Salts Effect on Isobaric VaporâLiquid Equilibrium for the Azeotropic

Article pubs.acs.org/jced

Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Salts Effect on Isobaric Vapor−Liquid Equilibrium for the Azeotropic Mixture 2‑Propanol + Water Liuyi Yin,* Yongbo Li, Hui Zhao, Quan-liang Li, Jun Wang, Fang Liu, and Li-Na Xiao College of Chemistry & Chemical Engineering, Zhoukou Normal University, Zhoukou 466001, China

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S Supporting Information *

ABSTRACT: Vapor−liquid equilibrium (VLE) data for the systems 2-propanol + water + calcium chloride, 2-propanol + water + magnesium chloride, 2-propanol + water + calcium nitrate, and 2-propanol + water + magnesium nitrate were measured at the pressure of 101.3 kPa. Experimental data of all ternary systems passed the thermodynamic consistency test by modified McDermott−Ellis method. Then, the effects of salts on the vapor phase mole fraction of 2-propanol and the relative volatility of 2-propanol to water were analyzed. Results show that the azeotropic point of the system 2-propanol and water can be removed with addition of the salts, and the salting-out effects follow the order calcium nitrate > calcium chloride > magnesium nitrate > magnesium chloride. Furthermore, the LIQUAC model was adopted to correlate the VLE experimental data of the systems. The comparative results of the average relative deviation (Δz)̅ and the corresponding standard deviations (σ) between the experimental and calculated values indicate that LIQUAC model is suitable for the VLE calculation for the systems of 2-propanol + water + salts.

1. INTRODUCTION 2-Propanol is a basic chemical widely used in industry as a solvent or as a chemical intermediate because of its excellent physical and chemical properties.1−6 Separation of the aqueous mixture of 2-propanol is often demanded in its production and recovery, which is also conducive to environmental protection. The mixture of 2-propanol and water forms a minimum boiling point azeotrope at atmospheric pressure.3 Therefore, 2-propanol dehydration cannot be achieved by conventional distillation, which requires special distillation, such as extractive distillation, salt distillation, pressure swing distillation, azeotropic distillation, and reactive distillation, etc.7 Since salt distillation has the ability to efficiently separate an azeotrope, it is regarded as a promising technique for the separation of 2-propanol and water. Reliable knowledge of vapor−liquid equilibrium (VLE) data for the system of 2-propanol and water is required for design of the salt distillation process. This is also particularly important for the selection of entrainers. In recent years, some researchers have reported on the VLE of the 2-propanol system with different solvents as the separation agent. Orchillés et al. measured the isobaric VLE data for the system 2-propanol + water +1-ethyl-3-methylimidazolium dicyanamide at 101.3 kPa.3 The isobaric VLE data of 2-propanol + water + ethylene glycol/glycerol/DESs at 100 kPa were determined by Zhang et al.1,5,8 To our best knowledge, the influence of the structural characteristics of the salts (calcium chloride, magnesium chloride, calcium nitrate, and magnesium nitrate) on isobaric VLE for the system of 2-propanol + water has not been © XXXX American Chemical Society

discussed, although relevant publications for VLE data at atmospheric pressure have been reported.9−11 In addition, calcium chloride, magnesium chloride, calcium nitrate, and magnesium nitrate are well dissolved in 2-propanol and water, and the solubility of the salts in 2-propanol are different than in water; therefore, the above four mentioned salts were adopted in this work to break the azeotrope of 2-propanol and water. Consequently,the purpose of this work is to provide the vapor−liquid equilibrium data for the systems 2-propanol + water, 2-propanol + water + calcium chloride, 2-propanol + water + magnesium chloride, 2-propanol + water + calcium nitrate, and 2-propanol + water + magnesium nitrate at 101.3 kPa. Meantime, the thermodynamic consistency of the measured VLE data was checked by the method of modified McDermott− Ellis test. Furthermore, the LIQUAC model was used to correlate the experimental VLE data.

2. EXPERIMENTAL SECTION 2.1. Chemicals. 2-Propanol was purchased from Tianjin Fuchen Chemical Reagents Factory with the mass fraction of 0.99. The purity of 2-propanol was checked and confirmed by gas chromatography (SP-3420A, Beijing Beifen-Ruili Analytical Instrument Co., Ltd.). The salts (calcium chloride, magnesium chloride, calcium nitrate, and magnesium nitrate) were provided by Tianjin Guangfu Fine Chemical Research Institute. Received: November 22, 2018 Accepted: April 5, 2019

A

DOI: 10.1021/acs.jced.8b01116 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Specifications of the Chemical Samples component

CAS Reg. No.

2-propanol calcium chloride magnesium chloride calcium nitrate magnesium nitrate

67-63-0 10043-52-4 7786-30-3 10124-37-5 10377-60-3

suppliers Tianjin Tianjin Tianjin Tianjin Tianjin

Fuchen Chemical Reagents Factory Guangfu Fine Chemical Research Institute Guangfu Fine Chemical Research Institute Guangfu Fine Chemical Research Institute Guangfu Fine Chemical Research Institute

mass fraction

water content

analysis method

≥0.99 ≥0.98 ≥0.98 ≥0.98 ≥0.98

0.005 0.007 0.006 0.007 0.005

GCa KFb KFb KFb KFb

a

Gas chromatography. bKarl−Fisher titration.

pressure 101.3 kPa were determined to test the performance of the equilibrium still. These data have been compared with the data series taken from the literature9,10 in Figure 1. It can be

The water content of the salts was checked by Karl Fisher titration (S-300, Shanghai Precision Science Instrument Co., Ltd.). 2-Propanol and salts were used without further purification. The deionized water was made by ultrapure water machine (EDI-200 L, Sanda Shui (Beijing) Technology Co., Ltd.) in our laboratory. The chemical specifications of these materials are shown in Table 1. 2.2. Apparatus and Procedures. The isobaric vapor− liquid equilibrium data were measured by the improved Rose equilibrium method, which was detailed in previous literature.12,13 The improved Rose device was connected with a pressure control system. The pressure control system consisted of a solenoid and throttle valves in series connected with a vacuum pump, a buffer vessel to damp pressure variations, a vacuum measure probe, and an on−off pressure controller actuating the solenoid valve.14 The pressure was measured by using a calibrated pressure transducer. The boiling of the still was achieved by an oil bath heater, and the Pt100 resistance temperature probe was inserted into the still to measure the equilibrium temperature with an accuracy of ±0.1 K. In each experiment, the ternary mixture of 2-propanol + water + salt was added into the equilibrium still, which was prepared by an electronic analytical balance (JJ224BF, G&G Measurement Plant) with the accuracy of ±0.0001 g. During the measurement, the liquid and condensed vapor phases were recirculated continuously to ensure sufficient contact. The vapor− liquid phase equilibrium was established when the equilibrium temperature was kept constant for 60 min. The vapor and liquid phase samples were withdrawn simultaneously by syringes with the volume of about 0.2 mL and put into the vials for analysis. The compositions of the samples were determined by gas chromatography (SP-3420A, Beijing Beifen-Ruili Analytical Instrument Co., Ltd.) equipped with a thermal conductivity detector (TCD) and a packing column. To avoid entry of salts into the GC column, a precolumn was used. The detailed operating conditions were as follows: hydrogen carrier gas flow, 30 cm3 min−1; injector temperature, 525 K; oven temperature, 455 K; detector temperature, 490 K. The salt mass fractions of the samples were gravimetrically determined by vacuum desiccation (DZF-6090, Shanghai LNB Instrument Co., Ltd.) at 398 K until the mass of the sample did not change, wherein 2-propanol and water were evaporated.15 Standard uncertainties were estimated to be 0.64 K for temperature and 0.05 kPa for pressure. Relative standard uncertainties for the vapor phase and liquid phase mole fractions of 2-propanol were estimated to be less than 0.017. The method for determining the uncertainties of T, p, and concentration of 2-propanol has been provided in the Supporting Information.

Figure 1. Comparison of the isobaric VLE data for the ternary system of 2-propanol (1) + water (2) + salt (3) at 101.3 kPa: ■, x1′ literature data9 for CaCl2; □, x1′ experimental data for CaCl2; ●, y1 literature data9 for CaCl2; ○, y1 experimental data for CaCl2; ▲, x1′ literature data10 for MgCl2; △, x1′ experimental data for MgCl2; ★, y1 literature data10 for MgCl2; ☆, y1 experimental data for MgCl2.

observed from Figure 1 that the measured VLE data are in good agreement with literature data.9,10 This indicates that the instrument is reliable. Therefore, the modified Rose still was used to measure the ternary vapor−liquid equilibrium data for the 2-propanol + water + salt system. The isobaric vapor−liquid equilibrium data for the ternary systems 2-propanol + water + salts (including calcium chloride, magnesium chloride, calcium nitrate, and magnesium nitrate) were experimentally determined by keeping the molality of salts nearly constant at 0.1, 0.2, 0.3, 0.4, 0.5, and 0.6, and their experimental values are given in Tables 2−5. In these tables, x1′ represents the mole fraction of 2-propanol in the liquid phase on the salts-free basis, m3 the liquid phase molality of the salts, T the equilibrium temperature, and y1 the vapor phase mole fraction of 2-propanol. For comparison, the isobaric vapor−liquid equilibrium data for the binary system 2propanol + water were also experimentally determined, which are given in Table 6. 3.2. Thermodynamic Consistency Test. To confirm the quality of the VLE data obtained, the consistency of the experimental results were checked by modified McDermott− Ellis test.16 According to this method, two experimental points (a and b) are thermodynamically consistent if D < Dmax. D and Dmax are respectively defined as follows:

3. RESULTS AND DISCUSSION 3.1. Experiment Results. Isobaric VLE data of the 2-propanol + water + CaCl2/MgCl2 ternary system with

n

D=

∑ (xib + xia)(ln γib − ln γia) i=1

B

(1)



Article

Table 2. Isobaric Vapor−Liquid Equilibrium Data for Liquid Phase Mole Fraction (Salts-Free Basis; x′), Liquid Phase Molality (m), Temperature (T), Vapor Phase Mole Fraction (y), Activity Coefficient (γ), Relative Volatility (α), and the Relative Deviation between the Experimental and Calculated Values of Temperature (ΔT), Vapor Phase Mole Fractions (Δy), for the Ternary System 2-Propanol (1) + Water (2) + Calcium Chloride (3) at p = 101.3 kPaa x′1

m3 (mol/kg)

T (K)

y1

γ1

γ2

α12

ΔT (%)

Δy (%)

0.0260 0.0560 0.0910 0.2006 0.3002 0.4004 0.5013 0.6001 0.7006 0.8009 0.9007 0.0260 0.0560 0.0910 0.2006 0.3002 0.4004 0.5013 0.6001 0.7006 0.8009 0.9007 0.0260 0.0560 0.0910 0.2006 0.3002 0.4004 0.5013 0.6001 0.7006 0.8009 0.9007 0.0260 0.0560 0.0910 0.2006 0.3002 0.4004 0.5013 0.6001 0.7006 0.8009 0.9007 0.0260 0.0560 0.0910 0.2006 0.3002 0.4004 0.5013 0.6001 0.7006 0.8009 0.9007 0.0260 0.0560 0.0910

0.1005 0.1002 0.1008 0.1007 0.1000 0.1000 0.1003 0.1000 0.1004 0.1003 0.1000 0.2001 0.2003 0.2013 0.2008 0.2000 0.2001 0.2002 0.2003 0.2001 0.2004 0.2000 0.3001 0.3007 0.3013 0.3009 0.3002 0.3004 0.2998 0.3005 0.3002 0.3004 0.3001 0.4001 0.4004 0.4021 0.4012 0.4003 0.4006 0.3997 0.4005 0.4002 0.4001 0.4005 0.5004 0.5003 0.5022 0.5012 0.5003 0.5008 0.5179 0.5008 0.5007 0.5001 0.5004 0.6004 0.6003 0.6014

363.15 359.85 356.45 354.95 354.30 354.05 353.65 353.55 353.35 353.35 354.35 363.15 358.15 356.15 354.65 354.20 353.95 353.65 353.55 354.15 354.35 354.55 363.65 358.85 356.85 354.45 354.05 354.85 354.65 354.55 354.65 355.55 355.65 362.75 358.75 355.75 354.35 353.95 354.65 354.75 354.85 354.95 355.05 355.65 362.55 357.25 355.55 354.25 353.95 354.55 354.65 355.25 355.35 355.65 356.45 362.55 357.15 354.55

0.3155 0.4375 0.4975 0.5480 0.5550 0.5780 0.5955 0.6481 0.6981 0.7781 0.8781 0.3150 0.4450 0.5150 0.5455 0.5580 0.5711 0.6081 0.6465 0.6965 0.7565 0.8665 0.3250 0.4650 0.5250 0.5681 0.5711 0.5855 0.6265 0.6464 0.7164 0.7864 0.8764 0.3360 0.4760 0.5360 0.5681 0.5755 0.5911 0.6464 0.6679 0.7076 0.7697 0.8689 0.3648 0.4780 0.5480 0.5881 0.6001 0.6181 0.6464 0.6912 0.7211 0.7919 0.8821 0.3748 0.4980 0.5480

8.99 6.57 5.25 2.79 1.94 1.53 1.28 1.17 1.09 1.06 1.02 8.99 7.15 5.52 2.82 1.96 1.52 1.31 1.17 1.06 1.00 1.01 9.12 7.29 5.48 2.96 2.03 1.51 1.30 1.13 1.07 0.99 0.98 9.78 7.51 5.86 2.98 2.06 1.54 1.34 1.16 1.05 0.99 0.98 10.72 8.01 6.05 3.11 2.15 1.62 1.36 1.18 1.06 1.00 0.97 11.03 8.39 6.31

1.02 0.98 1.04 1.13 1.30 1.46 1.71 1.86 2.15 2.38 2.52 1.02 1.03 1.02 1.15 1.30 1.49 1.66 1.88 2.10 2.52 2.75 0.99 0.97 0.97 1.11 1.28 1.40 1.53 1.81 1.93 2.12 2.45 1.01 0.96 0.99 1.11 1.27 1.39 1.44 1.69 1.98 2.34 2.61 0.97 1.01 0.98 1.07 1.20 1.31 1.46 1.55 1.87 2.07 2.29 0.96 0.98 1.02

17.2668 13.1111 9.8896 4.8314 2.9073 2.0511 1.4646 1.2273 0.9882 0.8717 0.7942 17.2268 13.5161 10.6069 4.7829 2.9429 1.9940 1.5436 1.2187 0.9807 0.7723 0.7156 18.0370 14.6515 11.0405 5.2417 3.1040 2.1153 1.6687 1.2182 1.0795 0.9152 0.7817 18.9564 15.3130 11.5390 5.2417 3.1603 2.1648 1.8186 1.3402 1.0342 0.8308 0.7307 21.5144 15.4362 12.1106 5.6897 3.4981 2.4237 1.8186 1.4916 1.1049 0.9460 0.8248 22.4577 16.7228 12.1106

0.19 −0.16 0.14 0.03 0.12 0.11 0.14 0.11 0.16 0.24 0.13 0.11 0.20 0.11 0.06 0.14 0.16 0.20 0.19 0.04 0.07 0.20 −0.13 −0.11 −0.19 0.06 0.16 −0.07 −0.03 −0.01 0 −0.15 0.01 2.01 0.65 0.01 0.02 0.17 0.29 0.33 0.32 0.37 0.50 0.70 −0.03 0.08 −0.08 −0.02 0.15 0.05 0.07 −0.06 −0.01 0.04 0.03 −0.13 −0.02 0.08

−1.61 −1.00 −0.98 −0.71 0.78 −0.02 1.79 −0.34 0.42 −0.45 −0.76 2.38 0.45 −1.85 1.67 1.91 2.66 0.98 1.01 1.54 3.05 0.92 3.37 −0.91 −1.30 −0.47 1.24 1.65 −0.73 2.12 −0.39 −0.24 0.12 −34.85 −11.47 −0.82 −5.22 2.14 2.15 −2.57 −0.10 7.73 18.19 31.83 −0.37 2.23 −0.53 −0.15 −0.45 −0.91 −1.16 −2.44 0.64 0.27 0.15 0.44 0.96 1.81

C



Article

Table 2. continued x1′

m3 (mol/kg)

T (K)

y1

γ1

γ2

α12

ΔT (%)

Δy (%)

0.2006 0.3002 0.4004 0.5013 0.6001 0.7006 0.8009 0.9007

0.6012 0.6006 0.6001 0.6083 0.6008 0.6007 0.6005 0.6006

353.95 354.25 354.85 355.15 355.35 355.65 356.25 356.95

0.6081 0.6165 0.6081 0.6464 0.6911 0.7311 0.7914 0.8901

3.26 2.19 1.58 1.33 1.18 1.06 0.98 0.96

1.03 1.14 1.33 1.43 1.55 1.79 2.04 2.10

6.1835 3.7474 2.3236 1.8186 1.4909 1.1619 0.9431 0.8929

−0.01 0.04 −0.02 −0.03 −0.02 0 −0.02 0.01

−1.65 −1.54 2.10 −0.08 −1.43 0.08 0.94 −0.43

u(T) = 0.64 K, uc(p) = 0.05 kPa, and ur,c(x1′) = ur,c(y1) = 0.017.

a

Table 3. Isobaric Vapor−Liquid Equilibrium Data for Liquid Phase Mole Fraction (Salts-Free Basis; x′), Liquid Phase Molality (m), Temperature (T), Vapor Phase Mole Fraction (y), Activity Coefficient (γ), Relative Volatility (α), and the Relative Deviation between the Experimental and Calculated Values of Temperature (ΔT), Vapor Phase Mole Fractions (Δy), for the Ternary System 2-Propanol (1) + Water (2) + Magnesium Chloride (3) at p = 101.3 kPaa x1′

m3(mol/kg)

T (K)

y1

γ1

γ2

α12

ΔT (%)

Δy (%)

0.0260 0.0560 0.0910 0.2006 0.3002 0.4004 0.5013 0.6001 0.7006 0.8009 0.9007 0.0260 0.0560 0.0910 0.2006 0.3002 0.4004 0.5013 0.6001 0.7006 0.8009 0.9007 0.0260 0.0560 0.0910 0.2006 0.3002 0.4004 0.5013 0.6001 0.7006 0.8009 0.9007 0.0260 0.0560 0.0910 0.2006 0.3002 0.4004 0.5013 0.6001 0.7006 0.8009 0.9007 0.0260

0.1001 0.1003 0.0997 0.1007 0.0998 0.1015 0.1001 0.1004 0.1002 0.1003 0.1002 0.1998 0.2001 0.1991 0.1996 0.2003 0.2002 0.2001 0.2005 0.2004 0.2003 0.2001 0.3002 0.3003 0.3011 0.2998 0.2998 0.3001 0.3003 0.3006 0.3001 0.3005 0.3004 0.3999 0.3996 0.3995 0.4003 0.4004 0.4001 0.4003 0.4005 0.4002 0.4001 0.4004 0.4997

363.55 359.35 357.15 355.05 354.75 354.45 354.15 354.05 353.95 354.15 354.85 363.45 359.35 356.45 355.75 355.55 354.45 354.35 354.25 354.15 355.45 355.15 363.25 358.75 356.25 355.15 355.15 355.15 355.15 355.15 355.25 355.75 356.25 363.05 358.05 356.05 354.55 355.45 355.55 355.65 355.75 355.85 356.65 357.55 362.95

0.3061 0.4267 0.4877 0.5450 0.5560 0.5760 0.6055 0.6481 0.7021 0.7782 0.8781 0.3199 0.4471 0.4999 0.5480 0.5611 0.5880 0.5991 0.6565 0.7065 0.7725 0.8766 0.3308 0.4532 0.5058 0.5755 0.5781 0.5855 0.6265 0.6464 0.7061 0.7714 0.8734 0.3450 0.4751 0.5252 0.5711 0.5881 0.5911 0.6264 0.6679 0.7172 0.7819 0.8779 0.3651

8.59 6.53 5.01 2.76 1.91 1.50 1.27 1.14 1.07 1.03 1.00 9.03 6.86 5.29 2.71 1.87 1.54 1.26 1.16 1.07 0.97 0.99 9.43 7.13 5.41 2.92 1.96 1.49 1.28 1.10 1.03 0.96 0.95 9.92 7.70 5.67 2.98 1.98 1.49 1.26 1.12 1.02 0.95 0.91 10.56

1.02 1.02 1.03 1.13 1.28 1.44 1.63 1.82 2.07 2.30 2.47 1.00 0.98 1.04 1.10 1.23 1.40 1.65 1.77 2.03 2.25 2.48 0.99 1.00 1.03 1.06 1.20 1.38 1.50 1.77 1.96 2.25 2.45 0.98 0.99 1.00 1.10 1.16 1.34 1.47 1.63 1.85 2.08 2.26 0.96

16.5254 12.5466 9.5094 4.7733 2.9191 2.0343 1.5269 1.2273 1.0072 0.8722 0.7942 17.6209 13.6314 9.9850 4.8314 2.9801 2.1372 1.4866 1.2736 1.0287 0.8441 0.7832 18.5180 13.9716 10.2235 5.4026 3.1942 2.1153 1.6687 1.2182 1.0267 0.8389 0.7606 19.7317 15.2578 11.0493 5.3063 3.3283 2.1648 1.6680 1.3402 1.0838 0.8912 0.7927 21.5423

0.12 0.04 0 0.07 0.05 0.05 0.06 0.03 0.06 0.08 0.07 0.08 −0.05 0.12 −0.14 −0.13 0.14 0.12 0.12 0.18 −0.09 0.20 0.04 0 0.07 −0.01 0 0.01 0 0.01 0.04 0.02 0.10 −0.01 0.06 0.01 0.11 −0.07 −0.04 −0.03 −0.02 0.03 −0.04 −0.05 −0.10

0.09 0.44 0.06 −0.97 −0.20 −0.38 −0.53 −0.89 −0.61 −0.81 −0.96 −0.66 −1.26 −0.14 0.13 0.27 −1.32 1.50 −1.41 −0.64 0.32 −0.57 0.33 0.57 1.37 −2.84 −1.16 0.43 −1.89 1.02 0.09 0.96 0.05 0.48 −0.87 0.41 −0.12 −1.23 0.87 −0.74 −1.30 −0.73 0.13 −0.18 −0.55

D



Article


m3(mol/kg)

T (K)

y1

γ1

γ2

α12

ΔT (%)

Δy (%)

0.0560 0.0910 0.2006 0.3002 0.4004 0.5013 0.6001 0.7006 0.8009 0.9007 0.0260 0.0560 0.0910 0.2006 0.3002 0.4004 0.5013 0.6001 0.7006 0.8009 0.9007

0.4999 0.4991 0.5004 0.4999 0.5003 0.4999 0.5005 0.5001 0.5001 0.5002 0.6001 0.6002 0.5999 0.6004 0.6001 0.6005 0.5999 0.6000 0.6001 0.6003 0.6002

357.85 355.95 354.45 355.25 355.65 355.85 356.15 356.75 357.15 358.15 362.85 357.85 355.85 354.45 355.15 355.65 355.95 356.75 356.75 357.15 357.75

0.4852 0.5450 0.5781 0.6011 0.6081 0.6264 0.6611 0.7111 0.7817 0.8728 0.3750 0.5052 0.5556 0.6011 0.6081 0.6181 0.6364 0.6711 0.7213 0.7911 0.8802

7.94 5.92 3.03 2.04 1.53 1.25 1.09 0.98 0.93 0.89 10.91 8.28 6.07 3.16 2.08 1.56 1.27 1.09 1.00 0.95 0.92

0.98 0.97 1.09 1.14 1.29 1.47 1.64 1.83 2.05 2.31 0.95 0.94 0.95 1.03 1.13 1.26 1.43 1.56 1.77 1.97 2.22

15.8879 11.9649 5.4604 3.5127 2.3236 1.6680 1.2999 1.0519 0.8902 0.7565 22.4769 17.2115 12.4885 6.0050 3.6171 2.4237 1.7412 1.3597 1.1060 0.9414 0.8100

−0.03 −0.09 0.09 −0.01 −0.01 0.01 0 −0.06 0 −0.02 −0.20 −0.18 −0.21 0.03 0.02 0.04 0.07 −0.05 0.09 0.17 0.28

0.40 −0.58 0.71 −1.71 −0.58 0.47 0.71 0.91 0.68 0.69 0.97 −0.29 0.20 −1.22 −1.16 −0.75 0.07 0.20 0.26 0.04 0.14

u(T) = 0.64 K, uc(p) = 0.05 kPa, and ur,c(x′1) = ur,c(y1) = 0.017.

a

Table 4. Isobaric Vapor−Liquid Equilibrium Data for Liquid Phase Mole Fraction (Salts-Free Basis; x′), Liquid Phase Molality (m), Temperature (T), Vapor Phase Mole Fraction (y), Activity Coefficient (γ), Relative Volatility (α), and the Relative Deviation between the Experimental and Calculated Values of Temperature (ΔT), Vapor Phase Mole Fractions (Δy), for the Ternary System 2-Propanol (1) + Water (2) + Calcium Nitrate (3) at p = 101.3 kPaa x1′

m3(mol/kg)

T (K)

y1

γ1

γ2

α12

ΔT (%)

Δy (%)

0.0260 0.0560 0.0910 0.2006 0.3002 0.4004 0.5013 0.6001 0.7006 0.8009 0.9007 0.0260 0.0560 0.0910 0.2006 0.3002 0.4004 0.5013 0.6001 0.7006 0.8009 0.9007 0.0260 0.0560 0.0910 0.2006 0.3002 0.4004 0.5013 0.6001 0.7006

0.1001 0.1002 0.1012 0.1000 0.1000 0.1001 0.1000 0.1001 0.1001 0.1002 0.1001 0.2010 0.2010 0.2010 0.2003 0.2002 0.1997 0.2000 0.2000 0.2003 0.2001 0.2001 0.3002 0.3004 0.3010 0.3001 0.3003 0.2999 0.2999 0.2997 0.3001

363.75 359.65 356.75 354.85 354.55 354.25 353.85 353.65 353.35 353.75 354.25 363.65 359.35 356.75 354.75 354.55 353.95 353.75 353.45 353.35 353.65 354.45 363.65 359.25 356.65 354.55 354.25 353.95 353.85 353.45 353.65

0.3075 0.4285 0.4915 0.5381 0.5603 0.5789 0.6115 0.6521 0.6982 0.7791 0.8681 0.3150 0.4351 0.5052 0.5511 0.5619 0.5881 0.6081 0.6565 0.7167 0.7865 0.8768 0.3118 0.4348 0.5008 0.5581 0.5711 0.5955 0.6281 0.6665 0.7261

8.57 6.48 5.13 2.75 1.94 1.52 1.30 1.17 1.09 1.04 1.01 8.82 6.67 5.28 2.83 1.95 1.57 1.31 1.19 1.12 1.06 1.02 8.75 6.71 5.27 2.90 2.01 1.59 1.35 1.22 1.13

1.01 1.00 1.04 1.16 1.27 1.44 1.63 1.83 2.15 2.33 2.73 1.00 1.00 1.01 1.13 1.27 1.43 1.65 1.83 2.03 2.27 2.55 1.01 1.01 1.03 1.13 1.27 1.41 1.57 1.79 1.94

16.6345 12.6392 9.6551 4.6425 2.9705 2.0587 1.5658 1.2491 0.9886 0.8768 0.7256 17.2268 12.9838 10.1990 4.8923 2.9898 2.1381 1.5436 1.2736 1.0811 0.9158 0.7846 16.9725 12.9680 10.0210 5.0329 3.1040 2.2046 1.6801 1.3318 1.1329

0.05 −0.07 0.07 0.03 −0.01 −0.02 0 0 0.07 0.02 0.04 0.08 −0.01 0.03 0.01 −0.05 0.04 0.01 0.05 0.07 0.06 −0.01 0.09 0.01 0.05 0.04 0.01 0.02 −0.02 0.05 0

−0.25 0.33 −0.25 1.10 0.17 0.37 −0.20 −0.24 1.09 −0.02 0.73 −1.59 −0.07 −1.90 −0.01 1.27 0.25 1.87 0.52 −0.28 −0.01 0.29 0.26 0.72 −0.30 −0.31 0.76 0.23 −0.13 0.21 −0.51

E



Article


m3(mol/kg)

T (K)

y1

γ1

γ2

α12

ΔT (%)

Δy (%)

0.8009 0.9007 0.0260 0.0560 0.0910 0.2006 0.3002 0.4004 0.5013 0.6001 0.7006 0.8009 0.9007 0.0260 0.0560 0.0910 0.2006 0.3002 0.4004 0.5013 0.6001 0.7006 0.8009 0.9007 0.0260 0.0560 0.0910 0.2006 0.3002 0.4004 0.5013 0.6001 0.7006 0.8009 0.9007

0.3002 0.3001 0.4001 0.4002 0.4011 0.3995 0.4002 0.3999 0.4001 0.3998 0.4003 0.4004 0.4001 0.5001 0.5002 0.5011 0.4990 0.5001 0.4994 0.5000 0.4999 0.5003 0.5001 0.5002 0.6002 0.6003 0.6012 0.5990 0.6001 0.5992 0.6002 0.6005 0.6001 0.6003 0.6004

353.85 354.45 364.55 359.55 356.75 354.65 354.45 353.85 353.75 353.55 353.75 354.15 354.55 364.55 359.55 356.55 355.05 354.45 353.85 353.75 353.65 353.85 354.15 354.65 364.25 359.55 356.55 354.65 354.45 354.15 353.85 353.75 353.85 354.25 354.75

0.7935 0.8865 0.3180 0.4418 0.5082 0.5681 0.5831 0.5978 0.6265 0.6764 0.7284 0.7994 0.8865 0.3148 0.4481 0.5068 0.5681 0.5871 0.6081 0.6465 0.6779 0.7379 0.8071 0.8939 0.3188 0.4481 0.5054 0.5681 0.6011 0.6081 0.6465 0.6879 0.7419 0.8012 0.8979

1.07 1.04 8.65 6.75 5.34 2.95 2.04 1.61 1.36 1.24 1.13 1.07 1.04 8.57 6.86 5.38 2.91 2.06 1.64 1.40 1.24 1.15 1.09 1.05 8.80 6.88 5.37 2.96 2.12 1.63 1.40 1.26 1.16 1.08 1.06

2.19 2.36 0.97 0.99 1.01 1.10 1.22 1.41 1.59 1.73 1.93 2.11 2.36 0.97 0.98 1.02 1.08 1.22 1.38 1.51 1.72 1.86 2.04 2.21 0.98 0.98 1.03 1.11 1.18 1.37 1.51 1.67 1.84 2.11 2.13

0.9553 0.8611 17.4674 13.3420 10.3221 5.2417 3.2604 2.2258 1.6687 1.3929 1.1461 0.9907 0.8611 17.2109 13.6867 10.2645 5.2417 3.3146 2.3236 1.8194 1.4025 1.2031 1.0401 0.9288 17.5319 13.6867 10.2071 5.2417 3.5127 2.3236 1.8194 1.4688 1.2284 1.0019 0.9696

0.02 0.01 −0.14 −0.07 0.01 0 −0.06 0.04 0.01 0.03 −0.01 −0.04 0.01 −0.12 −0.06 0.07 −0.12 −0.07 0.04 0.02 0.03 0 0 0.02 −0.01 −0.04 0.08 −0.01 −0.06 −0.04 0.01 0.03 0.04 0.02 0.05

−0.04 −0.33 −1.29 −0.40 −1.15 −1.26 −0.35 0.91 1.23 −0.21 0.11 −0.04 0.11 0.20 −1.38 −0.41 −0.60 −0.18 0.15 −0.94 0.52 −0.33 −0.36 −0.34 −0.88 −1.03 0.28 0.02 −1.77 1.00 −0.08 −0.11 −0.12 0.97 −0.44


a

ij

∑ (xib + xia)jjjjj 1 n

Dmax =

i=1

n

k

xia

+

1 1 1 yz + + zzzzΔx yia xib yib z {

for the ternary systems 2-propanol + water + calcium chloride/ magnesium chloride/calcium nitrate/magnesium nitrate are presented in Figures 2−6. The effect of different salts on the vapor−liquid equilibrium of the 2-propanol−water system is shown in Figure 2, which also included the salt-free data for comparison. It can be observed that, at a constant salt concentration, all of the four salts (calcium chloride, magnesium chloride, calcium nitrate, and magnesium nitrate) exhibited a salting-out effect. The vapor phase mole fraction of 2-propanol increased when compared to that of the salt-free system, which causes a shift in the azeotropic point toward higher concentration of 2-propanol. Figures 3−6 show the effect of salt concentration on VLE data for different salts. It can be seen from these figures that the content of 2-propanol increases in the vapor phase with increasing concentration of salts, which can be attributed to the nonideality of mixture. The nonideality of a ternary system can be represented using the activity coefficient (γ) of a mixture. Its definition is as follow:13,17

n

Δp p i=1 i=1 n ÅÄÅ ÑÉÑ Å ÑÑ 1 1 ÑΔT + ∑ (xib + xia)Bi ÅÅÅÅ + 2 2Ñ Å (Tb + Ci) ÑÑÑÑÖ ÅÅÇ (Ta + Ci) i=1

+ 2 ∑ |ln γib − ln γia|Δx +

∑ (xib + xia)

(2)

where n is the number of components; Δp, ΔT, and Δx are the errors in the measurement of the pressure, temperature, and mole fraction, respectively; Ai, Bi, and Ci are the pertinent coefficients in the Antoine equation. The results of the thermodynamic conformance test for some points of the four ternary systems are listed in Table 7. In Table 7, it can be observed that D < Dmax for all the considered data points, indicating that the experimental VLE data for the four systems are thermodynamically consistent, which confirm that the measured VLE data are reliable. 3.3. Effect of Salts on Vapor−Liquid Equilibrium. To explore the effect of salts on vapor−liquid equilibrium for azeotrope 2-propanol and water, the isobaric y1−x1′ diagrams

γi = yp /xipis i

(3)

where p is the total pressure, psi is the saturated vapor pressure of a pure component i, yi and xi are respectively the mole F



Article

Table 5. Isobaric Vapor−Liquid Equilibrium Data for Liquid Phase Mole Fraction (Salts-Free Basis; x′), Liquid Phase Molality (m), Temperature (T), Vapor Phase Mole Fraction (y), Activity Coefficient (γ), Relative Volatility (α), and the Relative Deviation between the Experimental and Calculated Values of Temperature (ΔT), Vapor Phase Mole Fractions (Δy), for the Ternary System 2-Propanol (1) + Water (2) + Magnesium Nitrate (3) at p = 101.3 kPaa x′1

m3(mol/kg)

T (K)

y1

γ1

γ2

α12

ΔT (%)

.

0.0260 0.0560 0.0910 0.2006 0.3002 0.4004 0.5013 0.6001 0.7006 0.8009 0.9007 0.0260 0.0560 0.0910 0.2006 0.3002 0.4004 0.5013 0.6001 0.7006 0.8009 0.9007 0.0260 0.0560 0.0910 0.2006 0.3002 0.4004 0.5013 0.6001 0.7006 0.8009 0.9007 0.0260 0.0560 0.0910 0.2006 0.3002 0.4004 0.5013 0.6001 0.7006 0.8009 0.9007 0.0260 0.0560 0.0910 0.2006 0.3002 0.4004 0.5013 0.6001 0.7006 0.8009 0.9007 0.0260 0.0560 0.0910

0.1001 0.1003 0.1002 0.1002 0.1001 0.1000 0.1001 0.0998 0.1001 0.1003 0.1002 0.2001 0.2002 0.2001 0.2001 0.1999 0.1999 0.1999 0.1998 0.2003 0.2001 0.2002 0.3002 0.3001 0.3003 0.3001 0.2999 0.2998 0.2997 0.2997 0.3001 0.3002 0.3001 0.4001 0.4002 0.4005 0.4001 0.3998 0.4000 0.3998 0.3997 0.4001 0.4002 0.4002 0.5001 0.5003 0.5006 0.5001 0.4998 0.4994 0.4998 0.4997 0.5002 0.5001 0.5003 0.6002 0.6003 0.6005

364.15 359.75 357.75 355.35 354.95 354.55 353.95 353.85 353.75 354.15 354.45 364.15 359.75 357.25 355.20 354.85 354.95 354.25 354.15 354.25 354.45 355.15 364.25 359.85 356.85 355.15 354.75 354.65 354.55 354.35 354.45 354.75 355.45 364.35 359.85 357.35 355.15 354.65 354.85 354.65 354.55 354.65 355.15 355.55 364.85 359.85 356.85 355.25 355.15 354.85 354.75 354.65 355.15 355.65 356.25 364.55 359.75 357.45

0.3067 0.4261 0.4767 0.5350 0.5560 0.5760 0.6011 0.6481 0.7021 0.7782 0.8781 0.3030 0.4283 0.4830 0.5411 0.5680 0.5811 0.6155 0.6565 0.7085 0.7861 0.8766 0.3050 0.4325 0.4915 0.5481 0.5611 0.5855 0.6181 0.6664 0.7164 0.7864 0.8788 0.3082 0.4348 0.4938 0.5565 0.5711 0.5911 0.6265 0.6679 0.7279 0.7979 0.8826 0.3108 0.4348 0.4948 0.5564 0.5781 0.6081 0.6265 0.6679 0.7279 0.7966 0.8802 0.3181 0.4387 0.5014

8.42 6.42 4.78 2.68 1.89 1.49 1.28 1.15 1.08 1.03 1.02 8.33 6.47 4.95 2.73 1.95 1.49 1.30 1.16 1.07 1.03 0.99 11.13 6.52 5.13 2.78 1.94 1.52 1.29 1.17 1.08 1.02 0.99 8.44 6.57 5.06 2.83 1.98 1.53 1.31 1.17 1.09 1.03 1.00 8.37 6.58 5.19 2.83 1.97 1.58 1.31 1.17 1.07 1.01 0.97 8.68 6.68 5.14

0.99 1.00 1.03 1.14 1.27 1.43 1.66 1.84 2.09 2.30 2.51 1.00 1.00 1.04 1.14 1.24 1.40 1.59 1.78 2.01 2.20 2.48 1.32 0.99 1.04 1.12 1.27 1.41 1.57 1.72 1.95 2.18 2.42 0.99 0.99 1.02 1.11 1.25 1.38 1.53 1.71 1.86 2.04 2.35 0.97 0.99 1.04 1.11 1.21 1.33 1.53 1.71 1.84 2.03 2.34 0.97 0.99 1.00

16.5721 12.5158 9.0995 4.5849 2.9191 2.0343 1.4991 1.2273 1.0072 0.8722 0.7942 16.2853 12.6289 9.3321 4.6989 3.0650 2.0773 1.5925 1.2736 1.0387 0.9136 0.7832 16.4400 12.8471 9.6551 4.8334 2.9801 2.1153 1.6101 1.3312 1.0795 0.9152 0.7994 16.6893 12.9680 9.7443 5.0004 3.1040 2.1648 1.6687 1.3402 1.1432 0.9815 0.8288 16.8936 12.9680 9.7834 4.9984 3.1942 2.3236 1.6687 1.3402 1.1432 0.9736 0.8100 17.4755 13.1752 10.0451

−0.01 −0.04 −0.15 −0.04 −0.06 −0.04 0.04 0 0.02 −0.02 0.07 0.01 −0.04 −0.01 0 −0.01 −0.13 0 −0.02 −0.04 −0.01 −0.03 2.07 −0.05 0.11 0.02 0.03 −0.01 −0.03 0 −0.01 0 −0.01 −0.01 −0.04 −0.02 0.03 0.08 −0.02 0 0.01 0.02 −0.01 0.07 −0.12 −0.03 0.13 0.02 −0.03 0.02 0.03 0.07 −0.02 −0.04 −0.01 −0.01 0.02 −0.02

−1.37 −0.23 1.83 0.85 0.16 0.15 0.86 −0.19 0.05 −0.25 −0.62 0.54 0.05 1.27 0.63 −0.97 0.34 −0.38 −0.40 0.10 −0.54 −0.01 0.75 −0.24 0.19 0.15 1.18 0.58 0.20 −0.93 −0.14 0.12 0.13 0.33 −0.16 0.39 −0.60 0.27 0.56 −0.21 −0.25 −0.93 −0.70 0.07 0.32 0.49 0.81 0.14 −0.13 −1.39 0.68 0.60 −0.19 0.03 0.68 −1.42 0.23 0.08

G



Article


m3(mol/kg)

T (K)

y1

γ1

γ2

α12

ΔT (%)

.

0.2006 0.3002 0.4004 0.5013 0.6001 0.7006 0.8009 0.9007

0.6001 0.6000 0.5999 0.5998 0.5998 0.6001 0.6002 0.6001

355.10 355.15 355.05 355.05 355.15 355.45 355.75 356.65

0.5604 0.5881 0.6081 0.6265 0.6679 0.7329 0.8071 0.8879

2.87 2.01 1.57 1.30 1.15 1.07 1.02 0.97

1.10 1.18 1.32 1.52 1.68 1.79 1.92 2.17

5.0801 3.3283 2.3236 1.6687 1.3402 1.1726 1.0401 0.8732

0.08 0.01 0.01 0.01 0.01 −0.01 0.04 0

0.09 −1.07 −0.58 1.50 1.38 −0.18 −0.74 0.11


a

Table 6. Isobaric Vapor−Liquid Equilibrium Data for Liquid Phase Mole Fraction (x), Temperature (T), Vapor Phase Mole Fraction (y), Relative Volatility (α), for the Binary System 2-Propanol (1) + Water (2) at p = 101.3 kPaa x1

T (K)

y1

α12

0.0260 0.0560 0.0910 0.2006 0.3002 0.4004 0.5013 0.6001 0.7006 0.8009 0.9007

364.05 359.65 357.25 355.45 354.75 354.35 353.85 353.65 353.55 353.75 354.05

0.2992 0.4213 0.5035 0.5234 0.542 0.5685 0.5962 0.6325 0.6952 0.7467 0.8456

15.9939 12.2722 10.1298 4.3764 2.7587 1.9730 1.4688 1.1469 0.9747 0.7328 0.6038

Figure 2. Isobaric y1−x1′ diagram for the system of 2-propanol (1) + water (2) with different salts at 0.6 mol/kg and 101.3 kPa: ●, salt free; □, calcium chloride; ○, magnesium chloride; △, calcium nitrate; ☆, magnesium nitrate; solid lines, model calculated results; x′, liquid phase mole fraction (salts-free basis); y, vapor phase mole fraction.


a

Table 7. Thermodynamic Consistency Check by the Modified Mcdermott−Ellis Test salt calcium chloride

magnesium chloride

calcium nitrate

magnesium nitrate

x′1

m3

0.3002 0.4004 0.5013 0.3002 0.4004 0.5013 0.5013 0.6001 0.7006 0.4004 0.5013 0.6001

0.2000 0.2001 0.2002 0.0998 0.1015 0.1001 0.5000 0.4999 0.5003 0.5999 0.5998 0.5998

D

Dmax

−0.0020 −0.0167

0.0764 0.2023

−0.0110 −0.0092

0.0764 0.3345

−0.0185 −0.0428

0.0739 0.1211

−0.0207 −0.0370

0.0751 0.1121

Figure 3. Isobaric y1−x1′ diagram for the system of 2-propanol (1) + water (2) + calcium chloride (3) at 101.3 kPa: ●, salt free; □, 0.2 mol/kg salt; ○, 0.4 mol/kg salt; △, 0.6 mol/kg salt; solid lines, model calculated results; x′, liquid phase mole fraction (salts-free basis); y, vapor phase mole fraction.

fraction of component i in the vapor phase and liquid phase. The saturated vapor pressure of pure component i (psi ) is estimated by the Antoine equation, and the constants of the Antoine equation are obtained from ref 3. It is observed that the activity coefficient of 2-propanol (Tables 2−5) increases with increasing salt concentration and consequently increases the vapor phase mole fraction of 2-pronanol. The azeotropic point of the mixture of 2-propanol and water moved and was eliminated with an increasing amount of salt. The salt concentration at which the azeotropic point disappears is 0.6 mol/kg for calcium nitrate, while greater content of the other three salts was needed to break the azeotropic point. This shows that calcium nitrate is more effective than calcium chloride, magnesium chloride, and magnesium nitrate to eliminate the azeotropic point of the binary system.

3.4. Effect of Salts on Relative Volatility. The relative volatility of 2-propanol (1) to water (2) was calculated by using the following equation:7,18 α12 =

y1 /x1 y2 /x 2

(4)

where yi and xi (salt-free) are respectively the mole fractions of component i in the vapor phase and liquid phase. The calculated results for the systems 2-propanol + water + calcium chloride/magnesium chloride/calcium nitrate/magnesium nitrate H



Article

Figure 4. Isobaric y1−x1′ diagram for the system of 2-propanol (1) + water (2) + magnesium chloride (3) at 101.3 kPa: ●, salt free; □, 0.2 mol/kg salt; ○, 0.4 mol/kg salt; △, 0.6 mol/kg salt; solid lines, model calculated results; x′, liquid phase mole fraction (salts-free basis); y, vapor phase mole fraction.

Figure 7. Relative volatility, α12, for the system of 2-propanol (1) + water (2) with different salts at 0.6 mol/kg and 101.3 kPa: ●, salt free; □, calcium chloride; ○, magnesium chloride; △, calcium nitrate; ☆, magnesium nitrate; solid lines, model calculated results; x′, liquid phase mole fraction (salts-free basis).

in water and sparingly in 2-propanol. Therefore, the relative volatility of 2-propanol to water increases by adding salt to the binary system. In addition, calcium nitrate is more effective than calcium chloride, magnesium chloride, and magnesium nitrate to exhibit a salting-out effect and then consequently increased the vapor phase mole fraction of 2-propanol. Thus, salts’ effects on the relative volatility of 2-propanol to water follow the order calcium nitrate > calcium chloride > magnesium nitrate > magnesium chloride as shown in Figure 7. The best entrainer among the various salts is chosen on the basis of relative volatility. The higher the relative volatility is, the better is the separation of the azeotrope. As a result, calcium nitrate can be selected as an appropriate salt for the separation of the azeotrope 2-propanol and water. It was further observed from Figures 8−11 that the relative volatility of 2-propanol to water increases with increasing

Figure 5. Isobaric y1−x1′ diagram for the system of 2-propanol (1) + water (2) + calcium nitrate (3) at 101.3 kPa: ●, salt free; □, 0.2 mol/kg salt; ○, 0.4 mol/kg salt; △, 0.6 mol/kg salt; solid lines, model calculated results; x′, liquid phase mole fraction (salts-free basis); y, vapor phase mole fraction.

Figure 8. Relative volatility (α12) for the system of 2-propanol (1) + water (2) + calcium chloride (3) at 101.3 kPa: ●, salt free; □, 0.2 mol/kg salt; ○, 0.4 mol/kg salt; △, 0.6 mol/kg salt; solid lines, model calculated results; x′, liquid phase mole fraction (salts-free basis).

Figure 6. Isobaric y1−x1′ diagram for the system of 2-propanol (1) + water (2) + magnesium nitrate (3) at 101.3 kPa: ●, salt free; □, 0.2 mol/kg salt; ○, 0.4 mol/kg salt; △, 0.6 mol/kg salt; solid lines, model calculated results; x′, liquid phase mole fraction (salts-free basis); y, vapor phase mole fraction.

content of the salts. This observation can be attributed to the combined effect of the cation and anion of the salt. Since salts possess greater attraction toward 2-propanol than that with water, the interaction between salts and 2-propanol become much stronger when salt concentration increases in the binary system of 2-propanol + water, which has been verified in

were listed in Tables 2−5. For comparison, the effects of different salts on relative volatility are plotted in Figure 7. The salts considered in the present study are preferentially soluble I



Article

pys = pss xsγs

(5)

where ys is the mole fraction of solvent s in the vapor phase, xs is the mole fraction of solvent s in the liquid phase based on the assumption of the total dissociation of the salt, pss is the saturated vapor pressure of the pure solvent s. The activity coefficient of the solvent s (γs) for electrolyte systems in mixed solvents has been correlated and predicted by a variety of models: e-NRTL,20 e-CPA,21 e-VR-SAFT,22 e-PC-SAFT,23 and LIQUAC.24,25 Because the LIQUAC model allows a reliable description of solvent activity coefficients in multicomponent systems for the calculation of the vapor−liquid equilibrium (VLE) up to high salt concentrations,26 the electrolyte model LIQUAC was applied to correlate the VLE data of the systems studied in this work. In the LIQUAC model, the activity coefficient is calculated by a long-range (LR), middle-range (MR), and a short-range (SR) term:24,26

Figure 9. Relative volatility (α12) for the system of 2-propanol (1) + water (2) + magnesium chloride (3) at 101.3 kPa: ●, salt free; □, 0.2 mol/kg salt; ○, 0.4 mol/kg salt; △, 0.6 mol/kg salt; solid lines, model calculated results; x′, liquid phase mole fraction (salts-free basis).

ln γs = ln γsLR + ln γsMR + ln γsSR

The LR term (ln ln γsLR =

γLR s )

2AMsdms b3ds

(6)

can be calculated as follows,

27

[1 + bI1/2 − (1 + bI1/2)−1 − 2 ln(1 + bI1/2)]

(7)

where A=

b=

1.327757 × 105dms1/2 (DmsT )3/2

(8)

6.359696dms1/2 (DmsT )1/2

(9)

where Dms is the relative dielectric constant of the solvent mixture, which can be calculated by a linear combination,24

Figure 10. Relative volatility (α12) for the system of 2-propanol (1) + water (2) + calcium nitrate (3) at 101.3 kPa: ●, salt free; □, 0.2 mol/kg salt; ○, 0.4 mol/kg salt; △, 0.6 mol/kg salt; solid lines, model calculated results; x′, liquid phase mole fraction (salts-free basis).

Dms =

∑ vs′Ds

(10)

s

where ν′s is the salt-free volume fraction of solvents. The dielectric constant of the pure component as a function of temperature (Ds) is described as follows:24 Ds = a + bT + cT 2 + dT 3 + eT 4

(11)

The density of the solvent mixture (dms) is described by the following equation:27 n

dms =

∑ νs′ds

(12)

s=1

where ds is the density of pure solvents, which can be calculated from the following simple formula:28

ds = Figure 11. Relative volatility (α12) for the system of 2-propanol (1) + water (2) + magnesium nitrate (3) at 101.3 kPa: ●, salt free; □, 0.2 mol/kg salt; ○, 0.4 mol/kg salt; △, 0.6 mol/kg salt; solid lines, model calculated results; x′, liquid phase mole fraction (salts-free basis).

W 5Vs

(13)

where W is the molecular weight of pure solvent. 27 The MR term (ln γMR s ) can be calculated as follows, ln γsMR =

Tables 2−5 that the activity coefficients of 2-propanol and water increase with increasing salt concentration. 3.5. Correlation of the VLE Data. Assuming ideal vapor phase behavior, vapor−liquid equilibria can be calculated using the follow simplified equation:19

∑ Bs ,l ml −

Ms ∑s ∑l [Bs , l + IBs′, l ]xs′ml M ms

l

− Ms ∑ ∑ [Bc , a + IBc′, a ]mc ma c

a

(l = c , a ) (14)

where J



Article

n

M ms =

Table 10. SR Interaction Parameters (aij)25

∑ xs′Ms

Bs , l = bs , l + cs , l exp( −1.2I1/2 + 0.250I )

(16)

Bc , a = bc , a + cc , a exp( −I1/2 + 0.125I )

(17)

Bs′, l = Bc′, a =

aij

H2O

2-propanol

cation

anion

H2O HOCH2OH cation anion

0 110.5 0 0

83.6 0 0 0

0 0 0 0

0 0 0 0

(15)

s=1

∂Bs , l

chloride/magnesium chloride/calcium nitrate/magnesium nitrate are listed in Table 11. According to the calculated values

(18)

∂I ∂Bc , a

Table 11. Average Relative Deviation (Δz)̅ and Standard Deviations (σ) for the Mole Fractions of the Vapor Phase (y1) and Equilibrium Temperature (T) of the LIQUAC Model

(19)

∂I

The SR term (ln γSR s ) can be described using the UNIQUAC model.25 The required parameters were taken directly from the literature24−26 and given in Tables 8−10.

Δz̅

Table 8. Relative van der Waals Group Volume (R) and Surface Area (Q) for LIQUAC26 solvent/ion

R

Q

2-propanol water Ca2+ Mg2+ Cl− NO3−

2.7790 0.9200 0.2626 0.1128 0.8257 1.6925

2.5080 1.400 0.4101 0.2334 0.8801 1.9745

s−l/c−a

b

(s,l/c,a)

0.81504 1.0523a −0.00158 −0.34260 0.01105 0.00050 −0.00128 0.03228 0.53799 0.45150 0.29533 0.28427

T

y1

T

calcium chloride magnesium chloride calcium nitrate magnesium nitrate

0.3976 −0.2012 −0.0665 0.0617

0.0392 0.0186 0.0057 0.0291

1.5064 0.8650 0.7396 0.6757

0.1098 0.0929 0.0493 0.2612

4. CONCLUSIONS Vapor−liquid equilibrium data for the ternary systems 2-propanol + water + calcium chloride/magnesium chloride/calcium nitrate/magnesium nitrate were determined at pressure of 101.3 kPa by using a modified Rose still. Meanwhile, the thermodynamic consistency of the experimental data was verified by the McDermott−Ellis method. Results show that the azeotropic point of the system 2-propanol + water moved and the relative volatility of 2-propanol to water increased with addition of salts. Particularly, calcium nitrate is more effective than calcium chloride, magnesium chloride, and magnesium nitrate to eliminate the azeotropic point of the binary system. The LIQUAC was used for the modeling of the ternary vapor− liquid equilibrium data. The calculated results are in good agreement with the experimental data.

cs,l/c,a −0.27148 −1.0860a 0.05220 0.69502 0.00641 0.01163 −0.00020 −0.00083 −0.57405 1.19298 −1.14211 1.72405

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.8b01116. Uncertainties of T, p, and concentration of 2-propanol (PDF)

a

Determined in the present work.

The relative deviations (Δ) between the experimental and calculated data for the mole fraction of 2-propanol in the vapor phase and equilibrium temperature are list in Tables 2−5. The average relative deviations (Δ̅ ) and the corresponding standard deviations (σ) between the experimental and calculated values for property z are expressed as follows:29

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected].

N

ORCID

Δ̅ (z) = (100/N ) ∑ ((zcal − zexp)/zexp)i

Liuyi Yin: 0000-0002-2014-009X

(20)

i=1

Funding

N

This work was supported by the Science Innovation Foundation of College of Chemistry & Chemical Engineering (Grant ZSHYCX1907) and School-Based Projects of Zhoukou Normal University (Grant ZKNUB2201701).

2 1/2

σ(z) = 100(1/(N − 1) ∑ ((zcal − zexp)/zexp)i ) i=1

y1

of Δ̅ (y1), Δ̅ (T), σ(y1), and σ(T), the LIQUAC model is suitable for the VLE calculation for the systems of 2-propanol + water + salts.

Table 9. MR Parameters between Solvents and Ions (s−l) as well as between Cations and Anions (c−a) for LIQUAC26 2-propanol−Ca2+ 2-propanol−Mg2+ 2-propanol−Cl− 2-propanol−NO3− water−Ca2+ water−Mg2+ water−Cl− water−NO3− Ca2+−Cl− Mg2+−Cl− Ca2+−NO3− Mg2+−NO3−

σ

salt

(21)

where zcal and zexp are respectively the calculated and experimental values. The values of Δ̅ (y1), Δ̅ (T), σ(y1), and σ(T) for the systems 2-propanol (1) + water (2) + calcium

Notes

The authors declare no competing financial interest. K



■

Article

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