Experimental and Computational Thermodynamic Properties of

Jul 21, 2015 - Values of excess molar volumes, V m E, of the binary mixtures in the liquid phase at T = 298.15 K have been derived from density measur...
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Experimental and Computational Thermodynamic Properties of (Benzyl Alcohol + Alkanols) Mixtures Razieh Sadat Neyband, Amin Yousefi, and Hosseinali Zarei* Department of Physical Chemistry, Faculty of Chemistry, Bu-Ali Sina University, Hamedan, Iran S Supporting Information *

ABSTRACT: Experimental data of densities, viscosities, and refractive indices of {(benzyl alcohol + methanol), ethanol, 1propanol, 2-propanol, 1-butanol, and 2-butanol} binary mixtures were measured at T = 298.15 K and ambient pressure (81 500 Pa) using an oscillating densimeter, Ubbelohde capillary viscometer, and digital Abbe refractometer, respectively. Values of excess molar volumes, VEm, of the binary mixtures in the liquid phase at T = 298.15 K have been derived from density measurements. The experimental data are used to calculate partial molar volumes, Vi, excess partial molar volumes, VEi , excess partial molar volumes at infinite dilution, VE,∞ i , deviations in the viscosity, Δη, and deviations in the refractive index, ΔnD, excess refractive index, nED, and kinematic viscosity, ν. The calculated quantities VEm, Δη, ΔnD, and nED have been correlated with the Redlich−Kister equation. The excess E,∞ partial molar volumes, VE,∞ i , and enthalpies, Hi , at infinite dilution of the binary mixtures were computed by ab initio method at the M05-2X/6-311++G** level of theory using PCM theory in the liquid phase. The general agreement found between the computational and the experimental liquid-phase data gives confidence to calculate the excess partial molar volumes and enthalpies at infinite dilution.

1. INTRODUCTION Knowledge of experimental and theoretical thermodynamic properties of liquid mixture behavior of industrially important chemicals has generated considerable interest and is the objects of increasing attention. Studies of the excess properties of liquid mixtures are of incredible potential for many applications and for theoretical aspect of the nature of molecular interactions. In this respect, great efforts have been devoted to the experimental studies of excess properties of mixtures.1−4 Understanding the physicochemical properties of the liquid mixtures can throw light on the nature of interaction of the solvent/solute. Intermolecular interactions are among the most fundamental forces, which strongly influence the physicochemical properties of matter. Due to the unique physicochemical properties of benzyl alcohol, this compound has been applied in many areas of science and finds some industrial applications. Benzyl alcohol is also used in shellac and in microscopy as an embedding material and in veterinary and pharmaceutical applications as an antimicrobial agent.5 Several experimental studies exist on thermodynamics data of these components.6−17 Thermodynamics properties at infinite dilution are important for applications, for example, separation of two substances and supplying useful information in the selection of the solvent suitable for a particular extraction, but also are important from the theoretical point of view. However, experimental process is time-consuming and may require a substantial cost, which could be much higher than the cost required for computational © XXXX American Chemical Society

study. Despite the remarkable interest of all these computational results, reliable characterization of thermodynamics properties to study computationally is limited and is not well understood yet. In this way, the number of computational approaches such as ab initio methods is increasing that analyze these questions in terms of the excess functions and intermolecular interactions for their mixtures, with the aim of correlating the structural and thermodynamics aspects which influence their behavior.18−24 A considerable portion of theoretical papers on solvent effects uses a continuum model for representing an averaged description of the solvent, which provided an economical way to introduce a description of the solute−solvent interactions. Experimental data of densities, viscosities, and refractive indices of {(benzyl alcohol + methanol), ethanol, 1-propanol, 2-propanol, 1-butanol, and 2-butanol} binary mixtures were measured at T = 298.15 K and ambient pressure (81 500 Pa) using an Anton Paar model DMA 4500 oscillating densimeter, Ubbelohde capillary viscometer, and digital Abbe refractometer, respectively. Excess molar volumes, VEm, partial molar volumes, Vi , kinematic viscosity, ν, deviations in the viscosity, Δη, and deviations in the refractive index, ΔnD, and excess refractive index, nED, for the binary mixtures have been calculated from Received: February 19, 2015 Accepted: July 6, 2015

A

DOI: 10.1021/acs.jced.5b00162 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 1. Specification of Chemical Samples, Density, ρ, Viscosities, η, and Refractive Indices, nD, of the Pure Components at T = 298.15 K and P = 81 500 Pa and Comparison With Literature Valuesa component

source

formula

ρ × 10−3

purity

kg·m exptl benzyl alcohol methanol ethanol 1-propanol 2-propanol 1-butanol 2-butanol

Merck Merck Merck Merck Merck Merck Merck

C7H8O CH4O C2H6O C3H8O C3H8O C4H10O C4H10O

>99.5% 99.8% >99.8% >99.8% >99.5% >99.8% (>99%)

η × 103

−3

lit.

1.04210 0.78655 0.78512 0.79954 0.78099 0.80607 0.80250

nD

Pa·s exptl 10

1.0416 0.7865128 0.7852232 0.799506 0.7808731 0.8057531 0.8027231

5.438 0.571 1.103 1.943 2.071 2.565 3.027

lit. 11

5.737 0.55128 1.11729 1.9326 2.04531 2.56429 3.00430

exptl

lit.

1.5381 1.3281 1.3594 1.3824 1.3749 1.3969 1.3946

1.534210 1.327534 1.359333 1.383033 1.375135 1.397333 1.395236

Standard uncertainties u are u(T) = 0.01 K for ρ, u(T) = 0.01 K for η and nD, u(p) = 0.5 kPa and the combined expanded uncertainty Uc are Uc(ρ) = 0.05 kg·m−3, Uc(η) = 3 × 10−6 Pa·s, Uc(nD) = 0.0002 (0.95 level of confidence). a

Figure 1. Optimized structures of the dimers of methanol + methanol, benzyl alcohol + methanol, and benzyl alcohol + benzyl alcohol.

The densimeter has a correction for the viscosity of the fluids. As the u-tube is oscillating, the sample will have the effect of damping the oscillation. This damping will be a function of the sample viscosity. The sample viscosity will also have the effect of apparently moving the oscillation nodes slightly, thus increasing the apparent volume of the cell. When these two effects are combined, the error is of the order ≈ 0.05 √η kg· m−3, where viscosity (η) is in mPa·s. The temperature in the cell was regulated to ± 0.01 K, with a solid-state thermostat. Temperature in the cell was measured by means of two integrated Pt 100 platinum thermometers. The apparatus was calibrated once a day with dry air and bidistilled fresh water. The binary mixtures were prepared just before use by mass, using a Mettler AB 204-N balance accurate to ± 0.1 mg. Before measurements, the chemicals were degassed by cooling and heating. Conversion to molar quantities was based on the relative atomic mass table of 1995 issued by IUPAC.38 Airtight stopper bottles were used for the preparation of the binary mixtures The viscosity of the pure components and the mixtures were measured with an Ubbelohde viscometer. An electronic digital stop watch with readability of 0.01 s was used for the flow time measurements. At least three repetitions of each data set were obtained, and the results were averaged. The temperature of the samples was controlled to 0.1 K with an external thermostat. The average uncertainty in dynamic viscosities, η, and kinematic viscosities, ν, are of the order of 3 × 10−6 Pa·s and 3 × 10−9 m2·s−1 respectively. Refractive indices were measured using a digital Abbe refractometer and with an uncertainty of 0.0002. The temperature was controlled to 0.1 K with circulating thermostat water to a jacketed sample vessel.

experimental data over the entire composition range. From the experimental results, the excess partial molar volumes, VEi , and excess partial molar volumes at infinite dilution, VE,∞ i , were calculated. The excess partial molar volumes and enthalpies at infinite dilution for the binary mixtures of benzyl alcohol + alkanols were calculated at liquid phase using the M05-2X/6311++G** density functional theory (DFT)25 by PCM (polarizable conductor model) method.26,27

2. EXPERIMENTAL SECTION 2.1. Materials. The specification of the pure chemicals is summarized in Table 1. The purities declared by the manufacturer were ascertained by comparing their measured densities, ρ, viscosities, η, and refractive indices, nD, with those reported in the literature values,610,11,28−36 which are listed in Table 1. The agreement between the experimental and literature data is good. All liquids were used without further purification. 2.2. Measurements. Binary mixtures were prepared by mixing a known mass of each liquid in an airtight and stoppered glass bottle. To avoid evaporation and solvent contamination, the solutions were used immediately after preparation. The masses were recorded on a Mettler AB-204 balance with an uncertainty of 1 × 10−7 kg. The estimated uncertainty in mole fraction was 0.0002. Densities were measured at 298.15 K with an Anton Paar DMA 4500 digital vibrating U-tube densimeter, with automatic viscosity correction. The estimated uncertainty of the measurements was 0.05 kg·m−3. The following relation holds for the period of vibration τ, and the density ρ, at the temperature T: ρ(T ) = a + bτ 2

(1)

3. RESULTS AND DISCUSSION Geometry optimization for the mixtures studied in this work is obtained from ab initio calculations of the benzyl alcohol (1) +

where a and b are the instrument constants determined by adjustment with bidistilled and degassed water and dry air.37 B

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Table 2. Experimental Densities, ρ, Experimental Dynamic Viscosities, η, Viscosity Deviations, Δη, Refractive Indices, nD, Refractive Index Deviations, ΔnD, Kinematic Viscosities, ν, for Benzyl Alcohol (1) + Alkanols (2) at T = 298.15 K and Ambient Pressure, 81 500 Paa x1

ρ × 10−3 kg·m

x1

−3

0000 0.0799 0.1599 0.2389 0.3216 0.4004 0.4803 0.5592 0.6400 0.7193 0.7983 0.8738 0.9559 1.0000

0.78655 0.83757 0.87729 0.90827 0.93494 0.95575 0.97348 0.98825 1.00142 1.01254 1.02221 1.03037 1.03822 1.04210

0.0000 0.0799 0.1601 0.2403 0.3162 0.3990 0.4797 0.5592 0.6409 0.7199 0.8005 0.8804 0.9599 1.0000

0.0000 0.0807 0.1619 0.2423 0.3212 0.3998 0.4808 0.5542 0.6358 0.7217 0.7985 0.8782 0.954 1.0000

0.78512 0.82311 0.85560 0.88457 0.90977 0.93173 0.95184 0.96838 0.98493 1.00067 1.01339 1.02549 1.03686 1.04210

0.0000 0.0815 0.1604 0.2408 0.3194 0.3989 0.4800 0.5598 0.6392 0.7105 0.7995 0.8795 0.9583 1.0000

0.0000 0.0794 0.1588 0.2407 0.3192 0.4006 0.4799 0.5591 0.6396 0.7200 0.8011 0.8803 0.9583 1.0000

0.79954 0.82712 0.85272 0.87746 0.89936 0.92071 0.94019 0.95841 0.97582 0.99209 1.00773 1.02202 1.03530 1.04210

0.0000 0.0799 0.1596 0.2399 0.3202 0.3990 0.4800 0.5598 0.6388 0.7189 0.7995 0.8800 0.9601 1.0000

0.0000 0.0824 0.1615 0.2401 0.3185 0.3962 0.4802 0.5611 0.6373 0.6887 0.7971

0.78099 0.81138 0.83814 0.86412 0.88776 0.90976 0.93209 0.95213 0.97047 0.98133 1.00412

0.0000 0.0813 0.1600 0.2395 0.3213 0.4006 0.4800 0.5597 0.6412 0.7178 0.8003

η × 103

Δη × 103

Pa·s

Pa·s

benzyl alcohol (1) + methanol (2) 0.571 0.000 0.768 −0.192 0.995 −0.356 1.270 −0.471 1.560 −0.550 1.923 −0.590 2.311 −0.594 2.713 −0.580 3.173 −0.517 3.647 −0.427 4.148 −0.319 4.657 −0.200 5.171 −0.073 5.438 0.000 benzyl alcohol (1) + ethanol (2) 1.103 0.000 1.299 −0.158 1.509 −0.289 1.759 −0.388 2.033 −0.455 2.333 −0.500 2.666 −0.518 3.025 −0.504 3.408 −0.465 3.775 −0.408 4.267 −0.302 4.732 −0.183 5.190 −0.067 5.438 0.000 benzyl alcohol (1) + 1-propanol (2) 1.943 0.000 2.111 −0.112 2.288 −0.213 2.485 −0.297 2.705 −0.358 2.950 −0.388 3.223 −0.398 3.509 −0.390 3.806 −0.370 4.128 −0.328 4.476 −0.261 4.842 −0.177 5.239 −0.060 5.438 0.000 benzyl alcohol (1) + 2-propanol (2) 2.071 0.000 2.189 −0.157 2.343 −0.268 2.528 −0.349 2.735 −0.418 2.970 −0.450 3.227 −0.461 3.507 −0.449 3.822 −0.408 4.137 −0.351 4.500 −0.266 C

nD

ΔnD

ν × 106 m2·s−1

1.3281 1.3668 1.4000 1.4262 1.4469 1.4668 1.4819 1.4939 1.5041 1.5135 1.5221 1.5295 1.5353 1.5381

0.0000 0.0219 0.0382 0.0476 0.0524 0.0549 0.0530 0.0484 0.0414 0.0342 0.0259 0.0165 0.0056 0.0000

0.726 0.917 1.134 1.397 1.671 2.013 2.375 2.745 3.168 3.601 4.057 4.517 4.979 5.285

1.3594 1.3852 1.4073 1.4272 1.4457 1.4616 1.4760 1.4890 1.5000 1.5083 1.5182 1.5266 1.5344 1.5381

0.0000 0.0112 0.0192 0.0248 0.0292 0.0309 0.0308 0.0296 0.0264 0.0219 0.0159 0.0101 0.0037 0.0000

1.405 1.578 1.764 1.989 2.236 2.505 2.801 3.120 3.458 3.780 4.210 4.612 5.005 5.217

1.3824 1.3998 1.4160 1.4315 1.4462 1.4596 1.4722 1.4841 1.4953 1.5058 1.5158 1.5255 1.5342 1.5381

0.0000 0.0050 0.0087 0.0118 0.0139 0.0151 0.0151 0.0145 0.0134 0.0115 0.0089 0.0061 0.0023 0.0000

2.430 2.552 2.682 2.833 3.007 3.205 3.428 3.661 3.901 4.162 4.443 4.738 5.059 5.218

1.3749 1.3931 1.4103 1.4273 1.4430 1.4570 1.4705 1.4830 1.4952 1.5057 1.5160

0.0000 0.0049 0.0093 0.0133 0.0157 0.0167 0.0173 0.0168 0.0157 0.0137 0.0105

2.652 2.700 2.796 2.927 3.078 3.260 3.462 3.684 3.936 4.188 4.479

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Table 2. continued x1

ρ × 10−3

x1

kg·m−3 0.8745 0.9526 1.0000

1.01922 1.03365 1.04210

0.8760 0.9590 1.0000

0.0000 0.0824 0.1602 0.2392 0.3206 0.3990 0.4803 0.5586 0.6394 0.7198 0.7993 0.8813 0.9604 1.0000

0.80607 0.82870 0.84952 0.87006 0.89078 0.91007 0.92952 0.94783 0.96622 0.98397 1.00109 1.01824 1.03425 1.04210

0.0000 0.0799 0.1607 0.2390 0.3199 0.3995 0.4799 0.5597 0.6396 0.7205 0.8005 0.8800 0.9594 1.0000

0.0000 0.0844 0.1766 0.2382 0.3241 0.4057 0.4807 0.5595 0.6410 0.7261 0.7997 0.8800 0.9595 1.0000

0.80250 0.82584 0.85073 0.86699 0.88847 0.90984 0.92764 0.94639 0.96522 0.98415 1.00045 1.01754 1.03395 1.04210

0.0000 0.0804 0.1590 0.2366 0.3196 0.3995 0.4795 0.5605 0.6456 0.7182 0.7998 0.8793 0.9593 1.0000

η × 103

Δη × 103

Pa·s

Pa·s

benzyl alcohol (1) + 2-propanol (2) 4.852 −0.168 5.243 −0.057 5.438 0.000 benzyl alcohol (1) + 1-butanol (2) 2.565 0.000 2.653 −0.142 2.780 −0.246 2.913 −0.339 3.065 −0.419 3.238 −0.475 3.434 −0.509 3.653 −0.520 3.908 −0.494 4.196 −0.439 4.514 −0.351 4.866 −0.228 5.240 −0.081 5.438 0.000 benzyl alcohol (1) + 2-butanol (2) 3.027 0.000 3.000 −0.221 3.038 −0.373 3.114 −0.484 3.229 −0.569 3.379 −0.612 3.564 −0.619 3.778 −0.600 4.031 −0.552 4.282 −0.477 4.592 −0.364 4.923 −0.224 5.260 −0.080 5.438 0.000

ΔnD

nD

ν × 106 m2·s−1

1.5247 1.5338 1.5381

0.0068 0.0024 0.0000

4.759 5.067 5.218

1.3969 1.4097 1.4224 1.4346 1.4469 1.4588 1.4705 1.4816 1.4924 1.5032 1.5137 1.5238 1.5333 1.5381

0.0000 0.0015 0.0028 0.0040 0.0048 0.0055 0.0058 0.0057 0.0052 0.0046 0.0038 0.0026 0.0009 0.0000

3.182 3.204 3.272 3.348 3.442 3.558 3.695 3.853 4.045 4.264 4.508 4.780 5.067 5.218

1.3946 1.4080 1.4207 1.4332 1.4463 1.4585 1.4700 1.4812 1.4928 1.5023 1.513 1.5233 1.5333 1.5381

0.0000 0.0019 0.0033 0.0046 0.0058 0.0066 0.0066 0.0062 0.0056 0.0046 0.0036 0.0025 0.0010 0.0000

3.772 3.638 3.591 3.594 3.637 3.722 3.843 3.991 4.172 4.358 4.590 4.839 5.088 5.218

Standard uncertainties u are u(T) = 0.01 K for ρ, u(T) = 0.01 K for η and nD, u(p) = 0.5 kPa, u(Δη × 103) = 0.004 Pa·s and the combined expanded uncertainty Uc are Uc(x1) = = 0.0002, Uc(ρ) = 0.05 kg·m−3, Uc(η) = 3 × 10−6 Pa·s, Uc(nD) = 0.0002, Uc(x1) = 0.0002, Uc(ν) = 3 × 10−9 m2·s−1, Uc(ϕ1) = 0.0002, Uc(ΔnD) = 0.0005 (0.95 level of confidence).

a

surrounded by a dielectric continuum of permittivity and continuum solution phase is a very dilute solution. This approach represents the solvent as a homogeneous polarizable continuum medium and places the solute in a cavity of realistic shape and size, which is defined in terms of interlocking spheres centered on the solute nuclei. The solute is represented by an accurate charge distribution obtained from quantum mechanical calculation.40−43 The coupling between the solute and the solvent is introduced by adding to the Hamiltonian of the isolated molecule, Ĥ °, and defining the effective Hamiltonian as following:44

alkanols (2) binary mixtures by using the Gaussian 03 program package.39 For the species included in this study, calculations have been performed at the M05-2X/6-311++G** levels concerning enthalpies and volumetric properties at infinite dilution. The resulting interacting pair structures obtained is shown in Figure 1. To confirm the minimum energy structures for {(benzyl alcohol + methanol), ethanol, 1-propanol, 2propanol, 1-butanol, and 2-butanol} dimers, frequency calculations were carried out using the density functional theory (DFT) theory. The frequency calculations can then be used to compute the enthalpy in the liquid phase on the same level of theory as used for all dimer structures. In the following as will be mentioned. step, we use these data to calculate HE,∞ i Geometry optimization was also employed for single-point evaluations to obtain volumetric property and excess partial molar volumes at infinite dilution will be computed using equation which will be cited. Calculations employing solvation corrections through use of the PCM method were performed. In this approach, the solute interacts with the solvent represented by a dielectric continuum model. The solute molecule is embedded into a cavity

Ĥ °Ψ = E Ψ

(2)

in vacuo

[Ĥ ° + VR̂ ]Ψ = E Ψ

in solution

(3)

where Ĥ ° is the Hamiltonian of the solute in vacuum (including nuclear repulsion terms), Ψ° and Ψ are the solute wave functions in vacuum and in solution, respectively, and V̂ R is a perturbation on the Hamiltonian of the solute through its reaction potential. In general, the solvent-induced term V̂ R is written as a sum of contributions from different physical D

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origins, related to dispersion, repulsion, and electrostatic forces between solute and solvent molecules and cavity term. We skip over the mathematical details of this formalism, and address the reader to references27,43−45 for detailed reviews concerning the PCM. According to this treatment, the excess molar enthalpies and volumes at infinite dilution XE,∞ 1(2) (X = V or H) can be computed as sol, ∞ X1E, ∞ = Xalkanol + benzyl.(solvent alkanols) sol, ∞ − 1/2Xalkanols + alkanols(solvent alkanols) sol, ∞ − 1/2Xbenzyl. + benzyl.(solvent benzyl.)

(4)

sol, ∞ X 2E, ∞ = Xalkanol + benzyl.(solvent benzyl.) sol, ∞ − 1/2Xalkanols + alkanols(solvent alkanols) sol, ∞ − 1/2Xbenzyl. + benzyl.(solvent benzyl.)

(5)

XE,∞ 1(2)

where excess molar enthalpies and volumes at infinite dilution of benzyl alcohol (benzyl.) (or alkanols) component refers to changes in enthalpy and volume of solution when sol,∞ passing from pure liquids Xsol,∞ alkanols+alkanols (or Xbenzyl.+benzyl.) to 46 their mixtures Xsol,∞ . The values of Xsol,∞ alkanols+benzyl. alkanols+alkanols, sol,∞ sol,∞ Xbenzyl.+benzyl. and Xalkanols+benzyl. were computed through frequency and single point calculations in solution phase on the optimized geometries. The extent of deviation of liquid mixtures from ideal behavior is expressed by excess functions. Excess molar volumes are the result of three contributions due to (i) interaction between unlike molecule, (ii) the free volume change, and (iii) change in internal pressure and reduced volume. The densities, ρ, viscosities, η, and refractive indices, nD, of the pure component and the binary mixtures were measured at 298.15 K and ambient pressure (81 500 Pa) and results of the study have been presented in Tables 1 and 2. The excess molar volumes, VEm, of the binary mixtures were calculated from density measurements according to the following equation:

Figure 2. Excess molar volume at 298.15 K of benzyl alcohol (1) + alkanols (2): solid lines were fitted from Redlich−Kister equation; ▲, methanol; ■, ethanol; ▼, ethanol from ref 15; ◇, 1-propanol; ◀, 1propanol from ref 6; ×, 2-propanol; □, 2-propanol from ref 6; △, 2propanol from ref 5; ○, 1-butanol; *, 2-butanol.

2-butanol > methanol >1-butanol > ethanol >2-propanol >1propanol. The refractive index deviations were calculated with an uncertainty of 0.0005 from the following equation:

2

VmE =

∑ xiM i(ρ−1 − ρi−1) i=1

2

(6)

ΔnD = nD −

where xi, Mi, and ρi are the mole fraction, molar mass, and density of the pure component i, respectively. The excess molar volumes of the binary mixtures are given in the Supporting Information and graphically represented in Figure 2. The VEm values are negative for the all binary mixtures over the entire range of composition. The average uncertainty in the excess molar volume was estimated to be 3 × 10−9 m3·mol−1. The viscosity deviation Δη, for binary mixtures were determined with an uncertainty of 0.004 mPa·s using the following equation:

∑ xiηi i=1

(8)

i=1

where nDi, nD, and xi are the refractive index of the component i, refractive index of the binary mixture and mole fraction, respectively. The results of ΔnD are presented in Table 2 and are graphically represented in Figure 4. The refractive index deviations are positive for mixtures of benzyl alcohol with all the alkanols studied here (Figure 4) and become more positive with a decrease in the chain length of the alkanols. The values of ΔnD at equimolar concentrations of benzyl alcohol and alkanols follow the order methanol > ethanol >2-propanol >1propanol >2-butanol >1-butanol. The excess refractive indices were calculated from the following equation:46

n

Δη = η −

∑ xinDi

(7)

where xi, ηi, and η refer respectively to the mole fraction and viscosities of its pure components and of the binary mixtures. Figure 3 indicates that the deviations in viscosity are negative in all the benzyl alcohol + alkanols binary mixtures. Similar kind of negative behavior was also observed by excess molar volumes of these mixtures. The absolute values of Δη at equimolar concentrations of benzyl alcohol and alkanols follow the order

id nDE = Δnmix − Δnmix

(9)

Δnmix = nmix − (ϕ1n1* − ϕ2n2*) id Δnmix =

E

(10)

ϕ1ϕ2(n1* − n2*)2 ϕ1n1* + ϕ2n2* + [ϕ1(n1*)2 + ϕ2(n2*)2 ]1/2

(11)

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Figure 3. Viscosity deviations of benzyl alcohol (1) + alkanols (2) at 298.15 K: ▲, methanol; ■, ethanol; □, ethanol at 293.15 K from ref 18, ◇, 1-propanol; ×, 2-propanol; ◆, 2-propanol from ref 5; ○, 1butanol; *, 2-butanol.

ϕ1 =

x1V1* * x1V1 + x 2V1*

Figure 4. Refractive index deviations at 298.15 K and at ambient pressure (81.5 kPa) of benzyl alcohol (1) and alkanols (2). Methanol (▲), Ethanol (■), 1-Propanol (◊), 2-Propanol ( × ), 1-Butanol (o), 2Butanol (*).

(12)

where Δnmix and Δnidmix are refractive index of mixing and ideal refractive index of mixing, ϕ1 is volume fraction, respectively. An asterisk indicates a pure substance and x1 and x2 are mole fractions.47 The results of nED are reported in the Supporting Information (Table S1). At 298.15 K, the negative nED is observed for benzyl alcohol + alkanols at low benzyl alcohol contents and the positive nED occurs at high benzyl alcohol contents (with the exception of benzyl alcohol + ethanol) (Supporting Information Figure S1). The average uncertainty in the excess refractive index was estimated to be 0.0006. The experimental data of VEm and nED were fitted to the Redlich−Kister equation:48

In these equations, n equals the number of experimental data and p is the number of adjustable parameters. The values of Ai parameters along with standard deviations data are listed in Table 3. The dynamic viscosity, η, and kinematic viscosities, ν, were determined according to following equation:

i=1

(13)

i−1

= ϕi(1 − ϕ1) ∑ Ai (1 − 2ϕ1) i=1

n i=1

(17)

(18)

where (∂VEm/∂xi)xj≠i.p.T is calculated from eq 13 using the parameters in Table 3. The Vi data were reported in Supporting Information (Table S1) with an uncertainty of 5 × 10−9 m3· mol−1. The excess partial molar volumes VEi , of a component in a binary mixture can be determined from the eq 18, which are negative over the whole compositions range

(14)

where xi and ϕi is the mole and volume fraction of component i, respectively. The Ai fitting coefficients were evaluated by least-squares method and the corresponding standard deviations, σ(Y), were calculated using the relation σ(Y ) = (∑ (Yexp, i − Ycal, i)2 /(n − p))1/2

υ = η/ρ

Vi̅ = VmE + V i* + (1 − xi)(∂VmE/∂xi)T , P

4

nDE

(16)

where k and c are viscometer constant, t and ρ are the efflux time and the density, respectively. The partial molar volumes, Vi , can be determined from excess molar volumes data using49

4

VmE/m 3·mol−1 = x1(1 − x1) ∑ Ai (1 − 2x1)i − 1

⎛ c⎞ η = ρ⎜kt − ⎟ ⎝ t⎠

ViE = Vi − V i*

(15) F

(19) DOI: 10.1021/acs.jced.5b00162 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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The following factors influence the excess volume: (a) dissociation of self-associated benzyl alcohol and alkanols, (b) interstitial accommodation of alkanols in −π···π− benzyl alcohol aggregates, and (c) weak hydrogen-bonding interaction (positive excess enthalpies with exception of benzyl alcohol + methanol14) between unlike molecules. Though the first factor contributes increase in excess volume, the last two factors contribute decrease in excess volumes, interstitial accommodation of alkanol in benzyl alcohol aggregates (packing effect) makes a negative contribution to VEm. From these reported excess volumes and excess enthalpies data,14 it can be pointed out that the second factor (b) is dominant in these systems. The maximum/minimum absolute values of VEm at equimolar concentrations are related to benzyl alcohol + ethanol/2butanol mixtures. It was shown in Figure 2 that the excess molar volumes of benzyl alcohol with ethanol, 1-propanol, and 2-propanol are in agreement with the reported data.5,6,15 The densities of pure liquids and their binary mixtures were measured by using single capillary pycnometer in ref 6. The reported data by Venkatramana et al.17 for benzyl alcohol with 1-propanol and 1-butanol are not good quantitative agreement with Nain et al.6 and this work data. The excess partial molar volumes at infinite dilution (VE,∞ 1 and VE,∞ 2 ) were obtained from the following equation:

Table 3. Coefficients of the Redlich−Kister Equation and Standard Deviations for VEm, Δη, ΔnD, and nED of Binary Mixtures at T = 298.15 K Y

A1

VEm × 106/ m3· mol−1 Δη/mPa·s ΔnD nED VEm × 106/ m3· mol−1 Δη/mPa·s ΔnD nED VEm × 106/ m3· mol−1 Δη/mPa·s ΔnD nED VEm × 106/ m3· mol−1 Δη/mPa·s ΔnD nED VEm

× 106/ −1

mol Δη/mPa·s ΔnD nED

m· 3

VEm × 106/ m3· mol−1 Δη/mPa·s ΔnD nED

A2

A3

A4

benzyl alcohol + methanol −2.1606 0.8875 −0.5306 −2.3840 0.4819 0.2037 0.2069 −0.0970 0.0265 0.0061 0.0236 −0.0081 benzyl alcohol + ethanol −2.4110 0.8900 −0.3544

0.3230

σ 0.005

0.0148 0.0139 −0.0067

0.004 0.0004 0.0005

−0.2149

0.003

0.2302 −0.0043 −0.0211

0.003 0.0006 0.0002

−0.0725

0.004

−1.6059 0.0592 0.0343 0.0603 −0.0107 0.0019 0.0023 0.0028 0.0001 benzyl alcohol +2-propanol −2.3716 0.5684 −0.1098

−0.2038 0.0570 0.0061

0.003 0.0001 0.0001

0.0040

0.005

−1.8412 0.1664 0.0860 0.0697 −0.0061 0.0047 0.0112 0.0077 −0.0039 benzyl alcohol +1-butanol −1.2552 0.1298 −0.0675

0.2538 0.0045 0.0063

0.002 0.0002 0.0002

−2.0706 0.1182 0.2017 0.1228 −0.0313 0.0071 0.0108 0.0190 −0.0060 benzyl alcohol +1-propanol −1.7783 0.4661 −0.1518

−2.0574 −0.3964 0.0968 0.0229 −0.0002 0.0012 −0.0008 0.0037 −0.0012 benzyl alcohol +2-butanol −1.2737 0.0429 −0.0627 −2.4822 0.0260 0.0024

0.2581 −0.0055 −0.0017

⎛ ∂V E ⎞ ViE, ∞ = ⎜ m ⎟ ⎝ ∂xi ⎠x = 0, T , p

(20)

i

−0.1234 0.3390 0.0038 0.0013 −0.0743

0.0548 0.0045 −0.0035

0.3852 0.0080 0.0074

0.003

The calculated excess partial molar volumes at infinite dilution are given in Table 4. The analyzing the limiting (at infinite dilution) quantities V iE,∞ , one may derive an information about solute−solvent interactions, independent of the composition effect, because solute−solute interactions can be theoretically neglected. Binary mixtures of benzyl alcohol (1) + alkanols (2) exhibit negative excess partial molar volumes at infinite dilution, as shown in Table 4. Thermodynamics studies of binary solutions of benzyl alcohol (1) + alkanols (2) at infinite dilution clearly show the effect of the large alkyl is groups on the solution behavior. The absolute trend for VE,∞ 1 methanol > ethanol >2-propanol >1-propanol >1-butanol >2butanol. For given binary mixtures, the negative values of VE,∞ 1 become larger as the size of alkyl chain decreases. The absolute experimental values of VE,∞ presented in Table 2 4 show clear trend as following: ethanol > 2-propanol > 1propanol > methanol > 2-butanol > 1-butanol. From Table 4, we see that the absolute values of the infinite dilution excess partial molar volumes of (benzyl alcohol (1) + 2-alkanols (2)) were more than those of (benzyl alcohol (1) + 1-alkanols (2)). for The excess partial molar volumes at infinite dilution VE,∞ 2

0.002 0.009 0.0001 0.003 0.003 0.0001 0.0001

Supporting Information Figure S2 show VE1 and VE2 curves for benzyl alcohol (1) + alkanols (2) as a function of the benzyl alcohol mole fraction. During mixing, the disruption of selfassociation of alkanols and benzyl alcohol occurs which makes a positive contribution to VEi , and the formation of a new −H···π− interation between them provides a negative contribution to VEi . The actual VEi values are resultant of the balance between the two positive and negative effects. The evidence obtained from these results point to the fact that negative effects are domain.

Table 4. Comparison of the Experimental and Computational Excess Partial Molar Volumes and Enthalpies at Infinite Dilution systems

benzyl benzyl benzyl benzyl benzyl benzyl

alcohol (1) + methanol (2) alcohol (1) + ethanol (2) alcohol (1) +1-propanol (2) alcohol (1) +2-propanol (2) alcohol (1) +1-butanol (2) alcohol (1) +2-butanol (2)

VE,∞ × 106 1

VE,∞ × 106 2

HE,∞ 1

HE,∞ 2

m3·mol−1

m3·mol−1

J·mol−1

J·mol−1

computational

experimental

computational

experimental

computational

experimental

computational

experimental

−3.735 −3.680 −2.387 −3.022 −1.222 −1.112

−3.902 −3.870 −2.324 −3.046 −1.329 −1.305

−1.548 −2.119 −1.617 −1.911 −1.180 −1.313

−1.481 −1.660 −1.536 −1.917 −1.316 −1.368

−157.5 910.0 580.2 890.4 838.0 1120.4

−140.3 1113.4 522.4

−708.9 589.4 351.8 795.8 789.5 813.4

−703.9 688.7 331.9

G

937.8

783.8

DOI: 10.1021/acs.jced.5b00162 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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of-the-art quantum-chemical computations allowed us to pave the route toward reliable studies of excess partial molar volumes and excess partial molar enthalpies at infinite dilution of binary mixtures.

benzyl alcohol (1) + alkanols (2) are less than the excess partial molar volumes at infinite dilution VE,∞ for all the mixtures. 1 The properties of these mixtures are examined and discussed in terms of the experimental and computational procedures. The excess partial molar volumes and enthalpies at infinite dilution were computed at the M05-2X/6-311++G** level of theory using PCM theory and they are given in Table 4. The computed excess partial molar volumes and enthalpies at infinite dilution were calculated from the difference between the volumes and enthalpies of solution when passing from pure liquids to their mixtures according to eqs 4 and 5.24,46 As can be seen in Table 4, the agreement between the experimental data of excess partial molar volumes at infinite dilution and computed data at the M05-2X/6-311++G** level of theory using the PCM for all of the binary mixtures is reasonable. To confirm the minimum energy structures and obtain enthalpy for benzyl alcohol−benzyl alcohol, benzyl alcohol− alkanols, and alkanols−alkanols dimers, frequency calculations were carried out using the M05-2X/6-311++G** density functional theory (DFT) in liquid phase by PCM method. The excess partial molar enthalpies at finite dilution, HE,∞ 1 , of the binary mixtures of benzyl alcohol (1) + alkanols (2), as obtained from the eqs 4 and 5, are collected in Table 4. In this case, it is possible to study the effect of introducing a methyl group in the alkanols on mixture properties. The agreement 14 between the experimental data of HE,∞ and the theoretically 1 calculated, was obtained in this study is reasonable (see Table 4). A similar trend is observed for HE,∞ at M05-2X/6-311++G** 2 levels of theory. This order is identical to the results obtained by experiment.14 On the other hand, ab initio approaches are able to provide accurate results for mixtures (see Table 4), clearly demonstrating the potentiality of computational chemistry experiments to become key tools for the prediction and understanding of excess partial molar enthalpies at finite dilution of all kinds of mixtures. It was previously reported that the accuracy of the M05-2X computations with suitable basis sets in the evaluation of excess partial molar enthalpy at infinite dilution allows us to draw a fully consistent interpretation of the available experimental data.24

■

ASSOCIATED CONTENT

S Supporting Information *

Excess molar volumes VEm, partial molar volumes Vi , excess refractive indices, nED (Table S1), and figures of excess refractive indices (Figure S1) and excess partial molar volumes (Figure S2). The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.5b00162.

■

AUTHOR INFORMATION

Corresponding Author

*Tel./Fax: +98 0813 8257407. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■ ■

ACKNOWLEDGMENTS The author would like to thank Bu-Ali Sina University for providing the necessary facilities to carry out the research. REFERENCES

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