Article pubs.acs.org/jced
Liquid Phase Equilibria of Aqueous Mixtures of Carboxylic Acids (C1−C4) with Ethylbenzene: Thermodynamic and Mathematical Modeling S. Laleh Seyed Saadat,† Ali Ghanadzadeh Gilani,*,† Hossein Ghanadzadeh Gilani,‡ Atefeh Kashef,† and Saeed Fallahi‡† †
Department of Chemistry, Faculty of Science and ‡Department of Chemical Engineering, University of Guilan, Rasht, Iran ‡† Young Researchers Club, Shiraz Branch, Islamic Azad University, Shiraz, Iran S Supporting Information *
ABSTRACT: Liquid−liquid equilibrium (LLE) data were experimentally determined and correlated for the aqueous solutions of a series of carboxylic acids (i.e., formic, acetic, propionic, and butyric acids) with ethylbenzene at a temperature of 298.15 K and p = 101.32 kPa. The ternary mixtures containing of the acids exhibit type-1 LLE behavior. The quality of the observed tie-lines was checked using the Othmer−Tobias equation. The correlations were carried out using the thermodynamic and statistical modeling. The activity coefficient models of UNIQUAC and NRTL were applied to fit the tie lines and values of the binary interaction parameters between each pair of components were obtained. The correlation of the tie lines was also carried out by a GMDH type-NN, which are in agreement with those obtained experimentally. In this work, experimental distribution coefficients and separation factors were estimated. Moreover, the Kamlet−Taft LSER model was employed to correlate these quantities and was interpreted in terms of intermolecular interactions. In of our previous publications,23−26 four of the most widely used carboxylic acids, that is, formic acid (FA), acetic acid (AA), propionic acid (PA), and butyric acid (BA) were used as solutes. Various effective factors, that is, the biphasic region, the intercept of the tie-lines, and the acid partitioning between the two phases were determined and interpreted. The {water + FA, AA, PA, and BA + ethylbenzene} ternary systems were investigated at a temperature of 298.15 K. The Othmer−Tobias27 correlation was utilized to check the reliability of the tie line results. Moreover, the LLE data were regressed using the UNIQUAC and NRTL models,28−30 and the model interaction parameters were obtained. A neural network of GMDH type was also employed to correlate the tie lines, and the results were compared with those from experimental data.31,32 In this work, separation factors were computed from the experimental distribution coefficient data and then were regressed by the Kamlet−Taft LSER model.33
1. INTRODUCTION Carboxylic acids are an important group of organic compounds that are produced by chemical synthetic or fermentation methods. As the fermentation is an environmentally friendly process, it may be considered as a suitable method in the acid production. Thus, the separation of these compounds from water has special economic importance.1−8 Moreover, the precise information about phase behavior of the ternary systems including carboxylic acid is always needed for setting up the industrial units. Until now, a number of solvents, generally alcohols,9−11 esters,12−15 hydrocarbons,16,17 and ketones18,19 have been tested by different researchers for recovery of these compounds. However, liquid− liquid equilibrium (LLE) studies are still required for different purposes. In the present work, ethylbenzene was chosen as a solvent for separation of the acids from aqueous solutions. The motivation of chosing this solvent is due to the following concerns. Ethylbenzene is a colorless and water-immiscible solvent, which is a member of volatile organic compounds (VOCs). It is a monocyclic aromatic hydrocarbon with a 0.59 D20 dipole moment and very low dielectric constant (ε = 2.4)21 that is found in petroleum products, such as gasoline. Moreover, ethylbenzene containing a polarizable aromatic ring is a weak H-bond acceptor (α = 0, β = 0.11, and π* = 0.49)22 thus it is possible to form hydrogen bonds in polar protic solutions. © XXXX American Chemical Society
2. EXPERIMENTAL SECTION 2.1. Materials. Formic, acetic, propionic, butyric acids, and ethylbenzene were supplied and were used as received. Purity of the acids and the solvent was confirmed by measurement of the Received: February 8, 2016 Accepted: July 27, 2016
A
DOI: 10.1021/acs.jced.6b00112 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 1. Source, Purity, r and q (UNIQUAC Structural Parameters), Refractive Index (nD), and Density (ρ) of the Pure Components at T = 298.15 K and p = 101.32 kPaa ρ/(kg·m−3)
nD
a
b
chemical name
supplier
mass fraction purity
r
formic acid (FA) acetic acid (AA) propionic acid (PA) butyric acid (BA) ethylbenzene (EB) water
Chemlab Merck Chemlab Merck Sigma
>0.99 >0.99 >0.99 >0.99 >0.99 redistilled and deionized
1.53 2.20 2.88 3.55 4.60 0.92
b
q
exp
lit
exp
lit
1.53 2.07 2.61 3.15 3.52 1.40
1.3710 1.3714 1.3807 1.3977 1.4930 1.3324
1.3714c 1.3715c 1.3809c 1.3975d 1.4932e 1.3325c
1219.50 1044.12 998.04 952.68 862.51 997.01
1220.00c 1049.42c 988.20c 952.80d 862.53e 997.05c
Standard uncertainties u are u(nD) = 0.0002, and u(ρ) = 5 kg·m−3, u(T) = 0.01 K, and u(p) = 0.40 kPa. bTaken from ref 35. cTaken from ref 20. Taken from ref 25. eTaken from ref 39.
d
refractive indices and densities of the liquids. Redistilled and deionized water was employed for the preparation of all solutions. Source, purity, and physical data of the used chemicals are presented in Table 1. 2.2. Experimental Procedure. Densities and refractive indices of the pure chemicals were determined by a Kyoto DA210 electronic density meter and a Abbe refractometer. The temperature of the samples was monitored using a digital thermometer (Lutron TM-917) and was kept constant within ±0.01 K. An analytical balance (AND, accuracy ±0.1 mg) was used for weighing the samples. The Karl Fisher titration was performed with a 870 KF Titrino plus titrator (Metrohm). Solubility curves of the {water + carboxylic acids + ethylbenzene} ternary systems were obtained at a temperature of 298.15 K using the cloud point data.25 The prepared mixtures of either (water + acid) or (ethylbenzene + acid) were poured into the glass cell by a micropipette (±0.001 mL) and titrated against either solvent or water until the turbidity had appeared. In order to minimize the experimental error, the measurements were repeated several times. Moreover, all the data were collected after waiting about 10 min in end point. Uncertainty in solubility values was estimated to be ±0.0050. The data for the acidcontaining systems are listed in Table S1. Tie-line data were obtained for the systems water + carboxylic acid + ethylbenzene at T = 298.15 K. The LLE measurements were performed in a glass cell (250 mL). The temperature accuracy was estimated to be ±0.01 K. The prepared samples were vigorously agitated by a magnetic stirring bar. For the studied systems, both the stirring and settle times were at least 4 h. A glass syringe was used to transfer the samples from the
Figure 1. Refractive index standard curves lying on the solubility curves for {water (1) + carboxylic acid (2) + ethylbenzene (3)} in aqueous phase (w11) at T = 298.15 K; black circle, FA; blue square, AA; red triangle, PA; green diamond, BA.
Table 2. Equations for Refractive Index (nD) as a Function of Water Mass Fraction (w11) in the Aqueous-Rich Phase at T = 298.15 K and p = 101.32 kPa for the Investigated Systemsa system
equationb
R2
water (1) + FA (2) + ethylbenzene (3) water (1) + AA (2) + ethylbenzene (3) water (1) + PA (2) + ethylbenzene (3) water (1) + BA (2) + ethylbenzene (3)
nD = −0.0523w11 + 1.3827 nD = −0.0656w11 + 1.4009 nD = −0.0854w11 + 1.4215 nD = −0.1529w11 + 1.4785
0.9904 0.9916 0.9949 0.9984
a
Standard uncertainties u are u(T) = 0.01 K, u(p) = 0.40 kPa, u(nD) = 0.0002, and u(w) = 0.005. bThe calculated standard error of the plot slope and intercept are 0.0025 and 0.0018, respectively.
Table 3. Experimental Tie-Line Data, Calculated UNIQUAC and NRTL Tie-Line Data in Mass Fraction for Water (1) + Carboxylic Acid (2) + Ethylbenzene (3) at T = 298.15 K and p = 101.32 kPaa aqueous phase mass fraction w11 (water)
organic phase mass fraction w21 (ACID)
exp
UNIQ
NRTL
exp
0.663 0.597 0.532 0.480 0.395 0.348
0.654 0.593 0.542 0.488 0.399 0.345
0.658 0.594 0.542 0.485 0.391 0.346
0.329 0.394 0.459 0.510 0.595 0.640
0.793 0.658 0.545
0.784 0.672 0.575
0.790 0.654 0.552
0.204 0.337 0.447
UNIQ
w13 (water) NRTL
exp
UNIQ
Water (1) + Formic Acid (2) + Ethylbenzene (3) 0.338 0.334 0.001 0.001 0.398 0.397 0.001 0.001 0.448 0.449 0.001 0.001 0.503 0.505 0.001 0.001 0.591 0.599 0.001 0.001 0.644 0.644 0.001 0.001 Water (1) + Acetic Acid (2) + Ethylbenzene (3) 0.213 0.207 0.001 0.002 0.323 0.341 0.002 0.002 0.417 0.440 0.002 0.002 B
w23 (ACID) NRTL
exp
UNIQ
NRTL
0.001 0.001 0.001 0.001 0.001 0.001
0.018 0.022 0.026 0.031 0.045 0.053
0.017 0.022 0.027 0.033 0.044 0.052
0.017 0.022 0.026 0.032 0.044 0.053
0.001 0.002 0.002
0.016 0.024 0.033
0.017 0.024 0.034
0.015 0.026 0.036
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Table 3. continued aqueous phase mass fraction w11 (water) exp
a
UNIQ
organic phase mass fraction w21 (ACID)
NRTL
exp
0.491 0.428 0.375
0.544 0.446 0.394
0.523 0.425 0.353
0.501 0.557 0.605
0.891 0.794 0.725 0.692 0.643 0.593
0.887 0.798 0.731 0.695 0.649 0.581
0.895 0.799 0.715 0.673 0.624 0.558
0.108 0.203 0.270 0.301 0.348 0.392
0.931 0.918 0.909 0.894 0.884 0.873
0.933 0.923 0.914 0.896 0.894 0.882
0.940 0.916 0.902 0.890 0.885 0.877
0.065 0.077 0.087 0.102 0.112 0.123
UNIQ
w13 (water) NRTL
exp
UNIQ
Water (1) + Acetic Acid (2) + Ethylbenzene (3) 0.446 0.468 0.002 0.002 0.539 0.561 0.002 0.002 0.588 0.628 0.003 0.002 Water (1) + Propionic Acid (2) + Ethylbenzene (3) 0.112 0.104 0.004 0.004 0.199 0.199 0.009 0.010 0.264 0.280 0.020 0.020 0.298 0.321 0.025 0.026 0.341 0.367 0.039 0.036 0.405 0.428 0.053 0.052 Water (1) + Butyric Acid (2) + Ethylbenzene (3) 0.063 0.056 0.006 0.006 0.073 0.080 0.014 0.015 0.082 0.094 0.023 0.023 0.100 0.106 0.038 0.038 0.102 0.111 0.073 0.094 0.114 0.119 0.138 0.132
w23 (ACID) NRTL
exp
UNIQ
NRTL
0.002 0.002 0.003
0.042 0.050 0.063
0.038 0.053 0.063
0.039 0.050 0.061
0.004 0.011 0.020 0.026 0.034 0.047
0.111 0.229 0.338 0.393 0.489 0.557
0.107 0.218 0.323 0.384 0.471 0.607
0.110 0.238 0.335 0.378 0.425 0.483
0.007 0.014 0.022 0.038 0.073 0.142
0.175 0.271 0.333 0.446 0.524 0.567
0.188 0.277 0.316 0.424 0.470 0.516
0.173 0.264 0.330 0.422 0.543 0.596
Standard uncertainties u are u(T) = 0.01 K, u(p) = 0.40 kPa, and u(w) = 0.005.
Figure 2. Ternary phase diagram for LLE of water (1) + carboxylic acid (2) + ethylbenzene (3) at T = 298.15 K; ●, experimental cloud points; o, experimental tie-lines; blue square, UNIQUAC calculated points; red triangle, NRTL calculated points; (a) FA (b) AA; (c) PA; (d) BA.
Table 4. Separation Factors (S), and Distribution Coefficients of Carboxylic Acids (D2) for Water (1) + Carboxylic Acid (2) + Ethylbenzene (3) at T = 298.15 K and p = 101.32 kPaa system
D2
S
water (1) + FA (2) + ethylbenzene (3)
0.054 0.055 0.057 0.061 0.075 0.084 0.079 0.072 0.073 0.083 0.090 0.103 1.036 1.124 1.254 1.309 1.408 1.421 2.685 3.500 3.846
71.9 65.8 60.3 59.0 49.2 48.4 52.1 31.5 22.0 19.3 16.1 14.4 256.3 103.8 44.5 36.1 23.4 16.0 396.7 226.3 154.7
water (1) + AA (2) + ethylbenzene (3)
water (1) + PA (2) + ethylbenzene (3)
water (1) + BA (2) + ethylbenzene (3)
Table 4. continued system
D2
S
4.397 4.698 4.618
102.9 57.2 29.2
a Standard uncertainties u are u(T) = 0.01 K, u(p) = 0.40 kPa, and u(S) = 0.2.
Figure 3. Plot of the separation factor (S) of the carboxylic acid as a function of mass fraction of the acids in the aqueous phase (w21) at T = 298.15 K; black circle, FA; blue square, AA; red triangle, PA; green diamond, BA. C
DOI: 10.1021/acs.jced.6b00112 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 5. Othmer−Tobias Equation Constants (A and B) and the Correlation Factor (R2) for the Ternary Systems at T = 298.15 K and p = 101.32 kPaa
Table 7. Experimental and Correlated Values (LSER) for Distribution Coefficients (D2) and Separation Factors (S) w3 (feed)
Othmer−Tobias correlation system
A
B
R2
water (1) + FA (2) + ethylbenzene (3) water (1) + AA (2) + ethylbenzene (3) water (1) + PA (2) + ethylbenzene (3) water (1) + BA (2) + ethylbenzene (3)
−3.4408 −3.1125 0.9043 7.3734
0.8688 0.7506 1.4535 3.4369
0.991 0.992 0.990 0.992
0.4449 0.3994 0.3636 0.3330 0.3080 0.2855 0.4434 0.4000 0.3640 0.3334 0.3076 0.2854 0.4433 0.4001 0.364 0.3334 0.3076 0.2854
Figure 4. Othmer−Tobias plot for the water (1) + carboxylic acid (2) + ethylbenzene (3) at T = 298.15 K; black circle, FA; blue square, AA; red triangle, PA; green diamond, BA.
0.4426 0.3995 0.3636 0.3334 0.3075 0.2855
organic phase (upper layer), and a bottoming tap was used to take the mixture from the aqueous layer. 2.3. Analysis. The mass fractions of the acids in the aqueous and organic phases were measured by NaOH titration. The water contents in the aqueous phase were determined using refractive index measurements. In this method, standard curves were first plotted using the refractive indices of the aqueous phase lying on the solubility curve. The standard curves for water in the aqueous phase at T = 298.15 K are shown in Figure 1. The refractive indices and their corresponding mass
log D2LSER
log D2exp.
log SLSER
log Sexp
water (1) + FA (2) + ethylbenzene (3) −1.2676 −1.2676 1.8567 −1.1380 −1.2596 1.6668 −1.0360 −1.2441 1.5174 −0.9488 −1.2147 1.3897 −0.8776 −1.1249 1.2854 −0.8134 −1.0757 1.1915 water (1) + AA (2) + ethylbenzene (3) −1.1024 −1.1024 1.7168 −0.9945 −1.1427 1.5488 −0.9050 −1.1367 1.4094 −0.8289 −1.0809 1.2909 −0.7647 −1.0458 1.1910 −0.7096 −0.9872 1.1051 water (1) + PA (2) + ethylbenzene (3) 0.0154 0.0154 2.4087 0.0139 0.0508 2.1740 0.0126 0.0983 1.9779 0.0116 0.1169 1.8116 0.0107 0.1486 1.6714 0.0099 0.1526 1.5508 water (1) + BA (2) + ethylbenzene (3) 0.4289 0.4289 2.5985 0.3872 0.5441 2.3454 0.3524 0.5850 2.1347 0.3231 0.6432 1.9574 0.2980 0.6719 1.8053 0.2767 0.6645 1.6761
1.8567 1.8182 1.7803 1.7709 1.6920 1.6848 1.7168 1.4983 1.3424 1.2856 1.2068 1.1584 2.4087 2.0162 1.6484 1.5575 1.3692 1.2041 2.5985 2.3547 2.1895 2.0124 1.7574 1.4654
fractions are listed in Table S2. Equations for refractive index nD as a function of w11 are given in Table 2. The water content in the organic layer was measured by the Karl Fischer method.34 Consequently, after determination of the mass of water and the acid in each phase, mass of the solvent was evaluated by equation ∑wi = 1. Uncertainty in the tie line data was estimated to be 0.005.
Table 6. Correlated Results from the UNIQUAC and NRTL Models and the Corresponding Binary Interaction Parameters (aij, aji, bij, and bji) for the Ternary Systems UNIQUAC i−j
aij/K
aji/K
1−2 1−3 2−3
624.74 −69.12 −507.88
−420.60 −966.44 157.46
1−2 1−3 2−3
−126.81 −184.63 −168.20
122.16 −974.68 −116.39
1−2 1−3 2−3
132.91 −277.55 272.28
−370.41 −860.01 −490.60
1−2 1−3 2−3
−146.11 −90.83 −515.93
−87.70 −5480.56 183.43
n
2
NRTL d
i−j
rmsd %
water (1) + FA (2) + ethylbenzene (3) 1−2 0.31 1−3 2−3 water (1) + AA (2) + ethylbenzene (3) 1−2 0.97 1−3 2−3 water (1) + PA (2) + ethylbenzene (3) 1−2 2.28 1−3 2−3 water (1) + BA (2) + ethylbenzene (3) 1−2 0.78 1−3 2−3
bij/K
bji/K
rmsdd %
−187.18 1687.35 1127.89
1001.37 1275.21 300.11
0.40
3669.76 2329.96 733.91
9998.79 1154.30 5119.25
1.63
436.71 2740.41 467.24
377.35 1449.33 −52.27
1.40
733.86 2351.80 −136.31
430.87 2092.65 733.78
1.44
3
exp cal 2 rmsd = (∑k = 1 ∑ j = 1 ∑i = 1 (wijk − wijk ) /6n)1/2
d
D
DOI: 10.1021/acs.jced.6b00112 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 8. Polynomial Equations of the GMDH Model for the Water (1) + Carboxylic Acid (2) + Ethylbenzene (3) Systems w11 (Mass Fraction of Water in Aqueous Phase) Y1 = Y2 = Y3 = Y4 = Y5 = w11 =
Y1 = Y2 = Y3 = Y4 = W21 =
Y1 = Y2 = Y3 = W13 =
Y1 = Y2 = Y3 = W23 =
− 0.6444 + 0.1747C + 3.2670 z1 + 0.0332C2 − 0.1982z12 − 0.5726(C) (z1) 2.4665 − 4.9133z2 − 9.8758z3 + 2.4467z22 + 9.8858z32 + 9.8367(z2) (z3) 2.4777 − 9.9007z1 − 4.9748z2 + 9.8907z12 + 2.4870z22 + 9.9398(z1) (z2) − 0.2042 + 0.9152Y1 + 0.7059Y2 + 0.1728Y12 − 0.4649Y22 − 0.1774(Y1) (Y2) −1.1017 + 0.2085C + 3.0478Y3 + 0.0278C2 − 0.9745Y32 − 0.3257(C) (Y3) − 0.0306 + 2.7753Y4 − 1.6570Y5 + 1.5381Y42 + 3.4039Y52 − 5.0440(Y4) (Y5) w21 (Mass Fraction of Carboxylic Acid in Aqueous Phase) 1.5664 − 0.1729C − 2.9517z1 − 0.0325C2 − 0.1359z12 + 0.5637(C) (z1) 0.05767 + 0.1081C + 1.5428z2 − 0.0325C2 − 0.04092z22 − 0.2796(C) (z2) 0.0000002 + 0.0033Y1 − 0.0033Y2 + 0.6526Y12 + 0.6597Y22 − 1.3124(Y1)(Y2) −2.4764 + 9.9161z2 + 4.9328z3 − 9.9264z22 − 2.4562z32 − 9.8760(z2) (z3) 0.0597 + 1.1457Y3 − 0.5523Y4 − 0.4012Y32 + 0.6947Y42 + 0.4088(Y3) (Y4) w13 (Mass Fraction of Water in Organic Phase)
Figure 5. Developed structure of GMDH-type-NN model for the water (1) + carboxylic acid (2) + ethylbenzene (3) ternary systems at T = 298.15 K; (a) w11, (b) w21, (c) w13, and (d) w23.
0.2191 + 0.0762C − 1.5541z1 + 0.0057C2 + 2.6241z12 − 0.2473(C)(z1) −0.1393 + 0.7490z3 + 1.9996Y1 − 0.9625z32 + 7.1931Y1 2 − 4.9878(z3) (Y1) − 0.0053 + 0.1053z2 − 0.5084Y1 − 0.2383z22 + 7.1354Y12 + 2.5423(z2) (Y1) 0.0000008 + 0.3761Y2 − 0.3658Y3 − 5.6048Y22 + 5.6017Y32 − 0.0016(Y2)(Y3) w23 (Mass Fraction of Carboxylic Acid in Organic Phase)
The separation factor with increasing alkyl chain length led to a decreased solubility in polar media. In fact by adding a methyl group to the carboxylic acid’s structure, the solubility in water decreases, and as can be seen from the figure the S-values increase in the order of the carboxylic acid chain length, that is, BA> PA > AA > FA. 3.2. Reliability of Tie-Lines. The Othmer−Tobias27 equation {ln[(1 − w33)/w33] = A + B ln[(1 − w11/w11]} was employed to verify the reliability of the tie lines where the subscripts 1 and 3 indicate water and solvent, respectively. A and B are the equation parameters, which are presented in Table 5 (see also Figure 4). As it is evident from the table, the correlation factors for all the systems are being approximately unity (R2 ≈ 1), which confirm the amount of reliability of the LLE data in the current investigation. 3.3. LLE Correlation. The local composition models NRTL and UNIQUAC were employed to correlate the measured tie-lines. The r and q (structural parameters) used for these ternary systems were computed by the Bondi method35 and are presented in Table 1. The optimum nonrandomness value (α) was sited at 0.3. The computed tie-lines for the studied systems are given in Table 3. From the tie-line data, the binary interaction parameters, aij = (uij − ujj)/R and bij = (gij − gjj)/R, were obtained.36 The goodness of the fit was tested using the root-mean square deviation.25 The model interaction parameters along with rmsd data for the studied systems are given in Table 6. 3.4. LSER Model Parameters. In the present work, the values of D2 and S were correlated using the Kamlet−Taft linear solvation energy relationship (LSER) parameters33 for the solvent
−0.1045 + 0.4391z1 − 0.9188C + 0.0070z12 + 2.5067C2 − 0.9454(z1) (C) 0.0597 − 0.0339C − 0.7640z2 + 0.0069C2 + 0.5639z22 + 0.4752(C)(z2) −0.1242 + 1.4153Y1 + 0.5766z3 − 0.2350Y12 − 0.6635z32 − 0.9099(Y1) (z3) −0.000003 + 0.0196Y2 − 0.0187Y3 − 1.4701Y22 − 1.3811Y32 + 2.8522(Y2)(Y3)
3. RESULTS AND DISCUSSION 3.1. Experimental Tie-Lines. Experimental tie-lines for the (water + carboxylic acid + ethylbenzene) systems were obtained at a temperature of 298.15 K. The experimental data for the investigated mixtures are summarized in Table 3. The corresponding experimental phase diagrams were plotted in Figure 2a−d. The regions of the biphasic area mainly depend on the alkyl chain length of the acid. It can be observed from the triangular diagrams, the biphasic area increases in the order of the systems including FA > AA > PA > BA. An important concept in the LLE studies is separation factor (S = D2/D1), which evaluates the efficiency of solute recovery by a solvent. Here, D2 = w23/w21 and D1 = w13/w11 are the distribution coefficients of the acid and water, respectively. The subscript 1, 2, and 3 indicate water, solute, and solvent, respectively. The values of D2 and S for the studied mixtures are listed in Table 4. As it can be observed in Figure 3, the S values reduce sharply as the concentration of the carboxylic acids in aqueous phase (w21) increases. For all the studied systems, the separation factors are greater than unity, which means that ethylbenzene has potential of extraction of these acids from aqueous solution. However, the butyric acid containing system exhibits larger S-values with respect to the other mixtures.
log D2 = log D20 + a ·α + b·β + c(π * + dδ)
(1)
log S = log S ° + a ·α + b·β + c(π * + dδ)
(2)
where α and β are a measure of the solvent H-bond donor and acceptor ability, respectively. π* is a scale of dipolarity/ polarizability, and δ is a discontinuous polarizability correction E
DOI: 10.1021/acs.jced.6b00112 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Figure 5 illustrates the model structure and the number of neurons in the hidden layers. For instance, “‘abcdaabc’” is the genome demonstration for the water content in the aqueous phase. a, b, c, and d indicate the acid carbon chain length and fee mass fractions (water, acid, and ethylbenzene), respectively. The LLE prediction from the GMDH model is illustrated in Figure 6. Calculated GMDH tie-lines are listed in Table S6. Using the GMDH model, an average RMSD value of 2.93% was obtained for the studied systems.
4. CONCLUSIONS The liquid equilibrium data for the {water + formic, acetic, propionic, or butyric acids + ethylbenzene} systems were measured at a temperature of 298.15 K and atmospheric pressure. As a result, formic acid is more soluble in the aqueous phase and butyric acid is the most soluble in the extract phase. Biphasic region was found to be larger in the order of formic acid > acetic acid > propionic acid > butyric acid. Distribution coefficient of acids (D2) were increased by the increase of carbon chain length of the acid. The separation factors illustrate the capability of ethylbenzene for removal of the studied acids from water. Among the studied systems, the system containing butyric acid exhibits the highest average separation factor. The UNIQUAC and NRTL solution models were employed to correlate the experimental tie-lines. These thermodynamic models provide satisfactory results for the systems containing carboxylic acids. The Kamlet−Taft polarity equation was used to correlate distribution coefficients and separation factors. A good correlation was found using the solvatochromic model. The results determined by the GMDH model are close to the experimental data and the average RMSD value for the GMDH model was 2.93%.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.6b00112. Additional tables (PDF)
Figure 6. GMDH-type NN model-predicted mass fractions in comparison with experimental data: o, experimental points, and + , predicted points; (a) w11, (b) w21, (c) w13, and (d) w23.
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AUTHOR INFORMATION
Corresponding Author
term (for ethylbenzene δ = 0). The coefficients a, b, and c contain solute and solvent properties. The values of the solvatochromic parameters α, β, and π* are 0.00, 0.15, and 0.51, respectively.22 The correlated values for the D2 and S together with experimental data are summarized in Table 7. The parameters of the LSER model are given in Tables S3 and S4. As can be seen in these systems, the dispersion force is one of the most effective factors which contribute in the solute solvents interactions. 3.5. GMDH Model. In this study, a statistical approach to neural network model was developed using experimental equilibria data.37 The LLE data were correlated by the group method of data handling (GMDH) model. In other words, GMDH is known also as Polynomial Neural Networks, which can be expressed by the Volterra functional series.38,32 The overall normalized compositions of the systems are given in Table S5. The carbon chain length of the acid and mass fractions of feed (z1, water; z2, acid; and z3, ethylbenzene) were employed for the inputs of the GMDH model. The mass fractions of water and acid in the both phase were employed as the model outputs. The polynomial equations express the relationship between input and output variables that are presented in Table 8.
*E-mail:
[email protected]. Tel/Fax: +981333333262. Notes
The authors declare no competing financial interest.
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