Experimental Measurements and Correlations of Excess Molar

Article pubs.acs.org/jced

Experimental Measurements and Correlations of Excess Molar Enthalpies for the Binary and Ternary Mixtures of (Cyclohexane, 1,4-Dioxane and Piperidine) or (Cyclohexane, Morpholine and Piperidine) at 308.15 K and Atmospheric Pressure Farid Brahim Belaribi,*,† Ghénima Boukais-Belaribi,† Atika Dahmoun,† Aomar Dahmani,† Amir H. Mohammadi,‡,§ and Dominique Richon‡,§ †

Laboratoire de Thermodynamique et Modélisation Moléculaire, Faculté de Chimie, Université des Sciences et de la Technologie Houari Boumediene, BP 32 El Alia, 16111 Bab Ezzouar, Alger Algérie ‡ MINES ParisTech, CEP/TEPCentre Energétique et Procédés, 35 Rue Saint Honoré, 77305 Fontainebleau, France § Thermodynamics Research Unit, School of Engineering, University of KwaZulu-Natal, Howard College Campus, King George V Avenue, Durban 4041, South Africa ABSTRACT: Excess molar enthalpies for the binary and ternary mixtures of (cyclohexane, 1,4-dioxane, and piperidine) and (cyclohexane, morpholine, and piperidine) were measured using a Calvet microcalorimeter at 308.15 K and atmospheric pressure. The empirical equations of Redlich−Kister and Cibulka were used to correlate the experimental excess molar enthalpies for the binary and ternary mixtures, respectively. The capability of artificial neural network algorithm to model these data is also studied.

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INTRODUCTION Excess thermodynamic properties of liquid mixtures are of great interest for the convenient design of industrial processes and also to provide useful information on molecular interactions required for optimizing thermodynamic model development. Excess molar enthalpy, especially, is an important thermodynamic tool to explore the behavior of liquid mixtures. Compared with the experimental data reported in the literature for binary systems, the experimental data for ternary mixtures remain quite scarce. Ethers and amines represent not only two technically important classes of compounds but also two interesting families of molecules from a theoretical point of view. Cyclic ethers are used as solvents in the chemical industry and may also serve as fuel additives in the future. Morpholine is a highly versatile industrial chemical with several applications. For example, it is widely used in organic synthesis and is a chemical intermediate to prepare pharmaceutical compounds. Piperidine is a structural element of many pharmaceutical drugs and is often used as a solvent for its mild basic properties. The substitution of O or NH for CH2groups in a saturated cyclic organic molecule, as cyclohexane, often results in a change in its polarity and thus provides an interesting series of hexacyclic compounds, such as tetrahydropyran (a monoether), 1,4-dioxane (a diether), piperidine (a self-associated amine), and morpholine (a self-associated amino-ether). These compounds which are of similar size and © 2014 American Chemical Society

shape and which differ in one or two functional groups (NH, O and CH2) are of interest for investigating the excess properties of their cyclohexane containing mixtures. Continuing our previous study on mixtures containing the above cited cyclic compounds,1−3 we report here experimental excess molar enthalpies, at 308.15 K and atmospheric pressure, for cyclohexane + 1,4-dioxane + piperidine and cyclohexane + morpholine + piperidine ternary mixtures and 1,4-dioxane or morpholine + piperidine constituent binaries. The data, for the other constituent binaries, were previously reported.1−3 The binary and ternary experimental data were measured using a Calvet microcalorimeter and were correlated using the empirical equations of Redlich−Kister4 and Cibulka,5 respectively. The capability of an artificial neural network (ANN) algorithm6 as an alternative method to model these (binary and ternary) data was also investigated. A survey of the open literature shows that few excess molar enthalpy data, in the temperature range (283.15 to 298.15) K, were reported for the binary mixtures of cyclohexane with piperidine, 1,4-dioxane, and tetrahydropyran and for piperidine with tetrahydropyran.7−10 To the best of our knowledge, no Received: January 25, 2014 Accepted: April 16, 2014 Published: April 25, 2014 1629

dx.doi.org/10.1021/je500088z | J. Chem. Eng. Data 2014, 59, 1629−1635

Journal of Chemical & Engineering Data

Article

Table 2. Measured Molar Enthalpies of Mixing, HEm,12+3, and Excess Molar Enthalpies, HEm,123, for the Ternary Mixture of Cyclohexane (1) + 1,4-Dioxane (2) + Piperidine (3) at 308.15 K and Atmospheric Pressurea

Table 1. Experimental and Calculated or Predicted Excess Molar Enthalpies, HEm,jk, for x Morpholine or 1,4-Dioxane + (1 − x) Piperidine Binary Systems, at 308.15 K and Atmospheric Pressurea mole fraction expt HEm,jk x

J·mol−1

0.126 0.200 0.330 0.435 0.499 0.601 0.701 0.802 0.901

105 157 *222 253 264 *262 236 187 109

0.113 0.200 0.297 0.401 0.515 0.600 0.703 0.825 0.900

357 *550 698 787 *817 780 667 451 274

calculated HEm,jk (using eq 2) J·mol−1

calculated/ predicted HEm,jk (using ANN) 100 AD (using eq 2)

J·mol−1

x Morpholine + (1 − x) Piperidine 106 1.0 110 156 0.6 158 222 0.0 215 254 0.4 248 264 0.0 270 261 0.4 270 237 0.4 244 187 0.0 181 109 0.0 102 x 1,4-Dioxane + (1 − x) Piperidine 358 0.3 366 549 0.2 539 698 0.0 686 790 0.4 795 815 0.2 818 778 0.3 777 670 0.4 667 451 0.0 453 273 0.4 277

mole fraction

mole fraction

x1

x2

mole fraction x3 HEm,123/J·mol−1

100 AD (using ANN)

0.180 0.160 0.140 0.120 0.100 0.080 0.060 0.040

4.8 0.6 3.2 2.0 2.3 3.1 3.4 3.2 6.4

0.450 0.400 0.350 0.300 0.250 0.150 0.100

2.5 2.0 1.7 1.0 0.1 0.4 0.0 0.4 1.1

0.720 0.640 0.558 0.480 0.400 0.320 0.239 0.157

a

Standard uncertainties u are u(T) = 0.02 K and u(x) = 0.0002, and the relative expanded standard uncertainty Ur for the excess enthalpies is Ur(HE) = 0.03 (0.95 level of confidence). AD = |(experimental value − predicted value)/experimental value|. All of the experimental data were used for developing the ANN,6 except the star marked data which were used for validation.

HEm,12+3

HEm,123

J·mol−1

J·mol−1

b

x1/x2 = 0.25; = 1036 0.720 0.100 0.640 0.200 0.560 0.300 0.480 0.400 0.400 0.500 0.320 0.600 0.240 0.700 0.160 0.800 x1/x2 = 1; HEm,12/J·mol−1 = 1619b 0.450 0.100 0.400 0.200 0.350 0.300 0.300 0.400 0.250 0.500 0.150 0.700 0.100 0.800 x1/x2 = 4; HEm,12/J·mol−1 = 1160b 0.180 0.100 0.160 0.200 0.140 0.302 0.120 0.400 0.100 0.500 0.080 0.600 0.060 0.701 0.039 0.804

185 303 392 453 490 505 475 403

1117 1131 1120 1075 1007 915 785 608

124 186 229 261 278 324 309

1581 1481 1361 1234 1086 809 633

193 325 412 447 492 489 428 344

1235 1253 1221 1142 1070 953 774 572

a

Standard uncertainties u are u(T) = 0.02 K and u(x) = 0.0002, and the relative expanded standard uncertainty Ur for the excess enthalpies is Ur(HE) = 0.03 (0.95 level of confidence). bThe values of HEm,12 at specified constant ratios x1/x2 were calculated using eq 2.

excess enthalpy data were reported in the open literature for morpholine + piperidine and 1,4-dioxane + piperidine binary mixtures and cyclohexane + 1,4-dioxane + piperidine and cyclohexane + morpholine + piperidine ternary systems.

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EXPERIMENTAL SECTION Materials. Cyclohexane (CAS No. 110-82-7) and piperidine (CAS No. 110-89-4) were Merck products, whereas morpholine (CAS No. 110-91-8) and 1,4-dioxane (CAS No. 123-91-1) were supplied by Fluka. The mole fractions purities were all greater than 0.99. All these chemicals were used without further purification. Experimental Apparatus and Procedure. The experimental enthalpy data were measured at atmospheric pressure by means of a flow calorimeter (Calvet microcalorimeter, model C80, Setaram, France). The temperature was maintained constant at (308.15 ± 0.02) K. The mixtures were prepared by mass using a Mettler PE 160 balance (precision ± 0.1 mg), ensuring a probable uncertainty in the mole fraction less than 10−3. The apparatus and procedures were tested by determining excess enthalpies for the standard system benzene + cyclohexane, and the results were found to differ by less than 3 % from those of Marsh.11 The uncertainty in the excess molar enthalpy is less than 3 %, regarding the performances of the used flow calorimeter. As in our previous studies,1−3 the excess molar enthalpy HEm,12+3 was

Figure 1. Excess molar enthalpies, HEm,jk/(J·mol−1), for binary systems, at T = 308.15 K. Solid symbols, experimental data; hollow sysmbols, results using ANN:6 (∗,☆), {x cyclohexane + (1 − x) morpholine3}; (◆,◇), {x cyclohexane + (1 − x) 1,4-dioxane1}; (●,○), {x cyclohexane + (1 − x) piperidine2}; (■,□) {x 1,4-dioxane + (1 − x) piperidine}; (▲,△), {x morpholine + (1 − x) piperidine}. Solid lines: fit experimental results with the Redlich−Kister equation.4 1630



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Table 3. Measured Molar Enthalpies of Mixing, HEm,12+3, and Excess Molar Enthalpies, HEm,123, for the Ternary Mixture of Cyclohexane (1) + Morpholine (2) + Piperidine (3) at 308.15 K and Atmospheric Pressurea mole fraction x1 0.180 0.160 0.140 0.120 0.100 0.080 0.060 0.400 0.349 0.300 0.252 0.200 0.150 0.718 0.638 0.558 0.241

mole fraction

mole fraction

HEm,12+3

HEm,123

x2

x3

J·mol−1

J·mol−1

58 56 54 44 32 41 67

1034 921 813 694 573 473 393

19 18 16 10 13 63

1501 1321 1134 951 758 623

145 223 263 308

1328 1274 1183 705

x1/x2 = 0.25; HEm,12/J·mol−1 = 1085b 0.719 0.101 0.637 0.203 0.560 0.300 0.479 0.401 0.399 0.501 0.318 0.602 0.240 0.700 x1/x2 = 1; HEm,12/J·mol−1 = 1865b 0.400 0.200 0.349 0.301 0.300 0.400 0.252 0.495 0.200 0.600 0.150 0.700 x1/x2 = 4; HEm,12/J·mol−1 = 1316b 0.181 0.101 0.161 0.201 0.141 0.301 0.061 0.698

Figure 3. Excess molar enthalpies, HEm,123, for the ternary mixtures of {cyclohexane (1) + morpholine (2) + piperidine (3)}, at 308.15 K: (▲,△) x1/x2 = 0.25; (●,○) x1/x2 = 1; (■,□) x1/x2 = 4. Solid symbols, experimental data; hollow symbols, results using ANN.6 Solid lines: calculated values using Cibulka’s equation.5

ternary mixture was obtained from the relationship

a

Standard uncertainties u are u(T) = 0.02 K and u(x) = 0.0002, and the relative expanded standard uncertainty Ur for the excess enthalpies is Ur(HE) = 0.03 (0.95 level of confidence). bThe values of HEm,12 at specified constant ratios x1/x2 were calculated using eq 2.

E E E Hm,123 = Hm,12 + 3 + (1‐x3)Hm,12

(1)

where x3 represents the mole fraction of piperidine and HEm,12 is the excess molar enthalpy of the particular binary mixture.

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RESULTS AND DISCUSSION The experimental excess molar enthalpy data, for piperidine + 1,4-dioxane or morpholine binary mixtures are presently reported in Table 1, whereas those for cyclohexane containing binary mixtures were previously reported.1−3 The data for all these binary mixtures are plotted in Figure 1. The experimental results for cyclohexane + 1,4-dioxane + piperidine and cyclohexane + morpholine + piperidine ternary mixtures are reported in Tables 2 and 3 and also plotted in Figures 2 and 3, respectively. Binary Correlation of Data. The experimental binary data were correlated using the Redlich−Kister equation4 n ‐1 i E Hm, jk /J·mol = x(1 − x) ∑ A i(2x − 1) i=0

(2)

where i represents the number of coefficients Ai and x stands for mole fraction of the first component in the binary mixture. The coefficients Ai, obtained by an unweighted least-squares regression method, are summarized in Table 4 together with the standard deviation s. The results of the correlations are reported in Table 1 and plotted also in Figure 1. Ternary Correlation of Data. The experimental ternary data were correlated using the empirical Cibulka equation:5

Figure 2. Excess molar enthalpies, HEm,123, for the ternary mixtures of {cyclohexane (1) + 1,4-dioxane (2) + piperidine (3)}, at 308.15 K. (▲,Δ) x1/x2 = 0.25; (●,○) x1/x2 = 1; (∗,☆) x1/x2 = 4. Solid symbols, experimental data; hollow symbols, results using ANN.6 Solid lines: calculated values using Cibulka’s equation.5

E E Hm,123 /J·mol−1 = Hm,bin /J·mol−1

+ x1x 2(1 − x1 − x 2)(B0 + B1x1 + B2 x 2)

determined for several pseudobinary mixtures in which component 3 (piperidine) was added to binary mixtures of components 1 (cyclohexane) and 2 (1,4-dioxane or morpholine). For this purpose, binaries with fixed mole ratios, x1/x2, were prepared by mass. Then, excess molar enthalpy HEm,123 of the

(3)

HEm,bin,

where known as the binary contribution to the excess molar enthalpy, is given by E E E E Hm,bin = Hm,12 + Hm,13 + Hm,23

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Table 4. Values of Coefficients Ai in eq 2 and Standard Deviation s for the Binary Mixtures of Cyclohexane, 1,4-Dioxane, Morpholine, and Piperidine binary system b

cyclohexane (1) + morpholine (2) cyclohexane (1) + 1,4-dioxane (2)c cyclohexane (1) + piperidine (2)d 1,4-dioxane (1) + piperidine (2) morpholine (1) + piperidine (2)

A0

A1

A2

A3

A4

s/(J·mol−1)a

7465.9 6477.2 3383.4 3263.5 1054.2

778.6 300.3 678.9 −96.6 164.3

−620.0 1438.0 26.5 71.6 53.3

984.4 958.3 428.9 −385.5 0

2060.9 −1002.6 528.5 0 0

2.2 3.0 1.6 1.9 0.7

a s = [∑iN= 1(HEi,exp − HEi,calc)/(N − p)]1/2 where N is the number of experimental data and p is the number of parameters of eq 2. bFrom ref 3. cFrom ref 1. dFrom ref 2.

Table 5. Values of Coefficients Bi in eq 3, for {Cyclohexane (1) + 1,4-Dioxane (2) + Piperidine (3)} and {Cyclohexane (1) + Morpholine (2) + Piperidine (3)} Ternary Systems ternary system cyclohexane (1) + 1,4dioxane (2) + piperidine (3) cyclohexane (1) + morpholine (2) + piperidine (3)

B0

B1

B2

s/(J·mol−1)a

141.9

−4055.2

−3439. 6

35.2

1471.8

−5218.4

−5406.0

29.5

constant ratios x1/x2 (approximate ratio values were 0.25, 1, and 4) of mole fractions of cyclohexane and 1,4-dioxan (or morpholine) in their binary mixtures were interpolated using eq 2. The parameters Bi of eq 3, determined by an unweighted least-squares regression method, are summarized in Table 5. The results of the correlations for {cyclohexane (1) + 1,4dioxane (2) + piperidine (3)} and {cyclohexane (1) + morpholine (2) + piperidine (3)} ternary systems are reported in Tables 6 and 7 and plotted in Figures 2 and 3, along with experimental ternary data. Contour lines of constant HEm,123, calculated from the Cibulka equation,5 are plotted in Figures 4 and 5. Figure 1 shows that all the investigated binary mixtures are formed endothermally, which indicates that the interactions between like molecules are more important than those between unlike molecules. Also, these mixtures present symmetric excess enthalpy behavior. Cyclohexane + morpholine and morpholine + piperidine mixtures have the largest (1865 J·mol−1) and the lowest (264 J·mol−1) excess molar enthalpy, respectively. The

s = [∑i N= 1(HEi,exp − HEi,calc)/(N − p)]1/2 where N is the number of experimental data and p is the number of parameters of eq 3.

a

where HEm,jk is the excess enthalpy calculated from the correlated data of the j−k pair (eq 2) using the ternary mole fractions xj and xk. This simplest method assumes that there are no ternary effects; that is, the ternary excess enthalpy is just a sum of the binary enthalpies of mixing. The values of HEm,12 at three specified

Table 6. Comparison between Measured and Calculated/Predicted Values of Excess Molar Enthalpies, HEm,123, for {Cyclohexane (1) + 1,4-Dioxane (2) + Piperidine (3)} Ternary System at 308.15 K and Atmospheric Pressurea mole fraction

mole fraction

mole fraction

expt HEm,123

calcd HEm,123 (using Cibulka equation5)

calcd HEm,123 (using ANN6)

x1

x2

x3

J·mol−1

J·mol−1

100 AD (using Cibulka equation5)

J·mol−1

100 AD (using ANN6)

0.180 0.160 0.140 0.120 0.100 0.079 0.060 0.040 0.450 0.400 0.350 0.301 0.249 0.150 0.100 0.719 0.640 0.558 0.479 0.399 0.320 0.239 0.157

0.720 0.639 0.562 0.480 0.399 0.317 0.239 0.158 0.450 0.400 0.350 0.301 0.249 0.150 0.100 0.180 0.160 0.139 0.120 0.100 0.080 0.060 0.039

0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.100 0.200 0.300 0.400 0.500 0.700 0.800 0.100 0.200 0.302 0.400 0.500 0.600 0.701 0.804

1117 1131 *1120 1075 1007 915 785 *608 1581 1481 1361 1234 1086 809 633 1235 1253 *1221 1142 *1070 953 774 572

1090 1128 1136 1107 1035 920 770 567 1555 1486 1402 1299 1163 801 572 1226 1239 1216 1158 1060 922 740 520

2.4 0.3 1.4 3.0 2.8 0.5 1.9 6.7 1.6 0.3 3.0 5.3 7.1 1.0 9.6 0.7 1.1 0.4 1.4 0.9 3.3 4.4 9.1

1099 1123 1119 1089 1023 910 761 583 1553 1471 1369 1248 1101 804 634 1232 1248 1222 1161 1061 927 765 576

1.6 0.7 0.1 1.3 1.6 0.5 3.1 4.1 1.8 0.7 0.6 1.1 1.4 0.6 0.2 0.2 0.4 0.1 1.7 0.8 2.7 1.2 0.7

AD = |(experimental value − predicted value)/experimental value|. All of the experimental data were used for developing the ANN,6 except the star marked data which were used for validation. a

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Table 7. Comparison between Measured and Calculated/Predicted Values of Excess Molar Enthalpies, HEm,123, for {Cyclohexane (1) + Morpholine (2) + Piperidine (3)} Ternary System, at 308.15 K and Atmospheric Pressurea mole fraction

mole fraction

mole fraction

expt HEm,123

calcd HEm,123 (using Cibulka equation5)

calcd HEm,123 (using ANN6)

x1

x2

x3

J·mol−1

J·mol−1

100 AD (using Cibulka equation5)

J·mol−1

100 AD (using ANN6)

0.180 0.160 0.140 0.120 0.100 0.080 0.060 0.395 0.349 0.300 0.252 0.200 0.150 0.718 0.638 0.558 0.241

0.719 0.637 0.560 0.479 0.399 0.318 0.240 0.400 0.349 0.300 0.252 0.200 0.150 0.181 0.161 0.141 0.061

0.101 0.203 0.300 0.401 0.501 0.602 0.700 0.206 0.301 0.401 0.495 0.601 0.700 0.101 0.201 0.301 0.698

1034 921 813 694 573 *473 393 *1501 1321 1134 *951 758 623 1328 1274 *1183 705

995 905 819 725 624 512 394 1473 1300 1131 966 773 583 1310 1269 1206 666

3.8 1.7 0.7 4.5 8.9 8.2 0.3 1.9 1.6 0.3 1.6 2.0 6.4 1.4 0.4 1.9 5.5

1028 926 812 690 574 470 377 1515 1324 1135 960 781 605 1312 1279 1220 696

0.6 0.5 0.1 0.6 0.2 0.6 4.1 0.9 0.2 0.1 0.9 3.0 2.9 1.2 0.4 3.1 1.3

AD = | (experimental value − predicted value)/experimental value |. All of the experimental data were used for developing the ANN,6 except the star marked data which were used for validation. a

Figure 4. Lines of constant ternary excess molar enthalpies, HEm,123, calculated with the Cibulka equation5 for {cyclohexane (1) + 1,4dioxane (2) + piperidine (3)} ternary system at 308.15 K.

Figure 5. Lines of constant ternary excess molar enthalpies, HEm,123, calculated with the Cibulka equation5 for {cyclohexane (1) + morpholine (2) + piperidine (3)} ternary system at 308.15 K.

experimental values of excess molar enthalpy are in the following sequences, morpholine > 1,4-dioxane > piperidine, for the cyclohexane containing binary mixtures, cyclohexane > 1,4-dioxane > morpholine, for the piperidine containing binary mixtures, and cyclohexane > piperidine, for the 1,4-dioxane containing binary mixtures. Figures 2 and 3 show that the two ternary systems are also formed endothermally. The calculated HEm,123 from the Cibulka equation,5 for the two ternary systems, are almost the same as those calculated from binary contribution, HEm,bin, since the ternary contribution, HEm,123 − HEm,bin, does not exceed 4 %, as can be seen from the last columns of Tables 6 and 7. Our experimental excess enthalpy results, for the binary mixtures of cyclohexane with piperidine or 1,4-dioxane, were already compared to literature data7,8 in our previous papers.1−3 As far as

we know, no excess molar enthalpy data were reported in the open literature for the other binary and ternary systems investigated in this work. Artificial Neural Network Algorithm. Artificial neural network algorithms are known to be effective to model complex systems. These models have large numbers of computational units connected in a massively parallel structure and do not require an explicit formulation of the mathematical or physical relationships of the handled problem.2,3,6 The ANNs are first subjected to a set of training data consisting of input data together with corresponding outputs. After a sufficient number of training iterations, the neural network learns the patterns in the data fed to it and creates an internal model, which it uses to make predictions for new inputs.2,3,6 1633



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Table 8. Number of Neurons, Hidden Layers, Experimental Data and the Type of Activation Function Used in this Algorithma

Table 9. Number of Neurons, Hidden Layers, Experimental Data, and the Type of Activation Function Used in this Algorithma

layer

number of neurons

layer

number of neurons

1 2 3

2 5 1

1 2 3

2 5 1

a

a

Number of hidden layers = 1; number of data used for training (and testing) = 46; number of data used for validation = 9; type of activation function, tangent sigmoid; input neurons, mole fractions of cyclohexane (1) and 1,4-dioxane (2); output neuron, HEm,123/(RT) In developing the ANN,6 three data corresponding to HEm,123 = 0 for pure compounds were also considered.

Number of hidden layers = 1; number of data used for training (and testing) = 37; number of data used for validation = 10; type of activation function, tangent sigmoid; input neurons, mole fractions of cyclohexane (1) and morpholine (2); output neuron, HEm,123/(RT). In developing the ANN,6 three data corresponding to HEm,123 = 0 for pure compounds were also considered.

Feed-forward neural networks are the most frequently used and are designed with one input layer, one output layer, and hidden layers.2,3,6 The number of neurons in the input and output layers equals to the number of inputs and outputs, respectively.2,3,6 The accuracy of the model depends on the architecture and parameters of the neural network.2,3,6 To develop the ANN, the data sets are generally subdivided into three groups corresponding to the following three steps: training, testing, and validation.2,3,6 After partitioning the data sets, the training set is used to adjust the parameters. All synaptic weights and biases are first initialized randomly. The network is then trained; its synaptic weights are adjusted by an optimization algorithm until it correctly emulates the input/output mapping by minimizing the average root-mean-square error.2,3,6 The testing set is used during the adjustment of the network’s synaptic weights to evaluate the algorithms performance on the data not used for adjustment and stops the adjusting if the error on the testing set increases. Finally, the validation set measures the generalization ability of the model after the fitting process.2,3,6 Tables 8 and 9 report a summary of the feed-forward ANN used in this work along with the number of neurons, hidden layers, experimental data, and type of activation function. Tables 1, 6, and 7 compare the measured and calculated/ predicted values of excess molar enthalpies for the systems of (cyclohexane, 1,4-dioxane, and piperidine) or (cyclohexane, morpholine, and piperidine). Table 1 lists the experimental and calculated or predicted excess molar enthalpy, HEm,jk, only for the constituent binaries piperidine + morpholine and piperidine +1,4-dioxane. The results, for the other constituent binaries, were previously reported.1−3 The results concerning all binary systems are plotted in Figure 1. With the use of the ANN algorithm,6 the values of absolute average deviation, AAD, for the constituent binaries cyclohexane + morpholine, cyclohexane + piperidine and morpholine + piperidine of the first ternary system, are determined as (0.9, 1.1 and 3.2) %, respectively. The AAD values for the constituent binaries cyclohexane +1,4-dioxane, 1,4-dioxane + piperidine, and cyclohexane + piperidine of the second ternary system are (0.8, 1.0 and 2.3) %, respectively. All of the experimental data were used for developing the ANN, except the star marked data which were used for validation. With the use of the Redlich−Kister equation,4 the AAD values for cyclohexane + morpholine, cyclohexane + piperidine and morpholine + piperidine binary systems, are determined as (0.1, 0.2 and 0.3) %. All the experimental data were used for developing the Redlich−Kister equation.4 Tables 6 and 7 show a comparison between measured and calculated/predicted values of the excess molar enthalpy, HEm,123,

for cyclohexane + 1,4-dioxane + piperidine and cyclohexane + morpholine + piperidine ternary systems. For both ternary systems, the AAD value is calculated as 3.0 using Cibulka5 equation, whereas, the AAD value is calculated as 1.2 using ANN.6 All of the experimental data were used for developing the ANN,6 except the star marked data which were used for validation. For developing the Cibulka equation,5 all the experimental data were used. Considering not all the experimental data in Tables 2 and 6 were used to develop the ANN, the ANN can be regarded a useful tool for modeling these systems with encouraging results with respect to Cibulka’s equation5 as shown in Table 6. Normally, experimental data on ternary systems are enough to develop a reliable ANN, while both binary and ternary data are required for the Cibulka’s equation. This can be regarded as one of the advantages of ANN over the Cibulka equation.

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CONCLUSION We report the experimental excess molar enthalpies at 308.15 K and atmospheric pressure for cyclohexane + 1,4-dioxane + piperidine and cyclohexane + morpholine + piperidine ternary systems and piperidine + 1,4-dioxane or morpholine constituent binaries. The results, for the other constituent binaries of these ternary mixtures, were previously reported.1−3 The Redlich− Kister equation was used to correlate the binary data while the Cibulka equation was employed to correlate the ternary data. A feed-forward artificial neural network algorithm was then used to model satisfactorily the above-mentioned experimental data with respect to Cibulka’s equation. Furthermore, the ANN presented in the present work has shown good predictive power for both ternary and binary systems.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected], [email protected]. Tel./Fax: + (213) 21 248008. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Boukais-Belaribi, G.; Mohammadi, A. H.; Belaribi, F. B.; Richon, D. Excess Molar Enthalpies for the Binary and Ternary Mixtures of Cyclohexane, Tetrahydropyran and 1,4-Dioxane at 308.15 K and Atmospheric Pressure: Experimental Measurements and Correlations. J. Chem. Eng. Data 2009, 54, 2513−2516. (2) Belaribi, F. B.; Boukais-Belaribi, G.; Mohammadi, A. H.; Richon, D. Excess Molar Enthalpies for the Binary and Ternary Mixtures of Cyclohexane, Tetrahydropyran and Piperidine at 308.15 K and

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Atmospheric Pressure: Experimental Measurements and Correlations. J. Chem. Eng. Data 2010, 55, 303−307. (3) Belaribi, F. B.; Dahmoun, A.; Dahmani, O.; Boukais-Belaribi, G.; Mohammadi, A. H.; Richon, D. Experimental Measurements and Correlations of Excess Molar Enthalpies for the Binary and Ternary Mixtures of (Cyclohexane, Tetrahydropyran and Morpholine) or (Cyclohexane, 1,4-Dioxane and Morpholine) at 308.15 K and Atmospheric Pressure. J. Chem. Eng. Data 2010, 55, 2833−2839. (4) Redlich, O.; Kister, A. T. Algebraic Representation of Thermodynamic Properties and the Classification of Solutions. Ind. Eng. Chem. 1948, 40/2, 345−348. (5) Cibulka, I. Estimation of Excess Volume and Density of Ternary Liquid Mixtures of Nonelectrolytes from Binary Data. Collect. Czech. Chem. Commun. 1982, 47, 1414−1419. (6) Chapoy, A.; Mohammadi, A. H.; Richon, D. Predicting the Hydrate Stability Zones of Natural Gases Using Artificial Neural Networks. Oil Gas Sci. Technol. Rev. IFP 2007, 62/5, 701−706. (7) Moelwyn-Hughes, E. A.; Thorpe, P. L. The Physical and Thermodynamic Properties of Some Associated Solutions. I. Dielectric Constants and Heats of Mixing. Proc. R. Soc. 1964, 277A, 423−436. (8) Brocos, P.; Calvo, E.; Bravo, R.; Pintos, M.; Amigo, A.; Roux, A. H.; Roux-Desgranges, G. Heat Capacities, Excess Enthalpies, And Volumes of Mixtures Containing Cyclic Ethers. 3. Binary Systems {Tetrahydrofuran, Tetrahydropyran, 1,4-Dioxane, or 1,3-Dioxolane + Cyclohexane or Toluene}. J. Chem. Eng. Data 1999, 44, 67−72. (9) Lafuente, C.; Cea, P.; Dominguez, M.; Royo, F. M.; Urieta, J. S. Excess Molar Enthalpies of Cyclic Ethers with Cyclohexane or Chlorocyclohexane. J. Solution Chem. 2001, 30 (9), 795−805. (10) Woycicki, W.; Sadowska, K. W. Heat and Volumes of Mixing in the System of Cyclohexane or Methylcyclohexane with Piperidine or Alphapipecoline. Bull. Acad. Polym. Sci., Ser. Sci. Chim. 1968, 16, 365−70. (11) Marsh, K. N. Excess Enthalpy and Excess Volume of Binary Mixtures Containing Cyclohexane, Benzene and Tetrachloromethane. Int. DATA Ser. Sel. Data Mixtures, Ser. A 1973, 1, 1−3.

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