- Email: [email protected]
CaCl2
Fluid Phase Equilibria 237 (2005) 219–223
Short communication
Salt effect on vapor–liquid equilibria for binary systems of propanol/CaCl2 and butanol/CaCl2 Jiquan Fu ∗ Center of Chemical Engineering, Beijing Key Laboratory, Beijing Institute of Clothing Technology, Beijing100029, P.R. China Received 13 July 2005; accepted 24 July 2005
Abstract The binary vapor–liquid equilibrium (VLE) data for salt-containing systems of 1-propanol/CaCl2 , 2-propanol/CaCl2 , 1-butanol/CaCl2 and 2-butanol/CaCl2 were determined and correlated. The UNIQUAC model was used to correlate the VLE data, and optimal parameters of the model were obtained. The results show that the UNIQUAC model is suitable to correlate the VLE data. © 2005 Elsevier B.V. All rights reserved. Keywords: Salt effect; Salt-containing; Vapor–liquid equilibrium; Correlation
1. Introduction The addition of a salt to a binary solution of volatile components usually changes the composition of vapor in equilibrium with the liquid due to interactions between the salt and the solvent components. This phenomenon, the so-called salt effect, has been used in a number of technical separation processes [1–3]. For example, aqueous solutions of ethanol or tert-butyl alcohol can be prepared through extractive distillation. The correlation and prediction of vapor–liquid behavior for salt-containing systems with mixed solvents have been examined by a number of investigators: [4–7] and so on. VLE data of salt-containing systems are important for both salt-containing distillation and salt-containing extractive distillation. Simple and accurate VLE models are needed for industrial design. In the salt-containing extractive distillation process, the extractive agent is a salt and a solvent, so it is necessary to deal with the VLE problem of multicomponent systems containing salt [8]. Salt-containing binary VLE data are often used to predict VLE data for salt-containing multicomponent systems [9]. For example, the salt effect on the vapor pressure of solu∗
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0378-3812/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2005.07.023
tions of methanol, ethanol and propanol, have been studied by Eric et al. [10] Skabichevskii [11,12] Janz and Tomkins [13] Vlaslow and Antonov [14] and Bao et al. [15]. However, VLE data for the systems 1-propanol/CaCl2 , 2-propanol/CaCl2 , 1butanol/CaCl2 and 2-butanol/CaCl2 have not been found in literature. In this work, VLE data for these systems have been measured at different salt concentrations and correlated with the UNIQUAC model.
2. Experimental 2.1. Materials The purities of the supplied components of 1-propanol, 2-propanol, 1-butanol and 2-butanol were 99.92% (wt.), 99.92% (wt.), 99.96%(wt.) and 99.95% (wt.), respectively, and the purity of CaCl2 was 99.60% (wt.). 2.2. Experimental equipment and measurement method A small boiling instrument was used to determine VLE data. The temperature was measured with a mercury-in-glass thermometer (1/10 ◦ C division), with correction made for the exposed part of thermometer. The pressure was controlled by
220
J. Fu / Fluid Phase Equilibria 237 (2005) 219–223
needle valve. The range of pressure fluctuation was less than 40.0 Pa. A device consisting of a 2200 type pressure sensor and PDRC-1C/2C type display supplied by the MKS corporation (Andover MA, USA), with a precision of ±13.3 Pa, was used to measure the pressure directly by the method of [15]. Pressure determination in salt-containing systems is different from that with pure material because small droplets of liquid appear in the vapor phase. The amount of solvent in these fogdrops must be determined in order to obtain an accurate liquid phase mole fraction. This amount has been determined by the method introduced in literature [15]. Saturated vapor pressure data of pure 1-propanol have also been measured, and comparison with literature data [16] is satisfactory. 2.3. Experimental results Because of salt solubility, the range of concentration change of the VLE data determined was limited. Even so, this kind of VLE data can be very useful for determining the parameters of local composition models. In theory, the concentration range of the data does have a major influence on the determination of the model parameters. In the system of 1-propanol/CaCl2 , the liquid phase mole fraction of CaCl2 ranged over 0.029–0.130 (about 1.5–8.0% wt.), and in the system of 2-propanol/CaCl2 , it was 0.023–0.104 (about 1.6–9.0% wt.). The results are shown in Tables 1 and 2, respectively. In the system of 1-butanol/CaCl2 , the liquid phase mole fraction range of CaCl2 was 0.010–0.050 (about 1.5–8.0% wt.), and in the system of 2-butanol/CaCl2 , it was 0.011–0.070 (about 1.6–9.0% wt.). The results are shown in Tables 3 and 4, respectively.
3. Correlation of VLE data for binary system A simple and effective VLE calculation method, “saltcontaining local composition model” (SCLCM), was used. The advantage of SCLCM is that salt-containing systems are dealt with by means of the local composition model of conventional miscible systems. The local composition model (Wilson, or NRTL, or UNIQAIC) uses the salt molecules as a “solvent component”. For example, in the ternary system of 2propanol/water/CaCl2 , three binary parameters of the model are needed: [1] 2-propanol/water, [2] 2-propanol/CaCl2 and [3] water/CaCl2 . In this way, we correlate or predict the VLE of these systems as a conventional miscible system. The most notable advantage of the SCLCM approach is that the calculation method and some software used for nonelectrolyte mixtures can be used directly in mixed solvent/salt systems, including software for simulation of distillation of non-electrolyte mixtures. VLE data for binary systems in this paper were correlated using UNIQUAC model [17] in the vapor–liquid equilibrium expression (yi Ps = γ i xi poi ). Thus the vapor phase was assumed to be an ideal gas. For salt-containing binary sys-
Table 1 VLE data for binary system of 1-propanol/CaCl2 P (kPa)
t (◦ C)
x1
100.8 96.2 92.3 88.0 84.0 78.2 74.5 70.6 100.5 96.4 92.1 87.9 83.7 78.5 74.5 70.7 99.9 96.2 92.0 87.9 83.7 79.8 74.4 71.9 99.7 95.9 91.8 87.9 83.7 80.1 75.9 71.9 99.5 96.0 92.0 88.0 83.8 80.0 75.9 71.9
97.13 96.07 94.83 93.58 92.45 90.66 89.47 88.10 97.40 96.38 95.16 94.03 92.69 91.15 89.78 88.41 97.92 97.01 95.81 94.69 93.37 92.20 90.53 89.61 98.57 97.65 96.64 95.43 94.20 92.98 91.66 90.44 99.38 98.57 97.45 96.33 95.06 93.89 92.57 91.25
0.9710 0.9710 0.9710 0.9710 0.9710 0.9710 0.9710 0.9710 0.9440 0.9440 0.9440 0.9440 0.9440 0.9440 0.9440 0.9440 0.9180 0.9180 0.9180 0.9180 0.9180 0.9180 0.9180 0.9180 0.8930 0.8930 0.8930 0.8930 0.8930 0.8930 0.8930 0.8930 0.8700 0.8700 0.8700 0.8700 0.8700 0.8700 0.8700 0.8700
a12 = 1180.02 T−1 , a21 = −435.62 T−1 .
tem, the salt was regarded as a nonvolatile component (ys = 0 and ysolvent = 1). The formula mentioned above was rewritten as Ps = γ i xi poi . Salt molecule was taken as the smallestparticle to define mole fraction in liquid phase, xi = ni / ni , i = salt and solvent. When Van der Waals radii of Ca2+ and Cl− are known, the r and q parameters in the UNIQUAC model can be worked out [18]. Here, the r and q values of CaCl2 were determined to be 1.42 and 1.86, respectively. The optimal parameters of UNIQUAC model were determined with the correlating method based on maximum likelihood theory [19]. The objective function is: 2 m c − xc )2 (x1i (pc − pe ) 2 (T C − T e ) 1i F= (1) + + σp2 σx21i σT2i i
In Eq. (1), σ 2 is the estimated variance of the measured variable, i.e. of pressure, temperature and liquid phase mole frac-
J. Fu / Fluid Phase Equilibria 237 (2005) 219–223
tion. These variances can be estimated from probable experimental uncertainties. Here, assumed standard deviations in the measured variables were: σpi = 133.3Pa, σTi = 0.05K, and σxli = 0.0010 [17]. The optimal UNIQUAC parameters are listed in the bottom of Tables 1–4. The correlation results for the binary VLE data are shown in Table 5. The differences in variables P, T and x1 are the mean deviations of pressure, temperature and liquid phase mole fraction for each solution. The results of correlation suggest that they are satisfactory. In order to show the influence of the salt on vapor pressure clearly, the relationship of vapor pressure with temperature for the four systems are shown in Figs. 1–4. First, the vapor pressure of 1-propanol, 2-propanol, 1-butanol and 2-butanol is decreased in the presence of CaCl2 . The salt mole fraction has an effect on the vapor pressure.
Table 2 VLE data for binary system of 2-propanol/CaCl2 P (kPa)
t (◦ C)
x1
99.8 96.1 92.0 88.1 84.0 80.0 76.0 71.9 99.3 95.9 92.0 87.9 84.0 80.0 76.0 72.1 99.2 96.5 92.1 88.0 84.2 80.2 74.7 72.2 99.3 96.2 92.2 87.9 83.9 80.3 75.9 72.0 99.7 96.1 90.0 88.0 83.8 80.0 75.8 71.7
82.10 81.30 80.30 79.10 78.00 76.80 75.60 74.30 82.50 81.71 80.65 79.59 78.46 77.26 76.05 74.76 82.70 82.10 81.00 79.89 78.78 77.67 75.95 75.06 83.13 82.42 81.33 80.20 79.06 77.97 76.56 75.37 83.69 82.83 81.77 80.70 79.59 78.38 77.07 75.81
0.9770 0.9770 0.9770 0.9770 0.9770 0.9770 0.9770 0.9770 0.9550 0.9550 0.9550 0.9550 0.9550 0.9550 0.9550 0.9550 0.9350 0.9350 0.9350 0.9350 0.9350 0.9350 0.9350 0.9350 0.9150 0.9150 0.9150 0.9150 0.9150 0.9150 0.9150 0.9150 0.8960 0.8960 0.8960 0.8960 0.8960 0.8960 0.8960 0.8960
a12 = 647.32 T−1 , a21 = −325.94 T−1 .
221
Table 3 VLE data for binary system of 1-butanol/CaCl2 P (kPa)
t (◦ C)
x1
101.103 94.131 86.904 81.731 73.678 67.332 59.292 53.785 100.851 93.571 86.571 80.505 73.212 67.998 60.265 53.705 101.051 93.598 87.358 81.025 74.705 67.745 61.212 53.865 100.891 93.598 86.864 79.918 73.332 66.665 59.999 53.332 102.344 93.624 86.611 82.345 73.465 66.665 59.932 53.239
117.6 115.6 113.5 111.8 109.2 106.7 103.5 101.0 118.0 116.0 114.0 112.1 109.4 107.5 104.2 101.3 118.4 116.0 114.3 112.2 110.1 107.6 105.0 101.8 118.5 116.5 114.5 112.4 110.1 107.7 105.0 102.0 119.4 116.8 115.0 113.4 110.4 107.9 105.0 102.1
0.9901 0.9901 0.9901 0.9901 0.9901 0.9901 0.9901 0.9901 0.9802 0.9802 0.9802 0.9802 0.9802 0.9802 0.9802 0.9802 0.9701 0.9701 0.9701 0.9701 0.9701 0.9701 0.9701 0.9871 0.9602 0.9602 0.9602 0.9602 0.9602 0.9602 0.9602 0.9602 0.9502 0.9502 0.9502 0.9502 0.9502 0.9502 0.9502 0.9502
a12 = 1066.69 T−1 , a21 = −544.48 T−1 .
Fig. 1. Salt effect on vapor pressure of 1-propanol.
222
J. Fu / Fluid Phase Equilibria 237 (2005) 219–223 Table 4 VLE data for binary system of 2-butanol/CaCl2
Fig. 2. Salt effect on vapor pressure of 2-propanol.
P (kPa)
t (◦ C)
x1
101.064 101.371 93.881 87.118 80.678 73.611 101.424 93.758 87.024 79.998 73.625 101.357 93.784 87.331 80.438 74.771 100.971 93.571 87.078 80.491 73.451 101.357 93.251 87.024 80.198 73.451 100.824 93.518 87.344 80.255 73.332
108.1 108.2 106.1 104.0 102.0 99.8 108.3 106.3 104.3 102.2 100.1 108.8 106.8 104.8 103.0 100.5 109.1 107.1 105.1 102.9 100.5 109.2 107.2 105.5 103.5 101.0 109.3 107.5 105.5 103.7 100.8
1.0 0.9894 0.9894 0.9894 0.9894 0.9894 0.9756 0.9756 0.9756 0.9756 0.9756 0.9567 0.9567 0.9567 0.9567 0.9567 0.9421 0.9421 0.9421 0.9421 0.9421 0.9375 0.9375 0.9375 0.9375 0.9375 0.9305 0.9305 0.9305 0.9305 0.9305
a12 = 872.43 T−1 , a21 = −445.87 T−1 .
Table 5 Correlation of VLE data for binary systems of propanol/CaCl2 and of butanol/CaCl2 Fig. 3. Salt effect on vapor pressure of 1-butanol.
System
P (kPa)
t (◦ C)
x1
Range of salt concentration
1-Propanol/CaCl2 2-Propanol/CaCl2 1-Butanol/CaCl2 2-Butanol/CaCl2
0.03 0.03 0.07 0.08
0.05 0.06 0.11 0.14
0.0001 0.0001 0.0003 0.0004
0.029–0.130 0.023–0.104 0.010–0.050 0.011–0.070
4. Conclusion Data for the systems 1-propanol/CaCl2 , 2-propanol/ CaCl2 , 1-butanol/CaCl2 and 2-butanol/CaCl2 have been measured and successfully correlated with the UNIQUAC.
Fig. 4. Salt effect on vapor pressure of 2-butanol.
List of symbols P total pressure, kPa T temperature, K t temperature, ◦ C x liquid mole fraction y vapor mole fraction
J. Fu / Fluid Phase Equilibria 237 (2005) 219–223
Greek letters ∆ difference between experimental γ activity coefficient σ standard deviation Subscripts P pressure T temperature x1 liquid phase component 1 s salt Superscripts c calculation value e experimental value o saturated vapor pressure i solvent component
References [1] W.F. Furter, Salt effect in distillation: a literature review. Part II, Can. J. Chem. Eng. 55 (1977) 229–329. [2] Z. Duan, L. Lei, R. Zhou, J. Yeng, W. Qiang, S. Ji, W. Jiang, Study on salt-containing extractive distillation. Part (I), Petrochem. Technol. (China) 9 (1980) 350–356. [3] L. Lie, Z. Duan, Y. Xu, W. Qian, R. Zhou, S. Ji, Study on saltcontaining extractive distillation. Part (II). Development of purification process for tertbutanol, Petrochem. Technol. (China) 11 (1982) 404–408. [4] B. Sander, A. Fredenslund, P. Rasmussem, Calculation of vapor–liquid equilibrium in mixed solvent/salt systems using an extended UNIQUAC equation, Chem. Eng. Sci. 41 (1984) 1171–1183. [5] P.G. Glugla, S.M. Sax, Vapor liquid equilibrium for salt-containing systems: a correlation of vapor pressure depression and prediction of multicomponent systems, AIChE J. 31 (1985) 1911–1914.
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[6] J. Fu, Correlation of vapor pressure of salt-containing systems and prediction of vapor–liquid equilibrium for multicomponents saltcontaining systems with local composition models, J. Chem. Ind. Eng. (China) 42 (1991) 642–645. [7] J.D. Li, H.M. Polka, J. Gmehling, A gE model for single and mixed solvent electrolyte systems. Part 1. Model and results for strong electrolytes, Fluid Phase Equil. 94 (1994) 89–94. [8] J. Fu, Salt-containing model for simulation of salt-containing extractive distillation, AIChE J. 42 (1996) 3364–3372. [9] J. Fu, Isobaric vapor liquid equilibrium for the methanol + ethanol + water + ammonium bromide system, J. Chem. Eng. Data 43 (1998) 403–408. [10] B. Eric, R. Guerry, D. Tassios, Salt Effect on the vapor pressure of pure solvents: methanol with seven salts at 24.9 ◦ C, J. Chem. Eng. Data 24 (1979) 9–11. [11] P.A. Skabichevskii, Osmotic coefficients of lithium chloride and bromide solutions in methanol, Russ. J. Phys. Chem. 44 (1969) 1141–1145. [12] P.A. Skabichevskii, Osmotic and activity coefficents of methanols solution of lithium nitrate and perchlorate, Russ. J. Phys. Chem. 42 (1970) 1168–1172. [13] G.J. Janz, P.T. Tomkins, Nonaqueous Electrolyte Handbook, vol. II, Academic Press, New York, 1973. [14] Yu.G. Vlaslov, P.P. Antonow, Activity of methanol and activity coefficients of salts in sodium choride–methanol and sodium bromide–methanol solutions at 25 ◦ C, Russ. J. Phys. Chem. 47 (1973) 1274–1277. [15] Q. Bao, Z. Cui, D. Gao, J. Li, C. Lu, T. Xiang, Determination and correlation for vapor pressure of salt-containing 2-propanol solution, J. Chem. Ind. Eng. (China) 41 (1990) 382–385. [16] H.Z. Lu, Handbook of Petrochemical Technology Basic Data, Chemical Industrial publication house, Beijing, 1994. [17] T.F. Anderson, J.M. Prausnitz, Application of the UNIQUAC equation to calculation of multicomponent phase equilibria. Part 1. Vapor–liquid equilibria, Ind. Eng. Chem. Process. Des. Dev. 17 (1978) 552–560. [18] A. Bondi, Physical Properties of Molecular Crystals, Liquids and Glasses, Wiley, New York, 1968. [19] T.F. Anderson, D.S. Abrams, E.A. Grens, Evaluation of parameters for nonlinear thermodynamic models, AIChE J. 24 (1978) 20–29.
Short communication
Salt effect on vapor–liquid equilibria for binary systems of propanol/CaCl2 and butanol/CaCl2 Jiquan Fu ∗ Center of Chemical Engineering, Beijing Key Laboratory, Beijing Institute of Clothing Technology, Beijing100029, P.R. China Received 13 July 2005; accepted 24 July 2005
Abstract The binary vapor–liquid equilibrium (VLE) data for salt-containing systems of 1-propanol/CaCl2 , 2-propanol/CaCl2 , 1-butanol/CaCl2 and 2-butanol/CaCl2 were determined and correlated. The UNIQUAC model was used to correlate the VLE data, and optimal parameters of the model were obtained. The results show that the UNIQUAC model is suitable to correlate the VLE data. © 2005 Elsevier B.V. All rights reserved. Keywords: Salt effect; Salt-containing; Vapor–liquid equilibrium; Correlation
1. Introduction The addition of a salt to a binary solution of volatile components usually changes the composition of vapor in equilibrium with the liquid due to interactions between the salt and the solvent components. This phenomenon, the so-called salt effect, has been used in a number of technical separation processes [1–3]. For example, aqueous solutions of ethanol or tert-butyl alcohol can be prepared through extractive distillation. The correlation and prediction of vapor–liquid behavior for salt-containing systems with mixed solvents have been examined by a number of investigators: [4–7] and so on. VLE data of salt-containing systems are important for both salt-containing distillation and salt-containing extractive distillation. Simple and accurate VLE models are needed for industrial design. In the salt-containing extractive distillation process, the extractive agent is a salt and a solvent, so it is necessary to deal with the VLE problem of multicomponent systems containing salt [8]. Salt-containing binary VLE data are often used to predict VLE data for salt-containing multicomponent systems [9]. For example, the salt effect on the vapor pressure of solu∗
Tel.: +86 10 64288146; fax: +86 10 64288146. E-mail address: [email protected].
0378-3812/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2005.07.023
tions of methanol, ethanol and propanol, have been studied by Eric et al. [10] Skabichevskii [11,12] Janz and Tomkins [13] Vlaslow and Antonov [14] and Bao et al. [15]. However, VLE data for the systems 1-propanol/CaCl2 , 2-propanol/CaCl2 , 1butanol/CaCl2 and 2-butanol/CaCl2 have not been found in literature. In this work, VLE data for these systems have been measured at different salt concentrations and correlated with the UNIQUAC model.
2. Experimental 2.1. Materials The purities of the supplied components of 1-propanol, 2-propanol, 1-butanol and 2-butanol were 99.92% (wt.), 99.92% (wt.), 99.96%(wt.) and 99.95% (wt.), respectively, and the purity of CaCl2 was 99.60% (wt.). 2.2. Experimental equipment and measurement method A small boiling instrument was used to determine VLE data. The temperature was measured with a mercury-in-glass thermometer (1/10 ◦ C division), with correction made for the exposed part of thermometer. The pressure was controlled by
220
J. Fu / Fluid Phase Equilibria 237 (2005) 219–223
needle valve. The range of pressure fluctuation was less than 40.0 Pa. A device consisting of a 2200 type pressure sensor and PDRC-1C/2C type display supplied by the MKS corporation (Andover MA, USA), with a precision of ±13.3 Pa, was used to measure the pressure directly by the method of [15]. Pressure determination in salt-containing systems is different from that with pure material because small droplets of liquid appear in the vapor phase. The amount of solvent in these fogdrops must be determined in order to obtain an accurate liquid phase mole fraction. This amount has been determined by the method introduced in literature [15]. Saturated vapor pressure data of pure 1-propanol have also been measured, and comparison with literature data [16] is satisfactory. 2.3. Experimental results Because of salt solubility, the range of concentration change of the VLE data determined was limited. Even so, this kind of VLE data can be very useful for determining the parameters of local composition models. In theory, the concentration range of the data does have a major influence on the determination of the model parameters. In the system of 1-propanol/CaCl2 , the liquid phase mole fraction of CaCl2 ranged over 0.029–0.130 (about 1.5–8.0% wt.), and in the system of 2-propanol/CaCl2 , it was 0.023–0.104 (about 1.6–9.0% wt.). The results are shown in Tables 1 and 2, respectively. In the system of 1-butanol/CaCl2 , the liquid phase mole fraction range of CaCl2 was 0.010–0.050 (about 1.5–8.0% wt.), and in the system of 2-butanol/CaCl2 , it was 0.011–0.070 (about 1.6–9.0% wt.). The results are shown in Tables 3 and 4, respectively.
3. Correlation of VLE data for binary system A simple and effective VLE calculation method, “saltcontaining local composition model” (SCLCM), was used. The advantage of SCLCM is that salt-containing systems are dealt with by means of the local composition model of conventional miscible systems. The local composition model (Wilson, or NRTL, or UNIQAIC) uses the salt molecules as a “solvent component”. For example, in the ternary system of 2propanol/water/CaCl2 , three binary parameters of the model are needed: [1] 2-propanol/water, [2] 2-propanol/CaCl2 and [3] water/CaCl2 . In this way, we correlate or predict the VLE of these systems as a conventional miscible system. The most notable advantage of the SCLCM approach is that the calculation method and some software used for nonelectrolyte mixtures can be used directly in mixed solvent/salt systems, including software for simulation of distillation of non-electrolyte mixtures. VLE data for binary systems in this paper were correlated using UNIQUAC model [17] in the vapor–liquid equilibrium expression (yi Ps = γ i xi poi ). Thus the vapor phase was assumed to be an ideal gas. For salt-containing binary sys-
Table 1 VLE data for binary system of 1-propanol/CaCl2 P (kPa)
t (◦ C)
x1
100.8 96.2 92.3 88.0 84.0 78.2 74.5 70.6 100.5 96.4 92.1 87.9 83.7 78.5 74.5 70.7 99.9 96.2 92.0 87.9 83.7 79.8 74.4 71.9 99.7 95.9 91.8 87.9 83.7 80.1 75.9 71.9 99.5 96.0 92.0 88.0 83.8 80.0 75.9 71.9
97.13 96.07 94.83 93.58 92.45 90.66 89.47 88.10 97.40 96.38 95.16 94.03 92.69 91.15 89.78 88.41 97.92 97.01 95.81 94.69 93.37 92.20 90.53 89.61 98.57 97.65 96.64 95.43 94.20 92.98 91.66 90.44 99.38 98.57 97.45 96.33 95.06 93.89 92.57 91.25
0.9710 0.9710 0.9710 0.9710 0.9710 0.9710 0.9710 0.9710 0.9440 0.9440 0.9440 0.9440 0.9440 0.9440 0.9440 0.9440 0.9180 0.9180 0.9180 0.9180 0.9180 0.9180 0.9180 0.9180 0.8930 0.8930 0.8930 0.8930 0.8930 0.8930 0.8930 0.8930 0.8700 0.8700 0.8700 0.8700 0.8700 0.8700 0.8700 0.8700
a12 = 1180.02 T−1 , a21 = −435.62 T−1 .
tem, the salt was regarded as a nonvolatile component (ys = 0 and ysolvent = 1). The formula mentioned above was rewritten as Ps = γ i xi poi . Salt molecule was taken as the smallestparticle to define mole fraction in liquid phase, xi = ni / ni , i = salt and solvent. When Van der Waals radii of Ca2+ and Cl− are known, the r and q parameters in the UNIQUAC model can be worked out [18]. Here, the r and q values of CaCl2 were determined to be 1.42 and 1.86, respectively. The optimal parameters of UNIQUAC model were determined with the correlating method based on maximum likelihood theory [19]. The objective function is: 2 m c − xc )2 (x1i (pc − pe ) 2 (T C − T e ) 1i F= (1) + + σp2 σx21i σT2i i
In Eq. (1), σ 2 is the estimated variance of the measured variable, i.e. of pressure, temperature and liquid phase mole frac-
J. Fu / Fluid Phase Equilibria 237 (2005) 219–223
tion. These variances can be estimated from probable experimental uncertainties. Here, assumed standard deviations in the measured variables were: σpi = 133.3Pa, σTi = 0.05K, and σxli = 0.0010 [17]. The optimal UNIQUAC parameters are listed in the bottom of Tables 1–4. The correlation results for the binary VLE data are shown in Table 5. The differences in variables P, T and x1 are the mean deviations of pressure, temperature and liquid phase mole fraction for each solution. The results of correlation suggest that they are satisfactory. In order to show the influence of the salt on vapor pressure clearly, the relationship of vapor pressure with temperature for the four systems are shown in Figs. 1–4. First, the vapor pressure of 1-propanol, 2-propanol, 1-butanol and 2-butanol is decreased in the presence of CaCl2 . The salt mole fraction has an effect on the vapor pressure.
Table 2 VLE data for binary system of 2-propanol/CaCl2 P (kPa)
t (◦ C)
x1
99.8 96.1 92.0 88.1 84.0 80.0 76.0 71.9 99.3 95.9 92.0 87.9 84.0 80.0 76.0 72.1 99.2 96.5 92.1 88.0 84.2 80.2 74.7 72.2 99.3 96.2 92.2 87.9 83.9 80.3 75.9 72.0 99.7 96.1 90.0 88.0 83.8 80.0 75.8 71.7
82.10 81.30 80.30 79.10 78.00 76.80 75.60 74.30 82.50 81.71 80.65 79.59 78.46 77.26 76.05 74.76 82.70 82.10 81.00 79.89 78.78 77.67 75.95 75.06 83.13 82.42 81.33 80.20 79.06 77.97 76.56 75.37 83.69 82.83 81.77 80.70 79.59 78.38 77.07 75.81
0.9770 0.9770 0.9770 0.9770 0.9770 0.9770 0.9770 0.9770 0.9550 0.9550 0.9550 0.9550 0.9550 0.9550 0.9550 0.9550 0.9350 0.9350 0.9350 0.9350 0.9350 0.9350 0.9350 0.9350 0.9150 0.9150 0.9150 0.9150 0.9150 0.9150 0.9150 0.9150 0.8960 0.8960 0.8960 0.8960 0.8960 0.8960 0.8960 0.8960
a12 = 647.32 T−1 , a21 = −325.94 T−1 .
221
Table 3 VLE data for binary system of 1-butanol/CaCl2 P (kPa)
t (◦ C)
x1
101.103 94.131 86.904 81.731 73.678 67.332 59.292 53.785 100.851 93.571 86.571 80.505 73.212 67.998 60.265 53.705 101.051 93.598 87.358 81.025 74.705 67.745 61.212 53.865 100.891 93.598 86.864 79.918 73.332 66.665 59.999 53.332 102.344 93.624 86.611 82.345 73.465 66.665 59.932 53.239
117.6 115.6 113.5 111.8 109.2 106.7 103.5 101.0 118.0 116.0 114.0 112.1 109.4 107.5 104.2 101.3 118.4 116.0 114.3 112.2 110.1 107.6 105.0 101.8 118.5 116.5 114.5 112.4 110.1 107.7 105.0 102.0 119.4 116.8 115.0 113.4 110.4 107.9 105.0 102.1
0.9901 0.9901 0.9901 0.9901 0.9901 0.9901 0.9901 0.9901 0.9802 0.9802 0.9802 0.9802 0.9802 0.9802 0.9802 0.9802 0.9701 0.9701 0.9701 0.9701 0.9701 0.9701 0.9701 0.9871 0.9602 0.9602 0.9602 0.9602 0.9602 0.9602 0.9602 0.9602 0.9502 0.9502 0.9502 0.9502 0.9502 0.9502 0.9502 0.9502
a12 = 1066.69 T−1 , a21 = −544.48 T−1 .
Fig. 1. Salt effect on vapor pressure of 1-propanol.
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J. Fu / Fluid Phase Equilibria 237 (2005) 219–223 Table 4 VLE data for binary system of 2-butanol/CaCl2
Fig. 2. Salt effect on vapor pressure of 2-propanol.
P (kPa)
t (◦ C)
x1
101.064 101.371 93.881 87.118 80.678 73.611 101.424 93.758 87.024 79.998 73.625 101.357 93.784 87.331 80.438 74.771 100.971 93.571 87.078 80.491 73.451 101.357 93.251 87.024 80.198 73.451 100.824 93.518 87.344 80.255 73.332
108.1 108.2 106.1 104.0 102.0 99.8 108.3 106.3 104.3 102.2 100.1 108.8 106.8 104.8 103.0 100.5 109.1 107.1 105.1 102.9 100.5 109.2 107.2 105.5 103.5 101.0 109.3 107.5 105.5 103.7 100.8
1.0 0.9894 0.9894 0.9894 0.9894 0.9894 0.9756 0.9756 0.9756 0.9756 0.9756 0.9567 0.9567 0.9567 0.9567 0.9567 0.9421 0.9421 0.9421 0.9421 0.9421 0.9375 0.9375 0.9375 0.9375 0.9375 0.9305 0.9305 0.9305 0.9305 0.9305
a12 = 872.43 T−1 , a21 = −445.87 T−1 .
Table 5 Correlation of VLE data for binary systems of propanol/CaCl2 and of butanol/CaCl2 Fig. 3. Salt effect on vapor pressure of 1-butanol.
System
P (kPa)
t (◦ C)
x1
Range of salt concentration
1-Propanol/CaCl2 2-Propanol/CaCl2 1-Butanol/CaCl2 2-Butanol/CaCl2
0.03 0.03 0.07 0.08
0.05 0.06 0.11 0.14
0.0001 0.0001 0.0003 0.0004
0.029–0.130 0.023–0.104 0.010–0.050 0.011–0.070
4. Conclusion Data for the systems 1-propanol/CaCl2 , 2-propanol/ CaCl2 , 1-butanol/CaCl2 and 2-butanol/CaCl2 have been measured and successfully correlated with the UNIQUAC.
Fig. 4. Salt effect on vapor pressure of 2-butanol.
List of symbols P total pressure, kPa T temperature, K t temperature, ◦ C x liquid mole fraction y vapor mole fraction
J. Fu / Fluid Phase Equilibria 237 (2005) 219–223
Greek letters ∆ difference between experimental γ activity coefficient σ standard deviation Subscripts P pressure T temperature x1 liquid phase component 1 s salt Superscripts c calculation value e experimental value o saturated vapor pressure i solvent component
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