Measurement and Prediction of Excess Properties of Binary Mixtures

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

pubs.acs.org/jced

Measurement and Prediction of Excess Properties of Binary Mixtures Methyl Decanoate + an Even-Numbered n‑Alkane (C6−C16) at 298.15 K Niklas Haarmann,† Adriel Sosa,‡ Juan Ortega,‡ and Gabriele Sadowski*,† †

Laboratory of Thermodynamics, TU Dortmund, Emil-Figge-Str. 70, D-44227 Dortmund, Germany Grupo de Ingeniería Térmica e Instrumentación, Universidad de Las Palmas de Gran Canaria, Campus Universitario de Tafira, 35071 Las Palmas de Gran Canaria, Spain

‡

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S Supporting Information *

ABSTRACT: The molar excess volumes vE of the three binary mixtures methyl decanoate + n-alkane (n-dodecane, n-tetradecane, and n-hexadecane) were measured at temperature T = 298.15 K and atmospheric pressure using a vibrating tube densitometer. Furthermore, the molar excess enthalpies hE of the six binary mixtures methyl decanoate + n-alkane (n-hexane, n-octane, n-decane, n-dodecane, ntetradecane, and n-hexadecane) were measured at the same ambient conditions using a Calvet microcalorimeter. Both excess properties showed an increase with the increasing chain length of the n-alkane. Two equations of state, that is, a heterosegmental approach of Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT) and SAFT-γ Mie, were applied to predict the excess properties of the respective binary mixtures. Very satisfying agreement between the experimental data and modeling results was obtained for both equations of state.

1. INTRODUCTION Fatty-acid methyl esters and methyl alkanoates, in particular, are used as biodiesel. However, blends with conventional diesel fuel, that is, hydrocarbons such as n-alkanes, are mostly applied. Methyl alkanoates and n-alkanes are completely miscible because of their similar molecular structure and intermolecular interactions. However, they do by far not exhibit ideal behavior. Hence, the mixing properties and the corresponding excess properties of the binary mixtures methyl alkanoate + n-alkane are of high importance. Over the last decades, the Ortega group carried out extensive measurements with regard to the thermodynamic properties of binary mixtures methyl alkanoate + n-alkane. In particular, the measurements were focused on the molar excess volumes vE and the molar excess enthalpies hE of these mixtures.1−21 In these works, all methyl alkanoates from methyl ethanoate to methyl pentadecanoate and all n-alkanes from n-pentane to nheptadecane have been considered. For most methyl alkanoates (methyl ethanoate, methyl propanoate, methyl butanoate, methyl pentanoate, methyl hexanoate, methyl heptanoate, methyl nonanoate, methyl undecanoate, methyl tridecanoate, and methyl pentadecanoate), both excess properties were measured with each n-alkane from n-pentane to nheptadecane at temperature T = 298.15 K and atmospheric pressure. While for the binary mixtures of methyl alkanoates (methyl octanoate, methyl decanoate, methyl dodecanoate, and methyl tetradecanoate) with an odd-numbered n-alkane, both excess properties were measured at the same ambient © XXXX American Chemical Society

conditions, there still remains a lack of experimental excess volume and excess enthalpy data for the binary mixtures comprising an even-numbered n-alkane. Hence, the molar excess volumes vE and the molar excess enthalpies hE of some binary mixtures of methyl decanoate with an even-numbered nalkane were measured in this work. However, experimental measurements, especially excess enthalpy measurements, are cost-intensive and time-consuming. Thus, the predictive thermodynamic modeling of both excess properties is preferable. To the best of our knowledge, the excess properties of the binary mixtures methyl alkanoate + n-alkane have so far only been modeled in a predictive manner by Haarmann et al.22 Applying a heterosegmental approach of the Perturbed Chain Statistical Associating Fluid Theory23 (PC-SAFT), the molar excess volumes vE and the molar excess enthalpies hE of various binary mixtures methyl alkanoate + n-alkane were predicted in very good agreement with the experimental data.24 In particular, Haarmann et al. predicted the molar excess volumes vE and the molar excess enthalpies hE of the binary mixtures methyl decanoate + n-alkane comprising oddnumbered n-alkanes. Very good predictions of the respective excess properties were obtained. Although not used to describe the excess properties of the binary mixtures methyl alkanoate + n-alkane, the group-contribution equation of state (EOS) Received: February 25, 2019 Accepted: May 9, 2019

A

DOI: 10.1021/acs.jced.9b00185 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Chemicals Used for Experiments in This Work compound

CAS number

supplier

methyl decanoate n-hexane n-octane n-decane n-dodecane n-tetradecane n-hexadecane

110-42-9 110-54-3 111-65-9 124-18-5 112-40-3 629-59-4 544-76-3

Sigma-Aldrich Sigma-Aldrich Merck Merck Sigma-Aldrich Sigma-Aldrich Merck

pretreatment degassed, degassed, degassed, degassed, degassed, degassed, degassed,

SAFT-γ Mie25,26 also showed satisfying results with regard to the predictive description of the excess properties of some binary mixtures n-alkyl ethanoate + n-alkane.25 Consequently, both the heterosegmental approach of PC-SAFT and SAFT-γ Mie were used in this work to predict the molar excess volumes vE and the molar excess enthalpies hE of the binary mixtures methyl decanoate + an even-numbered n-alkane and were compared with the measured experimental data.

analytical method

drying drying drying drying drying drying drying

GC, GC, GC, GC, GC, GC, GC,

purity/wt %

Karl-Fischer Karl-Fischer Karl-Fischer Karl-Fischer Karl-Fischer Karl-Fischer Karl-Fischer

99.3 >99.0 99.5 99.1 >99.0 99.3 >99.0

Table 2. Densities d0i and Refractive Indices nD of Pure Chemicals Measured at T = 298.15 K and Ambient Pressure p = 0.988 bara −3 dexp 0i /kg·m

compound

2. EXPERIMENTS In this work, the molar excess volumes vE and the molar excess enthalpies hE of a series of binary mixtures methyl decanoate + an even-numbered n-alkane were experimentally determined at temperature T = 298.15 K (u(T) = 0.01 K) and atmospheric pressure. 2.1. Chemicals. All chemicals used were from SigmaAldrich and Merck with the highest commercial purity. However, all chemicals supplied by the manufacturers were pretreated before the experiments and their purity was checked by gas chromatography (GC) before and after each pretreatment. It was observed that the purity of the chemicals slightly improved by degassing in an ultrasonic bath for several hours and subsequent treatment with a molecular sieve (0.3 nm from SAFC). Furthermore, the water content of the chemicals was determined using a Karl-Fischer C-20 coulometric titrator and it was found to be lower than 110 ppm for all chemicals. In Table 1, the chemicals used in this work are listed along with their supplier and their purities after pretreatment. Additionally, the density d0i (DMA-58 from Anton Paar) and the refractive index nD (Abbe refractometer 320 from Zuzi) of each pure compound were measured at temperature T = 298.15 K and atmospheric pressure. A comparison to literature values is given in Table 2. Moreover, some other chemicals were used to calibrate and evaluate the performance of the apparatus. Water was bidistilled and had a conductivity lower than 1 μS and density d0i = 997.04 kg·m−3 at temperature T = 298.15 K. The auxiliary compounds n-nonane, benzene, and cyclohexane were obtained from Sigma-Aldrich with purities higher than 99.0 wt % and were also subjected to the same pretreatment described above. The measured densities at T = 298.15 K were d0i = 753.85 kg·m−3 for n-nonane, d0i = 873.58 kg·m−3 for benzene, and d0i = 773.91 kg·m−3 for cyclohexane. 2.2. Measurements. The densities d0i of all pure compounds as well as the densities dmix of each binary mixture were experimentally determined at temperature T = 298.15 K (u(T) = 0.01 K) and ambient pressure p = 0.988 bar (u(p) = 0.05 bar) using a vibrating tube densitometer DMA-58 from Anton Paar (u(d) = 0.02 kg·m−3). The temperature was automatically controlled using the Peltier effect. The calibration of the apparatus was carried out with water and n-nonane as previously recommended by the authors.29

methyl decanoate n-hexane

868.02 654.81

n-octane

698.45

n-decane

726.61

n-dodecane

745.20

n-tetradecane n-hexadecane

759.17 769.80

−3 dlit 0i /kg·m 6

868.19 654.8427 654.7128 698.6227 698.2928 726.3527 726.1328 745.1827 745.1928 759.3628 770.1028

nexp D /-

nlit D /-

1.4235 1.3725

1.42326 1.372327 1.372328 1.395127 1.395128 1.409727 1.409828 1.419527 1.419628 1.427128 1.432528

1.3955 1.4100 1.4197 1.4273 1.4323

a

Standard uncertainties (0.68 level of confidence): u(p) = 0.05 bar, u(T) = 0.01 K, u(nD) = 2 × 10−4, instrument uncertainty: u(d0i) = 0.02 kg·m−3, the combined expanded uncertainty (0.95 level of confidence, k = 2) is uc(d0i) = 1 kg·m−3.

For each binary mixture, both excess properties were measured at 19 equidistantly distributed mole fractions xmethyl decanoate of methyl decanoate from 0.05 to 0.95 (0.05 increment). Each sample was prepared by mass using a Mettler-Toledo balance (model AB104-S/FACT) with an accuracy of ±1 × 10−4 g leading to an uncertainty u(x) lower than 2 × 10−4 in regard to the mole fraction. As expressed in eq 1, the molar excess volume vE was calculated as the difference between the molar volume vmix of the binary mixture and that of the hypothetical ideal mixture using the molar volumes v0i of each pure component i. 2

v E = vmix −

∑ xiv0i = i=1

x1M1 + x 2M 2 − dmix

2

∑ xi i=1

Mi d 0i

(1)

The molar volumes vmix and v0i were obtained from the measured densities dmix and d0i, respectively, where Mi is the molecular mass of component i. The uncertainty u(vE) of the molar excess volume vE was calculated to be lower than 2 × 10−9 m3·mol−1. The molar excess enthalpies hE were measured directly using a Calvet microcalorimeter C80 from Setaram thermostated at T = 298.15 K (u(T) = 0.01 K). The calorimeter was calibrated with the Joule effect applying a specified power of an external supply for a predefined time interval. To evaluate the excess enthalpy measurements, the molar excess enthalpy hE of the binary mixture benzene + cyclohexane was measured as a reference since its molar excess enthalpy is well-known in the literature. The experimental data obtained in this work were in very good agreement with the reference correlation of Murakami and Benson.30 The percentage average relative deviation (%ARD) is 1.96% and the uncertainty u(hE) of the B



Article

Figure 1. Schematic representation of the modeling concept of the heterosegmental approach of PC-SAFT (a) and SAFT-γ Mie (b) for an arbitrary binary mixture methyl decanoate + n-alkane (here: n-octane). Within the heterosegmental approach of PC-SAFT, a methyl decanoate molecule comprises a tail and a head domain representing the n-nonylic residue and the functional methyl-ester head moiety, respectively. Within SAFT-γ Mie, a methyl decanoate molecule is subdivided into the distinct functional chemical groups, such as methyl (CH3), methanediyl (CH2), and carboxylate (COO) groups. It should be emphasized that the illustrated number of segments per molecule does not reflect the actual values listed in Table 3.

excess enthalpy hE was calculated to be lower than 2 J·mol−1. The graphical comparison between the experimental data of this work and the reference curve by Murakami and Benson30 is shown in the Supporting Information.

decanoate was described as comprising two different types of segments (heterosegmental) forming a nonpolar tail domain and a polar head domain as illustrated in Figure 1a.24 While the tail domain represents the n-nonylic residue, the head domain comprises the polar functional methyl-ester head moiety (−COOCH3). Due to the similarity of the n-nonylic residue to n-nonane, the tail domain of methyl decanoate was described using the PC-SAFT pure component parameters of n-nonane according to the heterosegmental approach of PCSAFT proposed by Haarmann et al.24 Applying this approach, the following contributions were considered for the dimensionless residual Helmholtz energy ãres

3. MODELING Both the molar excess volume vE and the molar excess enthalpy hE of a binary mixture were calculated at ambient conditions (T = 298.15 K and p = 1.013 bar) in this work. The molar excess volume vE was obtained by applying the first expression of eq 1. For this purpose, the molar volumes vmix and v0i were calculated as the reciprocal value of the respective liquid density ρ, which was iteratively determined at T = 298.15 K and p = 1.013 bar using eq 2. i ∂a ̃res yzz p = ρRT jjjj1 + ρ z ∂ρ z{ k

a ̃res = a ̃hc + a disp ̃ + a dipol ̃

where the hard-chain contribution ã represents the hardchain reference fluid in PC-SAFT, which is perturbed due to dispersive (ãdisp) and dipolar (ãdipol) perturbations. In Table 3, the PC-SAFT parameters used in this work are given for methyl decanoate and the considered n-alkanes.

(2) res

In eq 2, kB is the Boltzmann constant and ã is the dimensionless residual Helmholtz energy. Moreover, the molar excess enthalpy hE was expressed as

Table 3. PC-SAFT Pure Component Parameters of Methyl Decanoate (Heterosegmental) and the n-Alkanes (Homosegmental) Used within This Work

2

hE = hres −

∑ xih0resi i=1

res

(3)

hres 0i

where h and are the molar residual enthalpy of the mixture and the pure component i, respectively. Both were determined from i ∂a ̃res ∂a ̃res yzz −T hres = jjjjρ zRT ∂T z{ k ∂ρ

(5) hc

(4)

where R is the universal gas constant. As can be seen from eqs 2 and 4, both excess properties depend on the dimensionless residual Helmholtz energy ãres. In this work, the dimensionless residual Helmholtz energy was obtained applying two EOSs, namely a heterosegmental approach of PC-SAFT proposed by Haarmann et al.24 and SAFT-γ Mie.25,26 Within PC-SAFT,23,31 a molecule is modeled as a coarsegrained chain of tangentially bonded spherical segments. Each segment of type k of component i is described by the segment number mik, the segment diameter σik, and the dispersion energy uik. A modified square-well potential is taken into account to describe dispersive interactions. An additional dipole moment μik can be taken into account for dipolar interactions.32 While each n-alkane was modeled as a nonpolar chain of identical segments (homosegmental), methyl

pure component i

mik/-

σik/Å

uik·k−1 B /K

μik/D

refs

methyl decanoate head domain tail domain n-hexane n-octane n-decane n-dodecane n-tetradecane n-hexadecane

1.9045 4.2079 3.0576 3.8176 4.6627 5.3060 5.9002 6.6485

3.4597 3.8448 3.7983 3.8373 3.8384 3.8959 3.9396 3.9552

243.48 244.51 236.77 242.78 243.87 249.21 254.21 254.70

2.51

24 23 23 23 23 23 23 23

In contrast to PC-SAFT, a molecule is modeled comprising fused and spherical segments within SAFT-γ Mie25,26 as depicted in Figure 1b. A molecule is subdivided into the distinct functional chemical groups representing various chemical moieties, where each functional chemical group k is composed of a number of v*k identical segments. Here, v*k equals one for all groups. Each segment in turn is geometrically characterized by the shape factor Sk and the segment diameter σk. The interaction between two identical segments is described by a Mie potential with variable repulsive (λrk) and attractive (λak) exponents and the dispersion energy εk. As methyl decanoate and the n-alkanes comprise three different functional chemical groups, the SAFT-γ Mie group C



Article

Table 4. SAFT-γ Mie Group Parameters Used within This Work group k

vk*/-

Sk/-

σk/Å

λrk/-

λak/-

εk·k−1 B /K

refs

CH3 CH2 COO

1 1 1

0.57255 0.22932 0.65264

4.0773 4.8801 3.9939

15.050 19.871 31.189

6.000 6.000 6.000

256.77 473.39 868.92

25 25 25

deviations between predicted results (pred) and experimental data (exp) were considered as percentage average relative deviation (% ARD). The % ARD of an arbitrary thermodynamic property f was calculated as

parameters for the methyl (CH3), methanediyl (CH2), and carboxylate (COO) groups were taken from the literature25 and are given in Table 4. To describe dispersive interactions between two unlike segments k and l, the unlike dispersion energies εkl were used and are given in Table 5. Within SAFT-γ

N f dpred 1 data % ARD = ∑ 1 − exp ·100% Ndata d = 1 fd

Table 5. SAFT-γ Mie Unlike Group Dispersion Energies εkl· 25 k−1 B /K Used within This Work group k/group l

CH3

CH2

COO

CH3 CH2 COO

256.77 350.77 402.75

350.77 473.39 498.86

402.75 498.86 868.92

where Ndata is the number of data points.

4. RESULTS AND DISCUSSION In this work, the molar excess volumes vE of the three binary mixtures methyl decanoate + n-alkane (n-dodecane (C12), ntetradecane (C14), and n-hexadecane (C16)) were measured at temperature T = 298.15 K and ambient pressure p = 0.988 bar. The obtained experimental data are given in Table 6 and are also depicted in Figure 2a along with the experimental data of the molar excess volumes vE of the three binary mixtures methyl decanoate + n-alkane (n-hexane (C6), n-octane (C8), and n-decane (C10)), which were taken from the literature.10 Moreover, the molar excess enthalpies hE of the six binary mixtures methyl decanoate + n-alkane (n-hexane (C6), noctane (C8), n-decane (C10), n-dodecane (C12), n-tetradecane (C14), and n-hexadecane (C16)) were measured at the same

Mie, the expression for the dimensionless residual Helmholtz energy ãres reads a ̃res = a ̃mono + a chain ̃

(7)

(6)

mono

where ã accounts for the dispersive interactions between the Mie segments and ãchain is the contribution due to the formation of chains from the Mie segments. It should be emphasized that for the binary mixtures methyl decanoate + n-alkane no parameters were adjusted to the experimental data using both EOSs. Hence, all modeling results in this work are predictions of the two EOSs. Here,

Table 6. Experimental Densities dmix and Molar Excess Volumes vE of Binary Mixtures Methyl Decanoate (1) + n-Alkane (2) at Temperature T = 298.15 K and Pressure p = 0.988 bar Measured in This Worka x1/-

dmix/kg·m‑3

vE × 109/m3·mol‑1

0.0000 0.0500 0.1000 0.1503 0.1998 0.2500 0.3001

745.20 750.68 756.24 761.93 767.59 773.38 779.28

0 93 170 226 275 318 337

0.0000 0.0498 0.1001 0.1502 0.1998 0.2496 0.2999

759.17 763.35 767.69 772.18 776.73 781.41 786.24

0 106 198 259 314 358 397

0.0000 0.0499 0.0998 0.1501 0.2000 0.2497 0.3006

769.80 773.10 776.60 780.26 783.98 787.88 791.99

0 122 204 272 344 387 430

x1/-

dmix/kg·m‑3

vE × 109/m3·mol‑1

Methyl Decanoate (1) + n-Dodecane (2) 0.3506 785.27 353 0.3996 791.16 361 0.4497 797.22 365 0.5002 803.37 366 0.5500 809.54 353 0.5998 815.74 340 0.6499 822.04 321 Methyl Decanoate (1) + n-Tetradecane (2) 0.3501 791.21 417 0.4001 796.26 436 0.4498 801.43 440 0.5001 806.77 440 0.5498 812.19 431 0.5997 817.76 416 0.6499 823.51 390 Methyl Decanoate (1) + n-Hexadecane (2) 0.3497 796.11 457 0.4001 800.47 486 0.4500 804.97 496 0.4997 809.64 492 0.5502 814.55 482 0.5995 819.57 453 0.6501 824.85 433

x1/-

dmix/kg·m‑3

vE × 109/m3·mol‑1

0.6994 0.7495 0.7996 0.8493 0.8997 0.9496 1.0000

828.35 834.79 841.30 847.78 854.45 861.18 868.02

290 257 219 183 135 69 0

0.6999 0.7501 0.7990 0.8490 0.8992 0.9500 1.0000

829.37 835.45 841.48 847.78 854.34 861.12 868.02

361 315 270 227 155 88 0

0.6996 0.7497 0.7997 0.8489 0.8992 0.9494 1.0000

830.28 835.95 841.91 847.93 854.43 861.11 868.02

387 345 277 221 131 57 0

a Standard uncertainties (0.68 level of confidence): u(p) = 0.05 bar, u(T) = 0.01 K, u(x) = 2 × 10−4, u(vE) = 2 × 10−9 m3·mol−1, instrument uncertainty: u(dmix) = 0.02 kg·m−3, the combined expanded uncertainty (0.95 level of confidence, k = 2) is uc(dmix) = 1 kg·m−3.

D



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Figure 2. Molar excess volumes vE (a) and molar excess enthalpies hE (b) of a series of binary mixtures methyl decanoate + n-alkane (n-hexane (C6), n-octane (C8), n-decane (C10), n-dodecane (C12), n-tetradecane (C14), and n-hexadecane (C16)) at temperature T = 298.15 K and pressure p = 0.988 bar. The symbols represent the experimental data. Except from the molar excess volumes of the three binary mixtures methyl decanoate + n-alkane (n-hexane (C6), n-octane (C8), and n-decane (C10)),10 the experimental data were measured in this work.

Regarding the molar excess enthalpies hE in Figure 2b, positive values can be found over the entire mole fraction range for all binary mixtures investigated. Accordingly, external energy is required to overcome the polar interactions between the polar head moieties of the methyl decanoate molecules as the presence of n-alkane molecules leads to an increase of the distance between the polar head moieties of the methyl decanoate molecules. Thus, all mixtures are endothermic. Also, here, an increase of the molar excess enthalpy hE can be seen with the increasing chain length of the n-alkane. Similar to the explanation for the molar excess volume vE, the distance and interaction between the polar head moieties of the methyl decanoate molecules are increasingly disturbed with the increasing chain length of the n-alkane. Hence, the required external energy, namely a positive molar excess enthalpy hE, increases with the increasing chain length of the n-alkane. Here, experimental data of binary mixtures comprising an nalkane with an even carbon number Cn are shown. However, the experimental data of both the molar excess volumes vE and the molar excess enthalpies hE of the binary mixtures methyl decanoate + n-alkane comprising odd-numbered n-alkanes are reported in the literature by the Ortega group at T = 298.15 K and atmospheric pressure (vE: refs12, 16, 21 hE: refs6, 7, 16, 17, 19, 20). It should be emphasized, that these experimental data are consistent with the experimental results of this work as they fit very well in the aforementioned trends with the increasing chain length of the n-alkane for both excess properties. With the new experimental data of this work in hand, both excess properties were predicted using a heterosegmental approach of PC-SAFT proposed by Haarmann et al.24 and the group-contribution EOS SAFT-γ Mie.25,26 In Figure 3, the full predictions of the molar excess volumes vE of the six binary mixtures methyl decanoate + n-alkane (n-hexane (C6), noctane (C8), n-decane (C10), n-dodecane (C12), n-tetradecane (C14), and n-hexadecane (C16)) are shown for both the heterosegmental approach of PC-SAFT and SAFT-γ Mie. The respective % ARDs are given in Table 8. In Figure 3a, it can be seen that both EOSs qualitatively predict a compressive volumetric effect for the binary mixture methyl decanoate + nhexane, which is in line with the experimental data. Although the heterosegmental approach of PC-SAFT slightly overestimates and SAFT-γ Mie underestimates the molar excess volume vE, both EOSs capture the correct position of the minimum of the molar excess volume vE with respect to the molar composition. For the binary mixture methyl decanoate + n-octane [Figure 3b], the heterosegmental approach of PC-

ambient conditions. In Table 7, the obtained experimental data are listed, which are also shown graphically in Figure 2b. To the best of our knowledge, there are no experimental excess volume and excess enthalpy data available in the literature for the binary mixtures under study. From the experimental data in Figure 2a, an increase of the molar excess volume vE can be observed with the increasing chain length of the n-alkane. While the excess volume of the binary mixture methyl decanoate + n-hexane (C6) shows entirely negative values indicating a compressive volumetric effect, the excess volume of the four binary mixtures methyl decanoate + n-alkane (n-decane (C10), n-dodecane (C12), ntetradecane (C14), and n-hexadecane (C16)) present entirely positive values expressing expansive volumetric effects. The binary mixture methyl decanoate + n-octane (C8) marks the change of sign presenting a sinuous course regarding the excess volume, where for increasing the mole fraction of methyl decanoate the volumetric effect changes from expansive to compressive. These experimental findings can be explained as follows: nalkane molecules shorter than the n-nonylic residue of methyl decanoate easily fit between the methyl decanoate molecules and only marginally get in contact with the polar head moieties of the methyl decanoate molecules. Consequently, more molecules can arrange within a given volume, which in turn leads to a compressive volumetric effect. As already explained by Haarmann et al.,24 the sinuous course of the molar excess volume always occurs for binary mixtures methyl alkanoate + n-alkane where the chain length of the methyl alkanoate is slightly higher than that of the n-alkane. Regarding the binary mixtures methyl decanoate + n-alkane, the sinuous course occurs for the binary mixture comprising n-octane (C8). The molecular arrangement of pure n-octane is disturbed by the introduction of polar head moieties of the methyl decanoate molecules. This leads to an expansive volumetric effect. With increasing mole fraction of methyl decanoate, a small amount of n-alkane molecules can arrange between a high amount of nnonylic residues of methyl decanoate leading to a compressive volumetric effect for high mole fractions of methyl decanoate. If the chain length of the n-alkane (n-decane (C10), n-dodecane (C12), n-tetradecane (C14), and n-hexadecane (C16)) exceeds that of the n-nonylic residue of methyl decanoate, the molecular arrangement of the n-alkylic residues of the molecules of both compounds is disturbed by the polar head moieties of the methyl decanoate molecules causing expansive volumetric effects over the entire mole fraction range. E



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Table 7. Experimental Molar Excess Enthalpies hE of Binary Mixtures Methyl decanoate (1) + n-Alkane (2) at Temperature T = 298.15 K and Pressure p = 0.988 bar Measured in This Worka x1/0.0000 0.0479 0.0943 0.1448 0.1927 0.2477 0.3077 0.0000 0.0551 0.1035 0.1540 0.2078 0.2514 0.3088 0.0000 0.0469 0.0985 0.1523 0.2018 0.2537 0.3062 0.0000 0.0512 0.1129 0.1513 0.2021 0.2513 0.2990 0.0000 0.0633 0.0922 0.1577 0.1964 0.2580 0.3045 0.0000 0.0636 0.1131 0.1619 0.2010 0.2575 0.3056

hE/J·mol‑1

x1/-

hE/J·mol‑1

x1/-

Methyl Decanoate (1) + n-Hexane (2) 0 0.3542 526 0.7032 160 0.4059 523 0.7520 266 0.4574 504 0.8028 339 0.5055 473 0.8496 440 0.5557 448 0.9014 478 0.6037 412 0.9328 513 0.6531 368 1.0000 Methyl Decanoate (1) + n-Octane (2) 0 0.3584 598 0.7066 165 0.3990 616 0.7511 289 0.4514 610 0.8069 397 0.5051 600 0.8577 474 0.5555 573 0.9098 530 0.5990 549 0.9561 573 0.6570 483 1.0000 Methyl Decanoate (1) + n-Decane (2) 0 0.3563 652 0.7078 138 0.4008 670 0.7597 277 0.4543 678 0.8086 383 0.5058 665 0.8592 480 0.5498 652 0.9058 557 0.6017 609 0.9566 628 0.6524 558 1.0000 Methyl Decanoate (1) + n-Dodecane (2) 0 0.3572 682 0.7089 165 0.4051 709 0.7524 318 0.4473 720 0.8098 422 0.5033 719 0.8525 496 0.5502 708 0.9019 591 0.5952 682 0.9586 638 0.6520 629 1.0000 Methyl Decanoate (1) + n-Tetradecane (2) 0 0.3597 736 0.7089 208 0.3944 769 0.7542 298 0.4492 793 0.8009 451 0.5076 794 0.8477 529 0.5535 775 0.8974 634 0.6070 722 0.9455 682 0.6586 675 1.0000 Methyl Decanoate (1) + n-Hexadecane (2) 0 0.3584 771 0.7034 197 0.3980 814 0.7512 339 0.4494 827 0.8015 449 0.4955 828 0.8493 539 0.5479 816 0.8995 641 0.5983 786 0.9495 710 0.6494 739 1.0000

resulting in a % ARD of 560.0%. It should be added that SAFT-γ Mie does not qualitatively predict the occurrence of a sinuous course for the molar excess volume of the binary mixture methyl decanoate + n-nonane. Regarding the molar excess volumes vE of the four binary mixtures methyl decanoate + n-alkane (n-decane (C10), ndodecane (C12), n-tetradecane (C14), and n-hexadecane (C16)), both EOSs not only correctly predict the expansive volumetric effects but are also in very good agreement with the experimental data. Comparing the predictions of both EOSs in Figure 3c−f and the % ARDs in Table 8, slightly better agreement with the experimental data can be observed for the heterosegmental approach of PC-SAFT since SAFT-γ Mie underestimates the molar excess volume vE of the four binary mixtures. PC-SAFT very accurately predicts the positions of the maxima of the molar excess volume vE with respect to the mole fraction of methyl decanoate, whereas the maxima predicted with SAFT-γ Mie are shifted to higher mole fractions of methyl decanoate when compared to the experimental data of the two binary mixtures methyl decanoate + n-alkane (ntetradecane (C14) and n-hexadecane (C16)) [Figure 3e,f]. However, overall, it can be stated that both EOSs capture the aforementioned increase of the molar excess volume vE with the increasing chain length of n-alkane in a fully predictive manner. For both EOSs, the full predictions of the molar excess enthalpies hE of the same six binary mixtures methyl decanoate + n-alkane (n-hexane (C6), n-octane (C8), n-decane (C10), ndodecane (C12), n-tetradecane (C14), and n-hexadecane (C16)) are depicted in Figure 4 and the respective % ARDs are tabulated in Table 8. Both the heterosegmental approach of PC-SAFT and SAFT-γ Mie predict an endothermic mixing behavior for all mixtures and capture the aforementioned increase of the molar excess enthalpy hE with the increasing chain length of the n-alkane. While the heterosegmental approach of PC-SAFT very accurately predicts the molar excess enthalpies hE of the three binary mixtures methyl decanoate + n-alkane (n-octane (C8), n-decane (C10), and n-dodecane (C12)), minor deviations can be found for the three binary mixtures methyl decanoate + nalkane (n-hexane (C6), n-tetradecane (C14), and n-hexadecane (C16)). Moreover, the position of the maxima of the molar excess enthalpies hE with respect to the molar composition is in remarkable agreement with the experimental maxima for all mixtures investigated here. Although the predictions of SAFT-γ Mie underestimate the experimental molar excess enthalpies hE for all six binary mixtures, the % ARDs are still lower than 25%, which is remarkable for a predictive description. Admittedly, the position of the maxima of the molar excess enthalpies hE with respect to the molar composition is shifted to slightly higher mole fractions of methyl decanoate when compared to the experimental maxima. It should clearly be emphasized that the descriptions of both excess properties are full predictions of the two EOSs and that no model parameter was adjusted to any experimental data of this work. For each thermodynamic model, an appropriate description of the very sensitive excess properties is a stringent test. Hence, the modeling results of both the heterosegmental approach of PC-SAFT and SAFT-γ Mie are very satisfying although the % ARD in Table 8 is greater than 20%.

hE/J·mol‑1 322 284 227 167 116 73 0 433 382 298 223 147 70 0 475 416 340 254 170 63 0 553 488 399 306 203 82 0 609 550 480 396 283 177 0 681 608 528 428 296 153 0

a Standard uncertainties (0.68 level of confidence): u(p) = 0.05 bar, u(T) = 0.01 K, u(x) = 2 × 10−4, relative standard uncertainties: ur(hE) = 0.02.

SAFT fully predicts the occurrence of the sinuous course of the molar excess volume vE. Despite a % ARD of 139.3% (Table 8), a remarkably good agreement with the experimental data can be seen in Figure 3b. In contrast, SAFT-γ Mie predicts an entirely negative course for the molar excess volume vE F



Article

Figure 3. Molar excess volumes vE of a series of binary mixtures methyl decanoate + n-alkane (n-hexane (a), n-octane (b), n-decane (c), ndodecane (d), n-tetradecane (e), and n-hexadecane (f)) at temperature T = 298.15 K and atmospheric pressure. The symbols represent the experimental data (ref 10 and this work). The modeling results of the heterosegmental approach of PC-SAFT and SAFT-γ Mie are shown as solid and dashed lines, respectively.

Table 8. % ARDs of the Modeling Results of the Molar Excess Volumes vE and the Molar Excess Enthalpies hE of a Series of Binary Mixtures Methyl Decanoate (1) + n-Alkane (2) at Temperature T = 298.15 K and Atmospheric Pressure Obtained in This Work excess volume vE

excess enthalpy hE

% ARD binary mixture methyl methyl methyl methyl methyl methyl

decanoate decanoate decanoate decanoate decanoate decanoate

+ + + + + +

n-hexane n-octane n-decane n-dodecane n-tetradecane n-hexadecane

% ARD

refs

PC-SAFT

SAFT-γ Mie

10 10 10 this work this work this work

27.27 139.3 26.94 12.74 8.55 11.15

35.52 560.0 9.55 19.07 17.00 20.13

5. CONCLUSIONS In this work, the molar excess volumes vE and the molar excess enthalpies hE of a series of binary mixtures methyl decanoate + n-alkane were measured at temperature T = 298.15 K and ambient pressure p = 0.988 bar using a vibrating tube densitometer and a Calvet microcalorimeter, respectively. For both excess properties, an increase with the increasing chain length of the n-alkane could be found when comparing the experimental data of the binary mixtures methyl decanoate + nalkane for each excess property.

refs this this this this this this

work work work work work work

PC-SAFT

SAFT-γ Mie

22.49 4.23 5.43 4.18 10.37 6.74

23.49 21.22 19.88 20.13 24.49 24.03

A heterosegmental approach of PC-SAFT and SAFT-γ Mie were applied to fully predict the molar excess volumes vE and the molar excess enthalpies hE of the six binary mixtures methyl decanoate + n-alkane (n-hexane, n-octane, n-decane, ndodecane, n-tetradecane, and n-hexadecane). Both EOSs captured the experimentally observed increase with the increasing chain length of the n-alkane for both excess properties. Overall, very good agreement with the experimental data was found using both EOSs. However, the heterosegmental approach of PC-SAFT [% ARD (vE) < 28% G



Article

Figure 4. Molar excess enthalpies hE of a series of binary mixtures methyl decanoate + n-alkane (n-hexane (a), n-octane (b), n-decane (c), ndodecane (d), n-tetradecane (e), and n-hexadecane (f)) at temperature T = 298.15 K and atmospheric pressure. The symbols represent the experimental data measured in this work. The modeling results of the heterosegmental approach of PC-SAFT and SAFT-γ Mie are shown as solid and dashed lines, respectively.

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(excluding n-octane); % ARD (hE) < 23%] showed overall lower % ARDs in comparison with SAFT-γ Mie [% ARD (vE) < 36% (excluding n-octane); % ARD (hE) < 25%].

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ACKNOWLEDGMENTS This work was performed as part of the Collaborative Research Center Transregio 63 “Integrated Chemical Processes in Liquid Multiphase Systems” (subproject A9). Financial support by the Deutsche Forschungsgemeinschaft (DFG: German Research Foundation) is gratefully acknowledged (TRR 63). Moreover, special gratitude is expressed to J.O. and all co-workers for giving N.H. the opportunity to work and live in the inspiring surroundings of Las Palmas de Gran Canaria.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.9b00185.

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Comparison of the excess enthalpy measurements of the binary mixture benzene + cyclohexane performed in this work to the reference data of Murakami and Benson (PDF)

ABBREVIATIONS % ARD percentage average relative deviation EOS equation of state GC gas chromatography PC-SAFT perturbed chain statistical associating fluid theory

AUTHOR INFORMATION

■

Corresponding Author

*E-mail: [email protected]. Phone: +49 2317552635.

LIST OF SYMBOLS

Roman Symbols

ORCID

ã

Juan Ortega: 0000-0002-8304-2171 Gabriele Sadowski: 0000-0002-5038-9152

Cn d f

Notes

The authors declare no competing financial interest. H

dimensionless Helmholtz energy per number of molecules (-) carbon number (-) density (kg·m−3) arbitrary thermodynamic property (-) DOI: 10.1021/acs.jced.9b00185 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article

molar enthalpy (J·mol−1) Boltzmann constant (J·K−1) number of segments (-) refractive index (-) number of data points (-) pressure (bar) universal gas constant (J·mol−1·K−1) shape factor (-) temperature (K) dispersion energy (PC-SAFT) (J) molar volume (cm3·mol−1) mole fraction (-)

h kB m nD Ndata p R S T u v x

(7) Ortega, J. HE {xCH3(CH2)v−1CO2CH3 (v = 5 or 6 or ... or 14) + (1 − x)CH3(CH2)11CH3, 298.15 K}. J. Chem. Thermodyn. 1991, 23, 327−331. (8) Ortega, J. Excess Enthalpies of (a Methyl Alkanoate + n-Nonane or n-Undecane) at the Temperature 298.15 K. J. Chem. Thermodyn. 1991, 23, 1057−1061. (9) Ortega, J. Excess Molar Enthalpies at the Temperature 298.15 K of (a Methyl n-Alkanoate + Pentane or Heptane). J. Chem. Thermodyn. 1992, 24, 1121−1125. (10) Ortega, J. Thermodynamic Properties of Non-Reacting Binary Systems of Organic Substances. Int. DATA Ser., Sel. Data Mixtures, Ser. A 2004, 32, 61−75. (11) Ortega, J. Thermodynamic Properties of Non-Reacting Binary Systems of Organic Substances. Int. DATA Ser., Sel. Data Mixtures, Ser. A 2004, 32, 76−87. (12) Ortega, J.; Alcalde, R. Determination and Algebraic Representation of Volumes of Mixing at 298.15 K of Methyl nAlkanoates (from Ethanoate to n-Pentadecanoate) with n-Pentadecane. Fluid Phase Equilib. 1992, 71, 49−62. (13) Ortega, J.; Gonzalez, E. Thermodynamic Properties of (a Methyl Ester + an n-Alkane). III. hE and vE for {xCH3(CH2)u1CO2CH3 (u=1 to 6) + (1-x)CH3(CH2)8CH3}. J. Chem. Thermodyn. 1993, 25, 495−501. (14) Ortega, J.; Gonzalez, E. Thermodynamic Properties of (a Methyl Ester + an n-Alkane). V. hE and vE for {xCH3(CH2)u1CO2CH3(u = 1 to 6) + (1-x)CH3(CH2)12CH3}. J. Chem. Thermodyn. 1993, 25, 1083−1088. (15) Ortega, J.; Gonzalez, E.; Matos, J. S.; Legido, J. L. Thermodynamic Properties of (a Methyl Ester + an n-Alkane) I. hE and vE for {xCH3(CH2)u−1CO2CH3 (u = 1 to 6) + (1 − x)CH3(CH2)6CH3}. J. Chem. Thermodyn. 1992, 24, 15−22. (16) Ortega, J.; Legido, J. L. Application of the UNIFAC and NittaChao Models to Describing the Behavior of Methyl Ester/Alkane Mixtures, and Experimental Data for (Methyl n-Alkanoates + nHeptadecane) Binary Mixtures. Fluid Phase Equilib. 1994, 95, 175− 214. (17) Ortega, J.; Legido, J. L.; Fernández, J.; Pías, L.; Paz Andrade, M. I. Measurements and Analysis of Excess Enthalpies of Ester + nAlkane Using the UNIFAC Model. Ber. Bunsen-Ges. Phys. Chem. 1991, 95, 128−135. (18) Ortega, J.; Matos, J. S.; Peña, J. A. Enthalpies of Mixing at 298.15 K of a Methyl Alkanoate (from Acetate to Pentanoate) with nAlkanes (n-Tridecane and n-Pentadecane). Thermochim. Acta 1990, 168, 121−126. (19) Ortega, J.; Matos, J. S.; Peña, J. A. Excess Molar Enthalpies of Methyl Alkanoates + n-Nonane at 298.15 K. Thermochim. Acta 1990, 160, 337−342. (20) Ortega, J.; Matos, J. S.; Peña, J. A. Experimental and Predicted Mixing Enthalpies for Several Methyl n-Alkanoates with n-Pentane at 298.15 K. Thermochim. Acta 1992, 195, 321−327. (21) Postigo, M. A.; Garcia, P. H.; Ortega, J.; Tardajos, G. Excess Molar Volumes of Binary Mixtures Containing a Methyl Ester (Ethanoate to Tetradecanoate) with Odd n-Alkanes at 298.15 K. J. Chem. Eng. Data 1995, 40, 283−289. (22) Haarmann, N.; Enders, S.; Sadowski, G. Heterosegmental Modeling of Long-Chain Molecules and Related Mixtures using PCSAFT: 1. Polar Compounds. Ind. Eng. Chem. Res. 2019, 58, 2551− 2574. (23) Gross, J.; Sadowski, G. Perturbed-Chain SAFT: An Equation of State Based on a Perturbation Theory for Chain Molecules. Ind. Eng. Chem. Res. 2001, 40, 1244−1260. (24) Haarmann, N.; Enders, S.; Sadowski, G. Heterosegmental Modeling of Long-Chain Molecules and Related Mixtures using PCSAFT: 1. Polar Compounds. Ind. Eng. Chem. Res. 2019, 2551−2574. (25) Papaioannou, V.; Lafitte, T.; Avendano, C.; Adjiman, C. S.; Jackson, G.; Muller, E. A.; Galindo, A. Group Contribution Methodology Based on the Statistical Associating Fluid Theory for Heteronuclear Molecules Formed from Mie Segments. J. Chem. Phys. 2014, 140, No. 054107.

Greek Symbols

ε λa λr μ v* ρ σ

dispersion energy (SAFT-γ Mie) (J) attractive exponent of Mie potential (-) repulsive exponent of Mie potential (-) dipole moment (D) number of identical segments per group (-) number density (m−3) segment diameter (Å)

Subscript

0i i k,l mix

pure component index component index type of segment mixture

Superscript

chain disp dipol E exp hc lit mono pred res

■

chain dispersion dipole excess experimental hard chain literature Mie segment−Mie segment interaction predicted residual

REFERENCES

(1) Garcia, P. H.; Postigo, M. A.; Ortega, J. Thermodynamic Properties of (a Methyl Ester + an n-Alkane). VIII. vE xCH3(CH2)u−3COOCH3+ (1−x)CH3(CH2)v−2CH3 with u= 6 to 16 and v = 5 to 13. J. Chem. Thermodyn. 1995, 27, 1249−1260. (2) Gonzalez, E.; Ortega, J. Thermodynamic Properties of (a Methyl Ester + an n-Alkane). IV. hE and vE for {xCH3(CH2)u-1CO2CH3 (u = 1 to 6) + (1-x)CH3(CH2)10CH3}. J. Chem. Thermodyn. 1993, 25, 801−806. (3) Gonzalez, E.; Ortega, J. Thermodynamic Properties of (a Methyl Ester + an n-Alkane) VI. hE and vE for {xCH3(CH2)u-1CO2CH3 (u = 1 to 6) + (1 - x)CH3(CH2)14CH3}. J. Chem. Thermodyn. 1994, 26, 41−47. (4) Gonzál ez, E.; Ortega, J.; Matos, J. S.; Tardajos, G. Thermodynamic Properties of (a Methyl Ester + an n-Alkane). II. hE and vE for {xCH3(CH2)u-1CO2CH3 (u = 1 to 6) + (1x)CH3(CH2)4CH3}. J. Chem. Thermodyn. 1993, 25, 561−568. (5) González, E.; Ortega, J.; Postigo, M. A.; Legido, J. L. Thermodynamic Properties of (a Methyl ester + an n-Alkane) VII. hE and vE for {xCH3(CH2)2u - 1CO2CH3 + (1 - x)CH3(CH2)2vCH3} for u = 4 to 7 and v = 2 to 7. J. Chem. Thermodyn. 1994, 26, 1301−1315. (6) Ortega, J. Measurements of Excess Enthalpies of {a Methyl nAlkanoate (from n-Hexanoate to n-Pentadecanoate) + n-Pentadecane} at 298.15 K. J. Chem. Thermodyn. 1990, 22, 1165−1170. I



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J


Measurement and Prediction of Excess Properties of Binary Mixtures

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