperature and overall molality of ammonia results in a decrease in total pressure as both gases are dissolved chemically. When nearly all ammonia present in the liquid phase is converted into ionic form, a rapid increase in the total pressure is observed. Increasing the overall amount of ammonia in the liquid phase at mole ratios O< tiso,/rizN~~ SO.5 results in an increase in total pressure. The opposite behaviour is observed for fisoz/Ifi~~a 21. Due to the strong chemical reactions, a decrease in the total pressure below the vapor pressure of pure water at the same temperature is observed at mole ratios 0.5< fi~o,/fi~~,
MODELING Fig. 2 shows a scheme of the model applied to correlate the new data. The model is a modification of the thermodynamic framework developed by Edwards et al. (1978). Due to the chemical reactions, the liquid phase contains ammonia and sulfur dioxide not only in molecular but also in ionic form. To calculate the true molalities of the species present in the hquid phase, the condition for chemical equilibrium yields the following expression for the thermodynamic equilibrium constant of reaction R:
(1) The following balance equations the liquid phase were applied:
for the overall amounts of ammonia and sulfur dioxide present in
Table
T
1: Exp. results for the simultaneous
mNH,
313.18 313.20 313.19 313.18 313.16 313.18 313.10 313.06
%OL
mol/kg
K
T P
T
MPa
K
of ammonia
G-L mol/ kg
3.192
0.000
0.0182
353.10
3.193
3.192 3.192
3.306 3.717
0.0232 0.0799
353.12 353.10
3.193 3.193
3.192 3.191 3.191
4.601 5.647 6.806 0.000 6.245
0.1968 0.3269 0.4534 0.0305 0.0341
353.10 353.11 353.11 353.12
3.193 3.193 3.192 3.193 3.192
3.705 4.974
6.085 6.085 6.085
6.960 7.468
0.1318 0.1860
313.11 313.12
6.085 6.085 6.085
7.643 8.748
0.2076 0.3408
333.09 333.12
3.194 3.193
0.000 0.702
313.15 313.11
solubility
353.11 353.09
0.000 0.556 1.183 1.908 2.ri.59 3.4’13
and sulfur dioxide in water
P
T
MPa
K
LYTL mol/kg
I P
MPa
0.1838
0.0944
373.06
3.191
0.000
0.0809 0.0683
372.98 373.07 373.01 373.09 373.06 373.09 373.09
3.190 3.191
0.000
3.191 3.191 3.191 3.191 3.191
2.720 3.184
0.0945 0.1140
373.08 373.08
3.191 3.191
4.019 4.620
0.5509 0.859
0.0459 0.0467 0.1365 0.2400
0.586 1.199 1.741 2.437
0.1841 0.1603 0.1274 0.1028 0.0954
353.11 353.10 353.10
3.193 3.193
4.990 5.506
0.689 0.695 0.865
3.192 3.192
5.997 7.693
1.006 1.443
372.99 373.19
3.190 3.190
5.720 7.450
1.379 2.045
353.09 353.15
6.083 6.082
0.1405 0.1346
372.88 372.88
6.086 6.086
0.2640 0.2489
333.12
3.193
1.407
0.0433 0.0373 0.0254
353.15
6.082
0.000 0.434 1.194
0.1183
372.86
6.086
0.000 0.648 0.713
333.11 333.12
3.193 3.193
2.462 3.030
0.0214 0.0214
353.15 353.15
6.082 6.082
2.116 2.764
0.0883 0.0601
372.88 372.90
6.086 6.086
1.548 2.028
0.2470 0.2077 0.1779
333.12 333.11 333.12
3.193 3.193 3.193
333.11 333.11 333.11 333.13
3.193 3.193 3.193 3.193
3.567 3.580 4.034 5.379 6.051 7.457 7.797
0.1133 0.1203 0.2236 0.5144
353.14 353.16 353.15 353.15 353.15 353.16 353.09
6.081 6.081 6.081 6.081 6.081 6.081 6.082
3.583 4.849 5.718 6.838 7.496 8.219 8.734
0.0434 0.0412 0.0469 0.3380 0.5785 0.831
372.93 372.94 372.92 372.87
2.675 3.297 3.837 5.125 5.814 6.220 6.757
0.1331 0.1072 0.0931 0.0950 0.0933 0.1978 0.4789
333.18 333.16
6.084 6.084 6.084 6.084
353.09 353.10
6.082 6.082
9.550 10.522
372.99 373.06 373.03 372.94 373.05
6.086 6.086 6.086 6.086 6.086 6.080 6.081 6.086 6.079
0.4934 1.020
373.03 373.13
6.080 6.079
6.770 7.734 8.724 10.182
333.17 333.18 333.18 333.18 333.19 333.18 333.17 The
6.083 6.084 6.084 6.084 6.083
(small)
0.646 0.890 0.945 0.0682 0.0602
0.000 0.941 1.953 6.306 6.587
1.005 1.254 1.542
0.0448 0.0752 0.1378 0.3220
7.349 7.861 8.483 9.537
0.4259 0.5631 0.771
decrease in the number of moles of water was calculated
amount of oxygen
from a balance for the total
present in the liquid phase:
1000 - nHSO; - ns@72, = MW
- nOH-
(4)
The charge balance yields nH+ $ n,H$
= nHso;
The total
pressure
P.Yw-ip’,:
=P;.&.e-v(
+ 2 ’ nsOg-
+ nOH-
.
and the vapor phase composition
(4 P. Yz . cp:’ = 4,” CT, P3
(5) were caiculated
using the equations
W(P-P:)).xW.y,
(f-3
R.T . f=P(
i=NHs,
SO*.
(7)
256
Figure I: Experimental results for the simultaneous sotubility water. oq l : experimental results, this work. correlation.
of ammonia and sulfur dioxide in
The caiCulation requires the knowledge of the temperature dependent equilibrium constants Kr-K4, the activity coefficients of all species present in the liquid phase, Henry’s constants H!‘J) for ammonia and sulfur dioxide in pure water, the vapor pressure, molar volume and dielectric constant of water as well as information on the vapor phase nonideality and the partial molar volumes of the dissolved gases. The equilibrium constant for reaction Kr was taken from Bieling et al. (1989), those for reactions 2 and 3 from Kawazuishi and Prausnitz ( 1988) wh ereas the equilibrium constant for the autoprotolysis of water was obtained from Edwards et al. (1978). Henry’s constants for ammonia and sulfur dioxide were obtained from Bieling et al. (1989) and Rumpf and Maurer (1992), respectively. The dielectric constant of pure water was taken from Bradley and Pitzer (1979). The vapor pressure and the molar volume of water were taken from Saul and Wagner (1987)., A truncated virial equation of state was used to calculate the fugacity coefficients. Pure component second virial coefhcients BNH~.NH~and EL,, were calculated from a correlation based on the data recommended by Dymond and Smith (1980). The second virial coefficient B soz,so2 and the mixed virial coefficients were taken from Hayden and O’Connell (1975). There exist few methods to calculate activity coefficients of both ionic and molecular solutes in concentrated electrolyte solutions. A well established method is
257
vapor sos
NHs
t
t
t
I
I
I
NHs
YOs
Hz0
NHs + Hz0 = NH: SOz + Hz0
Hz0
*
+ OH-
(1)
+ H+
(2)
= HSO;
= SO;-
HSO,
+ H+
(3)
H+ + OH-
(4) liquid
Figure the Pitzer
2: VLE and chemical
model
(Pitzer,
1973) as adapted
1000. GE = Jr(l)
R.T.n,.M,
reactions
+ C
’
in the ammonia-sulfur
by Edwards
m, (P!,:’ +
m,
”
Hz0
dioxide-water
system
et al. (1978):
P!,:’h(J))
W#W
+ C
ma. mJ
mk ’ T,J,k .
(8)
w.k#w
As seven dissolved species are considered in the liquid phase, that equation in principle requires 56 binary interaction parameters fi!,;‘, @,$) and 84 ternary param eters r,,+ where only four parameters $0) ) may be obtained from the binary subsystems. But (P(O) NH3,NHJr S02,so2, rNH~.NH~.NHa, TSo~So,,So~ this large number of unknown parameters may be reduced drastically by the following approximations: In the concentration range investigated, it seems to be reasonable to neglect all interaction parameters between two or more ionic species of the same sign of charge. As the concentrations of H+ and OH- are rather small in comparison to other species, all interaction parameters between those and other solute species are set to zero. Furthermore, molecular ammonia and sulfur dioxide are not simultaneously present in the liquid phase (cf. fig. 2), therefore, all parameters describing interactions between
those
species
are neglected.
The parameter
&kZ,NH3
was obtained
from a correlation
based on literature data for the solubility of ammonia in water whereas the parameter &~Z,so2 was taken from Rumpf and Maurer (1992) (cf. table 2). Further considerations (cf. Rumpf, 1992) s h owed that the following equations may be used to describe the interactions between the dissolved gases and the salts NH4HS0s, (NHd)sSOs:
B,t$,
rG.MX,MX=
r G,G,MX where showed
/3,$,+ v-
= v+
=
vt
u+
TG,G,M +
G is either that
TG,M,M
(9)
@, +
u-
2 u+ ’
V-
~G,M,,,’
+
V’
(10)
TG,X,X
(11)
rG,G,X
SOz or NHs and
M,X is either
NH:,HSO,
or NH:,SOi-.
A sensitivity
study
the parameters B$La,(NH,)lso,: B&,NH,HS~~~ ~NH~.NH~,(NH,)~so~, r NH~,(NH,)~sO~,(NH,)~SO~ and FS02,NH,HS03,NH,WS03 is sufficrent to correlate the new data within the experimental uncertainty. The temperature dependence of the binary interaction parameters was taken into account whereas it was neglected for the ternary parameters. The binary and ternary parameters were simultaneously fitted to the new results for the total pressure. The resulting numbers are given in table 2. Furthermore, table 2 re orts numbers for the temperature dependence of the P so2-, /$k+ HSO-, /$$+ soz-, rNH:,NH:,HSO; ionic interaction parameters /3$+ HSO-, pcH+ and rNH+ NH+ sozpart%
,‘,kss:res
including
which above
were deter&ed3from solutions
containing
data
;eportec!
ammonia
‘by johnstoye
and sulfur
dioxide
(51935) for the total (0.51
%so,/~fi~~,
and 51).
258 Table 2: Interaction dioxide in water
parameters
for describing
the simultaneous
solubility
of ammonia and sulfur
T,‘,/Ii
-0.00477
‘NH;,NH;,SO:-
-
273.15
473.15
293.15
393.15
313.15
373.15
308.15
368.15
-
Again, the influence of temperature on the ternary parameters was neglected whereas it was taken into account for the binary parameters. The combined set of parameters correlates the new data with an average relative deviation of only 2.6 % (I & I:;“=14 %, 1G II”- -4.8 kPa at T=313.06 I< and p=34.1 kPa). Table 3 reports relative and absolute deviations between the correlation of the present work and literature data. All of these authors (most of the data were reported more than thirty years ago) report partial pressures of sulfur dioxide in the order of about 10 kPa, therefore larger relative deviations Table 3: Comparison
of literature
data with the correlation
of the present work Source of data
323
14
2.0
-
37.3
-
303-323
24
14.7
-
51
-
303-368
103
13.0
228
36.3
8.6
12.5
-
-
0.01
-
0.8 2.4
0.34
1.2
Newall (1955) Sedov (1957)
1.5
Szarawara (1961)
259
are observed. But the absolute deviations are mostly less than 1 kPa. The numbers for psoz given by Berdyanskaya are mostly larger than those calculated from the correlation of the present work. The opposite behaviour is observed for the data given by Sedov (1957) and Szarawara (1961) whereas the data given by Jackson (1955), Johnstone (1955) and Newall (1955) show no systematic deviations.
CONCLUSIONS The simultaneous solubility of ammonia and sulfur dioxide in water was determined by a synthetic method at temperatures 313.15
ACKNOWLEDGEMENT Financial support of this investigation by the government of the Federal Republic (BMFT Grant No. 0326558 A), BASF AG, L u d wi‘g s h a f en and Lurgi AG, Frankfurt acknowledged.
LIST OF SYMBOLS coefficients a, b, c
B(o)
Cfs GE H(“) 1.w I KR
M m, m, n, n, N P PZ R T V X
z, Greek letters /$O), /j(i) V IY iJ+, vrf,,R 7
for temperature dependence of interaction parameters “observable” combination of binary interaction parameters activity of component i functions of ionic strength in Pitzers equation excess Gibbs energy
Henry’s constant of component i in water (on molality scale) ionic strength (=f . C, m, zf) equilibrium constant for chemical reaction R molar mass overall molality of component i true molality of component i overall number of moles of component i true number of moles of component i number of data points total pressure partial pressure of component i universal gas constant temperature partial molar volume mole fraction number of charges of component i binary interaction parameters fugacity coefficient “observable” combination of ternary interaction parameters activity coefficient number of cations and anions in salt MX stoichiometric coefficient of component i in reaction R ternary interaction parameter
of Germany is gratefully
260
Subscripts abs cal exp G i,j, k MX R rel w
Superscripts max min
absolute calculated experimental
S
tot *
gas component i, j, k Salt MX reaction R relative water
Definition of average absolute deviation: Definition of average relative deviation:
maximum minimum saturation total normalized to infinite dilution
1& laba=k . ~~=, 1pk,eol- pk,erp1 ) G Ire,= k Cr=‘=,1pktc~:~~~1
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, 1980. The virial coefficients of pure gases and mixtures.
Oxford
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J. M.
, 1975. A generalized method for predicting second virial coeffiDev., 14: 209-216.
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, 1935. Recovery of sulfur dioxide from waste gases. Ind. Eng. Chem., 27: 587-593.
Kawazuishi, K. and Prausnitz, J. M. , 1988. Correlation of vapor liquid equilibria ammonia-carbon dioxide-water. Ind. Eng. Chem. Res., 26: 1482-1485. Newall, H. E.
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, 1955. As cited by: Berdyanskaya et al., 1959.
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I. Theoretical
basis and general equations.
J.
Rumpf, B. and Maurer, G. , 1992. Solubility 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. Submitted to Fluid Phase Equilibria. Rumpf, B. , 1992. Untersuchungen zur Lijslichkeit reagierender Gase in Wasser und salzhaltigen wiilrigen Liisungen. Dissertation, Universitit Kaiserslautern. Saul, A. and Wagner, W. , 1987. International equations for the saturation water substance. J. Phys. Chem. Ref. Data, 16: 893-901. Sedov, N. V.
properties
of ordinary
, 1957. As cited by: Berdyanskaya et al., 1959.
Szarawara, J. , 1961. Studies on statics of the system: HsO-NHs-SO,. “solution-gas phase”. Chem. Stosowana, 3: 395-425.
II. Diphase equilibrium