5112
Ind. Eng. Chem. Res. 2008, 47, 5112–5118
Influence of a Single Salt (NaCl/Na2SO4) on the Solubility of Ammonia in Liquid Mixtures of (Water + Methanol) ´ lvaro Pe´rez-Salado Kamps, and Gerd Maurer* Dirk Scha¨fer,† Mathias Vogt, A Applied Thermodynamics, UniVersity of Kaiserslautern, D-67653 Kaiserslautern, Germany
New experimental results are reported for the influence of two single salts (sodium chloride and sodium sulfate) on the solubility of ammonia in liquid mixtures of water and methanol at 353 and 393 K. The mole fractions of methanol in the (gas-free and salt-free) solvent mixture of water and methanol were about 0.25, 0.5, and 0.75 in the experiments with sodium chloride and about 0.05 and 0.25 in the experiments with sodium sulfate. The molality of the salt varied between about 0.25 and 2 (0.15 and 1) mol/kg of the solvent mixture in the systems with sodium chloride (sodium sulfate). The maximum molality of ammonia was about 6.7 mol/kg of (water + methanol) for both temperatures and for both salts. The maximum total pressure above the liquid solutions was about 0.3 MPa (1 MPa) in the system containing sodium chloride at 353 K (393 K) and about 0.2 MPa (0.7 MPa) in the system with sodium sulfate at 353 K (393 K). The experimental results are used to test a thermodynamic framework which allows the influence of both single strong electrolytes on the solubility of ammonia in liquid mixtures of water and methanol to be predicted. The prediction results are in good agreement with the new experimental data. Introduction The simultaneous solubility of ammonia and so-called “sour gases” such as carbon dioxide, sulfur dioxide, and so forth in (aqueous as well as aqueous/organic) mixed solvents, which might also contain some strong electrolytes, must be known for the design of a variety of processes in the chemical and oil-related industries. Due to chemical reactions, such phase equilibria are rather complex. Developing a reliable model for the correlation (or even prediction) of the vapor-liquid-solid equilibrium in such systems is a difficult task. That task has to be based on a reliable and comprehensive database, which has to be determined experimentally. In previous work, we investigated the simultaneous solubility of ammonia and a sour gas (e.g., carbon dioxide) in aqueous solutions without as well as with additionally dissolved strong electrolytes. The thermodynamic model used for describing such phase equilibria relies on an extension of Pitzer’s model1 for the excess Gibbs energy of aqueous solutions of strong electrolytes. It requires a rather large number of binary and ternary interaction parameters. Some of these parameters can be determined from binary data {e.g., on the solubility of a single gas in water (e.g., ammonia in water) or from the activity of water in aqueous solutions of the dissolved salt (e.g., NaCl or Na2SO4 in water)} or from ternary data {e.g., on the influence of a dissolved salt on the solubility of a gas in water (e.g., ammonia in aqueous solutions of sodium chloride2 or sodium sulfate3,4) and on the vapor-liquid equilibrium of the system (ammonia + carbon dioxide + water)5}. As was shown previously, the thermodynamic model is able to predict correctly the influence of a strong electrolyte on the simultaneous solubility of ammonia and carbon dioxide in water.6,7 In ongoing work the thermodynamic framework is being extended from aqueous solutions to aqueous/organic solvent mixtures. In a first step we investigated the solubility of carbon dioxide in liquid mixtures of (water + methanol)8,9 as well as in liquid mixtures of (water + acetone).10 The influence of some * To whom correspondence should be addressed. Phone: +49 631 205 2410. Fax: +49 631 205 3835. E-mail:
[email protected]. † ¨ V-Su¨d, 68167 Mannheim, Germany. Current address: TU
single strong electrolytes (sodium chloride and sodium sulfate) on the vapor-liquid equilibrium of (water + methanol) was investigated as well.8,11,12 Furthermore, we investigated the influence of those two single strong electrolytes on the solubility of carbon dioxide in liquid mixtures of (water + methanol).13,14 In more recent publications that work was extended to the solubility of ammonia in liquid mixtures of (water + methanol).15,16 Here, we present new experimental data for the solubility of ammonia in liquid mixtures of (water + methanol) that also contain those two single strong electrolytes (sodium chloride or sodium sulfate). No such data can be found in the open literature. The temperature amounted to 353 and 393 K. The mole fraction of methanol in the gas-free and salt-free solvent mixture (of water and methanol) was about 0.25, 0.5, and 0.75 in the experiments with sodium chloride (about 0.05 and 0.25 in the experiments with sodium sulfate) as the dissolved strong electrolyte. The molality of the single salt varied between about 0.25 and 2 (0.15 and 1) mol per kilogram of the solvent mixture of (water + methanol) in the systems with sodium chloride (sodium sulfate). The solubility of the salts decreases strongly with increasing mole fraction of methanol in the liquid solvent mixture. Therefore, the experiments with sodium sulfate were limited to rather low methanol mole fractions. Ammonia is salted-out by both salts, and vice versa, ammonia reduces the solubility of the salts in the aqueous solvent mixtures. In the experimental series with sodium chloride, the maximum molality of ammonia (as well as of the salt) in the solvent mixture was always sufficiently low to avoid the precipitation of the salt. However, in the series with sodium sulfate, this may not always have been the case. The maximum molality of ammonia was about 6.7 mol/kg of (water + methanol) for both temperatures and for both single salts. The maximum total pressure above the liquid solutions was about 0.3 MPa (1 MPa) in the system containing sodium chloride at 353 K (393 K) and about 0.2 MPa (0.7 MPa) in the system with sodium sulfate at 353 K (393 K). The experimental results are used to test a thermodynamic model,8 which allows the influence of both single electrolytes on the solubility of ammonia in liquid mixtures of (water +
10.1021/ie071169p CCC: $40.75 2008 American Chemical Society Published on Web 05/29/2008
Ind. Eng. Chem. Res., Vol. 47, No. 15, 2008 5113 Table 1. Estimated Uncertainty ∆pi for the Experimental Results for the Partial Pressures pi of water (i ) W) and methanol (i ) M) water
methanol
pW
∆pW, kPa
pM
∆pM, kPa
pW, kPa e 40 40 < pW, kPa e 100 100 < pW, kPa
3 5 10
pM, kPa e 20 20 < pM, kPa e 50 50 < pM, kPa e 120 120 < pM, kPa
3 5 10 15
methanol) to be predicted. The prediction results are in good agreement with the new experimental data. Experimental Investigation Apparatus and Method. The type of experimental arrangement was already used in previous investigations for example on the simultaneous solubility of ammonia and carbon dioxide in aqueous solutions5 and on the solubility of ammonia in pure liquid methanol15 as well as in liquid mixtures of (water + methanol).16 Therefore, only an outline is repeated here. An evacuated thermostated cell (with a volume of about 1.6 dm3) was charged with a known amount (about 1 kg) of the salt-containing aqueous solution of methanol. The composition of that solvent mixture was known from its gravimetrical preparation. Afterward, ammonia was added step by step. The amount of ammonia added was known as ammonia was taken from a small tank that was weighed before and after each filling step. After each step, the phases were equilibrated before temperature, pressure, and vapor-phase volume were measured, and small vapor phase samples were taken and analyzed by online gas chromatography. The results were used together with the truncated virial equation of state for the vapor phase to determine the amounts of ammonia, water, and methanol in that vapor phase. The amounts of every single component in the liquid phase were determined from those results and the know amounts (and the composition) of the feed. The maximum absolute uncertainties of the experimental results are estimated to be 0.1 K for the temperature, 0.5 kPa for the total pressure, 0.001 mol · kg-1 for the molality of the salt in the liquid phase, and 0.0004 for the liquid phase mole fraction of a solvent component (on a gas- and salt-free basis). The relative uncertainty of the molality of ammonia in the liquid phase is estimated to be 0.5% at a maximum. The estimated absolute uncertainties for the partial pressures of water and methanol are given in Table 1. As the total pressure above the liquid is measured with a low uncertainty, the absolute uncertainty of the experimental results for the partial pressure of ammonia is estimated as the sum of the absolute uncertainties of the partial pressures of water and methanol. Substances and Sample Pretreatment. Ammonia (mole fraction g 0.99999) was purchased from Messer-Griesheim, Ludwigshafen, Germany. Methanol (mass fraction g 0.998) was purchased from Merck KGaA, Darmstadt, Germany. Methanol and double-distilled water were degassed before use. Sodium chloride (mass fraction g 0.995) and sodium sulfate (mass fraction g 0.99) were purchased from Carl Roth GmbH, Karlsruhe, Germany, and Merck KGaA, Darmstadt, Germany, respectively. Both salts were degassed and dried under vacuum. Experimental Results Tables 2 and 3 give the detailed experimental results for the solubility of ammonia in aqueous solutions of methanol that also contain either sodium chloride (Table 2) or sodium sulfate (Table
3) at temperatures T ≈ 353.1 K and T ≈ 393.2 K. The mole fraction of methanol in the gas-free and salt-free solvent mixture x˜M varied from 0.25 to 0.75 when sodium chloride was the dissolved electrolyte and from 0.05 to 0.25 when sodium sulfate was the dissolved electrolyte. The maximum molality of sodium chloride m j NaCl was about 2 mol · kg-1 in solvent mixtures with x˜M ≈ 0.25 and about 0.25 mol · kg-1 in solvent mixtures with x˜M ≈ 0.75. The maximum molality of sodium sulfate m j Na2SO4 was about 1 mol · kg-1 in solvent mixtures with x˜M ≈ 0.05 and about 0.15 mol · kg-1 in solvent mixtures with x˜M ≈ 0.25. The molality of ammonia in the liquid phase mNH3 ranged between about 1 and 6.7 mol · kg-1, resulting in total pressures p between about 0.1 MPa (0.07 MPa) and 1 MPa (0.7 MPa) with sodium chloride (sodium sulfate), respectively. In Tables 2 and 3, pNH3, pW, and pM denote the partial pressures of ammonia (NH3), water (W), and methanol (M) in the gaseous phase. Thermodynamic Modeling of the Gas Solubility Although the thermodynamic framework was described for a similar system (solubility of carbon dioxide in aqueous solutions of methanol that also contain a single strong electrolyte)13,14 the main ideas and equations are repeated here to allow for a better understanding. For the solVent components water and methanol, the reference state for the chemical potential in the liquid phase is the pure liquid component at temperature and pressure of the mixture. For the solute components ammonia and the salt (NaCl or Na2SO4), the reference state is a one molal solution of that gas (that salt) in the liquid, salt-free (gas-free) solvent mixture of (water + methanol), where the gas (the salt) experiences the same interactions as in infinite dilution in that solvent mixture. The vapor-liquid equilibrium condition results in the extended Raoult’s law for each solvent component psi φsi
[
]
Vi(p - psi ) exp ai ) yipφi (i ) W, M) RT
(1)
and in the extended Henry’s law for ammonia kH,NH3(T, p, x˜M)aNH3 ) yNH3pφNH3
(2)
pis, φis, and Vi are the vapor pressure, the fugacity coefficient of the saturated vapor, and the molar liquid volume, respectively, of a pure solvent component i at temperature T. R and p are the universal gas constant and the total pressure, respectively. ai is the activity of component i in the liquid phase. yi and φi are the mole fraction and the fugacity coefficient of component i in the vapor phase. The (molality scale based) Henry’s constant of NH3 in solvent mixtures of water and methanol kH,NH3(T, p, x˜M) is expressed as kH,NH3(T, p, x˜M) )
[
(0) kH,NH (T, x˜M) exp 3
∞ VNH (T, x˜M) · {p - ps(T, x˜M)} 3
RT
]
(3)
It depends on the temperature, the total pressure, and the composition of the gas- and salt-free solvent mixture. That composition is expressed through the mole fraction: x˜M )
nM ) 1 - x˜W nW + nM
(4)
nW and nM are the amounts of substance (the number of moles) (0) of water and methanol, respectively. kH,NH ˜ M) is Henry’s 3(T, x
5114 Ind. Eng. Chem. Res., Vol. 47, No. 15, 2008 Table 2. Experimental Results for the Vapor-Liquid Equilibrium of (Sodium Chloride + Ammonia + Water + Methanol) T, K
x˜M
m j NaCl, mol kg-1
mNH3, mol kg-1
pNH3, kPa
pW, kPa
pM, kPa
p, kPa
ppred, kPaa
353.0 353.1 353.0 353.2 353.1 353.1
0.2460 0.2460 0.2461 0.2461 0.2462 0.2462
2.005 2.005 2.005 2.004 2.004 2.004
0 1.358 2.417 3.713 4.800 5.939
0 18.8 40.4 70.7 90.4 115.6
32 34 34 30 33 32
75 73 67 64 61 59
106.4 125.7 141.7 164.7 184.2 205.9
105.4 126.1 143.1 166.5 186.7 209.4
353.1 353.1 353.1 353.1 353.1 353.2
0.5000 0.5001 0.5001 0.5002 0.5002 0.5002
0.733 0.733 0.733 0.733 0.733 0.733
0 1.215 2.522 3.652 4.864 6.030
0 17.3 48.0 76.5 108.4 138.7
26 28 27 26 25 25
106 107 101 95 92 89
132.0 151.6 175.6 198.1 224.9 253.4
133.2 153.3 177.8 200.8 227.5 256.0
353.1 353.1 353.1 353.1 353.1 353.1
0.7466 0.7467 0.7467 0.7467 0.7467 0.7467
0.255 0.255 0.255 0.255 0.255 0.255
0 1.657 2.876 3.983 4.975 5.869
0 37.0 73.9 107.1 139.6 170.3
18 19 17 17 17 16
137 132 126 123 117 115
154.6 188.2 216.9 246.3 273.7 300.7
155.2 189.9 218.4 246.8 273.8 299.9
393.2 393.2 393.0 393.0 393.2
0.2446 0.2449 0.2450 0.2451 0.2452
0.999 0.998 0.998 0.998 0.998
0 2.005 3.166 4.803 6.267
0 99.2 166.1 244.9 319.4
99 123 118 130 141
298 257 244 231 223
396.7 478.4 528.1 605.8 683.0
392.4 479.6 530.8 611.9 692.8
392.6 392.6 392.6 392.7
0.2460 0.2465 0.2466 0.2467
2.024 2.022 2.022 2.022
0 3.004 4.645 6.394
0 159.6 242.4 330.6
82 115 125 132
311 250 239 231
392.4 525.4 606.8 693.0
389.7 525.0 607.4 701.4
393.1 393.0 393.0 393.0 393.0 393.3 393.3 393.3
0.4969 0.4971 0.4972 0.4974 0.4975 0.4980 0.4982 0.4982
1.013 1.012 1.012 1.012 1.011 1.006 1.006 1.005
0 1.534 3.054 4.715 6.036 0 4.465 6.065
0 75.3 179.8 276.9 375.0 0 211.6 350.1
79 88 88 97 94 82 98 92
420 407 381 370 355 370 373 369
499.6 569.9 648.8 743.2 824.1 453.0 682.6 810.6
486.1 557.4 634.9 729.5 808.7 489.1 719.9 816.9
393.4 393.1 393.4 393.2 393.3 393.2 393.3
0.7617 0.7617 0.7618 0.7618 0.7618 0.7351 0.7353
0.370 0.371 0.370 0.370 0.370 0.356 0.356
0 1.401 3.294 4.472 5.846 0 6.730
0 32.9 162.8 261.5 377.7 0 453.5
57 60 59 54 51 63 55
511 552 532 512 498 495 472
568.5 645.6 753.6 827.6 926.7 557.5 980.7
566.9 638.5 756.8 832.2 930.8 557.6 980.8
a
ppred is the total pressure predicted from the model.
constant of NH3 in solvent mixtures of water and methanol at vanishing amounts of the gas in the liquid, that is, at the vapor ∞ pressure ps(T, x˜M) of that solvent mixture. VNH 3 is the partial molar volume of ammonia at infinite dilution in the solvent mixture. The vapor pressure and the molar volume of liquid methanol are calculated from correlation equations given by Reid et al.17 and Hales and Ellender,18 respectively. The vapor pressure and the molar volume of liquid water are calculated from correlation equations given by Saul and Wagner.19 The virial equation of state is used to calculate vapor phase fugacities. That virial equation was truncated after the second virial coefficient. The second virial coefficient Bii(T) of all pure components (ammonia, water, and methanol) are calculated from the correlation equations reported in refs 8 and 15. These equations are based on the experimental data compiled by Dymond and Smith,20 as recommended by Hayden and O’Connell.21 All mixed second virial coefficients Bij(T) (i + j) are estimated as proposed by the latter authors (for details, see ref 16).
The extension of Pitzer’s molality scale based equation for the excess Gibbs energy (GE) of aqueous electrolyte solutions1,22 to liquid solvent mixtures of two or more components (e.g., water + methanol) proposed by Pe´rez-Salado Kamps8 is applied here to calculate the activities of all (solute and solvent) species in the liquid phase. The equations are reported at full length in prior publications (for the gas solubility in salt-free as well as in salt-containing mixed solvents).8,13,14 Therefore, only a few essentials are repeated here. The activity of ammonia in the liquid solvent of water and methanol that also contains a salt Cυ+Aυ- (where υ+ and υare the stoichiometric coefficients of the cation and the anion of that salt, respectively) is the product of a dilution term and the activity coefficient of ammonia: aNH3 )
( ) mNH3 m°
γNH3
The activity coefficient of ammonia is:
(5)
( ) ( )
ln γNH3 ) 2 3
mNH3 m°
mNH3 m°
Ind. Eng. Chem. Res., Vol. 47, No. 15, 2008 5115 (0) βNH (T, x˜M) + 3,NH3
2
xi is the “true” mole fraction of a solvent component in the liquid mixture of (salt + ammonia + water + methanol) (cf. ref 21):
( )
µNH3,NH3,NH3(T, x˜M) + 2 3
( )
mCA (0) B (T, x˜M) + m° NH3,CA
mCA 2 ΓNH3,CA,CA(T, x˜M) + m° mNH3 mCA 6 Γ (T, x˜M) m° m° NH3,NH3,CA
( )( )
xi ) 1+
(6)
(0) βNH ˜ M) and µNH3,NH3,NH3(T, x˜M) describe the effects of 3,NH3(T, x interactions between ammonia molecules in the salt-free solvent mixture of water and methanol. These parameters are determined from experimental data for the solubility of ammonia in liquid (0) mixtures of (water + methanol). BNH ˜ M), ΓNH3,CA,CA(T, 3,CA(T, x x˜M), and ΓNH3,NH3,CA(T, x˜M) describe the effects of interactions between ammonia on one side and the ions of the salt Cυ+Aυon the other side in the solvent mixture. They have to be determined from experimental data for the solubility of ammonia in liquid mixtures of water, methanol, and that salt. The molalities of ammonia and the salt in the aqueous solution of methanol are abbreviated as mNH3 and m j CA, respectively, and mo ) 1 mol · kg-1. Thus, mNH3/mo and m j CA/mo are numbers which are equivalent to the numbers for the molalities of NH3 and Cυ+Aυ- in the solvent mixture. The activities of water, aW, and methanol, aM, are
ln aW ) ln xW - x˜M
( )(
(x) mCA ∂∆tGCA m° ∂x˜M
M/ RT
)]
(x) mCA ∂∆tGCA m° ∂x˜M
mNH3 m°
∂x˜M
)
mo
( ) [( ) ( M/ RT
)]
mNH3 m°
∂x˜M
)
mCA mo
(i ) W, M) /
M
(9)
M* is the (mean) relative molar mass of the solute-free solvent mixture divided by 1000. For the binary solvent mixture under consideration, it is / - M/W) M/ ) M/W + x˜M(MM /
(10) /
where MW ) 0.01801528 (for water) and MM ) 0.03204216 (for methanol). (x) (x) ∆tGNH 3 and ∆tGCA are the mole-fraction-scale-based molar Gibbs energies of transfer of ammonia and the salt, respectively, from pure water to the solvent mixture of water and methanol. Both depend on temperature, pressure, and the composition of (x) the (salt-free and gas-free) solvent mixture. ∆tGNH 3 can be expressed through the molality scale based Henry’s constant of ammonia in water as well as in liquid mixtures of (water + methanol):
(
(x) (T, p, x˜M) ) RT ln ∆tGNH 3
kH,NH3(T, p, x˜M) kH,NH3,W(T, p)
) ( ) - RT ln
M/ M/W
(11)
+ T,p
+ ln γW,UNIQUAC + ln γW,Pitzer + ln γW,conv
(x) ∂∆tGNH 3
( )]
+ (υ+ + υ-)
(x) ∆tGCA can be expressed through the molality scale based solubility product of the salt Cυ+Aυ- in water as well as in liquid mixtures of (water + methanol).
T,p
ln aM ) ln xM + x˜W
( )(
( ) [( ) (
(x) ∂∆tGNH 3
[( ) mNH3
x˜i
(7)
(x) ∆tGCA (T, x˜M) ) -RT ln
+ T,p
+ ln γM,UNIQUAC + ln γM,Pitzer + ln γM,conv
T,p
(8)
(
)
( )
ksp,CA(T, x˜M) M/ - (υ+ + υ-)RT ln / ksp,CA,W(T) MW (12)
(x) As usual, the influence of pressure on ∆tGCA as well on the aforementioned solubility products is neglected here. Subscripts UNIQUAC and Pitzer designate contributions from the UNIQUAC equation and from Pitzer’s equation, respectively, for the excess Gibbs energy GE. The contributions from
Table 3. Experimental Results for the Vapor-Liquid Equilibrium of (Sodium Sulfate + Ammonia + Water + Methanol) T, K
x˜M
m j Na2So4, mol kg-1
mNH3, mol kg-1
pNH3, kPa
pW, kPa
pM, kPa
p, kPa
ppred, kPaa
353.2 353.1 353.1 353.2 353.2 353.1 353.1 353.1 353.1 353.1 353.1 353.1 393.2 393.2 393.3 393.3 393.2 393.2 393.3 393.3 393.3 393.3
0.0492 0.0493 0.0493 0.0494 0.0494 0.0494 0.2481 0.2482 0.2483 0.2483 0.2483 0.2484 0.0482 0.0482 0.0483 0.0483 0.0484 0.2485 0.2484 0.2486 0.2487 0.2488
0.878 0.877 0.877 0.877 0.877 0.877 0.152 0.152 0.152 0.152 0.152 0.152 0.998 0.999 0.998 0.998 0.998 0.151 0.151 0.151 0.151 0.151
0 1.468 2.490 3.914 4.530 5.934 0 1.352 2.436 3.564 4.798 5.982 0 1.670 3.160 4.734 6.665 0 1.558 3.076 4.849 5.837
0 27.3 49.2 77.9 91.4 119.9 0 19.8 41.6 63.3 87.8 114.4 0 50.6 149.2 254.4 363.3 0 27.2 106.7 208.6 274.3
39 43 43 43 42 41 33 38 37 37 37 36 173 204 196 184 175 139 154 161 167 160
30 23 20 19 18 17 72 66 62 59 56 53 93 97 88 79 69 260 288 270 247 241
68.7 93.1 112.0 139.3 151.3 177.1 105.0 123.5 140.6 159.0 180.9 203.7 265.9 351.4 432.5 517.5 607.0 398.4 468.5 537.5 622.5 676.1
66.0 92.1 111.3 139.5 151.8 176.4b 103.8 123.6b 140.5b 159.5b 181.7b 204.6b 260.3 348.8 431.2 518.3b 605.9b 394.2 461.2 530.3b 616.0b 667.1b
a
ppred is the total pressure predicted from the model. b Denotes predicted precipitation of Na2SO4.
5116 Ind. Eng. Chem. Res., Vol. 47, No. 15, 2008
the UNIQUAC model (ln γW,UNIQUAC and ln γM,UNIQUAC) do not depend on the dissolved amount of the gas or on the dissolved amount of the salt. These contributions as well as the pure-component UNIQUAC size and surface parameters (for water and methanol) and the temperature dependent binary UNIQUAC parameters for interactions between water and methanol were taken from previous work.10 Because Pitzer’s GE equation is based on the molality scale, whereas the UNIQUAC equation is based on the mole fraction scale, socalled conversion terms (ln γW,conv and ln γM,conv) have to be considered in eqs 7 and 8 (cf. refs 8 and 13). ln γi,conv ) -
{
} [ { } ]
mNH3
mNH3 mCA + (υ+ + υ-) + M/ + ln 1 + m° m° m° mCA (υ+ + υ-) M/ (i ) W, M) (13) m°
The contributions from Pitzer’s equation to the activity coefficients of the solvent components water and methanol (ln γW,Pitzer and ln γM,Pitzer) are ln γW,Pitzer ) -M/WA - M/x˜MB
(14)
/ ln γM,Pitzer ) -MM A + M/x˜WB
(15)
where A ) (If ′ - f) +
( ) mNH3
( )
2
(0) βNH +2 3,NH3
mNH3
3
µNH3,NH3,NH3 + m° m° 2 mCA (0) (1) 2υ+υ+ βC,A exp(-2√I)} + {βC,A m° mCA 3 mCA mNH3 (0) φ 2 (υ+υ-)3/2CCA +2 B + m° m° m° NH3,CA mCA 2 mNH3 mCA mNH3 2 6 ΓNH3,CA,CA + 6 ΓNH3,NH3,CA (16) m° m° m° m°
( )
( ) ( )( ) ( )( ) ( )( ) ( ) ( ) ( ) ( ) ( ){ } ( )( ) ( ) ( )( ) ( )( )
∂f B) + ∂x˜M I
(0) mNH3 2 ∂βNH 3,NH3
m°
2υ+υ-
mCA m°
∂x˜M
2
mNH3 3 ∂µNH3,NH3,NH3
+
∂x˜M
m°
(0) (1) ∂βC,A ∂βC,A + g 2√I ∂x˜M ∂x˜M
The ionic strength I is calculated on the molality scale:
f′)
(
]
√I 2 + ln(1 + b√I) 1 + b√I b
(21)
I3⁄2
(22)
(1 + b√I)
∂f f 1 ∂d 3 ∂ε ) ∂x˜M I 2 d ∂x˜M ε ∂x˜M
]
(23)
2 [1 - (1 + x) exp(-x)] (24) x2 (1) φ β(0) C,A, βC,A, and CCA are binary and ternary interaction parameters between cations and anions of the salt Cυ+Aυ-. They also depend on the temperature and on the solute-free solvent mixture composition. These parameters are usually determined from experimental information on the mean ionic activity coefficient of the salt {from electromotive force (emf) measurements and salt solubility measurements}.8 During the calculation of the solubility of ammonia in a saltcontaining solvent mixture, one has to check for the solubility limit of that salt (or any hydration form of that salt) in the liquid mixture (ammonia + water + methanol). The present work takes account of the solubility of NaCl, Na2SO4, and Na2SO4 · 10H2O.16 That calculation requires an expression for the solubility product Ksp,Cυ+Aυ- · (H2O)υW(T, x˜M) of the salt Cυ+Aυ· (H2O)υW (which is based on the molality scale here) and an expression for aCυ+ · aAυ-, where aC and aA are the activities of the cation C and the anion A, respectively. g(x) )
+ υ+ υaυC+ · aAυ- ) υ+ υ-
(
mCA
)
(25)
(υ++υ-)
· γ(,CA
(26) mo γ(,CA is the mean ionic activity coefficient of the salt Cυ+Aυin the liquid mixture of (ammonia + water + methanol) on a molality scale basis. It is also calculated from the equation for the Gibbs excess energy resulting in (cf., e.g., ref 13)
[
(υ+z+2 + υ-z-2 ) 1 f′ + (υ+ + υ-) 2 mCA (0) (1) ( 2 υ+υ-{2βC,A + βC,A h 2√I)} + mo mNH3 mCA 2 φ (0) 3 (υ+υ-)3⁄2CCA +2 BNH + o 3,CA m mo mNH3 mCA mNH3 2 Γ + 3 ΓNH3,NH3,CA 6 NH ,CA,CA 3 mo mo mo
ln γ(,CA )
( ) ( ) ( )( )
(18)
)
[
( ) [
f(I, x˜M) is the Debye-Hu¨ckel term, as modified by Pitzer:
e2 1 Aφ ) (2πNAFm°)1⁄2 3 4πε0εrkBT
) -2Aφ
If ′ -f ) -2Aφ
(17)
where b ) 1.2. Aφ is the Debye-Hu¨ckel parameter:
x˜M
W
+
4I ( ln 1 + b√I) b
( ∂I∂f )
υυW Ksp,Cυ+Aυ-·(H2O)υ (T, x˜M) ) aυ+ C · aA · aW
(0) φ mCA 3 ∂CCA mCA mNH3 ∂BNH3,CA 3/2 +2 + (υ+υ-) m° m° m° ∂x˜M ∂x˜M mCA 2 mNH3 ∂ΓNH3,CA,CA mCA mNH3 2 ∂ΓNH3,NH3,CA +3 3 m° m° m° m° ∂x˜M ∂x˜M
f(I, x˜M) ) -Aφ
( )
mCA 1 υ+z+2 + υ-z-2) (20) ( 2 mo where z+ and z- are the number of charges on cation C and on anion A, respectively. Furthermore, I)
( ) ( )
]
(27)
where
3⁄2
(19)
NA, e, ε0, and kB are the Avogadro’s number, the electron charge, the electric permittivity of vacuum, and Boltzmann’s constant, respectively. The mass density F and the relative permittivity εr of the solute-free solvent mixture depend on the temperature and on the composition of the solute-free solvent mixture.
h(2√I) ) g(2√I) + exp(-2√I)
(28)
g(2√I ) is given by eq 24, where x ) 2√I . Physical Properties and Parameters for the System (Ammonia + Water + Methanol) The equations for describing the phase equilibrium of the system (ammonia + water + methanol) require Henry’s constant
Ind. Eng. Chem. Res., Vol. 47, No. 15, 2008 5117
kH,NH3(T, x˜M) for the solubility of ammonia in liquid mixtures ∞ of water and methanol, the partial molar volume VNH ˜ M) of 3(T, x ammonia at infinite dilution in the solvent mixture, one binary (0) parameter {βNH ˜ M)}, and one ternary parameter 3,NH3(T, x {µNH3,NH3,NH3(T, x˜M)} for interactions between ammonia molecules in the solvent mixture. Correlation equations for these physical properties and parameters were determined in previous work from experimental data on the solubility of ammonia in liquid mixtures of (water + methanol).16 They were adopted here. Physical Properties and Parameters for the Systems (Salt + Ammonia + Water + Methanol) Extending the correlation for the solubility of ammonia in liquid mixtures of (water + methanol) to the systems containing either NaCl or Na2SO4 requires the following. (1) The mass density F(T, x˜M) and the relative permittivity εr(T, x˜M) of the solute-free solvent mixture of (water + methanol): the correlation equations for these properties, which we developed in previous work,8 were utilized here. (2) The solubility products (on a molality scale basis) of NaCl, Na2SO4, and Na2SO4 · 10H2O in mixtures of (water + methanol) {Ksp,NaCl(T, x˜M), Ksp,Na2SO4(T, x˜M), and Ksp,Na2SO4 · 10 H2O(T, x˜M), respectively}. The correlation equations for these properties were taken from our preceding work as well.8,12 (0) (1) φ (3) Pitzer’s parameters βC,A (T, x˜M), βC,A (T, x˜M), and CCA (T, x˜M) for interactions {in the solvent mixture of (water + methanol)} between sodium (as the cation C) and either chloride or sulfate (as the anion A): we employ here the correlation equations for these parameters that we proposed in foregoing work.8,12 (4) Pitzer’s parameters B(0) ˜ M), ΓNH3,CA,CA(T, x˜M), and NH3,CA(T, x ΓNH3,NH3,CA(T, x˜M) for interactions (within the solvent mixture) between ammonia on one side and one of the salts (sodium chloride or sodium sulfate) on the other side. These parameters were assumed to depend linearly on the mole fraction of methanol in the solvent mixture (cf. refs 13 and 14): ω(T, x˜M) ) (1 - x˜M)ωW(T) + x˜MωM(T)
(29)
Pitzer’s parameters ωW for interactions in water were taken from Sing et al.2 (for NaCl as dissolved salt) and from Weyrich et al.4 (for Na2SO4 as dissolved salt). Because the solubility of both NaCl and Na2SO4 in pure methanol is very small, the corresponding parameters ωM for interactions in methanol were neglected; that is, they were set to zero. With the given set of properties and parameters the model can be used to predict the influence of either NaCl or Na2SO4 on the solubility of ammonia in liquid mixtures of (water + methanol). Comparison of Experimental Results with Prediction Results Figures 1–3 show a comparison between the experimental data and the model predictions for the total pressure p required to dissolve (at preset T, x˜M, and m j CA) a given amount of ammonia (mNH3) in liquid mixtures of water + methanol + either NaCl (Figures 1 and 2) or Na2SO4 (Figure 3). Table 4 gives the average absolute deviations between calculation results and experimental data for the total pressure and all partial pressures. Both salts reduce the solubility of ammonia in liquid mixtures of (water + methanol); that is, ammonia is salted-out by those salts. The presence of the salt results only in a slight increase
Figure 1. Influence of NaCl at constant temperature (T ≈ 353 K) on the total pressure above solutions of (ammonia + water + methanol): {[ (x˜M ≈ 0.25, m j NaCl ≈ 2 mol kg-1), 9 (x˜M ≈ 0.5, m j NaCl ≈ 0.73 mol kg-1), b (x˜M ≈ 0.75, m j NaCl ≈ 0.26 mol kg-1)} experimental results, this work; (solid line) prediction, this work; (dashed line) correlation for the salt-free system.16
Figure 2. Influence of NaCl at constant temperature (T ≈ 393 K) on the total pressure above solutions of (ammonia + water + methanol): {b (x˜M ≈ 0.25, m j NaCl ≈ 1 mol kg-1), [ (x˜M ≈ 0.25, m j NaCl ≈ 2 mol kg-1), 2 (x˜M ≈ 0.5, m j NaCl ≈ 1 mol kg-1), 9 (x˜M ≈ 0.75, m j NaCl ≈ 0.37 mol kg-1)} experimental results, this work; (solid line) prediction, this work; (dashed line) correlation for the salt-free system.16
of the total pressure. For example, and throughout the ammonia molality range investigated here, that increase is typically in the order of 3% (2%) at 293 K (393 K) when 1 mol of NaCl is added to 1 kg of (water + methanol) with x˜M ) 0.25. The influence of Na2SO4 on the solubility of ammonia is somewhat larger. As sodium sulfate is barely soluble in methanol,12 the experiments had to be restricted to rather low methanol fractions in the aqueous solvent. At higher methanol fractions the solubility of Na2SO4 is very small,12 and consequently the salting-out effect is also rather small. As indicated in Table 3 and in Figure 3, the model predicts the precipitation of Na2SO4 up from a certain amount of dissolved ammonia (i.e., saltingout of sodium sulfate by ammonia). For example, in a mixture with x˜M ) 0.25 and mNH3 ) 0 (6) mol · kg-1, the solubility of Na2SO4 at around 353 K is about 0.18 (0.073) mol/kg of (water + methanol). {That small amount of salt increases the total pressure by about 2.4 (1.2)%.} This phenomenon (salting-out of a salt by a gas) is well-known from experimental investigations on the influence of ammonia on the solubility of Na2SO4 in pure water13,14). Therefore the calculation results for the precipitation of sodium sulfate by addition of ammonia to an aqueous solution of methanol are no surprise. However, no precipitation was noticed in the experiments. This can be due either to very small amounts of the solid phase that escaped
5118 Ind. Eng. Chem. Res., Vol. 47, No. 15, 2008
Figure 3. Influence of Na2SO4 at constant temperature (T ≈ 353 and 393 K) on the total pressure above solutions of (ammonia + water + methanol): {b (T ≈ 353 K, x˜M ≈ 0.05, m j Na2SO4 ≈ 0.88 mol kg-1), [ (T ≈ 353 K, x˜M ≈ 0.25, m j Na2SO4 ≈ 0.15 mol kg-1), 9 (T ≈ 393 K, x˜M ≈ 0.05, m j Na2SO4 ≈ 1 mol kg-1), 2(T ≈ 393 K, x˜M ≈ 0.25, m j Na2SO4 ≈ 0.15 mol kg-1)} experimental results, this work; (solid line) prediction, this work; (dashed line) correlation for the salt-free system. The short bold lines mark the solubility limit of Na2SO4, as predicted from the model, see text and Table 3. Table 4. Comparison of Experimental and Calculated VLE Data for the Systems (Salt + Ammonia + Water + Methanol) T, K
salt
Na
|∆p, kPa|
|∆pNH3, kPa|
|∆pW, kPa|
|∆pM, kPa|
353 393
NaCl
15 18
1.7 8.2
2.7 29
2.8 7.3
3.6 33
353 393
Na2SO4
10 8
0.5 4.5
1.3 42
2.6 17
1.7 29
a
N N ) number of data points. |∆Z| ) 1/N · ∑i)1 |Zi,exp - Zi,calc|.
our attention (what we expect) or to a failure of the model to correctly predict the solid-liquid phase boundary. Conclusions In continuation of extensive experimental investigations on the simultaneous solubility of ammonia and sour gases in aqueous solutions, this paper reports new experimental results for the influence of the single salts NaCl and Na2SO4 on the solubility of ammonia in liquid mixtures of (water + methanol) at about 353 and 393 K. The new experimental data are used to validate a thermodynamic model that allows for the prediction of salt effects on gas solubility in mixed solvents. The experimentally observed salting-out of ammonia by both salts is reliably predicted by the model. Future work is directed to the correlation/prediction of such salt effects on the simultaneous solubility of ammonia and carbon dioxide in liquid mixtures of water and methanol. Acknowledgment Financial support of the experimental part of this investigation by the German Government (BMBF Grant No. 01/RK9808/8) and some industrial partners (BASF AG, Bayer AG, Degussa AG, Lurgi Oel Gas Chemie GmbH, Lurgi Energie and Entsorgung GmbH, and Siemens-Axiva GmbH & Co.KG) is gratefully acknowledged. Literature Cited (1) Pitzer, K. S. Thermodynamics of electrolytes. 1. Theoretical basis and general equations. J. Phys. Chem. 1973, 77, 268–277.
(2) Sing, R.; Rumpf, B.; Maurer, G. Solubility of ammonia in aqueous solutions of single electrolytes sodium chloride, sodium nitrate, sodium acetate, and sodium hydroxide. Ind. Eng. Chem. Res. 1999, 38, 2098–2109. (3) Rumpf, B.; Maurer, G. Solubility of ammonia in aqueous solutions of sodium sulfate and ammonium sulfate at temperatures from 333.15 to 433.15 K and pressures up to 3 MPa. Ind. Eng. Chem. Res. 1993, 32, 1780– 1789. (4) Weyrich, F.; Rumpf, B.; Maurer, G. Enthalpy of mixing of aqueous solutions of NH3 with aqueous solutions of Na2SO4 or (NH4)2SO4 at temperatures between 313 and 373 K. Thermochim. Acta 2000, 359, 11– 22. (5) Kurz, F.; Rumpf, B.; Maurer, G. Vapor-liquid-solid equilibria in the system NH3-CO2-H2O from around 310 to 470 K: new experimental data and modeling. Fluid Phase Equilib. 1995, 104, 261–275. (6) Kurz, F.; Rumpf, B.; Sing, R.; Maurer, G. Vapor-liquid and vaporliquid-solid equilibria in the system ammonia-carbon dioxide-sodium chloride-water at temperatures from 313 to 393 K and pressures up to 3 MPa. Ind. Eng. Chem. Res. 1996, 35, 3795–3802. (7) Bieling, V.; Kurz, F.; Rumpf, B.; Maurer, G. Simultaneous solubility of ammonia and carbon dioxide in aqueous solutions of sodium sulfate in the temperature range 313-393 K and pressures up to 3 MPa. Ind. Eng. Chem. Res. 1995, 34, 1449–1460. ´ . Model for the Gibbs excess energy of (8) Pe´rez-Salado Kamps, A mixed-solvent (chemical-reacting and gas-containing) electrolyte systems. Ind. Eng. Chem. Res. 2005, 44, 201–225. ´ .; Maurer, G. Solubility (9) Xia, J.; Jo¨decke, M.; Pe´rez-Salado Kamps, A of CO2 in (CH3OH + H2O). J. Chem. Eng. Data 2004, 49, 1756–1759. ´ .; Maurer, G. Experimental (10) Jo¨decke, M.; Pe´rez-Salado Kamps, A Investigation of the Solubility of CO2 in (Acetone + Water). J. Chem. Eng. Data 2007, 52, 1003–1009. ´ .; Maurer, G. Experimental (11) Jo¨decke, M.; Pe´rez-Salado Kamps, A investigation of the influence of NaCl on the vapor-liquid equilibrium of (CH3OH + H2O). J. Chem. Eng. Data 2005, 50, 138–141. ´ .; Vogt, M.; Jo¨decke, M.; Maurer, G. (12) Pe´rez-Salado Kamps, A Investigation of the (solid-liquid and vapor-liquid) equilibrium of the system H2O + CH3OH + Na2SO4. Ind. Eng. Chem. Res. 2006, 45, 454–466. ´ .; Jo¨decke, M.; Xia, J.; Vogt, M.; Maurer, (13) Pe´rez-Salado Kamps, A G. Influence of salts on the solubility of carbon dioxide in (water + methanol). Part I: sodium chloride. Ind. Eng. Chem. Res. 2006, 45, 1505– 1515. ´ .; Jo¨decke, M.; Vogt, M.; Xia, J.; Maurer, (14) Pe´rez-Salado Kamps, A G. Influence of salts on the solubility of carbon dioxide in (water + methanol). Part II: sodium sulfate. Ind. Eng. Chem. Res. 2006, 45, 3673– 3677. ´ .; Maurer, (15) Scha¨fer, D.; Xia, J.; Vogt, M.; Pe´rez-Salado Kamps, A G. Experimental investigation of the solubility of ammonia in methanol. J. Chem. Eng. Data 2007, 52, 1653–1659. ´ .; Maurer, G. (16) Scha¨fer, D.; Vogt, M.; Pe´rez-Salado Kamps, A Solubility of ammonia in liquid mixtures of (water + methanol). Fluid Phase Equilib. 2007, 261, 306–312. (17) Reid, C. R.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids, 4th ed.; McGraw-Hill: New York, 1987. (18) Hales, J. L.; Ellender, J. H. Liquid densities from 293 to 490 K of nine aliphatic alcohols. J. Chem. Thermodyn. 1976, 8, 1177–1184. (19) Saul, A.; Wagner, W. International equations for the saturation properties of ordinary water substance. J. Phys. Chem. Ref. Data 1987, 16, 893–901. (20) Dymond, J. H.; Smith, E. B. The Virial coefficients of pure gases and mixtures; Oxford University Press: Oxford, UK, 1980. (21) Hayden, J. G.; O’Connell, J. P. A generalized method for predicting second virial coefficients. Ind. Eng. Chem. Proc. Des. DeV. 1975, 14, 209– 216. (22) Pitzer, K. S. Ion Interaction Approach: Theory and Data Correlation. In ActiVity Coefficients in Electrolyte Solutions; Pitzer, K. S., Ed.; CRC Press: Boca Raton, FL, 1991; pp 75-155.
ReceiVed for reView August 28, 2007 ReVised manuscript receiVed March 10, 2008 Accepted March 26, 2008 IE071169P
