Estimation of excess molar volumes and theoretical viscosities of binary mixtures of benzene + n-alkanes at 298.15 K

Abstract

(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image)

Excess molar volumes, (......), have been derived from the literature viscosity data for the binary mixtures of benzene with n-hexane, n-octane, n-decane, n-dodecane, n-tetradecane, and n-hexadecane as a function of composition at 298.15 K and atmospheric pressure conditions. The ...... values were found to be positive over the entire composition range for all mixtures. Concentration dependence of ...... were fitted with Redlich-Kister polynomial equation to estimate the binary coefficients and standard errors. From density data, the partial molar volumes (V _m), partial molar volumes at infinite dilution (......), excess partial molar volumes at infinite dilution (......), and apparent molar volumes (V ), were calculated over the whole composition range as were the limiting apparent molar volumes at infinite dilution (......) and excess apparent molar volumes at infinite dilution (......). Viscosity of the binary mixtures of benzene with n-alkanes were estimated using Kendall-Monroe, Frenkel, Hind et al., Katti-Chaudhri, Grunberg-Nissan, Wilke and Herráez et al. equations. The agreement between experimental and predicted values for all systems was found to be quite reasonable as evidenced from computed standard deviation and average percentage deviation (APD). Wilke relation gives maximum deviations for all the systems in comparison to other methods employed. Other relations give comparatively good results.

http://crossmark.crossref.org/dialog/?doi=10.1007/s40090-016-0100-1&domain=pdf

Web End = Int J Ind Chem (2016) 7:391400 DOI 10.1007/s40090-016-0100-1

http://crossmark.crossref.org/dialog/?doi=10.1007/s40090-016-0100-1&domain=pdf

Web End = RESEARCH

Estimation of excess molar volumes and theoretical viscosities of binary mixtures of benzene + n-alkanes at 298.15 K

Omer El-Amin Ahmed Adam1,3 Akl M. Awwad2

Received: 27 July 2015 / Accepted: 21 September 2016 / Published online: 30 September 2016 The Author(s) 2016. This article is published with open access at Springerlink.com

Abstract Excess molar volumes, (VEm), have been derived from the literature viscosity data for the binary mixtures of benzene with n-hexane, n-octane, n-decane, n-dodecane, ntetradecane, and n-hexadecane as a function of composition at 298.15 K and atmospheric pressure conditions. The VEm values were found to be positive over the entire composition range for all mixtures. Concentration dependence of VEm were tted with

RedlichKister polynomial equation to estimate the binary coefcients and standard errors. From density data, the partial molar volumes (Vm), partial molar volumes at innite dilution (V0m), excess partial molar volumes at innite dilution (V0;Em), and apparent molar volumes (V/), were calculated over the whole composition range as were the limiting apparent molar volumes at innite dilution (V0/) and excess apparent molar volumes at innite dilution (V0;E/). Viscosity of the binary mixtures of benzene with n-alkanes were estimated using

Kendall-Monroe, Frenkel, Hind et al., Katti-Chaudhri, Grunberg-Nissan, Wilke and Herrez et al. equations. The agreement between experimental and predicted values for all systems was found to be quite reasonable as evidenced from

computed standard deviation and average percentage deviation (APD). Wilke relation gives maximum deviations for all the systems in comparison to other methods employed. Other relations give comparatively good results.

Keywords Density Viscosity Binary mixture Excess

molar volume Molecular interactions Viscosity

deviation

Introduction

Excess thermodynamic properties and deviations of non-thermodynamic ones from ideal behavior of binary liquid mixtures are fundamental for the design of industrial equipment and for the interpretation of the liquid state, particularly when polar components are involved [1]. These quantities have the advantage of illustrating the sign and magnitude of the nonideality [2].

Volumetric properties of binary mixtures are complex properties because they depend not only on solutesolute, solventsolvent and solutesolvent interactions, but also on the structural effects arising from interstitial accommodation due to the difference in molar volume and free volume between components present in the solution [3].

Partial molar properties are useful in providing information about solutesolvent interactions. This is because at innite dilution, solutesolute interactions disappear. Of course this information is of great interest because it is composition independent.

Alkanes are important series of homologous, nonpolar, and organic solvents. They have often been used in the study of solute dynamics because their physicochemical properties as a function of chain length are well-known [4]. They are also employed in a large range of chemical processes [5].

Electronic supplementary material The online version of this article (doi:http://dx.doi.org/10.1007/s40090-016-0100-1

Web End =10.1007/s40090-016-0100-1 ) contains supplementary material, which is available to authorized users.

& Omer El-Amin Ahmed Adam [email protected]

1 Chemistry Department, University of Kassala,P.O. Box 266, Kassala 31111, Sudan

2 Royal Scientic Society, P.O. Box 1438, Al-Jubaiha, Amman 11941, Jordan

3 Present Address: Chemistry Department, Faculty of Science and Arts in Baljurashi, Al baha University,P.O. Box 1988, Baljurashi 65635, Saudi Arabia

123

392 Int J Ind Chem (2016) 7:391400

Properties such as viscosity or surface tension are required in many empirical equations for different operations such as mass and heat transfer processes. Determination of equations that modelize the mass transfer process requires knowledge of the density, viscosity, and surface tension of the liquid phase [6].

The measurement of viscosity reveals information about the molecular packing, molecular motion, and various types of intermolecular interactions as related to size, shape, and chemical nature of the component molecules [7].

In recent years, there has been considerable interest in theoretical and experimental investigations of the excess thermodynamic properties of binary mixtures [8, 9].

Generally, VEm can be considered as a result of three types of interactions between component molecules of liquid mixtures [10, 11].(1) Physical interactions consisting mainly of dispersion forces or weak dipoledipole interaction making a positive contribution, (2) chemical or specic interactions, which include charge transfer, H-bonding and other complex formation interactions, resulting in a negative contribution, and (3) structural contribution due to differences in size and shape of the component molecules of the mixtures, due to tting of component molecules into each others structure, hereby reducing the volume and compressibility of the mixtures, resulting in a negative contribution.

In a previous work by Akl et al. [12], results of density and viscosity measurement were determined for binary mixtures of benzene ? n-alkanes at 298.15 K and atmospheric pressure. Excess molar volumes (VEm, excess molar viscosities (D lng), and excess molar activation energies, (DG*E) were calculated. The effect of orientational order of n-alkane on solution molar volumes and viscosities is investigated as well as the adequacy of the absolute rate and free volume theories to predict solution viscosities. For longer n-alkane DG*E and D lng are positive and associated with the orientational order.

In the present work, the data of density and viscosity reported in the literature [12] have been used to evaluate the excess molar volume (VEm) along with other derived parameters, such as partial molar volumes at innite dilution (V0m;1 and V0m;2), excess partial molar volumes at innite dilution (V0;Em;1 and V0;Em;2), apparent molar volumes (V/,1 and V/,2), limiting apparent molar volumes at innite dilution (V0/;1 and V0/;2) and excess apparent molar volumes at innite dilution (V0;E/;1 and V0;E/;2).

These parameters have been interpreted in terms of molecular interactions and structural effects. The work provides a test of various empirical equations to correlate viscosity data of binary mixtures in terms of pure component viscosities.

Theoretical analysis

Excess molar volume

Excess molar volumes (VEm), were calculated for the binary mixtures of benzene with n-hexane, n-octane, n-decane, ndodecane, n-tetradecane, and n-hexadecane using viscosity data by a correlation proposed by Singh [13]. According to the relation, the deviations in viscosity, Dg, and excess molar volumes, VEm, are related to each other as:

Dg K VEm 1

where, K is a tting parameter. The values of K for the investigated mixtures were evaluated using the experimentally reported Dg and VEm data [12] (Table 1).

From the experimental Dg data, VEm values at the whole mole fraction range were calculated at 298.15 K and results were presented in Table 2.

Figures 1,2,3showthatVEm valuescalculatedfrom viscosity data are positive over the entire composition range for all investigated mixtures and follow the sequence: n-hexane \ noctane \ n-decane \ n-dodecane \ n-tetradecane \ n-hexadecane. VEm values increase systematically (0.43031, 0.74732,0.89911, 1.01524, 1.06634 and 1.19575 cm3 mol-1) at benzene mole fraction (x1) range (0.398800.43415) as chain length increases, indicating volume expansion upon mixing of higher n-alkanes with benzene. With increasing size of n-alkanes, volume expansion will be larger, indicating dispersion type of interactions between the component liquids [14].

The volumetric behavior of this class of mixtures could be explained by random mixing model [15], and the interaction between benzene and n-alkane depends strongly on the size of the n-alkane. For each system studied it was observed that the excess molar volume is slightly skewed towards the benzene-rich region of the mole fraction. Calculated values of VEm compare well with those reported by Pea and Delgado [16] for all mixtures, Calvar et al.

[17] for benzene ? n-hexane, ?n-octane, and Letcher and Perkins [18] for benzene ? n-dodecane, ?n-hexadecane.

The excess molar volumes (VEm) were tted by the RedlichKister [19] polynomial equation:

VEm x21 x2 X

i n

i 0

Ai1 2x2i 2

where x2 is the mole fraction of n-alkane.

The appropriate degree (n) of Eq. (2) was determined by standard deviation (r) being calculated as:

r X VEexp VEcal2=N n 1

h i 1=2 3

where N is the total number of experimental points; (n ? 1) is the number of coefcients (Ai) in Eq. (2).

123

Int J Ind Chem (2016) 7:391400 393

Table 1 Values of tting parameter (K) of binary mixtures, and molar volumes of pure components (V m) at 298.15

System K/m Pa.s.cm-3.mol Vm*/cm3.mol-1

Benzene ? n-hexane -0.2145 Benzene 89.458

Benzene ? n-octane -0.1071 n-Hexane 131.540

Benzene ? n-decane -0.0719 n-Octane 163.531

Benzene ? n-dodecane -0.0931 n-Decane 195.913

Benzene ? n-tetradecane -0.1389 n-Dodecane 228.242

Benzene ? n-hexadecane -0.2116 n-Tetradecane 261.287

n-Hexadecane 294.066

Table 2 Values of excess molar volumes, VEm, calculated using Eq. (1) for binary mixtures for (x) nalkane ? (1-x) benzene at 298.15 K

VEm/ cm3.mol-1

(x) n-Hexane ? (1-x) benzene (x) n-Octane ? (1-x) benzene (x) n-Decane ? (1-x) benzene

0.05393 0.13220 0.04472 0.22234 0.03584 0.25984

0.11224 0.25405 0.09184 0.40061 0.10038 0.48841

0.20795 0.35508 0.17152 0.55951 0.20129 0.77266

0.30955 0.41102 0.29540 0.72549 0.29022 0.89092

0.41965 0.43031 0.40878 0.74732 0.39880 0.89911

0.50041 0.41434 0.49074 0.70538 0.49997 0.83648

0.59341 0.36720 0.58551 0.60583 0.59432 0.71743

0.68570 0.30241 0.73898 0.47019 0.70210 0.55340

0.79132 0.21284 0.92796 0.12684 0.83527 0.32117

0.88344 0.11426 0.91651 0.16049

(x) n-Dodecane ? (1-x)

Benzene

(x) n-Tetradecane ? (1-x) Benzene

(x) n-Hexadecane ? (1-x)

Benzene

0.04733 0.22407 0.04444 0.19194 0.05350 0.29540

0.10840 0.48939 0.09068 0.46134 0.09944 0.47192

0.20364 0.79727 0.21254 0.78494 0.21994 0.83828

0.29778 0.94472 0.41693 1.06634 0.32338 1.16970

0.41395 1.01524 0.51212 1.05153 0.43415 1.19575

0.51924 0.96690 0.62706 0.81988 0.51942 1.15131

0.61546 0.86817 0.71387 0.62522 0.64097 1.04078

0.72914 0.67885 0.80062 0.55735 0.69281 1.007280.80113 0.55101 0.88223 0.51832 0.83610 0.85819

0.92306 0.22493 0.94161 0.22225

Calculated values of Ai and r for all systems studied are given in Table 3.

Partial molar volume, Vm,1 and Vm,2, of benzene (1) and

n-alkanes (2), respectively, are given by:

Vm;1 VEm V m;1 1 x1 oVE ox

Vm;1 V m;1 x22 X

i n

i 0

Ai1 2x1i

2x1x22 X

i n

i 1

Ai1 2x1i 1 6

Vm;2 V m;2 x21 X

in

i0

1 P;T

4

Vm;2 VEm V m;2 x1 oVE ox

Ai1 2x1i

5

where Vm,1* and Vm,2* are the molar volumes of the pure

liquids (1) and (2), respectively. Combination of Eqs. (2), (4) and (5) leads to Eqs. (6) and (7) for Vm,1 and Vm,2:

1 P;T

2x21x2 X

in

i 1

Ai1 2x1i 1 7

123

394 Int J Ind Chem (2016) 7:391400

0.000.200.400.600.80

0.00 0.20 0.40 0.60 0.80 1.00

x2

Values of the partial molar volumes at innite dilution, V0m;1 and V0m;2, were obtained by the linear extrapolation of corresponding partial molar volumes using Eqs. (6) and (7). Extrapolation of Vm,1tox1 ? 0 results in V0m;1, and consequently, extrapolation of Vm;2 to x2 ! 0 results in

V0m;2. The excess partial molar volumes at innite dilution, V0;Em;1 and V0;Em;2, were calculated using the following relations [20]:

V0;Em;1 V0m;1 V m;1 8

V0;Em;2 V0m;2 V m;2 9

Apparent molar volumes of benzene V/,1 and apparent molar volume of n-alkanes V/,2 were calculated from experimental data using the following relations [21]:

V/;1

Vm x2V02

x1

m

V E

Fig. 1 Excess molar volume VEm versus x2 for benzene(1) with nhexane(2) and n-octane(2) at 298 K

0.00

1.20

q2 qx2M2

x1q q2

M1 q

10

1.00

0.80

V E

0.60

m

M2q 11

Extrapolation of V/;1 to x1 ! 0 and V/;2 to x2 ! 0

give the values of the limiting apparent molar volumes V0/;1

and V0/;2 at innite dilution, represented earlier as V0m;1 and V0m;2. The excess apparent molar volumes at innite dilution, V0;E/;1 and V0;E/;2 were also calculated by equations similar to Eqs. (8) and (9). The values V0m;1, V0/;1, Vm,1*,

V0;Em;1, V0;E/;1, V0m;2, V0/;2, Vm,2*, V0;Em;2 and V0;E/;2 for all six binary

mixtures at 298.15 K are listed in Table 4. An examination of data in Table 4 reveals that the values of V0m;1 and V0/;1 are nearly of the same magnitude, and the values of V0/;2

are slightly greater than V0m;2 for all binary mixtures. Values of V0;Em;1, V0;E/;1, V0;Em;2 and V0;E/;2 are positive over the entire composition range for all systems. This indicates that molar volumes and apparent molar volumes of both components in the mixture are larger than their respective values in the pure state, which indicates the presence of

0.40

V/;2

Vm x1V01

x2

q1 qx1M1

x2q q1

0.20

0.00 0.20 0.40 0.60 0.80 1.00

x2

Fig. 2 Excess molar volume VEm versus x2 for benzene(1) with ndecane(2) and n-dodecane(2) at 298 K

0.00

1.40

1.20

1.00

0.80

m

V E

0.60

0.40

0.20

0.00 1.00

Fig. 3 Excess molar volume VEm versus x2 for benzene(1) with ntetradecane(2) and n-hexadecane(2) at 298 K

Table 3 Coefcients Ai of

Eq. 2 and standard deviation, r, at 298.15 K

Binary mixture A0 A1 A2 A3 A4 r

Benzene ? n-hexane 0.0051 2.6233 -5.1111 3.4665 -0.9871 0.008

Benzene ? n-octane -0.0123 4.0913 -7.0177 4.2741 -1.3307 0.062

Benzene ? n-decane 0.0234 5.9634 -12.8940 9.8982 -2.9941 0.018

Benzene ? n-dodecane -0.0114 5.7372 -10.2400 6.5010 -1.9869 0.011

Benzene ? n-tetradecane -0.0279 6.2820 -12.5210 9.7973 -3.4848 0.080

Benzene ? n-hexadecane -0.0194 6.4531 -12.9770 12.9030 -6.3815 0.080

123

Int J Ind Chem (2016) 7:391400 395

Table 4 The values V0m;1, V0m;2, V0/;1, V0/;2, Vm,1*, Vm,2*, V0;Em;1, V0;Em;2, V0;E/;1 and V0;E/;2 for all six mixtures at 298.15 K

Benzene (1)1 V0m;1 V0/;1 Vm,1* V0;Em;1 V0;E/;1 V0m;2 V0/;2 Vm,2* V0;Em;2 V0;E/;2

n-Hexane(2) 90.111 91.082 89.458 0.653 1.620 131.754 133.143 131.540 0.214 1.603

n-Octane(2) 90.255 92.159 89.458 0.797 2.701 164.070 166.932 163.531 0.539 3.401

n-Decane(2) 91.397 92.423 89.458 1.939 2.965 196.460 200.061 195.913 0.547 4.148

n-Dodecane(2) 91.623 92.630 89.458 2.165 3.172 228.661 233.215 228.242 0.419 4.973

n-Tetradecane(2) 92.181 92.646 89.458 2.723 3.188 261.598 267.354 261.287 0.311 6.067

n-Hexadecane(2) 92.938 92.989 89.458 3.480 3.531 294.715 301.119 294.066 0.649 7.053

All quantities have the unit: cm3 mol-1

signicant solutesolute and solventsolvent interactions between like molecules in the mixture [22].

Correlation equations for viscosity

Viscosity data are given in Table 5 as a function of the mole fraction of the n-alkane at 298.15 K. The viscosity deviation was calculated according to the following equation:

Dg g x1 g1 x2 g2 12

where g1, g2 and g are the viscosities of component 1(benzene), component 2 (n-alkane) and the mixture, respectively. All mixtures deviate from ideality with a negative deviation, which indicate that dispersion forces are predominant between benzene and n-alkane [23].

Various equations are used in the literature to calculate the viscosity of mixtures in terms of pure component data. To carry out a comparative study, KendallMunroe, Frenkel, Hind et al., Katti-Chaudhri, Grunberg-Nissan, Wilke and Herrez et al. equations have been employed to estimate the viscosity of binary liquid mixtures of benzene ? n-alkanes.

1. Kendall-Monroe [24] derived Eq. (13) for analyzing the viscosity of binary mixtures based on zero adjustable parameter. This equation calculates the mixture viscosity as the cubic-root average of the component viscosities:

g x1g1=31 x2g1=323 13

2. Frenkel with the help of Eyrings model [25, 26] took into consideration the interaction between molecules and developed the following logarithmic relation for nonideal binary mixtures:

ln g x21 ln g1 x22 ln g2 2x1x2 ln g12 14 where, g12 is a constant attributed to unlike pair interactions. Its value is obtained from the following equation:

g12 0:5 g1 0:5 g2 15

3. Hind et al. [27] have suggested the following equation for the viscosity of binary liquid mixtures:

ln g x21 g1 x22 g2 2x1x2H12 16

where, H12 is the Hind interaction parameter and is attributed to unlike pair interactions, and other terms have their usual meaning.4. Katti-Chaudhri equation is expressed as [28]:

lngV x1 lng1V1 x2 lng2V2 x1x2 W=RT 17

where, W is the interaction energy parameter, V is the volume of the mixture, V1 and V2 are the volumes of component 1 and component 2, respectively.5. Grunberg and Nissan [29] have formulated equation to assess the molecular interactions leading to viscosity changes:

ln g x1 ln g1 x2 ln g2 x1x2G12 18 where, G12 is a constant, proportional to interchange energy, g is the dynamic viscosity and the subscripts 1, 2 and 12 stands for the pure components, benzene, nalkanes and mixtures, respectively.6. Wilke [30] proposed the viscosity equation:

g

x1g1

x1 x2/12

x2g2

x2 /21

19

where, /12 and /21 are calculated by the following equations:

/12

1

8 1 M1=M2

f g 1=2

1=2 M2=M11=4

g1 g2

20

M1M2 21

where, / and M are the volume fraction and molar mass, and the subscripts 1 and 2 stands for pure components benzene and n-alkane, respectively.

/21 /12

g2 g1

123

396 Int J Ind Chem (2016) 7:391400

Table 5 Viscosity deviation (gexp-gcalc.) for the binary mixtures at 298.15 K

Viscosity deviation (gexp.-gcalc.)

x2 gexp. (mPa.s) K. & M. Frenkel Hind Katti G. & N. Wilke Herrez et al.

Benzene ? n-hexane

0.05393 0.5662 -0.0248 0.0186 -0.0100 -0.0039 -0.0284 -0.0366 0.0134

0.11224 0.5225 -0.0476 0.0372 -0.0186 -0.0089 -0.0545 -0.0695 -0.0006

0.20795 0.4720 -0.0648 0.0754 -0.0168 -0.0060 -0.0762 -0.0983 -0.0146

0.30955 0.4294 -0.0735 0.1086 -0.0111 -0.0034 -0.0882 -0.1138 -0.0260

0.41965 0.3921 -0.0757 0.1319 -0.0045 -0.0024 -0.0923 -0.1182 -0.0342

0.50041 0.3712 -0.0720 0.1412 0.0012 -0.0009 -0.0889 -0.1133 -0.03580.59341 0.3533 -0.0626 0.1433 0.0082 0.0019 -0.0788 -0.1002 -0.0331

0.68570 0.3394 -0.0505 0.1335 0.0128 0.0039 -0.0649 -0.0823 -0.0280

0.79132 0.3268 -0.0347 0.1063 0.0139 0.0045 -0.0457 -0.0577 -0.0201

0.88344 0.3202 -0.0177 0.0703 0.0126 0.0056 -0.0245 -0.0314 -0.0097

Benzene ? n-octane

0.04472 0.5829 -0.0236 0.0245 -0.0102 -0.0073 -0.0238 -0.0407 0.0194

0.09184 0.5595 -0.0425 0.0514 -0.0162 -0.0115 -0.0429 -0.0748 0.0038

0.17152 0.5352 -0.0592 0.1007 -0.0145 -0.0088 -0.0599 -0.1115 -0.0127

0.29540 0.5061 -0.0767 0.1575 -0.0112 -0.0077 -0.0777 -0.1476 -0.0341

0.40878 0.4934 -0.0788 0.1931 -0.0028 -0.0025 -0.0800 -0.1561 -0.0418

0.49074 0.4904 -0.0743 0.2069 0.0043 0.0025 -0.0755 -0.1508 -0.0418

0.58551 0.4924 -0.0637 0.2094 0.0127 0.0088 -0.0649 -0.1345 -0.0368

0.73898 0.4929 -0.0494 0.1676 0.0113 0.0064 -0.0504 -0.1018 -0.0322

0.92796 0.5124 -0.0133 0.0620 0.0078 0.0058 -0.0136 -0.0300 -0.0084

Benzene ? n-decane0.03584 0.6003 -0.0179 0.0314 -0.0100 -0.0079 -0.0187 -0.0408 -0.0105

0.10038 0.5986 -0.0330 0.0958 -0.0125 -0.0091 -0.0351 -0.0912 -0.0125

0.20129 0.6012 -0.0517 0.1775 -0.0152 -0.0114 -0.0556 -0.1512 -0.0118

0.29022 0.6130 -0.0591 0.2346 -0.0124 -0.0095 -0.0641 -0.1824 -0.0041

0.39880 0.6372 -0.0589 0.2830 -0.0045 -0.0033 -0.0646 -0.1971 0.0105

0.49997 0.6648 -0.0541 0.3023 0.0025 0.0023 -0.0601 -0.1937 0.0234

0.59432 0.6949 -0.0457 0.2980 0.0089 0.0078 -0.0516 -0.1767 0.0336

0.70210 0.7313 -0.0347 0.2635 0.0126 0.0111 -0.0398 -0.1451 0.0386

0.83527 0.7784 -0.0197 0.1764 0.0114 0.0100 -0.0231 -0.0901 0.0321

0.91651 0.8085 -0.0097 0.0994 0.0076 0.0068 -0.0115 -0.0481 0.0204

Benzene ? n-dodecane

0.04733 0.6259 -0.0121 0.0685 -0.0040 0.0003 -0.0209 -0.0607 0.0023

0.10840 0.6476 -0.0267 0.1459 -0.0095 -0.0036 -0.0456 -0.1297 -0.0020

0.20364 0.6913 -0.0423 0.2471 -0.0137 -0.0066 -0.0742 -0.2121 -0.0098

0.29778 0.7491 -0.0464 0.3264 -0.0099 -0.0041 -0.0880 -0.2622 -0.0119

0.41395 0.8308 -0.0458 0.3862 -0.0040 -0.0007 -0.0945 -0.2926 -0.01340.51924 0.9153 -0.0394 0.4046 0.0031 0.0031 -0.0900 -0.2908 -0.0116

0.61546 0.9976 -0.0325 0.3881 0.0075 0.0047 -0.0808 -0.2691 -0.0100

0.72914 1.1016 -0.0224 0.3281 0.0105 0.0054 -0.0632 -0.2190 -0.0071

0.80113 1.1682 -0.0182 0.2644 0.0082 0.0027 -0.0513 -0.1765 -0.0073

0.92306 1.2912 -0.0060 0.1198 0.0056 0.0020 -0.0209 -0.0767 -0.0022

Benzene ? n-tetradecane

0.04444 0.6498 -0.0032 0.0880 -0.0031 0.0060 -0.0267 -0.0719 0.0062

0.09068 0.6807 -0.0182 0.1585 -0.0183 -0.0021 -0.0641 -0.1513 -0.0085

0.21254 0.8158 -0.0143 0.3427 -0.0162 0.0087 -0.1090 -0.2837 -0.0173

123

Int J Ind Chem (2016) 7:391400 397

Table 5 continued

Viscosity deviation (gexp.-gcalc.)

x2 gexp. (mPa.s) K. & M. Frenkel Hind Katti G. & N. Wilke Herrez et al.

0.41693 1.0787 -0.0065 0.5080 -0.0132 0.0023 -0.1481 -0.3987 -0.0389

0.51212 1.2214 0.0014 0.5283 -0.0074 -0.0032 -0.1461 -0.4035 -0.0412

0.62706 1.4234 0.0262 0.5173 0.0159 0.0050 -0.1139 -0.3558 -0.0223

0.71387 1.5787 0.0370 0.4645 0.0265 0.0059 -0.0868 -0.2996 -0.01050.80062 1.7163 0.0204 0.3534 0.0112 -0.0142 -0.0774 -0.2454 -0.0202

0.88223 1.8423 -0.0076 0.2084 -0.0143 -0.0371 -0.0720 -0.1828 -0.0361

Benzene ? n-hexadecane

0.05350 0.6803 -0.0033 0.1243 -0.0099 0.0082 -0.0625 -0.1211 0.0046

0.09944 0.7563 0.0058 0.2305 -0.0069 0.0223 -0.0999 -0.2034 0.0053

0.21994 0.9761 0.0297 0.4555 0.0007 0.0432 -0.1774 -0.3761 -0.0106

0.32338 1.1612 0.0217 0.5597 -0.0204 0.0161 -0.2475 -0.5023 -0.0564

0.43415 1.4290 0.0553 0.6532 0.0020 0.0155 -0.2530 -0.5420 -0.0568

0.51942 1.6488 0.0744 0.6772 0.0155 0.0024 -0.2436 -0.5407 -0.0554

0.64097 1.9721 0.0792 0.6287 0.0186 -0.0349 -0.2202 -0.5004 -0.0585

0.69281 2.1071 0.0662 0.5720 0.0078 -0.0603 -0.2131 -0.4755 -0.0676

0.83610 2.4922 0.0026 0.3239 -0.0393 -0.1200 -0.1816 -0.3581 -0.0940

0.94161 2.8871 0.0282 0.1558 0.0100 -0.0347 -0.0470 -0.1210 -0.0134

7. Herrez et al. [31] proposed a new correlation equation based on the linear behavior of binary mixtures:

g g1 g2 g1 x2 22

They introduce an exponential function of the mole fraction, x2, in Eq. 22 above, to yield:

g g1 g2 g1 x

Pni 0

Bi:xi2 2

23

which for n = 0 would be:

g g1 g2 g1 xBo 2 24

where, B0 is the universal exponent constant.

The predicted values of viscosities of the binary mixtures, using Eqs. (13), (14), (16), (17), (18), (19) and (24), including standard deviation, at 298.15 K were compared with the experimentally measured values, and results are presented in terms of viscosity deviations (Dg) (Table 5).

Validity of aforementioned relations has been checked by calculating the viscosity deviations. The average percentage deviation (APD) between calculated and experimental viscosity values is calculated by [32]:

APD

100 N

X

" #

gexp gcalj

gexp

25

where N is the number of data points in each set.

The interaction parameters of Eqs. (13), (14), (16), (17), (18), (19) and (24), along with APD and r values for all binary mixtures are presented in Table 6. A careful perusal

of Table 6 reveals that maximum deviations are obtained using Wilke relation for the prediction of viscosity of binary liquid mixtures under the present study while other relations give comparatively good results. The best results obtained by using KattiChaudhri relation. The trend of validity of the presently used relations is as follows: Katti-Chaudhri [ Hind et al. [ Herrez et al. [ Grunberg and

Nissan [ Kendall-Munroe [ Frenkel [ Wilke.The values of interaction parameters g12, H12, W/RT,

G12 and B0 are presented in Table 6. g12 and H12 values are positive for all binary mixtures and increases with increasing alkyl chain length of n-alkanes. Correlation parameter, W/RT has negative values for the rst two binary mixtures and has positive values for the rest of binary mixtures. The negatives values of W/RT suggest weak interactions, and positive values indicate strong interactions between the unlike molecules [33].

G12 values are negative for all binary mixtures except for the two last ones (n-tetradecane ? benzene and nhexadecane ? benzene). The negative values of G12 indicates the dominance of dispersion forces [34, 35], while the positive values are attributed to the presence of strong specic interactions between the mixture components [36, 37]. B0 values are positive for all binaries mixtures,

B0 [ 1 for mixtures where the sub index 1 represent the component of least viscosity (benzene ? n-decane, ?ndodecane, ?n-tetradecane, and ?n-hexadecane), whereas B0 \ 1 for mixtures where the sub index 2 represent the component of least viscosity (benzene ? n-hexane, ?noctane).

123

398 Int J Ind Chem (2016) 7:391400

Table 6 Adjustable parameters of Eqs. (13), (14), (16), (17), (18), (19) and (24), APD values and standard deviations of binary mixture viscosities at 298.15 K

Benzene ? nhexane

Benzene ? noctane

Benzene ? ndecane

Benzene ? ndodecane

Benzene ? ntetradecane

Benzene ? nhexadecane

Kendall and Monroe

r 0.056 0.058 0.042 0.032 0.019 0.046 APD 10.98 8.59 4.93 2.96 1.04 1.90 Frenkel

g12 0.4602 0.5651 0.7245 0.9907 1.3496 1.8445

r 0.059 0.0581 0.0432 0.040 0.023 0.024 APD 11.60 8.63 5.05 3.69 1.49 0.64

Hind et al.

H12 0.2800 0.4053 0.5996 0.8041 1.0721 1.3255

r 0.072 0.062 0.084 0.071 0.106 0.199 APD 13.55 8.73 1.24 0.76 1.02 0.71

Katti and Chaudhri

W/RT -0.5332 -0.3768 0.0132 0.3674 0.8304 1.2899

r 0.005 0.008 0.009 0.005 0.015 0.051 APD 0.84 1.06 0.99 0.32 0.58 1.82

Grunberg and Nissan

G12 -0.6226 -0.5840 -0.3170 -0.0891 0.2626 0.5781

r 0.005 0.009 0.014 0.014 0.009 0.023 APD 0.91 1.31 1.52 1.20 0.92 0.66

Wilke

/12 0.53315 0.56841 0.61068 0.66773 0.72554 0.78865

/21 1.16051 0.97753 0.80972 0.64889 0.53899 0.45366

r 0.088 0.109 0.143 0.215 0.272 0.407 APD 17.32 16.96 16.65 19.19 18.75 21.98

Herrez et al.

B0 0.5643 0.2123 2.8978 1.3382 1.2230 1.2425

r 0.024 0.029 0.023 0.009 0.026 0.052 APD 4.733 4.161 2.365 0.751 1.516 2.089

Conclusions

Excess molar volume have been calculated from the experimental viscosity data at 298.15 K for benzene ? nhexane, or ?n-octane, or ?n-decane, or ?n-dodecane, or ?n-tetradecane, or ? n-hexadecane binary mixtures.

The values of VEm, V0m;1, V0m;2, V0/;1, V0/;2, Vm,1*, Vm,2*,

V0;Em;1, V0;Em;2, V0;E/;1 and V0;E/;2 were calculated for all six mixtures at 298.15 K. The VEm values were found to be positive over the whole composition range for all mixtures.

Molar volumes and apparent molar volumes of both components in the mixture are larger than their respective values in the pure state. The order of interaction between benzene and n-alkanes follows the sequence: n-hexane\noctane \ n-decane \ n-dodecane \ n-tetradecane \ nhexadecane, i.e., the interaction increase with increasing chain length of the n-alkane.

Moreover, an attempt has been made to check the suitability of empirical and semiempirical relations for experimental viscosities data of n-alkanes ? benzene ts by taking into account a number of empirical adjustment coefcients. The predicted viscosities show good accuracy in comparison with the experimental viscosities. The trend of validity of the presently used relations is as follows: Katti-Chaudhri [ Hind et al. [ Herrez et al. [ Grunberg and Nissan [ Kendall-Munroe [

Frenkel [ Wilke.

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/

Web End =http://crea http://creativecommons.org/licenses/by/4.0/

Web End =tivecommons.org/licenses/by/4.0/ ), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

123

Int J Ind Chem (2016) 7:391400 399

References

1. Trres RB, Francesconi AZ, Volpe PLO (2003) Experimental study and modeling using the ERAS-Model of the excess molar volume of acetonitrilealkanol mixtures at different temperatures and atmospheric pressure. Fluid Phase Equilib 210:287306

2. Desnoyers JE, Perron G (1997) Treatment of excess thermodynamic quantities for liquid mixtures. J Solut Chem 26:749755

3. Trres RB, Francesconi AZ, Volpe PLO (2007) Volumetric properties of binary mixtures of acetonitrile and alcohols at different temperatures and atmospheric pressure. J Mol Liq 131(132):139144

4. Zhang Y, Venable RM, Pastor RW (1996) Molecular dynamics simulations of neat alkanes: the viscosity dependence of rotational relaxation. J Phys Chem 100:26522660

5. Aminabhavi TM, Aralaguppi MI, Gopalakrishna B, Khinnavar RS (1994) Densities, shear viscosities, refractive indices, and speeds of sound of bis(2-methoxyethyl) ether with hexane, heptane, octane, and 2,2,4-trimethylpentane in the temperature interval 298.15318.15 K. J Chem Eng Data 39:522528

6. Gmez-Daz D, Mejuto JC, Navaza JM, Rodrguez-Alvarez A (2002) Viscosities, densities, surface tensions, and refractive indexes of 2,2,4-trimethylpentane ? cyclohexane ? decane ternary liquid systems at 298.15K. J Chem Eng Data 47:872875

7. Oswal RL, Phalak RP (1992) Viscosities of nonelectrolyte liquid mixtures. I. Binary mixtures containing p-dioxane. Int J Thermophys 13:251267

8. Baragi JG, Aralaguppi MI, Kariduraganavar MY, Kulkarni SS, Kittur AS, Aminabhavi TM (2006) Excess properties of the binary mixtures of methylcyclohexane alkanes (C6 to C12) at

T = 298.15 K to T = 308.15 K. J Chem Thermodyn 38:75839. Garcia B, Alcalde R, Aparicio S, Leal JM (2002) Volumetric properties, viscosities and refractive indices of binary mixed solvents containing methyl benzoate. Phys Chem Chem Phys 4:58335840

10. Ali A, Nain AK, Sharma VK, Ahmad S (2004) Molecular interactions in binary mixtures of tetrahydrofuran with alkanols (C6, C8, C10): an ultrasonic and volumetric study. Indian J Pure Appl Phys 42:666673

11. Iloukhani H, Rezaei-Sameti M, Basiri-Parsa J (2006) Excess molar volumes and dynamic viscosities for binary mixtures of toluene ? n-alkanes (C5C10) at T = 298.15 K, comparison with Prigogine-Flory-Patterson theory. J Chem Thermodyn 38:975982

12. Awwad AM, Al-azzawi SF, Salman MA (1986) Volumes and viscosities of benzene ? n-alkane mixtures. Fluid Phase Equilib 31:171182

13. Singh PP (1988) Topological investigations of the viscous behavior of binary mixtures of non-electrolyte. Ind J Chem Sect A 27:469473

14. Yadava SS, Yadav N (2011) Excess molar volumes and refractive indices of binary mixtures of isopropylethanoate and symmetrical hydrocarbons at 308.15 K. Can J Chem Eng 89:576581

15. Kehiaian HV (1985) Thermodynamics of binary liquid organic mixtures. Pure Appl Chem 57(1):1530

16. Pea MD, Delgado JN (1975) Excess volumes at 323.15 K of binary mixtures of benzene with n-alkanes. J Chem Thermodyn 7:201204

17. Calvar N, Gmez E, Gonzlez B, Domnguez (2009) Experimental densities, refractive indices, and speeds of sound of 12 binary mixtures containing alkanes and aromatic compounds at T = 313.15 K. J Chem Thermodyn 41:939944

18. Letcher TM, Perkins DM (1984) Application of the Flory theory of liquid mixtures to excess volumes and enthalpies of

benzene ? cycloalkane and ?n-alkane mixtures. Thermochim Acta 77:26727419. Redlich O, Kister AT (1948) Thermodynamics of nonelectrolyte solutions-x-y-t relations in a binary system. Ind Eng Chem 40:341345

20. Sinha B (2010) Excess molar volumes, viscosity deviations and speeds of sound for some alkoxyethanols and amines in cyclohexanone at 298.15 K. Phys Chem Liq 48:183198

21. Egorov GI, Makarov DM (2012) Volumetric properties of the binary mixture of ethylene glycol ? tert-butanol at T = (278.15, 288.15, 298.15, 308.15, 323.15, 333.15, 348.15) K under atmospheric pressure. J Mol Liq 171:2936

22. Nain AK (2013) Densities and volumetric properties of butyl acrylate ? 1-butanol, or ?2-butanol, or ?2-methyl-1- propanol, or ?2-methyl-2-propanol binary mixtures at temperatures from 288.15 to 318.15 K. J Solution Chem 42:14041422

23. Ouerfelli N, Bouaziz M, Herrez JV (2013) Treatment of Herrez equation correlating viscosity in binary liquid mixtures exhibiting strictly monotonous distribution. Phys Chem Liq 51(1):5574

24. Babu CP, Kumar GP, Samatha K (2015) Comparison of experimental viscosities by theoretically for 1-bromopropane in chlorobenzene mixture at (303.15, 308.15, 313.15 and 318.15) K. Int J Adv Sci Tech 76:2734

25. Medvedevskikh Y, Khavunko O (2012) Phenomenological coefcients of the viscosity for low-molecular elementary liquids and solutions. Ch Ch T 6(4):363370

26. Dikio ED, Nelana SM, Isabirye DA, Ebenso EE (2012) Density, dynamic viscosity and derived properties of binary mixtures of methanol, ethanol, n-propanol, and n-butanol with pyridine at T = (293.15, 303.15, 313.15 and 323.15) K. Int J Electrochem Sci 7:1110111122

27. Hind RK, McLaughlin E, Ubbelohde AR (1960) Structure and viscosity of liquids camphor ? pyrene mixtures. Trans Faraday Soc 56:328330

28. Sanz LF, Gonzalez JA, de la Fuente IG, Cobos JC (2015) Thermodynamics of mixtures with strongly negative deviations from Raoults law. XII. Densities, viscosities and refractive indices at T = (293.15 to 303.15) K for (1-heptanol, or 1-decanol ? cyclohexylamine) systems. Application of the ERAS model to (1-alkanol ? cyclohexylamine) mixture. J Chem Thermodyn 80:161171

29. Hernndez-Galvn MA, Garca-Snchez F, Macas-Salinas R (2007) Liquid viscosities of benzene, n-tetradecane, and benzene ? n-tetradecane from 313 to 393 K and pressures up to60 MPa: experiment and modeling. Fluid Phase Equilib 262:5160

30. Wilke CR (1950) A viscosity equation for gas mixtures. J Chem Phys 18:517520

31. Herrez JV, Belda R, Dez O, Herrez M (2008) An equation for the correlation ofviscosities ofbinary mixtures. JSolut Chem 37:233248

32. Mahajan AR, Mirgane SR (2013) Excess molar volumes and viscosities for the binary mixtures of n-octane, n-decane, n-dodecane, and n-tetradecane with octan-2-ol at 298.15 K. J Thermodyn 2013:111

33. Venkatalakshmi V, Chowdappa A, Venkateswarlu P, Reddy KS (2014) Volumetric, speed of sound data and viscosity for the binary mixtures of 2-methylaniline with aliphatic ketones and cyclic ketones at different temperatures. Int J Innov Res Sci Eng Tech 3(11):1755617566

34. Sharma S, Thakkar K, Patel P, Makavana M (2013) Volumetric, viscometric and excess properties of binary mixtures of 1-iodobutane with benzene, toluene, o-xylene, m-xylene, p-xylene, and mesitylene at temperatures from 303.15 to 313.15 K. Adv Phys Chem 2013:112

35. Agarwal D, Singh M (2004) Viscometric studies of molecular interactions in binary liquid mixtures of nitromethane with some

123

400 Int J Ind Chem (2016) 7:391400

polar and non-polar solvents at 298.15K. J Indian Chem Soc 81:85085936. Dubey GP, Kumar K (2011) Thermodynamic properties of binary liquid mixtures of diethylenetriamine with alcohols at different temperatures. Thermochim Acta 524:717

37. Chand GP, Sankar MG, Ramachandran D, Rambabu C (2016) Densities, viscosities and speeds of sound of binary mixtures of 2-chloroaniline with o-chlorotoluene, m-chlorotoluene and p-chlorotoluene at different temperatures. J Solut Chem 45:153187

123