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acetic acid
Journal of Molecular Liquids 256 (2018) 471–479
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Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq
Vapor pressure measurements and predictions for the binary systems containing ionic liquid [EMIM][BF4] and formic acid/acetic acid Chengna Dai, Xiaohui Sui, Zhigang Lei ⁎ State Key Laboratory of Chemical Resource Engineering, Beijing Key Laboratory of Energy Environmental Catalysis, Beijing University of Chemical Technology, Box 266, Beijing 100029, China
a r t i c l e
i n f o
Article history: Received 5 January 2018 Received in revised form 7 February 2018 Accepted 14 February 2018 Available online 16 February 2018 Keywords: Formic acid Acetic acid Ionic liquid (IL) UNIFAC-Lei model COSMO-RS model Vapor pressure
a b s t r a c t The vapor pressures of the binary systems formic acid/acetic acid +1-ethyl-3-methylimidazolium tetrafluoroborate ([EMIM][BF4]) were measured using a modified equilibrium still at temperatures ranging from 323.15 to 358.15 K and IL contents ranging from 0.1 to 0.9 in mass fraction. The predictive thermodynamic models (i.e., UNIFAC-Lei and COSMO-RS models) were used to predict the vapor pressures with the ARDs of 4.54% and 22.24% for formic acid, respectively, and 6.38% and 16.43% for acetic acid, respectively. This indicates that the UNIFAC-Lei model can give a quantitative description with high accuracy, while the COSMO-RS model can only be used as a prior model to give a qualitative prediction. Moreover, the excess enthalpies and σ-profiles were calculated by the COSMO-RS model to achieve further understanding on the thermodynamic behavior at molecular scale. It was found that the hydrogen bonding interaction (HHB) plays a dominant role to the total excess enthalpy, and the HHB is mainly dependent on acid components. For IL, the contribution of anion is larger than that of cation as confirmed by the σ-profiles. © 2018 Elsevier B.V. All rights reserved.
1. Introduction Ionic liquid (IL) is a relatively new class of solvent composed of organic cation and inorganic or organic anion, most of which have a melting point below 100 °C [1]. It has caused extensive concern in many fields, especially in separation processes [2–10], due to the unique properties such as negligible vapor pressure and potential as “designer solvent”. Ester compounds are widely applied in many fields as common organic solvents and industrial raw materials, while acid impurities must be removed by special equipment to obtain refined products during the preparation process [11]. In many other industrial processes, the existing acid impurities must be deacidified to prevent pipe lines and devices from corrosion and blockage [12]. Moreover, the acid must be recovered from acidic waste water before discharge, avoiding the pollution of environment and waste of resources. Thus, the study about the separation of acid is significant in the protection of environment and utilization of resources. However, due to the low relative volatility of some acid with other components, the general distillation equipment can't fulfill the separation [13]. Extractive distillation is a special separation method commonly applied in the mixtures that can't be separated by conventional distillation. The entrainer or solvent is usually a volatile organic solvent,
⁎ Corresponding author. E-mail address: [email protected] (Z. Lei).
https://doi.org/10.1016/j.molliq.2018.02.067 0167-7322/© 2018 Elsevier B.V. All rights reserved.
while its recovery may cause high energy consumption and environment problems sometimes. Thus, extractive distillation with ILs as entrainers as a new separation technology was proposed in recent years [14–18]. Compare to traditional extractive distillation, the negligible vapor pressure of IL entrainer makes it easily recovered by a simple flash tank instead of a distillation recovery column. Thus, this technology can save the equipment investment and energy consumption, which is promising to be applied in the deacidification process. Until now, many studies have been carried out on the separation processes involving ILs. Undoubtedly, the thermodynamic properties such as phase equilibria (GLE, VLE, LLE, etc.) data, activity coefficient data, and excess enthalpy of the systems containing ILs are necessary for the design and optimization of separation processes and other applications of ILs [19–27]. However, the reports on vapor-liquid equilibrium (VLE) data of acid (formic acid and acetic acid) and IL binary systems are still scarce. In this work, the common ionic liquid [EMIM][BF4] was selected as the representative to investigate the VLE with the organic acids because of its economical price, good thermal stability, and relatively low viscosity. The aim of this work is to measure the vapor pressures of the binary systems of formic acid/acetic acid + [EMIM][BF4] at different temperatures and concentrations to study the effect of IL on VLE. Moreover, two predictive thermodynamic models (i.e., UNIFAC-Lei and COSMO-RS models) were used to predict the vapor pressures. To a further step, the COSMO-RS model was applied to analyze the excess enthalpies and σ-profiles of these two systems to investigate the molecular interactions at microscopic level.
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C. Dai et al. / Journal of Molecular Liquids 256 (2018) 471–479
pressure of pure solute i, which can be calculated by Antoine equation as follows
2. Experimental section 2.1. Materials
log P si =bar ¼ Ai −
Bi T=K þ C i
ð2Þ
Formic acid (mass fraction N0.985%) was obtained from Tianjin Guangfu Fine Chemical Research Institute, and acetic acid (mass fraction N99.5%) was obtained from Being Chemical Works. They were used directly without further purification. [EMIM][BF4] was obtained from Shanghai ChengJie Chemical Co., Ltd. with a purity N99.0 wt%. It was dried over a vacuum rotary evaporator at 358.15 K for 24 h to remove traces of water and other volatile impurities. The chemicals used in this work are listed in Table 1.
where the Antoine constants (Ai, Bi, and Ci) for formic acid and acetic acid were given in Table 2 [32,33]. The vapor phase is assumed to be pure solute (yi = 1) because of the negligible volatility of IL. Therefore, Eq. 3 can be simply rewritten as.
2.2. Apparatus and procedure
where i represents the component formic acid or acetic acid.
The experimental vapor pressures of binary systems were measured by a modified equilibrium still, the details of which can be seen in our previous work [31]. Before experiments, the U-type equilibrium still was thoroughly washed by anhydrous ethanol and then dried using air oven. The mixtures of (formic acid + [EMIM][BF4]) and (acetic acid + [EMIM][BF4]) with different compositions were prepared by weighting the IL and solutes with an electronic balance (type FA2104B, Shanghai Precision Scientific Instrument Co., China) with the precision of 0.001 g. About 15 mL formic acid/acetic acid + [EMIM] [BF4] mixture were added into the equilibrium still, filling with two thirds of the vacuole in volume. Connected the equilibrium still well, and put it into the thermostatic water bath at a given temperature measured by a digital temperature indicator (Type DP–AF, Nanning Sangli Electronic Equipment Company, China, 2014) with a precision of 0.01 K. Opened the condensed water, stirrer and heater, when the temperature reached the desired value. Opened the vacuum pump until the liquid mixture boiled in the equilibrium still. Then, the needle valve was slowly opened to leak into the air until the U-type tube was kept at the same level height on both sides. If the liquid level didn't change within 20 min, it was considered to reach the vapor-liquid equilibrium. The pressure of equilibrium still was measured by a precision digital pressure gauge (Type DP-AF, Nanjing Sangli Electronic Equipment Company, China, 2014) with a precision of 0.01 kPa. The vapor pressures of formic acid and acetic acid were first measured from 303.15 to 358.15 K to check the reliability of experimental apparatus.
3.1. UNIFAC-Lei model
ϕi P ¼ γ i xi P si
ð3Þ
The UNIFAC-Lei model was used to describe the vapor-liquid equilibrium of binary system containing IL, which has been applied by many authors [34–38]. In this model, components are divided as interaction groups, and the thermodynamic properties of components are the addition of group properties. The activity coefficient of component i is written as ln γi ¼ ln γCi þ lnγ Ri
where lnγCi represents the combinatorial contribution, which is relevant to the shape and size of functional groups, and is a function of two group parameters (Rk and Qk) for group k; and lnγRi represents the residual contribution due to the interaction between functional groups, and is a function of a pair of group interaction parameters (amn and anm) between groups m and n. There are five groups (CH3, CH2, HCOOH, COOH, and [MIM][BF4]) concerned in this work, and their group parameters (Rk and Qk) are listed in Table 3, which come from previous works [39,40]. The unknown group interaction parameters between main group COOH and [MIM][BF4] were obtained by correlating the experimental VLE data of formic acid + [EMIM][BF4] and acetic acid + [EMIM][BF4] binary systems as measured in this work, using the minimized average relative deviation between the experimental and P calculated vapor pressures as objective function (OF) (OF ¼ minfN1 N1 j
P cal −P exp P exp
jg). The new obtained parameters as well as the old parameters
3. Thermodynamic models
from references are given in Table 4.
For the binary system containing IL, the vapor-liquid equilibrium for solute i can be expressed as
3.2. COSMO-RS model
ϕi yi P ¼ γi xi P si
ð1Þ
where xi and yi and are the mole fractions of solute i in liquid and vapor phases, respectively; ϕi is the fugacity coefficient of solute i in vapor phase calculated by the Peng-Robinson (PR) equation of state at a certain temperature and pressure; P is the system pressure; and γi is the activity coefficient of solute i in liquid phase. Psi is the saturated
ð4Þ
In the COSMO-RS calculation, the IL molecular was described as a cation and an anion. Therefore, the binary mixture of IL and solute was considered as a hypothetical ternary system, which consists of cation, anion and solute. A transform between activity coefficient of solute i in the binary and ternary mixture should be made by γbin ¼ i
γtern xtern γtern i i ¼ i bin xbin 2−x i i
ð5Þ
Table 1 The properties (CAS-register number, water mass fraction ωH2O, density ρ, and refractive index nD) of used chemicals at T = 298.15 K and atmospheric pressure. Compounds
Formic acid Acetic acid [EMIM][BF4] a b c
CAS
64–18-6 64–19-7 N.F.
Puritya
98.5 99.5 99.0
ωH2O (ppm)b
14,030 1387 280c
Information provided by supplier. Water content was measured by Karl-Fischer titration. Water content was measured after drying over a vacuum rotary evaporator.
ρ (g·cm−3)
nD
Exp.
Lit.
Exp.
Lit.
1.21380 1.04341 1.28253
1.21410 [28] 1.04330 [29] 1.28230 [30]
1.36916 1.36975 1.41097
1.36939 [28] 1.36960 [29] 1.41090 [30]
C. Dai et al. / Journal of Molecular Liquids 256 (2018) 471–479 70
Table 2 Parameters of the Antoine equation used in this work.
Formic acid Acetic acid
Antoine parameters Ai
Bi
Ci
4.57631 6.4302
1608.22 1479.01
−21.8974 −56.34
50
265–385 290–430
40
Table 3 Group parameters of Rk and Qk in the UNIFAC-Lei model. Rk
Qk
CH3 CH2 HCOOH COOH [MIM][BF4]
0.9011a 0.6744a 1.528b 1.3013b 6.5669a
0.8480a 0.5400a 1.532b 1.2240b 4.0050a
b
30 20
Main groups
a
10 0 300
ð6Þ
In this work, the COSMO-RS calculations on activity coefficient, excess enthalpy and σ-profile were performed using COSMOthermX software (Version C30_1301, COSMOlogic GmbH & CO. KG, Leverkusen, Germany).
330
The vapor pressures of formic acid and acetic acid were measured from 303.15 to 358.15 K, and the experimental data were compared with the calculated values by the Antoine equation. The comparison between experimental vapor pressures and the calculated values was shown in Fig. 1, and the detailed data are given in Table 5. The average relative deviation (ARD) was calculated by N 1X P exp −P Antoine N 1 P exp
ð7Þ
where Pexp and PAntoine are the vapor pressures obtained by experiments and Antoine equation, respectively; and N is the number of data points. Table 4 Group binary interaction parameters (amn and anm) in the UNIFAC-Lei model. m
n
CH2 CH2 COOH
COOH [MIM][BF4] [MIM][BF4]
350
360
370
Fig. 1. Comparison between experimental vapor pressure and the calculated values by Antoine equation for formic acid and acetic acid. Scattered points, experimental data; Solid lines, calculated results by Antoine equation.
It is obvious that the experimental data agree well with the calculated values with the ARDs of 0.47% and 0.87%, proving the reliability of experimental apparatus and method used in this work. 4.2. Vapor pressures of two binary systems The vapor pressure data of the binary systems (formic acid + [EMIM][BF4] and acetic acid + [EMIM][BF4]) were measured at the temperatures ranging from 323.15 to 358.15 K. The detailed experimental data and predicted values by the UNIFAC-Lei and COSMO-RS models including temperature, pressure and solute concentration expressed in mass fraction, as well as the corresponding expanded uncertainties with 0.95 level of confidence expressed as U(T), U(P), and U(x), are listed in Tables 6 and 7. The details on the calculation of expanded
PAntonie (kPa)
U(T) (K)
U(P) (kPa)
100RD
Formic acid 303.15 7.27 313.15 11.21 318.15 13.99 323.15 17.42 328.15 21.31 333.15 25.80 338.15 30.88 343.15 37.46 348.15 44.26 353.15 52.75 358.15 62.23
7.22 11.34 14.05 17.29 21.14 25.67 30.98 37.17 44.35 52.64 62.16
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0.08 0.12 0.19 0.28 0.30 0.44 0.58 0.61 0.78 0.89 0.98
0.69 0.44 0.43 0.75 0.80 0.50 0.32 0.77 0.20 0.21 0.11
Acetic acid 303.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15
2.74 4.69 6.04 7.71 9.75 12.22 15.20 18.77 23.00 28.00 33.86
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0.04 0.05 0.06 0.08 0.10 0.14 0.18 0.26 0.34 0.42 0.58
1.11 1.30 0.98 1.85 0.91 0.74 1.74 0.37 0.00 0.29 0.27
T/K
4.1. Vapor pressures of formic acid and acetic acid
ARD ¼
340
Table 5 Experimental and calculated vapor pressures for pure components.
4. Results and discussion
c
320
T (K)
H m ¼ HMF þ HHB þ H vdw
b
310
Group parameters of Rk and Qk obtained from Ref. [39]. Group parameters of Rk and Qk obtained from Ref. [40].
where γbin and xbin are the activity coefficient and mole fraction of soli i ute i in the binary system of {formic acid/acetic acid + [EMIM][BF4]}, respectively; γtern and xtern are the corresponding values in the i i hypothetical ternary system of {formic acid/acetic acid + [EMIM]+ + [BF4]−}. More details on how to predict the activity coefficient of solutes in IL can be seen from the website at https://www.scm.com/doc/ Tutorials/COSMO-RS/Ionic_Liquids.html. The COSMO-RS model is also an efficient method to predict the excess enthalpy of the mixtures containing ILs [41–44], which mainly includes the electrostatic-Misfit interaction (HMF), hydrogen bonding interaction (HHB) and van der Waals interaction (HvdW). These contributions are expressed as:
a
formic acid acetic acid
60
Temperature range (K)
P (kPa)
Compounds
473
anm
amn b
663.5 1108.51a 50.9115c
Group binary interaction parameters obtained from Ref. [39]. Group binary interaction parameters obtained from Ref. [40]. Group binary interaction parameters obtained in this work.
315.3b 588.74a −131.9878c
Pexp (kPa)
2.68 4.56 6.12 7.57 9.84 12.13 14.94 18.70 23.00 27.92 33.77
Pexp and PAntonie are the experimental data and calculated values by the Antoine equation. U(T) and U(P) are the expanded uncertainties with 0.95 level of confidence of experimental temperature T and pressure Pexp. RD is the relative deviation between experimental data and calculated values.
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C. Dai et al. / Journal of Molecular Liquids 256 (2018) 471–479
Table 6 Experimental and predicted vapor pressures for the binary mixtures of formic acid (1) + [EMIM][BF4] (2). PUNIFAC-Lei (kPa)
PCOSMO (kPa)
γ1,exp
γ1,UNIFAC-Lei
γ1,COSMO
Φ1
U(T) (K)
U(P) (kPa)
U(x)
100RD(P) (UNIFAC-Lei)
100RD(P) (COSMO)
T = 323.15 K 0.101 3.64 0.201 6.08 0.301 8.11 0.401 10.85 0.500 11.83 0.601 14.62 0.700 15.50 0.801 15.86 0.901 17.28 1.000 17.42
3.64 6.73 9.33 11.47 13.16 14.52 15.55 16.34 16.95 17.40
1.86 3.73 5.68 7.68 9.70 11.64 13.45 15.02 16.32 17.29
0.6462 0.6761 0.7206 0.8418 0.8394 0.9708 0.9800 0.9647 1.0184 1.0010
0.6462 0.7482 0.8287 0.8899 0.9335 0.9640 0.9831 0.9939 0.9988 1.0000
0.3320 0.4165 0.5065 0.5993 0.6911 0.7777 0.8550 0.9193 0.9681 1.0000
0.9987 0.9978 0.9971 0.9961 0.9957 0.9947 0.9944 0.9943 0.9938 0.9937
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0.07 0.10 0.16 0.19 0.27 0.33 0.45 0.52 0.57 0.28
0.002 0.001 0.002 0.002 0.002 0.001 0.002 0.001 0.002 0.002
0.00 10.67 15.00 5.72 11.21 0.71 0.31 3.03 1.92 0.10
49.00 38.62 29.98 29.18 18.03 20.35 13.25 5.27 5.55 0.73
T = 328.15 K 0.101 4.73 0.201 7.24 0.301 11.98 0.401 14.50 0.500 15.82 0.601 17.44 0.700 19.02 0.801 19.74 0.901 19.73 1.000 21.31
4.46 8.24 11.43 14.05 16.11 17.77 19.03 20.00 20.73 21.29
2.26 4.56 6.96 9.42 11.88 14.26 16.45 18.37 19.95 21.14
0.6869 0.6585 0.8698 0.9194 0.9173 0.9468 0.9829 0.9813 0.9508 1.0008
0.6480 0.7499 0.8302 0.8911 0.9344 0.9646 0.9834 0.9941 0.9989 1.0000
0.3310 0.4167 0.5076 0.6008 0.6927 0.7791 0.8559 0.9198 0.9683 1.0000
0.9984 0.9975 0.9958 0.9950 0.9945 0.9940 0.9934 0.9932 0.9932 0.9926
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0.09 0.14 0.29 0.35 0.40 0.51 0.62 0.86 0.92 0.30
0.002 0.001 0.002 0.002 0.002 0.001 0.002 0.001 0.002 0.002
5.66 13.88 4.55 3.08 1.86 1.87 0.05 1.31 5.05 0.08
52.17 36.97 41.94 35.07 24.91 18.26 13.51 6.92 1.12 0.82
T = 333.15 K 0.101 5.70 0.200 9.96 0.301 12.85 0.401 16.73 0.500 17.81 0.601 20.60 0.700 22.16 0.801 23.78 0.901 25.41 1.000 25.80
5.43 10.03 13.91 17.10 19.60 21.61 23.14 24.32 25.22 25.89
2.74 5.55 8.46 11.46 14.46 17.34 20.00 22.32 24.23 25.67
0.6814 0.7460 0.7682 0.8730 0.8500 0.9201 0.9422 0.9723 1.0066 0.9965
0.6497 0.7512 0.8316 0.8923 0.9353 0.9652 0.9837 0.9942 0.9989 1.0000
0.3301 0.4170 0.5086 0.6022 0.6941 0.7803 0.8568 0.9203 0.9684 1.0000
0.9981 0.9967 0.9957 0.9944 0.9941 0.9931 0.9926 0.9921 0.9915 0.9914
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0.10 0.28 0.45 0.65 0.89 1.09 1.17 1.21 1.36 0.44
0.002 0.001 0.002 0.002 0.002 0.001 0.002 0.001 0.002 0.002
4.65 0.70 8.26 2.21 10.03 4.89 4.41 2.25 0.77 0.35
51.93 44.32 34.14 31.50 18.84 15.83 9.76 6.13 4.64 0.51
T = 338.15 K 0.101 7.79 0.200 12.71 0.301 14.92 0.401 20.50 0.500 22.42 0.601 26.76 0.700 28.46 0.801 29.15 0.901 30.01 1.000 30.88
6.58 12.14 16.83 20.68 23.70 26.14 27.98 29.39 30.47 31.29
3.30 6.70 10.23 13.86 17.48 20.96 24.16 26.95 29.25 30.98
0.7711 0.7881 0.7386 0.8854 0.8854 0.9886 1.0009 0.9862 0.9839 0.9869
0.6514 0.7528 0.8330 0.8934 0.9361 0.9657 0.9841 0.9944 0.9990 1.0000
0.3294 0.4173 0.5096 0.6036 0.6955 0.7815 0.8576 0.9207 0.9685 1.0000
0.9975 0.9959 0.9952 0.9934 0.9928 0.9914 0.9909 0.9907 0.9904 0.9901
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0.18 0.47 0.69 0.87 1.12 1.38 1.42 1.52 1.63 0.58
0.002 0.001 0.002 0.002 0.002 0.001 0.002 0.001 0.002 0.002
15.53 4.48 12.78 0.90 5.72 2.32 1.68 0.84 1.53 1.32
57.64 47.30 31.40 32.38 22.03 21.67 15.11 7.53 2.54 0.32
T = 343.15 K 0.101 7.31 0.200 14.32 0.301 17.50 0.401 23.99 0.500 27.03 0.601 32.06 0.700 35.16 0.801 36.38 0.901 37.12 1.000 37.46
7.91 14.60 20.24 24.87 28.50 31.42 33.64 35.34 36.63 37.60
3.95 8.04 12.30 16.67 21.02 25.19 29.02 32.36 35.10 37.17
0.6031 0.7398 0.7215 0.8628 0.8887 0.9858 1.0288 1.0237 1.0124 0.9962
0.6530 0.7544 0.8343 0.8945 0.9369 0.9663 0.9844 0.9945 0.9990 1.0000
0.3288 0.4177 0.5106 0.6049 0.6968 0.7826 0.8583 0.9211 0.9686 1.0000
0.9977 0.9956 0.9946 0.9926 0.9917 0.9901 0.9892 0.9888 0.9886 0.9885
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0.16 0.43 0.74 0.93 1.40 1.75 1.82 1.87 1.95 0.61
0.002 0.001 0.002 0.002 0.002 0.001 0.002 0.001 0.002 0.002
8.27 1.97 15.63 3.67 5.43 1.98 4.31 2.85 1.33 0.39
45.93 43.83 29.69 30.51 22.25 21.44 17.48 11.06 5.44 0.77
T = 348.15 K 0.101 9.32 0.200 17.61 0.301 20.59 0.401 29.25 0.500 35.81 0.601 40.17 0.700 41.64 0.801 42.65 0.901 43.83 1.000 44.26
9.47 17.47 24.20 29.75 34.11 37.59 40.22 42.24 43.78 44.94
4.71 9.61 14.71 19.93 25.12 30.09 34.65 38.62 41.89 44.35
0.6441 0.7618 0.7110 0.8805 0.9844 1.0331 1.0195 1.0044 1.0002 0.9848
0.6546 0.7559 0.8356 0.8955 0.9377 0.9668 0.9847 0.9947 0.9990 1.0000
0.3284 0.4181 0.5116 0.6061 0.6981 0.7836 0.8591 0.9214 0.9687 1.0000
0.9972 0.9948 0.9939 0.9913 0.9894 0.9881 0.9877 0.9874 0.9870 0.9869
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0.26 0.72 0.99 1.45 1.83 1.88 1.95 2.06 2.27 0.78
0.002 0.001 0.002 0.002 0.002 0.001 0.002 0.001 0.002 0.002
1.63 0.78 17.53 1.71 4.74 6.42 3.42 0.97 0.12 1.54
49.46 45.44 28.55 31.85 29.84 25.09 16.78 9.44 4.44 0.21
T = 353.15 K 0.101 14.23 0.200 21.32 0.301 25.57 0.401 31.92
11.28 20.80 28.80 35.36
5.59 11.42 17.49 23.71
0.8276 0.7764 0.7430 0.8092
0.6562 0.7574 0.8369 0.8966
0.3281 0.4186 0.5126 0.6074
0.9959 0.9939 0.9927 0.9909
0.01 0.01 0.01 0.01
0.64 0.86 1.34 1.71
0.002 0.001 0.002 0.002
20.71 2.45 12.64 10.79
60.75 46.45 31.58 25.73
x1
Pexp (kPa)
C. Dai et al. / Journal of Molecular Liquids 256 (2018) 471–479
475
Table 6 (continued) x1
Pexp (kPa)
PUNIFAC-Lei (kPa)
PCOSMO (kPa)
γ1,exp
γ1,UNIFAC-Lei
γ1,COSMO
Φ1
U(T) (K)
U(P) (kPa)
U(x)
100RD(P) (UNIFAC-Lei)
100RD(P) (COSMO)
0.500 0.601 0.700 0.801 0.901 1.000
40.25 44.90 48.56 50.21 51.91 52.75
40.56 44.68 47.83 50.22 52.05 53.45
29.87 35.76 41.16 45.86 49.72 52.64
0.9314 0.9720 1.0001 0.9945 0.9963 0.9869
0.9385 0.9673 0.9850 0.9948 0.9991 1.0000
0.6994 0.7847 0.8598 0.9218 0.9688 1.0000
0.9885 0.9872 0.9861 0.9857 0.9852 0.9849
0.01 0.01 0.01 0.01 0.01 0.01
1.96 2.05 2.17 2.23 2.36 0.89
0.002 0.001 0.002 0.001 0.002 0.002
0.76 0.49 1.51 0.03 0.28 1.33
25.79 20.35 15.24 8.66 4.22 0.20
T = 358.15 K 0.101 14.30 0.200 22.02 0.301 29.26 0.401 38.56 0.500 45.40 0.601 51.36 0.700 55.80 0.801 59.67 0.901 61.69 1.000 62.23
13.35 24.61 34.09 41.87 47.98 52.86 56.57 59.44 61.61 63.25
6.59 13.50 20.70 28.05 35.33 42.28 48.64 54.17 58.72 62.16
0.7044 0.6791 0.7195 0.8266 0.8888 0.9403 0.9718 0.9988 1.0004 0.9839
0.6577 0.7588 0.8382 0.8976 0.9392 0.9678 0.9853 0.9949 0.9991 1.0000
0.3280 0.4191 0.5136 0.6087 0.7006 0.7857 0.8604 0.9221 0.9689 1.0000
0.9961 0.9939 0.9920 0.9894 0.9875 0.9859 0.9847 0.9836 0.9830 0.9829
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0.68 0.90 1.67 1.82 2.07 2.42 2.58 2.61 2.67 0.98
0.002 0.001 0.002 0.002 0.002 0.001 0.002 0.001 0.002 0.002
6.63 11.74 16.49 8.58 5.68 2.92 1.38 0.39 0.13 1.63
53.90 38.70 29.26 27.25 22.17 17.67 12.83 9.21 4.82 0.11
Pexp and γ1,exp are the experimental vapor pressures and activity coefficients, respectively. PUNIFAC-Lei, PCOSMO, γ1,UNIFAC-Lei and γ1,COSMO are the predicted values by the UNIFAC-Lei or COSMO-RS model. U(T), U(P) and U(x) are the expanded uncertainties with 0.95 level of confidence of experimental temperature T, pressure Pexp, and solute mole fraction x1, respectively. RD(P) (UNIFAC-Lei) and RD(P) (COSMO) are the relative deviations of vapor pressures between experimental data and predicted values by the UNIFAC-Lei and COSMO-RS models, respectively.
uncertainties can be found in our previous work [7]. The relative deviation (RD) between experimental data and predicted values is defined as P −P exp RD ¼ cal P exp
ð8Þ
where Pexp and Pcal are the experimental and calculated vapor pressures, respectively. RD(P) (UNIFAC-Lei) and RD(P) (COSMO), as given in Tables 6 and 7, represent the relative deviations between experimental vapor pressures and calculated values by the UNIFAC-Lei and COSMORS models, respectively. The experimental and predicted vapor pressures by the UNIFAC-Lei model for the two binary systems at different temperatures are shown in Fig. 2. In the whole concentration range, formic acid and acetic acid are miscible with [EMIM][BF4]. With the increase of temperature, vapor pressures of binary mixtures also increase. Meanwhile, the vapor pressures first increase sharply with the increase of formic acid/ acetic acid concentration, and then tend to be smooth at high concentration range. That is, the addition of [EMIM][BF4] makes vapor pressure lower than that of pure solute at the same temperature, due to the strong interaction between IL and formic acid/acetic acid. Moreover, for both binary systems it is obvious that the predicted values by the UNIFAC-Lei model agree very well with experimental data in the whole concentration range, indicating that the UNIFAC-Lei model can give a quantitative description with high accuracy for predicting the VLE of these two binary systems {formic acid/acetic acid + [EMIM] [BF4]}. For a further step, the comparison among predicted results by the UNIFAC-Lei model, predicted results by the COSMO-RS model, and experimental data is illustrated in Fig. 3. It can be seen that the predicted accuracy by the COSMO-RS model is worse than that by the UNIFACLei model, especially at high temperature (353.15 K). However, the COSMO-RS model can give the same trend as experimental data. Thus, the COSMO-RS model can be used as a prior predictive model to give a qualitative prediction for vapor pressures. The average relative deviations (ARDs) for the UNIFAC-Lei and COSMO-RS models are 4.54% and 22.24% for formic acid + IL, respectively, while they are 6.38% and 16.43% for acetic acid + IL, respectively. 4.3. Analysis of the excess enthalpy To study the solution thermodynamics, an important property used to analyze the nature of molecular interactions in solutions is excess enthalpy Hm. The predicted excess enthalpies of binary systems {formic
acid/acetic acid and [EMIM][BF4]} at 298.15 K are presented in Fig. 4. It can be seen that the excess enthalpies of formic acid and IL system present both positive and negative values depending on formic acid concentration, as shown in Fig. 4(a). At low formic acid concentration region, the dominant interaction is hydrogen bonding (HHB) with positive value resulting in positive excess enthalpy, indicating the endothermicity of the mixture, whereas the negative van der Waals interaction (HvdW) plays a secondary role and the negative electrostatic interaction (HMF) contributes the least to the overall excess enthalpy. However, the contributions of van der Waals and electrostatic interactions can't be neglected, especially for systems containing formic acid, as shown in Fig. 4(a). Moreover, with the increase of formic acid concentration, the exothermicity of the mixture increases. When the mole concentration of formic acid is over 0.7, the negative excess enthalpy occurs mainly due to the contributions of HvdW and HMF. The contributions of formic acid molecule, [EMIM]+ cation, and [BF4]+ anion to HHB are shown in Fig. 5. It is clear that the endothermicity of the mixture is mainly dependent on formic acid molecule, while the anion and cation contribute negative values, and the contribution of anion is larger than that of cation. Thus, we can conclude that: 1) the addition of formic acid weakens the electrostatic interaction between [EMIM]+ and [BF4]−, resulting in a negative contribution of HMF; 2) the original hydrogen bondings between formic acid (HCOOH) molecules, and between [EMIM]+ and [BF4]− ions are ruptured, while the new hydrogen bondings between HCOOH and [EMIM]+, and between HCOOH and [BF4]− ion are formed in the mutual dissolution between formic acid and IL; 3) the new formed hydrogen bonding is stronger than that between [EMIM]+ and [BF4]−; and 4) the new formed hydrogen bonding interactions can't overcome the energy of HCOOH–HCOOH hydrogen bonding in the mixing process, resulting in positive excess enthalpies. However, when the concentration of formic acid is high, the increased HvdW and HMF can make a balance to the loss of HHB, even resulting in negative excess enthalpies. For acetic acid and [EMIM][BF4 ] mixture, the predicted excess enthalpies are illustrated in Fig. 4(b). Similarly, the positive H HB plays a dominant role, H vdw shows a secondary contribution and the HMF contributes slightly to Hm. But unlike the formic acid + IL system, the H MF of acetic acid + IL mixture is positive, indicating the strong electrostatic interaction between acetic acid molecule and cation/anion ions of IL. Moreover, the mixture present only positive values throughout the whole concentration range. That is, the negative H vdW can't makeup the energy of hydrogen bonding between acetic acid molecules, and the process becomes endothermic in nature.
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Table 7 Experimental and predicted vapor pressures for the binary mixtures of acetic acid (1) + [EMIM][BF4] (2). PUNIFAC-Lei (kPa)
PCOSMO (kPa)
γ1,exp
γ1,UNIFAC-Lei
γ1,COSMO
Φ1
U(T) (K)
U(P) (kPa)
U(x)
100RD(P) (UNIFAC-Lei)
100RD(P) (COSMO)
T = 323.15 K 0.101 2.29 0.201 3.57 0.300 4.85 0.400 5.74 0.501 6.44 0.601 6.92 0.700 7.51 0.800 7.56 0.901 7.59 1.000 7.57
1.86 3.25 4.31 5.13 5.80 6.34 6.78 7.16 7.47 7.73
1.56 2.74 3.68 4.46 5.12 5.71 6.24 6.75 7.23 7.71
1.1028 1.0213 1.0719 1.0810 1.0856 1.0758 1.0977 1.0520 1.0145 0.9792
0.8977 0.9300 0.9515 0.9663 0.9769 0.9849 0.9910 0.9957 0.9988 1.0000
0.7568 0.7883 0.8160 0.8414 0.8658 0.8901 0.9154 0.9420 0.9702 1.0000
0.9991 0.9986 0.9980 0.9977 0.9974 0.9972 0.9970 0.9970 0.9969 0.9969
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0.07 0.08 0.09 0.11 0.13 0.14 0.14 0.15 0.18 0.08
0.002 0001 0.002 0.002 0.001 0.001 0.002 0.002 0.001 0.002
18.60 8.94 11.23 10.61 10.01 8.45 9.72 5.36 1.55 2.13
31.71 23.11 24.07 22.35 20.50 17.54 16.87 10.74 4.69 1.81
T = 328.15 K 0.101 2.81 0.201 4.36 0.300 6.12 0.400 7.48 0.501 8.28 0.601 9.13 0.700 9.18 0.800 9.56 0.901 9.60 1.000 9.84
2.37 4.13 5.47 6.51 7.35 8.03 8.59 9.06 9.46 9.78
1.93 3.41 4.60 5.59 6.44 7.19 7.88 8.53 9.15 9.75
1.0698 0.9860 1.0691 1.1132 1.1030 1.1216 1.0603 1.0512 1.0141 1.0057
0.9026 0.9344 0.9551 0.9692 0.9792 0.9864 0.9919 0.9961 0.9989 1.0000
0.7376 0.7743 0.8059 0.8343 0.8611 0.8873 0.9139 0.9414 0.9701 1.0000
0.9989 0.9983 0.9976 0.9971 0.9968 0.9965 0.9964 0.9963 0.9963 0.9962
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0.08 0.09 0.11 0.14 0.16 0.19 0.22 0.23 0.27 0.10
0.002 0001 0.002 0.002 0.001 0.001 0.002 0.002 0.001 0.002
15.63 5.24 10.66 12.93 11.23 12.05 6.45 5.24 1.49 0.57
31.40 21.80 24.84 25.28 22.23 21.21 14.13 10.79 4.72 0.95
T = 333.15 K 0.101 2.96 0.201 5.27 0.300 7.08 0.400 9.15 0.501 10.50 0.601 11.44 0.700 11.63 0.800 11.87 0.901 12.01 1.000 12.13
2.99 5.21 6.88 8.19 9.25 10.09 10.79 11.37 11.87 12.28
2.36 4.20 5.70 6.95 8.03 8.99 9.87 10.69 11.47 12.22
0.8987 0.9502 0.9861 1.0854 1.1144 1.1198 1.0704 1.0400 1.0109 0.9880
0.9074 0.9386 0.9587 0.9721 0.9813 0.9880 0.9929 0.9966 0.9991 1.0000
0.7198 0.7610 0.7962 0.8275 0.8565 0.8845 0.9124 0.9408 0.9700 1.0000
0.9989 0.9980 0.9974 0.9966 0.9961 0.9958 0.9957 0.9956 0.9955 0.9955
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0.05 0.09 0.12 0.20 0.26 0.29 0.31 0.32 0.34 0.14
0.002 0001 0.002 0.002 0.001 0.001 0.002 0.002 0.001 0.002
0.97 1.22 2.78 10.44 11.94 11.77 7.24 4.17 1.17 1.22
20.32 20.26 19.51 24.03 23.50 21.39 15.15 9.96 4.51 0.76
T = 338.15 K 0.101 3.53 0.201 6.19 0.300 9.11 0.400 10.96 0.501 13.35 0.601 14.49 0.700 14.68 0.800 14.84 0.901 14.92 1.000 14.94
3.74 6.50 8.60 10.23 11.53 12.58 13.44 14.17 14.78 15.28
2.87 5.14 7.01 8.58 9.94 11.15 12.26 13.29 14.26 15.20
0.8614 0.8970 1.0194 1.0446 1.1383 1.1392 1.0853 1.0444 1.0087 0.9775
0.9120 0.9426 0.9621 0.9749 0.9834 0.9894 0.9938 0.9970 0.9992 1.0000
0.7031 0.7484 0.7869 0.8210 0.8521 0.8818 0.9109 0.9402 0.9698 1.0000
0.9987 0.9978 0.9968 0.9961 0.9952 0.9948 0.9948 0.9947 0.9947 0.9947
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0.09 0.12 0.19 0.24 0.30 0.43 0.57 0.68 0.75 0.18
0.002 0001 0.002 0.002 0.001 0.001 0.002 0.002 0.001 0.002
5.88 5.09 5.62 6.68 13.60 13.15 8.43 4.54 0.95 2.31
18.81 16.95 23.10 21.73 25.54 23.04 16.51 10.47 4.40 1.76
T = 343.15 K 0.101 4.33 0.201 7.74 0.300 11.36 0.400 13.84 0.501 15.88 0.601 17.02 0.700 17.97 0.800 18.18 0.901 18.43 1.000 18.70
4.64 8.07 10.66 12.67 14.28 15.57 16.63 17.51 18.26 18.89
3.46 6.25 8.55 10.51 12.21 13.73 15.11 16.39 17.61 18.77
0.8557 0.9081 1.0290 1.0677 1.0961 1.0833 1.0751 1.0355 1.0083 0.9899
0.9165 0.9466 0.9655 0.9775 0.9855 0.9908 0.9946 0.9974 0.9993 1.0000
0.6877 0.7366 0.7781 0.8147 0.8479 0.8792 0.9095 0.9396 0.9697 1.0000
0.9985 0.9973 0.9961 0.9953 0.9946 0.9942 0.9938 0.9938 0.9937 0.9936
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0.13 0.16 0.26 0.31 0.68 0.86 0.93 1.04 1.13 0.26
0.002 0001 0.002 0.002 0.001 0.001 0.002 0.002 0.001 0.002
7.11 4.24 6.17 8.45 10.10 8.53 7.48 3.67 0.90 1.02
20.08 19.30 24.72 24.07 23.11 19.35 15.93 9.84 4.47 0.37
T = 348.15 K 0.101 5.40 0.201 9.18 0.300 13.63 0.400 16.71 0.501 19.50 0.601 21.39 0.700 22.14 0.800 22.46 0.901 22.65 1.000 23.00
5.71 9.93 13.12 15.58 17.55 19.13 20.42 21.50 22.42 23.18
4.15 7.54 10.37 12.78 14.89 16.77 18.49 20.08 21.58 23.00
0.8705 0.8785 1.0067 1.0510 1.0971 1.1094 1.0795 1.0425 1.0099 0.9922
0.9209 0.9505 0.9687 0.9801 0.9874 0.9922 0.9955 0.9978 0.9994 1.0000
0.6733 0.7254 0.7697 0.8086 0.8438 0.8766 0.9081 0.9390 0.9696 1.0000
0.9982 0.9970 0.9955 0.9945 0.9936 0.9930 0.9927 0.9926 0.9925 0.9924
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0.15 0.18 0.28 0.54 0.72 1.01 1.12 1.24 1.31 0.34
0.002 0001 0.002 0.002 0.001 0.001 0.002 0.002 0.001 0.002
5.80 8.19 3.78 6.74 10.00 10.57 7.79 4.28 1.04 0.78
23.10 17.87 23.93 23.49 23.63 21.58 16.50 10.61 4.74 0.02
T = 353.15 K 0.101 7.07 0.201 11.49 0.300 16.59 0.400 19.90
6.99 12.14 16.03 19.03
4.95 9.04 12.49 15.45
0.9359 0.9028 1.0059 1.0274
0.9252 0.9542 0.9718 0.9826
0.6600 0.7149 0.7618 0.8028
0.9978 0.9964 0.9948 0.9937
0.01 0.01 0.01 0.01
0.16 0.21 0.48 0.82
0.002 0001 0.002 0.002
1.14 5.70 3.39 4.36
29.92 21.28 24.71 22.36
x1
Pexp (kPa)
C. Dai et al. / Journal of Molecular Liquids 256 (2018) 471–479
477
Table 7 (continued) x1
Pexp (kPa)
PUNIFAC-Lei (kPa)
PCOSMO (kPa)
γ1,exp
γ1,UNIFAC-Lei
γ1,COSMO
Φ1
U(T) (K)
U(P) (kPa)
U(x)
100RD(P) (UNIFAC-Lei)
100RD(P) (COSMO)
0.501 0.601 0.700 0.800 0.901 1.000
23.12 25.15 26.66 27.31 27.54 27.92
21.42 23.34 24.90 26.21 27.32 28.25
18.04 20.36 22.47 24.42 26.26 28.00
1.0677 1.0706 1.0667 1.0401 1.0075 0.9883
0.9893 0.9935 0.9963 0.9982 0.9995 1.0000
0.8398 0.8742 0.9068 0.9384 0.9694 1.0000
0.9927 0.9920 0.9916 0.9914 0.9913 0.9912
0.01 0.01 0.01 0.01 0.01 0.01
1.30 1.39 1.46 1.52 1.69 0.42
0.001 0.001 0.002 0.002 0.001 0.002
7.34 7.20 6.60 4.03 0.80 1.18
21.96 19.04 15.72 10.57 4.65 0.29
T = 358.15 K 0.101 7.37 0.201 12.90 0.300 18.92 0.400 23.75 0.501 28.07 0.601 31.55 0.700 32.42 0.800 32.71 0.901 33.29 1.000 33.77
8.49 14.75 19.46 23.10 25.99 28.31 30.18 31.75 33.09 34.22
5.88 10.79 14.96 18.56 21.72 24.56 27.14 29.52 31.75 33.86
0.8067 0.8378 0.9481 1.0130 1.0706 1.1087 1.0710 1.0288 1.0056 0.9870
0.9294 0.9578 0.9749 0.9851 0.9911 0.9948 0.9970 0.9986 0.9996 1.0000
0.6476 0.7051 0.7543 0.7973 0.8361 0.8718 0.9055 0.9378 0.9693 1.0000
0.9978 0.9961 0.9942 0.9928 0.9915 0.9904 0.9901 0.9901 0.9899 0.9897
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0.18 0.24 0.72 1.27 1.71 1.83 1.97 2.03 2.26 0.58
0.002 0001 0.002 0.002 0.001 0.001 0.002 0.002 0.001 0.002
15.21 14.32 2.83 2.76 7.42 10.28 6.91 2.93 0.60 1.32
20.22 16.37 20.95 21.87 22.61 22.17 16.30 9.75 4.62 0.28
Pexp and γ1,exp are the experimental vapor pressures and activity coefficients, respectively. PUNIFAC-Lei, PCOSMO, γ1,UNIFAC-Lei and γ1,COSMO are the predicted values by the UNIFAC-Lei or COSMO-RS model. U(T), U(P) and U(x) are the expanded uncertainties with 0.95 level of confidence of experimental temperature T, pressure Pexp, and solute mole fraction x1, respectively. RD(P) (UNIFAC-Lei) and RD(P) (COSMO) are the relative deviations of vapor pressures between experimental data and predicted values by the UNIFAC-Lei and COSMO-RS models, respectively.
70
P (kPa)
50 40
50
333.15 K 353.15 K
40
P (kPa)
60
60
323.15 K 328.15 K 333.15 K 338.15 K 343.15 K 348.15 K 353.15 K 358.15 K
30
30 20
20
10
10 0 0.0
(a)
(a) 0.2
0.4
x1
0.6
0.8
0 0.0
1.0
0.2
0.4
0.6
0.8
1.0
x1 30
30
P (kPa)
25 20
323.15 K 328.15 K 333.15 K 338.15 K 343.15 K 348.15 K 353.15 K 358.15 K
25
15
15
10
10
5
5 0 0.0
333.15 K 353.15 K
20
P (kPa)
35
(b) 0.2
0.4
0.6
0.8
0 0.0
1.0
x1 Fig. 2. Vapor pressures of binary mixtures at different temperatures: formic acid (1) + [EMIM][BF4] (2) (a) and acetic acid (1) + [EMIM][BF4] (2) (b). Solid lines, predicted values by the UNIFAC-Lei model; scattered points, experimental data.
(b)
0.2
0.4
0.6
0.8
1.0
x1 Fig. 3. Vapor pressures of binary mixtures at 333.15 and 353.15 K: formic acid (1) + [EMIM][BF4] (2) (a) and acetic acid (1) + [EMIM][BF4] (2) (b). Solid lines, predicted values by the UNIFAC-Lei model; dashed lines, predicted values by the COSMO-RS model; scattered points, experimental data.
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C. Dai et al. / Journal of Molecular Liquids 256 (2018) 471–479
2000
3000
HHB, formic acid-IL (J·mol-1)
Hformic acid-IL (J·mol-1)
1500 1000 500
Hm
0
HMF
-500
HHB
2000 1000
Cation contribution
0 -1000
Anion contribution
HvdW
-1000 -1500 0.0
Formic acid contribution
4000
HHB
(a) 0.2
0.4
0.6
0.8
(a)
-2000 0.0
1.0
0.2
0.4
x1 HHB
2000
x1
0.6
0.8
1.0
3000
Hm
HHB, acetic acid-IL (J·mol-1)
Hacetic acid-IL (J·mol-1)
Acetic acid contribution 1500 1000 500
HMF 0
0.0
0.2
0.4
x1
0.6
HHB 1000
Cation contribution
0
Anion contribution
-1000
HvdW
-500
2000
(b) 0.8
(b) -2000 0.0
1.0
Fig. 4. Excess enthalpies of binary mixtures calculated by the COSMO-RS model at 298.15 K: formic acid (1) + [EMIM][BF4] (2) (a) and acetic acid (1) + [EMIM][BF4] (2) (b).
0.2
0.4
x1
0.6
0.8
1.0
Fig. 5. Contributions of solute, cation and anion to the hydrogen bonding interaction in binary mixtures calculated by the COSMO-RS model at 298.15 K: (a) formic acid (1) + [EMIM][BF4] (2), and (b) acetic acid (1) + [EMIM][BF4].
5. Conclusions 4.4. Analysis of the σ-profiles In this work, the vapor pressure data of the binary systems formic acid/acetic acid + [EMIM][BF4], which are essential for separation 30 [EMIM] [BF4]
25
CH2O2 C 2 H4 O2
20
p (σ)
The normalized σ-profiles of formic acid, acetic acid, [EMIM]+ cation, and [BF4]− anion are shown in Fig. 6. It can be seen that for formic acid and acetic acid there is a main peak located at 0.012 e/Å2 in the positive polar region related to oxygen atom of carbonyl (C_O), which acts as hydrogen bond acceptor. Meanwhile, in the negative polar region there is a main peak at −0.02 and −0.017 e/Å2 for formic acid and acetic acid related to hydrogen atom of the hydroxyl (OH), which acts as hydrogen bond donor. For formic acid, there is another peak at −0.01 e/ Å2 responsible for weak hydrogen bond donor ability. Thus, the hydrogen bonding interaction between formic acid molecules is stronger than that between acetic acid molecules. For [EMIM]+ cation, the main peaks locate in the nonpolar region, and a peak at about −0.01 e/Å2 related to the hydrogen atom of the aromatic ring is responsible for the weak hydrogen bond donor ability of cation. For [BF4]− anion, there is a main peak located at 0.011 e/Å2 in the negative polar region, indicating the hydrogen bond acceptor capability of anion. Furthermore, the characteristic peak of anion is much stronger than that of cation. Thus, the σ-profiles obtained by the COSMO-RS model reveal that the hydrogen-bond interaction between solutes (formic acid/acetic acid) and [BF4]− is much stronger than that between solutes and [EMIM]+, indicating that the anion has a stronger influence on the thermodynamic properties of binary mixtures than the cation. This conforms to the different contributions of solute, cation and anion to the hydrogen bonding of mixtures as aforementioned (see Fig. 5).
15 10 5 0
-0.02
-0.01
0.00
0.01
0.02
σ (e/Å2) Fig. 6. σ-Profiles of formic acid, acetic acid, cation and anion calculated by the COSMO-RS model at 298.15 K.
C. Dai et al. / Journal of Molecular Liquids 256 (2018) 471–479
process design, were measured using a modified equilibrium still at temperatures ranging from 323.15 to 358.15 K and IL contents ranging from 0.1 to 0.9 in mass fraction. It was found that the addition of [EMIM][BF4] into solutes makes vapor pressure lower than that of pure solute at the same temperature, due to the strong interaction between IL and formic acid/acetic acid. On the other hand, the predictive thermodynamic models (i.e., UNIFAC-Lei and COSMO-RS models) were used to predict the vapor pressures with the ARDs of 4.54% and 22.24% for formic acid, respectively, and 6.38% and 16.43% for acetic acid, respectively. This indicates that the UNIFAC-Lei model can give a quantitative description with high accuracy, while the COSMO-RS model can only be used as a prior model to give a qualitative prediction. Moreover, the excess enthalpies and σ-profiles were calculated by the COSMO-RS model to achieve further understanding on the thermodynamic behavior at molecular scale. It was found that the hydrogen bonding interaction (HHB) plays a dominant role, whereas the van der Waals interaction (HvdW) plays a secondary role and the electrostatic interaction (HMF) contributes only slightly to the overall excess enthalpy. The hydrogen bonding interaction of the system (HHB) is mainly dependent on acid components. For IL, the contribution of anion is larger than that of cation, as confirmed by the σ-profiles. This work was presented by the close integration of experiment, calculation, and theoretical analysis. Acknowledgments This work is financially supported by the National Natural Science Foundation of China under Grants (Nos. 21476009, 21406007, and U1462104). References [1] J. Cai, X. Cui, Y. Zhang, R. Li, T. Feng, Vapor-liquid equilibrium and liquid-liquid equilibrium of methyl acetate + methanol + 1-ethyl-3-methylimidazolium acetate, J. Chem. Eng. Data 56 (2011) 282–287. [2] Z. Lei, C. Li, B. Chen, Extractive distillation: a review, Sep. Purif. Rev. 23 (2003) 121–213. [3] T. Zhou, L. Chen, Y. Ye, Z. Qi, H. Freund, K. Sundmacher, An overview of mutual solubility of ionic liquids and water predicted by COSMO-RS model, Ind. Eng. Chem. Res. 51 (2012) 6256–6264. [4] J. Han, C. Dai, Z. Lei, B. Chen, Gas drying with ionic liquids, AICHE J. 64 (2018) 606–619. [5] Z. Song, T. Zhou, J. Zhang, L. Chen, Z. Qi, Screening of ionic liquids for solventsensitive extraction - with deep desulfurization as an example, Chem. Eng. Sci. 129 (2015) 69–77. [6] D. Tao, F. Chen, Z. Tian, K. Huang, S.M. Mahurin, D. Jiang, S. Dai, Highly efficient carbon monoxide capture by carbanion-functionalized ionic liquids through C-Site interactions, Angew. Chem. Int. Ed. 56 (2017) 6843–6847. [7] C. Dai, L. Wu, G. Yu, Z. Lei, Syngas dehydration with ionic liquids, Ind. Eng. Chem. Res. 56 (2017) 14642–14650. [8] Z. Lei, C. Dai, J. Zhu, B. Chen, Extractive distillation with ionic liquids: a review, AICHE J. 60 (2014) 3312–3329. [9] F. Chen, K. Huang, Y. Zhou, Z. Tian, X. Zhu, D. Tao, D. Jiang, S. Dai, Multi-molar absorption of CO2 by the activation of carboxylate groups in amino acid ionic liquids, Angew. Chem. Int. Ed. 55 (2016) 7166–7170. [10] L. Qin, J. Li, H. Cheng, L. Chen, Z. Qi, W. Yuan, Association extraction for vitamin E recovery from deodorizer distillate by in situ formation of deep eutectic solvent, AICHE J. 63 (2017) 2212–2220. [11] H. Uslu, Extraction equilibria of 2,4,6-trinitrophenol by (amberlite LA2 + ester) solvents, Fluid Phase Equilib. 427 (2016) 175–179. [12] L. Shi, C. Wang, C. Zou, Corrosion failure analysis of L485 natural gas pipeline in CO2 environment, Eng. Fail. Anal. 36 (2014) 372–378. [13] G.R. Harvianto, K.J. Kang, M. Lee, Process design and optimization of an acetic acid recovery system in terephthalic acid production via hybrid extraction−distillation using a novel mixed solvent, Ind. Eng. Chem. Res. 56 (2017) 2168–2176. [14] J. Dhanalakshmi, P.S.T. Sai, A.R. Balakrishnan, Study of ionic liquids as entrainers for the separation of methyl acetate−methanol and ethyl acetate−ethanol systems using the COSMO-RS model, Ind. Eng. Chem. Res. 52 (2013) 16396–16405. [15] C. Dai, Z. Lei, X. Xi, J. Zhu, B. Chen, Extractive distillation with a mixture of organic solvent and ionic liquid as entrainer, Ind. Eng. Chem. Res. 53 (2014) 15786–15791. [16] M.T.G. Jongmans, B. Schuur, A.B. de Haan, Ionic liquid screening for ethylbenzene/ styrene separation by extractive distillation, Ind. Eng. Chem. Res. 50 (2011) 10800–10810. [17] T. Zhou, Z. Wang, Y. Ye, L. Chen, J. Xu, Z. Qi, Deep separation of benzene from cyclohexane by liquid extraction using ionic liquids as solvent, Ind. Eng. Chem. Res. 51 (2012) 5559–5564.
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Contents lists available at ScienceDirect
Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq
Vapor pressure measurements and predictions for the binary systems containing ionic liquid [EMIM][BF4] and formic acid/acetic acid Chengna Dai, Xiaohui Sui, Zhigang Lei ⁎ State Key Laboratory of Chemical Resource Engineering, Beijing Key Laboratory of Energy Environmental Catalysis, Beijing University of Chemical Technology, Box 266, Beijing 100029, China
a r t i c l e
i n f o
Article history: Received 5 January 2018 Received in revised form 7 February 2018 Accepted 14 February 2018 Available online 16 February 2018 Keywords: Formic acid Acetic acid Ionic liquid (IL) UNIFAC-Lei model COSMO-RS model Vapor pressure
a b s t r a c t The vapor pressures of the binary systems formic acid/acetic acid +1-ethyl-3-methylimidazolium tetrafluoroborate ([EMIM][BF4]) were measured using a modified equilibrium still at temperatures ranging from 323.15 to 358.15 K and IL contents ranging from 0.1 to 0.9 in mass fraction. The predictive thermodynamic models (i.e., UNIFAC-Lei and COSMO-RS models) were used to predict the vapor pressures with the ARDs of 4.54% and 22.24% for formic acid, respectively, and 6.38% and 16.43% for acetic acid, respectively. This indicates that the UNIFAC-Lei model can give a quantitative description with high accuracy, while the COSMO-RS model can only be used as a prior model to give a qualitative prediction. Moreover, the excess enthalpies and σ-profiles were calculated by the COSMO-RS model to achieve further understanding on the thermodynamic behavior at molecular scale. It was found that the hydrogen bonding interaction (HHB) plays a dominant role to the total excess enthalpy, and the HHB is mainly dependent on acid components. For IL, the contribution of anion is larger than that of cation as confirmed by the σ-profiles. © 2018 Elsevier B.V. All rights reserved.
1. Introduction Ionic liquid (IL) is a relatively new class of solvent composed of organic cation and inorganic or organic anion, most of which have a melting point below 100 °C [1]. It has caused extensive concern in many fields, especially in separation processes [2–10], due to the unique properties such as negligible vapor pressure and potential as “designer solvent”. Ester compounds are widely applied in many fields as common organic solvents and industrial raw materials, while acid impurities must be removed by special equipment to obtain refined products during the preparation process [11]. In many other industrial processes, the existing acid impurities must be deacidified to prevent pipe lines and devices from corrosion and blockage [12]. Moreover, the acid must be recovered from acidic waste water before discharge, avoiding the pollution of environment and waste of resources. Thus, the study about the separation of acid is significant in the protection of environment and utilization of resources. However, due to the low relative volatility of some acid with other components, the general distillation equipment can't fulfill the separation [13]. Extractive distillation is a special separation method commonly applied in the mixtures that can't be separated by conventional distillation. The entrainer or solvent is usually a volatile organic solvent,
⁎ Corresponding author. E-mail address: [email protected] (Z. Lei).
https://doi.org/10.1016/j.molliq.2018.02.067 0167-7322/© 2018 Elsevier B.V. All rights reserved.
while its recovery may cause high energy consumption and environment problems sometimes. Thus, extractive distillation with ILs as entrainers as a new separation technology was proposed in recent years [14–18]. Compare to traditional extractive distillation, the negligible vapor pressure of IL entrainer makes it easily recovered by a simple flash tank instead of a distillation recovery column. Thus, this technology can save the equipment investment and energy consumption, which is promising to be applied in the deacidification process. Until now, many studies have been carried out on the separation processes involving ILs. Undoubtedly, the thermodynamic properties such as phase equilibria (GLE, VLE, LLE, etc.) data, activity coefficient data, and excess enthalpy of the systems containing ILs are necessary for the design and optimization of separation processes and other applications of ILs [19–27]. However, the reports on vapor-liquid equilibrium (VLE) data of acid (formic acid and acetic acid) and IL binary systems are still scarce. In this work, the common ionic liquid [EMIM][BF4] was selected as the representative to investigate the VLE with the organic acids because of its economical price, good thermal stability, and relatively low viscosity. The aim of this work is to measure the vapor pressures of the binary systems of formic acid/acetic acid + [EMIM][BF4] at different temperatures and concentrations to study the effect of IL on VLE. Moreover, two predictive thermodynamic models (i.e., UNIFAC-Lei and COSMO-RS models) were used to predict the vapor pressures. To a further step, the COSMO-RS model was applied to analyze the excess enthalpies and σ-profiles of these two systems to investigate the molecular interactions at microscopic level.
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pressure of pure solute i, which can be calculated by Antoine equation as follows
2. Experimental section 2.1. Materials
log P si =bar ¼ Ai −
Bi T=K þ C i
ð2Þ
Formic acid (mass fraction N0.985%) was obtained from Tianjin Guangfu Fine Chemical Research Institute, and acetic acid (mass fraction N99.5%) was obtained from Being Chemical Works. They were used directly without further purification. [EMIM][BF4] was obtained from Shanghai ChengJie Chemical Co., Ltd. with a purity N99.0 wt%. It was dried over a vacuum rotary evaporator at 358.15 K for 24 h to remove traces of water and other volatile impurities. The chemicals used in this work are listed in Table 1.
where the Antoine constants (Ai, Bi, and Ci) for formic acid and acetic acid were given in Table 2 [32,33]. The vapor phase is assumed to be pure solute (yi = 1) because of the negligible volatility of IL. Therefore, Eq. 3 can be simply rewritten as.
2.2. Apparatus and procedure
where i represents the component formic acid or acetic acid.
The experimental vapor pressures of binary systems were measured by a modified equilibrium still, the details of which can be seen in our previous work [31]. Before experiments, the U-type equilibrium still was thoroughly washed by anhydrous ethanol and then dried using air oven. The mixtures of (formic acid + [EMIM][BF4]) and (acetic acid + [EMIM][BF4]) with different compositions were prepared by weighting the IL and solutes with an electronic balance (type FA2104B, Shanghai Precision Scientific Instrument Co., China) with the precision of 0.001 g. About 15 mL formic acid/acetic acid + [EMIM] [BF4] mixture were added into the equilibrium still, filling with two thirds of the vacuole in volume. Connected the equilibrium still well, and put it into the thermostatic water bath at a given temperature measured by a digital temperature indicator (Type DP–AF, Nanning Sangli Electronic Equipment Company, China, 2014) with a precision of 0.01 K. Opened the condensed water, stirrer and heater, when the temperature reached the desired value. Opened the vacuum pump until the liquid mixture boiled in the equilibrium still. Then, the needle valve was slowly opened to leak into the air until the U-type tube was kept at the same level height on both sides. If the liquid level didn't change within 20 min, it was considered to reach the vapor-liquid equilibrium. The pressure of equilibrium still was measured by a precision digital pressure gauge (Type DP-AF, Nanjing Sangli Electronic Equipment Company, China, 2014) with a precision of 0.01 kPa. The vapor pressures of formic acid and acetic acid were first measured from 303.15 to 358.15 K to check the reliability of experimental apparatus.
3.1. UNIFAC-Lei model
ϕi P ¼ γ i xi P si
ð3Þ
The UNIFAC-Lei model was used to describe the vapor-liquid equilibrium of binary system containing IL, which has been applied by many authors [34–38]. In this model, components are divided as interaction groups, and the thermodynamic properties of components are the addition of group properties. The activity coefficient of component i is written as ln γi ¼ ln γCi þ lnγ Ri
where lnγCi represents the combinatorial contribution, which is relevant to the shape and size of functional groups, and is a function of two group parameters (Rk and Qk) for group k; and lnγRi represents the residual contribution due to the interaction between functional groups, and is a function of a pair of group interaction parameters (amn and anm) between groups m and n. There are five groups (CH3, CH2, HCOOH, COOH, and [MIM][BF4]) concerned in this work, and their group parameters (Rk and Qk) are listed in Table 3, which come from previous works [39,40]. The unknown group interaction parameters between main group COOH and [MIM][BF4] were obtained by correlating the experimental VLE data of formic acid + [EMIM][BF4] and acetic acid + [EMIM][BF4] binary systems as measured in this work, using the minimized average relative deviation between the experimental and P calculated vapor pressures as objective function (OF) (OF ¼ minfN1 N1 j
P cal −P exp P exp
jg). The new obtained parameters as well as the old parameters
3. Thermodynamic models
from references are given in Table 4.
For the binary system containing IL, the vapor-liquid equilibrium for solute i can be expressed as
3.2. COSMO-RS model
ϕi yi P ¼ γi xi P si
ð1Þ
where xi and yi and are the mole fractions of solute i in liquid and vapor phases, respectively; ϕi is the fugacity coefficient of solute i in vapor phase calculated by the Peng-Robinson (PR) equation of state at a certain temperature and pressure; P is the system pressure; and γi is the activity coefficient of solute i in liquid phase. Psi is the saturated
ð4Þ
In the COSMO-RS calculation, the IL molecular was described as a cation and an anion. Therefore, the binary mixture of IL and solute was considered as a hypothetical ternary system, which consists of cation, anion and solute. A transform between activity coefficient of solute i in the binary and ternary mixture should be made by γbin ¼ i
γtern xtern γtern i i ¼ i bin xbin 2−x i i
ð5Þ
Table 1 The properties (CAS-register number, water mass fraction ωH2O, density ρ, and refractive index nD) of used chemicals at T = 298.15 K and atmospheric pressure. Compounds
Formic acid Acetic acid [EMIM][BF4] a b c
CAS
64–18-6 64–19-7 N.F.
Puritya
98.5 99.5 99.0
ωH2O (ppm)b
14,030 1387 280c
Information provided by supplier. Water content was measured by Karl-Fischer titration. Water content was measured after drying over a vacuum rotary evaporator.
ρ (g·cm−3)
nD
Exp.
Lit.
Exp.
Lit.
1.21380 1.04341 1.28253
1.21410 [28] 1.04330 [29] 1.28230 [30]
1.36916 1.36975 1.41097
1.36939 [28] 1.36960 [29] 1.41090 [30]
C. Dai et al. / Journal of Molecular Liquids 256 (2018) 471–479 70
Table 2 Parameters of the Antoine equation used in this work.
Formic acid Acetic acid
Antoine parameters Ai
Bi
Ci
4.57631 6.4302
1608.22 1479.01
−21.8974 −56.34
50
265–385 290–430
40
Table 3 Group parameters of Rk and Qk in the UNIFAC-Lei model. Rk
Qk
CH3 CH2 HCOOH COOH [MIM][BF4]
0.9011a 0.6744a 1.528b 1.3013b 6.5669a
0.8480a 0.5400a 1.532b 1.2240b 4.0050a
b
30 20
Main groups
a
10 0 300
ð6Þ
In this work, the COSMO-RS calculations on activity coefficient, excess enthalpy and σ-profile were performed using COSMOthermX software (Version C30_1301, COSMOlogic GmbH & CO. KG, Leverkusen, Germany).
330
The vapor pressures of formic acid and acetic acid were measured from 303.15 to 358.15 K, and the experimental data were compared with the calculated values by the Antoine equation. The comparison between experimental vapor pressures and the calculated values was shown in Fig. 1, and the detailed data are given in Table 5. The average relative deviation (ARD) was calculated by N 1X P exp −P Antoine N 1 P exp
ð7Þ
where Pexp and PAntoine are the vapor pressures obtained by experiments and Antoine equation, respectively; and N is the number of data points. Table 4 Group binary interaction parameters (amn and anm) in the UNIFAC-Lei model. m
n
CH2 CH2 COOH
COOH [MIM][BF4] [MIM][BF4]
350
360
370
Fig. 1. Comparison between experimental vapor pressure and the calculated values by Antoine equation for formic acid and acetic acid. Scattered points, experimental data; Solid lines, calculated results by Antoine equation.
It is obvious that the experimental data agree well with the calculated values with the ARDs of 0.47% and 0.87%, proving the reliability of experimental apparatus and method used in this work. 4.2. Vapor pressures of two binary systems The vapor pressure data of the binary systems (formic acid + [EMIM][BF4] and acetic acid + [EMIM][BF4]) were measured at the temperatures ranging from 323.15 to 358.15 K. The detailed experimental data and predicted values by the UNIFAC-Lei and COSMO-RS models including temperature, pressure and solute concentration expressed in mass fraction, as well as the corresponding expanded uncertainties with 0.95 level of confidence expressed as U(T), U(P), and U(x), are listed in Tables 6 and 7. The details on the calculation of expanded
PAntonie (kPa)
U(T) (K)
U(P) (kPa)
100RD
Formic acid 303.15 7.27 313.15 11.21 318.15 13.99 323.15 17.42 328.15 21.31 333.15 25.80 338.15 30.88 343.15 37.46 348.15 44.26 353.15 52.75 358.15 62.23
7.22 11.34 14.05 17.29 21.14 25.67 30.98 37.17 44.35 52.64 62.16
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0.08 0.12 0.19 0.28 0.30 0.44 0.58 0.61 0.78 0.89 0.98
0.69 0.44 0.43 0.75 0.80 0.50 0.32 0.77 0.20 0.21 0.11
Acetic acid 303.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15
2.74 4.69 6.04 7.71 9.75 12.22 15.20 18.77 23.00 28.00 33.86
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0.04 0.05 0.06 0.08 0.10 0.14 0.18 0.26 0.34 0.42 0.58
1.11 1.30 0.98 1.85 0.91 0.74 1.74 0.37 0.00 0.29 0.27
T/K
4.1. Vapor pressures of formic acid and acetic acid
ARD ¼
340
Table 5 Experimental and calculated vapor pressures for pure components.
4. Results and discussion
c
320
T (K)
H m ¼ HMF þ HHB þ H vdw
b
310
Group parameters of Rk and Qk obtained from Ref. [39]. Group parameters of Rk and Qk obtained from Ref. [40].
where γbin and xbin are the activity coefficient and mole fraction of soli i ute i in the binary system of {formic acid/acetic acid + [EMIM][BF4]}, respectively; γtern and xtern are the corresponding values in the i i hypothetical ternary system of {formic acid/acetic acid + [EMIM]+ + [BF4]−}. More details on how to predict the activity coefficient of solutes in IL can be seen from the website at https://www.scm.com/doc/ Tutorials/COSMO-RS/Ionic_Liquids.html. The COSMO-RS model is also an efficient method to predict the excess enthalpy of the mixtures containing ILs [41–44], which mainly includes the electrostatic-Misfit interaction (HMF), hydrogen bonding interaction (HHB) and van der Waals interaction (HvdW). These contributions are expressed as:
a
formic acid acetic acid
60
Temperature range (K)
P (kPa)
Compounds
473
anm
amn b
663.5 1108.51a 50.9115c
Group binary interaction parameters obtained from Ref. [39]. Group binary interaction parameters obtained from Ref. [40]. Group binary interaction parameters obtained in this work.
315.3b 588.74a −131.9878c
Pexp (kPa)
2.68 4.56 6.12 7.57 9.84 12.13 14.94 18.70 23.00 27.92 33.77
Pexp and PAntonie are the experimental data and calculated values by the Antoine equation. U(T) and U(P) are the expanded uncertainties with 0.95 level of confidence of experimental temperature T and pressure Pexp. RD is the relative deviation between experimental data and calculated values.
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Table 6 Experimental and predicted vapor pressures for the binary mixtures of formic acid (1) + [EMIM][BF4] (2). PUNIFAC-Lei (kPa)
PCOSMO (kPa)
γ1,exp
γ1,UNIFAC-Lei
γ1,COSMO
Φ1
U(T) (K)
U(P) (kPa)
U(x)
100RD(P) (UNIFAC-Lei)
100RD(P) (COSMO)
T = 323.15 K 0.101 3.64 0.201 6.08 0.301 8.11 0.401 10.85 0.500 11.83 0.601 14.62 0.700 15.50 0.801 15.86 0.901 17.28 1.000 17.42
3.64 6.73 9.33 11.47 13.16 14.52 15.55 16.34 16.95 17.40
1.86 3.73 5.68 7.68 9.70 11.64 13.45 15.02 16.32 17.29
0.6462 0.6761 0.7206 0.8418 0.8394 0.9708 0.9800 0.9647 1.0184 1.0010
0.6462 0.7482 0.8287 0.8899 0.9335 0.9640 0.9831 0.9939 0.9988 1.0000
0.3320 0.4165 0.5065 0.5993 0.6911 0.7777 0.8550 0.9193 0.9681 1.0000
0.9987 0.9978 0.9971 0.9961 0.9957 0.9947 0.9944 0.9943 0.9938 0.9937
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0.07 0.10 0.16 0.19 0.27 0.33 0.45 0.52 0.57 0.28
0.002 0.001 0.002 0.002 0.002 0.001 0.002 0.001 0.002 0.002
0.00 10.67 15.00 5.72 11.21 0.71 0.31 3.03 1.92 0.10
49.00 38.62 29.98 29.18 18.03 20.35 13.25 5.27 5.55 0.73
T = 328.15 K 0.101 4.73 0.201 7.24 0.301 11.98 0.401 14.50 0.500 15.82 0.601 17.44 0.700 19.02 0.801 19.74 0.901 19.73 1.000 21.31
4.46 8.24 11.43 14.05 16.11 17.77 19.03 20.00 20.73 21.29
2.26 4.56 6.96 9.42 11.88 14.26 16.45 18.37 19.95 21.14
0.6869 0.6585 0.8698 0.9194 0.9173 0.9468 0.9829 0.9813 0.9508 1.0008
0.6480 0.7499 0.8302 0.8911 0.9344 0.9646 0.9834 0.9941 0.9989 1.0000
0.3310 0.4167 0.5076 0.6008 0.6927 0.7791 0.8559 0.9198 0.9683 1.0000
0.9984 0.9975 0.9958 0.9950 0.9945 0.9940 0.9934 0.9932 0.9932 0.9926
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0.09 0.14 0.29 0.35 0.40 0.51 0.62 0.86 0.92 0.30
0.002 0.001 0.002 0.002 0.002 0.001 0.002 0.001 0.002 0.002
5.66 13.88 4.55 3.08 1.86 1.87 0.05 1.31 5.05 0.08
52.17 36.97 41.94 35.07 24.91 18.26 13.51 6.92 1.12 0.82
T = 333.15 K 0.101 5.70 0.200 9.96 0.301 12.85 0.401 16.73 0.500 17.81 0.601 20.60 0.700 22.16 0.801 23.78 0.901 25.41 1.000 25.80
5.43 10.03 13.91 17.10 19.60 21.61 23.14 24.32 25.22 25.89
2.74 5.55 8.46 11.46 14.46 17.34 20.00 22.32 24.23 25.67
0.6814 0.7460 0.7682 0.8730 0.8500 0.9201 0.9422 0.9723 1.0066 0.9965
0.6497 0.7512 0.8316 0.8923 0.9353 0.9652 0.9837 0.9942 0.9989 1.0000
0.3301 0.4170 0.5086 0.6022 0.6941 0.7803 0.8568 0.9203 0.9684 1.0000
0.9981 0.9967 0.9957 0.9944 0.9941 0.9931 0.9926 0.9921 0.9915 0.9914
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0.10 0.28 0.45 0.65 0.89 1.09 1.17 1.21 1.36 0.44
0.002 0.001 0.002 0.002 0.002 0.001 0.002 0.001 0.002 0.002
4.65 0.70 8.26 2.21 10.03 4.89 4.41 2.25 0.77 0.35
51.93 44.32 34.14 31.50 18.84 15.83 9.76 6.13 4.64 0.51
T = 338.15 K 0.101 7.79 0.200 12.71 0.301 14.92 0.401 20.50 0.500 22.42 0.601 26.76 0.700 28.46 0.801 29.15 0.901 30.01 1.000 30.88
6.58 12.14 16.83 20.68 23.70 26.14 27.98 29.39 30.47 31.29
3.30 6.70 10.23 13.86 17.48 20.96 24.16 26.95 29.25 30.98
0.7711 0.7881 0.7386 0.8854 0.8854 0.9886 1.0009 0.9862 0.9839 0.9869
0.6514 0.7528 0.8330 0.8934 0.9361 0.9657 0.9841 0.9944 0.9990 1.0000
0.3294 0.4173 0.5096 0.6036 0.6955 0.7815 0.8576 0.9207 0.9685 1.0000
0.9975 0.9959 0.9952 0.9934 0.9928 0.9914 0.9909 0.9907 0.9904 0.9901
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0.18 0.47 0.69 0.87 1.12 1.38 1.42 1.52 1.63 0.58
0.002 0.001 0.002 0.002 0.002 0.001 0.002 0.001 0.002 0.002
15.53 4.48 12.78 0.90 5.72 2.32 1.68 0.84 1.53 1.32
57.64 47.30 31.40 32.38 22.03 21.67 15.11 7.53 2.54 0.32
T = 343.15 K 0.101 7.31 0.200 14.32 0.301 17.50 0.401 23.99 0.500 27.03 0.601 32.06 0.700 35.16 0.801 36.38 0.901 37.12 1.000 37.46
7.91 14.60 20.24 24.87 28.50 31.42 33.64 35.34 36.63 37.60
3.95 8.04 12.30 16.67 21.02 25.19 29.02 32.36 35.10 37.17
0.6031 0.7398 0.7215 0.8628 0.8887 0.9858 1.0288 1.0237 1.0124 0.9962
0.6530 0.7544 0.8343 0.8945 0.9369 0.9663 0.9844 0.9945 0.9990 1.0000
0.3288 0.4177 0.5106 0.6049 0.6968 0.7826 0.8583 0.9211 0.9686 1.0000
0.9977 0.9956 0.9946 0.9926 0.9917 0.9901 0.9892 0.9888 0.9886 0.9885
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0.16 0.43 0.74 0.93 1.40 1.75 1.82 1.87 1.95 0.61
0.002 0.001 0.002 0.002 0.002 0.001 0.002 0.001 0.002 0.002
8.27 1.97 15.63 3.67 5.43 1.98 4.31 2.85 1.33 0.39
45.93 43.83 29.69 30.51 22.25 21.44 17.48 11.06 5.44 0.77
T = 348.15 K 0.101 9.32 0.200 17.61 0.301 20.59 0.401 29.25 0.500 35.81 0.601 40.17 0.700 41.64 0.801 42.65 0.901 43.83 1.000 44.26
9.47 17.47 24.20 29.75 34.11 37.59 40.22 42.24 43.78 44.94
4.71 9.61 14.71 19.93 25.12 30.09 34.65 38.62 41.89 44.35
0.6441 0.7618 0.7110 0.8805 0.9844 1.0331 1.0195 1.0044 1.0002 0.9848
0.6546 0.7559 0.8356 0.8955 0.9377 0.9668 0.9847 0.9947 0.9990 1.0000
0.3284 0.4181 0.5116 0.6061 0.6981 0.7836 0.8591 0.9214 0.9687 1.0000
0.9972 0.9948 0.9939 0.9913 0.9894 0.9881 0.9877 0.9874 0.9870 0.9869
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0.26 0.72 0.99 1.45 1.83 1.88 1.95 2.06 2.27 0.78
0.002 0.001 0.002 0.002 0.002 0.001 0.002 0.001 0.002 0.002
1.63 0.78 17.53 1.71 4.74 6.42 3.42 0.97 0.12 1.54
49.46 45.44 28.55 31.85 29.84 25.09 16.78 9.44 4.44 0.21
T = 353.15 K 0.101 14.23 0.200 21.32 0.301 25.57 0.401 31.92
11.28 20.80 28.80 35.36
5.59 11.42 17.49 23.71
0.8276 0.7764 0.7430 0.8092
0.6562 0.7574 0.8369 0.8966
0.3281 0.4186 0.5126 0.6074
0.9959 0.9939 0.9927 0.9909
0.01 0.01 0.01 0.01
0.64 0.86 1.34 1.71
0.002 0.001 0.002 0.002
20.71 2.45 12.64 10.79
60.75 46.45 31.58 25.73
x1
Pexp (kPa)
C. Dai et al. / Journal of Molecular Liquids 256 (2018) 471–479
475
Table 6 (continued) x1
Pexp (kPa)
PUNIFAC-Lei (kPa)
PCOSMO (kPa)
γ1,exp
γ1,UNIFAC-Lei
γ1,COSMO
Φ1
U(T) (K)
U(P) (kPa)
U(x)
100RD(P) (UNIFAC-Lei)
100RD(P) (COSMO)
0.500 0.601 0.700 0.801 0.901 1.000
40.25 44.90 48.56 50.21 51.91 52.75
40.56 44.68 47.83 50.22 52.05 53.45
29.87 35.76 41.16 45.86 49.72 52.64
0.9314 0.9720 1.0001 0.9945 0.9963 0.9869
0.9385 0.9673 0.9850 0.9948 0.9991 1.0000
0.6994 0.7847 0.8598 0.9218 0.9688 1.0000
0.9885 0.9872 0.9861 0.9857 0.9852 0.9849
0.01 0.01 0.01 0.01 0.01 0.01
1.96 2.05 2.17 2.23 2.36 0.89
0.002 0.001 0.002 0.001 0.002 0.002
0.76 0.49 1.51 0.03 0.28 1.33
25.79 20.35 15.24 8.66 4.22 0.20
T = 358.15 K 0.101 14.30 0.200 22.02 0.301 29.26 0.401 38.56 0.500 45.40 0.601 51.36 0.700 55.80 0.801 59.67 0.901 61.69 1.000 62.23
13.35 24.61 34.09 41.87 47.98 52.86 56.57 59.44 61.61 63.25
6.59 13.50 20.70 28.05 35.33 42.28 48.64 54.17 58.72 62.16
0.7044 0.6791 0.7195 0.8266 0.8888 0.9403 0.9718 0.9988 1.0004 0.9839
0.6577 0.7588 0.8382 0.8976 0.9392 0.9678 0.9853 0.9949 0.9991 1.0000
0.3280 0.4191 0.5136 0.6087 0.7006 0.7857 0.8604 0.9221 0.9689 1.0000
0.9961 0.9939 0.9920 0.9894 0.9875 0.9859 0.9847 0.9836 0.9830 0.9829
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0.68 0.90 1.67 1.82 2.07 2.42 2.58 2.61 2.67 0.98
0.002 0.001 0.002 0.002 0.002 0.001 0.002 0.001 0.002 0.002
6.63 11.74 16.49 8.58 5.68 2.92 1.38 0.39 0.13 1.63
53.90 38.70 29.26 27.25 22.17 17.67 12.83 9.21 4.82 0.11
Pexp and γ1,exp are the experimental vapor pressures and activity coefficients, respectively. PUNIFAC-Lei, PCOSMO, γ1,UNIFAC-Lei and γ1,COSMO are the predicted values by the UNIFAC-Lei or COSMO-RS model. U(T), U(P) and U(x) are the expanded uncertainties with 0.95 level of confidence of experimental temperature T, pressure Pexp, and solute mole fraction x1, respectively. RD(P) (UNIFAC-Lei) and RD(P) (COSMO) are the relative deviations of vapor pressures between experimental data and predicted values by the UNIFAC-Lei and COSMO-RS models, respectively.
uncertainties can be found in our previous work [7]. The relative deviation (RD) between experimental data and predicted values is defined as P −P exp RD ¼ cal P exp
ð8Þ
where Pexp and Pcal are the experimental and calculated vapor pressures, respectively. RD(P) (UNIFAC-Lei) and RD(P) (COSMO), as given in Tables 6 and 7, represent the relative deviations between experimental vapor pressures and calculated values by the UNIFAC-Lei and COSMORS models, respectively. The experimental and predicted vapor pressures by the UNIFAC-Lei model for the two binary systems at different temperatures are shown in Fig. 2. In the whole concentration range, formic acid and acetic acid are miscible with [EMIM][BF4]. With the increase of temperature, vapor pressures of binary mixtures also increase. Meanwhile, the vapor pressures first increase sharply with the increase of formic acid/ acetic acid concentration, and then tend to be smooth at high concentration range. That is, the addition of [EMIM][BF4] makes vapor pressure lower than that of pure solute at the same temperature, due to the strong interaction between IL and formic acid/acetic acid. Moreover, for both binary systems it is obvious that the predicted values by the UNIFAC-Lei model agree very well with experimental data in the whole concentration range, indicating that the UNIFAC-Lei model can give a quantitative description with high accuracy for predicting the VLE of these two binary systems {formic acid/acetic acid + [EMIM] [BF4]}. For a further step, the comparison among predicted results by the UNIFAC-Lei model, predicted results by the COSMO-RS model, and experimental data is illustrated in Fig. 3. It can be seen that the predicted accuracy by the COSMO-RS model is worse than that by the UNIFACLei model, especially at high temperature (353.15 K). However, the COSMO-RS model can give the same trend as experimental data. Thus, the COSMO-RS model can be used as a prior predictive model to give a qualitative prediction for vapor pressures. The average relative deviations (ARDs) for the UNIFAC-Lei and COSMO-RS models are 4.54% and 22.24% for formic acid + IL, respectively, while they are 6.38% and 16.43% for acetic acid + IL, respectively. 4.3. Analysis of the excess enthalpy To study the solution thermodynamics, an important property used to analyze the nature of molecular interactions in solutions is excess enthalpy Hm. The predicted excess enthalpies of binary systems {formic
acid/acetic acid and [EMIM][BF4]} at 298.15 K are presented in Fig. 4. It can be seen that the excess enthalpies of formic acid and IL system present both positive and negative values depending on formic acid concentration, as shown in Fig. 4(a). At low formic acid concentration region, the dominant interaction is hydrogen bonding (HHB) with positive value resulting in positive excess enthalpy, indicating the endothermicity of the mixture, whereas the negative van der Waals interaction (HvdW) plays a secondary role and the negative electrostatic interaction (HMF) contributes the least to the overall excess enthalpy. However, the contributions of van der Waals and electrostatic interactions can't be neglected, especially for systems containing formic acid, as shown in Fig. 4(a). Moreover, with the increase of formic acid concentration, the exothermicity of the mixture increases. When the mole concentration of formic acid is over 0.7, the negative excess enthalpy occurs mainly due to the contributions of HvdW and HMF. The contributions of formic acid molecule, [EMIM]+ cation, and [BF4]+ anion to HHB are shown in Fig. 5. It is clear that the endothermicity of the mixture is mainly dependent on formic acid molecule, while the anion and cation contribute negative values, and the contribution of anion is larger than that of cation. Thus, we can conclude that: 1) the addition of formic acid weakens the electrostatic interaction between [EMIM]+ and [BF4]−, resulting in a negative contribution of HMF; 2) the original hydrogen bondings between formic acid (HCOOH) molecules, and between [EMIM]+ and [BF4]− ions are ruptured, while the new hydrogen bondings between HCOOH and [EMIM]+, and between HCOOH and [BF4]− ion are formed in the mutual dissolution between formic acid and IL; 3) the new formed hydrogen bonding is stronger than that between [EMIM]+ and [BF4]−; and 4) the new formed hydrogen bonding interactions can't overcome the energy of HCOOH–HCOOH hydrogen bonding in the mixing process, resulting in positive excess enthalpies. However, when the concentration of formic acid is high, the increased HvdW and HMF can make a balance to the loss of HHB, even resulting in negative excess enthalpies. For acetic acid and [EMIM][BF4 ] mixture, the predicted excess enthalpies are illustrated in Fig. 4(b). Similarly, the positive H HB plays a dominant role, H vdw shows a secondary contribution and the HMF contributes slightly to Hm. But unlike the formic acid + IL system, the H MF of acetic acid + IL mixture is positive, indicating the strong electrostatic interaction between acetic acid molecule and cation/anion ions of IL. Moreover, the mixture present only positive values throughout the whole concentration range. That is, the negative H vdW can't makeup the energy of hydrogen bonding between acetic acid molecules, and the process becomes endothermic in nature.
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C. Dai et al. / Journal of Molecular Liquids 256 (2018) 471–479
Table 7 Experimental and predicted vapor pressures for the binary mixtures of acetic acid (1) + [EMIM][BF4] (2). PUNIFAC-Lei (kPa)
PCOSMO (kPa)
γ1,exp
γ1,UNIFAC-Lei
γ1,COSMO
Φ1
U(T) (K)
U(P) (kPa)
U(x)
100RD(P) (UNIFAC-Lei)
100RD(P) (COSMO)
T = 323.15 K 0.101 2.29 0.201 3.57 0.300 4.85 0.400 5.74 0.501 6.44 0.601 6.92 0.700 7.51 0.800 7.56 0.901 7.59 1.000 7.57
1.86 3.25 4.31 5.13 5.80 6.34 6.78 7.16 7.47 7.73
1.56 2.74 3.68 4.46 5.12 5.71 6.24 6.75 7.23 7.71
1.1028 1.0213 1.0719 1.0810 1.0856 1.0758 1.0977 1.0520 1.0145 0.9792
0.8977 0.9300 0.9515 0.9663 0.9769 0.9849 0.9910 0.9957 0.9988 1.0000
0.7568 0.7883 0.8160 0.8414 0.8658 0.8901 0.9154 0.9420 0.9702 1.0000
0.9991 0.9986 0.9980 0.9977 0.9974 0.9972 0.9970 0.9970 0.9969 0.9969
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0.07 0.08 0.09 0.11 0.13 0.14 0.14 0.15 0.18 0.08
0.002 0001 0.002 0.002 0.001 0.001 0.002 0.002 0.001 0.002
18.60 8.94 11.23 10.61 10.01 8.45 9.72 5.36 1.55 2.13
31.71 23.11 24.07 22.35 20.50 17.54 16.87 10.74 4.69 1.81
T = 328.15 K 0.101 2.81 0.201 4.36 0.300 6.12 0.400 7.48 0.501 8.28 0.601 9.13 0.700 9.18 0.800 9.56 0.901 9.60 1.000 9.84
2.37 4.13 5.47 6.51 7.35 8.03 8.59 9.06 9.46 9.78
1.93 3.41 4.60 5.59 6.44 7.19 7.88 8.53 9.15 9.75
1.0698 0.9860 1.0691 1.1132 1.1030 1.1216 1.0603 1.0512 1.0141 1.0057
0.9026 0.9344 0.9551 0.9692 0.9792 0.9864 0.9919 0.9961 0.9989 1.0000
0.7376 0.7743 0.8059 0.8343 0.8611 0.8873 0.9139 0.9414 0.9701 1.0000
0.9989 0.9983 0.9976 0.9971 0.9968 0.9965 0.9964 0.9963 0.9963 0.9962
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0.08 0.09 0.11 0.14 0.16 0.19 0.22 0.23 0.27 0.10
0.002 0001 0.002 0.002 0.001 0.001 0.002 0.002 0.001 0.002
15.63 5.24 10.66 12.93 11.23 12.05 6.45 5.24 1.49 0.57
31.40 21.80 24.84 25.28 22.23 21.21 14.13 10.79 4.72 0.95
T = 333.15 K 0.101 2.96 0.201 5.27 0.300 7.08 0.400 9.15 0.501 10.50 0.601 11.44 0.700 11.63 0.800 11.87 0.901 12.01 1.000 12.13
2.99 5.21 6.88 8.19 9.25 10.09 10.79 11.37 11.87 12.28
2.36 4.20 5.70 6.95 8.03 8.99 9.87 10.69 11.47 12.22
0.8987 0.9502 0.9861 1.0854 1.1144 1.1198 1.0704 1.0400 1.0109 0.9880
0.9074 0.9386 0.9587 0.9721 0.9813 0.9880 0.9929 0.9966 0.9991 1.0000
0.7198 0.7610 0.7962 0.8275 0.8565 0.8845 0.9124 0.9408 0.9700 1.0000
0.9989 0.9980 0.9974 0.9966 0.9961 0.9958 0.9957 0.9956 0.9955 0.9955
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0.05 0.09 0.12 0.20 0.26 0.29 0.31 0.32 0.34 0.14
0.002 0001 0.002 0.002 0.001 0.001 0.002 0.002 0.001 0.002
0.97 1.22 2.78 10.44 11.94 11.77 7.24 4.17 1.17 1.22
20.32 20.26 19.51 24.03 23.50 21.39 15.15 9.96 4.51 0.76
T = 338.15 K 0.101 3.53 0.201 6.19 0.300 9.11 0.400 10.96 0.501 13.35 0.601 14.49 0.700 14.68 0.800 14.84 0.901 14.92 1.000 14.94
3.74 6.50 8.60 10.23 11.53 12.58 13.44 14.17 14.78 15.28
2.87 5.14 7.01 8.58 9.94 11.15 12.26 13.29 14.26 15.20
0.8614 0.8970 1.0194 1.0446 1.1383 1.1392 1.0853 1.0444 1.0087 0.9775
0.9120 0.9426 0.9621 0.9749 0.9834 0.9894 0.9938 0.9970 0.9992 1.0000
0.7031 0.7484 0.7869 0.8210 0.8521 0.8818 0.9109 0.9402 0.9698 1.0000
0.9987 0.9978 0.9968 0.9961 0.9952 0.9948 0.9948 0.9947 0.9947 0.9947
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0.09 0.12 0.19 0.24 0.30 0.43 0.57 0.68 0.75 0.18
0.002 0001 0.002 0.002 0.001 0.001 0.002 0.002 0.001 0.002
5.88 5.09 5.62 6.68 13.60 13.15 8.43 4.54 0.95 2.31
18.81 16.95 23.10 21.73 25.54 23.04 16.51 10.47 4.40 1.76
T = 343.15 K 0.101 4.33 0.201 7.74 0.300 11.36 0.400 13.84 0.501 15.88 0.601 17.02 0.700 17.97 0.800 18.18 0.901 18.43 1.000 18.70
4.64 8.07 10.66 12.67 14.28 15.57 16.63 17.51 18.26 18.89
3.46 6.25 8.55 10.51 12.21 13.73 15.11 16.39 17.61 18.77
0.8557 0.9081 1.0290 1.0677 1.0961 1.0833 1.0751 1.0355 1.0083 0.9899
0.9165 0.9466 0.9655 0.9775 0.9855 0.9908 0.9946 0.9974 0.9993 1.0000
0.6877 0.7366 0.7781 0.8147 0.8479 0.8792 0.9095 0.9396 0.9697 1.0000
0.9985 0.9973 0.9961 0.9953 0.9946 0.9942 0.9938 0.9938 0.9937 0.9936
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0.13 0.16 0.26 0.31 0.68 0.86 0.93 1.04 1.13 0.26
0.002 0001 0.002 0.002 0.001 0.001 0.002 0.002 0.001 0.002
7.11 4.24 6.17 8.45 10.10 8.53 7.48 3.67 0.90 1.02
20.08 19.30 24.72 24.07 23.11 19.35 15.93 9.84 4.47 0.37
T = 348.15 K 0.101 5.40 0.201 9.18 0.300 13.63 0.400 16.71 0.501 19.50 0.601 21.39 0.700 22.14 0.800 22.46 0.901 22.65 1.000 23.00
5.71 9.93 13.12 15.58 17.55 19.13 20.42 21.50 22.42 23.18
4.15 7.54 10.37 12.78 14.89 16.77 18.49 20.08 21.58 23.00
0.8705 0.8785 1.0067 1.0510 1.0971 1.1094 1.0795 1.0425 1.0099 0.9922
0.9209 0.9505 0.9687 0.9801 0.9874 0.9922 0.9955 0.9978 0.9994 1.0000
0.6733 0.7254 0.7697 0.8086 0.8438 0.8766 0.9081 0.9390 0.9696 1.0000
0.9982 0.9970 0.9955 0.9945 0.9936 0.9930 0.9927 0.9926 0.9925 0.9924
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0.15 0.18 0.28 0.54 0.72 1.01 1.12 1.24 1.31 0.34
0.002 0001 0.002 0.002 0.001 0.001 0.002 0.002 0.001 0.002
5.80 8.19 3.78 6.74 10.00 10.57 7.79 4.28 1.04 0.78
23.10 17.87 23.93 23.49 23.63 21.58 16.50 10.61 4.74 0.02
T = 353.15 K 0.101 7.07 0.201 11.49 0.300 16.59 0.400 19.90
6.99 12.14 16.03 19.03
4.95 9.04 12.49 15.45
0.9359 0.9028 1.0059 1.0274
0.9252 0.9542 0.9718 0.9826
0.6600 0.7149 0.7618 0.8028
0.9978 0.9964 0.9948 0.9937
0.01 0.01 0.01 0.01
0.16 0.21 0.48 0.82
0.002 0001 0.002 0.002
1.14 5.70 3.39 4.36
29.92 21.28 24.71 22.36
x1
Pexp (kPa)
C. Dai et al. / Journal of Molecular Liquids 256 (2018) 471–479
477
Table 7 (continued) x1
Pexp (kPa)
PUNIFAC-Lei (kPa)
PCOSMO (kPa)
γ1,exp
γ1,UNIFAC-Lei
γ1,COSMO
Φ1
U(T) (K)
U(P) (kPa)
U(x)
100RD(P) (UNIFAC-Lei)
100RD(P) (COSMO)
0.501 0.601 0.700 0.800 0.901 1.000
23.12 25.15 26.66 27.31 27.54 27.92
21.42 23.34 24.90 26.21 27.32 28.25
18.04 20.36 22.47 24.42 26.26 28.00
1.0677 1.0706 1.0667 1.0401 1.0075 0.9883
0.9893 0.9935 0.9963 0.9982 0.9995 1.0000
0.8398 0.8742 0.9068 0.9384 0.9694 1.0000
0.9927 0.9920 0.9916 0.9914 0.9913 0.9912
0.01 0.01 0.01 0.01 0.01 0.01
1.30 1.39 1.46 1.52 1.69 0.42
0.001 0.001 0.002 0.002 0.001 0.002
7.34 7.20 6.60 4.03 0.80 1.18
21.96 19.04 15.72 10.57 4.65 0.29
T = 358.15 K 0.101 7.37 0.201 12.90 0.300 18.92 0.400 23.75 0.501 28.07 0.601 31.55 0.700 32.42 0.800 32.71 0.901 33.29 1.000 33.77
8.49 14.75 19.46 23.10 25.99 28.31 30.18 31.75 33.09 34.22
5.88 10.79 14.96 18.56 21.72 24.56 27.14 29.52 31.75 33.86
0.8067 0.8378 0.9481 1.0130 1.0706 1.1087 1.0710 1.0288 1.0056 0.9870
0.9294 0.9578 0.9749 0.9851 0.9911 0.9948 0.9970 0.9986 0.9996 1.0000
0.6476 0.7051 0.7543 0.7973 0.8361 0.8718 0.9055 0.9378 0.9693 1.0000
0.9978 0.9961 0.9942 0.9928 0.9915 0.9904 0.9901 0.9901 0.9899 0.9897
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0.18 0.24 0.72 1.27 1.71 1.83 1.97 2.03 2.26 0.58
0.002 0001 0.002 0.002 0.001 0.001 0.002 0.002 0.001 0.002
15.21 14.32 2.83 2.76 7.42 10.28 6.91 2.93 0.60 1.32
20.22 16.37 20.95 21.87 22.61 22.17 16.30 9.75 4.62 0.28
Pexp and γ1,exp are the experimental vapor pressures and activity coefficients, respectively. PUNIFAC-Lei, PCOSMO, γ1,UNIFAC-Lei and γ1,COSMO are the predicted values by the UNIFAC-Lei or COSMO-RS model. U(T), U(P) and U(x) are the expanded uncertainties with 0.95 level of confidence of experimental temperature T, pressure Pexp, and solute mole fraction x1, respectively. RD(P) (UNIFAC-Lei) and RD(P) (COSMO) are the relative deviations of vapor pressures between experimental data and predicted values by the UNIFAC-Lei and COSMO-RS models, respectively.
70
P (kPa)
50 40
50
333.15 K 353.15 K
40
P (kPa)
60
60
323.15 K 328.15 K 333.15 K 338.15 K 343.15 K 348.15 K 353.15 K 358.15 K
30
30 20
20
10
10 0 0.0
(a)
(a) 0.2
0.4
x1
0.6
0.8
0 0.0
1.0
0.2
0.4
0.6
0.8
1.0
x1 30
30
P (kPa)
25 20
323.15 K 328.15 K 333.15 K 338.15 K 343.15 K 348.15 K 353.15 K 358.15 K
25
15
15
10
10
5
5 0 0.0
333.15 K 353.15 K
20
P (kPa)
35
(b) 0.2
0.4
0.6
0.8
0 0.0
1.0
x1 Fig. 2. Vapor pressures of binary mixtures at different temperatures: formic acid (1) + [EMIM][BF4] (2) (a) and acetic acid (1) + [EMIM][BF4] (2) (b). Solid lines, predicted values by the UNIFAC-Lei model; scattered points, experimental data.
(b)
0.2
0.4
0.6
0.8
1.0
x1 Fig. 3. Vapor pressures of binary mixtures at 333.15 and 353.15 K: formic acid (1) + [EMIM][BF4] (2) (a) and acetic acid (1) + [EMIM][BF4] (2) (b). Solid lines, predicted values by the UNIFAC-Lei model; dashed lines, predicted values by the COSMO-RS model; scattered points, experimental data.
478
C. Dai et al. / Journal of Molecular Liquids 256 (2018) 471–479
2000
3000
HHB, formic acid-IL (J·mol-1)
Hformic acid-IL (J·mol-1)
1500 1000 500
Hm
0
HMF
-500
HHB
2000 1000
Cation contribution
0 -1000
Anion contribution
HvdW
-1000 -1500 0.0
Formic acid contribution
4000
HHB
(a) 0.2
0.4
0.6
0.8
(a)
-2000 0.0
1.0
0.2
0.4
x1 HHB
2000
x1
0.6
0.8
1.0
3000
Hm
HHB, acetic acid-IL (J·mol-1)
Hacetic acid-IL (J·mol-1)
Acetic acid contribution 1500 1000 500
HMF 0
0.0
0.2
0.4
x1
0.6
HHB 1000
Cation contribution
0
Anion contribution
-1000
HvdW
-500
2000
(b) 0.8
(b) -2000 0.0
1.0
Fig. 4. Excess enthalpies of binary mixtures calculated by the COSMO-RS model at 298.15 K: formic acid (1) + [EMIM][BF4] (2) (a) and acetic acid (1) + [EMIM][BF4] (2) (b).
0.2
0.4
x1
0.6
0.8
1.0
Fig. 5. Contributions of solute, cation and anion to the hydrogen bonding interaction in binary mixtures calculated by the COSMO-RS model at 298.15 K: (a) formic acid (1) + [EMIM][BF4] (2), and (b) acetic acid (1) + [EMIM][BF4].
5. Conclusions 4.4. Analysis of the σ-profiles In this work, the vapor pressure data of the binary systems formic acid/acetic acid + [EMIM][BF4], which are essential for separation 30 [EMIM] [BF4]
25
CH2O2 C 2 H4 O2
20
p (σ)
The normalized σ-profiles of formic acid, acetic acid, [EMIM]+ cation, and [BF4]− anion are shown in Fig. 6. It can be seen that for formic acid and acetic acid there is a main peak located at 0.012 e/Å2 in the positive polar region related to oxygen atom of carbonyl (C_O), which acts as hydrogen bond acceptor. Meanwhile, in the negative polar region there is a main peak at −0.02 and −0.017 e/Å2 for formic acid and acetic acid related to hydrogen atom of the hydroxyl (OH), which acts as hydrogen bond donor. For formic acid, there is another peak at −0.01 e/ Å2 responsible for weak hydrogen bond donor ability. Thus, the hydrogen bonding interaction between formic acid molecules is stronger than that between acetic acid molecules. For [EMIM]+ cation, the main peaks locate in the nonpolar region, and a peak at about −0.01 e/Å2 related to the hydrogen atom of the aromatic ring is responsible for the weak hydrogen bond donor ability of cation. For [BF4]− anion, there is a main peak located at 0.011 e/Å2 in the negative polar region, indicating the hydrogen bond acceptor capability of anion. Furthermore, the characteristic peak of anion is much stronger than that of cation. Thus, the σ-profiles obtained by the COSMO-RS model reveal that the hydrogen-bond interaction between solutes (formic acid/acetic acid) and [BF4]− is much stronger than that between solutes and [EMIM]+, indicating that the anion has a stronger influence on the thermodynamic properties of binary mixtures than the cation. This conforms to the different contributions of solute, cation and anion to the hydrogen bonding of mixtures as aforementioned (see Fig. 5).
15 10 5 0
-0.02
-0.01
0.00
0.01
0.02
σ (e/Å2) Fig. 6. σ-Profiles of formic acid, acetic acid, cation and anion calculated by the COSMO-RS model at 298.15 K.
C. Dai et al. / Journal of Molecular Liquids 256 (2018) 471–479
process design, were measured using a modified equilibrium still at temperatures ranging from 323.15 to 358.15 K and IL contents ranging from 0.1 to 0.9 in mass fraction. It was found that the addition of [EMIM][BF4] into solutes makes vapor pressure lower than that of pure solute at the same temperature, due to the strong interaction between IL and formic acid/acetic acid. On the other hand, the predictive thermodynamic models (i.e., UNIFAC-Lei and COSMO-RS models) were used to predict the vapor pressures with the ARDs of 4.54% and 22.24% for formic acid, respectively, and 6.38% and 16.43% for acetic acid, respectively. This indicates that the UNIFAC-Lei model can give a quantitative description with high accuracy, while the COSMO-RS model can only be used as a prior model to give a qualitative prediction. Moreover, the excess enthalpies and σ-profiles were calculated by the COSMO-RS model to achieve further understanding on the thermodynamic behavior at molecular scale. It was found that the hydrogen bonding interaction (HHB) plays a dominant role, whereas the van der Waals interaction (HvdW) plays a secondary role and the electrostatic interaction (HMF) contributes only slightly to the overall excess enthalpy. The hydrogen bonding interaction of the system (HHB) is mainly dependent on acid components. For IL, the contribution of anion is larger than that of cation, as confirmed by the σ-profiles. This work was presented by the close integration of experiment, calculation, and theoretical analysis. Acknowledgments This work is financially supported by the National Natural Science Foundation of China under Grants (Nos. 21476009, 21406007, and U1462104). References [1] J. Cai, X. Cui, Y. Zhang, R. Li, T. Feng, Vapor-liquid equilibrium and liquid-liquid equilibrium of methyl acetate + methanol + 1-ethyl-3-methylimidazolium acetate, J. Chem. Eng. Data 56 (2011) 282–287. [2] Z. Lei, C. Li, B. Chen, Extractive distillation: a review, Sep. Purif. Rev. 23 (2003) 121–213. [3] T. Zhou, L. Chen, Y. Ye, Z. Qi, H. Freund, K. Sundmacher, An overview of mutual solubility of ionic liquids and water predicted by COSMO-RS model, Ind. Eng. Chem. Res. 51 (2012) 6256–6264. [4] J. Han, C. Dai, Z. Lei, B. Chen, Gas drying with ionic liquids, AICHE J. 64 (2018) 606–619. [5] Z. Song, T. Zhou, J. Zhang, L. Chen, Z. Qi, Screening of ionic liquids for solventsensitive extraction - with deep desulfurization as an example, Chem. Eng. Sci. 129 (2015) 69–77. [6] D. Tao, F. Chen, Z. Tian, K. Huang, S.M. Mahurin, D. Jiang, S. Dai, Highly efficient carbon monoxide capture by carbanion-functionalized ionic liquids through C-Site interactions, Angew. Chem. Int. Ed. 56 (2017) 6843–6847. [7] C. Dai, L. Wu, G. Yu, Z. Lei, Syngas dehydration with ionic liquids, Ind. Eng. Chem. Res. 56 (2017) 14642–14650. [8] Z. Lei, C. Dai, J. Zhu, B. Chen, Extractive distillation with ionic liquids: a review, AICHE J. 60 (2014) 3312–3329. [9] F. Chen, K. Huang, Y. Zhou, Z. Tian, X. Zhu, D. Tao, D. Jiang, S. Dai, Multi-molar absorption of CO2 by the activation of carboxylate groups in amino acid ionic liquids, Angew. Chem. Int. Ed. 55 (2016) 7166–7170. [10] L. Qin, J. Li, H. Cheng, L. Chen, Z. Qi, W. Yuan, Association extraction for vitamin E recovery from deodorizer distillate by in situ formation of deep eutectic solvent, AICHE J. 63 (2017) 2212–2220. [11] H. Uslu, Extraction equilibria of 2,4,6-trinitrophenol by (amberlite LA2 + ester) solvents, Fluid Phase Equilib. 427 (2016) 175–179. [12] L. Shi, C. Wang, C. Zou, Corrosion failure analysis of L485 natural gas pipeline in CO2 environment, Eng. Fail. Anal. 36 (2014) 372–378. [13] G.R. Harvianto, K.J. Kang, M. Lee, Process design and optimization of an acetic acid recovery system in terephthalic acid production via hybrid extraction−distillation using a novel mixed solvent, Ind. Eng. Chem. Res. 56 (2017) 2168–2176. [14] J. Dhanalakshmi, P.S.T. Sai, A.R. Balakrishnan, Study of ionic liquids as entrainers for the separation of methyl acetate−methanol and ethyl acetate−ethanol systems using the COSMO-RS model, Ind. Eng. Chem. Res. 52 (2013) 16396–16405. [15] C. Dai, Z. Lei, X. Xi, J. Zhu, B. Chen, Extractive distillation with a mixture of organic solvent and ionic liquid as entrainer, Ind. Eng. Chem. Res. 53 (2014) 15786–15791. [16] M.T.G. Jongmans, B. Schuur, A.B. de Haan, Ionic liquid screening for ethylbenzene/ styrene separation by extractive distillation, Ind. Eng. Chem. Res. 50 (2011) 10800–10810. [17] T. Zhou, Z. Wang, Y. Ye, L. Chen, J. Xu, Z. Qi, Deep separation of benzene from cyclohexane by liquid extraction using ionic liquids as solvent, Ind. Eng. Chem. Res. 51 (2012) 5559–5564.
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