Densities, Viscosities, and Correlations for the Ternary System of

Article pubs.acs.org/jced

Densities, Viscosities, and Correlations for the Ternary System of Ethanol + Methylbenzene + 2‑Methyl-2-propanol and Its Binary Subsystems at T = 298.15 and 318.15 K Guan-Hong Lai and Chein-Hsiun Tu* Department of Applied Chemistry, Providence University, Shalu, Taichung 43301, Taiwan R.O.C. ABSTRACT: Densities and viscosities of the ternary system (ethanol + methylbenzene + 2-methyl-2-propanol) and its binary subsystems were measured at T = 298.15 and 318.15 K and atmospheric pressure. Densities were determined using a vibrating-tube densimeter. Viscosities were found with an automatic microviscometer based on the rolling ball principle. From the experimental data, the excess molar volumes (V E) and deviations in viscosity (Δη) were derived. The binary V E and Δη data were correlated with the Redlich−Kister equation. The ternary V E and Δη data were fitted to the equation based on Cibulka and the equation of Singh et al., respectively. The values of V E and Δη were used to discuss the nature of mixing behaviors for the mixtures, and leading to these excess values is perhaps due to the complex formation and/or accommodation between molecules. To describe the ternary system, several mixtures with specially designated concentrations of 2-methyl-2-propanol were considered.

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various engineering applications involving fluid flow and heat and mass transfer. Considering these respects, the densities (ρ) and viscosities (η) for the ternary system (ethanol + methylbenzene + 2-methyl-2-propanol) and its constituent binaries (ethanol + methylbenzene, ethanol + 2-methyl-2-propanol, and methylbenzene + 2-methyl-2-propanol) were measured at T = 298.15 and 318.15 K and atmospheric pressure (0.1 MPa). The ternary mixtures were specially prepared with several selected concentrations of 2-methyl-2-propanol. These experimental data are used to calculate the excess molar volumes (V E) and viscosity deviations (Δη). Meanwhile, smooth representations of V E and Δη for the ternary mixtures were performed with an emphasis on the 2-methyl-2-propanol addition. This information may be important for appraising the potential reformulations of gasoline involving ethanol and 2-methyl-2propanol. In the past, referring to the ThermoLit of NIST,8 the densities were measured by Ogiwara et al.9 and GonzalezOlmos et al.10 at T = 298.15 K and Moravkova et al.11 at T = 318.15 K for ethanol + methylbenzene. The experimental densities and viscosities at T = 298.15 and 318.15 K were reported by Wang et al.12 for ethanol + 2-methyl-2-propanol. At T = 298.15 K, Atik13 and Kwak et al.14 have investigated the densities for ethanol + methylbenzene; in addition, Peña et al.15 carried out the same determination for methylbenzene + 2-methyl-2-propanol. By using a continuous dilution dilatometer,

INTRODUCTION The oxygenated compounds such as alcohols and ethers are often added in the reformulation of gasoline to improve the octane rating and air-pollution reducing capability of gasoline. Among them, ethanol has its largest single use as an engine fuel and/or fuel additive because of its high oxygen content, antiknocking properties, and relatively low cost in production. When properly blended, ethanol can reduce emission levels of particulates, hydrocarbons, carbon monoxide, and nitrogen oxides. Ethanol in fuel can be produced from the fermentation of carbohydrates (starch, sugars) by yeasts.1 2-Methyl-2-propanol is commonly used as a solvent and can be readily obtained from the catalytic hydration of isobutylene and other organic sources.2 At present, 2-methyl-2-propanol with its good affinity for hydrocarbons is receiving much attention in energy issues as a gasoline antiknock agent, neat fuel, and/or oxygenate fuel constituent in gasoline.3 Gasoline is a complex mixture with hundreds of different molecules containing mainly paraffinic, olefin, and aromatic hydrocarbons. In a typical gasoline liquid, aromatic hydrocarbons are the constituents of great magnitude because of their high octane numbers and existing levels.4−7 With the addition of ethanol or 2-methyl-2-propanol, for instance, intermolecular interactions between the π-electrons of the aromatic hydrocarbons and the hydroxyl groups of these alcohols can bring about some fascinating but complicated behaviors of the mixtures. Experimental property studies of the simplified mixtures can bring us with both fundamental and modeling information for the behaviors. Of these properties, excess molar volumes and viscosity deviations are needed for the theoretical understanding toward molecular interactions in solutions and also in © XXXX American Chemical Society

Received: January 31, 2016 Accepted: July 7, 2016

A

DOI: 10.1021/acs.jced.6b00096 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Chemical Sources, Purities, and Analysis Methods for Pure Components

a

compound

CAS RNa

source

initial mass fraction purity

purification method

final mass fraction purity

analysis method

ethanol 2-methyl-2-propanol methylbenzene

64-17-5 75-65-0 108-88-3

Merck Merck Merck

>0.999 >0.990 >0.998

none none none

0.999 0.998 0.999

GCb Karl Fischerc GC Karl Fischer GC

Chemical Abstract Service Registry Number. bGas−liquid chromatography. cKarl Fischer moisture meter.

Pardo et al.16 obtained the experimental excess molar volumes at T = 298.15 K for ethanol + methylbenzene. However, we are not aware of any other data in the literature regarding the mixtures presented in this study so far.

Apparatus and Measurements. A set with compositions varying from 0.10 to 0.90 mole fractions for the binary systems (ethanol + methylbenzene, ethanol + 2-methyl-2-propanol, and methylbenzene + 2-methyl-2-propanol) along with a wide range of compositions for the ternary system of ethanol + methylbenzene + 2-methyl-2-propanol were used in the measurement over the densities and viscosities at T = 298.15 and 318.15 K and P = 0.1 MPa. The ternary mixtures were prepared by mixing known masses of the components, so that, while the mass fractions of 2-methyl-2-propanol were kept constant (0.10, 0.20, 0.30, 0.40, 0.50, 0.60, 0.70, and 0.80), the mole fractions of the other two components were varied to have 45 ternary mixtures. The weights required in the entire work are obtained by means of a Precisa (type 262SMA-FR) balance accurate to within ±0.0001 g. The possible error of composition in mole fraction was estimated to be 1 × 10−4. Precautions have been taken in order to avoid evaporation losses and air dissolved during the experiment. More detailed experimental procedure can be seen in our earlier study.37 Densities were measured using an Anton Paar vibratingtube densimeter (type DMA-5000) with an accuracy of ±2 × 10−6 g/cm3. The temperature was automatically controlled by means of a built-in Peltier thermostat to ±0.01 K. Calibration was carried out under atmospheric pressure using Millipore quality water and dry air. The densities were measured with a relative standard uncertainty of 0.001. The maximum error in excess molar volume resulting from the propagation of errors, considering the uncertainty in the density measurement, the uncertainty of the composition in mole fraction, and the possible error with 3 × 10−3 cm3/mol referring to the measurement of volume changing of mixing (ref 12), was 0.003 cm3·mol−1. Viscosities were determined with an Anton Paar microviscometer (type AMVn). The AMVn uses the rolling-ball principle, where a gold-covered steel ball (1.5 mm in diameter) rolls down an inclined and inside sample filled glass capillary with an inner diameter of 1.6 mm. The accuracy of the flow-time measurement is less than 0.002 s. The temperature was maintained by an Anton-Paar thermostat to ±0.05 K. The relative standard uncertainty in the viscosity measurement was estimated at 0.005. Apparatus calibration was performed by using Millipore quality water.

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EXPERIMENTAL SECTION Materials. The chemicals used were of analytical grade and supplied by Merck (Germany). Ethanol and 2-methyl-2propanol were stored over molecular sieves (Merck 0.4 nm beads) to prevent water absorption. All of the chemicals were used without any further purification. The purity of the chemicals was checked using a PerkinElmer Autosystem gas chromatograph (GC), and no impurity peak was detected. The sources, purities, and analysis methods of the chemicals are presented in Table 1. The measured densities and viscosities at working temperatures 298.15 and 318.15 K for the pure components are in good agreement with the accepted literature values as shown in Table 2.17−36 Table 2. Measured Densities (ρ) and Viscosities (η) of Pure Components with Literature Values at Working Temperatures and P = 0.1 MPaa ρ (g·cm−3) component ethanol

2-methyl-2-propanol

methylbenzene

η (mPa·s)

T/K

exptl

lit.

exptl

lit.

298.15

0.78501

1.084

1.0826c 1.090d

318.15

0.76754

0.752

0.75e 0.759g

298.15

0.78099

4.426

318.15

0.75966

298.15

0.86201

318.15

0.84351

0.78492b 0.78493c 0.78506d 0.76758e 0.76760f 0.76762g 0.7807h 0.78078i 0.78100j 0.75952k 0.75967m 0.75987n 0.86165o 0.86201p 0.86219q 0.8436r 0.84349t 0.8435u

4.3839h 4.433k 4.438l 1.685k 1.705l 1.736n 0.553o 0.5525r 0.554s 0.4428r 0.4491u

1.706

0.533

0.447

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RESULTS AND DISCUSSION In Tables 3 and 4, the experimental data of densities (ρ) and excess molar volumes (V E) are listed as a function of the mole fraction of component at T = 298.15 and 318.15 K for the binary systems of ethanol (1) + methylbenzene (2), ethanol (1) + 2-methyl-2-propanol (3), and methylbenzene (2) + 2-methyl2-propanol (3) and the ternary system of ethanol (1) + methylbenzene (2) + 2-methyl-2-propanol (3). The measured viscosities (η) and the deviations in the viscosity (Δη) of the ternary system and constituent binaries at both temperatures are shown in Tables 5 and 6. Increasing temperature is expected to decrease the values of ρ and η. The V E values of the mixture

a The standard uncertainties u are u(T) = 0.01 K for ρ, u(T) = 0.05 K for η, and u(P) = 1 kPa. The relative standard uncertainties ur are ur(ρ) = 0.001 and ur(η) = 0.005. bMatkowska et al., 2002.17 cRiddick et al., 1986.18 dChen et al., 2001.19 eZafarani-Moattar and Tohidifar, 2008.20 fGómez and Sólimo, 2002.21 gZafarani-Moattar and MajdanCegincara, 2008.22 hTejraj et al., 1994.23 iCarrasco et al., 2008.24 j Mussari and Postigo, 2000.25 kAnsón et al., 2005.26 lTRC Themodynamic Tables, 1971.27 mBravo-Sanchez et al., 2010.28 nOrtega et al., 2005.29 oSong et al., 2007.30 pYang et al., 2006.31 qHarris, 2000.32 r Hafez and Hartland, 1976.33 sPanda and Singh, 1999.34 tNain et al., 2008.35 uSong et al., 2008.36

B



Article

Table 3. Experimental Component Mole Fractions (x), Densities (ρ), and Excess Molar Volumes (V E) for the Ternary System Ethanol (1) + Methylbenzene (2) + 2-Methyl-2-propanol (3) and Binary Subsystems at T = 298.15 K and P = 0.1 MPaa x1

x2

ρ (g·cm−3)

V E (cm3·mol−1)

x1

x2

ρ (g·cm−3)

V E (cm3·mol−1)

0.1003 0.2002 0.3000 0.4000 0.5002 0.6001 0.7000 0.8000 0.9000 0.0450 0.0820 0.1518 0.2870 0.4085 0.5174 0.6167 0.7070 0.7896 0.8654 0.9355 0 0 0 0 0 0 0 0 0 0.0886 0.1779 0.2686 0.3599 0.4529 0.5471 0.6422 0.7387

0.8997 0.7998 0.7000 0.6000 0.4998 0.3999 0.3000 0.2000 0.1000 0 0 0 0 0 0 0 0 0 0 0 0.0822 0.1678 0.2564 0.3488 0.4458 0.5468 0.6525 0.7621 0.8787 0.7954 0.7115 0.6264 0.5399 0.4531 0.3648 0.2754 0.1847

0.85716 0.85238 0.84727 0.84165 0.83535 0.82822 0.81995 0.81035 0.79887 0.78192 0.78251 0.78311 0.78369 0.78395 0.78415 0.78431 0.78442 0.78455 0.78472 0.78485 0.78659 0.79296 0.79978 0.80709 0.81500 0.82334 0.83208 0.84126 0.85102 0.84743 0.84365 0.83943 0.83462 0.82924 0.82301 0.81579 0.80725

0.049 0.037 0.008 −0.028 −0.064 −0.093 −0.106 −0.105 −0.071 −0.097 −0.154 −0.196 −0.205 −0.180 −0.152 −0.122 −0.090 −0.063 −0.042 −0.019 0.223 0.369 0.475 0.538 0.554 0.532 0.483 0.392 0.266 0.217 0.150 0.086 0.027 −0.024 −0.062 −0.087 −0.092

0.8365 0.0776 0.1563 0.2373 0.3203 0.4055 0.4927 0.5825 0.6741 0.7685 0.0849 0.1708 0.2617 0.3572 0.4573 0.5623 0.6728 0.0851 0.1761 0.2742 0.3799 0.4943 0.6182 0.0844 0.1775 0.2835 0.4009 0.5345 0.0747 0.1606 0.2590 0.3775 0.0709 0.1573 0.2667 0.0643 0.1559

0.0929 0.6944 0.6250 0.5537 0.4805 0.4055 0.3286 0.2496 0.1686 0.0854 0.5817 0.5115 0.4363 0.3573 0.2745 0.1879 0.0967 0.4811 0.4107 0.3348 0.2533 0.1648 0.0686 0.3847 0.3177 0.2411 0.1561 0.0597 0.2986 0.2409 0.1749 0.0948 0.2122 0.1576 0.0888 0.1299 0.0766

0.79707 0.83827 0.83524 0.83177 0.82781 0.82321 0.81783 0.81159 0.80423 0.79523 0.82908 0.82587 0.82201 0.81732 0.81154 0.80448 0.79557 0.82043 0.81722 0.81314 0.80784 0.80091 0.79163 0.81232 0.80922 0.80479 0.79865 0.78994 0.80489 0.80221 0.79833 0.79232 0.79771 0.79508 0.79063 0.79108 0.78831

−0.069 0.334 0.242 0.157 0.081 0.018 −0.027 −0.063 −0.083 −0.061 0.381 0.257 0.148 0.056 −0.011 −0.055 −0.061 0.412 0.260 0.128 0.028 −0.037 −0.051 0.406 0.232 0.090 −0.008 −0.050 0.391 0.214 0.070 −0.029 0.335 0.148 0.000 0.241 0.050

a

The standard uncertainties u are u(T) = 0.01 K and u(P) = 1 kPa. The relative standard uncertainty ur is ur(ρ) = 0.001. The expanded uncertainty U is U(V E) = 0.003 cm3·mol−1 (0.95 level of confidence).

to derive the binary coefficients (ak):

were obtained from the experimental density data according to the following equation: ⎛1

N

V E/(cm 3·mol‐1) =

∑ xiMi⎜⎜ i=1

⎝ρ

−

1⎞ ⎟⎟ ρi ⎠

m

ΔQ ij = xixj ∑ ak (xi − xj)k

where ΔQ ij refers to the V E/(cm3·mol−1) or Δη/(mPa·s) for the binary i + j system and xj = 1 − xi. The standard deviation is defined as usual:

(1)

where xi, Mi, ρi, and N are the mole fraction, molecular weight, the measured density of pure component i, and the number of components in the mixture, respectively. The Δη values were calculated from a mole fraction basis as

⎡ n (ΔQ calc − ΔQ expt)2 ⎤1/2 i i ⎥ δ = ⎢∑ n−p ⎢⎣ i = 1 ⎥⎦

N

Δη /(mPa·s) = η −

∑ xiηi i=1

(3)

k=0

(4)

where n and p denote the number of data points and parameters used in fitting the data, respectively, and ΔQ stands for V E or Δη. In each case, the optimum number of coefficients (ak) was determined from an examination of the residuals as a function of composition and the variation of standard deviation. The fit parameters and standard deviations (δ) are given in Table 7. The δ values of binary V E lie between 0.002 and

(2)

where η and ηi stand for the viscosity of the mixture and pure liquid i, respectively. All of the binary quantities (V E and Δη) have been fitted to the Redlich−Kister equation38 by the method of least-squares C



Article

Table 4. Experimental Component Mole Fractions (x), Densities (ρ), and Excess Molar Volumes (V E) for the Ternary System Ethanol (1) + Methylbenzene (2) + 2-Methyl-2-propanol (3) and Binary Subsystems at T = 318.15 K and P = 0.1 MPaa x1

x2

ρ (g·cm−3)

V E (cm3·mol−1)

x1

x2

ρ (g·cm−3)

V E (cm3·mol−1)

0.1004 0.2002 0.3003 0.4003 0.5000 0.6001 0.7001 0.7996 0.9000 0.0450 0.0820 0.1516 0.2872 0.4083 0.5174 0.6168 0.7072 0.7896 0.8656 0.9355 0 0 0 0 0 0 0 0 0 0.0887 0.1776 0.2682 0.3599 0.454 0.5471 0.6426 0.7385

0.8996 0.7998 0.6997 0.5997 0.5000 0.3999 0.2999 0.2004 0.1000 0 0 0 0 0 0 0 0 0 0 0 0.0822 0.1676 0.2565 0.3491 0.4459 0.5467 0.6524 0.7627 0.8788 0.7954 0.7113 0.6265 0.5403 0.4513 0.3643 0.2752 0.1849

0.83810 0.83320 0.82801 0.82239 0.81620 0.80919 0.80121 0.79197 0.78091 0.76137 0.76226 0.76335 0.76469 0.76559 0.76620 0.76659 0.76691 0.76715 0.76735 0.76746 0.76530 0.77188 0.77896 0.78664 0.79484 0.80343 0.81243 0.82189 0.83202 0.82798 0.82415 0.81999 0.81527 0.80986 0.80395 0.79702 0.78888

0.126 0.134 0.115 0.080 0.038 −0.002 −0.036 −0.057 −0.049 −0.187 −0.271 −0.350 −0.393 −0.384 −0.348 −0.292 −0.235 −0.176 −0.119 −0.058 0.258 0.413 0.524 0.579 0.589 0.569 0.523 0.438 0.297 0.307 0.244 0.178 0.115 0.051 −0.004 −0.049 −0.077

0.8364 0.0771 0.1567 0.2376 0.3202 0.4057 0.4933 0.5824 0.6741 0.7684 0.0835 0.1707 0.2627 0.3573 0.4575 0.5627 0.6733 0.0852 0.1764 0.2742 0.3801 0.4941 0.6182 0.0846 0.1781 0.2832 0.4014 0.5345 0.0746 0.161 0.2601 0.3776 0.0708 0.1576 0.2665 0.0647 0.1554

0.0930 0.6948 0.6248 0.5534 0.4807 0.4055 0.3283 0.2494 0.1685 0.0857 0.5833 0.5112 0.4356 0.3573 0.2746 0.1874 0.0961 0.4812 0.4105 0.3346 0.2529 0.1648 0.0686 0.3847 0.3170 0.2412 0.1558 0.0594 0.2989 0.2406 0.1735 0.0946 0.2121 0.1576 0.0889 0.1301 0.0767

0.77912 0.81859 0.81559 0.81219 0.80833 0.80391 0.79877 0.79285 0.78580 0.77735 0.80958 0.80609 0.80238 0.79796 0.79257 0.78584 0.77748 0.80053 0.79745 0.79353 0.78862 0.78224 0.77365 0.79226 0.78930 0.78531 0.77974 0.77184 0.78469 0.78220 0.77870 0.77352 0.77741 0.77511 0.77135 0.77066 0.76838

−0.079 0.419 0.321 0.228 0.146 0.066 −0.002 −0.062 −0.099 −0.109 0.405 0.315 0.187 0.074 −0.024 −0.097 −0.141 0.451 0.283 0.133 −0.002 −0.108 −0.169 0.429 0.234 0.052 −0.097 −0.201 0.399 0.196 0.002 −0.163 0.319 0.094 −0.124 0.206 −0.041

a

The standard uncertainties u are u(T) = 0.01 K and u(P) = 1 kPa. The relative standard uncertainty ur is ur(ρ) = 0.001. The expanded uncertainty U is U(V E) = 0.003 cm3·mol−1 (0.95 level of confidence).

0.007 cm3·mol−1, and those of Δη are between 0.001 and 0.009 mPa·s. The ternary V E and Δη data were correlated using the expression as suggested by Cibulka39 and Singh et al.40 The Cibulka equation:

with δ values from the fitting are presented in Table 8, respectively, and the standard deviation (δ) is defined as eq 4. As can be seen in this table, both equations correlated in a similar result for V E, but a somewhat better fitting is obtained for Δη from Cibulka, which has the δ values at T = 298.15 K, for example, are 0.023 mPa·s by Cibulka and 0.047 mPa·s by Singh et al. The observed V E may be the resultant of several factors which can be roughly known as physical, chemical, and geometrical contributions.41,42 The physical interactions involve mainly nonspecific forces which are weak interactions between unlike molecules giving a positive contribution. The chemical or specific interaction results in volume contraction upon mixing, and these interactions include theformation of hydrogen bonds and other complex-forming interactions providing a negative contribution. Structure effects occurring from geometrical accommodation of one component into the other, because of the differences in the molar volume and/or free volume between components, lead to negative contributions to V E. In the present

ΔQ 123 = ΔQ 12 + ΔQ 13 + ΔQ 23 + x1x 2x3 × (C0 + C1x1 + C2x 2)

(5)

The Singh et al. equation: ΔQ 123 = ΔQ 12 + ΔQ 13 + ΔQ 23 + x1x 2x3 × (C0 + C1x1(x 2 − x3) + C2x12(x 2 − x3)2 )

(6)

where ΔQ123 refers to the ternary V E (cm3·mol−1) and Δη (mPa·s) and ΔQij is the binary contribution given by eq 3. The ternary parameters (C0, C1, and C2) were determined with the optimization algorithm similar to that used for obtaining the binary parameters, ak. The coefficients of eqs 5 and 6 together D



Article

Table 5. Experimental Component Mole Fractions (x), Viscosities (η), and Viscosity Deviations (Δη) for the Ternary System Ethanol (1) + Methylbenzene (2) + 2-Methyl-2-propanol (3) and Binary Subsystems at T = 298.15 K and P = 0.1 MPaa x1

x2

η (mPa·s)

Δη (mPa·s)

x1

x2

η (mPa·s)

Δη (mPa·s)

0.1005 0.2013 0.3002 0.4003 0.5001 0.6001 0.7000 0.8000 0.9000 0.0450 0.0820 0.1518 0.2870 0.4085 0.5174 0.6167 0.7070 0.7896 0.8654 0.9355 0 0 0 0 0 0 0 0 0 0.0884 0.1786 0.2685 0.3605 0.4528 0.5469 0.6421 0.7387

0.8995 0.7987 0.6998 0.5997 0.4999 0.3999 0.3000 0.2000 0.1000 0 0 0 0 0 0 0 0 0 0 0 0.0822 0.1678 0.2564 0.3488 0.4458 0.5468 0.6525 0.7621 0.8787 0.7959 0.7103 0.6266 0.5403 0.4526 0.3649 0.2754 0.1846

0.549 0.559 0.577 0.606 0.644 0.693 0.754 0.831 0.926 4.314 4.195 3.939 3.395 2.860 2.384 2.026 1.749 1.532 1.349 1.205 2.579 1.625 1.184 0.991 0.868 0.744 0.624 0.562 0.561 0.576 0.595 0.622 0.659 0.706 0.763 0.833 0.920

−0.057 −0.101 −0.135 −0.159 −0.174 −0.179 −0.170 −0.147 −0.104 0.038 0.043 0.021 −0.072 −0.201 −0.313 −0.339 −0.314 −0.255 −0.185 −0.095 −1.528 −2.151 −2.249 −2.084 −1.831 −1.564 −1.275 −0.912 −0.462 −0.472 −0.483 −0.480 −0.470 −0.455 −0.422 −0.380 −0.322

0.8364 0.0776 0.1562 0.2373 0.3204 0.4053 0.4928 0.5825 0.6739 0.7685 0.0834 0.1710 0.2620 0.3575 0.4571 0.5627 0.6734 0.0852 0.1767 0.2739 0.3795 0.4939 0.6185 0.0844 0.1784 0.2830 0.4004 0.5338 0.0748 0.1599 0.2600 0.3778 0.0708 0.1578 0.2671 0.0653 0.1545

0.0929 0.6944 0.6252 0.5540 0.4807 0.4055 0.3286 0.2494 0.1689 0.0854 0.5843 0.5110 0.4359 0.3571 0.2747 0.1873 0.0960 0.4809 0.4104 0.3350 0.2534 0.1648 0.0692 0.3849 0.3170 0.2413 0.1563 0.0603 0.2987 0.2410 0.1736 0.0942 0.2119 0.1574 0.0890 0.1297 0.0780

1.026 0.616 0.642 0.678 0.723 0.778 0.845 0.926 1.023 1.146 0.682 0.731 0.793 0.873 0.972 1.099 1.260 0.777 0.852 0.953 1.083 1.252 1.477 0.906 1.017 1.185 1.403 1.706 1.103 1.256 1.473 1.780 1.410 1.656 2.038 1.936 2.376

−0.245 −0.861 −0.840 −0.809 −0.770 −0.723 −0.661 −0.587 −0.496 −0.381 −1.202 −1.145 −1.069 −0.975 −0.863 −0.722 −0.544 −1.502 −1.395 −1.260 −1.094 −0.885 −0.614 −1.747 −1.585 −1.361 −1.080 −0.702 −1.916 −1.702 −1.412 −1.018 −1.959 −1.633 −1.151 −1.694 −1.156

a

The standard uncertainties u are u(T) = 0.05 K and u(P) = 1 kPa. The relative standard uncertainty ur is ur(η) = 0.005. The expanded uncertainty U is U(Δη) = 0.005 mPa·s (0.95 level of confidence).

forces giving a positive contribution to V E. For the system of ethanol + methylbenzene, a sigmoid shape is observed with the positive values of V E located at early compositions (x ≤ 0.4) of ethanol. The S-shaped result on V E may be explained as a balance between positive contributions (hydrogen bond rupture and dispersive interactions between unlike molecules) and negative contributions (intermolecular dipolar interactions and geometrical fitting between components). The values of V E becomes more negative from T = 298.15 to 318.15 K for ethanol + 2-methyl-2-propanol. However, with the remaining systems, V E values are found to increase with an increase of temperature, indicating the positive contribution to the V E value from the cleavage of the alcohol−alcohol complex likely happens to affect these mixtures. As illustrated in Figure 1, the V E values of methylbenzene + 2-methyl-2-propanol are larger when compared with those of the ethanol + methylbenzene or + 2-methyl-2-propanol, which may be due to the formation of weak molecule complexes and negligence in structure contribution. Alternately, the V E values of ethanol + 2-methyl-2-propanol

investigation, ethanol, having the smallest molar volume among the components, is strongly self-associated through hydrogen bonding, but methylbenzene, with the π-electrons of benzene rings in the molecules, does not exhibit this property. For higher alcohols such as 2-methyl-2-propanol, structure contribution is negligible, and its association ability decreases due to the chain length and position of the −OH group. In Figure 1a and b, we have plotted the experimental and fitted values of V E as a function of composition for the binary systems at T = 298.15 and 318.15 K, respectively. As can be seen, our data are in good agreement with the literature values. Over the entire composition range, the V E values are negative for the binary system of ethanol + 2-methyl-2-propanol, while the positive values were found for methylbenzene + 2-methyl-2propanol. The intermolecular interactions and geometrical fitting between ethanol and 2-methyl-2-propanol molecules lead to weak dispersion and/or hydrogen bond effects, giving a negative contribution to V E. The physical interactions between 2-methyl2-propanol and methylbenzene molecules involve mainly dispersion E



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Table 6. Experimental Component Mole Fractions (x), Viscosities (η), and Viscosity Deviations (Δη) for the Ternary System Ethanol (1) + Methylbenzene (2) + 2-Methyl-2-propanol (3) and Binary Subsystems at T = 318.15 K and P = 0.1 MPaa x1

x2

η (mPa·s)

Δη (mPa·s)

x1

x2

η (mPa·s)

Δη (mPa·s)

0.1004 0.2004 0.2997 0.4007 0.5007 0.5998 0.6998 0.7999 0.8998 0.0450 0.0820 0.1516 0.2872 0.4083 0.5174 0.6168 0.7072 0.7896 0.8656 0.9355 0 0 0 0 0 0 0 0 0 0.0884 0.1783 0.2685 0.3594 0.4527 0.5558 0.6427 0.7384

0.8996 0.7996 0.7003 0.5993 0.4993 0.4002 0.3002 0.2001 0.1002 0 0 0 0 0 0 0 0 0 0 0 0.0822 0.1676 0.2565 0.3491 0.4459 0.5467 0.6524 0.7627 0.8788 0.7954 0.7112 0.6261 0.5409 0.4534 0.3544 0.2750 0.1849

0.439 0.442 0.449 0.464 0.483 0.508 0.542 0.585 0.641 1.724 1.721 1.692 1.577 1.442 1.308 1.188 1.078 0.983 0.895 0.817 1.171 0.899 0.744 0.649 0.582 0.528 0.486 0.461 0.454 0.452 0.460 0.473 0.490 0.513 0.548 0.582 0.631

−0.057 −0.101 −0.135 −0.159 −0.174 −0.179 −0.170 −0.147 −0.104 0.061 0.093 0.131 0.145 0.125 0.096 0.071 0.046 0.030 0.014 0.004 −0.432 −0.596 −0.639 −0.617 −0.563 −0.490 −0.399 −0.285 −0.146 −0.169 −0.181 −0.189 −0.192 −0.190 −0.182 −0.165 −0.138

0.8358 0.0782 0.1571 0.2368 0.3200 0.4055 0.4924 0.5827 0.6740 0.7685 0.0836 0.1703 0.2620 0.3569 0.4571 0.5630 0.6731 0.0854 0.1765 0.2742 0.3800 0.4910 0.6186 0.0841 0.1782 0.2829 0.4016 0.5344 0.0746 0.1598 0.2605 0.3778 0.0707 0.1575 0.2666 0.0648 0.1570

0.0933 0.6946 0.6246 0.5538 0.4806 0.4057 0.3288 0.2496 0.1690 0.0853 0.5835 0.5116 0.4361 0.3574 0.2745 0.1872 0.0962 0.4857 0.4108 0.3347 0.2532 0.1662 0.0688 0.3853 0.3169 0.2414 0.1558 0.0594 0.2989 0.2411 0.1735 0.0942 0.2109 0.1572 0.0888 0.1301 0.0788

0.692 0.473 0.485 0.501 0.523 0.550 0.585 0.628 0.683 0.753 0.504 0.526 0.555 0.594 0.644 0.712 0.800 0.546 0.581 0.628 0.691 0.777 0.900 0.609 0.660 0.733 0.838 0.993 0.690 0.756 0.852 0.998 0.815 0.913 1.072 0.996 1.150

−0.099 −0.284 −0.285 −0.281 −0.273 −0.258 −0.238 −0.208 −0.168 −0.113 −0.387 −0.374 −0.352 −0.322 −0.280 −0.222 −0.143 −0.467 −0.439 −0.395 −0.333 −0.251 −0.129 −0.532 −0.477 −0.400 −0.289 −0.129 −0.568 −0.494 −0.387 −0.229 −0.558 −0.445 −0.267 −0.484 −0.307

a

The standard uncertainties u are u(T) = 0.05 K and u(P) = 1 kPa. The relative standard uncertainty ur is ur(η) = 0.005. The expanded uncertainty U is U(Δη) = 0.005 mPa·s (0.95 level of confidence).

Table 7. Coefficients (ak) of the Redlich−Kister Equation for the Binary Systems and Coefficients (Ck) of the Cilbulka Equation for the Ternary System in the Correlations of V E and Δη ΔQij

T (K)

a0

V E (cm3·mol−1)

298.15 318.15 298.15 318.15

−0.2537 0.1581 −0.6984 −0.4693

Δη (mPa·s)

V E (cm3·mol−1) Δη (mPa·s)


298.15 318.15 298.15 318.15 298.15 318.15 298.15 318.15

a1

a2

Ethanol (1) + Methylbenzene (2) −0.6388 0.05508 −0.7959 0.05988 −0.1745 −0.1117 −0.1476 −0.08665 Ethanol (1) + 2-Methyl-2-propanol (3) −0.6080 0.5505 −0.7200 −1.422 0.7137 −0.2732 −1.151 −1.410 0.9969 0.4030 −0.5244 0.3648 Methylbenzene (2) + 2-Methyl-2-propanol (3) 2.196 −0.4443 0.3399 2.336 −0.4232 0.8167 −6.752 5.312 −6.958 −2.108 1.397 −1.283 F

a3

a4

δ × 103

−0.2937 −0.6196 −0.2216 −0.1986

0.2216 0.5441 −0.2946 −0.3213

1.7 2.9 1.5 1.5

0.6527 1.164 0.2476 −0.2415 0.4243 0.2818 6.322 1.707

−1.432

0.7602 0.5563 −1.058 −1.038

5.3 6.5 9.1 1.4 3.8 4.5 3.0 4.1



Article

Table 8. Coefficients (Ck) of the Cilbulka Equation and Singh et al. Equation in the Correlations of V E and Δη for the Ternary System of Ethanol (1) + Methylbenzene (2) + 2-Methyl-2-propanol (3) ΔQ123

T (K)

V E (cm3·mol−1)

298.15 318.15 298.15 318.15

Δη (mPa·s)


298.15 318.15 298.15 318.15

C0

C1

Cilbulka 1.463 2.195 −19.47 −10.55 Singh et al. −1.638 −0.7410 −4.077 −3.156

Figure 1. Variation of V E with xi at (a) T = 298.15 K and (b) T = 318.15 K for the binary systems: ethanol (1) + methylbenzene (2), xi = x1, (○) this work, (▲) Moravkova et al.,6 (●) Gonzalez-Olmos et al.,7 (▽) Atik,8 (◇) Pardo et al.;11 ethanol (1) + 2-methyl-2-propanol (3), xi = x1, (△) this work, (■) Wang et al.;5 methylbenzene (2) + 2-methyl-2propanol (3), xi = x2, (□) this work, (⧫) Peña et al.10 The solid lines are calculated from the Redlich−Kister equation.

−3.387 −3.876 17.78 6.906 −7.870 −7.085 40.68 21.62

δ × 103

C2 −5.295 −4.532 26.71 14.06 36.84 23.69 −102.2 −74.22

22.5 21.3 33.0 22.7 23.1 22.3 47.3 25.5

Figure 2. Variation of Δη with xi at (a) T = 298.15 K and (b) T = 318.15 K for the binary systems: ethanol (1) + methylbenzene (2), xi = x1, (○) this work; ethanol (1) + 2-methyl-2-propanol (3), xi = x1, (△) this work, (▲) Wang et al.;5 methylbenzene (2) + 2-methyl-2propanol (3), xi = x2, (□) this work. The solid lines are calculated from the Redlich−Kister equation. G



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Figure 4. Plots of viscosity deviation, Δη, of the ternary system ethanol (1) + methylbenzene (2) + 2-methyl-2-propanol (3) against the mole fraction of methylbenzene, x2, with various mass fractions of 2-methyl-2-propanol (w) at (a) T = 298.15 K and (b) T = 318.15 K: (Δ) w = 0.10, (□) w = 0.20, (◇) w = 0.30, (▽) w = 0.4 0, (●) w = 0.50, (▲) w = 0.60, (■) w = 0.70, and (⧫) w = 0.80. The symbols represent experimental data, and the solid lines denote the calculated values.

Figure 3. Plots of excess molar volume, V E, of the ternary system ethanol (1) + methylbenzene (2) + 2-methyl-2-propanol (3) against the mole fraction of methylbenzene, x2, with various mass fractions of 2-methyl-2-propanol (w) at (a) T = 298.15 K and (b) T = 318.15 K: (Δ) w = 0.10, (□) w = 0.20, (◇) w = 0.30, (▽) w = 0.40, (●) w = 0.50, (▲) w = 0.60, (■) w = 0.70, and (⧫) w = 0.80. The symbols represent experimental data, and the solid lines denote the calculated values.

The values of Δη at T = 298.15 and 318.15 K are compared as a function of composition in Figure 2a and b for the three binary systems, respectively. It can be seen that our data of ethanol + 2-methyl-2-propanol are in good agreement with the literature ones. For ethanol + 2-methyl-2-propanol, the Δη values are positive except for some negative values observed in the ethanol-rich region at T = 298.15 K. The Δη values are found to increase with a rise in temperature for all of the binary systems. The binary Δη values vary from −2.249 to 0.145 mPa·s (Tables 5 and 6). It is observed that the Δη values show the order as methylbenzene +2-methyl-2-propanol < ethanol + methylbenzene < ethanol +2-methyl-2-propanol at T = 318.15 K. A more efficient packing in the pure liquids or a larger steric obstacle to the accommodation between mixing molecules is probably the reason for a more negative Δη value.

mixtures are more negative than those of the ethanol + methylbenzene, which imply that a stronger interaction and packing effect likely exists between ethanol and 2-methyl-2-propanol molecules. According to Kauzman and Eyring,43 the viscosity of a mixture is strongly related to liquid structure and consequently to the molecular interactions between the components of the mixture. The negative values of Δη are caused by inclusion of the small molecule to the structure of the big molecules44,45 and/or dominance of dispersion forces between components. The positive values may be attributed to the presence of specific interactions between them. The dependence of Δη on both composition and temperature may be explained as a balance between these positive contributions and negative contributions. H



Article

Figure 6. Curves of constant Δη (mPa·s) for the ternary system of ethanol (1) + methylbenzene (2) + 2-methyl-2-propanol (3) at (a) T = 298.15 K and (b) T = 318.15 K.

Figure 5. Curves of constant V E (cm3·mol−1) for the ternary system of ethanol (1) + methylbenzene (2) + 2-methyl-2-propanol (3) at (a) T = 298.15 K and (b) T = 318.15 K.

Δη at all compositions with a minimum value near the methylbenzene + 2-methyl-2-propanol side at x = 0.25 of methylbenzene. These values of V E and Δη imply that the chemical interactions or structure stacking among the molecules during the mixing process may assume the control of the results.

In Figure 3a and b, the experimental and calculated V E values for the ternary system of ethanol (1) + methylbenzene (2) + 2-methyl-2-propanol (3) at T = 298.15 and 318.15 K were presented as a function of the mole fraction of methylbenzene (x2) referring to different mass fractions of 2-methyl-2-propanol (w). The V E values are found to increase with increasing temperature and amount of 2-methyl-2-propanol in the mixtures. In Figure 4a and b, we compare the experimental and fitted ternary Δη at these two temperatures as a function of x2 for different values of w. The ternary Δη values are shown to increase as a rise of temperature but decrease with increasing amount of 2-methyl-2-propanol. The experimental values of V E and Δη agree well with the calculated ones from the correlations. The curves of constant V E and Δη for the ternary mixtures were also plotted respectively in Figures 5 and 6. As can be seen in Figure 5a and b, except for some negative results occurred in the ethanol-rich and methylbenzene-poor region, the ternary V E values are positive and have a maximum close to the methylbenzene +2-methyl-2-propanol side at x = 0.45 of methylbenzene. Figure 6a and b shows the negative values of ternary

■

CONCLUSIONS This paper reports the experimental data of density (ρ) and viscosity (η) for the ternary system of ethanol + methylbenzene + 2-methyl-2-propanol and its constituent binaries (ethanol + methylbenzene, ethanol + 2-methyl-2-propanol, and methylbenzene + 2-methyl-2-propanol) at T = 298.15 and 318.15 K and atmospheric pressure. Increasing temperature from 298.15 to 318.15 K decreases the values of ρ and η. From the experimental ρ and η data, the calculated excess molar volumes (V E) and deviations in viscosity (Δη) were correlated satisfactorily using the Redlich−Kister equation for the binary systems and the Cibulka equation and Singh et al. equation for the ternary mixtures. The V E values are negative for the binary system of ethanol + 2-methyl-2-propanol, while the positive values were found for I



Article

(10) Gonzalez-Olmos, R.; Iglesias, M.; Mattedi, S. Influence of Temperature on Thermodynamics of Ethanol + Hydrocarbon Gasoline Additives. Phys. Chem. Liq. 2010, 48, 337−384. (11) Morávková, L.; Wagner, Z.; Sedláková, Z.; Linek, J. Volumetric Behaviour of Binary and Ternary Liquid Systems composed of Ethanol, Isooctane, and Toluene at Temperatures from (298.15 to 328.15) K. Experimental Data and Correlation. J. Chem. Thermodyn. 2011, 43, 1906−1916. (12) Wang, C. C.; Chen, H. W.; Tu, C. H. Densities, Viscosities, and Refractive Indices for Binary and Ternary Mixtures of Ethanol, 2Methylpropan-2-ol, and 2,2,4-Trimethylpentane. J. Chem. Eng. Data 2005, 50, 1687−1693. (13) Atik, Z. Experimental and Predicted Volumetric and Refractive Index Properties of Ternary Mixtures of Iodoethane with Toluene and Alcohols at Temperature 298.15 K and Pressure 101 kPa. J. Chem. Thermodyn. 2006, 38, 201−208. (14) Kwak, H.-Y.; Oh, J.-H.; Park, S.-J.; Paek, K.-Y. Isothermal Vapor Liquid Equilibrium at 333.15 K and Excess Volumes and Molar Refractivity Deviations at 298.15 K for the Ternary System Di-Butyl Ether (1) + Ethanol (2) + Toluene (3) ant Its Binary Subsystems. Fluid Phase Equilib. 2007, 262, 161−168. (15) Peña, M. P.; Martínez-Soria, V.; Montón, J. B. Densities, Refractive Indices, and Derived Excess Properties of the Binary Systems tert-Butyl Alcohol + Toluene, + Methylcyclohexane, and + Isooctane and Toluene + Methylcyclohexane, and the Ternary System tert-Butyl Alcohol + Toluene + Methylcyclohexane at 298.15 K. Fluid Phase Equilib. 1999, 166, 53−65. (16) Pardo, F.; Van Ness, C. Volume Changes of Mixing of Some Ethanol + Hydrocarbon Systems. J. Chem. Eng. Data 1965, 10, 163− 165. (17) Matkowska, D.; Goldon, A.; Hofman, T. Densities and Viscosities of the Binary Mixtures of Chloroethylenes with Some Aliphatic Alcohols. J. Chem. Eng. Data 2010, 55, 685−693. (18) Riddick, A.; Bunger, W. B.; Sakano, T. K. Organic Solvents. Physical Properties and Method of Purification, 4th ed.; Wiley Interscience: New York, 1986. (19) Chen, S.; Fang, W.; Yao, J.; Zong, H. Density and Refractive Index at 298.15 K and Vapor-Liquid Equilibria at 101.3 kPa for Binary Mixtures of Ethanol + N-Methylpiperazine. J. Chem. Eng. Data 2001, 46, 596−600. (20) Zafarani-Moattar, M. T.; Tohidifar, N. Vapor−Liquid Equilibria, Density, Speed of Sound, and Viscosity for the System Poly(ethylene glycol) 400 + Ethanol at Different Temperatures. J. Chem. Eng. Data 2008, 53, 785−793. (21) Gόmez, A. C.; Sόlimo, H. N. Density, Viscosity, Excess Molar Volume, Viscosity Deviation, and Their Correlations for Formamide + Three Alkan-1-ols Binary Systems. J. Chem. Eng. Data 2002, 47, 796− 800. (22) Zafarani-Moattar, M. T.; Majdan-Cegincara, N. Vapor−Liquid Equilibria, Density, Speed of Sound, and Viscosity for the System Poly(ethylene glycol) 400 + Ethanol at Different Temperatures. J. Chem. Eng. Data 2008, 53, 2211−2216. (23) Tejraj, M.; Aminabhavi, T. M.; Gopalkrishna, B. Densities, Viscosities, and Refractive Indices of the Binary Mixtures of Bis(2methoxyethyl) Ether with 1-Propanol, 1-Butanol, 2-Methyl-1-propanol, and 2-Methyl-2-propanol. J. Chem. Eng. Data 1994, 39, 865−867. (24) Carrasco, A.; Pérez-Navarro, M.; Gascón, I.; López, M. C.; Lafuente, C. Densities and Viscosities of the Ternary Mixtures 2Methyl-1-propanol (or 2-Methyl-2-propanol) + N-Hexane + 1Chlorobutane at 298.15 K. J. Chem. Eng. Data 2008, 53, 1223−1227. (25) Mussari, L.; Postigo, M. Viscosity Measurements for the Binary Mixtures of 1,2-Dichloroethane or 1,2-Dibromoethane with Isomeric Butanols. J. Chem. Eng. Data 2000, 45, 86−91. (26) Ansón, A.; Garriga, R.; Martínez, S.; Pérez, P.; Gracia, M. Densities and Viscosities of Binary Mixtures of 1-Chlorobutane with Butanol Isomers at Several Temperatures. J. Chem. Eng. Data 2005, 50, 677−682.

the system of methylbenzene + 2-methyl-2-propanol. For the system of ethanol + methylbenzene, the curves of V E reveal a sigmoid shape with a small magnitude at both temperatures, which may imply that a weak interaction exists between unlike molecules. For the system of ethanol + 2-methyl-2-propanol, the values of V E become more negative from T = 298.15 to 318.15 K. However, with the remaining binary systems, V E values are found to increase with an increase of temperature, indicating the cleavage of the alcohol−alcohol complex may be responsible for this behavior. The ternary V E values are found to increase with increasing temperature and amount of 2-methyl-2-propanol in the mixtures. The observed V E values vary from −0.201 to 0.451 cm3·mol−1. The values of Δη are positive for ethanol + 2-methyl-2propanol except that some negative values are observed in the ethanol-rich region. For the remaining binary systems, the Δη values are negative over the entire composition range. The Δη values increase with an increase of temperature, and this behavior suggests that the interstitial accommodation between unlike molecules is not an easy process for the mixture when the temperature is low. As can be expected from the behavior of binary mixtures, the values of ternary Δη are negative at all compositions and distribute from −1.959 to −0.099 mPa·s. The ternary Δη values are shown to increase as the temperature rises but decrease with increasing amount of 2-methyl-2-propanol.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +886 4 26328001. Fax: +886 4 26327554. E-mail: [email protected]. Funding

The authors wish to extend their deep gratitude for the support by the Providence University of Republic of China under the fund of PU104-11100-A01. Notes

The authors declare no competing financial interest.

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K


Densities, Viscosities, and Correlations for the Ternary System of

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