2012
Ind. Eng. Chem. Res. 1998, 37, 2012-2019
Solubility of Carbon Dioxide in Aqueous Solutions Containing Acetic Acid or Sodium Hydroxide in the Temperature Range from 313 to 433 K and at Total Pressures up to 10 MPa Bernd Rumpf, Jianzhong Xia, and Gerd Maurer* Lehrstuhl fu¨ r Technische Thermodynamik, Universita¨ t Kaiserslautern, D-67653 Kaiserslautern, Federal Republic of Germany
The solubility of carbon dioxide in aqueous solutions containing acetic acid and in aqueous solutions containing sodium hydroxide was measured in the temperature range from 313 to 433 K and total pressures up to 10 MPa. The molalities of acetic acid or sodium hydroxide in the liquid phase were about 4 and 1 mol/kg, respectively. Experimental results are reported and compared to correlations and predictions. Introduction The solubilities of weak electrolyte gases like ammonia, carbon dioxide, sulfur dioxide, or hydrogen sulfide in aqueous phases must be known in many applications, e.g., in the field of environmental protection or for the production of fertilizers. The basic design of equipment to separate such mixtures requires information on phase equilibrium and caloric effects and often also information on reaction and mass-transfer kinetics. As part of an ongoing project dealing with the thermodynamic description of phase equilibria in aqueous systems containing ammonia, sour gases (like carbon dioxide), and strong electrolytes, the solubility of carbon dioxide in aqueous solutions containing acetic acid or sodium hydroxide was measured in the temperature range from 313 to 433 K at total pressures up to about 10 MPa. Pitzer’s model for the excess Gibbs energy is used to correlate the data. Experimental results are reported and compared to the results of the correlations and predictions. Experimental Section The experimental equipment was basically the same as that used in previous work on the solubility of carbon dioxide in aqueous electrolyte solutions (see, for example, Rumpf and Maurer, 1993); therefore, only a short outline of the apparatus and procedure is given here. A thermostated high-pressure cell equipped with two sapphire windows is filled with carbon dioxide. After equilibration, the temperature and pressure are measured. The solvent is added stepwise by a high-pressure displacer until the gas is completely dissolved in the liquid phase. Thereafter, the pressure is decreased in small steps by withdrawing very small amounts of the liquid mixture until the first stable bubble appears. The mass of the gas filled into the cell is either calculated from the Bender equation of state (Bender, 1970) using the known volume of the cell and the experimental results for temperature and pressure or determined by weighing. The mass of the solvent needed to dissolve the gas is calculated from the displacement of the * To whom correspondence should be addressed. E-mail:
[email protected]. Phone: +49 631 205 2410. Fax: +49 631 205 3835.
displacer piston and the density of the solvent (Washburn, 1928). Pressure is determined by pressure transducers (WIKA GmbH, Klingenberg, Germany) with ranges of 0-0.6, 0-1.6, and 0-10 MPa. The transducers were calibrated against a high-precision pressure gauge (Desgranges & Huot, Aubervilliers, France) before and after each series of measurements. The maximum uncertainty in the pressure measurement is about 0.1% of each transducer’s maximum reading. The temperature was determined with two calibrated platinum resistance thermometers placed in the thermostated bath around the cell. The uncertainty in the temperature measurement is less than (0.1 K. The aqueous solutions were prepared in a storage tank by dissolving known amounts of acetic acid or sodium hydroxide in water. The relative uncertainty of the molality of these components in the aqueous solution is less than (0.1%. Substances Carbon dioxide (g99.995 mol %; Messer-Griesheim, Ludwigshafen, Germany) was used without further purification. Acetic acid (g99.8 mass %) and sodium hydroxide (g99 mass %) were purchased from Riedel de Haen AG, Seelze, Germany, and further dried and purified under vacuum. Deionized water was further purified by vacuum distillation. Results Results for the System CO2-CH3COOH-H2O. The experimental results for the solubility of carbon dioxide in aqueous solutions containing acetic acid are given in Table 1. Six isotherms in the range from 313 to 433 K were investigated. The overall molality of acetic acid in the liquid phase was about 4 mol/kg; the overall molality of carbon dioxide ranged up to 1.7 mol/ kg. Measured total pressures ranged up to about 8.3 MPa. In Figure 1, some of the experimental results for the total pressure at 313 and 433 K are compared to calculated results for the solubility of carbon dioxide in pure water. As can be seen from that figure, the addition of carbon dioxide to an aqueous solution containing a fixed molality of acetic acid at first causes a nearly linear increase in the total pressure above the
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Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998 2013 Table 1. Experimental Results for the Solubility of Carbon Dioxide in Aqueous Solutions of Acetic Acid m j CO2 m j HAc 10p T (K) (mol/kg) (mol/kg) (MPa) 313.15 313.17 313.18 313.17 313.17 313.15 313.17 313.15 313.15 313.14 313.15 313.15 333.20 333.19 333.19 333.19 333.19 333.19 333.20 353.21 353.19 353.20 353.20 353.20 353.19 353.19 353.19
0.0909 0.2129 0.4279 0.8570 1.2798 1.2819 1.7305 0.1064 0.2145 0.4306 0.8605 1.3961 0.1137 0.2135 0.4305 0.8575 1.2860 1.2882 1.4232 0.1165 0.1170 0.2137 0.4259 0.4259 0.8641 1.1932 1.1970
3.9984 3.9984 3.9984 3.9984 3.9984 3.9984 3.9984 3.8664 3.8664 3.8664 3.8664 3.8664 3.8664 3.8664 3.8664 3.8664 3.8664 3.8664 3.8664 3.8664 3.8664 3.8664 3.8664 3.8664 3.8664 3.8664 3.8664
2.787 6.540 13.37 28.49 46.17 46.32 71.27 3.328 6.651 13.85 29.12 52.55 5.044 9.076 18.56 39.40 64.92 65.17 76.83 6.471 6.651 11.46 23.13 23.22 49.29 74.07 74.10
m j CO2 m j HAc 10p T (K) (mol/kg) (mol/kg) (MPa) 393.22 393.22 393.22 393.22 393.22 393.22 393.22 413.23 413.23 413.23 413.22 413.23 413.23 413.23 433.24 433.24 433.27 433.25 433.24 433.25 433.24 433.25 433.24
0 0.1206 0.2138 0.2140 0.4320 0.8110 1.0918 0 0.1292 0.1295 0.2072 0.4197 0.8004 1.0514 0 0 0.1258 0.2138 0.4306 0.4322 0.7574 1.0185 1.0225
3.8517 3.8517 3.8517 3.8517 3.8517 3.8517 3.8517 3.8517 3.8517 3.8517 3.8517 3.8517 3.8517 3.8517 3.8517 3.8517 3.8517 3.8517 3.8517 3.8517 3.8517 3.8517 3.8517
1.960 9.934 16.04 16.10 31.00 58.96 81.76 3.557 12.59 12.62 18.04 33.27 62.26 82.77 6.062 6.072 15.14 21.44 37.19 37.28 61.94 82.77 82.98
Figure 1. Solubility of carbon dioxide in aqueous solutions of acetic acid: O, experimental results, this work; - - -, calculated results for the system CO2-H2O.
solution. In the temperature range investigated here, the solubilitysas in the binary system carbon dioxidewatersdecreases with increasing temperature. Comparing the experimental results for the ternary system to the results for the solubility of carbon dioxide in pure water shows that acetic acid (at a fixed overall molality of carbon dioxide and a fixed temperature) causes a large decrease in the total pressure. Thus, for example at 313 K and an overall molality of carbon dioxide of 0.9 mol/kg, the total pressure above an aqueous solution containing about 4 mol/kg of acetic acid is about 2.97 MPa, whereas it is about 5.07 MPa in the binary system carbon dioxide-water; i.e., a decrease in the total pressure by about 41% is observed. Obviously the decrease of the solubility of carbon dioxide due to the presence of another acid in the aqueous phase is overcompensated by the increase caused by the better solubility of carbon dioxide in the organic solvent acetic acid.
Table 2. Experimental Results for the Solubility of Carbon Dioxide in Aqueous Solutions of Sodium Hydroxide m j CO2 m j NaOH 10p T (K) (mol/kg) (mol/kg) (MPa) 313.14 313.19 313.19 313.18 313.17 313.18 313.18 313.18 313.16 333.19 333.18 333.18 333.18 333.19 333.18 333.18 333.18 333.18 353.21 353.20 353.19 353.19 353.19 353.19 353.20 353.19 393.23 393.22 393.21 393.22 393.22 393.23 393.23 393.22 393.23 393.23 393.22 393.22 393.22
0.9186 0.9793 1.1540 1.1569 1.1602 1.3843 1.5824 1.7855 1.9513 0.8554 0.9225 1.0661 1.0685 1.2670 1.3963 1.5636 1.6836 1.7228 0.8625 0.9037 0.9984 1.1826 1.3107 1.4641 1.4702 1.6227 0 0.3846 0.7136 0.9005 0.9021 0.9029 0.9030 0.9040 0.9923 1.1674 1.3821 1.4024 1.5161
0.9613 0.9613 0.9613 0.9613 0.9613 0.9613 0.9613 0.9613 0.9613 0.9613 0.9613 0.9613 0.9613 0.9613 0.9613 0.9613 0.9613 0.9613 0.9613 0.9613 0.9613 0.9613 0.9613 0.9613 0.9613 0.9613 0.9569 0.9569 0.9569 0.9569 0.9569 0.9569 0.9569 0.9569 0.9569 0.9569 0.9569 0.9569 0.9569
0.534 1.860 11.62 11.64 11.82 25.27 41.89 59.00 79.11 0.583 1.092 9.523 9.393 24.41 37.57 56.71 73.40 80.09 0.763 1.791 7.767 23.18 38.08 58.49 60.22 84.88 1.923 2.143 2.143 3.750 3.321 3.341 3.830 3.261 10.05 31.43 65.00 69.29 89.16
m j CO2 m j NaOH 10p T (K) (mol/kg) (mol/kg) (MPa) 413.24 413.25 413.23 413.23 413.25 413.25 413.23 413.24 413.24 413.25 413.21 433.23 433.24 433.24 433.15 433.23 433.19 433.17 313.16 313.16 313.17 313.17 313.17 313.17 313.18 313.19 313.17 313.17 313.18 333.19 333.20 333.19 333.17 333.20 333.18 333.20 353.19 353.20 353.19 353.21 353.19 353.20
0 0.6825 0.8644 0.8688 0.9033 1.0778 1.1432 1.2708 1.4175 1.4611 1.4801 0 0.7771 0.8191 0.9057 1.0860 1.3116 1.5128 0.0804 0.1619 0.4354 0.8669 0.8748 1.1726 1.4541 1.8030 1.8244 1.9682 2.0522 0.8142 1.0735 1.0753 1.2866 1.4957 1.7304 1.8073 0.7862 1.0085 1.2219 1.3483 1.6040 1.7381
0.9569 3.501 0.9569 3.670 0.9569 4.469 0.9569 4.509 0.9569 5.078 0.9569 21.51 0.9569 30.99 0.9569 50.74 0.9569 76.43 0.9569 82.97 0.9569 87.94 0.9613 5.971 0.9613 6.520 0.9613 6.809 0.9613 7.936 0.9613 25.48 0.9613 59.77 0.9613 96.96 1.0441 0.137 1.0441 0.237 1.0441 0.327 1.0441 0.127 1.0441 0.147 1.0441 7.585 1.0441 20.03 1.0441 52.81 1.0441 55.15 1.0441 72.44 1.0441 101.63 1.0441 0.257 1.0441 4.290 1.0441 4.550 1.0441 23.23 1.0441 43.63 1.0441 70.08 1.0441 83.15 1.0441 0.656 1.0441 1.565 1.0441 19.70 1.0441 34.01 1.0441 69.97 1.0441 94.13
Results for the System CO2-NaOH-H2O. The results for the solubility of carbon dioxide in aqueous solutions containing about 1 mol of sodium hydroxide/ kg of water are given in Table 2. Temperature ranged from 313 to 433 K; the maximum overall molality of carbon dioxide was about 1.95 mol/kg. Total pressures ranged up to 9.7 MPa. Some of the experimental results for the total pressure are plotted in Figure 2 together with the prediction from the Pitzer model (see below). As was expected, the addition of carbon dioxide to a solution containing a fixed overall molality of sodium hydroxide at first results only in a slight change in the total pressure as nearly all carbon dioxide is dissolved in ionic form, i.e., as carbonate and bicarbonate ions. When the overall amount of carbon dioxide in the liquid phase nearly equals the overall amount of sodium hydroxide, the total pressure above the aqueous solution steeply increases. As in the system carbon dioxide-water, the solubility decreases with increasing temperature. Modeling CO2-CH3COOH-H2O. Figure 3 shows a scheme of the model applied to correlate the new data for the solubility of carbon dioxide in aqueous solutions of acetic
2014 Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998
n j HAc ) nHAc + nAc-
(7)
n j H2O ) nH2O + nHCO3- + nCO32- + nOH-
(8)
the condition for chemical equilibrium is used to calculate the true amounts in the liquid phase. The phase equilibrium conditions for carbon dioxide, acetic acid, and water are
(
pywφ′′w ) psw φsw exp
(
(m) pyiφ′′i ) Hi,w (T,psw) exp
Figure 2. Solubility of carbon dioxide in aqueous solutions of sodium hydroxide: O, 0, 4, experimental results, this work; s, prediction, this work.
)
vw(p - psw) aw RT
)
(9)
∞ vi,w (p - psw) miγ* i RT i ) HAc, CO2 (10)
Furthermore, the dimerization of acetic acid in the vapor phase (however, the dimerization was neglected in the liquid phase)
2CH3COOH h (CH3COOH)2
(11)
is considered through the equilibrium condition
K h p(T) )
Figure 3. VLE and chemical reactions in the system CO2CH3COOH-H2O.
acid. Due to chemical reactions in the liquid phase, carbon dioxide and acetic acid are dissolved not only in molecular but also in ionic form. Four chemical reactions are considered in the liquid phase:
CO2 + H2O h HCO3- + H+
(1)
HCO3- h CO32- + H+
(2)
H2O h H+ + OH-
(3)
CH3COOH h CH3COO- + H+
(4)
The condition for chemical equilibrium in the liquid phase is
KR(T) )
∏i aνi
i,R
(5)
Together with the balance equations for the overall number of moles of carbon dioxide, acetic acid, and water
n j CO2 ) nCO2 + nHCO3- + nCO32-
(6)
y(HAc)2φ′′(HAc)2 p0 (yHAcφ′′HAc)2 p
(12)
The model requires the knowledge of the temperatureh p, the dependent equilibrium constants K1-K4 and K activities of all species present in the liquid phase, Henry’s constants for acetic acid and carbon dioxide dissolved in pure water, the vapor pressure psw and molar volume vw of pure water, and the partial molar ∞ for i representing carbon dioxide and volumes vi,w acetic acid, as well as information on the fugacity coefficients in the vapor phase. Equilibrium constants for reactions 1-3 were obtained from Bieling et al. (1989) (cf. Table 3), and those for reaction 4 were calculated from the Giauqe functions for CH3COOH and CH3COO- as given by Brewer (1982) (cf. appendix 3). The equilibrium constant K h p for the dimerization of acetic acid in the vapor phase was taken from Bu¨ttner and Maurer (1983) (cf. Table 3). Henry’s constant for the solubility of carbon dioxide in water was obtained from Rumpf and Maurer (1993) (cf. Table 4), whereas that of acetic acid was determined in this work (see below). The vapor pressure and molar volume of pure water were taken from Saul and Wagner (1987). Fugacity coefficients in the vapor phase were calculated from the virial equation of state truncated after the second virial coefficient. The second virial coefficients of water and carbon dioxide were calculated from correlations based on the data recommended by Dymond and Smith (1980) (cf. Table 5). Mixed second virial coefficient BCO2,w was taken from Hayden and O’Connell (1975). The second virial coefficient of acetic acid as well as mixed virial coefficients BHAc,w and BCO2,HAc had to be set to zero due to the lack of experimental informa∞ of carbon dioxide tion. The partial molar volume vCO 2,w dissolved in water at infinite dilution was calculated according to the method by Brelvi and O’Connell (1972). Due to the limited experimental data, the partial molar volume of acetic acid dissolved in water at infinite dilution had to be set to zero (cf. Table 6). Activity coefficients of all species were calculated from the Pitzer
Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998 2015 Table 3. Equilibrium Constants for Chemical Reactions 1-4 (Edwards et al., 1978; Bu 1 ttner and Maurer, 1983; Bieling et al., 1989)
ln KR ) AR/(T/K) + BR ln(T/K) + CR(T/K) + DR reaction
AR
BR
CR × 102
DR
CO2 + H2O h HCO3- + H+ -7742.6 -14.506 -2.8104 102.28 HCO3- h CO32- + H+ -8982.0 -18.112 -2.2249 116.73 H2O h H+ + OH-13445.9 -22.4773 0 140.932 2CH3COOH h 7928.7 -19.1001 (CH3COOH)2
Table 4. Henry’s Constant for the Solubilities of Acetic Acid and Carbon Dioxide in Pure Water (m) ln Hi,w (T,psw)/(MPa‚kg‚mol-1) ) Ai,w + Bi,w/(T/K) + Ci,w(T/K) + Di,w ln(T/K)
i
Ai,w
Bi,w
Ci,w
Di,w
CO2 CH3COOH
192.876 52.9967
-9624.4 -8094.25
0.01441
-28.749 -6.41203
Table 5. Pure Component Second Virial Coefficients (273 e T/K e 473)
Bi,i/(cm3/mol) ) ai,i + bi,i(ci,i/(T/K))di,i i
ai,i
bi,i
ci,i
di,i
CO2 H2O
65.703 -53.53
-184.854 -39.29
304.16 647.3
1.4 4.3
Table 6. Mixed Second Virial Coefficients and Partial Molar Volumes for CO2 at Infinite Dilution in Water T (K)
BCO2,w (cm3/mol)
∞ vCO (cm3/mol) 2,w
313.15 333.15 373.15 393.15 413.15 433.15
-163.1 -144.6 -115.7 -104.3 -94.3 -85.5
33.4 34.7 38.3 40.8 43.8 47.5
(1973) equation for the excess Gibbs energy of an electrolyte solution (cf. appendix 1). The dielectric constant of pure water was calculated according to the equations of Bradley and Pitzer (1979). To correlate the new experimental results for the solubility of carbon dioxide in aqueous solutions of acetic acid, first Henry’s constant for the solubility of acetic acid in water was determined from vapor-liquid equilibrium data in the system CH3COOH-H2O. Rewriting eq 10 for acetic acid yields
ln
f ′′HAc v∞HAc,w(p - psw) + ln γ* ) ln H(m) + HAc,w HAc (13) mHAc RT
allowing the determination of H(m) HAc,w from an extrapolation procedure. Thus, Henry’s constant for the solubility of acetic acid in water was determined from isothermal experimental data (p, T, m j HAc, yjHAc) on vapor-liquid equilibrium in the binary system acetic acid-water in the temperature range from 298 to 363 K (Arich and Tagliavini, 1958; Achavya and Rao, 1947; Campbell et al., 1963; Tsiparis and Smorigaite, 1964; Vrevsky et al., 1927) as follows: In the first step, the true molality mHAc of acetic acid in the liquid phase was calculated from the experimental overall molality m j HAc by solving the equilibrium conditions for reactions
3 and 4. In that step, all interaction parameters were set to zero; i.e., the activity coefficient of acetic acid was set to 1, whereas those for water and the ionic species were approximated by the modified Debye-Hu¨ckel term as used in Pitzer’s equations. Next, the condition for chemical equilibrium in the vapor phase (cf. eq 12) was used to calculate the true mole fraction yHAc from the experimental overall mole fraction yjHAc, thus yielding an estimate for the fugacity f HAc ′′ of acetic acid monomers in the vapor phase. The results obtained for the isothermal experimental data were plotted versus the overall amount of acetic acid in the liquid phase and extrapolated to m j HAc ) 0, thus yielding a number for (cf. eq 13). The results obtained in the temperH(m) HAc,w ature range from 298 to 363 K were correlated by -1 s ln H(m) HAc,w(T,pw)/(MPa‚kg‚mol ) ) AHAc,w + BHAc,w/(T/K) + CHAc,w ln(T/K) (14)
with coefficients AHAc,w, BHAc,w, and CHAc,w given in Table 4. In the next step, interaction parameters for Pitzer’s equation were determined. Preliminary calculations showed that due to the comparably small dissociation constant of acetic acid the (calculated) ionic strength in the binary system acetic acid-water did not exceed 0.02 mol/kg. Therefore, all interaction parameters involving charged species were set to zero. Finally, only (0) and τHAc,HAc,HAc (treated as Pitzer parameters βHAc,HAc independent of temperature) were fitted to the experimental results for the total pressure and the overall mole fractions of acetic acid in the vapor phase in the temperature range from 298 to 363 K and overall molalities of acetic acid up to about 25 mol/kg. The results for the interaction parameters are given in Table 7. Due to the influence of activity coefficients on the calculated numbers for the true molality of acetic acid in the liquid phase, the above-described procedure, in principle, should be performed once more, taking into account interaction parameters. However, in view of the limited availability of experimental data, such a procedure did not seem to be appropriate. Thus, we currently recommend to use Henry’s constant H(m) HAc,w from Table 4 together with interaction parameters from Table 7. As an example, in Figure 4 experimental data for the total pressure in the acetic acid-water system are compared to calculated results. Relative deviations in the total pressure do not exceed 4.2%. Furthermore, in Figure 5 the experimental results for the overall mole fraction of acetic acid in the vapor phase are compared to the results of the present correlation. In the next step, Henry’s constant and interaction parameters for the acetic acid-water system were preassigned and the solubility of carbon dioxide in aqueous solutions of acetic acid was modeled. As in that system two weak acids are simultaneously present in the liquid phase, the chemical equilibria of eqs 1-4 predominantly lie on the left side. Therefore, all parameters describing interactions between neutral carbon dioxide and charged species were set to zero. (0) , τCO2,CO2,HAc) Finally, only two parameters (βCO 2,HAc were fitted to the new experimental results in the temperature range from 313 to 433 K. The temperature
2016 Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998 Table 7. Interaction Parameters for Pitzer’s Equation for the Systems CH3COOH-H2O, CO2-CH3COOH-H2O, and CO2-NaOH-H2O
f(T) ) q1 + q2/(T/K) + q3/(T/K)2 parameter (0) βCO 2,HCO3 (0) βCO + 2,Na (0) βHAc,HAc
τHAc,HAc,HAc (0) βCO 2,HAc τCO2,CO2,HAc
q1
q2
0.0843 -0.1666 -0.05761 0.00084 -0.09046 -0.02079
-16.15 110.66
q3
Tmin (K)
Tmax (K)
-11347.5
313 313 298
473 473 363
NH3-CO2-H2O CO2-Na2SO4-H2O CH3COOH-H2O
Kurz et al. (1995) Rumpf and Maurer (1993) this work
313
433
CO2-CH3COOH-H2O
this work
13.37 5.977
Figure 4. Total pressure above aqueous solutions containing acetic acid: +, ×, ], 0, O, 4, experimental results, Campbell et al., 1963; Arich and Rao, 1947; Vrevsky et al., 1927; Tsiparis and Smorigaite, 1964; s, correlation, this work.
Figure 5. CH3COOH-H2O. Overall mole fractions of acetic acid in the vapor phase (experimental results as taken from the data collection by Gmehling et al., 1981): +, T ) 298 K; ×, T ) 313 K; ], T ) 333 K; 0, T ) 343 K; O, T ) 353 K; 4, T ) 363 K; s, correlation, this work.
dependence of those parameters had to be taken into account. It was approximated by
f(T) ) q1 + q2/(T/K)
(15)
The results are given in Table 7. In Figure 6, the new experimental results for the system CO2-CH3COOHH2O are compared to the results of the correlation. The average relative deviation in the total pressure is 2%,
subsystem
source
Figure 6. Solubility of carbon dioxide in 1 m aqueous solutions of acetic acid: O, 0, 4, 9, b, ], 3, experimental results, this work; s, correlation, this work.
the maximum relative deviation is 4.7% at T ) 433 K, and m j CO2 ) 1.02 mol/kg where p ) 8.3 MPa. It should be noted that the influence of the chemical reactions in the liquid phase in the system CO2-CH3COOH-H2O is small due to the fact that two acids are simultaneously present (the calculated ionic strength is less than about 0.01 mol/kg). However, in view of modeling the solubility of carbon dioxide in aqueous systems containing salts of acetic acid like sodium acetate or ammonium acetate (where the chemical reactions have an important influence), it seems to be reasonable to include the (small) effect of the chemical reactions also in the system CO2-CH3COOH-H2O. CO2-NaOH-H2O. Figure 7 shows a scheme of the model to predict the solubility of carbon dioxide in aqueous solutions of sodium hydroxide. In the liquid phase, reactions 1-3 are considered, whereas sodium hydroxide is assumed to be fully dissociated. Hence, there are seven species (i.e., CO2, H2O, HCO3-, CO32-, Na+, H+, and OH-) present in the liquid phase. The interaction parameters for the Pitzer model can be divided into three groups: 1. Parameters describing interactions between neutral solutes: Due to the low solubility of carbon dioxide in water, all binary and ternary parameters describing interactions between neutral solute carbon dioxide were set to zero. 2. Parameters describing interactions between charged species: For the system sodium hydroxide-water, interaction parameters were taken from Pabalan and Pitzer (1987) (cf. appendix 2). For aqueous solutions of sodium bicarbonate and sodium carbonate, parameters were taken from Peiper and Pitzer (1982) (cf. appendix 2).
Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998 2017
Acknowledgment Financial support of this investigation by the government of the Federal Republic of Germany (BMFT Grant No. 0326558 C), BASF AG (Ludwigshafen), Bayer AG (Leverkusen), Degussa AG (Hanau), Hoechst AG (Frankfurt), Linde KCA (Dresden), and Lurgi AG (Frankfurt) is gratefully acknowledged. Nomenclature
Figure 7. VLE and chemical reactions in the system CO2NaOH-H2O.
3. Parameters describing interactions between neutral solute carbon dioxide and charged species: For interactions between carbon dioxide and sodium ions, (0) parameter βCO was taken from Rumpf and Maurer 2,Na+ (1993), and those describing interactions between carbon dioxide and dissolved bicarbonate or carbonate ions (0) (0) (i.e., βCO - and βCO ,CO 2-) were taken from Kurz 2,HCO3 2 3 et al. (1995), respectively (cf. Table 7). Due to the low concentration of hydrogen and hydroxide ions, all interaction parameters between those species and carbon dioxide were set to zero. That set of parameters allows a prediction of the solubility of carbon dioxide in aqueous solutions containing sodium hydroxide. A comparison between predicted and experimentally determined total pressures is shown in Figure 2. The experimental results for the total pressure above CO2 + NaOH + H2O are predicted with an average relative deviation of 9%. However, that deviation mostly results from a few data points at carbon dioxide molalities m j CO2 e m j NaOH where the total pressure is nearly not changed by the addition of carbon dioxide. In that low pressure range, the absolute uncertainty in the pressure readings can reach up to 5%. If one neglects data points with relative deviations larger than about 10% (mostly at ratios m j CO2/m j NaOH e 1 and measured total pressures on the order of the vapor pressure of pure water), the average relative deviation reduces to 2.2%. Conclusions The solubility of carbon dioxide in aqueous solutions containing acetic acid or sodium hydroxide was measured in the temperature range from 313 to 433 K at total pressures up to about 10 MPa. Molalities of acetic acid and sodium hydroxide were about 4 and 1 mol/kg, respectively. A model is presented to describe the simultaneous chemical and phase equilibria. The model is able to correlate the new experimental data for CO2CH3COOH-H2O within the experimental uncertainty. With interaction parameters solely determined from binary (salt-water) and ternary (ammonia-carbon dioxide-water) systems, the model is able to quantitatively predict vapor-liquid equilibria in the system CO2-NaOH-H2O.
Ai,w, ..., Di,w ) coefficients for the temperature dependence of Henry’s constants AR, ..., DR ) coefficients for the temperature dependence of equilibrium constants Aφ ) Debye-Hu¨ckel parameter ai,i, ..., di,i ) coefficients for the temperature dependence of second virial coefficients ai ) activity of component i b ) constant in the modified Debye-Hu¨ckel expression Bi,j ) second virial coefficient for interactions between species i and j Cφ ) third virial coefficient in Pitzer’s equation D ) relative dielectric constant of water e ) charge of proton f ) function for the temperature dependence of an interaction parameter fi ) fugacity of component i f1, f2, f3 ) functions in Pitzer’s equation GE ) excess Gibbs energy hi,f ) standard enthalpy of formation of component i (m) Hi,w ) Henry’s constant for the solubility of gas i in pure water (on molality scale) I ) ionic strength (on molality scale) k ) Boltzmann’s constant KR ) equilibrium constant for chemical reaction R (on molality scale) K h p ) equilibrium constant for the dimerization of acetic acid in the vapor phase Mw ) molar mass of water (kg/mol) m j i ) overall molality of component i mi ) true molality of component i n j i ) overall number of moles of component i ni ) true number of moles of component i NA ) Avogadro’s number p ) total pressure p0 ) standard pressure qi ) coefficients for the temperature dependence of interaction parameters R ) universal gas constant t ) Celsius temperature T ) absolute temperature v ) partial molar volume x ) variable in Pitzer’s equation y ) mole fraction in vapor yj ) overall mole fraction in vapor zi ) number of charges of component i Greek Letters R ) constant in Pitzer’s equation β(0), β(1) ) binary interaction parameters in Pitzer’s equation γ* ) activity coefficient normalized to infinite dilution (on molality scale) 0 ) vacuum permittivity µi ) chemical potential of component i
2018 Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998 νi,R ) stoichiometric coefficient of component i in reaction R F ) mass density τ ) ternary interaction parameter in Pitzer’s equation φi ) Giauqe function of component i φ ) fugacity coefficient Subscripts
Differentiation of eq 16 yields the activity coefficient of the dissolved species i:
2 ln γ* i ) -Aφzi
2
f ) formation HAc ) acetic acid i, j, k ) components i, j, k max ) maximum min ) minimum R ) reaction R or reference w ) water
(
xI
+
2 b
1 + bxI (0) (1) mj(βi,j + βi,j f2(x)) - z2i
∑ j*w
)
ln(1 + bxI) + (1) mjmkβj,k f3(x) + ∑ ∑ j*wk*w 3 ∑ ∑ mjmkτi,j,k (21) j*wk*w
where f3 is defined as
f3(x) )
Superscripts m ) on molality scale s ) saturation * ) normalized to infinite dilution ∞ ) infinite dilution ′ ) liquid phase ′′ ) gas phase 0 ) reference state
( (
) )
1 x2 -x 1 1 + x + e 2 Ix2
The activity of water follows from the Gibbs-Duhem equation
ln aw )
(
∑∑
∑∑ ∑
∑
i*wj*wk*w
Pitzer’s (1973) equation for the excess Gibbs energy of an aqueous, salt-containing system is
RTnwMw
) f1(I) +
(0) (1) mimj(βi,j + βi,j f2(x)) + ∑ ∑ i*wj*w
∑ ∑ ∑ mimjmkτi,j,k
)
I1.5 (0) (1) -x Mw 2Aφ mimj(βi,j + βi,j e ) i*wj*w 1 + bxI mimjmkτi,j,k + mi) (23) Mw(2
Appendix 1. Brief Outline of Pitzer’s Model
GE
(22)
(16)
i*wj*wk*w
i*w
For systems containing a single salt Mν+Xν-, the binary and ternary parameters involving two or more species of the same sign of charge are usually neglected. The ternary parameters τM,X,X and τM,M,X are usually reported as third virial coefficients Cφ for the osmotic coefficient. Instead of rewriting eqs 21 and 23 in terms of Cφ, the ternary parameter τM,X,X was set to zero and parameters τM,M,X were calculated from numbers reported for Cφ:
(0) (1) where βi,j and βi,j are binary and τi,j,k are ternary interaction parameters, respectively. The function f1(I) is a modified Debye-Hu¨ckel term
1:1 salt
1 τM,M,X ) Cφ 3
4I f1(I) ) -Aφ ln(1 + bxI) b
2:1 salt
τM,M,X )
(17)
(24)
x2 φ C 6
(25)
where I is the ionic strength
I)
1
∑i
mizi2
2
(18)
and b ) 1.2 (kg/mol)1/2. Aφ is the Debye-Hu¨ckel parameter for the osmotic coefficient
Aφ )
(
)(
F′w 1 2πNA 3 1000
1/2
)
e2 4π0DkT
3/2
(19)
Appendix 2. Interaction Parameters for Pitzer’s Equation Tables 8 and 9 report relations for the temperature dependence of interaction parameters. T is the temperature in Kelvin and TR ) 298.15 K. Table 8. Ion Interaction Parameters for Aqueous Solutions of NaHCO3 and Na2CO3 (Peiper and Pitzer, 1982)
f(T) ) q1 + q2(T - TR) + q3(T - TR)2
The function f2 is defined as
f2(x) )
2 (1 - (1 + x)e-x) 2 x
(20)
where x ) RxI. For the salts considered here, R ) 2.0 (kg/mol)1/2.
salt
parameter
q1
q2 × 103
q3 × 105
NaHCO3
β(0) β(1) β(0) β(1) Cφ
0.028 0.044 0.0362 1.51 5.2 × 10-3
1.0 1.1 1.79 2.05
-1.3 -2.15 -2.11 -8.4
Na2CO3
Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998 2019 Table 9. Ion Interaction Parameters for Aqueous Solutions of NaOH (Pabalan and Pitzer, 1987)a
Literature Cited
f(T) ) q1 + q2p + (q3 + q4p)/T + q5 ln T + (q6 + q7p)T + q11 + q12p q10 (q8 + q9p)T 2 + + T - 227 647 - T
Achavya, M. V. R.; Rao, M. N. Trans. 1ndian Inst. Chem. Eng. 1947. As cited by Gmehling et al. (1981).
parameter
β(0)
β(1)
q1
2.768 247 8 × 102
q2 q3
-2.813 177 8 × 10-3 -7.375 544 3 × 103
q4 q5
3.701 254 0 × 10-1 -4.935 997 0 × 101
q6
1.094 510 6 × 10-1
q7 q8
7.178 873 3 × 10-6 -4.021 850 6 × 10-5
q9 q10 q11 q12
-5.884 740 4 × 10-9 1.193 112 2 × 101 2.482 496 3 -4.821 741 0 × 10-3
4.628 697 7 × 102 0.0 -1.029 418 1 × 104 0.0 -8.596 058 1 × 101 2.390 596 9 × 10-1 0.0 -1.079 589 4 × 10-4 0.0 0.0 0.0 0.0
Arich, G.; Tagliavini, G. Ric. Sci. 1958. As cited by Gmehling et al. (1981). Bender, E. Equations of state exactly representing the phase behaviour of pure substances. Proceedings of the 5th Symposium on Thermophysical Properties; ASME: New York, 1970; p 227.
Cφ
4.053 477 8 × 10-4 4.536 496 1 × 102
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.
-5.171 401 7 × 10-2 2.968 077 2
Bradley, D. J.; Pitzer, K. S. Thermodynamics of electrolytes. 12. Dielectric properties of water and Debye-Hu¨ckel parameters to 350 °C and 1 kbar. J. Phys. Chem. 1979, 83, 1599.
-1.668 689 7 × 101
-6.516 166 7 × 10-3 -1.055 303 73 × 10-6 2.376 578 6 × 10-6 8.989 340 5 × 10-10 -6.892 389 9 × 10-1 -8.115 628 6 × 10-2 0.0
a In the equation, p is the pressure (bar). In the pressure range considered here, p was set equal to the saturation pressure of pure water.
Brelvi, S. W.; O’Connell, J. P. Corresponding states correlations for liquid compressibility and partial molal volumes of gases at infinite dilution in liquids. AIChE J. 1972, 18, 1239. Brewer, L. Thermodynamic values for desulfurization processes. In Flue gas desulfurization; Hudson, J. L., Rochelle, G. T., Eds.; ACS Symposium Series 188; American Chemical Society: Washington, DC, 1982; p 1. Bu¨ttner, R.; Maurer, G. Dimerisierung einiger organischer Sa¨uren in der Gasphase. Ber. Bunsen-Ges. Phys. Chem. 1983, 87, 877. Campbell, A. N.; Kartzmak, E. M.; Gieske, J. M. T. M. Can. J. Chem. 1963. As cited by Gmehling et al. (1981). Dymond, J. H.; Smith, E. B. The virial coefficients of pure gases and mixtures; Oxford University Press: Oxford, U.K., 1980.
Appendix 3. Equilibrium Constant for the Dissociation of Acetic Acid in Water
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.
Brewer (1982) reported values for the Giauqe func0 0 tions φi ) -(µi,f (T) - hi,f (298.15 K))/RT and standard 0 (298.15 K) for various subenthalpies of formation hi,f stances. Standard thermodynamics yields the equilibrium constant for the dissociation of acetic acid:
Gmehling, J.; Onken, U.; Arlt, W. VLE data collection: Aqueous organic systems; DECHEMA Chemistry Data Series, DECHEMA: Frankfurt/Main, Germany, 1981; Vol. I, part 1a.
ln K4 ) -φHAc + φH+ + φAc- +
Kurz, F.; Rumpf, B.; Maurer, G. Vapor-liquid-solid phase equilibria in the system NH3-CO2-H2O from around 310 to 470 K: New experimental data and modeling. Fluid Phase Equilib. 1995, 104, 261.
(
)
0 0 h0HAc,f (298.15 K) - hH +,f (298.15 K) - hAc-,f (298.15 K) RT (26)
The following values as taken from Brewer were used:
φHAc ) 21.43 + 2.7 × 10-3t - 1.17 × 10-5t2 + 3.58 × 10-7t3 (27) φAc- ) 10.42 + 1.64 × 10-3t - 3.71 × 10-5t2 + 9.1 × 10-8t3 (28) φH+ ) 0
(29)
(30)
0 hAc -,f (298.15 K) ) -58 454 K R
(31)
(298.15 K) )0K R
Peiper, J. C.; Pitzer, K. S. Thermodynamics of aqueous carbonate solutions including mixtures of sodium carbonate, bicarbonate and chloride. J. Chem. Thermodyn. 1982, 14, 613. Pitzer, K. S. Thermodynamics of electrolytes. 1. Theoretical basis and general equations. J. Phys. Chem. 1973, 77, 268. Rumpf, B.; Maurer, G. An experimental and theoretical investigation on the solubility of carbon dioxide in aqueous electrolyte solutions. Ber. Bunsen-Ges. Phys. Chem. 1993, 97, 85. Saul, A.; Wagner, W. International equations for the saturation properties of ordinary water substance. J. Phys. Chem. Ref. Data 1987, 16, 893.
Vrevsky, M. S.; Mishenko, K. P.; Muromtsef, B. A. Zh. Russ. Fiz. Khim. Obshch. 1927. As cited by Gmehling et al. (1981).
(298.15 K) ) -58 410 K R
0 hH +,f
Pabalan, R. T.; Pitzer, K. S. Thermodynamics of NaOH(aq) in hydrothermal solutions. Geochim. Cosmochim. Acta 1987, 51, 829.
Tsiparis, I. N.; Smorigaite, N. Yu. Zh. Obshch. Khim. 1964. As cited by Gmehling et al. (1981).
0 The values for hi,f (298.15 K)/R:
h0HAc,f
Hayden, J. G.; O’Connell, J. P. A generalized method for predicting second virial coefficients. Ind. Eng. Chem. Process Des. Dev. 1975, 14, 209.
(32)
Washburn, E. W. International critical tables of numerical data. Physics, Chemistry and Technology; McGraw-Hill: New York and London, 1928; Vol. III.
Received for review September 16, 1997 Revised manuscript received February 2, 1998 Accepted February 9, 1998 IE9706626
