1780
Znd. Eng. Chem. Res. 1993,32, 1780-1789
Solubility of Ammonia in Aqueous Solutions of Sodium Sulfate and Ammonium Sulfate at Temperatures from 333.15 K to 433.15 K and Pressures up to 3 MPa Bernd Rumpf and Gerd Maurer' Lehrstuhl fiir Technische Thermodynamik, Universitat Kaiserslautern, 0-67653Kaiserslautern, Federal Republic of Germany
As part of an ongoing project dealing with experimental and theoretical work on phase equilibria in aqueous solutions containing weak electrolyte gases like ammonia, hydrogen cyanide, sulfur dioxide, or carbon dioxide, the solubility of ammonia in aqueous solutions of sodium sulfate and ammonium sulfate was measured by a synthetic method in the temperature range from 333.15 to 433.15 K at total pressures up to 3 MPa. The model proposed by Edwards et al. is used to correlate the data. That model is extended t o include the formation of one or more solid phases. Experimental results and the correlations are reported and compared with literature data and other correlations.
Introduction The solubility of electrolyte gases like ammonia, carbon dioxide, sulfur dioxide, and hydrogen cyanide must be known for designing separation equipment in many technical applications. Typical examples are applications in the chemical and oil-related industries and in the field of environmental protection. In most cases,the correlation and prediction of phase equilibria in aqueous systems containing the weak base ammonia and acid gases is an extremely difficult task, caused partially by chemical reactions in the liquid phase as well as by the possible formation of one or more solid phases. There exist several methods to describe phase equilibria in such complex systems. However, as long as experimental data on such phase equilibria is as scarce as it is at the moment, these models cannot be tested and improved. There is a lack of experimental data not only on the simultaneous solubility of ammonia and sour gases in aqueous phases, but also for the single gas solubilities in aqueous salt containing solutions. These data are mainly needed to develop predictive models. In continuation of a recent work on the solubility of carbon dioxide in aqueous salt containing solutions (Rumpf and Maurer, 19931, this contribution reports on experimental results for the solubility of ammonia in aqueous solutions of sodium sulfate and ammonium sulfate in the temperature range from 333.15 to 433.15 K, at total pressures up to 3 MPa, and up to 4 m salt solutions. Experimental Section The apparatus for measuring the solubility of a gas in liquids was described before in detail (Rumpf and Maurer, 1992;Rumpf, 1992);therefore only the principal features of the method are described here. In an experiment, a thermostated high-pressure optical cell (material: Hastelloy C or stainless steel) is partially filled with a known amourit of the solvent. A known amount of gas is added from a storage tank. More aqueous solvent is added by an calibrated high-pressure displacer until the gas is fully dissolved. After equilibration, the pressure in the cell is reduced stepwise by withdrawing very small amounts of the liquid mixture out of the cell until the first stable bubble appears. The mass of the gas (about 0.7-14 g) charged into the cell is determined by weighing with an uncertainty of
* Author to whom correspondence should be addressed.
k0.008 g. The mass of the solvent needed to dissolve the gas is calculated from the displacement of the displacer piston and the known densities (Lo Surdo et al., 1982; Rumpf, 1992) of the aqueous salt containing solutions. The pressure is measured by means of pressure transducers. Before and after each series of measurements, the transducers were calibrated against a high-precision pressure gauge. 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. Temperature was determined with two calibrated platinum resistance thermometers placed in the heating jacket of the cell with an estimated maximum uncertainty of f O . l K. The salt-containingsolutions were prepared in a storage tank. The concentration of the salt in the aqueous solution was determined gravimetrically with an uncertainty of = 0.3%. about Am&,
Substances Ammonia (199.999mol 95 ) was purchased from Messer Griesheim, Ludwigshafen, and used without further purification. Deionized water was degassed by vacuum distillation. Sodium sulfate (199mass 95 ) and ammonium sulfate (199.5 mass 5%) were purchased from Riedel de Haln, Seelze,and Merck GmbH, Darmstadt, respectively. The salts were degassed and dried under vacuum for several hours.
Results The experimental results for the solubility of ammonia in aqueous solutions of sodium sulfate are given in Table I. Two salt molalities (IfE~~fio, = 1 and 2 mol/kg) were investigated in the temperature range from 333.15to 433.15 K. The gas molality ranged up to about 19 corresponding to total pressures up to about 2.1 MPa. The results for the system NH~-(NH~)zSO~-H~O (fi(~~,)= f i2 oand , 4 mol/kg, &ma,- = 24 mol/kg) which cover the same temperature range at pressures up to 3 MPa are given in Table 11. For both systems,the formation of a solid phase of sodium or ammonium sulfate was observed at high concentrations of ammonia. Therefore, the number of observed phases ( T ) is also given in Tables I and 11. A t very low concentrations of ammonia, the total pressure is below the solubility pressure of ammonia in pure water. At higher molalities of the dissolved gas,
0 1993 American Chemical Society 0888-58~5/93/2632-1780~04.oo/o
Ind. Eng. Chem. Res., Vol. 32, No. 8,1993 1781
-0.5 0
5
10
RNH3l(rnol. kg-')
20
.,
Figure 1. Solubility of ammonia in aqueous solutions of sodium sulfate: differences in the total pressures above the salt-containing and salt-free aqueous phases a t 433 K. (n,O, 0 ) Experimental results, this work (0) f i ~ . r 9 0 (= 1mollkg, LV; (m) m ~ = 1 emol/ ~ kg, S L Y (0) = 2 mollkg, LV; ( 0 )f i ~ y=~2 mol/kg, ~ , SLV. vapor
"'
HzO
~
t
M,+X,-
.(LY~O),~ '
I
Figure 2. VLE and SLE in the ammonia-ealt-water systems.
ammonia is salted out by both salts. As long as no formation of a solid phase is observed (cf. Tables I and 11), an increase in the concentration of the salt results in an increase in the total pressure. Thus for example a t 433 K the totalpressure above an aqueous solution containing 1mol of sodium sulfate and 4.6 mol of ammonia is about 0.1 MPa higher than that above the salt-free solution, corresponding to a relative change in the total pressure of about 10%. The formation of a solid phase results in a slight change of slope of the isotherms. As the number of degrees of freedom of a ternary system in three-phase equilibrium is reduced to 2, at a given temperature and molality of ammonia the total pressure above the salt-containing solution as well as the concentration of the salt in the liquid phase are no longer variable. Figure 1demonstrates the influence of sodium sulfate on the solubility of ammonia. For 433 K, the difference in the total pressures above the salt-containing and saltfree aqueous phases @with 8(113 - @without dt) are plotted versus the amount of dissolved ammonia. Increasing the amount of ammonia in the liquid phase at constant temperature and constant overall molality of sodium sulfate results in an nearly linear increase in the pressure difference. Adding more ammonia causes precipitation of sodium sulfate. The formation of a solid results in a change of slope. At 433 K, the solubility of sodium sulfate in pure water is about 3 mol/kg (Linke and Seidell, 1965). By adding about 8.1 mol of ammonia/kg, it is reduced to 1mol/kg. For a 2 m sodium sulfate solution, the addition of only about 2.9 mol of ammonia/kg causes solid precipitation. Similar results are observed at other temper-
atures. Table I11 gives the solubility limita determined from the new measurements together with their estimated uncertainties. Note that at lower temperatures the uncertainties are somewhat larger as the observed pressure differences are rather small. Adding more ammonia to a solution in three-phase equilibrium with constant overall amount of a salt reduces the salting-out effect on ammoniaas the true concentration of the salt in the liquid phase is reduced. Therefore, the boiling point curves for the salt-free and salt-containing solutions approach each other at high molalities of ammonia (cf. Figure 1). A similar behavior is observed for the system "3(N&)2SOr-H20. Due to the high solubility of ammonium sulfate (about 6.6 mol/kg a t 333.15 K (Linke and Seidell, 1965)),in the present work only at the lowest temperature and large molalities of both ammonia and ammonium =4 sulfate (T = 333 K, am, = 15.8 mol/kg, ~(NH,)Bo, mol/kg; cf. Table 11) was solid precipitation observed. Thermodynamic Treatment Figure 2 shows a scheme of the model applied to correlate the new data. At the concentrations discussed here, the dissociation of dissolved ammonia in the liquid phase can be neglected. The phase equilibrium conditions for water and the dissolved gas yield
(2) where @G,w(T,pk) denotes Henry's constant for the solubility of ammonia in pure water. The formation of one or more solid phases is included in the model as follows: For a salt M,X, which is fully dissociated in the liquid phase M,+X,
-
u+M2++ u-XE-
(3)
in equilibrium with a solid phase M,+X,.(H20), the phase equilibrium condition yields
K,(T,p) = a $ z + a ~ z , _ a ~ (4) K,(T,p)is the solubility product for the formation of solid Mv+Xv-*(HzO)uw: RT In K,= P ~ . ~ ~ O , ~ -, (P&(T,P) T , P ) - ~,P;E(T,P) (5) where p n . , ~ p o , p and p;? are the chemical potentials of the pure sokphase, t#e dissolved salt a t infinite dilution, and pure water, respectively. In the pressure range discussed here, the influence of pressure on the solubility product can be neglected. Pitzer's model (Pitzer, 1973) as modified by Edwards et al. (1978) was used to calculate the activity coefficients of both ionic and molecular species. For an aqueoussystem containing a nonreacting gas Gand a fully dissociated salt M,X, Pitzer's equation results in the followingexpression for the activity coefficient of the dissolved gas In Th = In Tk(rn,=O)
+ 2 m ~ $ ' : +~ 3rn,2rGmm +
~%~JG (6) , G , M x where m, is the true molality of the dissolved salt in the liquid phase and TRG is the overall molality of the dissolved gas. The parameters B$!=, IIc,m,m,and rG,G&fX are
1782 Ind. Eng. Chem. Res., Vol. 32, No. 8, 1993 Table I. Exwrimental Results for the Solubility of Ammonia in Aqueous Solutionr of Sodium Sulfate
333.18 333.22 333.14 333.14 333.14 333.16 333.14 333.29 333.13 333.18 333.14 353.14 353.12 353.17 353.13 353.14 353.17 353.13 353.13 353.13 353.14 353.14 353.13 353.13 353.14 353.14 353.12 353.16 353.16 353.11 353.16 393.14 393.14 393.14 393.19 393.14 393.15 392.82 393.15 393.13 393.15 393.14 393.13 393.08 393.12 393.10 393.14 413.15 413.15 413.19 413.13 413.20 413.20 413.20 413.16
0.0 1.728 4.257 5.284 6.645 8.988 9.447 9.632 11.870 11.662 16.133 0.0 1.867 2.218 3.046 3.328 4.578 5.128 5.257 7.647 7.654 8.962 9.190 9.508 10.308 10.247 11.174 12.252 12.926 13.884 17.154 0.0 1.870 2.528 2.910 3.633 4.218 4.943 6.481 8.001 8.047 8.472 11.663 12.041 14.471 17.365 18.215 0.0 1.504 2.157 4.525 6.345 7.962 8.578 8.804
1.003 1.003 1.003 1.003 1.003 1.003 1.003 0.998 1.003 1.003 1.003 1.003 1.003 0.983 0.983 1.003 1.004 0.983 1.003 0.983 1.003 1.003 0.983 0.983 0.983 1.003 1.010 1.004 1.004 1.010 1.004 1.004 1.004 1.004 0.993 1.004 1.007 1.010 1.007 1.010 1.004 1.004 1.010 0.993 1.010 1.010 1.007 1.007 0.993 0.993 0.993 0.993 0.993 0.993 1.007
0.189 0.440 0.705 0.874 1.092 1.290 1.361 1.301 1.568 1.612 2.022 0.454 0.945 1.007 1.167 1.275 1.484 1.645 1.737 2.138 2.183 2.441 2.432 2.487 2.616 2.577 2.704 3.073 3.126 3.284 3.960 1.906 3.001 3.442 3.634 4.018 4.405 4.719 5.673 6.48 6.53 6.81 8.35 8.44 9.70 11.13 11.68 3.468 4.819 5.368 7.35 8.81 10.37 10.97 11.07
2 2 2 2 2 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 2 2 2 2 2 3 3 3
"observablt combinations of the second and third virial coefficients Bij and r i j k as used in Pitzer's originalequation (for details see Rumpf and Maurer (1993)):
B$!m = u+/3:k 2
+ vJ38k
(7)
= v+ ?G,M,M + zv+v-rG,M,X + v-2'G,X,X (9) ~ G , G , M X= Y + ~ G , G , M+ ~ - ~ G , G , x Equations for the mean ionic activity coefficient of the dissolved salt and for the activity of water are given in Appendix 1. To correlate the new results, Henry's constant for the solubility of ammonia in pure water was taken from Bieling et al., (1989) (cf. Table IV). The influence of pressure on Henry's constant for ammonia was estimated using the partial molar volume of ammonia in water as given by Brelvi and O'Connell (1972) (cf. Table V). The vapor pressure and molar volume of pure water were calculated rG,MX,MX
413.17 413.21 413.17 413.17 413.17 413.17 413.17 433.13 433.12 433.09 433.16 433.13 433.13 433.13 433.12 433.13 433.13 353.15 353.15 353.16 353.15 353.16 353.16 353.16 353.16 353.16 413.18 413.19 413.18 413.18 413.16 413.17 413.18 413.17 413.19 413.17 413.17 413.18 413.16 413.18 433.15 433.14 433.16 433.14 433.15 433.15 433.15 433.14 433.16 433.15 433.15 433.14 433.16 433.14 433.15
8.949 9.460 9.597 9.618 10.664 11.174 13.568 0.0 2.886 4.619 7.327 7.631 8.842 10.127 10.833 10.983 13.234 0.0 1.278 1.398 2.528 3.444 4.566 6.030 8.513 13.768 0.0 1.020 1.242 2.279 3.306 3.891 4.310 5.292 5.920 5.926 7.950 10.375 10.726 17.564 0.0 1.164 1.851 2.325 2.824 3.268 3.933 4.871 5.425 6.312 6.505 7.603 8.414 12.043 13.032
1.007 0.993 1.007 1.007 1.007 1.007 1.007 0.994 0.994 0.994 0.994 0.994 0.994 0.994 0.994 0.994 0.994 2.002 2.002 2.002 2.002 2.002 2.002 2.002 2.002 2.002 1.999 1.999 1.999 1.999 1.999 1.999 1.999 1.999 1.999 1.999 1.999 1.999 1.999 1.999 2.002 2.002 2.002 2.002 2.002 2.002 2.002 2.002 2.002 2.002 2.002 2.002 2.002 2.002 2.002
11.15 11.34 11.44 11.45 12.02 12.59 14.32 5.98 9.46 11.60 14.93 15.31 16.66 17.89 18.54 18.73 21.02 0.436 0.791 0.892 1.167 1.501 1.649 1.861 2.254 3.166 3.366 4.399 4.807 5.919 6.87 7.30 7.70 8.45 8.91 8.84 10.25 11.92 12.16 17.03 5.78 7.65 8.61 9.33 10.11 10.67 11.47 12.43 13.21 14.05 14.28 15.30 16.18 19.85 20.83
3 3 3 3 3 3 3 2 2 2 2 2 3 3 3 3 3 2 2 2 2 2 3 3 3 3 2 2 2 2 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3
from the equations of Saul and Wagner ( 87) (cf. Appendix 4). Fugacity coefficients in the vapor phase were calculated using the virial equation of state truncated after the second virial coefficient. Pure component virial coefficients Bmsm8and B , , were calculated from a correlation based on the data collection by Dymond and Smith (1980) (cf. Table VI). The mixed second virial , determined as recommended by coefficient B N ~ ,was Hayden and O'Connell(l975)(cf. Table V). The dielectric constant of pure water was taken from Bradley and Pitzer (1979) (cf. Appendix 3). Besides those interaction parametersalready mentioned above, some more parameters are needed. The interaction was obtained from selected data on parameter /3%,* the solubility of ammonia in pure water (Clifford and Hunter, 1933; Gillespie and Wilson, 1982; Guillevic et al., 1985;Mollier, 1908;Miiller et al., 1988;Pawlikowski et al., 1982; Pierre, 1959; Rizvi and Heidemann, 1987; Wilson,
Ind. Eng. Chem. Res., Vol. 32,No. 8,1993 1783 Table 11. Experimental Results for the Solubility of Ammonia in Aqueous Solutions of Ammonium Sulfate
T, K
m m , moVkg
333.13 333.13 333.11 333.13 333.13 333.08 333.14 333.07 333.10 333.17 333.20 353.13 353.14 353.14 353.16 353.14 353.17 353.13 353.13 353.16 353.16 353.14 393.18 393.15 393.16 393.13 393.17 393.16 393.16 393.16 393.18 393.14 393.14 413.11 413.16 413.15 413.11 413.16 413.15 433.14 433.16 433.17 433.16 433.25 433.14 433.14 433.14
0.0 2.277 3.801 4.743 6.967 7.049 10.358 13.841 16.120 18.366 23.667
~RJHSW,, mol&
2.000 1.999 2.000 2.000 2.000 1.999 2.000 1.999 2.000 1.999 1.999 1.999 1.999 1.999 1.999 1.999 1.999 1.999 1.999 1.999 1.999 1.999 1.982 1.982 1.982 1.982 1.982 1.982 1.982 1.982 1.982 1.982 1.982 1.982 1.982 1.982 1.982 1.982 1.982 2.010 2.010 2.010 2.010 2.010 2.010 2.010 2.010
0.0 1.852 4.091
5.644 7.213 8.752 9.308 10.514 14.406 14.838 17.612 0.0 2.303 3.521 6.186 6.413 7.863 9.815 12.080 16.288 18.531 22.178 0.0 3.034 6.213 8.849 13.609 17.151 0.0 1.092 2.159 2.499 3.355 4.486 5.072 6.248
10p,MPa 0.185 0.524 0.651 0.798 1.035 1.060 1.426 1.920 2.244 2.649 3.644 0.445 0.906
1.438 1.767 2.096 2.391 2.502 2.852 3.835 3.886 4.563 1.855 3.532 4.042 5.799 5.911 6.61 7.87 9.41 12.06 13.57 16.00 3.367 6.40 9.77 11.78 16.06 19.42 5.81 7.30 8.76 9.18 10.47 11.92 12.61 14.13
T
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
Table 111. Solubility Limits in the System NHrNaaS04-HaO Determined from the New Measurements
T, K 333.18 353.14 353.14 393.12 413.14 413.14 433.15 433.15
mol/k 1.003 0.997 2.002 1.005 1.0 1.999 0.994 2.002
Ip1~.80.,
am,moVk
T,K
mrn8,mol/kg 8.219 10.461 14.231 16.194 0.0 1.424 2.814 5.455 7.079 8.568 11.673 15.786 0.0 1.493 2.511 4.534 6.176 8.974 10.038 10.871 13.733 16.228 0.0 2.036 6.065 8.629 9.693 12.020 15.347 0.0 2.348 3.044 7.325 7.444 9.121 13.434 14.664 16.496 0.0 1.802 2.206 5.030 5.761 8.312 13.494 16.431
433.14 433.26 433.16 433.16 333.13 333.13 333.12 333.13 333.13 333.13 333.14 333.13 353.15 353.11 353.15 353.15 353.13 353.15 353.15 353.16 353.15 353.14 393.15 393.16 393.15 393.14 393.15 393.16 393.16 413.17 413.17 413.17 413.17 413.15 413.17 413.17 413.16 413.17 433.16 433.16 433.16 433.16 433.16 433.16 433.16 433.16
T, K
u k w , cm*/mol
333.15 353.15 393.15 413.15 433.15
30.7 32.1 36.2 38.9 42.2
-1879.02
2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
B M , , ~cms/mol , -244.7 -212.5 -165.3 -147.8 -133.1
Bii/(cms/mol) = ai + bi component i
HzO
3.932
r
Table V. Partial Molar Volume of Ammonia in Water at Infinite Dilution and the Mixed Second Virial Coefficient between Ammonia and Water
"S
B"&W
10nMPa 16.61 19.68 24.23 26.72 0.181 0.518 0.751 1.268 1.540 1.776 2.249 2.732 0.420 1.096 1.291 1.800 2.294 2.828 3.257 3.475 4.186 4.892 1.738 3.414 6.22 8.23 8.88 10.64 12.83 3.204 5.866 6.53 11.07 11.20 12.99 17.34 18.52 20.56 5.426 8.55 8.98 13.59 14.71 18.41 25.80 29.90
Table VI. Pure Component Second Virial Coefficients
Table IV. Henry's Constant for the Solubility of Ammonia in Pure Water
AWW
IAm,so,,moVkg 2.010 2.010 2.010 2.010 3.934 3.934 3.934 3.934 3.934 3.934 3.934 3.934 3.934 3.930 3.934 3.934 3.930 3.934 3.934 3.930 3.930 3.934 3.930 3.930 3.930 3.930 3.930 3.930 3.930 4.016 4.016 4.016 4.016 4.016 4.016 4.016 4.016 4.016 4.016 4.016 4.016 4.016 4.016 4.016 4.016 4.016
CmW -365134.1
1924;Wilson et al., 1978;Wucherer, 1932)(cf. Table VII). For sodium sulfate-water, the ion interaction parameters were taken from Rogers and Pitzer (1981)(cf. Appendix 2). For ammonium sulfate-water, interaction parameters
(&r -
ai
bi
Ci
4.06 -53.53
-117.7 -39.29
405.6 641.3
di 2.6 4.3
were determined from vapor pressure data reported by Nikolski (1959). The resulting numbers for the temperature-dependent ion interaction parameters are given in Table VIII. In the binary system sodium sulfate-water, unhydrated sodium sulfate precipitates at temperatures above 308.15 K. Below that temperature, mirabilite (NazSOc(Hz0)d precipitates (Linke and Seidell, 1965). For ammonium
1784 Ind. Eng. Chem. Res., Vol. 32, No. 8, 1993 Table VIJ. Interaction Parameters for the Systems NHa-NarSO4-HaO and NHs-(NHi)aS04-H20: f(T)= a t b/(T/K) parameter a b T d K T d K -0.034 14.59 273.15 473.15 B%& 333.15 433.15 B%,,N.JJO, -0.192 138.5 -0.091 88.62 333.15 433.15 B%,,("380, 333.15 433.15 rma,N@&,h80t 0.0284 -15.03 rm8r"3.900("3fio, -0.0116 1.5213 333.15 433.15 ~"*,NH*,(NHSBO, 0.0037 -1.827 333.15 433.15
I 0 :fiNo,so,=l mollkg O,O,A,V,
0,
r,e: LN,,,,,=2rnollkg
Table VIII. Interaction Parameters for the System (NH4)aSOi-HzO: f ( T ) a + b / ( T / R ) parameter a b T d K TJK (0) 0.1170 -9.342 313.15 383.15 BNH,+,so4c 7.488 -2479 313.15 383.15 B%'+~,% -0.5045 313.15 383.15 7m+,so,a,so,a -5.832 X lo-' Table IX. Temperature Dependence of the Solubility Products lnK,=- A' + B, ln(T/K) + C,(T/K) (T/K)
+ D,
(12)
solid A, Bs c. D. 7 ' d K T-JK NaBO4 6561.6 60.36 4.13442 -326.526 308.15 473.15 (NH&SOI 28179.9 193.697 -0,3146 -1104.258 298.15 473.15
sulfate-water, only unhydrated ammonium sulfate precipitates in the temperature range considered here. In principle, the temperature dependence of the solubility product K, may be calculated from experimental information on the heat capacities of the solid phase and of the dissolved salt in infinite dilution as well as from information on the standard Gibbs energies of formation of the involved species (cf. eq 5). Applying that procedure to the system sodium sulfate-water using heat capacities and Gibbs energies of formation as given by Pitzer (1987) resulted in somewhat larger deviationsbetween calculated solubility limits and experimental data reported by Linke and Seidell (1965) at temperatures above 308.15 K. Therefore, the solubility product for the formation of sodium sulfate was determined from experimental solubility data as reported by Linke and Seidel(l965) using ion interaction parameters as given by Rogers and Pitzer (1981). The resulting numbers for the temperature dependence of the solubility product are given in Table IX. For mirabilite, good results were obtained using the solubility product as given by Pitzer (1987). Therefore, those numbers were adopted (cf. Appendix 5). The thermodynamic properties of aqueous ammonium sulfate solutions are not well-known. Therefore, the solubility product for this salt had to be determined from the solubility data given by Linke and Seidell(1965)using ion interaction parameters as given in Table VIII. The resulting numbers for the temperature dependence of the solubility product are also given in Table IX. Correlating the new results for the solubilityof ammonia in aqueous salt containing solutions requires interaction parameters defined in eqs 7-9. For NH3-NazSOd-Hz0, parameters @ &.! ,N o4and rma,Na@OcNa@04 were fitted to the results for t fiextal pressure. For NH~-(NH~)zSO~HzO, as rather high concentrations of both salt and gas were investigated, the binary parameter BEha,("Jfio4 as well as both ternary parameters r ~ ( N H 4 ) f i O , ~ " , ) f i O 4 and hJ"HNHa,(NH,)&304 turned out to be significant. At the high concentrations investigated, the model is very sensitive to the interaction parameters. Therefore, the temperature
Figure 3. Solubility of ammonia in aqueous solutione of sodium sulfate. ( O , O , A, V, 0 ,0, 'I,*)Experimental results, thk work. (-) Correlation, thh work. (- -) Calculated solubility limit for an 1 m sodium sulfate solution. (- -) calculatedsolubility limit for an 2 m sodium sulfate solution.
-
-
A
I
I
v-
0
Figure 4. Solubilityof ammoniain aqueoussolutione of ammonium 0, A, V, 0, 0 , A, 'I,*)Experimental results, this sulfate. (0, work. (-) Correlation, this work.
dependence of the interaction parameters had to be taken into account. The resulting numbers are reported in Table VII. Figures 3 and 4 are to demonstrate the results of the correlation. For NH~-N~zSOI-HZO, calculated solubility limits for the formation of sodium sulfate are also included. Except at very high molalities of ammonia, the model describes the new results nearly within the experimental uncertainties. The results for NH3-NazSO4-HzO are correlated with an average deviation in the total pressure of 2.8%. The maximum relative deviation is 14% at T = 333.18 K and p = 0.16MPa corresponding to an absolute
Ind. Eng. Chem. Res., Vol. 32, No. 8,1993 1785 01
B 5a OOE
006
0
0.04
002
IIn
0. 8
303
308
313
310
TI K
Figure 5. Solubility of ammonia in aqueous solutions of sodium sulfate. ( 0 )Experimental results, Perman (1901). (-) Calculated results, thia work.
deviation of 22 kPa. Similar results are obtained for "3(NH&304-H20 = 3.2%, )APlrelwmax = le%, IAplab,max = 17.5 kPa a t T = 353.11K a n d p = 0.11 MPa).
(IGId
Comparison with Literature Data
"0
5
10
20
Figure 6. Solubility of sodium sulfate in aqueous ammoniacal solutions. (0) Experimental results, D'Ans and Schreiner (cf. Linke and Seidell, 1965). ( 0 )Experimental results, H ill and Koucks (cf. Linke and Seidell, 1965). (A)Experimental results, Belopolskii et al. (cf. Linke and Seidell, 1965). (-) calculated results, this work.
that composition, the correlation of the present work predicts a partial pressure of 2.1 kPa whereas Gaus (1900) reports a value of 1.92 kPa. Benoit (1961)investigated the solubility of ammonia in aqueous solutions of ammonium sulfate at temperatures between 298.15 and 371.1 K. Unfortunately, the partial pressures of ammonia were only given in small figures which cannot be evaluated with sufficient accuracy. Several investigations on the solubility of strong electrolytes in aqueous ammoniacal solutions are known (cf. Silcock, 1979). As an example, Figure 6shows the solubility limits of ammonium sulfate in aqueous ammoniacal solutions a t 298.15 K calculated from the correlation presented here together with experimental results as taken from Silcock's (1979)compilation. Obviously, there are large discrepancies between the results reported by D'Ans and Schreiner (1910), Hill and Koucks (1937), and Belopolskii et al. (1928)(cf. Linke and Seidell, 1965).The correlation of the present work is in good agreement with the data of D'Ans and Schreiner (1910). In view of the discrepanciesbetween the experimentalresults of different authors and taking into account that the correlation of the present work was extrapolatedto 298.15K, it is obvious that further experimental work on solubility limits of strong electrolytes in ammoniacal solutions is required. Clegg and Brimblecombe (1989)regressed interaction parameters for Pitzer's model from salt solubility, partial pressure, and partitioning data a t temperatures around 298 K. Using these interaction parameters for "3(NH4)2SO4-H2OYthe calculated total pressures tend to overestimate the salting-out effect on ammonia especially at higher temperatures (cf. Figure 7).
Literature data on the solubility of ammonia in aqueous solutions of sodium or ammonium sulfate are rather scarce. All published data for the total pressure or the partial pressure of ammonia were reported at temperatures below those investigated here. Perman (1901)measured the solubility of ammonia in aqueous solutions of sodium sulfate at temperatures between 298.15 and 319.15K and pressures up to 90 kPa. Figure 5 shows a comparison with the correlation of the present work. At the lowest molality of ammonia investigated (about 6 m),the correlation predicts pressures which are typically about 3-4% below Perman's results. Larger deviations (up to 8% ) are observed for = 9.5 mol/kg and l f i ~ ~ f =i ~0.38 , mol/kg, e.g., for a series of measurements which-following that author-is not as precise as the others because the molality of ammonia could not be determined properly. At the highest molality of ammonia (about 12.5m)a good agreement between the correlation and the experimental results reported by Perman (1901)is observed. The relative deviations for the total pressure do not exceed 5 96. At this molality of ammonia,the model predicts the formation of a solid phase of sodium sulfate for the whole temperature range investigated. The average relative deviation for the total pressure reported by Perman (1901)and that calculated from the present correlation is 3.8%. If one rejects the series of measurements at = 9.5 mol/kg and ? b ~ ~= f0.38 i ~ ~ moltkg, the average deviation reduces to only 2.3%. Conclusions Gaus (1900) investigated the salting-out effect on The solubility of ammonia in aqueous solutions of ammonia for several salts at 298.15K. For NHs-(NH4)2sodium sulfate and ammonium sulfate was determined by SO4-Hz0, a single data point for the partial pressure of a synthetic method in a wide range of temperature and ammonia over an solution containing 1 mol of NH3 and composition. The modification of Pitzer's model proposed 0.4 mol of (NH4)2S04 per kg of water was reported. For
1786 Ind. Eng. Chem. Res., Vol. 32,No. 8,1993 I
/
3,
0
I
I
k = Boltzmann constant
K, = solubility product for solid phase M = molar mass (kg/mol) mi = overall molality of component i mi = true molality of component i N = number of data points N A = Avogadro number ni = number of moles of component i p = total pressure qi = parameters for temperature dependence of ionic interaction parameters R = universal gas constant s = entropy T = temperature Vi = parameters for the temperature dependence of dielectric constant u = internal energy u = partial molar volume x = variable in Pitzer’s equation y = mole fraction in vapor zi = number of charges of component i
a
0
10
20
ENH3 /(mol,kg-’) Figure 7. Solubility of ammonia in aqueoussolutionsof ammonium sulfate. (0,0 , A, V, 0) Experimental results, this work. (-) Correlation, Clegg and Brimblecombe (1989).
by Edwards et al. (1978) was used to describe the results. The model was extended to include the coexistence of one or more solid phases. Interaction parameters were determined from the new measurements. A comparison with the very limited literature data in nearly all cases yields a good to fair agreement.
Acknowledgment Financial support of this investigation by the government of the Federal Republic of Germany (BMFT Grant No. 0326558 A), BASF AG, Ludwigshafen, and Lurgi AG, Frankfurt, is gratefully acknowledged. Nomenclature A,, B,, C,, D, = coefficients for temperature dependence of solubility product A+ = Debye-HQckel parameter for the osmotic coefficient al, ..., (26 = coefficients in Wagner’s equation for the vapor pressure of pure water a, b = coefficientsfor temperature dependence of interaction parameters ai = activity of component i aq = in aqueous solution b = parameter in modified Debye-Hiickel expression b l , ..., be = coefficientsin Wagner’s equation for the density of pure water Bi = second virial coefficient B($) = “observable” combination of binary interaction parameters C+ = interaction parameter in Pitzer’s equation c, = heat capacity at constant pressure D = relative dielectric constant d,, d, dl,..., d5 = coefficients in Wagner’s equation for the entropy and enthalpy of pure water e = charge of proton f1, fi, f3 = functions of ionic strength in Pitzer’s equation G E = excess Gibbs energy = Henry’s constant of component i in water (on molality scale) h = enthalpy I = ionic strength
Greek Letters a,a0 = constants in Wagner’s equation for the enthalpy and entropy of pure water 01 = constant in Pitzer’s equation P), = binary interaction parameters in Pitzer’e equation I? = “observable”combination of ternary interaction parameters y = activity coefficient eo = vacuum permittivity 19 = reduced temperature, cf. eq 36 X i j = binary interaction parameter in Pitzer’s equation pi = chemical potential of component i v+, v- = number of cations and anions in salt MX ?r = number of phases p a = mass density of liquid water 7 = ternary interaction parameter in Pitzer’s equation cp = fugacity coefficient cp, cpo = constants in Wagner’s equation for the enthalpy and entropy of pure water Subscripts abs = absolute c = critical property cal = calculated exp = experimental f = formation G = gas i, j , k = component i, j , k liq = liquid MX = salt MX max = maximum min = minimum R = reference re1 = relative 8 = salt w = water Superscripts s = saturation tot = total 0 = standard state * = normalized to infinite dilution m = infinite dilution
ILGI~~ = (l/mxf=&k,,A - Pk,exp(= definition of average absolute deviation
Ind. Eng. Chem. Res., Vol. 32, No. 8,1993 1787
IGln,= ( l / m ~ : l l @ & , d- Pk,sxp)/P&,expl= definition of average relative deviation
Appendix 1: Brief Outline of Pitzer's Model Pitzer's (1973)equation for the excess Gibbs energy of an aqueous, salt-containing system is
TM,M,X
from the reported values for C6: TM,M= ~ (2112/6)6
(23)
Appendix 2: Interaction Parameters for Pitzer's Equation This section reports values for the temperature dependence of ionic interaction parameters for sodium sulfate as reported by Rogersand Pitzer (1981). These parameters are consistent with b = 1.2. TR = 298.15 K.
The function f l ( I ) is a modified Debye-Htickel term
41 f l ( I )= -A#T ln(1 + bI1l2)
(14)
where I is the ionic strength 2
ag'"
-2q,T2-qBTR 2 - q 7 T ~ +
a T ) T=TR
Aij(I) is the ionic strength dependent second virial coefficient:
Aij(I) =
a$) + B 3 2 ( x )
(17)
are binary interaction parameters. The where @): and function f 2 is defined as 2
f z ( x ) = -(1X2
(1
+ x)e")
)
526q8( TR& ? 6 3 2(TR263 - 263)2 (25)
The empirical constant b = 1.2 for all electrolytes. A6 is the Debye-Hiickel parameter for the osmotic coefficient
+
'12(
T Z1 E -
T R - 263
) (26)
680q13( ( T - i 8 0 ) T - (TR-6 8 0 ) T ~
(18)
where x = d I 2 . For salts considered here, a = 2.0. Differentiation of eq 13 yields the activity coefficient of the dissolved species i: In 7;= -A,z: 1
+ bI'/'
b
where f 3 is defined as
The activity of water turns out to be
For systems containing a single salt M,,X,-, the binary and ternary parameters involving two or more species of the same sign of charge are usually neglected. The ternary parameters T M , X ~ T, M , M ~are usually reported as third virial coefficients 0 for the osmotic coefficient. Instead of rewriting eqs 19 and 22 in terms of 0, we preferred to set TM,X,X to zero and calculated the ternary parameter
0.01869 1.0994 0.005549 0.002349 0.005958 -0.000479 -1.03611 X 1od 3.00299 X lea -1.43441 X 10'
98 t~g 910
911
418 918
914 916
-6.66894XlO-1 -3.235513 X lo-' 6.76652 X le1 -1.88769 X 101 -2.06974 X le1 1.46744X 108 5.14316 X 1o-b 3.45791 X le'
Appendix 3: Dielectric Constant of Pure Water The relative dielectric constant of water is (Bradley and Pitzer, (1979)):
1788 Ind. Eng. Chem. Res., Vol. 32, No. 8, 1993
D(T,p) = U,exp(U,T
+ U3?a)+ C ( T ) In (B:;::L) (30)
where
of the chemical potentials of the involved species is required. Standard thermodynamics yields the equation to calculate the change of the chemical potential of species i from a reference temperature TR to T at constant pressure:
I .
U1 3.4279X 102 Ur -2.0525 Uz -5.0866X le Us 3.1159X 108 9.4690X
le7 ue
-1.8289X 10'
U7
Us
ug
-8.0325 X 103 4.2142X 108 2.1417
In these equations, p is the pressure in bar. Note: In the range investigated here, p was set equal to the saturation pressure of pure water.
where p i ( T ~and ) s~(TR) are the chemical potential and entropy at TR. The heat capacity at constant pressure cp,i is a function of temperature. The following expressions as taken from Pitzer (1987) were used for the temperature dependence of the heat capacity of NazSO~(H20)10(s) and Na,SOr(aq):
Appendix 4: Equations for the Vapor Pressure pa, Saturated Liquid Density p&, Entropy , ' s and
Enthalpy h' of Pure Water
(J.rnol-'.K-')
Equations by Saul and Wagner (1987):
b,81s/3
+ b5843/3+ b,8110/3 (34) (35)
s;=(p+--
where (37)
-
6045 (42) (T - 263)
~ i ,(Tf -TR)S~ + [&.(T)
- ~ L ( T R ) ~ -s ~ ~ + w ~ ~ T[iw(T)- S L ( T R ) ~ S ~(43) ~+W~~~
(36)
8 = 1- TIT,
+ 7.6405T -
Besides the chemical potentials of the solid phase and the dissolved salt, the chemical potential of pure liquid water must be known. Saul and Wagner (1987) give equations for the internal energy and entropy of saturated liquid water (cf. Appendix 4). As Saul and Wagner (1987) use reference states for enthalpy and entropy (u; = 0, S& = 0 at the triple point of water) different from those required here, the final equation for the chemical potential of saturated liquid water is pW=
1 dPi P; d T
= -1206.2
1.23672 X lO-,?a
5 = 1+ b,O1I3 + b,O2l3 + b385/3+ Pc
0
C~,N@04(w)
where pLJ and s z are the standard Gibbs energy of formation and the standard entropy of saturated liquid water. The followingnumbers were used for the standard Gibbs energy and standard entropy (Pitzer, (1987)): species i Na+(aq) S04Yaq) NazS0dHzO)ds) HzO(liq)
- &(RT,) 105.651 300.386 1471.15 95.6635
s!/ R 7.096 2.42 71.21 8.409
Literature Cited Benoit, R. L. Ammonia vapor pressure of ammoniacal Solutions of ammonium and copper(I1) sulfates. J. Chem. Eng. Data 1961,6, -7.86823 1.83991 -11.7811 22.6705
a6
ae
bl
bz
bs
-15.9393 1.77516 1.99206 1.10123
b4
bs be
-0.512506 -1.75263 -45.4485 -6.75615 X 106
161-166.
Bieling, V.; Rumpf, B.; Strepp, F.; Maurer, G. An evolutionary optimization method for modeling the solubility of ammonia and carbon dioxide in aqueous solutions. Fluid Phase Equilib. 1989, 53,251-259.
lo00 J/kg
di
"dTc
dz
-1135.481615639 2318.9142
da d4 ds
-5.71756 X 10-8 2689.81 129.889 -137.181 9.68874 X le1
Critical properties of water: p c = 22.064 MPa; Tc= 647.14 K; pc = 322.0 kg/m3.
Appendix 5: Solubility Product for the Formation of NazSOd*(HzO)lo To calculate the solubility product for the formation of a solid phase M,+X,(H20),,the temperature dependence
Bradley, D. J.; Pitzer, K. S. Thermodynamics of electrolytes. 12. Dielectric properties of water and Debye-Hackel parameters to 350 OC and 1 kbar. J. Phys. Chem. 1979,83, 1699-1603. Brelvi, S. W.; OConnell, J. P. Corresponding states correlations for liquid compressibilityand partial molal volumes of gases at infinite dilution in liquids. MChE J. 1972, 18, 1239-1243. Clegg, S. L.; Brimblecombe,P. Solubility of ammonia in pure aqueous and multicomponent solutions. J. Phys. Chem. 1989,93,72377248.
Clifford,I. L.; Hunter, E. The system ammonia-waterat temperatures up to 150 C and at pressures up to 20 atmospheres. J. Phys. Chem. 1933,37,101-118. Dymond, J. H.; Smith, E. B. The uirial coefficientsofpuregasesand mixtures; Oxford University Press: Oxford, UK, 1980; pp 208213.
Ind. Eng. Chem. Res., Vol. 32, No. 8,1993 1789 Edwards, T. J.; Maurer, G., Newman, J.; Prausnitz, J. M. Vaporliquid equilibria in multicomponent aqueous solutions of volatile weak electrolytes. AIChE J. 1978,24,966-976. Gaus, W. f h r den Einfluee von Neutralealzen auf die Tension des Ammoniaks aus wheriger Ldeung. Anorg. Chem. 1900,25,236264.
Gilleepie, P.; Wilson, G. M. 'Vapor-liquid and liquid-liquid equilibria: water-methane, water-carbon dioxide, water-hydrogen Gas Prosulfide, water-n-pentane, water-methane-n-pentane"; cessom Association, Research Report 48, Tuba, OK, 1982. Guillevic,J. L.; Richon, D.; Renon, H.Vapor-liquid equilibrium data for the binary system water-ammonia at 403.1,453.1 and 503.1 K up to 7.0 MPa. J. Chem. Eng. Data 1985,30,332-335. Hayden, J.; OConnell, J. P. A generalized method for predicting second virialcoefficienta. Znd. Eng. Chem.ProcessDes. Dev. 1975, 14,209-216.
Linke, W. F.; Seidell, A. Solubilities of inorganic and metal organic compounds, 4th ed.;American Chemical Society: Washington, DC, 1965; Vols. 1and 2. Lo Surdo, A.; Alzola, E. M.; Mdero, F. J. The (p,v,T) properties of concentrated aqueous electrolytes. I. Densities and apparent molar volumes of NaCl, N a 8 0 4 ,MgCl2 and MgSO4 solutions from 0.1 mol/kg to saturation and from 273.16 K to 323.15 K. J. Chem. Thermodyn. 1982,14,649-662. Mollier, H. Dampfdruck von wmrigen Ammoniaklbungen. VDZ-
2. 1908,52, 1315-1320. MiUler, G.; Bender, E.; Maurer, G. Das Dampf-Flksigkeitqleichgewicht des ternben Systems Ammoniak-Kohlendioxid-Wasser bei hohen Wassergehaltenim Bereichzwischen373 and 473 Kelvin. Ber. Bunsen-Ges. Phys. Chem. 1988,92,148-160. Nikolski, B. P. Handbuch des Chemikers; VEB Verlag Technik: Berlin, 1959; Vol. 3. Pawlikowski, E. M.; Newman, J.; Prausnitz, J. M. Phase equilibria for aqueous solutions of ammonia and carbon dioxide. Znd. Eng. Chem. Process Des. Dev. 1982,4,764-770. Perman, E. P. Influence of sodium sulfate on the vapor pressure of aqueous ammonia solution. J. Chem. SOC.1901, 79,725-729. Pierre, B. Total vapor pressure in bar over ammonia-water solutions. Kyltek, Tidsk. 1989,14, 89-90.
Pitzer, K. S. Thermodynamics of electrolytes. 1. Theoretical basis and general equations. J. Phys. Chem. 1973, 77,268-277. Pitzer, K. S. Athermodynamic model for aqueous solutions of liquidlike density. Rev. Mineral. 1987,17,97-142. Rizvi, 5.S. H.; Heidemann, R.A. Vapor-liquidequilibriainammoniawater system. J. Chem. Eng. Data 1987,32,183-191. Rogers, P. 5. Z.;Pitzer, K. S. High-temperature thermodynamic properties of aqueous sodium sulfate solutions. J. Phys. Chem. 1981,86,2886-2895.
Rumpf, B. Untersuchungen zur Ldelichkeit reagierender Gase in Waseer und salzhaltigen whrigen XAeungen. Dissertation, Universiat Kaiserslautern, 1992. 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 P h e Equilib. 1992,81,241-260. Rumpf, B.; Maurer, G. An experimental and theoretical investigation on the solubility of carbon dioxide in aqueous solutions of strong electrolytes. Ber. Bunsen-Ges, Phys. Chem. 1993,97,85-97. Saul, A.; Wagner, W. International equations for the saturation properties of ordinary water substance. J.Phys. Chem.Ref.Data 1987,16,893-901.
Silcock, H.L. Solubilities of inorganic and organic compounds; Pergamon: Oxford, 1979;Vol. 111, Part 111. Wilson, T. A. Properties of aqua ammonia Part 1. Refrig.Eng. 1924, 10, 248-252. Wilson, G. M.; Owens, R. S.; Roe, M. R. 'Sour water equilibria: Ammonia volality down to ppm levels. Effect of electrolytes on ammoniavolatility"; Gas Processors Association,Research Report 34, Tulsa, OK, 1978. Wucherer,J. MessungvonDruck, Temperatur and Zusammensetzung der fliiaaigen und dampff6rmigen Phase von Ammoniak-Wassergemiechen im SHttigungszustand. 2.Gesante KBlte-Znd. 1992,39, 97-140.
Received for review December 1, 1992 Revised manuscript received March 23, 1993 Accepted April 7, 1993
