Solubility of Ammonia in Aqueous Solutions of Single Electrolytes

solutions containing 2-6 mol of the single electrolytes .... (0), βij. (1), and τijk, respectively between dissolved spe- cies, i.e., ammonia, and t...
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Ind. Eng. Chem. Res. 1999, 38, 2098-2109

Solubility of Ammonia in Aqueous Solutions of Single Electrolytes Sodium Chloride, Sodium Nitrate, Sodium Acetate, and Sodium Hydroxide Rudolf Sing, Bernd Rumpf, and Gerd Maurer* Lehrstuhl fu¨ r Technische Thermodynamik, Fachbereich Maschinenbau und Verfahrenstechnik, Universita¨ t Kaiserslautern, Postfach 3049, D-67653 Kaiserslautern, Germany

Experimental results for the solubility of ammonia in 2-6 m aqueous solutions of four single electrolytes (NaCl, NaNO3, CH3COONa, and NaOH) at temperatures from 313 to 393 K and pressures up to about 0.7 MPa are reported. The experimental results are compared to correlations/predictions. Introduction The solubility of ammonia in aqueous solutions of the single electrolytes NaCl, NaNO3, CH3COONa, and NaOH was measured as an extension of a series of experimental investigations on the solubility of the single gases ammonia,1,2 carbon dioxide,3-8 sulfur dioxide,9-11 and hydrogen cyanide9 in water and aqueous solutions of electrolytes. Experimental results are reported for the solubility of ammonia in aqueous solutions containing 2-6 mol of the single electrolytes in 1 kg of water at temperatures from 313 to 393 K and pressures up to about 0.7 MPa. The new experimental data are compared to correlations/predictions, where the excess Gibbs energy of the liquid phase is described by Pitzer’s equation for aqueous electrolyte solutions12 and the properties of the vapor are approximated by the virial equation of state truncated after the second virial coefficient. Experimental Section The experimental procedure differs from that used in previous investigations of that series (e.g., Rumpf and Maurer9). However, it is basically the same as that used in previous investigations on the simultaneous solubility of ammonia and carbon dioxide in water and aqueous solutions.13-18 Therefore, only a short description is repeated here. A thermostated, evacuated cell (volume ≈ 2 dm3) is filled with a known amount of an aqueous solution of a single electrolyte. After equilibration, the pressure is measured and known amounts of ammonia are added. After equilibration, the pressure, temperature, and volume of the vapor phase are measured and a small sample of the vapor phase is taken and analyzed by gas chromatography. From these direct experimental data the amounts of water, ammonia, and the electrolyte in the liquid phase are determined. A detailed description of the experimental procedure as well as of the experimental uncertainties was given by Sing.20 Therefore, only the uncertainties are given here. The temperature is measured by platinum resistance thermometry with an uncertainty of (0.1 K. The pressure is measured with a pressure transducer which forms the bottom of the cell, with an uncertainty of (0.5 kPa. * To whom all correspondence should be addressed. Phone: +49-631-2052410. Fax: +49-631-2053835. E-mail: gmaurer@ rhrk.uni-kl.de.

A gas chromatograph with a Hayesep P column and a thermal conductivity cell was used for analyzing the vapor phase. The calibration of the gas chromatographic analysis was performed with binary, gaseous mixtures prepared by charging the evacuated cell with pure water and ammonia. The amount of water vapor was calculated from the total pressure, the temperature, and the volume of the cell. The amount of ammonia was determined gravimetrically. The uncertainty of the gas chromatographic analysis is estimated to result in an uncertainty of (2% in the partial pressure of ammonia and (4% in the partial pressure of water. However, at 313 Ksbecause of the low vapor pressure of watersthe uncertainty of the partial pressure of water increases to about (8%. The aqueous solutions of NaCl, NaNO3, CH3COONa, and NaOH were prepared by dissolving known amounts of the pure solids into a known amount of deionized, bidistilled, and degassed water. The amounts were determined gravimetrically using high-resolution balances. The relative uncertainty in the molality of the electrolyte solute in an aqueous solution which is charged to the cell is below ≈0.3%. In a typical experiment the volume of the vapor phase was about 1000 cm3 and the amount of charged liquid solution was about 1000 g. The maximum experimental uncertainties are (5 cm3 for the vapor phase volume and (0.5 g for the amount of the liquid solution. The amount of ammonia in the cell is known with a relative uncertainty of less than 0.1%. Substances Ammonia (>99.999 mol %; either from Linde AG, Mainz, Germany, or from Messer-Griesheim, Ludwigshafen, Germany) was used as provided. With the exception of sodium chloride, which was purchased from Carl Roth GmbH, Karlsruhe, Germany, all electrolyte solutes were purchased from Riedel-de Haen AG, Seelze, Germany, in high quality (NaCl, >99.5 mass %; NaNO3, >99.5 mass %; CH3COONa, >99.0 mass %; NaOH, >99.0 mass %) and further dried under vacuum. Deionized water was further purified and degassed by vacuum distillation. Results Table 1 gives an overview of the experiments of the present work for the solubility of ammonia in aqueous

10.1021/ie980572g CCC: $18.00 © 1999 American Chemical Society Published on Web 04/02/1999

Ind. Eng. Chem. Res., Vol. 38, No. 5, 1999 2099

solutions. The experiments were performed at 313.15, 353.15, and 393.15 K. The minimum and maximum molalities of the electrolyte solute were 2 and 6 mol/kg, respectively. The maximum molality of ammonia in the liquid was about 21 mol/kg. The maximum pressure was 0.7 MPa. In order to test the reliability of the equipment for investigating the solubility of a very soluble gas in aqueous solutions, some measurements were performed for the solubility of ammonia in pure water. The results of those measurements are given in Table 2. The experimental results for the solubility of ammonia in aqueous electrolyte solutions are given in Tables 3-6. In a typical series of experiments, the gas chromatograph was calibrated before and after each series. In some cases (but only for sodium chloride and sodium nitrate as electrolyte solutes), the calibration curves from those (two) experiments did not agree with each other within the estimated uncertainty of the vaporphase analysis. Therefore, for those experiments only the temperature, the molality of dissolved ammonia, and the total pressure but no experimental data for the vapor-phase composition are given (cf. Tables 3 and 4). All numbers are average results from at least four single measurements.

Table 1. Experimental Conditions of the Present Investigation salt

T (K)

NaCl

mMX (mol/kg)

max mNH 3 (mol/kg)

pmax (MPa)

N

4.0 6.0 2.0 4.0 6.0 2.0 3.8 6.0 4.0 6.0 4.0 6.0 4.0 6.0 4.0 5.8 4.0 6.0 4.0 5.9 3.0 6.0 4.0 6.0 4.0 6.0

16.8 17.4 15.8 15.0 21.2 9.9 9.7 9.8 17.5 18.7 20.2 17.2 10.5 11.4 17.9 19.4 17.6 16.0 5.6 8.1 14.7 15.1 15.1 14.1 5.8 4.4

0.10 0.10 0.35 0.34 0.49 0.69 0.68 0.68 0.09 0.09 0.40 0.32 0.65 0.67 0.13 0.16 0.47 0.46 0.68 0.7 0.13 0.21 0.55 0.66 0.68 0.68

7 (+9)a 7 (+8)a 9 10 10 8 6 7 7 (+8)a 7 10 8 9 7 8 8 9 9 6 6 9 8 10 8 7 7

313.15 353.15 393.15

NaNO3

313.15 353.15 393.15

NaAc

313.15 353.15 393.15

NaOH

313.15 353.15 393.15

Modeling a

The solubility of ammonia in water and aqueous solutions is modeled by applying the extended Raoult’s law for water

(∫

psw(T)φsw(T) exp

)

pure p vw (T,p)liq

psw

dp aw ) pywφ′′w

RT

(1)

(m) (m) (T,p)mNH3γNH ) yNH3pφ′′NH3 HNH 3,w 3

)

(∫

(m) HNH (T)exp 3,w

(2)

v∞ (T,p) p NH3,w

psw

RT

The activity of water aw and the activity coefficient of a dissolved species i γ(m) were calculated using i Pitzer’s model for the Gibbs excess energy of electrolyte solutions:12

ln aw )

and the extended Henry’s law for ammonia

(m) (T,p) HNH 3,w

Vapor-phase composition not determined.

)

dp

(3)

of The vapor pressure psw and the molar volume vpure w water were taken from Saul and Wagner.15 Henry’s constant (on molality scale) for the solubility of ammonia in water was taken from Bieling et al.:16

∑j yjBij - Bmix)RT

ln φi ) (2

Bmix )

∑i ∑j yiyjBij

(5) (6)

The virial coefficients were calculated as described previously.16

∑ ∑ ∑ mimjmkτijk - i*w ∑ mi

i*w j*w k*w

[

) -Aφzi2 ln γ(m) i

2

3.932 - 1879.02/(T/K) - 355134.1/(T/K)2 (4)

p

∑∑

β(1) ij exp(-RxIm)] - 2

(m) (T,psw)/(MPa‚kg‚mol-1) ) ln HNH 3,w

The partial molal volume of ammonia at infinite dilution in water was calculated according to the method by Brelvi and O’Connell.21 That method requires “characteristic” molar volumes of ammonia and water which + ) 65.2 cm3 were taken from Edwards et al.:22 vNH 3 + mol-1 and vw ) 46.4 cm3 mol-1. Vapor-phase fugacity coefficients were calculated using the virial equation of state truncated after the second coefficient:

{

Im1.5 2Aφ mimj[β(0) ij + 1000 i*w j*w 1 + bxIm Mw

exp(-RxIm)

]

+

1 + bxIm

∑ mjBij -

j*w

xIm zi2

[

R2Im2

2 b

]

}

(7)

ln(1 + bxIm) +

(

)

R2 1 - 1 + RxIm + Im × 2

mjmkβ(1) ∑ ∑ jk + 3 ∑ ∑ mjmkτijk j*w k*w j*w k*w

(8)

with

Bij(Im) ) β(0) ij +

2β(1) ij

[1 - (1 + RIm) exp(-RxIm)] (8a) R2Im

Parameters R and b were set according to Pitzer:12 R ) 2 (kg/mol)1/2; b ) 1.2 (kg/mol)1/2. Im is the ionic strength on molality scale:

Im )

1

∑

zj2mj 2j*w

(9)

2100 Ind. Eng. Chem. Res., Vol. 38, No. 5, 1999 Table 2. Experimental Results for the Solubility of Ammonia in Water T (K)

mNH3 (mol/kg)

10pNH3 (MPa)

10pw (MPa)

10p (MPa)

313.15 313.19 313.16 313.16 313.16 313.19 313.17 313.15 313.16 313.17 313.17 313.16 353.18 353.16 353.17 353.14 353.15 353.13 353.16 353.13 353.14 353.15 353.15 353.14 353.13 353.16 353.15 353.14 353.15 353.15 393.16 393.17 393.16 393.14 393.16 393.16

0 3.002 ( 0.003 3.679 ( 0.003 3.802 ( 0.006 4.164 ( 0.003 4.938 ( 0.004 5.766 ( 0.004 7.637 ( 0.006 9.469 ( 0.007 10.831 ( 0.008 12.829 ( 0.010 15.667 ( 0.012 0 1.899 ( 0.008 3.040 ( 0.004 3.405 ( 0.004 3.771 ( 0.015 3.831 ( 0.004 3.854 ( 0.005 5.981 ( 0.007 6.794 ( 0.023 6.825 ( 0.008 6.990 ( 0.007 7.251 ( 0.009 7.253 ( 0.008 10.439 ( 0.011 11.517 ( 0.032 11.964 ( 0.011 15.155 ( 0.014 18.993 ( 0.017 0 3.176 ( 0.007 3.664 ( 0.008 5.747 ( 0.011 7.149 ( 0.014 10.403 ( 0.019

0 0.109 ( 0.009 0.139 ( 0.010 0.137 ( 0.043 0.157 ( 0.010 0.185 ( 0.011 0.221 ( 0.011 0.317 ( 0.011 0.411 ( 0.012 0.476 ( 0.013 0.593 ( 0.013 0.779 ( 0.014 0 0.286 ( 0.015 0.453 ( 0.018 0.541 ( 0.019 0.586 ( 0.022 0.564 ( 0.021 0.595 ( 0.021 0.961 ( 0.031 1.111 ( 0.029 1.114 ( 0.027 1.167 ( 0.026 1.179 ( 0.028 1.162 ( 0.028 1.818 ( 0.031 2.033 ( 0.036 2.142 ( 0.032 2.854 ( 0.034 3.795 ( 0.038 0 1.508 ( 0.042 1.647 ( 0.045 2.674 ( 0.057 3.407 ( 0.064 5.159 ( 0.075

0.075 ( 0.005 0.071 ( 0.008 0.066 ( 0.008 0.071 ( 0.041 0.068 ( 0.008 0.070 ( 0.008 0.066 ( 0.007 0.061 ( 0.007 0.058 ( 0.007 0.058 ( 0.007 0.056 ( 0.006 0.054 ( 0.006 0.474 ( 0.005 0.459 ( 0.016 0.463 ( 0.018 0.431 ( 0.019 0.442 ( 0.019 0.471 ( 0.020 0.445 ( 0.019 0.425 ( 0.027 0.414 ( 0.021 0.417 ( 0.021 0.394 ( 0.021 0.431 ( 0.022 0.443 ( 0.022 0.408 ( 0.023 0.383 ( 0.022 0.371 ( 0.021 0.354 ( 0.021 0.335 ( 0.020 1.983 ( 0.005 1.840 ( 0.042 1.920 ( 0.044 1.837 ( 0.052 1.785 ( 0.055 1.673 ( 0.058

0.075 0.180 0.205 0.208 0.224 0.255 0.288 0.378 0.469 0.534 0.649 0.832 0.474 0.745 0.916 0.972 1.028 1.035 1.040 1.386 1.525 1.531 1.561 1.610 1.605 2.226 2.416 2.512 3.208 4.129 1.983 3.348 3.567 4.511 5.192 6.832

zj is the number of charges of species j. The dielectric constant of water is needed for the calculation of the Debye-Hu¨ckel parameter Aφ. It was taken from Bradley and Pitzer.23 Because the protonation of ammonia in the aqueous solutions can be neglected (under the experimental conditions of the present work), the model requires binary and ternary interaction parameters (1) β(0) ij , βij , and τijk, respectively between dissolved species, i.e., ammonia, and the cations and anions of the dissolved electrolytes. However, when a gas is dissolved in an aqueous solution of a single electrolyte, there is no possibility to separate the influence of the cations from those of the anions on the gas solubility. Therefore, it is common practice to replace the parameters which characterize interactions between the gaseous solute and the ions by a parameter which summarizes the interactions between the gaseous solute and the dissolved electrolyte. For example, when all binary param(1) between ammonia and an ionic species j are eters βNH 3,j (1) neglected (i.e., βNH ) 0), eqs 7 and 8 for the activity of 3,j water and the activity coefficient of ammonia in an aqueous solution of a single 1:1 electrolyte MX can be rewritten as

ln aw ) ln aw(mNH3 ) 0) Mw (0) + 3mMXΓNH3,MX,MX + {m m (2BNH 3,MX 1000 MX NH3 (0) 3mNH3ΓNH3,NH3,MX) + mNH3(1 + mNH3βNH + 3,NH3 2 τ )} mNH 3 NH3,NH3,NH3

where (0) (0) (0) BNH ) βNH + + βNH ,X3,MX 3,M 3

(10)

ΓNH3,MX,MX ) τNH3,M+,M+ + 2τNH3,M+,X- + τNH3,X-,X- (11) ΓNH3,NH3,MX ) τNH3,NH3,M+ + τNH3,NH3,X-

(12)

(0) , ΓNH3,MX,MX, and ΓNH3,NH3,MX Thus, parameters BNH 3,MX describe the influence of the electrolyte MX on the solubility of ammonia in water. At constant temperature and constant partial pressure of a gas the influence of small amounts of a strong electrolyte on the solubility of a gas at moderate partial pressure is usually expressed using a Setchenov parameter Si,MX. For the influence of an electrolyte MX on the solubility of ammonia, that Setchenov equation is

(MX) (0) (T,pNH3) ) mNH (T,pNH3) exp(-SNH3,MXmMX) mNH 3 3

(13)

As can be seen from a comparison with eqs 2 and 8b, the Setchenov parameter is proportional to the osmotic (0) second virial coefficient BNH : 3,MX (0) SNH3,MX ) 2BNH 3,MX

(13a)

(7a)

(m) (m) (0) ) ln γNH (mMX ) 0) + 2mMXBNH + ln γNH 3 3 3,MX 2 3mNH Γ + 6mNH3mMXΓNH3,MX,MX (8b) 3 NH3,NH3,MX

A positive Setchenov coefficient expresses salting out, i.e., a reduction of the solubility of ammonia by the presence of an electrolyte MX (at constant temperature and partial pressure of ammonia).

Ind. Eng. Chem. Res., Vol. 38, No. 5, 1999 2101 Table 3. Experimental Results for the Solubility of Ammonia in Aqueous Solutions of Sodium Chloride T (K)

mNaCl (mol/kg)

mNH3 (mol/kg)

10pNH3 (MPa)

10pw (MPa)

10p (MPa)

313.14 313.15 313.15 313.15 313.15 313.15 313.15 313.17 313.17 313.17 313.17 313.17 313.17 313.18 313.18 313.18 313.15 313.15 313.14 313.15 313.14 313.14 313.15 313.18 313.17 313.17 313.17 313.17 313.18 313.18 313.19 353.14 353.14 353.14 353.15 353.16 353.16 353.15 353.15 353.15 353.16 353.16 353.15 353.17 353.17 353.17 353.16 353.17 353.16 353.16 353.14 353.14 353.14 353.14 353.12 353.13 353.14 353.14 353.14 353.14 393.15 393.14 393.15 393.16 393.17 393.14 393.17 393.16 393.12 393.12 393.10 393.14 393.12 393.12 393.17 393.16 393.17 393.17 393.18 393.19 393.18

4.007 ( 0.0034 4.007 ( 0.0034 4.007 ( 0.0034 4.007 ( 0.0034 4.007 ( 0.0034 4.007 ( 0.0034 4.007 ( 0.0034 4.021 ( 0.0034 4.021 ( 0.0034 4.021 ( 0.0034 4.021 ( 0.0034 4.021 ( 0.0034 4.021 ( 0.0034 4.021 ( 0.0034 4.021 ( 0.0034 4.021 ( 0.0034 6.000 ( 0.0044 5.999 ( 0.0044 5.999 ( 0.0044 5.999 ( 0.0044 5.999 ( 0.0044 5.999 ( 0.0044 5.999 ( 0.0044 6.007 ( 0.0044 6.007 ( 0.0044 6.007 ( 0.0044 6.007 ( 0.0044 6.007 ( 0.0044 6.007 ( 0.0044 6.007 ( 0.0044 6.007 ( 0.0044 1.998 ( 0.0024 1.998 ( 0.0024 1.998 ( 0.0024 1.998 ( 0.0024 1.998 ( 0.0024 1.998 ( 0.0024 1.998 ( 0.0024 1.998 ( 0.0024 1.998 ( 0.0024 4.010 ( 0.0033 4.010 ( 0.0033 4.009 ( 0.0033 4.009 ( 0.0033 4.009 ( 0.0033 4.009 ( 0.0033 4.009 ( 0.0033 4.009 ( 0.0033 4.009 ( 0.0033 4.009 ( 0.0033 6.008 ( 0.0044 6.008 ( 0.0044 6.008 ( 0.0044 6.008 ( 0.0044 6.008 ( 0.0044 6.007 ( 0.0044 6.007 ( 0.0044 6.007 ( 0.0044 6.007 ( 0.0044 6.007 ( 0.0044 2.007 ( 0.0024 2.007 ( 0.0024 2.007 ( 0.0024 2.006 ( 0.0024 2.006 ( 0.0024 2.006 ( 0.0024 2.006 ( 0.0024 2.006 ( 0.0024 3.784 ( 0.0031 3.783 ( 0.0031 3.782 ( 0.0031 3.782 ( 0.0031 3.782 ( 0.0031 3.781 ( 0.0031 6.039 ( 0.0044 6.038 ( 0.0044 6.037 ( 0.0044 6.036 ( 0.0044 6.036 ( 0.0044 6.036 ( 0.0044 6.035 ( 0.0044

0 1.715 ( 0.002 3.846 ( 0.004 6.491 ( 0.007 9.291 ( 0.009 12.903 ( 0.012 16.836 ( 0.015 0 2.135 ( 0.003 4.297 ( 0.005 6.470 ( 0.007 8.626 ( 0.009 10.789 ( 0.011 12.865 ( 0.013 15.039 ( 0.015 17.090 ( 0.017 0 1.657 ( 0.003 3.912 ( 0.005 6.576 ( 0.007 9.761 ( 0.010 13.454 ( 0.013 17.426 ( 0.016 0 2.356 ( 0.003 4.750 ( 0.005 7.170 ( 0.008 9.377 ( 0.010 11.860 ( 0.013 14.211 ( 0.015 16.589 ( 0.017 0 1.140 ( 0.003 2.611 ( 0.005 4.301 ( 0.007 6.269 ( 0.009 8.327 ( 0.012 10.750 ( 0.014 13.534 ( 0.017 15.852 ( 0.020 0 1.693 ( 0.011 3.379 ( 0.022 5.017 ( 0.032 6.751 ( 0.042 8.339 ( 0.052 9.922 ( 0.062 11.509 ( 0.072 13.140 ( 0.083 15.016 ( 0.093 0 1.529 ( 0.012 3.820 ( 0.023 6.121 ( 0.034 8.957 ( 0.046 11.891 ( 0.058 14.423 ( 0.069 16.678 ( 0.080 18.933 ( 0.091 21.197 ( 0.102 0 0.495 ( 0.002 1.280 ( 0.005 2.636 ( 0.009 3.992 ( 0.012 5.559 ( 0.015 7.334 ( 0.019 9.943 ( 0.023 0 1.953 ( 0.006 3.911 ( 0.011 5.992 ( 0.015 8.059 ( 0.019 9.793 ( 0.023 0 1.782 ( 0.006 3.604 ( 0.011 5.422 ( 0.015 7.302 ( 0.019 8.438 ( 0.022 9.771 ( 0.025

0 0.075 ( 0.009 0.171 ( 0.009 0.298 ( 0.011 0.447 ( 0.012 0.661 ( 0.013 0.926 ( 0.014

0.063 ( 0.005 0.060 ( 0.008 0.058 ( 0.006 0.056 ( 0.006 0.051 ( 0.006 0.048 ( 0.006 0.045 ( 0.005

0 0.078 ( 0.009 0.184 ( 0.009 0.314 ( 0.010 0.483 ( 0.011 0.700 ( 0.013 0.965 ( 0.014

0.056 ( 0.005 0.055 ( 0.008 0.052 ( 0.006 0.050 ( 0.006 0.048 ( 0.006 0.045 ( 0.005 0.043 ( 0.005

0 0.202 ( 0.014 0.443 ( 0.017 0.744 ( 0.022 1.113 ( 0.026 1.525 ( 0.028 2.029 ( 0.030 2.653 ( 0.033 3.203 ( 0.035 0 0.315 ( 0.015 0.641 ( 0.022 0.942 ( 0.027 1.290 ( 0.030 1.603 ( 0.035 1.939 ( 0.038 2.274 ( 0.042 2.651 ( 0.045 3.087 ( 0.050 0 0.295 ( 0.014 0.748 ( 0.023 1.193 ( 0.028 1.771 ( 0.032 2.393 ( 0.038 2.965 ( 0.042 3.488 ( 0.048 4.037 ( 0.053 4.612 ( 0.058 0 0.252 ( 0.011 0.638 ( 0.024 1.340 ( 0.039 2.048 ( 0.050 2.882 ( 0.059 3.846 ( 0.066 5.306 ( 0.074 0 1.060 ( 0.032 2.133 ( 0.048 3.288 ( 0.058 4.442 ( 0.066 5.432 ( 0.071 0 1.033 ( 0.031 2.075 ( 0.045 3.118 ( 0.054 4.165 ( 0.061 4.817 ( 0.064 5.582 ( 0.068

0.439 ( 0.005 0.420 ( 0.017 0.420 ( 0.017 0.407 ( 0.019 0.390 ( 0.020 0.367 ( 0.020 0.353 ( 0.021 0.330 ( 0.020 0.317 ( 0.019 0.402 ( 0.005 0.384 ( 0.015 0.359 ( 0.018 0.357 ( 0.019 0.337 ( 0.019 0.335 ( 0.020 0.320 ( 0.019 0.321 ( 0.020 0.302 ( 0.019 0.294 ( 0.019 0.361 ( 0.005 0.352 ( 0.014 0.325 ( 0.017 0.318 ( 0.018 0.297 ( 0.018 0.285 ( 0.018 0.270 ( 0.017 0.267 ( 0.017 0.258 ( 0.017 0.249 ( 0.016 1.853 ( 0.005 1.835 ( 0.020 1.823 ( 0.029 1.773 ( 0.040 1.727 ( 0.046 1.671 ( 0.050 1.624 ( 0.053 1.552 ( 0.055 1.707 ( 0.005 1.640 ( 0.035 1.566 ( 0.045 1.501 ( 0.049 1.448 ( 0.051 1.407 ( 0.052 1.526 ( 0.005 1.464 ( 0.033 1.410 ( 0.042 1.336 ( 0.045 1.310 ( 0.047 1.277 ( 0.048 1.250 ( 0.048

0.063 0.135 0.229 0.354 0.499 0.709 0.972 0.063 0.153 0.250 0.352 0.462 0.581 0.713 0.853 0.996 0.056 0.132 0.236 0.365 0.530 0.746 1.008 0.057 0.164 0.275 0.394 0.511 0.651 0.795 0.954 0.439 0.621 0.863 1.151 1.503 1.892 2.383 2.983 3.520 0.402 0.698 0.999 1.300 1.627 1.937 2.259 2.595 2.953 3.32 0.361 0.647 1.073 1.511 2.068 2.679 3.235 3.755 4.296 4.861 1.853 2.086 2.461 3.113 3.775 4.553 5.471 6.858 1.707 2.700 3.700 4.788 5.890 6.838 1.526 2.497 3.485 4.454 5.476 6.093 6.832

2102 Ind. Eng. Chem. Res., Vol. 38, No. 5, 1999 Table 4. Experimental Results for the Solubility of Ammonia in Aqueous Solutions of Sodium Nitrate T (K)

mNaNO3 (mol/kg)

mNH3 (mol/kg)

313.15 313.15 313.15 313.16 313.16 313.15 313.15 313.15 313.15 313.14 313.15 313.15 313.14 313.15 313.15 313.15 313.14 313.16 313.15 313.15 313.16 313.15 353.11 353.14 353.14 353.13 353.14 353.14 353.13 353.14 353.14 353.15 353.13 353.13 353.15 353.14 353.12 353.11 353.14 353.15 393.14 393.14 393.13 393.15 393.16 393.17 393.17 393.18 393.17 393.17 393.18 393.15 393.14 393.14 393.13 393.12

3.993 ( 0.0029 3.993 ( 0.0029 3.993 ( 0.0029 3.993 ( 0.0029 3.993 ( 0.0029 3.993 ( 0.0029 3.993 ( 0.0029 3.993 ( 0.0029 3.994 ( 0.0029 3.994 ( 0.0029 3.994 ( 0.0029 3.994 ( 0.0029 3.994 ( 0.0029 3.994 ( 0.0029 3.993 ( 0.0029 6.034 ( 0.0040 6.034 ( 0.0040 6.034 ( 0.0040 6.033 ( 0.0040 6.033 ( 0.0040 6.033 ( 0.0040 6.033 ( 0.0040 4.002 ( 0.0029 4.002 ( 0.0029 4.002 ( 0.0029 4.002 ( 0.0029 4.002 ( 0.0029 4.002 ( 0.0029 4.002 ( 0.0029 4.002 ( 0.0029 4.001 ( 0.0029 4.001 ( 0.0029 5.998 ( 0.0039 5.998 ( 0.0039 5.998 ( 0.0039 5.998 ( 0.0039 5.998 ( 0.0039 5.997 ( 0.0039 5.997 ( 0.0039 5.997 ( 0.0039 4.024 ( 0.0029 4.023 ( 0.0029 4.023 ( 0.0028 4.022 ( 0.0028 4.022 ( 0.0028 4.043 ( 0.0030 4.041 ( 0.0030 4.041 ( 0.0030 4.040 ( 0.0030 5.998 ( 0.0039 5.997 ( 0.0039 5.996 ( 0.0039 5.996 ( 0.0039 5.995 ( 0.0039 5.994 ( 0.0039 5.994 ( 0.0039

0 1.931 ( 0.003 3.885 ( 0.005 5.806 ( 0.007 7.807 ( 0.009 9.719 ( 0.011 11.703 ( 0.013 13.642 ( 0.015 0 1.623 ( 0.002 3.872 ( 0.005 6.571 ( 0.007 9.679 ( 0.010 13.312 ( 0.012 17.488 ( 0.016 0 1.696 ( 0.003 4.278 ( 0.005 7.140 ( 0.008 10.463 ( 0.011 14.409 ( 0.014 18.712 ( 0.017 0 1.433 ( 0.012 3.557 ( 0.023 5.898 ( 0.035 8.262 ( 0.046 10.651 ( 0.058 13.063 ( 0.069 15.416 ( 0.081 17.820 ( 0.092 20.174 ( 0.103 0 1.636 ( 0.004 4.216 ( 0.008 6.827 ( 0.011 9.390 ( 0.015 12.056 ( 0.018 14.638 ( 0.021 17.183 ( 0.025 0 1.682 ( 0.005 3.380 ( 0.010 5.241 ( 0.014 7.038 ( 0.017 0 5.271 ( 0.012 8.699 ( 0.018 10.476 ( 0.021 0 2.139 ( 0.007 4.228 ( 0.012 6.358 ( 0.016 8.464 ( 0.021 10.586 ( 0.025 11.428 ( 0.027

NH3-H2O. There are a lot of experimental data already available for the vapor-liquid equilibrium of the binary system (ammonia + water)sfor a recent survey cf. Tillner-Roth and Friend.24 The new data agree with reliable literature data within the experimental uncertainty. A comparison with some selected literature data is shown in Figure 1. For a description of the vapor-liquid equilibrium of that binary system, Pitzer’s model requires a binary (0) ) as well as a ternary (τNH3,NH3,NH3) parameter (βNH 3,NH3 for interactions between dissolved ammonia molecules. These parameters were determined by Weyrich25 and Rumpf et al.26 from literature data on the vapor-liquid equilibrium and the heat of dilution of the binary system

10pNH3 (MPa)

0 0.065 ( 0.009 0.156 ( 0.010 0.269 ( 0.011 0.411 ( 0.012 0.593 ( 0.013 0.834 ( 0.014 0 0.071 ( 0.009 0.178 ( 0.009 0.300 ( 0.011 0.450 ( 0.012 0.643 ( 0.013 0.879 ( 0.015 0 0.233 ( 0.013 0.585 ( 0.022 0.977 ( 0.028 1.380 ( 0.033 1.811 ( 0.038 2.274 ( 0.043 2.737 ( 0.048 3.237 ( 0.054 3.746 ( 0.059 0 0.265 ( 0.013 0.689 ( 0.021 1.118 ( 0.025 1.554 ( 0.028 2.021 ( 0.031 2.499 ( 0.034 2.988 ( 0.036 0 0.792 ( 0.027 1.602 ( 0.043 2.493 ( 0.054 3.381 ( 0.061 0 2.506 ( 0.053 4.196 ( 0.066 5.074 ( 0.071 0 1.019 ( 0.032 2.012 ( 0.047 3.004 ( 0.057 3.987 ( 0.064 4.986 ( 0.071 5.408 ( 0.073

10pw (MPa)

10p (MPa)

0.066 ( 0.005 0.063 ( 0.009 0.059 ( 0.007 0.057 ( 0.006 0.053 ( 0.006 0.051 ( 0.006 0.047 ( 0.005 0.062 ( 0.005 0.059 ( 0.008 0.056 ( 0.006 0.053 ( 0.006 0.050 ( 0.006 0.048 ( 0.006 0.045 ( 0.005 0.415 ( 0.005 0.404 ( 0.014 0.381 ( 0.018 0.362 ( 0.019 0.351 ( 0.020 0.337 ( 0.020 0.317 ( 0.019 0.310 ( 0.019 0.298 ( 0.019 0.292 ( 0.019 0.392 ( 0.005 0.387 ( 0.014 0.369 ( 0.018 0.355 ( 0.019 0.339 ( 0.019 0.327 ( 0.019 0.314 ( 0.019 0.304 ( 0.019 1.738 ( 0.005 1.690 ( 0.031 1.631 ( 0.041 1.577 ( 0.047 1.501 ( 0.049 1.743 ( 0.005 1.579 ( 0.047 1.481 ( 0.051 1.447 ( 0.052 1.640 ( 0.005 1.580 ( 0.034 1.505 ( 0.043 1.452 ( 0.047 1.404 ( 0.049 1.367 ( 0.050 1.327 ( 0.050

0.066 0.139 0.216 0.294 0.380 0.466 0.563 0.663 0.066 0.127 0.215 0.326 0.464 0.644 0.881 0.062 0.130 0.234 0.353 0.500 0.692 0.924 0.415 0.636 0.966 1.339 1.731 2.148 2.591 3.048 3.535 4.038 0.392 0.652 1.058 1.473 1.892 2.348 2.813 3.292 1.738 2.482 3.234 4.070 4.882 1.743 4.085 5.677 6.522 1.640 2.599 3.517 4.456 5.391 6.353 6.734

NH3-H2O: (0) βNH /(kg/mol) ) -0.01979 + 9.864/(T/K) (14a) 3,NH3

τNH3,NH3,NH3/(kg/mol)2 ) 0.005539 - 0.1789/(T/K) 0.000861 ln(T/K) (14b) Figure 1 shows a comparison between the new experimental data, the results from the correlation by Rumpf et al.,26 and selected literature.27-30 The new experimental data agree within the experimental uncertainty with the predictions as well as with most literature data. For example, the arithmetic average of

Ind. Eng. Chem. Res., Vol. 38, No. 5, 1999 2103 Table 5. Experimental Results for the Solubility of Ammonia in Aqueous Solutions of Sodium Acetate T (K)

mCH3COONa (mol/kg)

mNH3 (mol/kg)

10pNH3 (MPa)

10pw (MPa)

10p (MPa)

313.17 313.17 313.17 313.16 313.17 313.14 313.16 313.15 313.16 313.16 313.16 313.16 313.15 313.16 313.16 313.16 353.16 353.15 353.14 353.14 353.15 353.14 353.12 353.13 353.13 353.14 353.14 353.13 353.13 353.14 353.12 353.13 353.13 353.12 393.13 393.13 393.14 393.15 393.14 393.15 393.12 393.14 393.13 393.15 393.14 393.15

3.995 ( 0.0030 3.995 ( 0.0030 3.995 ( 0.0030 3.995 ( 0.0030 3.995 ( 0.0030 3.995 ( 0.0030 3.995 ( 0.0030 3.995 ( 0.0030 5.756 ( 0.0038 5.756 ( 0.0038 5.756 ( 0.0038 5.756 ( 0.0038 5.756 ( 0.0038 5.756 ( 0.0038 5.755 ( 0.0038 5.755 ( 0.0038 4.011 ( 0.0030 4.011 ( 0.0030 4.011 ( 0.0030 4.010 ( 0.0030 4.010 ( 0.0030 4.010 ( 0.0030 4.010 ( 0.0030 4.010 ( 0.0030 4.010 ( 0.0030 6.014 ( 0.0041 6.014 ( 0.0041 6.014 ( 0.0041 6.014 ( 0.0041 6.014 ( 0.0041 6.013 ( 0.0041 6.013 ( 0.0041 6.013 ( 0.0041 6.013 ( 0.0041 3.977 ( 0.0029 3.976 ( 0.0029 3.976 ( 0.0029 3.975 ( 0.0029 3.975 ( 0.0029 3.975 ( 0.0029 5.866 ( 0.0038 5.864 ( 0.0038 5.863 ( 0.0038 5.863 ( 0.0038 5.862 ( 0.0038 5.862 ( 0.0038

0 1.084 ( 0.002 2.773 ( 0.004 4.799 ( 0.006 7.752 ( 0.009 10.748 ( 0.012 14.058 ( 0.015 17.948 ( 0.018 0 1.112 ( 0.002 2.821 ( 0.004 5.019 ( 0.007 7.759 ( 0.010 11.016 ( 0.013 15.001 ( 0.016 19.385 ( 0.020 0 1.094 ( 0.003 3.464 ( 0.007 5.766 ( 0.010 8.139 ( 0.014 10.440 ( 0.017 12.825 ( 0.020 15.218 ( 0.023 17.627 ( 0.027 0 1.331 ( 0.004 3.360 ( 0.008 5.499 ( 0.012 7.641 ( 0.015 9.726 ( 0.019 11.796 ( 0.022 13.925 ( 0.026 16.032 ( 0.029 0 1.989 ( 0.007 3.956 ( 0.012 5.850 ( 0.017 7.689 ( 0.021 8.580 ( 0.024 0 2.121 ( 0.008 3.918 ( 0.014 5.897 ( 0.019 7.179 ( 0.023 8.061 ( 0.026

0 0.061 ( 0.008 0.161 ( 0.009 0.288 ( 0.010 0.462 ( 0.011 0.675 ( 0.012 0.934 ( 0.013 1.271 ( 0.014 0 0.074 ( 0.008 0.192 ( 0.009 0.349 ( 0.010 0.553 ( 0.011 0.817 ( 0.012 1.164 ( 0.013 1.575 ( 0.015 0 0.235 ( 0.012 0.773 ( 0.021 1.312 ( 0.025 1.888 ( 0.028 2.468 ( 0.030 3.092 ( 0.033 3.745 ( 0.035 4.423 ( 0.037 0 0.323 ( 0.014 0.838 ( 0.021 1.390 ( 0.024 1.957 ( 0.027 2.519 ( 0.029 3.091 ( 0.031 3.693 ( 0.033 4.305 ( 0.035 0 1.230 ( 0.035 2.477 ( 0.051 3.685 ( 0.060 4.879 ( 0.066 5.421 ( 0.070 0 1.428 ( 0.037 2.634 ( 0.051 3.965 ( 0.060 4.831 ( 0.065 5.417 ( 0.068

0.062 ( 0.005 0.061 ( 0.008 0.058 ( 0.006 0.055 ( 0.006 0.051 ( 0.006 0.049 ( 0.006 0.046 ( 0.005 0.044 ( 0.005 0.057 ( 0.005 0.056 ( 0.008 0.054 ( 0.006 0.051 ( 0.006 0.049 ( 0.006 0.043 ( 0.005 0.040 ( 0.005 0.038 ( 0.005 0.399 ( 0.005 0.396 ( 0.014 0.375 ( 0.019 0.357 ( 0.020 0.342 ( 0.020 0.330 ( 0.020 0.316 ( 0.019 0.305 ( 0.019 0.296 ( 0.019 0.360 ( 0.005 0.357 ( 0.015 0.340 ( 0.018 0.325 ( 0.019 0.311 ( 0.019 0.301 ( 0.018 0.293 ( 0.018 0.284 ( 0.018 0.275 ( 0.017 1.695 ( 0.005 1.627 ( 0.037 1.546 ( 0.046 1.481 ( 0.050 1.412 ( 0.051 1.422 ( 0.052 1.554 ( 0.005 1.480 ( 0.038 1.423 ( 0.045 1.371 ( 0.048 1.334 ( 0.049 1.329 ( 0.050

0.062 0.122 0.219 0.342 0.513 0.724 0.980 1.315 0.057 0.130 0.246 0.400 0.602 0.860 1.204 1.613 0.399 0.631 1.148 1.669 2.230 2.798 3.408 4.051 4.719 0.360 0.680 1.178 1.715 2.268 2.820 3.384 3.977 4.580 1.695 2.857 4.023 5.166 6.291 6.842 1.554 2.908 4.057 5.337 6.165 6.746

the deviations between the experimental results and the predictions for the total pressure (at preset temperature and ammonia molality in the liquid) is about 1 kPa, which corresponds to a relative deviation of less than 0.5%. The arithmetic averages between the measured and the predicted partial pressures of ammonia and water are 1.4% and 2%, respectively. Solubility of Ammonia in Aqueous Solutions of Univalent Electrolytes NH3-H2O-NaCl. The presence of sodium chloride in the aqueous phase reduces the solubility of ammonia; i.e., ammonia is salted out by sodium chloride. This can be seen in Figure 2. However, that salting-out effect is small. For example, the partial pressure of ammonia above a salt-free aqueous solution containing 8 mol of ammonia in 1 kg of water at 353 K is 0.14 MPa while it is 0.16 MPa when the liquid additionally contains 4 mol of sodium chloride. For modeling the liquid phase, besides the interaction parameters already required in the system NH3-H2O, (0) i.e., βNH and τNH3,NH3,NH3, additional parameters for 3,NH3

interactions between sodium and chloride ions as well as between ammonia and sodium chloride are required. The parameters for interactions between sodium and chloride ions were taken from Silvester and Pitzer.31 They are given in Appendix I. (0) Parameters BNH and ΓNH3,NH3,NaCl were fitted to 3,NaCl the experimental data given in Table 2 by minimizing the difference between calculated and measured pressures (at given temperature and composition of the aqueous phase), resulting in

(0) BNH /(kg/mol) ) 0.02435 - 0.17531/(T/K) (15a) 3,NaCl

and

ΓNH3,NH3,NaCl/(kg/mol)2 ) -0.00031

(15b)

With that set of parameters the experimental results for the total pressure are reproduced with an arithmetic average error of 1.2%. The maximum (relative) deviation is 2.7% (at 353.15 K, mNH3 ) 15.9 mol/kg, mNaCl ) 2 mol/ kg, i.e., at p ) 0.35 MPa). The arithmetic average errors

2104 Ind. Eng. Chem. Res., Vol. 38, No. 5, 1999 Table 6. Experimental Results for the Solubility of Ammonia in Aqueous Solutions of Sodium Hydroxide T (K)

mNaOH (mol/kg)

mNH3 (mol/kg)

10pHN3 (MPa)

10pw (MPa)

10p (MPa)

313.14 313.14 313.15 313.15 313.15 313.15 313.14 313.15 313.15 313.15 313.16 313.14 313.15 313.15 313.14 313.15 313.15 353.13 353.15 353.14 353.15 353.14 353.14 353.14 353.15 353.15 353.14 353.12 353.12 353.14 353.14 353.14 353.14 353.13 353.13 393.13 393.15 393.15 393.15 393.17 393.15 393.15 393.17 393.18 393.18 393.18 393.17 393.18 393.18

2.999 ( 0.0035 2.999 ( 0.0035 2.999 ( 0.0035 2.999 ( 0.0035 2.999 ( 0.0035 2.999 ( 0.0035 2.999 ( 0.0035 2.999 ( 0.0035 2.999 ( 0.0035 5.994 ( 0.0050 5.994 ( 0.0050 5.994 ( 0.0050 5.993 ( 0.0050 5.993 ( 0.0050 5.993 ( 0.0050 5.993 ( 0.0050 5.993 ( 0.0050 3.982 ( 0.0039 3.982 ( 0.0039 3.982 ( 0.0039 3.982 ( 0.0039 3.982 ( 0.0039 3.982 ( 0.0039 3.982 ( 0.0039 3.982 ( 0.0039 3.982 ( 0.0039 3.981 ( 0.0039 5.960 ( 0.0049 5.960 ( 0.0049 5.960 ( 0.0049 5.960 ( 0.0049 5.960 ( 0.0049 5.959 ( 0.0049 5.959 ( 0.0049 5.959 ( 0.0049 4.006 ( 0.0040 4.006 ( 0.0040 4.006 ( 0.0040 4.005 ( 0.0040 4.005 ( 0.0040 4.004 ( 0.0040 4.004 ( 0.0040 5.995 ( 0.0050 5.995 ( 0.0050 5.995 ( 0.0050 5.994 ( 0.0050 5.993 ( 0.0050 5.993 ( 0.0050 5.993 ( 0.0050

0 0.999 ( 0.002 2.612 ( 0.004 4.550 ( 0.006 6.603 ( 0.008 8.666 ( 0.010 10.752 ( 0.012 13.004 ( 0.014 14.672 ( 0.015 0 0.963 ( 0.002 2.433 ( 0.004 4.195 ( 0.006 6.303 ( 0.008 8.846 ( 0.011 11.982 ( 0.014 15.121 ( 0.017 0 0.480 ( 0.002 1.480 ( 0.005 2.802 ( 0.007 4.243 ( 0.009 5.583 ( 0.012 7.614 ( 0.015 9.673 ( 0.017 12.266 ( 0.021 15.053 ( 0.024 0 1.028 ( 0.004 3.097 ( 0.008 5.190 ( 0.012 7.305 ( 0.015 9.442 ( 0.019 11.770 ( 0.022 14.104 ( 0.026 0 0.379 ( 0.003 0.819 ( 0.005 1.565 ( 0.009 3.165 ( 0.014 4.816 ( 0.018 5.806 ( 0.021 0 0.350 ( 0.003 0.739 ( 0.006 1.518 ( 0.010 3.003 ( 0.015 3.747 ( 0.018 4.359 ( 0.021

0 0.077 ( 0.008 0.194 ( 0.009 0.341 ( 0.010 0.505 ( 0.011 0.680 ( 0.012 0.865 ( 0.012 1.081 ( 0.013 1.250 ( 0.013 0 0.142 ( 0.009 0.353 ( 0.010 0.597 ( 0.011 0.886 ( 0.011 1.232 ( 0.011 1.664 ( 0.012 2.111 ( 0.013 0 0.171 ( 0.013 0.508 ( 0.017 0.957 ( 0.022 1.442 ( 0.024 1.893 ( 0.026 2.578 ( 0.027 3.288 ( 0.029 4.190 ( 0.031 5.189 ( 0.033 0 0.518 ( 0.017 1.527 ( 0.023 2.494 ( 0.025 3.440 ( 0.027 4.379 ( 0.028 5.388 ( 0.030 6.390 ( 0.032 0 0.362 ( 0.014 0.782 ( 0.026 1.493 ( 0.039 2.965 ( 0.054 4.458 ( 0.062 5.337 ( 0.066 0 0.469 ( 0.017 0.985 ( 0.029 2.006 ( 0.042 3.849 ( 0.055 4.734 ( 0.059 5.447 ( 0.061

0.066 ( 0.005 0.060 ( 0.007 0.059 ( 0.007 0.056 ( 0.006 0.052 ( 0.006 0.049 ( 0.006 0.046 ( 0.005 0.043 ( 0.005 0.044 ( 0.005 0.055 ( 0.005 0.054 ( 0.007 0.051 ( 0.006 0.047 ( 0.006 0.043 ( 0.005 0.040 ( 0.005 0.040 ( 0.005 0.038 ( 0.005 0.400 ( 0.005 0.391 ( 0.017 0.385 ( 0.017 0.369 ( 0.019 0.353 ( 0.020 0.336 ( 0.020 0.317 ( 0.019 0.296 ( 0.018 0.281 ( 0.018 0.261 ( 0.017 0.356 ( 0.005 0.354 ( 0.017 0.327 ( 0.019 0.303 ( 0.019 0.288 ( 0.018 0.269 ( 0.017 0.255 ( 0.017 0.244 ( 0.016 1.699 ( 0.005 1.685 ( 0.022 1.668 ( 0.031 1.627 ( 0.040 1.553 ( 0.049 1.470 ( 0.052 1.468 ( 0.054 1.543 ( 0.005 1.531 ( 0.025 1.512 ( 0.033 1.459 ( 0.042 1.399 ( 0.049 1.366 ( 0.050 1.349 ( 0.051

0.066 0.137 0.253 0.397 0.557 0.729 0.912 1.124 1.293 0.055 0.196 0.403 0.644 0.928 1.273 1.705 2.149 0.400 0.562 0.893 1.326 1.794 2.228 2.895 3.584 4.471 5.451 0.356 0.872 1.854 2.797 3.728 4.648 5.643 6.634 1.699 2.047 2.450 3.120 4.518 5.928 6.805 1.543 1.999 2.496 3.465 5.247 6.097 6.796

for the partial pressures of ammonia and water are 2.3% and 1.3%, respectively. NH3-H2O-NaNO3. The influence of sodium nitrate on the solubility of ammonia in water is smaller than that of sodium chloride. As is shown in Figure 3, small amounts of sodium nitrate (up to ≈2 mol/kg) reduce the solubility of ammonia (salting out) while with a further increase of the salt molality the solubility of ammonia increases, resulting even in salting in at sodium nitrate molalities above mNaNO3 ≈5.2 mol/kg. At 313 K the effect of sodium nitrate on the total pressure is nearly within the experimental uncertainty ((0.5 kPa), while at 393 K the maximum difference between the pressure above an (6 m) aqueous solution of sodium nitrate and the saltfree solutions reaches about 5 kPa. The influence of sodium nitrate on the solubility of ammonia in water was modeled in the same way as that described before for the influence of sodium chloride. The parameters for interactions between sodium and nitrate ions in an aqueous solution at 298.15 K were taken from Pitzer.32 The influence of temperature on these parameters was estimated using the experimental data for the total pressure above an aqueous solution of sodium nitrate, which were taken at the beginning of each series of experiments on the solubility of

ammonia in aqueous solutions of sodium nitrate (cf. Table 4). (0) βNa +,NO -/(kg/mol) ) 3

0.00388 + 0.04938{1 - 298.15/(T/K)} (16a) (1) βNa +,NO -/(kg/mol) ) 3

0.21151 + 8.6493(1 - 298.15/(T/K)} (16b) τNa+,Na+,NO3-/(kg/mol)2 ) -0.00002 - 0.0001{1 - 298.15/(T/K)}/3 (16c) That set of parameters was checked against literature data on the vapor pressure above aqueous solutions of sodium nitrate by Shpigel and Mishchenko,33 Puchkov and Matashkin,34 and Apelblat.35 These literature data are well described by the present correlation (cf. Table 7). Similarly to the system with sodium chloride, the influence of sodium nitrate on the solubility of ammonia (0) was described by two parameters, BNH and 3,NaNO3 ΓNH3,NH3,NaNO3, for interactions between dissolved ammonia and sodium nitrate. These parameters were fitted

Ind. Eng. Chem. Res., Vol. 38, No. 5, 1999 2105 Table 7. Vapor Pressure above Aqueous Solutions of Sodium Nitrate: Comparison of Experimental Data from the Literature with the Correlation of the Present Work max mNaNO 3 (mol/kg)

T (K) 283.15-313.15 274.15-348.15 423.15-473.15

Figure 1. Solubility of ammonia in water. Exptl. results: +, Wilson;27 ×, Wucherer;28 0, Clifford and Hunter;29 3, Mu¨ller;30 O, this work. Calculation: s.

12.23 16.65 10.35

N

|∆p|

ref Apelblat35

7 1.79 97 0.63 Shpigel and Mishchenko33 14 0.88 Puchkov and Matashkin34

average error of 0.8%. The maximum (relative) deviation is 2.5% (at 313.15 K, mNH3 ) 1.6 mol/kg, mNaNO3 ) 6 mol/kg, i.e., at p ) 13 kPa). The arithmetic average errors for the partial pressures of ammonia and water are 1.6% and 3.4%, respectively. NH3-H2O-CH3COONa. Sodium acetate causes a salting-out effect on ammonia. That influence is rather strong. For example, at 353 K the pressure to dissolve 11.8 mol of ammonia in 1 kg of water is 0.21 MPa, while it is 0.31 MPa when additionally there are 6 mol of sodium acetate in 1 kg of water. That salting-out effect increases with increasing temperature. For example, the difference in the partial pressure of ammonia ∆pNH3 ) pNH3,w+CH3COONa - pNH3,w required to dissolve 8 mol of ammonia in a 6 m aqueous solution of sodium acetate increases from 23 kPa at 313 K to 70 kPa at 353 K and to about 160 kPa at 393 K. The influence of sodium acetate on the solubility of ammonia in water was modeled as described above, e.g., for sodium chloride. The parameters for interactions between sodium and acetate ions in water at 298.15 K were taken from Pitzer.32 However, because of the lack of experimental data, the influence of the temperature on those parameters had to be neglected:

Figure 2. NH3-H2O-NaCl: Difference in the partial pressure of ammonia caused by the presence of sodium chloride.

(0) βNa +,CH COO-/(kg/mol) ) 0.13723 3

(18a)

(1) βNa +,CH COO-/(kg/mol) ) 0.34195 3

(18b)

3τNa+,Na+,CH3COO-/(kg/mol)2 ) -0.00474

(18c)

The influence of sodium acetate on the solubility of (0) ammonia was described by parameters BNH 3,CH3COONa and ΓNH3,NH3,CH3COONa. Both parameters were fitted to the new experimental data given in Table 5 as described above: (0) BNH /(kg/mol) ) 3,CH3COONa

-0.02688 + 26.86428/(T/K) (19a) and Figure 3. NH3-H2O-NaNO3: Difference in the partial pressure of ammonia caused by the presence of sodium nitrate.

to the new experimental data given in Table 3, as described above for the system with sodium chloride: (0) BNH /(kg/mol) ) 0.00276 + 2.7323/(T/K) (17a) 3,NaNO3

and

ΓNH3,NH3,NaNO3/(kg/mol)2 ) -0.0004

(17b)

With that set of parameters, the experimental results for the total pressure are reproduced with an arithmetic

ΓNH3,NH3,CH3COONa/(kg/mol)2 ) -0.00041 (19b) Figure 4 shows a comparison between the new experimental results and the correlation for the total pressure. The arithmetic average deviation between the experimental results and the correlation is 1.7% for the pressure, 2.5% for the partial pressure of ammonia, and 5.3% for the partial pressure of water. These comparatively large deviations are at least partially caused by neglecting the influence of temperature on the interaction parameters for the binary system CH3COONaH2O. NH3-H2O-NaOH. Sodium hydroxide has the largest influence on the solubility of ammonia of all electrolytes investigated in the present work. Under all experimen-

2106 Ind. Eng. Chem. Res., Vol. 38, No. 5, 1999

Figure 4. Solubility of ammonia in aqueous solutions of sodium acetate. Exptl. results: 3, mCH3COONa ) 4 mol/kg; O, mCH3COONa ) 6 mol/kg. Correlation: s.

Figure 5. Solubility of ammonia in aqueous solutions of sodium hydroxide. Exptl. results: 3, mNaOH ) 4 mol/kg; O, mNaOH ) 6 mol/ kg. Correlation: s.

tal conditions sodium hydroxide reveals a salting-out effect on ammonia. That influence increases with increasing temperature. For example, the difference in the partial pressures of ammonia ∆pNH3 ) pNH3,H2O+NaOH pNH3,H2O required to dissolve 4 mol of ammonia in a 6 m aqueous solution of sodium hydroxide increases from 46 kPa at 313 K to 110 kPa at 353 K and to about 300 kPa at 393 K. The influence of sodium hydroxide on the solubility of ammonia in water was modeled following the outline given above for the other electrolytes investigated. The parameters for interactions between sodium and hydroxide ions in water were taken from Pabalan and Pitzer.36 They are given in Appendix II. The influence of sodium hydroxide on the solubility of (0) ammonia was described by parameters BNH and 3,NaOH ΓNH3,NH3,NaOH. Both parameters were fitted to the new experimental data given in Table 6 as described above:

Table 8. Setchenov Parameters for the Influence of Some Electrolytes on the Solubility of Ammonia in Aqueous Solutions

(0) BNH /(kg/mol) ) -0.01029 + 40.66414/(T/K) 3,NaOH (20a)

and

ΓNH3,NH3,NaOH/(kg/mol)2 ) -0.00072

(20b)

SNH3,MX/(kg/mol) MX

313.15 K

353.15 K

393.15 K

NaCl NaNO3 CH3COONa NaOH Na2SO4a (NH4)2SO4a NH4Clb NH4NO3b CH3COONH4b

0.048 -0.012 0.118 0.239 0.501 0.384 -0.011 -0.070 0.060

0.048 -0.010 0.098 0.210 0.400 0.320 -0.033 -0.050 0.058

0.048 -0.008 0.083 0.186 0.321 0.269 0.022 -0.034 0.057

a

Rumpf and Maurer.1

b

Predicted from eqs 13b and 21.

used to calculate the Setchenov constants for the influence of ammonium chloride, ammonium acetate, and ammonium nitrate on the solubility of ammonia in water by

1 (0) (0) (0) (0) BNH ) (BNH - BNH ) + BNH 3,NH4X 3,(NH4)2SO4 3,(Na)2SO4 3,NaX 2 (21) and

Figure 5 shows a comparison between the new experimental results and the correlation for the total pressure. The arithmetic average deviation between the experimental results and the correlation is 1.2% for the pressure (the maximum deviation is 2.8 % at 313.15 K, mNH3 ) 14.7 mol/kg, mNaOH ) 3 mol/kg, i.e., at p ) 129 kPa), 2.1% for the partial pressure of ammonia, and 2.7% for the partial pressure of water. Setchenov Parameters Setchenov parameters calculated from osmotic second virial coefficients determined in the present work are given in Table 8 together with results for the solubility of ammonia in aqueous solutions of sodium sulfate and ammonium sulfate.1 Furthermore, these results can be

(0) SNH3,NH4X ) 2BNH 3,NH4X

(13b)

where X ) Cl-, CH3COO-, or NO3-. From that table one recognizes that sodium ions reveal a stronger salting-out effect on ammonia than ammonium ions and the salting-out effect on ammonia decreases from SO42to OH- to CH3COO- to Cl- to NO3-. Thus, among the sodium salts, only sodium nitrate reveals a salting-in effect, while among the ammonium salts the nitrate as well as the chloride reveals a salting-in effect on ammonia. The predictions for the influence of the ammonium salts on the solubility of ammonia have been confirmed quantitatively by Sing.20

Ind. Eng. Chem. Res., Vol. 38, No. 5, 1999 2107

Conclusions The solubility of ammonia in water and in aqueous solutions of single univalent electrolytes sodium chloride, sodium nitrate, sodium acetate, and sodium hydroxide was measured at temperatures from about 313 to 393 K at total pressures of up to about 0.7 MPa. The electrolyte molalities were between 2 and 6 mol/kg. The maximum molality of ammonia in the liquid phase was about 20 mol/kg. The experimental results are correlated by applying an extension of Pitzer’s equation for the excess Gibbs energy of aqueous solutions of electrolytes. In most cases the results from the correlation agree with the experimental data within experimental uncertainty. Acknowledgment Financial support of this investigation by the government of the Federal Republic of Germany (BMFT Grant 0326558 C), by BASF AG (Ludwigshafen), Bayer AG (Leverkusen), Degussa AG (Hanau), Hoechst AG (Frankfurt), Linde-KCA AG (Dresden), and Lurgi GmbH (Frankfurt) is gratefully acknowledged. Nomenclature Aφ ) Debye-Hu¨ckel parameter a ) activity a1...12 ) parameters in the expression for interaction parameters Bij ) second virial coefficient for interactions between species i and j Bmix ) second virial coefficient of a mixture B(0) i,j ) osmotic second virial coefficient in Pitzer’s equation b ) constant in Pitzer’s equation f ) function (m) HNH ) Henry’s constant for the solubility of NH3 in 3,w water on molality scale i, j, k ) species i, j, and k I ) ionic strength M ) molecular weight m ) molality (MX) mNH ) molality of ammonia dissolved in an aqueous 3 solution of electrolyte MX at constant temperature and partial pressure of ammonia (0) mNH ) molality of dissolved ammonia in pure water at 3 constant temperature and partial pressure of ammonia N ) number of experimental data sets p ) pressure pi ) partial pressure of component i R ) universal gas constant Si,MX ) Setchenov parameter (influence of MX on the solubility of i) T ) temperature v ) molar volume v+ i ) characteristic molal volume of component i in the method of Brelvi and O’Connell ∞ vi,w ) partial molar volume of component i infinitely diluted in water y ) mole fraction in the vapor phase z ) number of charges Greek Letters R ) constant in Pitzer’s equation (0) (1) (1) β(0) ij ) βji ; βij ) βji ) binary parameters for interactions between species i and j in Pitzer’s equation ∆ ) difference

∆pNH3 ) pNH3,w+CH3COONa - pNH3,w ) difference in the partial pressure of NH3 for dissolving a constant amount of NH3 in an aqueous solution of CH3COONa and water, respectively pcalc - pexp 1 N |∆p| ) × 100 ) arithmetic average N k)1 pexp deviation for the pressure Γi,j,k ) osmotic third virial coefficient in Pitzer’s equation γ(m) ) activity coefficient on molality scale normalized i according to Henry’s law φi ) fugacity coefficient of component i τijk ) τjik ) τikj ) τjkl ) τkij ) τkji ) ternary interaction parameter in Pitzer’s equation

∑

(|

|)

Subscripts calc ) calculated CH3COONa ) sodium acetate CH3COO- ) acetate Cl- ) chloride exp ) experimental i, j, k ) components i, j, and k liq ) liquid MX ) 1:1 electrolyte of cation M+ and anion XM+ ) cation of 1:1 electrolyte MX m ) on molality scale Na+ ) sodium ion NaCl ) sodium chloride Na2SO4 ) sodium sulfate NaNO3 ) sodium nitrate NaOH ) sodium hydroxide NH3 ) ammonia (NH4)2SO4 ) ammonium sulfate NH4X ) ammonium salt of acid HX NO3- ) nitrate OH- ) hydroxide R ) reference w ) water X- ) anion of 1:1 electrolyte MX Superscripts ′′ ) vapor phase ∞ ) at infinite dilution max ) maximum (m) ) on molality scale pure ) pure component s ) saturation

Appendix I: Interaction Parameters of Pitzer’s Model for the Binary System NaCl-H2O The parameters for interactions between sodium and chloride ions were taken from Silvester and Pitzer.31 (0) -1 βNa +,Cl-/(kg/mol) ) 0.0765 - 777.03{(T/K)

(TR/K)-1} - 4.4706 ln(T/TR) + 0.008946(T/K TR/K) - 3.3158 × 10-6{(T/K)2 - (TR/K)2} (AI.1) (1) -5 (T/K βNa +Cl-/(kg/mol) ) 0.2664 + 6.1608 × 10

TR/K) + 1.0715 × 10-6{(T/K)2 - (TR/K)2} (AI.2) 3τNa+,Na+,Cl-/(kg/mol)2 ) 0.00127 + 33.317{(T/K)-1 (TR)-1} + 0.09421 ln(T/TR) - 4.655 × 10-5{(T/K) - (TR/K)} (AI.3) where TR ) 298.15 K.

2108 Ind. Eng. Chem. Res., Vol. 38, No. 5, 1999 Table 9. Coefficients for Equation AII.1 (from Pabalan and Pitzer36)

a1 a2 a3 a4 a5 a6 a7 a8 a9 a10 a11 a12

(0) βNa +,OH-/ (kg/mol)

(1) βNa +,OH-/ (kg/mol)

3τNa+,Na+,OH-/ (kg/mol)2

-2.768 25 × 102 -2.813 18 × 10-3 -7.375 54 × 103 3.701 25 × 10-1 -4.935 99 × 101 1.094 51 × 10-1 7.178 87 × 10-6 -4.021 85 × 10-5 -5.884 74 × 10-9 1.193 11 × 101 2.482 50 -4.821 74 × 10-3

4.628 70 × 102

-1.668 69 × 101 4.053 48 × 10-4 4.536 50 × 102 -5.171 40 × 10-2 2.968 08 -6.516 17 × 10-3 -1.055 304 × 10-6 2.376 58 × 10-6 8.989 34 × 10-10 -6.892 39 × 10-1 -8.115 63 × 10-2

-1.029 41 × 104 -8.596 06 × 101 2.390 60 × 10-1 -1.079 59 × 10-4

Appendix II: Interaction Parameters of Pitzer’s Model for the Binary System NaOH-H2O Pabalan and Pitzer36 published interaction param(0) (1) + + - for the binary eters βNa +,OH-, βNa+,OH-, and τNa ,Na ,OH system NaOH-H2O for temperatures between 273.15 and 623.15 K, which depend on temperature and pressure:

a3 + a4(p/bar) + T/K a5 ln(T/K) + [a6 + a7(p/bar)](T/K) +

f(T,p) ) a1 + a2(p/bar) +

[a8 + a9(p/bar)](T/K)2 + a10 a11 + a12(p/bar) + (AII.1) (T/K) - 227.0 647.0 - (T/K) In the present work pressure p was approximately by the vapor pressure of pure water psw. The coefficients are given in Table 9. Literature Cited (1) Rumpf, B.; Maurer, G. Solubility of ammonia in aqueous solutions of sodium and ammonium sulfate at temperatures from 333.15 K to 433.15 K and pressures up to 3 MPa. Ind. Eng. Chem. Res. 1993, 32, 1780. (2) Rumpf, B.; Maurer, G. Solubility of ammonia in aqueous solutions of phosphoric acid: Model development and application. J. Solution Chem. 1994, 23, 37. (3) 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. (4) Rumpf, B.; Nicolaisen, H.; Maurer, G. Solubility of carbon dioxide in aqueous solutions of ammonium chloride at temperatures from 313 K to 433 K and pressures up to 10 MPa. Ber. Bunsen-Ges. Phys. Chem. 1994, 98, 1077. (5) Rumpf, B.; Nicolaisen, H.; O ¨ cal, C.; Maurer, G. Solubility of carbon dioxide in aqueous solutions of sodium chloride: Experimental results and correlation. J. Solution Chem. 1994, 23, 431. (6) Rumpf, B.; Xia, J.; Maurer, G. An experimental investigation on the solubility of carbon dioxide in aqueous solutions containing sodium nitrate or ammonium nitrate at temperatures from 313 to 433 K and pressures up to 10 MPa. J. Chem. Thermodyn. 1997, 29, 1101. (7) Rumpf, B.; Xia, J.; Maurer, G. Solubility of carbon dioxide in aqueous solutions containing acetic acid or sodium hydroxide in the temperature range from 313 to 433 K and total pressures up to 10 MPa. Ind. Chem. Eng. Res. 1998, 37, 2012. (8) Xia, J.; Rumpf, B.; Maurer, G. Solubility of carbon dioxide in aqueous solutions containing sodium acetate or ammonium acetate at temperatures from 313 to 433 K and pressures up to 10 MPa. Fluid Phase Equilib. 1999, 155, 107.

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Received for review September 4, 1998 Revised manuscript received January 29, 1999 Accepted February 9, 1999 IE980572G