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Density, Viscosity, Speed of Sound, Bulk Modulus, Surface Tension, and Flash Point of Binary Mixtures of Butylbenzene + Linear Alkanes (n‑Decane, n‑Dodecane, n‑Tetradecane, n‑Hexadecane, or n‑Heptadecane) at 0.1 MPa Dianne J. Luning Prak,*,† Bridget G. Lee,† Jim S. Cowart,‡ and Paul C. Trulove† †

Chemistry Department, and ‡Mechanical Engineering Department, United States Naval Academy 572M Holloway Road, Annapolis, Maryland 21402, United States S Supporting Information *

ABSTRACT: This work reports physical property measurements of binary mixtures of butylbenzene with n-decane, n-dodecane, n-tetradecane, n-hexadecane, or n-heptadecane. Densities and viscosities were measured at temperatures from (293.15 to 373.15) K, and speeds of sound were measured at temperatures from (293.15 to 333.15) K, except for those of n-heptadecane, which were measured starting at 303.15 K. Densities increased with increasing mole fraction of butylbenzene. Excess molar volumes were positive and increased with increasing alkane chain length, except for those of heptadecane which were similar to those of n-hexadecane. Analysis of excess molar volumes using the Prigogine−Flory−Patterson model showed that the interaction term contributed more to excess molar volume than the free volume or P* term. As the mole fraction of butylbenzene increased, speeds of sound increased for n-decane and n-dodecane mixtures but decreased for other alkane mixtures to values below those of both pure components before increasing again. Viscosities decreased as the mole fraction of butylbenzene increased except for those of some n-decane mixtures, which were below those of butylbenzene and n-decane. Viscosity mole fraction data were fit using the three-body McAllister model. Bulk moduli and surface tension increased with increasing mole fraction of butylbenzene, and flash points fell between those of the individual components. These mixtures can be used as surrogates for petroleum-based fuels.

1. INTRODUCTION Decane, dodecane, hexadecane (cetane), and n-butyl benzene are among the model compounds used to study the combustion of petroleum-based jet fuels and diesel fuels.1−4 Model compounds are chosen because petroleum-based fuels can contain hundreds of compounds each of which can participate in potentially thousands of chemical reactions; the combustion kinetics of each component and the interactions of the components during the reactions may not be fully known; and the computation of the kinetics of all these reactions (especially multicomponent blends) is challenging. The combustion of fuels in an engine can be broken down into chemical reaction processes and physical processes. Physical processes during fuel injection include atomization, entrainment, vaporization, and mixing.5 Examining the combustion of individual fuel components can help determine the contribution of physical processes to engine combustion behavior. Caton et al.5 reported that the contributions of physical delay and chemical delay to ignition delay were similar for n-hexane and 1-hexene, but that physical delay was much smaller than chemical delay for cylcohexane. Hamilton et al.6 modeled the ignition delay measured in a Humvee engine to determine the contributions of chemical and physical ignition delay to overall ignition delay of n-hexadecane. They found that chemical delay contributed more to overall ignition delay than did the physical delay. Studies of the combustion behavior of This article not subject to U.S. Copyright. Published XXXX by the American Chemical Society

model compounds has also led to useful chemical kinetic models (both reduced and detailed). For example, researchers have studied the combustion of butylbenzene in air mixtures and reported more than 50 hydrocarbon radicals formed by hydrogen abstraction and oxidation at the various carbons along the butyl chain as well as on the phenyl ring itself.7−9 Many studies have also been done to determine the chemical kinetics involved in linear alkane oxidation.4,10−12 Mixtures of models compounds, often called surrogate mixtures, are useful for building an understanding of the physical properties and chemical reactions of complex fuel mixtures. Surrogate fuels can provide a baseline for engine performance, and they can help in making predictions for the more complex fuel.13−16 Cowart et al.17 modeled the ignition delay measured in a Yanmar L48 V direct-injection diesel engine with a unit pump system to determine the contributions of chemical and physical ignition delay to the overall ignition delay of mixtures of isocetane and cetane, which are surrogate mixtures for hydroprocessed renewable diesel fuel from algae. They found that for cetane, the physical and chemical ignition delays are similar, but as the amount of isocetane increased, Received: June 29, 2016 Accepted: December 16, 2016

A

DOI: 10.1021/acs.jced.6b00542 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Chemical Information

a

chemical Name

CAS number

molar mass (g/mol)a

source/lot number

mole fraction purity

analysis method

butylbenzene (C12H14) n-decane (C10H22) n-dodecane (C12H26) n-tetradecane (C14H30) n-hexadecane (C16H34) n-heptadecane (C17H36)

104-51-8 124-18-5 112-40-3 629-59-4 544-76-3 629-78-7

134.22 ± 0.01 142.28 ± 0.01 170.33 ± 0.01 198.39 ± 0.01 226.44 ± 0.02 240.47 ± 0.02

TCI/Y3XBD Aldrich/MKBL7589 V Aldrich/MKBN7489 V Aldrich/STBD3071 V Alfa Aesar/10177143 Aldrich/STBF5986 V

0.999 0.994 0.995 0.997 0.994 0.999

GCb GCb GCb GCb GCb GCb

Calculated using values in ref 36. bGas−liquid chromatography, as specified in the Certificates of Analysis provided by the chemical suppliers.

Table 2. Comparison of the Measured Densities of Butylbenzene, n-Decane, n-Dodecane, n-Tetradecane, n-Hexadecane, and n-Heptadecane with Literature Valuesa this studya /kg·m−3

lit./kg·m−3

293.15

860.51

303.15

852.49

859.50 ± 0.60 , 860.052 , 860.15 ± 0.35m, 860.25 ± 0.30m, 861.26e 851.3b, 852.16 ± 0.10m, 852.23e, 852.428c, 852.43 ± 0.50m 844.6b, 844.82 ± 0.51m, 845.172c 837.00 ± 0.67m, 838.509c 729.95 ± 0.10d, 730.41 ± 0.2%g 722.3k, 722.32 ± 0.09d, 722.64 ± 0.2%g 714.67 ± 0.08d, 714.7k, 714.87 ± 0.2%g 706.98 ± 0.09d, 707.08 ± 0.2%g 699.25 ± 0.09d, 699.26 ± 0.2%g 691.40 ± 0.2%g, 691.45 ± 0.10d 683.49 ± 0.2%g, 683.59 ± 0.13d 675.52 ± 0.2%g, 675.64 ± 0.15d 667.47 ± 0.2%g, 667.59 ± 0.18d 749.09 ± 0.28d, 749.37 ± 0.2%g, 749.89 ± 0.5f 741.64 ± 0.5f, 741.70 ± 0.29d, 741.96 ± 0.2%g 734.34 ± 0.30d, 734.35 ± 0.5f, 734.58 ± 0.2%g 726.99 ± 0.32d, 727.04 ± 0.5f, 727.18 ± 0.2%g 719.64 ± 0.33d, 719.69 ± 0.5f, 719.78 ± 0.2%g 712.2 ± 0.5f, 712.27 ± 0.34d, 712.37 ± 0.2%g 704.7 ± 0.5f, 704.88 ± 0.35d, 704.92 ± 0.2%g

T/K butylbenzene

n-decane

n-dodecane

313.15

844.43

323.15 293.15

836.34 729.87

303.15

722.31

313.15

714.69

323.15

707.02

333.15

699.28

343.15

691.5

353.15

683.6

363.15

675.6

373.15

667.5

293.15

748.79

303.15

741.54

313.15

734.25

323.15

726.94

333.15

719.59

343.15

712.2

353.15

704.7

m

c

n-tetradecane

n-hexadecane

n-heptadecane

T/K

this studya /kg·m−3

lit./kg·m−3

363.15

697.2

373.15

689.6

293.15

762.71

303.15 313.15 323.15

755.65 748.58 741.50

333.15

734.40

343.15 353.15 363.15 373.15 293.15

727.5 720.3 713.1 705.8 773.52

303.15

766.58

313.15

759.66

323.15

752.74

333.15

745.82

343.15

738.8

353.15 363.15 373.15 303.15 313.15 323.15 333.15 343.15 353.15 363.15 373.15

731.9 724.9 717.8 771.02 764.16 757.30 750.45 743.7 736.8 729.8 723.0

697.1 ± 0.5f, 697.44 ± 0.36d, 697.43 ± 0.2%g 689.6 ± 0.5f, 689.89 ± 0.2%g, 689.94 ± 0.38d 762.75,l 762.91 ± 0.10d, 763.15 ± 0.11d 755.66,l 755.94 ± 0.20d, 756.5j, 748.83 ± 0.28d, 741.83 ± 0.34d, 742.50 ± 0.15,d 734.45 ± 0.30,d 734.50 ± 0.20,d 734.90 ± 0.41d, 728.04 ± 0.48d, 721.24 ± 0.54d, 714.46 ± 0.59d, 707.71 ± 0.63d, 773.43 ± 0.06d, 773.69i, 773.7 ± 0.2h 766.59 ± 0.05d, 766.75i, 766.8 ± 0.2h 759.55i, 759.83i, 759.9 ± 0.2h, 759.71 ± 0.07d 752.64i, 752.80 ± 0.12d, 752.9 ± 0.2h, 752.91i 745.73i, 745.86 ± 0.18d, 745.99i, 746.0 ± 0.2h 738.90 ± 0.25d, 739.0 ± 0.2h, 739.07i 731.9 ± 0.2h, 731.90 ± 0.31d 724.8 ± 0.2h, 724.88 ± 0.38d 717.7 ± 0.2h, 717.84 ± 0.44d 771.15 ± 0.50d 764.29 ± 0.54d 757.44 ± 0.58d 750.60 ± 0.61d 743.76 ± 0.62d 736.91 ± 0.62d 730.04 ± 0.62d 723.16 ± 0.62d

a Standard uncertainties u are u(T) = 0.01 K, and expanded uncertainties Uc are Uc(ρ) = 0.07 kg·m−3 for T < 353.15 K and Uc(ρ) = 0.2 kg·m−3 for T ≥ 353.15 K (level of confidence = 0.95, k = 2). The average pressure for these measurements was 0.102 MPa with an expanded uncertainty Uc(P) = 0.001 MPa (level of confidence = 0.95, k = 2). bReference 41. cReference 42. dReference 43. Equations for best density: Decane: ρ/kg·m3 = 999.915 − [1.25380 × T/K] + [1.72986 × 10−3 (T/K)2] − [2.02727 × 10−6 (T/K)3]. Dodecane: ρ/kg·m3 = 1046.13 − [1.49513 × T/K] + [2.35839 × 10−3 (T/K)2] − [2.43796 × 10−6 (T/K)3]. Tetradecane: ρ/kg·m3 = 1093.4 − [1.73979 × T/K] + [2.82238 × 10−3 (T/K)2] − [2.49190 × 10−6 (T/K)3]. Hexadecane: ρ/kg·m3 = 956.848 − [0.557634× T/K] + [2.68578 × 10−4 (T/K)2] − [1.24436 × 10−7 (T/K)3]. Heptadecane: ρ/kg·m3 = 1026.08 − [1.11241 × T/K] + [1.28506 × 10−3 (T/K)2] − [1.28491× 10−6 (T/K)3]. eReference 49. fReference 32. g Reference 40. hReference 31. iReference 44. jReference 45. kReference 46. lReference 47. mReference 48.

chemical ignition delay period to physical ignition delay period ranged from 1 to 5 for the hydroprocessed algae based fuel and from 0.2 to 4 for cetane depending on the model conditions, the injection pressure, and the engine speed.18 Other surrogate mixture combustion studies have focused solely on

the chemical delay increased in its contribution to the overall ignition delay. Mixtures containing 35% isocetane in cetane best matched the ignition delay of the hydroprocessed algae based fuel. When this analysis was applied to the same engine with a Bosch CP4 common rail pump, it was found that the ratio of B

DOI: 10.1021/acs.jced.6b00542 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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Table 3. Experimental Densities, Dynamic Viscosities, and Kinematic Viscosities of Mixtures of Butylbenzene (1) + n-Decane from T = (293 to 373) K and 0.1 MPaa ρ

η

ν

ρ

η

ν

ρ

η

ν

w1

x1

kg·m−3

mPa·s

mm2·s−1

kg·m−3

mPa·s

mm2·s−1

kg·m−3

mPa·s

mm2·s−1

0.0000 0.1002 0.2001 0.3000 0.4000 0.4999 0.6001 0.6999 0.8002 0.8999 1.0000

0.0000 0.1055 0.2096 0.3124 0.4141 0.5145 0.6140 0.7120 0.8094 0.9051 1.0000

729.88 740.90 752.30 764.12 776.38 789.08 802.32 816.03 830.38 845.04 860.51

1.26 1.24 1.22 1.21 1.19 1.19 1.19 1.20 1.20 1.22 1.21

722.31 733.32 744.67 756.43 768.66 781.31 794.51 808.16 822.46 837.07 852.49

1.10 1.08 1.07 1.06 1.05 1.04 1.04 1.05 1.05 1.06 1.07

714.69 725.64 736.97 748.70 760.89 773.50 786.65 800.26 814.51 829.07 844.43

0.0000 0.1002 0.2001 0.3000 0.4000 0.4999 0.6001 0.6999 0.8002 0.8999 1.0000

0.0000 0.1055 0.2096 0.3124 0.4141 0.5145 0.6140 0.7120 0.8094 0.9051 1.0000

707.02 717.94 729.23 740.92 753.07 765.64 778.75 792.31 806.52 821.03 836.34

0.869 0.858 0.849 0.842 0.837 0.834 0.833 0.835 0.839 0.847 0.852

699.29 710.17 721.43 733.08 745.19 757.73 770.80 784.32 798.48 812.95 828.21

0.779 0.770 0.762 0.756 0.752 0.749 0.749 0.751 0.754 0.760 0.767

691.5 702.3 713.5 725.1 737.2 749.7 762.7 776.1 790.3 804.7 819.9

0.0000 0.1002 0.2001 0.3000 0.4000 0.4999 0.6001 0.6999 0.8002 0.8999 1.0000

0.0000 0.1055 0.2096 0.3124 0.4141 0.5145 0.6140 0.7120 0.8094 0.9051 1.0000

683.6 694.4 705.6 717.1 729.2 741.7 754.6 768.0 782.1 796.5 811.7

0.638 0.633 0.628 0.624 0.621 0.620 0.620 0.621 0.623 0.628 0.635

675.6 686.4 697.5 709.1 721.1 733.5 746.4 759.9 773.9 788.3 803.4

0.586 0.581 0.577 0.574 0.571 0.571 0.571 0.572 0.574 0.578 0.584

667.5 678.2 689.3 700.9 712.8 725.3 738.2 751.6 765.6 779.9 795.0

T = 293.15 K 0.922 0.917 0.917 0.921 0.928 0.940 0.957 0.981 1.00 1.03 1.05 T = 323.15 K 0.615 0.616 0.619 0.624 0.630 0.639 0.649 0.661 0.677 0.695 0.713 T = 353.15 K 0.436 0.439 0.443 0.447 0.453 0.460 0.467 0.477 0.488 0.500 0.516

T = 303.15 K 0.794 0.792 0.794 0.798 0.805 0.816 0.830 0.849 0.866 0.891 0.910 T = 333.15 K 0.545 0.547 0.549 0.555 0.560 0.568 0.577 0.589 0.602 0.618 0.636 T = 363.15 K 0.396 0.399 0.402 0.407 0.412 0.419 0.426 0.434 0.444 0.456 0.469

T = 313.15 K 0.693 0.693 0.696 0.700 0.707 0.716 0.727 0.743 0.760 0.781 0.801 T = 343.15 K 0.486 0.488 0.492 0.496 0.502 0.509 0.518 0.528 0.540 0.554 0.571 T = 373.15 K 0.362 0.365 0.369 0.373 0.378 0.384 0.391 0.399 0.408 0.419 0.430

0.969 0.955 0.944 0.935 0.929 0.925 0.924 0.928 0.932 0.942 0.948 0.702 0.696 0.689 0.684 0.681 0.679 0.679 0.680 0.683 0.688 0.696 0.542 0.538 0.535 0.532 0.530 0.530 0.530 0.531 0.533 0.537 0.541

a

x1 is the mole fraction of butylbenzene in the (butylbenzene + n-decane) mixture and w1 is the mass fraction of butylbenzene in the (butylbenzene + n-decane) mixture. Standard uncertainties u are u(T) = 0.01 K, and expanded uncertainties Uc are Uc(η) = 0.007 mPa·s, Uc(ν) = 0.007 mm2·s−1, Uc(ρ) = 0.07 kg·m−3 at T < 343.15 K and Uc(ρ)= 0.2 kg·m−3at T ≥ 343.15 K (level of confidence = 0.95, k = 2) and combined expanded uncertainties of Uc(ν) = 0.007 mm2·s−1, Uc(x1) = 0.0002, and Uc(w1) = 0.0001. The average pressure for these measurements was 0.102 MPa with an expanded uncertainty Uc(P) = 0.001 MPa (level of confidence = 0.95, k = 2).

chemical kinetic models. Comandini, et al.3 investigated the autoignition of n-decane and its mixtures with butylbenzene and butylcyclohexane and developed chemical kinetic models of the combustion process. Yu and Ester1 studied the thermal oxidation of n-butylbenzene, n-dodecane, and their mixtures as a way to understand the overall oxidation of a jet fuel. This oxidation process is important because jet fuel is commonly used as a coolant to dissipate the heat generated by the aircraft components, as well as a fuel in the combustion processes, and such oxidation could cause the formation of solid compounds within the combustion system that adversely impact the transport and combustion of the fuels.1 While many studies have examined the specific combustion behaviors of butylbenzene and other alkylbenzenes with linear alkanes and cycloalkanes,1,3,7,13 the physical properties of butylbenzene and alkane mixtures that can be used to understand the physical

contributions to engine combustion behavior have not been reported. The goal of this study was to measure some of the key properties that can impact the physical delay period in engine combustion. Density, viscosity, and surface tension impact the injection, atomization, entrainment, and mixing process in a diesel engine and have been included in numerical simulations of the vaporization and spray processes for droplets of fuel or surrogate fuel mixtures in engines.19−25 A factor that can affect fuel injection timing is bulk modulus, which can be calculated from speed of sound and density measurements.16,26−29 In this work, the densities, viscosities, surface tensions, speeds of sound, and flash points were measured for butylbenzene, decane, dodecane, tetradecane, hexadecane, and heptadecane, and binary mixtures of butylbenzene and each alkane, and the bulk moduli were calculated. Flash point was also included as an indicator of C

DOI: 10.1021/acs.jced.6b00542 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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Table 4. Experimental Densities, Dynamic Viscosities, and Kinematic Viscosities of Mixtures of Butylbenzene (1) + n-Dodecane from T = (293 to 373) K and 0.1 MPaa ρ

η

ν

ρ

η

ν

ρ

η

ν

w1

x1

kg·m−3

mPa·s

mm2·s−1

kg·m−3

mPa·s

mm2·s−1

kg·m−3

mPa·s

mm2·s−1

0.0000 0.1004 0.2005 0.3001 0.4000 0.5000 0.5996 0.7111 0.7994 0.8999 1.0000

0.0000 0.1241 0.2414 0.3524 0.4583 0.5593 0.6552 0.7575 0.8349 0.9194 1.0000

748.79 758.28 768.11 778.18 788.60 799.56 810.70 823.88 834.67 847.33 860.51

1.96 1.82 1.70 1.60 1.51 1.44 1.37 1.31 1.26 1.22 1.21

741.54 750.96 760.73 770.74 781.11 791.97 803.03 816.12 826.84 839.40 852.49

1.67 1.56 1.47 1.39 1.32 1.26 1.21 1.15 1.12 1.08 1.07

734.25 743.61 753.32 763.26 773.56 784.35 795.32 808.33 818.96 831.44 844.43

0.0000 0.1004 0.2005 0.3001 0.4000 0.5000 0.5996 0.7111 0.7994 0.8999 1.0000

0.0000 0.1241 0.2414 0.3524 0.4583 0.5593 0.6552 0.7575 0.8349 0.9194 1.0000

726.94 736.23 745.87 755.75 765.97 776.69 787.58 800.50 811.06 823.44 836.34

1.26 1.19 1.13 1.08 1.04 0.993 0.956 0.920 0.894 0.869 0.852

719.59 728.82 738.39 748.19 758.34 768.98 779.81 792.63 803.11 815.41 828.21

1.11 1.06 1.01 0.966 0.928 0.892 0.860 0.829 0.808 0.785 0.767

712.2 721.2 730.8 740.5 750.7 761.2 771.9 784.7 795.1 807.2 819.9

0.0000 0.1004 0.2005 0.3001 0.4000 0.5000 0.5996 0.7111 0.7994 0.8999 1.0000

0.0000 0.1241 0.2414 0.3524 0.4583 0.5593 0.6552 0.7575 0.8349 0.9194 1.0000

704.7 713.7 723.2 732.9 743.0 753.4 764.0 776.7 787.0 799.1 811.7

0.890 0.852 0.817 0.786 0.757 0.733 0.709 0.685 0.669 0.652 0.635

697.2 706.1 715.6 725.1 735.2 745.5 756.0 768.6 778.9 790.9 803.4

0.805 0.773 0.743 0.716 0.691 0.670 0.649 0.628 0.614 0.599 0.584

689.6 698.5 707.8 717.3 727.2 737.5 747.9 760.5 770.7 782.6 795.0

T = 293.15 K 1.47 1.38 1.31 1.24 1.19 1.15 1.11 1.08 1.06 1.04 1.05 T = 323.15 K 0.916 0.879 0.846 0.817 0.793 0.771 0.753 0.736 0.725 0.716 0.713 T = 353.15 K 0.627 0.608 0.591 0.576 0.563 0.552 0.542 0.532 0.526 0.521 0.516

T = 303.15 K 1.24 1.17 1.12 1.07 1.03 0.996 0.968 0.941 0.925 0.909 0.910 T = 333.15 K 0.801 0.771 0.745 0.722 0.703 0.686 0.671 0.657 0.649 0.640 0.636 T = 363.15 K 0.562 0.546 0.532 0.519 0.508 0.499 0.491 0.483 0.478 0.473 0.469

T = 313.15 K 1.06 1.01 0.968 0.931 0.900 0.873 0.850 0.829 0.816 0.804 0.801 T = 343.15 K 0.706 0.683 0.662 0.643 0.627 0.614 0.602 0.590 0.583 0.576 0.571 T = 373.15 K 0.506 0.493 0.481 0.471 0.461 0.454 0.447 0.440 0.436 0.432 0.430

1.44 1.36 1.28 1.22 1.16 1.11 1.07 1.03 0.997 0.967 0.948 0.992 0.947 0.905 0.869 0.836 0.807 0.779 0.752 0.733 0.714 0.696 0.734 0.706 0.680 0.657 0.634 0.615 0.597 0.578 0.565 0.552 0.541

a

x1 is the mole fraction of butylbenzene in the (butylbenzene + n-dodecane) mixture, and w1 is the mass fraction of butylbenzene in the (butylbenzene + n-dodecane) mixture. Standard uncertainties u are u(T) = 0.01 K, and expanded uncertainties Uc are Uc(η) = 0.007 mPa·s, Uc(ρ)= 0.07 kg·m−3 at T < 343.15 K and Uc(ρ) = 0.2 kg·m−3at T ≥ 343.15 K, and combined expanded uncertainties of Uc(ν) = 0.007 mm2·s−1, Uc(x1) = 0.0002, and Uc(w1) = 0.0001 (level of confidence = 0.95, k = 2). The average pressure for these measurements was 0.102 MPa with an expanded uncertainty Uc(P) = 0.001 MPa (level of confidence = 0.95, k = 2).

mass and molar mass in Table 1 to be 0.0001 and 0.0002, respectively.

fuel combustibility; it is part of the specifications for military diesel fuel; and it has been included in other studies on surrogate fuel mixtures.30 These measurements can be used by numerical modelers who are trying to include physical delay processes in their combustion models along with the chemical kinetic behavior.

3. METHODS The methods used in this study to measure density, speed of sound, viscosity, surface tension, and flash point are the same as those used in previous studies.31−35 An Anton Paar DSA 5000 density and sound analyzer was used to measure density and speed of sound at temperatures ranging from (293.15 and 333.15) K, and an Anton Paar SVM 3000 Stabinger viscometer was used to measure viscosity and density from (293.15 to 373.15) K. The DSA 5000 was adjusted daily using degassed ultrapure water, and its density measurement was also checked using a NIST-certified density standard (Certificate Standard Reference Material 211d, toluene liquid density-extended range). It was cleaned between samples with hexane and or

2. MATERIALS The chemicals in this study, butylbenzene, n-decane, n-dodecane, n-tetradecane, n-hexadecane, and n-heptadecane were used as received from the supplier (Table 1). Mixtures were prepared at room temperature by sequentially pipetting each compound into a clean vial and weighing on a Mettler Toledo AG204 analytical balance that has an error of 0.0004 g. The vial was then sealed with a cap fitted with a Teflon septa and mixed. The combined expanded uncertainties (level of confidence = 0.95, k = 2) in the mass fraction and mole fractions were calculated from the D

DOI: 10.1021/acs.jced.6b00542 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 5. Experimental Densities, Dynamic Viscosities, and Kinematic Viscosities of Mixtures of Butylbenzene (1) + n-Tetradecane from T = (293 to 373) K and 0.1 MPaa ρ

η

ν

ρ

η

ν

ρ

η

ν

w1

x1

kg·m−3

mPa·s

mm2·s−1

kg·m−3

mPa·s

mm2·s−1

kg·m−3

mPa·s

mm2·s−1

0.0000 0.1003 0.2004 0.3033 0.4024 0.4996 0.6000 0.6998 0.7999 0.8997 1.0000

0.0000 0.1414 0.2704 0.3915 0.4988 0.5961 0.6892 0.7751 0.8553 0.9299 1.0000

762.71 770.92 779.61 788.74 797.91 807.14 817.10 827.32 837.74 849.02 860.51

3.02 2.67 2.38 2.14 1.94 1.78 1.63 1.51 1.41 1.32 1.21

755.65 763.79 772.41 781.46 790.54 799.68 809.54 819.66 829.96 841.12 852.49

2.48 2.22 2.00 1.81 1.65 1.53 1.41 1.31 1.22 1.15 1.07

748.58 756.65 765.18 774.14 783.14 792.18 801.94 811.95 822.15 833.19 844.43

0.0000 0.1003 0.2004 0.3033 0.4024 0.4996 0.6000 0.6998 0.7999 0.8997 1.0000

0.0000 0.1414 0.2704 0.3915 0.4988 0.5961 0.6892 0.7751 0.8553 0.9299 1.0000

741.50 749.49 757.94 766.81 775.71 784.66 794.32 804.22 814.31 825.22 836.34

1.78 1.62 1.48 1.36 1.25 1.17 1.09 1.02 0.958 0.902 0.852

734.40 742.31 750.67 759.45 768.25 777.11 786.65 796.45 806.42 817.22 828.21

1.54 1.41 1.30 1.20 1.11 1.04 0.969 0.911 0.857 0.810 0.767

727.5 735.2 743.4 752.0 760.8 769.6 779.0 788.7 798.5 809.2 819.9

0.0000 0.1003 0.2004 0.3033 0.4024 0.4996 0.6000 0.6998 0.7999 0.8997 1.0000

0.0000 0.1414 0.2704 0.3915 0.4988 0.5961 0.6892 0.7751 0.8553 0.9299 1.0000

720.3 728.0 736.1 744.6 753.3 762.0 771.3 780.9 790.6 801.1 811.7

1.19 1.10 1.02 0.955 0.891 0.839 0.789 0.744 0.704 0.667 0.635

713.1 720.7 728.7 737.1 745.7 754.3 763.5 773.0 782.5 793.0 803.4

1.07 0.992 0.925 0.864 0.810 0.764 0.720 0.681 0.646 0.612 0.584

705.8 713.3 721.2 729.5 738.0 746.5 755.6 764.9 774.3 784.7 795.0

T = 293.15 K 2.30 2.06 1.86 1.69 1.55 1.44 1.34 1.25 1.18 1.12 1.05 T = 323.15 K 1.32 1.21 1.12 1.04 0.973 0.915 0.863 0.818 0.780 0.744 0.713 T = 353.15 K 0.858 0.804 0.754 0.711 0.671 0.639 0.608 0.581 0.557 0.534 0.516

T = 303.15 K 1.88 1.70 1.54 1.42 1.31 1.22 1.14 1.07 1.02 0.965 0.910 T = 333.15 K 1.130 1.05 0.973 0.908 0.853 0.806 0.762 0.725 0.691 0.662 0.636 T = 363.15 K 0.760 0.715 0.674 0.637 0.604 0.576 0.550 0.526 0.505 0.486 0.469

T = 313.15 K 1.56 1.42 1.31 1.21 1.12 1.05 0.987 0.932 0.886 0.843 0.801 T = 343.15 K 0.980 0.912 0.852 0.800 0.753 0.716 0.678 0.647 0.619 0.592 0.571 T = 373.15 K 0.679 0.641 0.606 0.575 0.547 0.523 0.500 0.480 0.461 0.444 0.430

2.08 1.88 1.71 1.56 1.43 1.33 1.23 1.15 1.08 1.01 0.95 1.35 1.24 1.15 1.06 0.990 0.930 0.871 0.820 0.775 0.732 0.696 0.962 0.899 0.841 0.789 0.741 0.700 0.662 0.627 0.596 0.566 0.541

a

x1 is the mole fraction of butylbenzene in the (butylbenzene + n-tetradecane) mixture, and w1 is the mass fraction of butylbenzene in the (butylbenzene + n-tetradecane) mixture. Standard uncertainties u are u(T) = 0.01 K, and expanded uncertainties Uc are Uc(η) = 0.007 mPa·s, Uc (ρ) = 0.07 kg·m−3 at T < 343.15 K and Uc(ρ) = 0.2 kg·m−3at T ≥ 343.15 K, and combined expanded uncertainties of Uc(ν) = 0.007 mm2·s−1, Uc(x1) = 0.0002, and Uc(w1) = 0.0001 (level of confidence = 0.95, k = 2). The average pressure for these measurements was 0.102 MPa with an expanded uncertainty Uc(P) = 0.001 MPa (level of confidence = 0.95, k = 2).

ethanol and dried. The SVM 3000 was checked daily with a Cannon Certified Viscosity reference Standard, S3 and periodically with Cannon Certified Viscosity reference Standard, N1. It was cleaned between samples with hexane and dried. At least two samples of each compound or mixture were measured using each instrument. The replicate measurements were used to determine the standard deviation. A Kruss DS100 drop shape analyzer was used to measure the surface tension of each individual component or mixture. In drop shape analysis, the Young-LaPlace equation is fit to the shape of a droplet formed on the tip of a needle. The fitting process requires inputting air density, organic liquid density, and the needle diameter. The disposable needle diameter was measured using a Mitutoyo micrometer. For each liquid tested, at least three drops were formed, and at least 19 surface tension measurements were taken for each drop.

These measurements were used to determine the average and standard deviation of surface tension. A Setaflash Series 8 closed cup flash point tester model 82000-0 (Stanhope-Seta) was used in temperature ramping mode to measure flash point. The 82000-0 model conforms to ASTM D3828 (gas ignition option), ASTM D1655 (gas ignition option), ASTM D3278, ASTM D7236, and ASTM E502, as given in the manufacturer’s literature. For each liquid, at least two measurements of flash point were taken from which the average and standard deviation were determined. To determine the expanded uncertainty of all these measurements, the standard deviation of the measurement as described previously was multiplied by 2. When a normal distribution is assumed, multiplying by a coverage factor of 2 is related to a 95% confidence interval. In determining the combined expanded uncertainty of the derived values, the error for the factors that E

DOI: 10.1021/acs.jced.6b00542 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 6. Experimental Densities, Dynamic Viscosities, and Kinematic Viscosities of Mixtures of Butylbenzene (1) + n-Hexadecane from T = (293 to 373) K and 0.1 MPaa ρ

η

ν

ρ

η

ν

ρ

η

ν

w1

x1

kg·m−3

mPa·s

mm2·s−1

kg·m−3

mPa·s

mm2·s−1

kg·m−3

mPa·s

mm2·s−1

0.0000 0.1005 0.2003 0.2889 0.3999 0.5000 0.5988 0.7008 0.7999 0.8997 1.0000

0.0000 0.1586 0.2971 0.4067 0.5293 0.6278 0.7158 0.7981 0.8709 0.9380 1.0000

773.52 780.89 788.51 795.49 804.56 813.07 821.75 831.10 840.48 850.32 860.51

4.47 3.74 3.18 2.78 2.38 2.08 1.84 1.63 1.46 1.32 1.21

766.58 773.89 781.43 788.33 797.29 805.70 814.27 823.49 832.73 842.44 852.49

3.58 3.04 2.62 2.32 2.01 1.78 1.59 1.42 1.28 1.16 1.07

759.66 766.88 774.34 781.16 790.00 798.30 806.75 815.84 824.96 834.53 844.43

0.0000 0.1005 0.2003 0.2889 0.3999 0.5000 0.5988 0.7008 0.7999 0.8997 1.0000

0.0000 0.1586 0.2971 0.4067 0.5293 0.6278 0.7158 0.7981 0.8709 0.9380 1.0000

752.74 759.88 767.24 773.97 782.69 790.88 799.21 808.17 817.16 826.58 836.34

2.45 2.13 1.88 1.69 1.49 1.34 1.22 1.10 1.01 0.921 0.852

745.82 752.86 760.13 766.76 775.36 783.43 791.64 800.47 809.32 818.61 828.21

2.07 1.83 1.63 1.47 1.31 1.19 1.08 0.983 0.903 0.830 0.767

738.8 745.8 752.9 759.5 767.9 775.9 783.9 792.7 801.4 810.6 819.9

0.0000 0.1005 0.2003 0.2889 0.3999 0.5000 0.5988 0.7008 0.7999 0.8997 1.0000

0.0000 0.1586 0.2971 0.4067 0.5293 0.6278 0.7158 0.7981 0.8709 0.9380 1.0000

731.9 738.8 745.8 752.3 760.5 768.4 776.2 784.9 793.5 802.5 811.7

1.56 1.40 1.26 1.15 1.04 0.951 0.872 0.802 0.741 0.686 0.635

724.9 731.6 738.6 744.9 753.1 760.8 768.5 777.1 785.4 794.3 803.4

1.38 1.24 1.13 1.04 0.941 0.863 0.794 0.732 0.678 0.629 0.584

717.8 724.5 731.3 737.5 745.5 753.1 760.8 769.1 777.5 786.1 795.0

T = 293.15 K 3.45 2.92 2.50 2.21 1.91 1.69 1.52 1.36 1.23 1.12 1.05 T = 323.15 K 1.84 1.62 1.44 1.31 1.17 1.06 0.972 0.891 0.822 0.761 0.713 T = 353.15 K 1.14 1.03 0.939 0.868 0.792 0.731 0.677 0.630 0.588 0.550 0.516

T = 303.15 K 2.74 2.35 2.05 1.83 1.60 1.43 1.29 1.17 1.06 0.976 0.910 T = 333.15 K 1.55 1.37 1.24 1.13 1.02 0.929 0.856 0.787 0.731 0.680 0.636 T = 363.15 K 1.00 0.910 0.833 0.773 0.708 0.656 0.610 0.569 0.532 0.500 0.469

T = 313.15 K 2.22 1.94 1.71 1.54 1.36 1.23 1.11 1.01 0.932 0.859 0.801 T = 343.15 K 1.32 1.18 1.07 0.986 0.893 0.821 0.757 0.702 0.653 0.610 0.571 T = 373.15 K 0.887 0.811 0.746 0.695 0.639 0.594 0.553 0.517 0.484 0.456 0.430

2.93 2.53 2.20 1.97 1.72 1.54 1.38 1.24 1.13 1.03 0.948 1.79 1.59 1.42 1.30 1.16 1.06 0.966 0.885 0.814 0.752 0.696 1.24 1.12 1.02 0.942 0.857 0.788 0.727 0.673 0.623 0.580 0.541

a

x1 is the mole fraction of butylbenzene in the (butylbenzene + n-hexadecane) mixture, and w1 is the mass fraction of butylbenzene in the (butylbenzene + n-hexadecane) mixture. Standard uncertainties u are u(T) = 0.01 K, and expanded uncertainties Uc are Uc(η) = 0.008 mPa·s, Uc(ρ) = 0.07 kg·m−3 at T < 343.15 K and Uc(ρ)= 0.2 kg·m−3at T ≥ 343.15 K, and combined expanded uncertainties of Uc(ν) = 0.009 mm2·s−1, Uc(x1) = 0.0002, and Uc(w1) = 0.0001 (level of confidence = 0.95, k = 2). The average pressure for these measurements was 0.102 MPa with an expanded uncertainty Uc(P) = 0.001 MPa (level of confidence = 0.95, k = 2).

of the measurements. The density values of the binary mixtures of butylbenzene with n-decane, n-dodecane, n-tetradecane, n-hexadecane, or n-heptadecane are given in Tables 3, 4, 5, 6, and 7, respectively. As the mole fraction of butylbenzene in any of the alkanes increases, the density (ρ) increases (Figure 1). The relationships, however, are not linear. The density-mole fraction data were fit to eq 1 with increasing integer values of m until the standard error as calculated by eq 2 was less than the combined expanded uncertainty of the measurements. The fit with the smallest standard error is reported here.

contributed to these values was propagated (positive square root of the sum of the variances). The result of this value was multiplied by the coverage factor of 2.

4. RESULTS 4.1. Density. To test the accuracy of the density measured by the DSA 5000, the measured values for the NIST-certified toluene standard were compared with the reported values. Results given in the Supporting Information show that the measured values agree with the reported values37 within the reported standard uncertainty of the measurements, therefore the DSA 5000 is accurately reporting density values. A comparison of the reported density values of butylbenzene and the linear alkanes with values reported in the literature is given in Table 2. The pure components densities match most of the reported values within the expanded uncertainty

m

ρ /kg·m−3 =

∑ Ajx1 j j=0

F

(1) DOI: 10.1021/acs.jced.6b00542 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 7. Experimental Densities, Dynamic Viscosities, and Kinematic Viscosities of Mixtures of Butylbenzene (1) + nHeptadecane from T = (303 to 373) K and 0.1 MPaa ρ

η

ν

ρ

η

ν

ρ

η

ν

w1

x1

kg·m−3

mPa·s

mm2·s−1

kg·m−3

mPa·s

mm2·s−1

kg·m−3

mPa·s

mm2·s−1

0.0000 0.1001 0.1965 0.3211 0.5001 0.6279 0.7951 1.0000

0.0000 0.1662 0.3047 0.4587 0.6419 0.7515 0.8742 1.0000

771.02 777.94 784.91 794.08 808.08 818.66 833.23 852.49

4.22 3.51 2.99 2.47 1.93 1.64 1.35 1.07

764.16 771.00 777.87 786.92 800.73 811.14 825.49 844.43

3.42 2.89 2.49 2.08 1.65 1.42 1.18 0.948

757.30 764.03 770.84 779.75 793.34 803.60 817.71 836.34

0.0000 0.1001 0.1965 0.3211 0.5001 0.6279 0.7951 1.0000

0.0000 0.1662 0.3047 0.4587 0.6419 0.7515 0.8742 1.0000

750.45 757.11 763.79 772.56 785.94 796.02 809.90 828.21

2.38 2.06 1.81 1.55 1.25 1.09 0.922 0.767

743.70 750.12 756.65 765.40 778.47 788.40 802.00 819.90

2.04 1.78 1.58 1.36 1.11 0.974 0.837 0.696

736.8 743.1 749.6 758.1 771.0 780.7 794.1 811.7

0.0000 0.1001 0.1965 0.3211 0.5001 0.6279 0.7951 1.0000

0.0000 0.1662 0.3047 0.4587 0.6419 0.7515 0.8742 1.0000

729.8 736.1 742.4 750.8 763.4 773.0 786.1 803.4

1.56 1.38 1.22 1.07 0.899 0.806 0.694 0.584

723.0 729.0 735.2 743.5 755.8 765.2 778.1 795.0

T = 303.15 K 3.25 2.73 2.35 1.96 1.56 1.35 1.13 0.910 T = 333.15 K 1.79 1.56 1.38 1.20 0.981 0.865 0.747 0.636 T = 363.15 K 1.14 1.01 0.909 0.805 0.687 0.623 0.546 0.469

T = 313.15 K 2.61 2.23 1.94 1.64 1.32 1.15 0.967 0.801 T = 343.15 K 1.52 1.33 1.19 1.04 0.861 0.768 0.671 0.571 T = 373.15 K 1.00 0.891 0.811 0.725 0.628 0.567 0.499 0.430

T = 323.15 K 2.14 1.85 1.62 1.39 1.14 1.00 0.844 0.713 T = 353.15 K 1.30 1.16 1.04 0.906 0.763 0.684 0.602 0.516

2.83 2.42 2.11 1.79 1.44 1.24 1.03 0.852 1.77 1.55 1.39 1.19 0.990 0.876 0.758 0.635

1.39 1.22 1.10 0.976 0.831 0.741 0.641 0.541

a

x1 is the mole fraction of butylbenzene in the (butylbenzene + n-heptadecane) mixture, and w1 is the mass fraction of butylbenzene in the (butylbenzene + n-heptadecane) mixture. Standard uncertainties u are u(T) = 0.01 K, and expanded uncertainties Uc are Uc(η) = 0.007 mPa·s, Uc(ρ)= 0.07 kg·m−3 at T < 343.15 K and Uc(ρ) = 0.2 kg·m−3 at T ≥ 343.15 K, and combined expanded uncertainties of Uc(ν) = 0.009 mm2·s−1, Uc(x1) = 0.0002, and Uc(w1) = 0.0001 (level of confidence = 0.95, k = 2). The average pressure for these measurements was 0.102 MPa with an expanded uncertainty Uc(P) = 0.001 MPa (level of confidence = 0.95, k = 2).

density, Pm,cal is the fitted density, N is the number of experimental data, and n is the number of parameters in the fitting equation. Microsoft Excel 2010 was used to fit the data. The fitting parameters are given in Table 8 for n-decane and n-dodecane where m = 3 and in Table 9 for n-tetradecane, n-hexadecane, and n-heptadecane where m = 4, and the fits are good as shown in Figure 1 for 303.15 K. 4.2. Speed of Sound and Bulk Modulus. The speed of sound values of butylbenzene and the linear alkanes measured herein are given as a function of temperature in Table 10 along with literature values. The values measured in the current study agree with most of the reported values within the expanded uncertainty of the measurements. The speeds of sound for the NIST toluene standard also compare favorably to those previously measured as given in the Supporting Information.38−40 The speed of sound values of binary mixtures of butylbenzene and each linear alkane are given in Table 11 as a function of the mole fraction of butylbenzene (x1). As the mole fraction of the butylbenzene increases in mixtures with either n-decane or n-dodecane, the speed of sound steadily increases as shown in Figure 2. For butylbenzene mixtures with n-tetradecane, n-hexadecane, or n-heptadecane, however, the speed of sound decreases as mole fraction of butylbenzene increases until a minimum is reached, and then increases to the value of butylbenzene. Other binary mixtures containing aromatic

Figure 1. Densities of binary mixtures of butylbenzene (1) with △, n-decane; ■, dodecane; ○, tetradecane; ▲, hexadecane; or □, heptadecane at 303.15 K. Lines shown are polynomial fits with equations and coefficients in Tables 8 and 9.

σ=

∑ (Pmeasured − Pm,cal)2 N−n

(2)

In these equations, Aj is the fitting parameters, x1 is the mole fraction of butylbenzene in the mixture, Pmeasured is the measured G

DOI: 10.1021/acs.jced.6b00542 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 8. Correlation of Density to Mole Fraction of Butylbenzene, x1, in Binary Mixtures with Linear Alkanes (n-Decane or n-Dodecane) and the Excess Molar Volume (VmE) at a Specified Mole Fraction (x1), T = (293.15 to 373.15) K, and 0.1 MPaa T/K

A3 −3

a

A1

Ao

R2

σ

102.3 ± 0.6 101.9 ± 0.6 101.6 ± 0.6 101.3 ± 0.6 100.9 ± 0.6 100.7 ± 0.9 100.5 ± 0.8 100.3 ± 0.6 99.7 ± 0.9

729.87 ± 0.06 722.31 ± 0.06 714.69 ± 0.06 707.02 ± 0.06 699.28 ± 0.06 691.4 ± 0.1 683.6 ± 0.1 675.6 ± 0.1 667.4 ± 0.1

0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999

0.03 0.03 0.03 0.03 0.03 0.04 0.04 0.03 0.04

75.1 ± 1.2 74.6 ± 1.2 74.1 ± 1.2 73.6 ± 1.2 73.1 ± 1.2 72.0 ± 1.8 72.1 ± 2.1 71.3 ± 2.0 70.6 ± 1.7

748.74 ± 0.13 741.49 ± 0.14 734.20 ± 0.13 726.89 ± 0.13 719.54 ± 0.13 712.1 ± 0.2 704.6 ± 0.2 697.1 ± 0.2 689.5 ± 0.2

0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999

0.06 0.06 0.06 0.06 0.06 0.09 0.11 0.11 0.09

A2

n-Decane: ρ/kg·m = + A2x1 + A1 x1 + Ao 293.15 7.1 ± 0.9 21.3 ± 1.4 303.15 7.1 ± 0.9 21.2 ± 1.4 313.15 7.0 ± 0.9 21.1 ± 1.4 323.15 7.0 ± 0.9 21.1 ± 1.3 333.15 6.9 ± 0.9 21.1 ± 1.3 343.15 7.1 ± 1.3 20.6 ± 2.0 353.15 7.4 ± 1.2 20.2 ± 1.8 363.15 7.5 ± 1.0 20.0 ± 1.5 373.15 6.5 ± 1.3 21.3 ± 2.0 n-Dodecane: ρ/kg·m−3 = A3x13 + A2x12 + A1 x1 + Ao 293.15 19.7 ± 1.9 16.9 ± 2.9 303.15 19.6 ± 1.9 16.7 ± 2.9 313.15 19.4 ± 1.9 16.6 ± 2.9 323.15 19.3 ± 1.9 16.5 ± 2.9 333.15 19.1 ± 1.8 16.4 ± 2.8 343.15 17.9 ± 2.9 17.7 ± 4.4 353.15 18.6 ± 3.3 16.3 ± 5.1 363.15 18.3 ± 3.2 16.6 ± 4.8 373.15 18.0 ± 2.6 16.8 ± 4.0 A3x13

x1 and VEm/cm3·mol−1

2

x1 = 0.5145 0.16 0.16 0.15 0.15 0.14 0.12 0.12 0.11 0.09 x1 = 0.5593 0.28 0.28 0.28 0.28 0.28 0.28 0.27 0.28 0.28

The “±” for the coefficients Ao , A1, A2, A3 represent the 95% confidence interval. The σ is the standard error of the fit as given by eq 2.

Table 9. Correlation of Density to Mole Fraction of Butylbenzene, x1, in Binary Mixtures with Linear Alkanes (n-Tetradecane, n-Hexadecane, or n-Heptadecane) and the Excess Molar Volume (VEm) at a Specified Mole Fraction (x1), T = (293.15 to 373.15) K, and 0.1 MPaa T/K

A4

A3

A2

n-Tetradecane: ρ/kg·m−3 = A4 x1 4 + A3 x1 3 + A2 x1 2 + A1 x1 + Ao 293.15 24.1 ± 10.3 −17.4 ± 20.9 38.3 ± 13.7 303.15 23.9 ± 10.1 −17.4 ± 20.5 38.0 ± 13.4 313.15 23.6 ± 10.0 −17.2 ± 20.3 37.5 ± 13.3 323.15 23.3 ± 9.9 −16.9 ± 20.0 37.0 ± 13.1 333.15 23.0 ± 9.8 −16.6 ± 19.8 36.5 ± 13.0 343.15 20.3 ± 12.9 −13.6 ± 26.2 36.2 ± 17.1 353.15 18.6 ± 12.2 −10.2 ± 24.9 33.4 ± 16.3 363.15 18.0 ± 13.3 −9.7 ± 26.9 33.0 ± 17.6 373.15 19.0 ± 14.0 −11.9 ± 28.4 33.9 ± 18.6 n-Hexadecane: ρ/kg·m−3 = A4 x14 + A3 x13 + A2 x12 + A1 x1 + Ao 293.15 28.0 ± 2.6 −15.6 ± 2.6 33.3 ± 2.6 303.15 27.7 ± 4.0 −15.7 ± 8.1 33.0 ± 5.3 313.15 27.2 ± 3.8 −15.3 ± 7.8 32.3 ± 5.1 323.15 26.8 ± 3.8 −15.0 ± 7.7 31.8 ± 5.0 333.15 26.4 ± 3.6 −14.9 ± 7.4 31.3 ± 4.8 343.15 22.3 ± 6.1 −7.3 ± 12.5 26.3 ± 8.2 353.15 22.7 ± 7.1 −8.2 ± 14.5 26.1 ± 9.5 363.15 24.8 ± 7.3 −13.2 ± 14.9 29.0 ± 9.7 373.15 18.6 ± 3.6 −2.2 ± 7.3 22.4 ± 4.8 n-Heptadecane: ρ/kg·m−3 = A4 x14 + A3 x13 + A2 x12 + A1 x1 + Ao 303.15 35.2 ± 12.3 −24.8 ± 24.8 34.8 ± 15.9 313.15 34.3 ± 11.8 −23.9 ± 23.9 33.9 ± 15.3 323.15 34.5 ± 11.4 −25.1 ± 23.0 34.4 ± 14.7 333.15 33.1 ± 11.4 −22.9 ± 23.0 35.0 ± 14.8 343.15 34.8 ± 7.9 −28.8 ± 16.0 37.3 ± 10.2 353.15 33.5 ± 6.5 −26.2 ± 13.1 34.8 ± 8.4 363.15 31.3 ± 10.9 −22.3 ± 22.1 31.6 ± 14.2 373.15 32.8 ± 7.7 −26.9 ± 15.5 35.0 ± 9.9

A1

Ao

R2

σ

52.8 ± 3.1 52.4 ± 3.1 51.9 ± 3.0 51.5 ± 3.0 50.9 ± 3.0 49.6 ± 3.9 49.6 ± 3.7 49.0 ± 4.0 48.1 ± 4.2

762.72 ± 0.20 755.66 ± 0.20 748.59 ± 0.20 741.51 ± 0.19 734.41 ± 0.19 727.5 ± 0.3 720.3 ± 0.2 713.1 ± 0.3 705.8 ± 0.3

0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999

0.08 0.08 0.08 0.08 0.08 0.11 0.10 0.11 0.11

41.2 ± 2.6 40.9 ± 1.2 40.5 ± 1.2 40.0 ± 1.1 39.5 ± 1.1 39.8 ± 1.8 39.2 ± 2.1 38.0 ± 2.2 38.4 ± 1.1

773.53 ± 0.08 766.59 ± 0.08 759.66 ± 0.07 752.75 ± 0.07 745.83 ± 0.08 738.8 ± 0.1 731.9 ± 0.1 724.9 ± 0.1 717.8 ± 0.1

0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999

0.03 0.03 0.03 0.03 0.03 0.05 0.06 0.06 0.03

36.2 ± 3.4 35.9 ± 3.3 35.2 ± 3.2 35.0 ± 3.2 32.9 ± 2.2 32.8 ± 1.8 33.0 ± 3.1 31.1 ± 2.1

771.0 ± 0.2 764.2 ± 0.2 757.3 ± 0.2 750.5 ± 0.2 743.7 ± 0.1 736.8 ± 0.1 729.8 ± 0.2 723.0 ± 0.1

0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999

0.07 0.06 0.06 0.06 0.04 0.03 0.06 0.04

x1 and VEm/cm3·mol−1 x1 = 0.4988 0.35 0.35 0.35 0.34 0.34 0.35 0.36 0.37 0.37 x1 = 0.5293 0.42 0.41 0.41 0.40 0.40 0.40 0.41 0.41 0.41 x1 = 0.4587 0.41 0.40 0.39 0.39 0.38 0.40 0.38 0.40

The “±” for the coefficients Ao , A1, A2, A3, and A4 represent the 95% confidence interval. The σ is the standard error of the fit as given by eq 2. a

H

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Table 10. Comparison of Measured Speed of Sound Values with Literature Valuesa T = 293.15 K

T = 303.15 K

this study lit.

1253.8 ± 1.1 1253.4g 1254m

1214.5 ± 1.0 1210l, 1213.5g 1215m, 1215.1f

this study lit.

1297.9 1297m 1297.6 ± 0.3e 1298.25o 1301.2 ± 0.5%g

1259.6 1259m 1259.3 ± 0.3e, 1260.9 ± 0.5%g 1261.2f

this study lit.

1331.2 1331.3q, 1331.54o

this study lit.

1357.3 1357.0 ± 0.3h, 1357.1i, 1357.7j

this study lit. this study lit.

1353.7 1341.31d, 1353.4c

T = 313.15 K n-Decane 1175.7 ± 0.9 1174.5 g, 1175.3l 1175.4n, 1177k n-Dodecane 1221.9 1221.4 ± 0.3e 1221.8 ± 0.5%g

n-Tetradecane 1256.4 1256.2q 1256.5f n-Hexadecane 1320.0 1283.4 1319.5 ± 0.3h, 1282.8n, 1319.6i, 1320.0,f 1282.8 ± 0.3h, 1320.2j 1283k, 1283.4i, 1283.4j n-Heptadecane 1330.9 ± 1.0 1294.5 ± 0.9 1331.9p 1295.4p Butylbenzene 1314.9 1276.6 1302.11d, 1308b, 1314.3c 1264.92d, 1275.7c, 1276b 1293.6 1293.9f

T = 323.15 K

T = 333.15 K

1137.3 ± 0.9 1136.3g 1139k

1099.3 ± 0.8 1098.8n, 1098.9g 1099k, 1099.2f

1184.7 1183.8 ± 0.5%g 1184.2 ± 0.3e

1148.0 1146.6 ± 0.5%g 1147.3 ± 0.3e 1147.4f

1220.1

1184.1 1183.6q 1184.0f

1247.5 1246.8 ± 0.3h, 1246.9i, 1247.4j, 1248k

1212.1 1211.2n, 1211.4f 1211.6i, 1212k, 1212.3j

1258.8 ± 0.7 1259.3p

1223.8 ± 0.6 1223.9p

1238.7 1228.70d

1201.4

a Standard uncertainties u are u(T) = 0.01 K, and expanded uncertainties Uc are Uc(c) = 0.5 m·s−1 (level of confidence = 0.95, k = 2) unless otherwise indicated by “±” symbol. The average pressure for these measurements was 0.102 MPa with an expanded uncertainty Uc(P) = 0.001 MPa (level of confidence = 0.95, k = 2). bReference 41. cReference 50. dReference 42. eReference 32. fReference 51. gReference 40. hReference 33. iReference 44. j Reference 52. kReference 53. lReference 46. mReference 54. nReference 55. oReference 56. pReference 57. qReference 95.

less closely packed in the mixture than they are as pure liquids, while a negative excess molar volume means they are more closely packed. The excess molar volumes (VEm) of butylbenzene with each linear alkane were calculated using the following equation:

compounds have been reported to have speeds of sound lower than their components. Such behavior has been seen in binary mixtures of toluene or ethylbenzene with n-hexadecane, cyclohexane, and ethyoxyethanols, and with ethylbenzene in 1-nonanol or 2-decanol.38,58−60 The isentropic bulk modulus of each binary mixture, Ks, was calculated at each temperature and ambient pressure from the speed of sound (c) and density (ρ) by Ks/Pa = (c 2/m 2·s−2)(ρ /kg·m−3)

VmE =

M1x1 + M 2x 2 Mx Mx − 11 − 2 2 ρm ρ1 ρ2

(4)

in which ρm is the density of the mixture, ρ1 and ρ2 are the pure component densities, M1 and M2 are the molar masses, and x1 and x2 are the mole fractions of butylbenzene as component 1 and the linear alkane as component 2. The calculated excess molar volumes are shown in Figure 3 for 303.15 K and are given at a mole fraction of butylbenzene close to 0.5 at all temperatures in Tables 8 and 9. The excess molar volumes are positive values and do not change significantly over the temperature range studied, except for mixtures containing decane in which the excess molar volume decreases slightly as temperature increases (Tables 9 and 10). Increasing the carbon chain length from 10 to 16 causes an increase in excess molar volume, but the values for hexadecane and heptadecane are similar. For the 6-carbon n-hexane, the excess molar volume of n-hexane and butylbenzene calculated from data in Rice and Teja61 was negative. This overall trend of increasing excess molar volume with increasing carbon chain length on linear alkanes is similar to the reported data for binary mixtures of linear alkanes with methylbenzene (toluene) or ethylbenzene. Iloukhani et al.62 (2006) reported negative excess molar volumes for n-pentane

(3)

The calculated values are given in Table 12. The bulk modulus increases with increasing mole fraction of butylbenzene in the binary mixture with all linear alkanes tested and with decreasing temperature. The wide range of values for bulk modulus would significantly impact injection timing in an engine. As bulk modulus increases, the start of injection occurs sooner (crank angle degree is advanced) because the fuel is less compressible.16 While testing petroleum diesel and biodiesel, Tat and van Gerpen29 found that the injection pressure pulse for biodiesel was advanced in comparison with that of the petroleum diesel. Approximately 0.5° of the timing advance they measured was attributed to the bulk modulus of the biodiesel being 169 MPa greater than that of the petroleum-based fuel.29 In the current study, the range of bulk moduli is largest for butyl benzene and decane mixtures, 429 MPa, which suggests that these mixtures would have measurable differences in their start of injection. 4.3. Excess Molar Volume. One way to examine the packing of molecules in mixtures is to calculate the excess molar volume. Positive excess molar volumes suggest that the molecules are I

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Table 11. Speeds of Sound, m·s−1, of Binary Mixtures of Butylbenzene (1) + n-Decane, + n-Dodecane, + n-Tetradecane, + n-Hexadecane, or + n-Heptadecane from T = (293.15 to 333.15) K and 0.1 MPaa Butylbenzene (1) + n-Decane (2) T/K

x1 = 0.1055

x1 = 0.2096

x1 = 0.3124

293.15 303.15 313.15 323.15 333.15

1259.2 1220.2 1181.5 1143.3 1105.6

1266.3b 1227.4 ± 0.7 1188.9 ± 0.7 1150.8b 1113.2b

1273.8 1235.0 1196.6 1158.7 1121.2

T/K

x1 = 0.1241

x1 = 0.2414

x1 = 0.3524

293.15 303.15 313.15 323.15 333.15

1300.2 1262.0 1224.4 1187.2 1150.5

1302.8 1264.8 1227.2 1190.0 1153.4

1306.4 1268.4 1230.8 1193.7 1157.0

T/K

x1 = 0.1414

x1 = 0.2704

x1 = 0.3915

293.15 303.15 313.15 323.15 333.15

1330.1 1292.6b 1255.6 1219.1 1183.2

1329.5 1292.1 1255.1 1218.6 1182.7

1329.7 ± 0.7 1292.3 1255.3 1218.7 1182.7

T/K

x1 = 0.1586

x1 = 0.2971

x1 = 0.4067

293.15 303.15 313.15 323.15 333.15

1353.2 1316.1 1279.5 1243.6 1208.2

1350.1 1313.0 1276.4 1240.4 1204.9

1347.8 1310.7 1274.1 1238.0 1202.5

x1 = 0.4141

x1 = 0.5145

x1 = 0.6140

x1 = 0.7120

x1 = 0.8094

x1 = 0.9051

1301.1 1262.6 1224.4 1186.7 1149.5

1312.2 1273.7 1235.6 1197.9 1160.7

1324.5 ± 0.9 1286.0 ± 0.9 1247.9 ± 0.8 1210.2 ± 0.8 1173.0 ± 0.8

1338.2 1299.4 1261.2 1223.5 1186.3

x1 = 0.7575

x1 = 0.8349

x1 = 0.9194

1328.6 1290.4 1252.5 1215.2 1178.4

1335.5 1297.0 1259.1 1221.6 1184.6

1343.9 1305.4 1267.3 1229.7 1192.5

1282.1 1291.3 ± 0.8 1243.5 1252.5 1205.2 1214.3 1167.3 1176.6 1129.9 1139.3 Butylbenzene (1) + n-Dodecane (2) x1 = 0.4583

x1 = 0.5593

x1 = 0.6552

1310.3 1315.4 1272.3 1277.3 1234.7 1239.7 1197.6 1202.5 1161.0 1165.8 Butylbenzene (1) + n-Tetradecane (2) x1 = 0.4988

x1 = 0.5961

x1 = 0.6892

1330.9 ± 0.7 1332.5b 1293.4 ± 0.7 1294.9b 1256.3 ± 0.8 1257.6 1219.6 ± 0.7 1220.9 1183.5 ± 0.7 1184.7 Butylbenzene (1) + n-Hexadecane (2) x1 = 0.5293

x1 = 0.6278

1321.3 1283.1 1245.4 1208.1 1171.3

1334.9 1297.2 1259.8 1223.0 1186.6

x1 = 0.7158

1346.0 1345.0 1308.8 1307.7 1272.1 1270.8 1235.9 1234.4 1200.2 1198.6 Butylbenzene (1) + n-Heptadecane (2)

1345.1 1307.6 1270.5 1233.9 1197.8

x1 = 0.7751

x1 = 0.8553

x1 = 0.9299

1338.1 1300.2 1262.7 1225.6 1189.1

1342.1 1303.8 1266.1 1228.9 1192.1

1347.7 ± 0.9 1309.2 ± 1.1 1271.2 ± 1.0 1233.7 ± 1.0 1196.7 ± 0.9

x1 = 0.7981

x1 = 0.8709

x1 = 0.9380

1346.3 1308.5 1271.1 1234.3 1197.9

1347.8 1309.7 1272.1 1235.0 1198.3

1350.4 1312.0 1274.0 1236.6 1199.6

T/K

x1 = 0.1662

x1 = 0.3047

x1 = 0.4587

x1 = 0.6419

x1 = 0.7515

x1 = 0.8742

303.15 313.15 323.15 333.15

1325.3 ± 0.7 1289.0 1253.3 1218.1

1321.4 ± 0.8 1285.0 1249.2 1214.0

1316.9 ± 0.7 1280.3 1244.5 1209.1

1312.4 1275.9 1239.7 1204.0

1311.3 ± 0.8 1274.1 1237.6 1201.6

1311.0 1273.6 1236.6 1200.1

a

x1 is the mole fraction of butylbenzene in binary mixtures with n-decane, n-dodecane, n-tetradecane, n-hexadecane, or n-heptadecane. Standard uncertainties u are u(T) = 0.01 K, and expanded uncertainties Uc are Uc(c) = 0.5 m·s−1, and combined expanded uncertainties of Uc(x1) = 0.0002 (level of confidence = 0.95, k = 2) unless indicated by the “±“ symbol or superscripted with letter b when they are higher. The average pressure for these measurements was 0.102 MPa with an expanded uncertainty Uc(P) = 0.001 MPa (level of confidence = 0.95, k = 2). bThe expanded uncertainties Uc is Uc (c) = 0.6 m·s−1 (level of confidence = 0.95, k = 2).

n-heptane, n-octane, n-nonane, and n-decane in toluene mixtures at 298.15 K. In their work, similar values of excess molar volumes were found for binary mixtures of toluene with n-nodecane and n-decane. Asfour et al.63 also reported positive values of excess molar volumes of binary mixtures toluene with octane, decane, dodecane, tetradecane, and hexadecane that increased with carbon chain length, but similar excess molar volumes were not seen until the carbon number on the linear alkane had increased to 14 and 16. For ethylbenzene and n-alkane binary mixtures, Awwad et al.64 reported negative excess molar volumes for n-hexane in ethylbenzene mixtures and positive values for ethylbenzene with linear alkanes containing 7, 8, 9, 10, 12, 14, and 16 carbons at 298.15 K. All the excess molar volumes differed from each other and increased with increasing number of carbons. Asfour et al.63 also reported positive excess molar volumes for octane, tetradecane, and hexadecane in mixtures with ethylbenzene, but the excess molar volumes for toluene mixtures with tetradecane and hexadecane were similar to each other.

Figure 2. Speeds of sound of binary mixtures of butylbenzene (1) with △, n-decane; ■, n-dodecane; ○, n-tetradecane; ▲, n-hexadecane; or □, n-heptadecane at 303.15 K.

and n-hexane in toluene mixtures and positive excess molar volumes values that increased with carbon chain length for J

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Table 12. Values of Bulk Modulus, MPa, of Binary Mixtures of Butylbenzene (1) + n-Decane, + n-Dodecane, + n-Tetradecane, + n-Hexadecane, and + n-Heptadecane from T = (293.15 to 333.15) K and 0.1 MPaa Butylbenzene (1) + n-Decane (2) T/K

x1 = 0.000

x1 = 0.1055

293.15 303.15 313.15 323.15 333.15

1148 ± 1.5 1066 ± 1.3 989 ± 1.1 915 846

1175 1092 1013 938 868

x1 = 0.2096 x1 = 0.3124 1206 1122 1042 966 894

x1 = 0.4141

x1 = 0.5145

x1 = 0.6140

x1 = 0.7120

x1 = 0.8094

1405 1311 1222 1137 1057

1457 ± 1.3 1360 ± 1.3 1268 ± 1.2 1181 ± 1.1 1099

1513 1413 1319 1229 1144

1577 1474 1376 1283 1195

x1 = 0.7575

x1 = 0.8349

x1 = 0.9194

x1 = 1.000

1454 1359 1268 1182 1101

1489 1391 1298 1210 1127

1530 1430 1335 1245 1160

1577 1474 1376 1283 1195

1276 1316 ± 1.1 1358 1188 1226 1267 1105 1141 1179 1026 1060 1097 951 983 1018 Butylbenzene (1) + n-Dodecane (2)

1240 1154 1072 995 922

T/K

x1 = 0.000

x1 = 0.1241

x1 = 0.2414

x1 = 0.3524

293.15 303.15 313.15 323.15 333.15

1261 1177 1096 1020 948

1282 1196 1115 1038 965

1304 1217 1134 1056 982

1328 1240 1156 1077 1002

x1 = 0.4583

x1 = 0.5593

x1 = 0.6552

1354 1384 1415 1264 1292 1322 1179 1205 1233 1099 1123 1149 1022 1045 1070 Butylbenzene (1) + n-Tetradecane (2)

T/K

x1 = 0.000

x1 = 0.1414

x1 = 0.2704

x1 = 0.3915

293.15 303.15 313.15 323.15 333.15

1351 1264 1182 1104 1030

1364 1276 1193 1114 1039

1378 1290 1205 1126 1050

1395 1305 1220 1139 1062

T/K

x1 = 0.000

x1 = 0.1586

x1 = 0.2971

x1 = 0.4067

293.15 303.15 313.15 323.15 333.15

1425 1336 1251 1171 1096

1430 1340 1256 1175 1099

1437 1347 1262 1180 1104

1445 1354 1268 1186 1109

x1 = 0.4988

x1 = 0.5961

x1 = 0.6892

1413 1433 1456 1322 1341 1362 1236 1253 1273 1154 1170 1188 1076 1091 1108 Butylbenzene (1) + n-Hexadecane (2) x1 = 0.5293

x1 = 0.6278

x1 = 0.7158

x1 = 0.9051 x1 = 1.000

x1 = 0.7751

x1 = 0.8553

x1 = 0.9299

x1 = 1.000

1481 1386 1294 1208 1126

1509 1411 1318 1230 1146

1542 1442 1346 1256 1170

1577 ± 1.4 1474 ± 1.7 1376 ± 1.5 1283 ± 1.4 1195 ± 1.3

x1 = 0.7981

x1 = 0.8709

x1 = 0.9380

x1 = 1.000

1506 1410 1318 1231 1149

1527 1428 1335 1246 1162

1551 1450 1355 1264 1178

1577 1474 1376 1283 1195

1458 1471 1487 1366 1378 1392 1278 1289 1302 1195 1205 1217 1117 1125 1136 Butylbenzene (1) + n-Heptadecane (2)

T/K

x1 = 0.0000

x1 = 0.1662

x1 = 0.3047

x1 = 0.4587

x1 = 0.6419

x1 = 0.7515

x1 = 0.8742

x1 = 1.000

303.15 313.15 323.15 333.15

1366 1280 1200 1124

1366 1281 1200 1123

1371 1284 1203 1126

1377 1290 1208 1129

1392 1304 1219 1139

1408 ± 1.2 1317 1231 1149

1432 1339 1250 1166

1474 1376 1283 1195

a

x1 is the mole fraction of butylbenzene in binary mixtures with n-decane, n-dodecane, n-tetradecane, n-hexadecane, or n-heptadecane. Standard uncertainties u are u(T) = 0.01 K, and combined expanded uncertainties Uc are Uc (bulk modulus) = 1 MPa, Uc (x1) = 0.0002 (level of confidence = 0.95, k = 2) unless indicated by the “±“ symbol when they are higher.

subdivides the excess molar volume into an interaction term, a free volume term, and a pressure term as shown in eq 5 below with its terms defined by eqs 6−12. ∼1/3 ∼2/3 ⎡χ ⎤ (V − 1)V VE = θ2ψ1⎢ 12 ⎥ − 1/3 * * ⎡ ⎤ ∼ 4 x1V1 + x 2V 2 ⎣ P1* ⎦ − 1⎥⎦ ⎢⎣ 3 V

()

Interactional term

⎤ ∼ ∼ ⎡ 14 ∼−1/3 ∼ ∼ (V1 − V2)⎢⎣ 9 V − 1⎥⎦ (V − V2)(P1* − P2*) + ψ1ψ2 + 1 ψ1ψ2 ⎡ 4 ∼−1/3 ⎤ [P1*ψ2 − P2*ψ1] − 1⎦⎥ ⎣⎢ 3 V Pressure term

( )

()

Free volume term

(5)

The interaction term accounts for changes in the excess molar volume due to differences in the chemical nature of the two components and contains a single fitting parameter χ12. The free volume term accounts for differences in the thermal expansion behavior of the components and is a measure of differences in the shape, size, and conformation of the molecules.66 This term is always negative. The pressure term or P* term accounts for differences in the internal pressures and reduced volumes of

Figure 3. Excess molar volumes of binary mixtures of butylbenzene (1) with △, n-decane; ■, n-dodecane; ○, n-tetradecane; ▲, n-hexadecane; or □, n-heptadecane at 303.15 K. Lines shown are fits to Redlich−Kister equation in Table 14. Error bars are the positive square root of the sum of the variances of each variable in eq 4.

One way to interpret excess molar volumes is to model the data using the Prigogine−Flory−Patterson model,65 which K

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Table 13. Prigogine−Flory−Patterson Model Input Parameters at T = 303.15 K n-butylbenzene

n-decane

n-dodecane

n-tetradecane

n-hexadecane

n-heptadecane

0.943 245.49 0.851 1.11 1.24 127 157.44 395 1.275

1.05 316.84 1.15 0.916 1.26 156 196.98 440 0.95

0.980 378.46 1.03 0.955 1.25 184 229.71 448 0.93

0.935 440.79 0.939 0.996 1.24 210 259.74 462 0.91

0.904 504.26 0.894 1.01 1.23 240 295.39 464 0.90

0.894 537.01 0.873 1.02 1.23 254 311.88 469 0.89 (est)

103·α/(K−1)a cp /(J·mol−1·K−1)b 103·β/(MPa−1)c γ/ MPa·K−1 Ṽ i Vi*/ cm3·mol−1 vi/cm3·mol−1 Pi*/(MPa−1) si /(A−1)d

a

Based on equation α=−

∂(ln ρi ) ∂T

where density values at (293.15, 303.15 and 313.15) K from the current study were used, except for those for n-heptadecane where values from (303.15 and 313.15) K were used. These values agree with values predicted by correlations from ref 73 reported in ref 67 at 303.15 K of (1.06 × 10−3, 0.986 × 10−3, and 0.902 × 10−3) K−1 for n-decane, n-dodecane, and n-hexadecane, respectively. The α values predicted by correlations of Orwoll and Flory67 for n-hexadecane at 303.15 K of 0.904 K−1 also agree well with the current value. The value predicted in reference Rossinni et al.73 for n-heptadecane, 0.866 × 10−3 K−1, is lower than the value calculated herein. Their prediction of 0.858 × 10−3 K−1 for 298.15 K is also lower than the value reported by Madariaga et al.74 of 0.905 K−1 for the same temperature. For tetradecane, the value reported herein of 0.935 × 10−3 K−1 is higher than the values in ref 95, 0.920 × 10−3 K−1 and predicted in ref 73, 0.888 × 10−3 K−1. bHeat capacity values, cp, for linear alkanes were interpolated from refs 40 and 75 and the values for butylbenzene were calculated from correlation in ref 76. cIsothermal compressibility, β, is based on

βi =

TMiα12 ⎤ 1 ⎡⎢ 1 ⎥ + 2 ρi ⎢⎣ ui cp ⎥⎦

Here density, ρ, and speed of sound, u, at 303.15 K are in Tables 2 and 11, temperature, T = 303.15 K, molar mass, M, is given in Table 1, and α and cp are given in the current table for each component, i. For comparison, this equation was used to calculate the isothermal compressibility of n-butylbenzene at 333.15 K to be 1032.4 MPa−1, which is slightly less than 1039.8 MPa−1 reported by Chylinski et al.77 The thermal pressure coefficient, γ = α/β that was calculated to be 1.00 MPa·K−1 for hexadecane at 303.15 K from a correlation in Orwoll and Flory67 compares well with a value for 1.01 MPa·K−1 from the current work. dSurface area to volume ratios were averages of values found in refs 65 and 68−72, except for that for heptadecane, which was estimated based on the trends in the values for the other alkanes.

the components. The variables in eq 5 are based on the experimental temperature, T, thermal expansion coefficients (αi), isothermal compressibility (βi), molar volume (vi), thermal pressure coefficient (γ), and surface area to volume ratio (si) of the individual component that make up the mixture. These properties are given in Table 13. The reduced volume of each component, Ṽ i, is given by67 3 ⎡ ⎡ 4 ⎤⎤ α 1 T + ⎢ ⎣ 3 i ⎦⎥ Vĩ = ⎢ ⎥ ⎢⎣ 1 + α T ⎥⎦

Characteristic volume of each component v V i* = i V1̃ Characteristic pressure of each component 2

Pi* =

()

(6)

θ1 = 1 − θ2 =

65

Contact energy fraction P1*ϕ1 P1*ϕ1 + P2*ϕ2

(8)

Hard-core volumetric fraction ϕ1 = 1 − ϕ2 =

x1V1* * x1V1 + x 2V 2*

(11)

s1ϕ1 s1ϕ1 + s2ϕ2

(12)

The surface area to volume ratio, si, for each component was determined several different ways. The values shown in Table 14 for the linear alkanes are averages or estimates from reported values.65,68−72 A second method used correlations from Bondi.78 Yu et al.71 also used the ratio of s2 over s1 as a second fitting parameter (χ12 is the first fitting parameter in eq 5) and its associated equations, so this approach was also tested. The values of χ12 in the oneparameter fits and the values of χ12 and s2/s1 in the two-parameter fits were determined for excess molar volumes at 303.15 K by minimizing the sum of the square of the difference between the values calculated by the model in eq 5, V E and the values calculated from the experimental data (shown in Figure 3) in eq 4, VmE

(7)

based on the following additional equations:65,67

Ψ1 = 1 − Ψ2 =

TVĩ αi 2 = TVĩ γi βi

The molecular surface area (contact energy) fraction, θi,65 is given by

which is used to calculate the reduced volume of the mixture, Ṽ , Ṽ = Ψ1V1̃ + Ψ2V2̃

(10)

min ∑ (V E − VmE)2

(9) L

(13) DOI: 10.1021/acs.jced.6b00542 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 14. Calculated Contributions of Interaction Term, Free Volume Term, and Presure P* Term in Prigogine−Flory−Patterson (PFP) Model to the Excess Molar Volumes at Experimentally Measured Mole Fractions and to Excess Molar Volumes at x1 = 0.5000 Predicted by Redlich−Kister Fit to Mole Fraction−Excess Molar Volume Data and 303.15 K VE cm3·mol−1

σ × 102 x1

ϕ1

ψ1

Ṽ

n-Butylbenzene (1) + n-Decane (2) 0.5145 0.463 0.436 1.25

free volume term 2

2.90 3.50 3.98 3.55

0.096 0.096 0.095 0.098

−0.026 −0.026 −0.026 −0.025

0.083 0.084 0.084 0.083

0.153 0.154 0.153 0.156

0.158

7.59 9.17 8.59 9.24

0.255 0.254 0.255 0.257

−0.003 −0.003 −0.004 −0.003

0.037 0.037 0.037 0.036

0.288 0.287 0.288 0.290

0.282

11.1 13.5 12.8 12.9

0.361 0.374 0.371 0.358

−0.0002 −0.0002 −0.0002 −0.0002

−0.010 −0.010 −0.010 −0.010

0.351 0.363 0.361 0.348

0.348

13.51 16.52 16.30 16.50

0.457 0.471 0.470 0.466

−0.004 −0.004 −0.004 −0.004

−0.055 −0.055 −0.055 −0.054

0.396 0.412 0.411 0.408

0.414

14.76 17.86 16.00 17.87 16.19

0.513 0.502 0.510 0.496 0.496

−0.007 −0.007 −0.007 −0.007 −0.007

−0.076 −0.076 −0.076 −0.073 - 0.073

0.431 0.419 0.427 0.417 0.417

0.431

θ2

cm3·mol−1

χ12

1.08a 0.745b 0.586c 0.745b

0.556 0.464 0.405 0.478

1.1 0.68 0.62

0.551 0.455 0.487 0.514

1.4 1.1 0.98

0.639 0.542 0.570 0.541

2.6 2.1 2.1

0.642 0.542 0.549 0.571

2.9 0.40 0.38

0.541 0.438 0.496 0.582 0.632

1.8 2.2 0.84

0.5000 0.549 0.422 1.25 n-Butylbenzene (1) + n-Dodecane (2) 0.5593 0.467 0.436 1.24 1.07a 0.729b 0.831c 0.5000 0.408 0.378 1.24 0.729b n-Butylbenzene (1) + n-Tetradecane (2) 0.4988 0.376 0.340 1.24 1.07a 0.714b 0.797c 0.5000 0.377 0.341 1.24 0.714b n-Butylbenzene (1) + n-Hexadecane (2) 0.5293 0.373 0.336 1.23 1.07a 0.706b 0.724c 0.5000 0.334 0.299 1.23 0.706b n-Butylbenzene (1) + n-Heptadecane (2) 0.6419 0.473 0.431 1.23 1.06a 0.698b 0.883c 0.5000 0.346 0.308 1.23 0.698b 0.858c

P* term 3

interaction term 1

s2/s1

total PFP model

expt or R−K fit

0.156d

0.290d

0.348

0.408d

0.417d

a Group contribution to van der Waals volume and surface area from ref 78. bValues from Table 14. cValue fit along with χ12. dExcess molar volume predicted at x1 = 0.5000 from Redlich−Kister fit of excess molar volumes determined in this study. ΔVE (decane) = x1 x2 [0.622 + 0.082(x1 − x2) − 0.038(x1 − x2)2] σ = 0.0064 cm3·mol. ΔVE (dodecane) = x1 x2 [1.16 + 0.176(x1 − x2) − 0.056(x1 − x2)2 ] σ = 0.0100 cm3·mol. ΔVE (tetradecane) = x1 x2 [1.39 + 0.255(x1 − x2) + 0.470(x1 − x2)2 ] σ = 0.0173 cm3·mol. ΔVE (hexadecane) = x1 x2 [1.63 + 0.389(x1 − x2) + 0.092(x1 − x2)2 ] σ = 0.0035 cm3·mol. ΔVE (heptadecane) = x1 x2 [1.67 + 0.653(x1 − x2) + 0.288(x1 − x2)2] σ = 0.0103 cm3·mol.

group contribution78 and those calculated from si values in the literature,65,68−72 except for that in the decane system in which the s2/s1 was smaller than both estimates. Other researchers who have reported the contributions of these three terms to the excess molar volumes for binary mixtures of alkylbenzenes with linear alkanes have used the value of excess molar volume at a mole fraction of 0.5, which they calculated by first fitting their excess molar volume and mole fraction data to a Redlich−Kister expression and solving the equation for excess molar volume at x1 = 0.5000. To see if this approach changes the relative contributions of the three terms in the equation, the excess molar volumes at x1 = 0.5000 in the current study were determined by fitting the data to the Redlich−Kister equation:

These calculations were performed using the GRG nonlinear engine of the SOLVER function in Microsoft Excel 2010. The results of the fitting operation and the contributions of interaction term (term 1), the free volume term (term 2), and the pressure P* term (term 3) to the measured excess molar volume are given in Table 14. For decane, the three terms in eq 5 contribute to the excess molar volume (Table 14). As the carbon chain length increases on the linear alkane, the interaction term (term 1) increases and becomes the dominant term in the equation; the free volume term (term 2) has a much smaller influence, and the pressure P* term (term 3) goes from a positive contributor to excess molar volume to a negative contributor to excess molar volume. The various ways used to calculate s2/s1 did change the value of χ12, but did not significantly change the general trends for the interaction term, free volume term, and pressure P* term. The three ways to calculate χ12 can be compared using the standard error of the fit (eq 2), where Pmeasured is the value from the data and Pm,cal is the excess molar volume from the Prigogine−Flory−Patterson model, which are given in Table 14. In general, the group contribution method78 had the largest standard error of the fit and the two parameter fit (χ12 and s2/s1) has the smallest standard error. The s2/s1 ratios that were fit in the two-parameter fit fell between those values estimated using

2

ΔV E = x1x 2 ∑ Aj (x1 − x 2) j j=0

= x1x 2{A 0 + A1(x1 − x 2) + A 2 (x1 − x 2)2 }

(14)

and solving for x1 = 0.5000. These fits are shown in Figure 3 for 303 K with the values at X = 0.5000 given in Table 14. The values of the coefficients and the standard error of the fit at 303 K are given in the footnote in Table 14. The calculated excess molar volume at x1 = 0.5000 was then used in eq 5 to calculate χ12. Such an approach produced the same trends found above, namely M

DOI: 10.1021/acs.jced.6b00542 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 15. Comparison of the Measured Viscosities of Butylbenzene, n-Decane, n-Dodecane, n-Tetradecane, n-Hexadecane, and n-Heptadecane with Literature Valuesa mPa·s T/K butylbenzene

n-decane

n-dodecane

this study

a

293.15

1.05 ± 0.05

303.15

0.91 ± 0.03

313.15 323.15 333.15 343.15 353.15 363.15 373.15 293.15

0.80 ± 0.01 0.71 ± 0.01 0.636 0.571 0.516 0.469 0.430 0.922

303.15

0.794

313.15

0.693

323.15

0.615

333.15 343.15

0.545 0.486

353.15

0.436

363.15 373.15

0.396 0.362

293.15

1.47

303.15 313.15

1.24 1.06

323.15 333.15

0.916 0.801

343.15 353.15

0.706 0.627

mPa·s a

lit.

T/K

1.032c, 1.034d 1.035c, 1.050c, 1.07c 0.893d, 0.894c, 0.895c, 0.9035c, 0.901b 0.787b, 0.781c, 0.79c 0.684c, 0.7015c 0.614c, 0.6237c 0.63c 0.550c 0.497c, 0.5045c, 0.51c 0.450c, 0.4586c 0.42c 0.909c, 0.911l, 0.9135f, 0.9183c, 0.9204c, 0.924c, 0.927c, 0.9284c 0.784c, 0.7842c, 0.787l, 0.7898f, 0.7913c, 0.7964c, 0.8018c, 0.814c 0.686c, 0.6906f, 0.6924c, 0.696c, 0.6968c, 0.7010c 0.607m, 0.6097f, 0.6141c, 0.6148c, 0.6192c 0.5428f, 0.546c, 0.5462c,0.5517c 0.4868f, 0.4890c, 0.4951c, 0.4985c 0.4393f, 0.4409c, 0.441c, 0.4476c 0.3986f, 0.3996c, 0.4068c 0.360m, 0.363c, 0.3635f, 0.3638c,0.3715c 1.48 ± 0.1%g, 1.487 ± 0.5%f, 1.49 ± 0.008e, 1.50 ± 1%h 1.245 ± 0.5%f, 1.25 ± 0.008e 1.06 ± 0.008e, 1.060 ± 0.5%f, 1.062 ± 0.1%g, 1.07 ± 1%h 0.915 ± 0.5%f, 0.916 ± 0.008e 0.799 ± 0.008e, 0.799 ± 0.5%f, 0.81 ± 1%h 0.704 ± 0.008e, 0.705 ± 0.5%f 0.625 ± 0.008e, 0.628 ± 0.5%f, 0.634 ± 1%h

363.15 373.15

0.562 0.506

293.15

2.30

303.15

1.88

313.15

1.56

323.15 333.15 343.15 353.15 363.15 373.15 293.15

1.32 1.13 0.980 0.858 0.760 0.679 3.45

303.15 313.15

2.74 2.22

323.15 333.15

1.84 1.55

343.15 353.15

1.32 1.14

363.15 373.15 303.15 313.15 323.15 333.15 343.15 353.15 363.15 373.15

1.00 0.887 3.25 2.61 2.14 1.79 1.52 1.30 1.14 1.00

n-tetradecane

n-hexadecane

n-heptadecane

this study

lit. 0.560 ± 0.008e, 0.563 ± 0.5%f 0.506 ± 0.008e, 0.508 ± 0.5%f, 0.510 ± 1%h 2.29, 2.319c, 2.33 ± 1%h, 2.342c, 2.346n 1.8292c, 1.882c, 1.895j, 1.897n, 1.910c 1.566c, 1.590c, 1.594n, 1.60 ± 1 %h 1.324c, 1.345c 1.136c, 1.15 ± 1%h, 1.154c 0.9870c, 1.002c 0.8676c, 0.878 ± 1%h, 0.8798c 0.7693c, 0.7795c 0.6877c, 0.692 ± 1%h, 0.6985c 3.44 ± 0.01i, 3.447g, 3.484c, 3.505c 2.72 ± 0.01i, 2.748c, 2.766c 2.21 ± 0.01i, 2.223c, 2.23 ± 1 %h 2.243g 1.82 ± 0.01i, 1.840c, 1.866c 1.53 ± 0.01i, 1.550c, 1.56 ± 1 %h 1.573c 1.31 ± 0.01i, 1.326c, 1.346c 1.13 ± 0.01i, 1.152c, 1.16 ± 1 %h 1.166c 0.99(0) ± 0.01i, 1.010c, 1.021c 0.87(6) ± 0.01i, 0.896 ± 1%h 3.284c, 3.296c 2.620c, 2.650c 2.144c, 2.176c, 2.1696 1.790c, 1.820c 1.522c, 1.546c 1.312c, 1.330c 1.146c, 1.158c 1.011c, 1.018c

Standard uncertainties u are u(T) = 0.01 K, and expanded uncertainties Uc(μ) = 0.008 mPa·s unless otherwise indicated by “±” symbol, (level of confidence = 0.95, k = 2). bReference 41. cReference 79. dReference 49. eReference 32. fReference 41. gReference 80. hReference 81. iReference 31. j Reference 45. lReference 54. mReference 82. nReference 83. a

x1 = 0.5 and 0.6 to fit parameters in the Prigogine−Flory− Patterson model does successfully predict excess molar volumes at other mole fractions. In their studies on mixtures containing ethylbenzene and n-alkanes from 6 carbons to 16 carbons, Awwad et al.64 found that for n-hexane, all three terms contributed to the excess molar volume. As the number of carbons on the linear alkane increased, the contribution of the interaction parameter (term 1) increased and became the dominant contributor to excess molar volume as was found in the current study for butylbenzene. The sign of the pressure term (P* term) in their study changed from negative to positive when transitioning from n-decane to n-dodecane, whereas the sign of the P* term in the current study changes from positive to negative when going from dodecane to tetradecane. The free volume term for the ethylbenzene system was most negative for n-hexane, became less negative for n-heptane through n-decane, and then became more negative at higher numbers of carbon atoms.64 In contrast, Iloukhani et al.62 reported that the

for mixtures containing linear alkanes with carbon chain lengths longer that those of decane, term 1 increases and becomes the dominant term in the equation, term 2 has a much smaller influence, and term 3 goes from a positive contributor to excess molar volume to a negative contributor to excess molar volume. Yu et al.71 showed that fitting the Prigogine−Flory−Patterson model to only two experimental values of excess molar volume near their maximums, such as values at x1 = 0.5 and 0.6, could successfully predict the excess molar volumes at other mole fractions. In the current study, this approach was taken using the excess molar volumes for two experimental values near x1 = 0.5 and s2/s1 values from Table 13. The fitted χ12 values and standard errors of the fit were similar to values found with the use of all the data and the use of the excess molar volume at x1 = 0.5000 from the Redlich−Kister expression. The results of these fits are given in the Supporting Information. These results support the assertion by Yu et al.71 that values using excess molar volumes at N

DOI: 10.1021/acs.jced.6b00542 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 16. McAllister Equation (eq 14) Coefficient and Associated Standard Error (eq 2) for Binary Mixtures of Butylbenzene (1) + n-Decane, + n-Dodecane, + n-Tetradecane,+ n-Hexadecane, or + n-Heptadecane from T = (293.15 to 373.15) K and 0.1 MPa T/K

ν12/mm2·s−1

ν21/mm2·s−1

Butylbenzene (1) + n-Decane (2) 293.15 1.20 1.16 303.15 1.04 1.03 313.15 0.913 0.919 323.15 0.822 0.831 333.15 0.737 0.748 343.15 0.666 0.680 353.15 0.608 0.620 363.15 0.562 0.570 373.15 0.524 0.528 Butylbenzene (1) + n-Dodecane (2) 293.15 1.30 1.63 303.15 1.16 1.41 313.15 1.04 1.24 323.15 0.936 1.10 333.15 0.849 0.976 343.15 0.773 0.877 353.15 0.705 0.793 363.15 0.646 0.723 373.15 0.592 0.664 Butylbenzene (1) + n-Tetradecane (2) 293.15 1.72 2.25 303.15 1.48 1.91 313.15 1.29 1.64 323.15 1.13 1.43 333.15 1.01 1.26 343.15 0.903 1.12 353.15 0.817 1.01 363.15 0.746 0.910 373.15 0.686 0.829 Butylbenzene (1) + n-Hexadecane (2) 293.15 2.06 3.15 303.15 1.78 2.60 313.15 1.55 2.19 323.15 1.37 1.86 333.15 1.21 1.62 343.15 1.09 1.42 353.15 0.982 1.25 363.15 0.892 1.13 373.15 0.814 1.02 Butylbenzene (1) + n-Heptadecane (2) 303.15 2.10 2.94 313.15 1.77 2.47 323.15 1.52 2.11 333.15 1.32 1.82 343.15 1.18 1.58 353.15 1.05 1.39 363.15 0.972 1.22 373.15 0.915 1.08

103·σ/mm2·s−1 4.12 1.94 1.08 0.88 0.29 0.38 0.39 0.24 0.23

Figure 4. Viscosities of binary mixtures of butylbenzene (1) with △, n-decane; ■, n-dodecane; ○, n-tetradecane; ▲, n-hexadecane; or □, n-heptadecane at 303.15 K. Lines shown are fits to the McAllister Equation with coefficients in Table 16.

6.24 3.26 1.63 1.31 0.74 0.47 0.39 0.36 0.37

Table 17. Comparison of the Measured Flash Points and Surface Tensions of Butylbenzene, n-Decane, n-Dodecane, n-Tetradecane, n-Hexadecane, and n-Heptadecanea with Literature Valuesb surface tension/mN·m‑1

flash point/K

5.84 3.56 2.13 0.67 0.47 0.87 0.60 0.52 0.51

this study lit.

Butylbenzene 329.0 ± 2 322c, 323d 330e, 344 f n-Decane 321.6 319.3g, 321h 324 c, 325.0 ± 0.5i n-Dodecane 352.7 ± 2 347f, 352h n-Tetradecane 380.7 373.15g 382.5 ± 2.7c 383.55 ± 1.0i 385f n-Hexadecane 406 ± 2 407 ± 2j, 408k,l, 409 f

this study lit.

417 ± 2 421c

this study lit. this study lit. this study lit. this study lit.

7.36 4.41 1.97 1.96 0.76 0.84 0.54 0.47 0.37

29.1@ 294.2 K 29.1n 23.8@ 294.6 K 23.7n 25.1 @ 294.1 K 25.3n 26.2@ 294.6 K 26.4n

27.4 @ 294.8 K 27.3l @ 294.3 K 27.4m @ 294.8 K

n-Heptadecane

7.91 2.34 3.09 2.38 2.29 4.06 5.03 2.00

a

Since n-heptadecane is not a liquid at room temperature, its surface tension was not measured. bExpanded uncertainties Uc are Uc(flash point) = 2 K, Uc(surface tension) = 0.2 mN·m−1, u(T) = 0.01 K for surface tension (level of confidence = 0.95, k = 2). cReference 85. d Reference 86. eReference 87. fReference 88. gReference 89. h Reference 90. iReference 91. jReference 92. kReference 93. l Reference 33. mBased on linear regression of values found in references; found in ref 33. nInterpolated value based on data in ref 94.

contribution of the interaction term for mixtures of toluene with n-alkanes from 6 carbons to 10 carbons decreased as carbon number increased and the P* transitioned from negative to positive between octane and nonane. The only similarity between the toluene results in that study and butylbenzene in the current study was that the free volume term was less important at longer carbon chain lengths.

4.4. Viscosity. The viscosities of butylbenzene and the linear alkanes measured herein are given as a function of temperature in Table 15 along with literature values. The viscosities of the pure components match most of the reported values within the expanded uncertainty of the measurements. The viscosities of the binary mixtures of butylbenzene with n-decane, n-dodecane, O

DOI: 10.1021/acs.jced.6b00542 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 18. Surface Tensions and Flash Points of Binary Mixtures of Butylbenzene (1) + n-Decane, + n-Dodecane, + n-Tetradecane, n-Hexadecane, or + n-Heptadecanea x1 0.1055 0.2096 0.3124 0.4141 0.5145 0.6140

surface tension (mN·m−1)

flash point (K)

Butylbenzene (1) + n-Decane (2) 23.9 322.(6) ± 2 24.3 322.(6) ± 2 24.6 323.(9) ± 2 24.9 323.(9) ± 2 25.4 325.(1) ± 2 25.8 325.(1) ± 2

325.(3) ± 2 326.(3) ± 2.8 0.9051 27.9 328.(1) ± 2 Butylbenzene (1) + n-Hexadecane (2) 0.1586 27.5 366.7 ± 2 0.2971 27.3 353.7 ± 2 0.4067 27.6 346.7 ± 2 0.5293 27.8 341.7 ± 2 0.6278 27.9 338.7 ± 2 0.7158 28.0 336.7 ± 2 0.7981 28.2 334.9 ± 4 0.8709 28.4 333.3 ± 2 0.9380 28.7 331.4 ± 4 0.7120 0.8094

26.5 26.7

x1

surface tension (mN·m−1)

flash point (K)

Butylbenzene (1) + n-Tetradecane (2) 0.1414 26.5 361.7 ± 2 0.2704 26.7 352.2 ± 2 0.3915 27.0 346.7 ± 2 0.4988 27.0 341.5 ± 2.3 0.5961 27.3 339.2 ± 2.3 0.6892 27.3 337.2 ± 2 0.7751 0.8553

27.8 28.0

336.2 ± 2 332.2 ± 2

0.9299 28.3 331.2 ± 2.8 Butylbenzene (1) + n-Heptadecane (2) 0.1662 27.6 368 ± 2 0.3047 27.7 356 ± 2 0.4587 28.0 345.(7) ± 2.8 0.6419 28.2 338.(3) ± 2.3 0.7515 28.3 338 ± 5 0.8742 29.2 333.(9) ± 4.7

x1

surface tension (mN·m−1)

flash point (K)

Butylbenzene (1) + n-Dodecane (2) 25.4 348.(0) ± 2 26.0 343.(7) ± 2 26.3 340.(3) ± 2 26.2 337.(7) ± 2 26.7 335.(7) ± 2 27.0 335.(5) ± 2.3 0.7575 27.5 332.(7) ± 2 0.8349 27.7 332.(3) ± 2

0.1241 0.2414 0.3524 0.4583 0.5593 0.6552

0.9194

28.4

329.(3) ± 2

a x1 is the mole fraction of butylbenzene in binary mixtures with n-alkanes (n-decane, n-dodecane, n-tetradecane, n-hexadecane, or n-heptadecane). Expanded uncertainties Uc are Uc(surface tension) = 0.2 mN·m−1 and flash point Uc(flash point) are indicated by the symbol “±”, and combined expanded uncertainties of Uc (x1) = 0.0002 (level of confidence = 0.9545, k = 2). Surface tension measurements were taken at room temperature, 294.5 ± 1 K.

n-tetradecane, n-hexadecane, or n-heptadecane are given in Tables 3, 4, 5, 6, and 7, respectively. As the mole fraction of butylbenzene increases, the viscosity for all the mixtures decreases. For decane, the viscosity appears to dip slightly below the values for both components at some mixture compositions (Figure 4). The kinematic viscosity data were fit using the McAllister three-body model:84

indicating that it requires greater energy for the molecules to slide past each other. 4.5. Surface Tension and Flash Point. The flash points and surface tensions of butylbenzene and the linear alkanes measured herein are given as a function of temperature in Table 17 along with literature values. The flash points and surface tensions of the pure compounds agree with literature values within the expanded uncertainty of the measurement. The flash points and surface tensions are given in Table 18 for the mixtures of butylbenzene in the various alkanes as a function of the mole fraction of butylbenzene, x1. As the mole fraction of butylbenzene in all alkane mixtures increased, the surface tension increased. Since n-heptadecane is a semisolid at room temperature, no surface tension measurement was taken. Pfohl et al.96 showed plots of surface tension for n-heptadecane near its bulk melting point (∼295 K) and surface melting temperature (∼297 K) that ranged from approximately 26.3 to 27.4 mN·m−1. The surface tension values of butylbenzene and n-heptadecane mixtures measured herein are above those surface tensions. Such a result is consistent with the general trend in surface tension of the butylbenzene/ n-heptadecane mixtures that shows an increase in surface tension with increasing butylbenzene concentration. As the mole fraction of butylbenzene in decane increased, the flash point increased, while for all other alkanes, as the mole fraction of butylbenzene increased, the flashpoint decreased. For all mixtures, the trend was not linear.

ln νm = x13 ln ν1 + 3x12x 2 ln ν1,2 + 3x1x 2 2 ln ν2,1 + x 2 3 ln ν2 ⎛1⎛ ⎛ M ⎞ M ⎞⎞ − ln⎜x1 + x 2 2 ⎟ + 3x12x 2 ln⎜⎜ ⎜2 + 2 ⎟⎟⎟ M1 ⎠ M1 ⎠⎠ ⎝ ⎝3⎝ ⎛1⎛ ⎛M ⎞ M ⎞⎞ + 3x1x 2 2 ln⎜⎜ ⎜1 + 2 2 ⎟⎟⎟ + x 2 3 ln⎜ 2 ⎟ M1 ⎠⎠ ⎝ M1 ⎠ ⎝3⎝

(15)

In this equation, νm is the kinematic viscosity of the binary mixture, x1 and x2 are the mole fractions, ν1 and ν2 are the kinematic viscosities of the pure components, and M1 and M2 are the molar masses of butylbenzene as component 1 and a linear alkane as component 2. The interaction parameters ν2,1 and ν1,2 were determined by minimizing the sum of the square of the difference between the value calculated by the model in eq 15 and the measured kinematic viscosity of the binary mixture. These calculations were performed using the GRG nonlinear engine of the SOLVER function in Microsoft Excel 2010. Equation 2 was used to determine the standard error for the fit, σ, in which Pmeasured is the measured viscosity and Pm,cal is the fitted viscosity. The fitted values of ν2,1, and ν1,2 and the standard errors of the fits are given in Table 16 at each temperature. Figure 4 shows that the model fits the data well. The interaction parameters increase in value as the number of carbons on the linear alkane increases

5. CONCLUSIONS The density, viscosity, speed of sound, surface tension, and flash point of binary mixtures of butylbenzene with decane, dodecane, tetradecane, hexadecane, and heptadecane were measured in this study. Most of the pure component measurements fell within P

DOI: 10.1021/acs.jced.6b00542 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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values reported in the literature. Third-order and fourth-order polynomials were used to fit the mole fraction/density data. The excess molar volumes of the mixtures did not vary significantly with temperature, except for the decane mixtures in which the value declined slightly with increasing temperature. When the values for the various alkanes were compared, alkanes with longer carbon chains tended to have higher excess molar volumes. Modeling these data with the Prigogine−Flory−Patterson model yielded results that suggested that the interaction term increases in importance in comparison with the free volume and pressure terms as the carbon chain on the linear alkane increases. Viscosity/mol fraction data were fit using the Mcallister threebody model and the interactions parameters increase as the linear alkane increases in length, indicating that it requires greater energy for the molecules to slide past each other. Increases in the mole fraction of butyl benzene in the mixtures resulted in a steady increase in speed of sound values for decane and dodecane, but for the other alkanes, speeds of sound were measured that were below the speeds of sound of the individual components in the mixtures. The flash point, surface tension, and bulk moduli for the mixtures increased with increasing concentrations of butylbenzene in the mixtures.

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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.6b00542. Densities and speeds of sound for the NIST-Certified toluene standard; Prigogine−Flory−Patterson model fits using (1) two measured excess molar volume values near x1 = 0.5 and (2) the excess molar volume at x1 = 0.5 predicted from the Redlich−Kister expression that had been fit to all experimental excess molar volumes (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: (410) 293-6339. Fax: (410) 2932218. ORCID

Dianne J. Luning Prak: 0000-0002-5589-7287 Funding

This work was funded by the Office of Naval Research, Grant Nos. N0001415WX01853 and N0001416WX01648, thanks to Maria Medeiros. Notes

The authors declare no competing financial interest.

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REFERENCES

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