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

Densities and Viscosities for Binary Liquid Mixtures of Pentanol Isomers from (288.15 to 328.15) K at 0.1 MPa ́ ez,*,† Leidy T. Vargas-Ibań ̃ez,† Gustavo A. Iglesias-Silva,‡ Jose ́ J. Cano-Gom † Hector J. Amezquita-Garcia, and Felipe de Jesús Cerino-Coŕ dova† †

J. Chem. Eng. Data Downloaded from pubs.acs.org by UNIV AUTONOMA DE COAHUILA on 04/05/19. For personal use only.

Facultad de Ciencias Químicas, Universidad Autónoma de Nuevo León, San Nicolás de los Garza, Nuevo León, C.P. 66455, México ‡ Departamento de Ingeniería Química, Instituto Tecnológico de Celaya Celaya, Guanajuato, C.P. 38010, México S Supporting Information *

ABSTRACT: This paper presents densities and viscosities of binary mixtures of 1pentanol + 2-pentanol, 1-pentanol + 2-methyl-1-butanol, and 2-pentanol + 2-methyl1-butanol from (288.15 to 328.15) K over the entire concentration range at atmospheric pressure. Experimental densities and viscosities are measured using a vibrating tube densimeter and a glass capillary viscometer, respectively. The relative standard uncertainties estimated in the density and viscosity were 4.8 × 10−4 and 0.01, respectively. Densities and viscosities of the binary mixtures are compared with the limits established by the diesel fuel standard (EN 590). The binary mixtures of 1pentanol + 2-methyl-1-butanol, and 2-pentanol + 2-methyl-1-butanol could be considered as alternative substitutes for diesel fuel. Excess molar volume values suggest that these mixtures behave as ideal solutions. Viscosity deviations are negative for all of the mixtures investigated in this study. The Redlich−Kister equation is used to represent the behavior of the excess molar volumes and viscosity deviations as a ́ and McAllister equations correlate the function of the composition. The Nava-Rios kinematic viscosity values with an average absolute percentage deviation of 0.139% and 0.203%, respectively.

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atmospheric pressure. Bravo-Sánchez et al.16,19 measured the density and viscosity of binary mixtures of butanol isomers from (308.15 to 343.15) K at 0.1 MPa. The authors found that 2-butanol + 2-methyl-1-propanol, 1-butanol + 2-methyl-1propanol, and 1-butanol + 2-butanol mixtures form ideal solutions at their given condition. Unfortunately, the density and viscosity of binary mixtures of pentanol isomers have not been reported in the literature. In this study, we have measured experimental densities and viscosities of binary mixtures of 1-pentanol + 2-pentanol, 1pentanol + 2-methyl-1-butanol, and 2-pentanol + 2-methyl-1butanol from (288.15 to 328.15) K at 0.1 MPa over the entire composition range. The densities and viscosities of the binary mixtures are compared with the limits established by the diesel ́ et fuel standard (EN 590).15 The McAllister55 and Nava Rios 56 al. equations have been used to correlate the kinematic viscosity of these mixtures. These equations can be used in the design of fuel injection system components and combustion chamber. Also, the interaction parameters in the McAllister55 ́ et al.56 equations have been used to evaluate the and Nava Rios contribution of three-body interactions between pentanol

INTRODUCTION Thermodynamic and transport properties of pure substances and mixtures are important in the design of heat and mass transfer equipment as well as in the development of predictive models.1 Densities and viscosities of binary mixtures of linear and branched alcohols have been studied by different research groups to understand the intermolecular interactions present in these mixtures.1−7 Alcohols are mainly used as solvents in the manufacture of lacquers, paints, hydraulic fluids, and in the extraction of fats. Also, alcohol mixtures can be used as oxygenating fuels or alternative fuels.1 Recently, butanol and pentanol isomers represent an alternative as partial or total substitutes for diesel fuel due to the energy crisis and because they have a greater regeneration in the life cycle.8−12 Density and viscosity impact on the design of fuel injection system components (fuel pump, filter, and transfer valves) and the fuel spray characteristics in the combustion chamber.13,14 The EN 59015 standard set the limits for the density and viscosity of diesel fuel. These norms establish that the viscosity has to be measured at 313.15 K while the density is measured at 288.15 K. However, to elucidate the temperature effect on these properties, it is important to extend the temperature range. Densities and viscosities have been measured for 1butanol,1,3,5,16,17 2-butanol,16,18−21 isobutyl alcohol,16−20 tertbutanol,16,18−20 1-pentanol,5,22−38 2-pentanol,23,24,39−50 and 2methyl-1-butanol23,43,49,51−54 at different temperatures and © XXXX American Chemical Society

Special Issue: Latin America Received: October 26, 2018 Accepted: March 28, 2019

A

DOI: 10.1021/acs.jced.8b00979 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Sample Information chemical name

source

CAS no.

initial purity mass fraction

purification method

analysis method

1-pentanol 2-pentanol 2-methyl-1-butanol

Sigma-Aldrich Merck Merck

71-41-0 6032-29-7 137-32-6

0.998 0.997 0.999

none none none

GCa GCa GCa

a

Gas chromatography provided by the supplier.

composition range. Density and viscosity measurements of pure pentanol isomers are compared with values reported in the literature,5,22−54 as shown in Table 2. The average absolute percentage deviations (AAPD) between our density measurements and literature values are (0.035, 0.036, and 0.103) % for 1-pentanol, 2-pentanol, and 2-methy1-butanol, respectively. The AAPD is calculated as,

isomers on the viscosity value of the mixture. The excess molar volumes and viscosity deviations values are correlated using the Redlich−Kister57 equation.

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EXPERIMENTAL SECTION Samples. Sigma-Aldrich supplied 1-pentanol with a mass fraction purity of 0.998; Merck supplied 2-pentanol and 2methyl-1-butanol with a mass fraction purity of 0.997 and 0.999, respectively. Table 1 shows the specifications of these reagents. The mixtures are prepared gravimetrically using an analytical balance (Ohaus, OHAUS00240) with an accuracy of 0.1 mg. The standard uncertainty estimated in the molar fraction is 0.002. Once prepared, the samples are placed in airtight containers to prevent exposure to air. In addition, molecular sieves (5 Å) are placed together with 1-pentanol, 2pentanol, and 2-methyl-1-butanol to avoid moisture absorption. Apparatus and Procedures. The densities of the pure alcohols and binary blends have been determined using a vibrating tube densimeter (Anton Paar, DMA 5000). The repeatability of the density and temperature set by the manufacturer are 1 × 10−6 g·cm−3 and 0.001 K, respectively. The fluid density value is related to the oscillation period of the vibrating tube filled with the interest sample under the action of a harmonic electromagnetic force. The densimeter calibration is performed frequently using ultrapure water and dry air as reference fluids.16 We have estimated the relative standard uncertainty in the density to be 4.8 × 10−4. Kinematic viscosity has been measured using a CannonFenske capillary viscometer (size 75) with a viscosity range from (1.6 to 8) cSt. The viscometer is placed inside a container with water connected to a recirculating bath (Fisher Scientific, Isotemp 3016D) for temperature control. Pt-100 thermometer is used to monitor the temperature with a standard uncertainty of 0.03 K. The kinematic viscosity value is obtained by multiplying the falling time of the sample through a capillary by the calibration constant of the viscometer, as v = K (T ) · t

AAPD =

l N |Y exp − Y lit orcalc| | o 100 o o o i i m } ∑ exp o o o N o i=1 Yi n ~

Yexp i

(2)

Ycalc i

where N is the data number; and are the experimental and literature values (calculated), respectively. Our kinematic viscosity measurements of pure alcohols are consistent with literature values within an AAPD of (0.730, 0.993, and 1.013)% for 1-pentanol, 2-pentanol, and 2-methy1-butanol, respectively. Tables 3−5 show the experimental densities and viscosities of the binary mixtures of 1-pentanol + 2-pentanol, 1pentanol + 2-methyl-1-butanol, and 2-pentanol + 2-methyl-1butanol from (288.15 to 328.15) K as a function of the mole fraction. As expected, the densities of the three binary mixtures decrease as the temperature increases at fixed composition. The viscosities of the binary mixture of 2-pentanol + 2-methyl1-butanol show a decrease as the molar fraction of 2-pentanol increases at fixed temperature. On the other hand, we have found that the kinematic viscosity of the binary mixture of 1pentanol + 2-methyl-1-butanol presents a minimum value at around x1 = 0.9 over the entire temperature range. Lapuerta et al.59,60 mention that this condition could be attributed to a synergistic effect due to the interaction between different components in the system. For the mixture of 1-pentanol + 2pentanol, the viscosities decrease with increasing molar fraction of 1-pentanol at temperatures of 288.15, and 293.15 K. Nevertheless, this behavior changes at temperatures higher than 298.15 K, that is, the viscosities increase as the molar fraction of 1-pentanol increases. This occurs because the dynamic viscosity of 1-pentanol is less than that of 2-pentanol at temperatures of 288.15 and 293.15 K, while at temperatures from (298.15 to 328.15) K, the dynamic viscosity of 1pentanol is greater than that of 2-pentanol, as shown in Figure 1. The temperature effect on the dynamic viscosity values for binary mixtures of pentanol isomers follows the order of 2pentanol + 2-methyl-1-butanol > 1-pentanol + 2-methyl-1butanol > 1-pentanol + 2-pentanol at mole fractions from (0 to 0.7) over the entire temperature range. At mole fractions, x1 = (0.8 to 1), the reduction in the viscosity values of the mixture of 1-pentanol + 2-pentanol is more significant than the mixture of 1-pentanol + 2-methyl-1-butanol. On the other hand, the temperature effect on the density values for these binary mixtures follows the order of 1-pentanol + 2-pentanol > 2-pentanol + 2-methyl-1-butanol > 1-pentanol + 2-methyl-1-butanol at mole fractions of (0 to 0.3) for the whole range of temperature. At mole fractions higher than 0.3, the reduction in the density values of the mixture of 2-pentanol

(1) 2 −1

where ν is the kinematic viscosity of the mixture in mm ·s , t is the falling time in seconds, and K(T) is the temperaturedependent calibration constant in mm2·s−2. Each kinematic viscosity measured is an average of five runs. A digital chronometer is used to measure the falling time with an accuracy of 0.01 s. We have estimated the relative standard uncertainty in the viscosity to be 0.01. The propagation error formula is used to estimate the standard uncertainties in density, viscosity, excess molar volume, and viscosity deviation.58

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RESULTS In this work, we have measured experimental densities and viscosities for binary mixtures of 1-pentanol + 2-pentanol, 1pentanol + 2-methyl-1-butanol, and 2-pentanol + 2-methyl-1butanol from (288.15 to 328.15) K at 0.1 MPa over the entire B



Article

Table 2. Comparison between the Experimental Pure Component Liquid Density, ρ (g·cm−3), and Viscosity, η (mPa·s), at Temperature T and Literature Values at Pressure p = 0.1 MPaa ρ/g·cm−3

η/mPa·s

T/K

this work

lit.

288.15

0.81856

293.15

0.81492

298.15

0.81126

303.15

0.80757

308.15

0.80386

313.15

0.80011

0.8187027 0.8183029 0.8183230 0.8146222 0.8150027 0.8148028 0.8146829 0.8146330 0.8146831 0.8144132 0.8147035 0.8145336 0.8141238 0.8109422 0.8108324 0.8107026 0.8112927 0.8111028 0.8110329 0.8109630 0.8107932 0.8111033 0.8107537 0.8072023 0.8075827 0.8074028 0.8073729 0.8072630 0.8071032 0.8073035 0.8071138 0.803605 0.8034522 0.8034026 0.8038327 0.8037028 0.8036729 0.8033832 0.8037033 0.7998024 0.7997025 0.8000527 0.7999028 0.7999429 0.7997830 0.7998035 0.7997838

318.15

0.79632

323.15

0.79248

0.796205 0.7961922 0.7961727 0.7961028 0.7961729 0.7961033 0.7905025 0.7922028 0.7923629

AAPD % 1-Pentanol 0.017 0.032 0.029 0.037 0.010 0.015 0.029 0.036 0.029 0.063 0.027 0.048 0.098 0.039 0.053 0.069 0.004 0.020 0.028 0.037 0.058 0.020 0.063 0.046 0.001 0.021 0.025 0.038 0.058 0.033 0.057 0.032 0.051 0.057 0.004 0.020 0.024 0.060 0.020 0.039 0.051 0.007 0.026 0.021 0.041 0.039 0.041 0.015 0.016 0.019 0.028 0.019 0.028 0.250 0.035 0.015

C

this work

lit.

AAPD %

4.698

4.83127 4.65529 4.68230 4.03222 4.15527 4.03228 4.01129 4.02530 4.04632 4.06136 4.10938

2.831 0.915 0.341 0.272 2.770 0.272 0.791 0.445 0.074 0.445 1.632

3.501

3.51922 3.51026 3.59527 3.48428 3.47429 3.49730 3.49932 3.50034

0.514 0.257 2.685 0.486 0.771 0.114 0.057 0.029

3.028

3.05623 3.11527 3.02628 3.02329 3.02230 3.03732 3.05234

0.925 2.873 0.066 0.165 0.198 0.297 0.793

2.671

2.63922 2.64826 2.66627 2.64028 2.64229 2.64732 2.66434

1.198 0.861 0.187 1.161 1.086 0.899 0.262

2.335

2.34027 2.31428 2.32029 2.31230 2.33534

0.214 0.899 0.642 0.985 0.000

2.052

2.06622 2.08527 2.03728 2.04529

0.682 1.608 0.731 0.341

1.810

1.80128 1.81029

0.497 0.000

4.043



Article

Table 2. continued ρ/g·cm−3 T/K

this work

328.15

0.78861

288.15

0.81334

293.15

0.80938

298.15

0.80535

303.15

0.80124

308.15

0.79705

313.15

0.79278

318.15

0.78842

323.15

0.78399

328.15

0.77946

288.15

0.82335

293.15

0.81964

298.15

0.81585

303.15

0.81212

308.15

0.80829

η/mPa·s lit.

AAPD %

0.8128042 0.8141043 0.8090439 0.8093040 0.8092945 0.8049724 0.8050139 0.8053040 0.8047042 0.8059043 0.8052445 0.8050546 0.8054047 0.8054048 0.8053750 0.8013023 0.8009039 0.8012040 0.8019944 0.8008846 0.8012048 0.7970040 0.7966042 0.7977043 0.7968946 0.7969550 0.7924224 0.7927040 0.7936041 0.7926246 0.7925048 0.7884040 0.7881042 0.7897043 0.7883550 0.7843041 0.7840050 0.7796749 0.7791750

1-Pentanol 0.003 0.023 0.039 0.014 0.027 2-Pentanol 0.066 0.093 0.042 0.010 0.011 0.047 0.042 0.006 0.081 0.068 0.014 0.037 0.006 0.006 0.002 0.007 0.042 0.005 0.094 0.045 0.005 0.006 0.056 0.082 0.020 0.013 0.045 0.010 0.103 0.020 0.035 0.003 0.041 0.162 0.009 0.040 0.001 0.027 0.037

0.8210043 0.8221453 0.8185153 0.8198054 0.8149043 0.8153751 0.8147853 0.8159054 0.8110023 0.8110053 0.8077043

2-Methyl-1-butanol 0.285 0.147 0.138 0.020 0.116 0.059 0.131 0.006 0.138 0.138 0.073

0.7925035 0.7926638 0.7883028 0.7885029 0.7884033

D

this work

lit.

AAPD %

1.607

1.59828 1.60829

0.560 0.062

5.057

5.07942 5.26743 4.17249

0.435 4.153 0.048

3.398

3.38142 3.44543 3.42147

0.500 1.383 0.677

2.820

2.88223 2.88841 2.88744 2.83446 2.80048

2.199 2.411 2.376 0.496 0.709

2.336

2.34042 2.39243 2.34846 2.33048

0.170 2.397 0.514 0.257

1.990

2.01741 1.97946 1.99048 1.99349

1.357 0.553 0.000 0.151

1.706

1.67542 1.71843

1.817 0.703

1.472 1.306

1.46641 1.47549 1.30349

0.408 0.204 0.230

6.439

6.46843

0.450

5.300

5.28549

0.283

4.501

4.49249

0.200

3.825

3.80152

0.627

3.265

3.36143

2.940

4.174



Article

Table 2. continued ρ/g·cm−3 T/K

η/mPa·s

this work

313.15

0.80441

318.15

0.80047

323.15

0.79647

328.15

0.79241

lit.

AAPD %

this work

lit.

AAPD %

2.783

3.29552 2.84352

0.919 2.156

2.379

2.34143 2.34152

1.597 1.597

2.060

2.05749

0.146

1.787

1.79149

0.224

2-Methyl-1-butanol 0.139 0.101 0.138 0.024 0.153 0.046 0.127 0.016 0.121 0.041

0.8071753 0.8036052 0.8033053 0.8046054 0.8017043 0.8001052 0.7994553 0.7966052 0.7955153 0.7968054

−4

Standard uncertainties: ur(η) = 0.01, u(T) = 0.03 K for viscosity, and ur(ρ) = 4.8 × 10 , u(T) = 0.01 K for density and u(p) = 10 kPa.

a

Table 3. Experimental Densities, ρ (g·cm−3), Excess Molar Volumes, VE (cm3·mol−1), Viscosities, η (mPa·s), and Viscosity Deviations, Δη (mPa·s), at Temperature T, and Mole Fraction x, for the System 1-Pentanol (1) + 2-Pentanol (2) at Pressure p = 0.1 MPaa ρ x1

η

VE −3

g·cm

0.000 0.100 0.200 0.298 0.400 0.500 0.601 0.699 0.798 0.901 1.000

0.81334 0.81391 0.81450 0.81505 0.81560 0.81613 0.81666 0.81715 0.81763 0.81810 0.81856

0.000 0.100 0.200 0.298 0.400 0.500 0.601 0.699 0.798 0.901 1.000

0.80124 0.80198 0.80270 0.80336 0.80402 0.80467 0.80532 0.80592 0.80650 0.80706 0.80757

0.000 0.100 0.200 0.298 0.400 0.500 0.601 0.699 0.798 0.901 1.000

0.78842 0.78937 0.79029 0.79113 0.79196 0.79277 0.79358 0.79434 0.79506 0.79575 0.79632

−1

cm ·mol 3

mPa·s

T = 288.15 K 0.000 5.057 −0.007 4.988 −0.016 4.929 −0.021 4.881 −0.024 4.842 −0.025 4.806 −0.024 4.772 −0.022 4.741 −0.017 4.714 −0.008 4.697 0.000 4.698 T = 303.15 K 0.000 2.820 −0.015 2.815 −0.027 2.815 −0.033 2.819 −0.035 2.833 −0.037 2.852 −0.038 2.875 −0.035 2.901 −0.029 2.932 −0.017 2.974 0.000 3.028 T = 318.15 K 0.000 1.706 −0.023 1.726 −0.042 1.751 −0.052 1.778 −0.056 1.809 −0.059 1.842 −0.059 1.878 −0.058 1.916 −0.049 1.956 −0.030 1.997 0.000 2.052

Δη mPa·s

ρ

η

VE −3

g·cm

0.000 −0.033 −0.057 −0.069 −0.071 −0.071 −0.069 −0.065 −0.056 −0.036 0.000

0.80938 0.81000 0.81063 0.81121 0.81179 0.81236 0.81292 0.81344 0.81395 0.81445 0.81492

0.000 −0.026 −0.047 −0.063 −0.071 −0.073 −0.070 −0.064 −0.054 −0.034 0.000

0.79705 0.79785 0.79863 0.79935 0.80006 0.80076 0.80145 0.80211 0.80274 0.80333 0.80386

0.000 −0.014 −0.024 −0.032 −0.036 −0.038 −0.037 −0.032 −0.026 −0.020 0.000

0.78399 0.78502 0.78601 0.78692 0.78782 0.78869 0.78956 0.79038 0.79117 0.79188 0.79248

−1

cm ·mol 3

mPa·s

T = 293.15 K 0.000 4.174 −0.009 4.141 −0.020 4.114 −0.025 4.095 −0.027 4.079 −0.028 4.065 −0.028 4.054 −0.026 4.047 −0.021 4.045 −0.010 4.044 0.000 4.043 T = 308.15 K 0.000 2.336 −0.017 2.354 −0.031 2.373 −0.038 2.392 −0.042 2.416 −0.044 2.442 −0.044 2.472 −0.042 2.504 −0.036 2.540 −0.021 2.587 0.000 2.671 T = 323.15 K 0.000 1.472 −0.026 1.498 −0.048 1.522 −0.059 1.546 −0.065 1.575 −0.067 1.607 −0.069 1.642 −0.067 1.679 −0.059 1.718 −0.035 1.762 0.000 1.810

Δη mPa·s

ρ

VE −3

g·cm

0.000 −0.020 −0.034 −0.040 −0.042 −0.043 −0.041 −0.035 −0.025 −0.012 0.000

0.80535 0.80603 0.80670 0.80731 0.80793 0.80854 0.80914 0.80970 0.81024 0.81078 0.81126

0.000 −0.016 −0.030 −0.044 −0.054 −0.061 −0.066 −0.067 −0.064 −0.051 0.000

0.79278 0.79365 0.79449 0.79528 0.79605 0.79680 0.79754 0.79825 0.79892 0.79956 0.80011

0.000 −0.008 −0.018 −0.027 −0.032 −0.034 −0.033 −0.030 −0.023 −0.015 0.000

0.77946 0.78057 0.78164 0.78265 0.78363 0.78457 0.78550 0.78638 0.78722 0.78798 0.78861

−1

cm ·mol 3

η

Δη

mPa·s

mPa·s

T = 298.15 K 0.000 3.398 −0.012 3.388 −0.023 3.382 −0.028 3.377 −0.031 3.373 −0.032 3.371 −0.033 3.377 −0.030 3.385 −0.025 3.402 −0.014 3.434 0.000 3.501 T = 313.15 K 0.000 1.990 −0.020 2.016 −0.036 2.039 −0.046 2.063 −0.049 2.090 −0.051 2.119 −0.052 2.152 −0.050 2.188 −0.042 2.226 −0.025 2.272 0.000 2.335 T = 328.15 K 0.000 1.306 −0.029 1.317 −0.053 1.335 −0.069 1.359 −0.077 1.387 −0.080 1.418 −0.081 1.450 −0.078 1.486 −0.067 1.524 −0.040 1.564 0.000 1.607

0.000 −0.020 −0.037 −0.052 −0.067 −0.078 −0.084 −0.085 −0.078 −0.057 0.000 0.000 −0.008 −0.020 −0.030 −0.037 −0.043 −0.045 −0.043 −0.039 −0.029 0.000 0.000 −0.020 −0.031 −0.037 −0.039 −0.039 −0.037 −0.030 −0.023 −0.013 0.000

a Standard uncertainties: u(x1) = 0.002, ur(ρ) = 4.8 × 10−4, u(VE) = 0.057 cm3·mol−1, ur(η) = 0.01, u(Δη) = 0.041 mPa·s, u(T) = 0.01 K for density, u(T) = 0.03 K for viscosity, and u(p) = 10 kPa.

E



Article

Table 4. Experimental Densities, ρ (g·cm−3), Excess Molar Volumes, VE (cm3·mol−1), Viscosities, η (mPa·s), and Viscosity Deviations, Δη (mPa·s), at Temperature T, and Mole Fraction x, for the System 1-Pentanol (1) + 2-Methyl-1-butanol (2) at Pressure p = 0.1 MPaa ρ x1

η

VE −3

g·cm

0.000 0.100 0.200 0.300 0.399 0.500 0.600 0.699 0.799 0.899 1.000

0.82335 0.82286 0.82237 0.82188 0.82140 0.82092 0.82044 0.81996 0.81950 0.81903 0.81856

0.000 0.100 0.200 0.300 0.399 0.500 0.600 0.699 0.799 0.899 1.000

0.81212 0.81164 0.81117 0.81071 0.81026 0.80980 0.80934 0.80889 0.80845 0.80800 0.80757

0.000 0.100 0.200 0.300 0.399 0.500 0.600 0.699 0.799 0.899 1.000

0.80047 0.80002 0.79960 0.79918 0.79876 0.79834 0.79793 0.79752 0.79711 0.79670 0.79632

−1

cm ·mol 3

mPa·s

T = 288.15 K 0.000 6.439 0.001 6.245 0.003 6.036 0.004 5.819 0.004 5.595 0.004 5.361 0.004 5.128 0.004 4.916 0.003 4.741 0.002 4.697 0.000 4.698 T = 303.15 K 0.000 3.825 0.003 3.725 0.004 3.630 0.005 3.518 0.005 3.402 0.005 3.287 0.005 3.197 0.005 3.114 0.004 3.051 0.003 3.018 0.000 3.028 T = 318.15 K 0.000 2.379 0.004 2.329 0.006 2.281 0.006 2.232 0.006 2.187 0.006 2.141 0.006 2.103 0.006 2.070 0.006 2.041 0.005 2.028 0.000 2.052

Δη mPa·s

ρ

η

VE −3

g·cm

0.000 −0.021 −0.054 −0.098 −0.149 −0.208 −0.266 −0.304 −0.307 −0.176 0.000

0.81964 0.81915 0.81866 0.81819 0.81771 0.81724 0.81677 0.81630 0.81584 0.81538 0.81492

0.000 −0.020 −0.035 −0.068 −0.104 −0.140 −0.150 −0.153 −0.137 −0.090 0.000

0.80829 0.80782 0.80736 0.80692 0.80647 0.80603 0.80558 0.80515 0.80471 0.80428 0.80386

0.000 −0.018 −0.032 −0.049 −0.061 −0.074 −0.079 −0.081 −0.077 −0.057 0.000

0.79647 0.79604 0.79563 0.79522 0.79482 0.79442 0.79402 0.79363 0.79324 0.79285 0.79248

−1

cm ·mol 3

mPa·s

T = 293.15 K 0.000 5.300 0.002 5.146 0.003 4.998 0.004 4.837 0.005 4.677 0.005 4.516 0.005 4.362 0.004 4.196 0.003 4.062 0.002 4.046 0.000 4.043 T = 308.15 K 0.000 3.265 0.004 3.176 0.005 3.099 0.005 3.007 0.006 2.921 0.006 2.831 0.006 2.765 0.005 2.701 0.005 2.660 0.004 2.648 0.000 2.671 T = 323.15 K 0.000 2.060 0.004 2.016 0.006 1.980 0.006 1.942 0.007 1.908 0.007 1.877 0.006 1.850 0.006 1.823 0.006 1.801 0.005 1.791 0.000 1.810

Δη mPa·s

ρ

VE −3

g·cm

0.000 −0.028 −0.050 −0.086 −0.120 −0.155 −0.184 −0.224 −0.233 −0.123 0.000

0.81585 0.81537 0.81490 0.81443 0.81397 0.81351 0.81305 0.81260 0.81215 0.81170 0.81126

0.000 −0.030 −0.048 −0.080 −0.107 −0.137 −0.144 −0.148 −0.131 −0.083 0.000

0.80441 0.80395 0.80351 0.80307 0.80264 0.80221 0.80178 0.80135 0.80093 0.80051 0.80011

0.000 −0.020 −0.030 −0.043 −0.053 −0.058 −0.060 −0.062 −0.059 −0.044 0.000

0.79241 0.79200 0.79160 0.79122 0.79084 0.79046 0.79008 0.78970 0.78933 0.78896 0.78861

−1

cm ·mol 3

η

Δη

mPa·s

mPa·s

T = 298.15 K 0.000 4.501 0.003 4.383 0.004 4.255 0.005 4.129 0.005 3.988 0.005 3.848 0.005 3.720 0.005 3.604 0.004 3.507 0.003 3.489 0.000 3.501 T = 313.15 K 0.000 2.783 0.004 2.717 0.005 2.657 0.006 2.590 0.006 2.528 0.006 2.468 0.006 2.419 0.006 2.365 0.005 2.327 0.004 2.323 0.000 2.335 T = 328.15 K 0.000 1.787 0.005 1.753 0.006 1.725 0.007 1.697 0.007 1.669 0.007 1.645 0.007 1.624 0.006 1.609 0.006 1.598 0.005 1.594 0.000 1.607

0.000 −0.019 −0.046 −0.072 −0.114 −0.153 −0.181 −0.198 −0.195 −0.113 0.000 0.000 −0.022 −0.036 −0.059 −0.076 −0.091 −0.095 −0.105 −0.098 −0.057 0.000 0.000 −0.015 −0.026 −0.036 −0.046 −0.052 −0.055 −0.052 −0.045 −0.032 0.000


+ 2-methyl-1-butanol is more significant than the other binary mixtures. The European standard norm (EN 590)15 establishes that the limit density values for a diesel fuel are 0.82 g·cm−3 and 0.845 g·cm−3 at 288.15 K. For the mixtures of 1-pentanol + 2methyl-1-butanol, and 2-pentanol + 2-methyl-1-butanol, the densities are within the limits established in the EN 59015 standard at molar fractions between (0 to 0.6), and (0 to 0.3), respectively. The mixture of 1-pentanol + 2-pentanol does not meet the limits of the EN 59015 standard. The kinematic viscosity limits established by EN 59015 are 2 mm2·s−1 and 4.5 mm2·s−1 at 313.15 K. Our experimental viscosities values for all of the mixtures investigated in this work are within these limits for the whole composition range. The values of the kinematic viscosities for these binary mixtures at 313.15 K are reported in the Supporting Information (Table S1). The binary mixtures of 1-pentanol + 2-methyl-1-butanol and 2-pentanol + 2-methyl-1-butanol meet the diesel fuel standard

(EN 590) for density and viscosity in the concentration range mentioned above. These binary mixtures could be considered as alternative substitutes for diesel fuel, it will be expecting spray characteristics and fluid dynamics through the fuel injection system comparable to conventional diesel. Excess molar volumes, VE, have been calculated from the experimental densities of pure alcohols and their mixtures using ij 1 ij 1 1 yz 1 yz V E /(cm 3·mol−1) = x1M1jjjj − zzzz + x 2M 2jjjj − zzzz ρ1 { ρ2 { kρ kρ

(3)

where xi, and Mi are the mole fraction and molar mass of the component i; ρ and ρi are the density of the mixture and of the pure components, respectively; and i indicates pure species 1 or 2. F



Article

Table 5. Experimental Densities, ρ (g·cm−3), Excess Molar Volumes, VE (cm3·mol−1), Viscosities, η (mPa·s), and Viscosity Deviations, Δη (mPa·s), at Temperature T, and Mole Fraction x, for the System 2-Pentanol (1) + 2-Methyl-1-butanol (2) at Pressure p = 0.1 MPaa ρ x1

η

VE −3

g·cm

0.000 0.100 0.200 0.301 0.400 0.500 0.600 0.700 0.800 0.900 1.000

0.82335 0.82237 0.82139 0.82041 0.81944 0.81845 0.81747 0.81647 0.81545 0.81440 0.81334

0.000 0.100 0.200 0.301 0.400 0.500 0.600 0.700 0.800 0.900 1.000

0.81212 0.81109 0.81004 0.80898 0.80792 0.80685 0.80578 0.80470 0.80362 0.80249 0.80124

0.000 0.100 0.200 0.301 0.400 0.500 0.600 0.700 0.800 0.900 1.000

0.80047 0.79936 0.79821 0.79703 0.79586 0.79468 0.79349 0.79229 0.79109 0.78984 0.78842

−1

cm ·mol 3

mPa·s

T = 288.15 K 0.000 6.439 −0.004 6.154 −0.008 5.978 −0.012 5.830 −0.015 5.687 −0.018 5.556 −0.020 5.435 −0.020 5.323 −0.017 5.232 −0.009 5.154 0.000 5.057 T = 303.15 K 0.000 3.825 −0.009 3.585 −0.016 3.460 −0.021 3.355 −0.025 3.253 −0.028 3.163 −0.030 3.093 −0.032 3.028 −0.031 2.973 −0.024 2.910 0.000 2.820 T = 318.15 K 0.000 2.379 −0.015 2.199 −0.024 2.110 −0.030 2.037 −0.035 1.968 −0.039 1.910 −0.041 1.869 −0.041 1.835 −0.040 1.805 −0.033 1.764 0.000 1.706

Δη mPa·s

ρ

η

VE −3

g·cm

0.000 −0.148 −0.185 −0.194 −0.200 −0.192 −0.175 −0.148 −0.102 −0.041 0.000

0.81964 0.81865 0.81765 0.81665 0.81565 0.81464 0.81363 0.81260 0.81157 0.81050 0.80938

0.000 −0.140 −0.164 −0.168 −0.170 −0.160 −0.130 −0.093 −0.048 −0.011 0.000

0.80829 0.80723 0.80615 0.80506 0.80397 0.80286 0.80176 0.80064 0.79952 0.79836 0.79705

0.000 −0.112 −0.135 −0.140 −0.142 −0.132 −0.106 −0.073 −0.035 −0.010 0.000

0.79647 0.79533 0.79413 0.79291 0.79170 0.79047 0.78924 0.78800 0.78675 0.78547 0.78399

−1

cm ·mol 3

mPa·s

T = 293.15 K 0.000 5.300 −0.005 5.034 −0.011 4.881 −0.016 4.762 −0.019 4.649 −0.021 4.548 −0.023 4.459 −0.023 4.377 −0.021 4.314 −0.014 4.251 0.000 4.174 T = 308.15 K 0.000 3.265 −0.011 3.047 −0.018 2.928 −0.024 2.830 −0.028 2.735 −0.032 2.653 −0.034 2.589 −0.035 2.530 −0.034 2.482 −0.027 2.422 0.000 2.336 T = 323.15 K 0.000 2.060 −0.017 1.898 −0.026 1.817 −0.033 1.754 −0.037 1.696 −0.041 1.649 −0.043 1.618 −0.044 1.590 −0.042 1.560 −0.036 1.525 0.000 1.472

Δη mPa·s

ρ

VE −3

g·cm

0.000 −0.154 −0.193 −0.199 −0.200 −0.189 −0.166 −0.135 −0.085 −0.035 0.000

0.81585 0.81484 0.81383 0.81281 0.81179 0.81075 0.80972 0.80868 0.80763 0.80654 0.80535

0.000 −0.125 −0.152 −0.156 −0.159 −0.147 −0.119 −0.085 −0.039 −0.007 0.000

0.80441 0.80333 0.80222 0.80108 0.79995 0.79881 0.79767 0.79651 0.79535 0.79414 0.79278

0.000 −0.104 −0.126 −0.130 −0.130 −0.117 −0.090 −0.058 −0.030 −0.006 0.000

0.79241 0.79124 0.78999 0.78872 0.78746 0.78619 0.78491 0.78362 0.78233 0.78100 0.77946

−1

cm ·mol 3

η

Δη

mPa·s

mPa·s

T = 298.15 K 0.000 4.501 −0.007 4.249 −0.013 4.106 −0.019 3.990 −0.022 3.882 −0.025 3.787 −0.027 3.703 −0.028 3.625 −0.027 3.564 −0.021 3.496 0.000 3.398 T = 313.15 K 0.000 2.783 −0.013 2.586 −0.021 2.481 −0.027 2.398 −0.032 2.317 −0.036 2.248 −0.038 2.196 −0.038 2.151 −0.038 2.112 −0.030 2.062 0.000 1.990 T = 328.15 K 0.000 1.787 −0.019 1.649 −0.028 1.578 −0.035 1.525 −0.040 1.476 −0.044 1.440 −0.046 1.418 −0.047 1.396 −0.045 1.371 −0.038 1.346 0.000 1.306

0.000 −0.142 −0.175 −0.179 −0.178 −0.162 −0.136 −0.103 −0.054 −0.012 0.000 0.000 −0.118 −0.143 −0.147 −0.149 −0.139 −0.111 −0.076 −0.037 −0.008 0.000 0.000 −0.090 −0.112 −0.117 −0.118 −0.106 −0.081 −0.055 −0.031 −0.009 0.000


of VE is smaller than the standard uncertainty estimated in the excess molar volume, u(VE) = 0.057 cm3·mol−1. The binary mixture of 1-pentanol + 2-pentanol presents absolute maximum values of VE greater than the u(VE) at temperatures of (318.15 to 328.15) K and molar compositions of (0.3 to 0.8). Thus, these binary mixtures do not behave as ideal solutions to these conditions. Table 3 shows negative values of VE for the mixture of 1-pentanol + 2-pentanol over entire composition range. Negative excess molar volumes indicate the presence of interactions between 1-pentanol and 2-pentanol molecules, such as dipole−dipole interactions, stronger dispersion force, and formation of hydrogen bonding, leading to a compaction of the mixture molecules.17 Also, the structural effects arising from the interstitial accommodation between 1-pentanol and 2-pentanol molecules, contribute to a more compact structure and a more negative excess molar volume. Nain61 mentions that this occurs due to differences in molar volumes and free volumes between the components. In

The standard uncertainty estimated in the excess molar volume is 0.057 cm3·mol−1. Tables 3−5 show the values of the excess molar volumes for the mixtures investigated in this work. The binary mixture of 1-pentanol + 2-methyl-1-butanol shows slight positive deviations from ideality at all temperatures. Mixtures of 1-pentanol + 2-pentanol, and 2-pentanol + 2-methyl-1-butanol present small negative deviations of the VE over the entire compositions range and at all temperatures. Nevertheless, the VE values are so small that the mixtures of 1pentanol + 2-methyl-1-butanol, and 2-pentanol + 2-methyl-1butanol behave almost as ideal solutions (VE → 0) at the conditions considered in this work, as shown in Figure 2. This behavior represents a decrease of the compaction of the molecules due to the rupture of the hydrogen bonds between different alcohol molecules and suggests that the volume of the mixtures becomes a weighted composition average of the volume of the pure components.17 This condition occurs only for those binary mixtures where the absolute numerical value G



Article

Figure 1. Densities, ρ, and viscosities, η, of pure pentanol isomers as a function of temperature, T: △, 1-pentanol; ●, 2-pentanol, ■, 2methyl-1-butanol.

addition, excess molar volume decreases as temperature increases, indicating the domain of structural effects on to hydrogen bonds at higher temperatures.62 Bravo-Sánchez et al.16,19 reported excess molar volumes for binary mixtures of 1butanol + 2-butanol, 1-butanol + 2-methyl-1-propanol, and 2butanol + 2-methyl-1-propanol from (308.15 to 343.15) K at atmospheric pressure. The authors found that these mixtures behave as ideal solutions. The molecular structure of pure butanol isomers present in the binary mixtures investigated by Bravo-Sánchez et al.16,19 is similar to the structure of the pentanol isomers investigated in this work. The difference is the number of carbons of the radical, but the number of carbon is the same in each of the components as in Bravo-Sánchez et al.16,19 Therefore, the behavior of the VE (VE → 0) is expected so our results agree with their findings. Viscosity deviations have been calculated from the experimental viscosities using

Figure 2. Excess molar volumes, VE, of binary mixtures as a function of mole fraction x1: (a) 1-pentanol (2) + 2-pentanol (2); (b) 1pentanol (1) + 2-methyl-1-butanol (2); (c) 2-pentanol (1) + 2methyl-1-butanol (2): ●, 288.15 K; ○, 293.15 K; ▼, 298.15 K; △, 303.15 K; ■, 308.15 K; □, 313.15 K; ◆, 318.15 K; ◇, 323.15 K; ▲, 328.15 K; and ―, corresponds to eq 5.

2

Δη /(mPa·s) = η −

∑ xiηi i=1

deviations increase as the temperature increases for the mixtures of 1-pentanol + 2-methyl-1-butanol, and 2-pentanol + 2-methyl-1-butanol. Minimum value of viscosity deviation, Δηmin, is present at x1 = 0.8 for a binary mixture of 1-pentanol + 2-methyl-1-butanol at 288.15, and 293.15 K. From (298.15 to 323.15) K, minimum values of Δη are present at x1 = 0.7, while at 328.15 K the value of Δηmin is shifted to a molar composition of 0.6. In this way, the viscosity deviation presents asymmetrical and negative behavior over the entire composition range at each temperature for this mixture. This behavior can be attributed to the difference in molecular structure of the 1-pentanol regarding to 2-methyl-1-butanol.17 For the mixture of 2-pentanol + 2-methyl-1-butanol, the minimum values of viscosity deviation are present at molar compositions around x1 = 0.4 from (288.15 to 328.15) K. On the other hand, it is interesting to note the behavior of the viscosity deviation of the mixture 1-pentanol + 2-pentanol. First, the minimum value of Δη for this mixture increases of −0.071 to −0.043 mPa·s at

(4)

where η is the dynamic viscosity of the mixture; ηi is the viscosity of the pure component; xi is the mole fraction; and i denotes species 1 or 2. Tables 3−5 show that the viscosity deviations are negative for all of the mixtures from (288.15 to 328.15) K considered in this study. The standard uncertainty estimated in the viscosity deviation is 0.041 mPa·s. The mixtures that show a small deviation from the weighted composition average of the pure components are 1-pentanol + 2-pentanol at all temperatures, and 1-pentanol + 2-methy1−1-butanol at high temperatures. Figure 3 shows the Δη for all of the mixtures from (288.15 to 328.15) K. Likewise, the temperature effect on the numerical value of the viscosity deviation for these mixtures follows the order of 1-pentanol + 2-methyl-1-butanol > 2-pentanol + 2methyl-1-butanol > 1-pentanol + 2-pentanol. The viscosity H



Article

difference in the molecular structure and chemical nature between the pentanol isomers.17 This observation indicates that ideal solutions for equilibrium properties differ from those of transport properties.16 Excess molar volume and viscosity deviation have been correlated using the Redlich−Kister57 equation n

Y E = x1x 2 ∑ ai(x1 − x 2)i

(5)

i=0

where YE is the VE or Δη; x1 and x2 are the molar fractions of components 1 and 2; and ai are temperature-dependent Table 6. Parameters for Redlich−Kister57 Equation to Calculate Excess Molar Volumes, VE (cm3·mol−1) T/K

a0

a1

1-pentanol + 2pentanol

288.15

−0.1020

−0.0055

0.0094

0.0010

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 288.15

−0.1169 −0.1309 −0.1512 −0.1767 −0.2070 −0.2380 −0.2746 −0.3247 0.0174

−0.0069 −0.0110 −0.0152 −0.0236 −0.0289 −0.0368 −0.0504 −0.0640 0.0010

−0.0109 −0.0394 −0.0545 −0.0764 −0.0912 −0.1157 −0.1333 −0.1225 −0.0006

0.0011 0.0009 0.0010 0.0011 0.0012 0.0013 0.0016 0.0018 0.0001

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 288.15

0.0190 0.0202 0.0212 0.0226 0.0233 0.0243 0.0254 0.0262 −0.0734

0.0006 0.0005 0.0002 0.0003 0.0004 0.0003 0.0000 0.0000 −0.0459

0.0076 0.0134 0.0185 0.0207 0.0283 0.0325 0.0335 0.0346 −0.0092

0.0000 0.0001 0.0001 0.0002 0.0002 0.0003 0.0003 0.0003 0.0006

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15

−0.0855 −0.0989 −0.1105 −0.1240 −0.1383 −0.1502 −0.1590 −0.1684

−0.0511 −0.0697 −0.0777 −0.0807 −0.0847 −0.0856 −0.0873 −0.0891

−0.0417 −0.0787 −0.1031 −0.1175 −0.1408 −0.1553 −0.1768 −0.2007

0.0007 0.0014 0.0017 0.0020 0.0021 0.0023 0.0028 0.0029

1-pentanol + 2methyl-1butanol

2-pentanol + 2methyl-1butanol

Figure 3. Viscosity deviations, Δη, of binary mixtures as a function of mole fraction x1: (a) 1-pentanol (2) + 2-pentanol (2); (b) 1-pentanol (1) + 2-methyl-1-butanol (2); (c) 2-pentanol (1) + 2-methyl-1butanol (2): ●, 288.15 K; ○, 293.15 K; ▼, 298.15 K; △, 303.15 K; ■, 308.15 K; □, 313.15 K; ◆, 318.15 K; ◇, 323.15 K; ▲, 328.15 K; and ―, corresponds to eq 5.

temperatures of 288.15 K, and 293.15 K, respectively; this condition occurs at a molar composition of 0.5. However, at 298.15 K the viscosity deviation decreases to −0.085 mPa·s, and subsequently it shows an increase as the temperature increases, as shown in Figure 2. Negative deviations in Δη occur at molar compositions between 0.5 and 0.7. This behavior occurs because the dynamic viscosity of 1-pentanol, η1, is less than that of 2-pentanol, η2, at 288.15 and 293.15 K, while at temperatures higher than 293.15 K the η1 > η2, as shown in Figure 1. In this way, the temperature effect on the dynamic viscosity of the pure alcohols impacts the tendency of viscosity deviations. Negative deviations in Δη indicate the presence of dipole− dipole interactions resulting from the dominance of the dispersion forces among the alcohols present in the mixture.63 The presence of these interactions can be attributed to the

a2

σ (cm3·mol−1)

system

adjustment parameters. Tables 6 and 7 show the value of these parameters together with the standard deviation expressed as ÄÅ N E,exp ÉÑ1/2 ÅÅ ∑ (J − JiE,calc )2 ÑÑÑÑ ÅÅ i = 1 i ÑÑ σ = ÅÅÅ ÑÑ ÅÅ N−n (6) ÅÇ ÑÑÖ where JiE,exp or calc represents experimental and calculated values by the Redlich−Kister57 equation; N is the number of experimental data; and n is the number of parameters. The a0 and a1 parameters in eq 5 are different from zero, this is an indication of the interassociation between the molecules of pentanol isomers according to Redlich−Kister.57 Also, the a2 parameter is determined only when high-precision experimental measurements are taken.57 I



Article

Table 7. Parameters for Redlich−Kister57 Equation to Calculate Viscosity Deviations, Δη (mPa·s) system 1-pentanol +2-pentanol

1-pentanol +2-methyl-1-butanol

2-pentanol +2-methyl-1-butanol

T/K

a0

a1

a2

σ (cm3·mol−1)

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15

−0.2876 −0.1713 −0.3054 −0.2922 −0.2408 −0.1688 −0.1472 −0.1371 −0.1569 −0.8519 −0.6337 −0.6083 −0.5121 −0.5274 −0.3594 −0.2878 −0.2274 −0.2051 −0.7614 −0.7422 −0.6399 −0.6108 −0.5680 −0.5440 −0.5042 −0.4459 −0.4056

0.0067 0.0454 −0.2133 −0.0258 −0.1723 −0.1002 −0.0150 −0.0266 0.0428 −1.2244 −0.9119 −0.7330 −0.4843 −0.4054 −0.2767 −0.2238 −0.1355 −0.1004 0.4368 0.5483 0.6177 0.6026 0.5747 0.5966 0.5110 0.5098 0.4355

−0.1700 −0.0102 −0.1668 −0.0659 −0.1735 −0.0517 −0.0476 0.0199 −0.0362 −0.5769 −0.7695 −0.2823 −0.1557 −0.1152 −0.1463 −0.1641 −0.1667 −0.0613 −0.4032 −0.4072 −0.2641 −0.2249 −0.1557 −0.1878 −0.1534 −0.1620 −0.1512

0.0019 0.0019 0.0030 0.0020 0.0046 0.0024 0.0020 0.0013 0.0006 0.0139 0.0230 0.0074 0.0071 0.0040 0.0045 0.0035 0.0033 0.0015 0.0174 0.0167 0.0170 0.0182 0.0158 0.0160 0.0136 0.0112 0.0084

́ et al.56 equation to correlate We have used the Nava-Rios the kinematic viscosity of binary mixtures. This equation is based on quadratic mixing rules for nonrandom mixtures. The kinematic viscosity can be evaluated as

bias =

(7)

where νm is the kinematic viscosity of the mixture; Mmix is a weighted composition average of the molar mass of the pure components; xi and Mi are the mole fraction and molar mass of component i; and δν12, δg*12, and δg*21 are temperaturedependent adjustment parameters related to a characteristic activation energy difference of molecular interactions.56 The term Mijk is the average molar mass of the mixture, defined as Mijk =

(Mi + Mj + Mk) 3

npts

∑ i=1

(viexp − vicalc) viexp

(9)

where νiexp and νicalc are the experimental and calculated kinematic viscosities, and N is the number of experimental ́ et al.56 equation correlates the kinematic data. The Nava-Rios viscosity within average absolute percentage deviations of (0.037, 0.103, and 0.277) % for the 1-pentanol + 2-pentanol, 1pentanol + 2-methyl-1-butanol, and 2-pentanol + 2-methyl-1butanol mixtures, respectively. The maximum absolute percentage deviation is presented for the binary mixture of 1-pentanol + 2-methyl-1-butanol with a value of 0.999% followed by the 2-pentanol + 2-methyl-1-butanol mixture with 0.889%. Figure 4 shows the percentage relative deviations of experimental viscosities and calculated by eq 7. Relative deviations are randomly distributed around zero. The mixture of 2-pentanol + 2-methyl-1-butanol shows relative deviations greater than the other two mixtures. However, the numerical values of the relative deviations for these mixtures are lower than the relative standard uncertainty estimated in the viscosity. In eq 7 the interaction parameter δν 12 is representative of three-body interactions of the type (1 + 1 + 2) and (1 + 2 + 2), while the parameters δg12 * , and δg21 * are associated to the interactions of the type (1 + 1 + 2) and (1 + 2 + 2), respectively. In terms of sensibility, the contribution of the interaction parameters of eq 7 to the kinematic viscosity value follows the order of δν12 > δg21 * > δg12 * for the mixture of 1-pentanol (1) + 2-methyl-1-butanol (2) over the entire range of temperature. This indicates that the interactions between two molecules of 1-pentanol with a molecule of 2-methyl-1butanol and one molecule of 1-pentanol with two molecules of

ln νm/(mm 2·s−1) = −ln(M mix ) + x1 ln ν1 + x1 ln(M1) + x 2 ln ν2 + x 2 ln(M 2) ÄÅ ÅÅ Å * ) + x 23 ln(δg * ) + x1x 2 ÅÅÅln(δν12) + x13 ln(δg12 21 ÅÅ ÅÇ É 3 3 yÑ Ñ ij M112 yz ij M122 zzÑÑÑ j z j z + x1 lnjj 2 zz + x 2 lnjj Ñ jM M z j M M 2 zzÑÑÑ k 1 2{ k 1 2 {ÑÖ

100 N

(8)

Table 8 shows the value of the interaction parameters, δν12, δg12 * , and δg21 * together with the average absolute percentage deviation (AAPD), σ, maximum absolute percentage deviation (MAPD) and bias J



Article

Table 8. Parameters for the Nava-Rios et al.56 Equation T/K

δν12

δg12 *

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15

0.9568 0.9594 0.9279 0.9079 0.9272 0.9378 0.9407 0.9333 0.9221

0.9487 1.0060 0.8760 0.9721 0.8691 0.9346 0.9843 1.0043 1.0135

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15

0.9614 0.9625 0.9266 0.8856 0.8679 0.9023 0.9088 0.9193 0.8956

0.5643 0.6054 0.6438 0.7833 0.7641 0.7727 0.7840 0.8108 0.8947

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15

0.9141 0.8901 0.8873 0.8573 0.8448 0.8700 0.7900 0.8240 0.8200

1.0006 1.0502 1.1375 1.2234 1.2876 1.1981 1.4600 1.3600 1.3000

δg21 *

AAPD %

1-Pentanol + 2-Pentanol 0.9514 0.020 0.9825 0.019 1.0129 0.031 0.9886 0.047 1.0091 0.069 1.0279 0.043 0.9794 0.040 1.0307 0.044 0.9166 0.018 1-Pentanol + 2-Methyl-1-butanol 1.0698 0.123 1.0161 0.192 1.0870 0.124 1.1917 0.076 1.1342 0.096 1.0600 0.117 1.0327 0.065 0.9806 0.084 1.0476 0.048 2-Pentanol + 2-Methyl-1-butanol 0.8665 0.142 0.8221 0.159 0.8140 0.191 0.8324 0.223 0.8244 0.235 0.6900 0.373 0.7900 0.441 0.6700 0.384 0.6610 0.345

bias %

σ (mm2·s−1)

MAPD %

0.003 −0.003 −0.023 0.005 −0.026 0.002 −0.020 −0.015 −0.011

0.002 0.002 0.002 0.002 0.005 0.002 0.003 0.001 0.001

0.082 0.045 0.120 0.086 0.310 0.163 0.251 0.090 0.070

0.089 0.116 0.085 −0.057 −0.037 0.037 0.002 0.014 −0.029

0.022 0.022 0.013 0.008 0.006 0.006 0.003 0.003 0.002

0.934 0.999 0.699 0.362 0.310 0.363 0.178 0.211 0.175

−0.003 −0.021 −0.024 −0.023 −0.030 −0.066 −0.029 −0.080 −0.140

0.016 0.015 0.015 0.019 0.016 0.015 0.016 0.011 0.009

0.383 0.441 0.532 0.868 0.807 0.641 0.889 0.739 0.563

parameters to the viscosity follows the order of δν12 > δg12 * > δg21 *. Likewise, we have used the McAllister55 equation to correlate the kinematic viscosity of the binary mixtures considered in this study. This equation establishes the presence of molecular interactions between three adjacent bodies for binary mixtures in a dimensional plane. The McAllister55 equation is ln νm/(mm 2·s−1) = x13 ln ν1 + 3x12x 2 ln ν12 + 3x1x 22 ln ν21 + x 23 ln ν2 − ln[x1 + x 2M 2 /M1] + 3x12x 2 ln[(2 + M 2 /M1)/3] + 3x1x 22 ln[(1 + 2M 2 /M1)/3] + x 23 ln(M 2 /M1)

(10)

where νm is the kinematic viscosity of the mixture; νi, xi, and Mi are the kinematic viscosity, mole fraction, and molar mass of component i; ν12 and ν21 are temperature-dependent parameters; and i denotes species 1 or 2. The parameters ν12 and ν21 are related with the interactions of the type (1 + 1 + 2) and (1 + 2 + 2), respectively. Table 9 shows the value of these parameters together with the average absolute percentage deviation, bias, standard deviation, and maximum absolute percentage deviation for all of the mixtures investigated in this work. The parameters in eqs 7, and 10 have been determined using a least-squares method provided by Microsoft Excel Solver. The McAllister55 equation correlates the kinematic viscosity within an AAPD of (0.084, 0.238, and 0.286) % for

Figure 4. Percent relative deviations Δν = ν(exp.) − ν(calc.) of experimental kinematic viscosities ν(exp.) of pentanol isomers mixtures from values ν(calc.) obtained with the correlation of ́ et al.56 as a function of the temperature T: ○, 1-pentanol Nava-Rios (1) + 2-pentanol (2); □, 1-pentanol (1) + 2-methyl-1-butanol (2); ▲, 2-pentanol (1) + 2-methyl-1-butanol (2).

2-methyl-1-butanol, contribute in greater proportion to the kinematic viscosity value of the mixture. For the binary mixtures of 1-pentanol (1) + 2-pentanol (2), and 2-pentanol (1) + 2-methyl-1-butanol (2), this condition occurs at temperatures below than 313.15 K. At temperatures of (318.15 to 328.15) K, the contribution of the interaction K



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Table 9. Parameters for the McAllister55 Equation system 1-pentanol + 2-pentanol

1-pentanol + 2-methyl-1-butanol

2-pentanol + 2-methyl-1-butanol

T/K

ν12

ν21

AAPD %

bias %

σ mm2·s−1

MAPD %

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15

5.7751 4.9668 4.0702 3.5456 3.0339 2.6801 2.3815 2.0896 1.8746 5.5962 4.8528 4.1810 3.6589 3.1781 2.8292 2.5018 2.2333 1.9809 6.5840 5.4570 4.5862 3.8874 3.3064 2.8300 2.3999 2.1143 1.8535

5.9234 5.0047 4.1967 3.4753 3.0043 2.6089 2.2388 1.9664 1.7096 7.3407 6.0652 5.2071 4.4180 3.7726 3.2492 2.8069 2.4362 2.1409 6.8656 5.5656 4.6529 3.8547 3.2121 2.7198 2.3244 1.9887 1.7520

0.095 0.026 0.124 0.065 0.171 0.072 0.067 0.053 0.084 0.427 0.430 0.280 0.117 0.145 0.202 0.223 0.244 0.095 0.220 0.236 0.255 0.271 0.361 0.360 0.330 0.278 0.194

−0.013 −0.012 −0.067 −0.017 −0.062 −0.045 −0.039 0.025 −0.013 −0.020 0.027 −0.137 −0.097 −0.042 0.010 −0.128 −0.090 −0.075 −0.164 −0.124 −0.113 −0.010 0.075 0.002 0.068 0.000 −0.032

0.008 0.002 0.008 0.004 0.009 0.004 0.003 0.002 0.002 0.038 0.034 0.019 0.008 0.008 0.009 0.009 0.009 0.003 0.026 0.024 0.022 0.019 0.017 0.015 0.015 0.012 0.007

0.204 0.057 0.369 0.166 0.640 0.277 0.307 0.188 0.148 0.866 0.951 0.747 0.326 0.384 0.484 0.738 0.745 0.338 0.768 0.907 0.970 0.944 0.791 0.801 1.137 1.127 0.777

the 1-pentanol + 2-pentanol, 1-pentanol + 2-methyl-1-butanol, and 2-pentanol + 2-methyl-1-butanol mixtures, respectively. The MAPD values for these blends follow the order of 2pentanol + 2-methyl-1-butanol >1-pentanol + 2-methyl-1butanol >1-pentanol + 2-pentanol. All parameters are statistically valid within a 95% confidence interval. Figure 5 shows the relative deviations for these mixtures as a function of

temperature. Relative deviations are randomly distributed around zero for all of the blends investigated. In eq 10 the contribution of the terms to the kinematic viscosity value follows the order of 3x1x22 ln ν21 > 3x21x2 ln ν12 > x32 ln ν2 > x31 ln ν1 for the binary mixture of 1-pentanol (1) + 2-methyl-1butanol (2) over the entire temperature range. This indicates that the interactions between one molecule of 1-pentanol with two molecules of 2-methyl-1-butanol and between two molecules of 1-pentanol with a molecule 2-methyl-1-butanol, contribute in greater proportion to the kinematic viscosity of the mixture. The same occurs for the mixtures of 1-pentanol (1) + 2-pentanol and 2-pentanol (1) + 2-methyl-1-butanol (2), but at temperatures of (288.15 to 293.15) K, and (288.15 to 303.15) K, respectively. At the other temperatures, the contribution of the terms of eq 10 to the kinematic viscosity follows the order of 3x21x2 ln ν12 > 3x1x22 ln ν21 > x32 ln ν2 > x31 ln ν1 for these binary mixtures. ́ et al.56 equation correlates In this work, the Nava-Rios slightly better the kinematic viscosity than the McAllister55 equation.

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CONCLUSIONS In this study, we have measured the densities and viscosities of binary mixtures of 1-pentanol + 2-pentanol, 1-pentanol + 2methyl-1-butanol, and 2-pentanol +2-methyl-1-butanol from (288.15 to 328.15) K over the entire composition range. Density and viscosity values of the pure pentanol isomers agree with values reported in literature within average absolute percentage deviations of 0.058% and 0.912%, respectively. Densities and viscosities of these binary mixtures have compared with the limits established by the diesel fuel

Figure 5. Percent relative deviations Δν = ν(exp.) − ν(calc.) of experimental kinematic viscosities ν(exp.) of pentanol isomers mixtures from values ν(calc.) obtained with the correlation of McAllister55 as a function of the temperature T: ○, 1-pentanol (1) + 2-pentanol (2); □, 1-pentanol (1) + 2-methyl-1-butanol (2); ▲, 2pentanol (1) + 2-methyl-1-butanol (2). L



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(4) Kumagai, A.; Yokoyama, C. Liquid Viscosity of Binary Mixtures of Methanol with Ethanol and 1-Propanol from 273.15 to 333.15 K. Int. J. Thermophys. 1998, 19, 3−13. (5) Saleh, M. A.; Akhtar, S.; Begum, S.; Ahmed, M. S.; Begum, S. K. Density and Viscosity of 1-Alkanols. Phys. Chem. Liq. 2004, 42, 615− 623. (6) Aucejo, A.; Burguet, M. C.; Muñoz, R. Densities, Viscosities, and Refractive Indices of Some Binary Liquid Systems of Ethanol + Isomers of Hexanol at 298.15 K. J. Chem. Eng. Data 1996, 41, 1131− 1134. (7) Hussein, N. M.; Asfour, A.-F. A. Densities and Kinematic Viscosities of Ten Binary 1-Alkanol Liquid Systems at Temperatures of (293.15 and 298.15) K. J. Chem. Eng. Data 2009, 54, 2948−2952. (8) Li, L.; Wang, J.; Wang, Z.; Liu, H. Combustion and Emissions of Compression Ignition in a Direct Injection Diesel Engine Fueled with Pentanol. Energy 2015, 80, 575−581. (9) Elfasakhany, A.; Mahrous, A. F. Performance and Emissions Assessment of N-Butanol−methanol−gasoline Blends as a Fuel in Spark-Ignition Engines. Alexandria Eng. J. 2016, 55, 3015−3024. (10) Karabektas, M.; Hosoz, M. Performance and Emission Characteristics of a Diesel Engine Using Isobutanol-Diesel Fuel Blends. Renewable Energy 2009, 34, 1554−1559. (11) Mack, J. H.; Schuler, D.; Butt, R. H.; Dibble, R. W. Experimental Investigation of Butanol Isomer Combustion in Homogeneous Charge Compression Ignition (HCCI) Engines. Appl. Energy 2016, 165, 612−626. (12) Tsujimura, T.; Pitz, W. J.; Gillespie, F.; Curran, H. J.; Weber, B. W.; Zhang, Y.; Sung, C. J. Development of Isopentanol Reaction Mechanism Reproducing Autoignition Character at High and Low Temperatures. Energy Fuels 2012, 26, 4871−4886. (13) Ramírez-Verduzco, L. F.; García-Flores, B. E.; RodríguezRodríguez, J. E.; Jaramillo-Jacob, R. Prediction of the Density and Viscosity in Biodiesel Blends at Various Temperatures. Fuel 2011, 90, 1751−1761. (14) Shu, Q.; Wang, J.; Peng, B.; Wang, D.; Wang, G. Predicting the Surface Tension of Biodiesel Fuels by a Mixture Topological Index Method, at 313 K. Fuel 2008, 87, 3586−3590. (15) EN 590:2013. Automotive fuels-Diesel-Requirements and test methods; European Committee for Standardization: Brussels, Belgium, 2013. (16) Bravo-Sánchez, M. G.; Iglesias-Silva, G. A.; Estrada-Baltazar, A.; Hall, K. R. Densities and Viscosities of Binary Mixtures of N-Butanol with 2-Butanol, Isobutanol, and Tert-Butanol from (303.15 to 343.15) K. J. Chem. Eng. Data 2010, 55, 2310−2315. (17) Cano-Gómez, J. J.; Iglesias-Silva, G. A.; Cortez-Sánchez, L. D.; Castillo-Escobedo, M. T. Densities and Viscosities for Binary Liquid Mixtures of Butan-1-ol + Propane-1,2-Diol, + Butane-1,2-Diol and 2Methylpropan-1-ol + Propane-1,2-Diol, + Butane-1,2-Diol from 298.15 to 333.15 K at 0.1 MPa. J. Chem. Eng. Data 2017, 62, 4252−4265. (18) Martínez, S.; Garriga, R.; Pérez, P.; Gracia, M. Densities and Viscosities of Binary Mixtures of Butanenitrile with Butanol Isomers at Several Temperatures. J. Chem. Eng. Data 2000, 45, 1182−1188. (19) Bravo-Sánchez, M. G.; Iglesias-Silva, G. A.; Estrada-Baltazar, A.; Hall, K. R. Densities and Viscosities of Binary Mixtures of 2-Butanol + Isobutanol, 2-Butanol + Tert-Butanol, and Isobutanol + Tert-Butanol from (308.15 to 343.15) K. J. Chem. Eng. Data 2013, 58, 2538−2544. (20) Weng, W. L. Densities and Viscosities for Binary Mixtures of Anisole with 2-Butanol, 2-Methyl-1-Propanol, and 2-Methyl-2Propanol. J. Chem. Eng. Data 1999, 44, 788−791. (21) Aralaguppi, M. I.; Jadar, C. V.; Aminabhavi, T. M. Density, Viscosity, Refractive Index, and Speed of Sound in Binary Mixtures of Acrylonitrile with Methanol, Ethanol, Propan-1-ol, Butan-1-ol, Pentan-1-ol, Hexan-1-ol, Heptan-1-ol, and Butan-2-ol. J. Chem. Eng. Data 1999, 44, 216−221. (22) Al-Jimaz, A. S.; Al-Kandary, J. A.; Abdul-Latif, A. H. M. Densities and Viscosities for Binary Mixtures of Phenetole with 1Pentanol, 1-Hexanol, 1-Heptanol, 1-Octanol, 1-Nonanol, and 1-

standard (EN 590). The binary mixtures of 1-pentanol + 2methyl-1-butanol, and 2-pentanol + 2-methyl-1-butanol could be considered as alternative substitutes for diesel fuel at molar fractions of (0 to 0.6), and (0 to 0.3), respectively. The excess molar volumes values are so small that the binary mixtures of 1-pentanol + 2-methyl-1-butanol, and 2-pentanol + 2-methyl1-butanol essentially behave as ideal solutions. Negative deviations from ideality are noted for the VE for the mixture of 1-pentanol + 2-pentanol at temperatures of (318.15 to 328.15) K. This behavior indicates the presence of dipole− dipole interactions, stronger dispersion forces, and formation of hydrogen bonding between 1-pentanol and 2-pentanol molecules. The numerical value of viscosity deviation is negative for all of the mixtures investigated in this work. Negative deviations are the result of the dispersion forces, and to the difference in the molecular structure among the alcohols present in the mixture. Redlich−Kister57 equation correlates the excess molar volumes and viscosity deviations over the ́ et al.56 and entire temperature range. The Nava-Rios 55 McAllister equations correlate the kinematic viscosity within an average absolute percentage deviation of 0.139% and 0.203%, respectively.

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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.8b00979.

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Experimental kinematic viscosities of binary mixtures of 1-pentanol + 2-pentanol, 1-pentanol + 2-methyl-1butanol, and 2-pentanol + 2-methyl-1-butanol at 313.15 K and 0.1 MPa (PDF)

AUTHOR INFORMATION

Corresponding Author

*Tel.: 011 52 81 8329 4000. Fax: (81) 8376 2929. E-mail: jose. [email protected]. ORCID

Gustavo A. Iglesias-Silva: 0000-0001-7260-2308 José J. Cano-Gómez: 0000-0003-3761-7736 Funding

This work was supported by the Consejo Nacional de Ciencia and Tecnologiá (CONACyT) [CB-2016-285320]; and the Universidad Autónoma de Nuevo León (UANL) [Paicyt, IT609-18]. Notes

The authors declare no competing financial interest.

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