Static Permittivities of Isomeric Butanol Mixtures at Temperatures from

Oct 15, 2012 - Department of Physical Chemistry of Solutions, University of Łódź, 90-236 Łódź, Pomorska 163, Poland. ‡ Dielectric Research Laboratory ...
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Static Permittivities of Isomeric Butanol Mixtures at Temperatures from (288.15 to 308.15) K Krzysztof Klimaszewski,† Agnieszka Boruń,† Adam Bald,*,† and Ram Jeewan Sengwa‡ †

Department of Physical Chemistry of Solutions, University of Łódź, 90-236 Łódź, Pomorska 163, Poland Dielectric Research Laboratory, Department of Physics, Jai Nairain Vyas University, Jodhpur 342 005, India

‡

ABSTRACT: The relative static permittivities (εr) of six binary mixtures of four isomeric butanols are reported for various mole fractions over entire composition range at (288.15, 293.15, 298.15, 303.15, and 308.15) K. The excess values of εr and the permittivity temperature coefficients (∂lnεr/∂T) have been calculated. The excess parameters have been fitted to the Redlich−Kister polynomial equation. The results of the measurements have been used in the analysis of hydrogen-bond interactions between unlike molecules occurring in the alcohol−alcohol mixtures.

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INTRODUCTION

EXPERIMENTAL SECTION Analytical grade reagents purchased from Aldrich were used. Liquids were stored in dark bottles over molecular sieves (Sigma, (0.3 to 0.4) nm) to reduce the water content. Reagents employed in the present work are included in Table 1. Before use, they were double-distilled and degassed in an ultrasound bath.

Dielectric studies of binary liquid mixtures are important for understanding the character of the intermolecular interactions between different molecules in the mixture, especially due to the dipole−dipole interactions and the hydrogen bond (H-bond) formed between unlike molecules in the mixture. The relative static permittivity, εr, is a macroscopic property, which gives information about the ability of mixture components to form Hbond intermolecular associates. The investigations on temperature-dependent variation of the εr values of dipolar liquids provides knowledge about the dynamics of the microstructures and changes in the molecular interaction behavior.1 Dipole moments of the dipolar molecules are related to the polarity of the −OH groups, and due to this fact they are similar to most of the alcohols. Despite this fact the variation of εr values for mixtures of alcohols as a function of their composition is almost exclusively associated with the behavior of H-bond intermolecular interactions of different molecules. Alcohols are an important class of industrial and laboratory solvents and have been a frequent object of dielectric investigations,1−27 both in their pure form1,5,7,8 as well as in mixtures with the water and various dipolar liquids.6,9,14−17 Although authors analyzed the temperature dependence of permittivity,12,13 the investigations dealing with temperature dependence of permittivity in liquid binary mixtures have not been explored in detail so far. The aim of this work is to present the precise experimental εr values of six different mixtures of four isomeric butanols, each one mixed with another, over the whole range of concentrations and at five temperatures from (288.15 to 308.15) K. The work is a continuation of our previous studies on the dielectric properties of various alcohol−alcohol mixtures in relation to the molecular conformation in H-bonded complex systems.13,14,18−20 © 2012 American Chemical Society

Table 1. Specification of Chemicals chemical name

source

initial mole fraction purity

purification method

n-BuOHa i-BuOHb s-BuOHc t-BuOHd

Aldrich Aldrich Aldrich Aldrich

≥ 0.994 0.995 ≥ 0.995 ≥ 0.997

redistillation redistillation redistillation redistillation

a

n-BuOH = butan-1-ol. bi-BuOH = 2-methylpropan-1-ol. cs-BuOH = butan-2-ol. dt-BuOH = 2-methylpropan-2-ol.

Apparatus. Measurements of relative static permittivity, εr, were made using a dielectrometer constructed in the Institute of Chemistry at University of Łódź. For capacity measurement, a self-excited method was used. The apparatus used (the measuring cell was from DK- meter GK-68, VEB MWLGermany) and the detailed method of measurements are described in previous papers.19,20 All of the solutions were prepared by mass using an analytical balance (Sartorius RC 210D) with an uncertainty of 1·10−5 g. The uncertainty of composition of mixtures was 0.0001 mole fraction. The solutions were degassed and warmed tentatively to a temperature higher than the one used in the measurements. The measurements were made at a temperature defined for a given mixture for all of the compositions and then conducted at incrementally increasing Received: July 10, 2012 Accepted: October 4, 2012 Published: October 15, 2012 3164

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temperatures. The uncertainty of the measured εr was estimated at about ± 0.06. The εr values and their relative temperature coefficient (∂lnεr/∂T) were compared with the corresponding literature values (Table 2).2,4,24,28−31 The comparison shows a very reasonable agreement. Table 2. Experimental and Corresponding Literature Values of Relative Static Permittivity (εr) and Relative Static Permittivity Temperature Coefficient (∂lnεr/∂T) at 298.15 K for Four Isomeric Butanols at p = 0.1 MPaa (∂lnεr/∂T)/K−1

εr this work n-BuOH

17.58

i-BuOH s-BuOH

17.96 16.60

t-BuOH

12.49b

lit. 2,24

17.51 17.4328 17.934,24 16.564,24 17.028 12.474,24

this work

lit.

−0.00782

−0.0077129

−0.00829 −0.01058

−0.0086029 −0.0099030,31

−0.01637

−0.0146030,31

Figure 2. Excess relative static permittivity temperature coefficient, (∂lnεr/∂T)E, as a function of the mole fraction for binary mixtures of butyl alcohols at 298.15 K: ○, n-BuOH (1) + i-BuOH (2); ●, n-BuOH (1) + s-BuOH (2); □, n-BuOH (1) + t-BuOH (2); ▲, i-BuOH (1) + sBuOH (2); ■, i-BuOH (1) + t-BuOH (2); ×, s-BuOH (1) + t-BuOH (2).

a

Standard uncertainties u are u(T) = 0.01 K, u(p) = 10 kPa and the combined expanded uncertainties Uc are Uc(εr) = 0.06, and Uc(∂lnεr/ ∂T) = 0.00007 K−1 (level of confidence = 0.95). bValue extrapolated.20

polynomial, and n is the degree of the polynomial. The nonlinear least-squares fitting procedure was used to fit the polynomials to the data. The adjustable parameters, ai, their standard errors σ, and the standard deviations, σ(εEr ) are listed in Table 4. The standard errors of all fits indicate that the above equation fits the experimental data very well. Figure 1 shows the excess relative static permittivitties εEr as a function of composition for all investigated isomeric butanols binary mixtures at 298.15 K. The relationships εr = f(x2) are monotonic. Therefore, the character of these relationships (increasing or decreasing) depends only on the value of the relative permittivity of pure components of mixtures. For pure alcohols, it is possible to place the relative permittivity values (Table 2) in the order:

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RESULTS AND DISCUSSION The experimental values of εr for the investigated binary mixtures at (288.15, 293.15, 298.15, 303.15, and 308.15) K are reported in Table 3.

εr(i‐BuOH) > εr(n‐BuOH) > εr(s‐BuOH) > εr(t ‐BuOH)

As can be seen, there is the dependence of εr on the type of an alcohol (the smallest for tertiary alcohol, the largest for primary one). This can be connected with an ability of alcohol to create intermolecular hydrogen bonds of the linear type. The increase in the value of εr is certainly related to the formation of intermolecular H-bonded linear associates. Probably, they are formed most easily in i-BuOH, and the hardest in t-BuOH. A more detailed analysis of the changes in permittivity value for the mixtures can be performed based on the dependence εEr = f(x2). As can be seen in Figure 1 only in one case, the values εEr are slightly negative (n-BuOH + i-BuOH); the others are positive. The observed values εEr for the studied systems (for the same composition of mixtures) can be ordered in the series:

Figure 1. Excess relative permittivity, εEr , as a function of the mole fraction for binary mixtures of butyl alcohols at 298.15 K: ○, n-BuOH (1) + i-BuOH (2); ●, n-BuOH (1) + s-BuOH (2); □, n-BuOH (1) + tBuOH (2); ▲, i-BuOH (1) + s-BuOH (2); ■, i-BuOH (1) + t-BuOH (2); ×, s-BuOH (1) + t-BuOH (2).

The excess relative static permittivity values εEr were calculated from the experimental data of εr by using the mole-fractionweighted additive mixture law: εrE = εr − (x1εr1 + x 2εr2)

εrE(n‐BuOH + i‐BuOH) < εrE(n‐BuOH + s‐BuOH) < εrE(i‐BuOH + s‐BuOH) < εrE(s‐BuOH + t ‐BuOH) < εrE(i‐BuOH + t ‐BuOH) < εrE(n‐BuOH + t ‐BuOH)

(1)

The greatest positive values of εEr can be observed for mixtures of t-BuOH as one of the constituent, and the greater the differences in the types of alcohols are, the greater εEr are; that is, the εEr values for mixtures of tertiary butanol, t-BuOH, with the primary one are much higher than that of the secondary butanol, s-BuOH. In the case of mixtures of the secondary s-butanol with primary butanols the εEr values are very small and comparable to the estimated experimental uncertainty in the value of εr. In the case

(where εr1 and εr2 denote relative static permittivities of components 1 and 2) and next they were fitted to the Redlich−Kister equation32−34 n

εrE = x1x 2 ∑ ai(x 2 − x1)i i=0

(2)

The variables x1 and x2 denote the mole fractions of both components, the parameters ai are the coefficients of the 3165

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Table 3. Experimental Values of Relative Static Permittivity εr at Mole Fraction x2 of Isomeric Butanol Mixtures at Different Temperatures and at Pressure p = 0.1 MPaa εr (n-BuOH (1) + i-BuOH (2)) x2

288.15 K

0.0000 0.0505 0.1011 0.1496 0.2001 0.2488 0.3011 0.3497 0.3990 0.4511 0.5021 0.5489 0.6004 0.6488 0.6975 0.7510 0.8004 0.8480 0.8995 0.9506 1.0000

19.01 19.03 19.05 19.06 19.08 19.10 19.12 19.14 19.16 19.18 19.21 19.23 19.26 19.28 19.31 19.34 19.37 19.40 19.43 19.47 19.51

293.15 K

298.15 K

303.15 K

18.28 17.58 16.91 18.30 17.59 16.92 18.31 17.61 16.93 18.33 17.62 16.94 18.34 17.63 16.95 18.36 17.65 16.97 18.38 17.66 16.98 18.40 17.68 16.99 18.41 17.70 17.01 18.43 17.71 17.02 18.44 17.73 17.04 18.46 17.75 17.06 18.50 17.77 17.07 18.52 17.79 17.09 18.55 17.81 17.11 18.57 17.83 17.13 18.60 17.86 17.15 18.62 17.88 17.17 18.65 17.90 17.19 18.68 17.93 17.21 18.71 17.96 17.23 εr (n-BuOH (1) + t-BuOH (2))

εr (n-BuOH (1) + s-BuOH (2)) 308.15 K

x2

288.15 K

16.26 16.26 16.27 16.28 16.29 16.31 16.32 16.33 16.34 16.36 16.37 16.39 16.40 16.42 16.43 16.45 16.46 16.48 16.50 16.52 16.53

0.0000 0.0501 0.0987 0.1506 0.1998 0.2503 0.2986 0.3512 0.3977 0.4497 0.4998 0.5501 0.6011 0.6490 0.7005 0.7511 0.7986 0.8498 0.9006 0.9487 1.0000

19.01 18.97 18.93 18.89 18.86 18.82 18.79 18.75 18.72 18.69 18.67 18.64 18.61 18.59 18.57 18.55 18.53 18.51 18.50 18.48 18.47

308.15 K

x2

288.15 K

16.26 16.12 15.97 15.81 15.62 15.44 15.25 15.07 14.87 14.63 14.42 14.15 13.89 13.59 13.25 12.89 12.49 12.04 11.55 11.00 10.40

0.0000 0.0488 0.1011 0.1488 0.2005 0.2489 0.3013 0.3511 0.3993 0.4473 0.4984 0.5512 0.5999 0.6490 0.7017 0.7502 0.7989 0.8510 0.9003 0.9499 1.0000

19.51 19.46 19.41 19.36 19.31 19.25 19.20 19.14 19.09 19.03 18.98 18.92 18.87 18.81 18.76 18.71 18.66 18.61 18.56 18.51 18.47

293.15 K

298.15 K

18.28 18.24 18.20 18.15 18.11 18.07 18.03 17.99 17.95 17.91 17.87 17.83 17.79 17.76 17.72 17.68 17.65 17.62 17.58 17.55 17.51 εr (i-BuOH

303.15 K

17.58 16.91 17.54 16.86 17.49 16.81 17.44 16.76 17.40 16.71 17.35 16.65 17.30 16.60 17.25 16.54 17.20 16.49 17.16 16.43 17.11 16.37 17.06 16.32 17.01 16.26 16.96 16.20 16.91 16.14 16.86 16.07 16.81 16.01 16.76 15.95 16.71 15.88 16.66 15.82 16.60 15.75 (1) + s-BuOH (2))

308.15 K 16.26 16.21 16.16 16.10 16.05 15.99 15.93 15.87 15.81 15.74 15.68 15.61 15.54 15.47 15.40 15.32 15.25 15.17 15.09 15.01 14.94

x2

288.15 K

0.0000 0.0501 0.1012 0.1503 0.2003 0.2497 0.2990 0.3490 0.3993 0.4505 0.5001 0.5511 0.5998 0.6490 0.7001 0.7503 0.8003 0.8497 0.8990 0.9500 1.0000b

19.01 18.96 18.93 18.85 18.75 18.61 18.48 18.36 18.25 18.13 18.01 17.89 17.74 17.60 17.39 17.15 16.84 16.45 15.96 15.29 14.49

x2

288.15 K

293.15 K

298.15 K

303.15 K

308.15 K

x2

288.15 K

293.15 K

298.15 K

303.15 K

308.15 K

0.0000 0.0497 0.0999 0.1502 0.2002 0.2497 0.2998 0.3507 0.4003 0.4497 0.4998

19.51 19.46 19.37 19.24 19.09 18.94 18.78 18.60 18.43 18.26 18.11

18.71 18.65 18.52 18.38 18.24 18.08 17.89 17.71 17.53 17.36 17.15

17.96 17.85 17.74 17.57 17.43 17.25 17.08 16.88 16.70 16.49 16.30

17.23 17.09 16.96 16.78 16.62 16.42 16.22 16.01 15.80 15.57 15.34

16.53 16.37 16.21 16.05 15.84 15.63 15.44 15.20 14.97 14.74 14.47

0.0000 0.0511 0.1003 0.1512 0.1990 0.2498 0.3007 0.3500 0.3997 0.4502 0.5011

18.47 18.35 18.24 18.11 17.97 17.85 17.71 17.55 17.42 17.25 17.09

17.51 17.39 17.25 17.13 16.98 16.83 16.67 16.54 16.36 16.19 16.00

16.60 16.47 16.35 16.22 16.06 15.92 15.77 15.60 15.44 15.27 15.09

15.75 15.62 15.46 15.31 15.15 14.98 14.79 14.62 14.44 14.25 14.05

14.94 14.80 14.64 14.47 14.28 14.10 13.92 13.75 13.54 13.34 13.14

293.15 K

298.15 K

18.28 18.21 18.16 18.04 17.92 17.79 17.63 17.50 17.35 17.22 17.06 16.91 16.73 16.54 16.31 16.03 15.70 15.26 14.77 14.15 13.38 εr (i-BuOH

303.15 K

17.58 16.91 17.49 16.81 17.42 16.68 17.29 16.53 17.15 16.37 16.99 16.19 16.85 16.01 16.69 15.83 16.53 15.65 16.38 15.45 16.19 15.25 16.01 15.02 15.82 14.79 15.58 14.51 15.32 14.21 15.00 13.88 14.63 13.48 14.21 13.03 13.71 12.53 13.15 11.97 12.49 11.34 (1) + t-BuOH (2))

3166

293.15 K

298.15 K

18.71 18.66 18.61 18.55 18.49 18.43 18.38 18.31 18.25 18.19 18.13 18.06 18.00 17.94 17.88 17.81 17.75 17.69 17.63 17.57 17.51 εr (s-BuOH

303.15 K

17.96 17.23 17.90 17.17 17.85 17.11 17.78 17.05 17.72 16.98 17.66 16.92 17.59 16.85 17.53 16.78 17.46 16.70 17.39 16.63 17.32 16.56 17.25 16.48 17.18 16.40 17.10 16.32 17.03 16.24 16.96 16.16 16.89 16.08 16.81 16.00 16.74 15.92 16.67 15.83 16.60 15.75 (1) + t-BuOH (2))

308.15 K 16.53 16.47 16.40 16.34 16.27 16.20 16.13 16.05 15.97 15.89 15.81 15.73 15.65 15.56 15.48 15.39 15.30 15.21 15.12 15.03 14.94

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Table 3. continued εr (i-BuOH (1) + t-BuOH (2))

εr (s-BuOH (1) + t-BuOH (2))

x2

288.15 K

293.15 K

298.15 K

303.15 K

308.15 K

x2

288.15 K

293.15 K

298.15 K

303.15 K

308.15 K

0.5501 0.6012 0.6490 0.7003 0.7510 0.8007 0.8499 0.9002 0.9489 1.0000b

17.93 17.74 17.53 17.30 17.02 16.68 16.30 15.80 15.21 14.49

16.96 16.74 16.50 16.24 15.93 15.59 15.17 14.67 14.08 13.38

16.07 15.83 15.58 15.28 14.96 14.59 14.17 13.69 13.13 12.49

15.07 14.80 14.52 14.20 13.84 13.46 13.03 12.53 11.97 11.34

14.22 13.93 13.61 13.27 12.91 12.49 12.06 11.55 11.01 10.40

0.5497 0.6007 0.6511 0.7010 0.7497 0.8005 0.8488 0.9003 0.9496 1.0000b

16.89 16.70 16.50 16.28 16.03 15.76 15.49 15.19 14.84 14.49

15.83 15.64 15.42 15.17 14.93 14.68 14.39 14.07 13.72 13.38

14.90 14.72 14.50 14.26 14.03 13.78 13.50 13.18 12.84 12.49

13.84 13.62 13.41 13.17 12.89 12.63 12.32 12.01 11.68 11.34

12.92 12.70 12.47 12.23 11.96 11.68 11.39 11.07 10.74 10.40

a x2 is the mole fraction of second constituents. Standard uncertainties u are u(T) = 0.01 K, u(p) = 10 kPa, u(x2) = 0.0001 and the combined expanded uncertainties Uc are Uc(εr) = 0.06 (level of confidence = 0.95). bValue extrapolated.20

Table 4. Coefficients of the Redlich−Kister Equation and Their Standard Errors for Excess Relative Static Permittivity, εEr , of Isomeric Butanol Mixtures at 298.15 K ai n-BuOH + i-BuOH n-BuOH + s-BuOH n-BuOH + t-BuOH i-BuOH + s-BuOH i-BuOH + t-BuOH s-BuOH + t-BuOH

ao

Δao

a1

Δa1

a2

Δa2

σ

−0.13766 0.04998 4.71305 0.15901 4.27744 2.18343

0.00985 0.00941 0.02824 0.01135 0.01477 0.02080

0.00412 −0.01843 2.98171 −0.10231 2.42788 0.82067

0.01198 0.01141 0.03428 0.01377 0.01793 0.02525

0.03562 0.00428 2.10962 −0.03133 1.88151 −0.03133

0.02457 0.02343 0.07041 0.02821 0.03678 0.05189

0.003 0.003 0.010 0.004 0.004 0.005

factor impacting the εEr values is the type of alcohol. Furthermore, the maxima in εEr (x2) plots (Figure 1) for n-BuOH + t-BuOH, iBuOH + t-BuOH, and s-BuOH + t-BuOH are around x2 ≈ 0.6 which confirms the formation of 2:1 molar ratio stable adduct of t-BuOH to the n-BuOH/i-BuOH/s-BuOH. The additional information about intermolecular interactions in the studied systems is provided from the analysis of the changes in the temperature coefficient of εr:

of mixtures of two primary alcohols (n-BuOH + i-BuOH) the values of εEr are even slightly negative, but also comparable to the estimated error εr. Positive values of εEr may indicate an increase in the number of H-bonded parallel aligned dipoles in the linear intermolecular associates or an increase in their stability.13−17,20 This effect is greater for mixtures containing different type alcohols (primary and tertiary)the greater the difference, the bigger the εEr value. The type of an alcohol (primary, secondary, and tertiary) is connected with the surrounding of the hydroxyl groups that form hydrogen bonds. This may suggest that the main role in Hbonded intermolecular interactions in the studied systems is played by steric hindrances. Compared to the tertiary butanol (tBuOH), secondary alcohols, and especially primary ones, where the −OH group is located peripherally, it probably enables the formation of the linear type intermolecular associates. Finally, it causes an excess growth of εEr values. For mixtures of primary butyl alcohols (i.e., n-BuOH + i-BuOH) and mixtures of primary butyl alcohols with the secondary butanol (i.e., n-BuOH + sBuOH and i-BuOH + s-BuOH), these effects play a much smaller role. Our previous studies have shown that, for mixtures of methanol with ethanol, propyl alcohols, and butyl alcohols, the εEr values are definitely negative,20 and so the sign of εEr is opposite to that for a mixture of butyl alcohols studied in this work. Moreover, the previous study20 shows that the greater the difference in the size of alcohol molecules (e.g., methanol and the second component) in the mixture is, the more negative values of εEr are. For mixtures of methanol with butyl alcohols, it is clear that the mixtures of methanol with t-butanol have εEr values less negative than that of the mixtures of methanol with n-butanol and s-butanol. Thus, the impact of the type of alcohol (primary, secondary, tertiary) in a mixture is clear. In this study (mixtures of butyl alcohols) the different size of molecules of mixture components is of course much less significant. The main decisive

∂εr ∂ln εr = εr ∂T ∂T

(3)

From the experimental values of εr, the values of relative static permittivity temperature coefficient, (∂lnεr/∂T) and its excess values, (∂lnεr/∂T)E, were calculated. Values of (∂lnεr/∂T)E were calculated from the equation: ⎛ ∂ ln εr ⎞E ⎛ ∂ ln εr ⎞ ⎛ ∂ ln εr1 ⎞ ⎛ ∂ ln εr2 ⎞ ⎟ ⎜ ⎟ =⎜ ⎟ − x1⎜ ⎟ − x 2⎜ ⎝ ∂T ⎠ ⎝ ∂T ⎠ ⎝ ∂T ⎠ ⎝ ∂T ⎠ (4)

Obtained values of (∂lnεr/∂T) were collected in Table 5. The Redlich−Kister procedure was adjusted to the calculated values, in a similar way as previously. n ⎛ ∂ ln εr ⎞E ⎜ ⎟ = x1x 2 ∑ bi(x 2 − x1)i ⎝ ∂T ⎠ i=0

(5)

The coefficients bi of Redlich−Kister eq 5 and the standard deviation σ(∂lnεr/∂T)E are listed in Table 6. Figure 2 shows the values of (∂lnεr/∂T)E as a function of composition x2 for all investigated butanol mixtures at 298.15 K. In the case of pure butyl alcohols, one may observe (from Table 5) the dependence: 3167

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Table 5. Experimental Values of Relative Static Permittivity Temperature Coefficient, (∂lnεr/∂T) at Mole Fraction Concentration of Second Constituents, for Each Isomeric Butanol Mixture at 298.15 Ka n-BuOH (1) + i-BuOH (2) x2

(∂lnεr/∂T)·103/K−1

0.0000 −7.81 0.0505 −7.86 0.1011 −7.87 0.1496 −7.90 0.2001 −7.90 0.2488 −7.90 0.3011 −7.92 0.3497 −7.95 0.3990 −7.93 0.4511 −7.95 0.5021 −7.98 0.5489 −7.97 0.6004 −8.05 0.6488 −8.03 0.6975 −8.09 0.7510 −8.10 0.8004 −8.14 0.8480 −8.13 0.8995 −8.16 0.9506 −8.20 1.0000 −8.28 i-BuOH (1) + s-BuOH (2)

n-BuOH (1) + s-BuOH (2) x2

(∂lnεr/∂T)·103/K−1

0.0000 −7.81 0.0501 −7.86 0.0987 −7.91 0.1506 −7.98 0.1998 −8.06 0.2503 −8.17 0.2986 −8.26 0.3512 −8.34 0.3977 −8.43 0.4497 −8.60 0.4998 −8.71 0.5501 −8.87 0.6011 −9.01 0.6490 −9.17 0.7005 −9.35 0.7511 −9.55 0.7986 −9.72 0.8498 −9.96 0.9006 −10.18 0.9487 −10.41 1.0000 −10.60 i-BuOH (1) + t-BuOH (2)

n-BuOH (1) + t-BuOH (2) x2

(∂lnεr/∂T)·103/K−1

0.0000 −7.81 0.0501 −8.10 0.1012 −8.51 0.1503 −8.81 0.2003 −9.10 0.2497 −9.34 0.2990 −9.60 0.3490 −9.91 0.3993 −10.26 0.4505 −10.74 0.5001 −11.14 0.5511 −11.76 0.5998 −12.27 0.6490 −12.96 0.7001 −13.62 0.7503 −14.31 0.8003 −14.99 0.8497 −15.64 0.8990 −16.21 0.9500 −16.51 1.0000 −16.57 s-BuOH (1) + t-BuOH (2)

x2

(∂lnεr/∂T)·103/K−1

x2

(∂lnεr/∂T)·103/K−1

x2

(∂lnεr/∂T)·103/K−1

0.0000 0.0488 0.1011 0.1488 0.2005 0.2489 0.3013 0.3511 0.3993 0.4473 0.4984 0.5512 0.5999 0.6490 0.7017 0.7502 0.7989 0.8510 0.9003 0.9499 1.0000

−8.28 −8.35 −8.43 −8.47 −8.55 −8.62 −8.69 −8.79 −8.91 −9.01 −9.12 −9.23 −9.35 −9.48 −9.62 −9.77 −9.93 −10.08 −10.25 −10.40 −10.60

0.0000 0.0497 0.0999 0.1502 0.2002 0.2497 0.2998 0.3507 0.4003 0.4497 0.4998 0.5501 0.6012 0.6490 0.7003 0.7510 0.8007 0.8499 0.9002 0.9489 0.0000

−8.28 −8.66 −8.89 −9.09 −9.32 −9.60 −9.79 −10.08 −10.40 −10.77 −11.20 −11.63 −12.14 −12.69 −13.28 −13.87 −14.52 −15.10 −15.67 −16.18 −16.57

0.0000 0.0511 0.1003 0.1512 0.1990 0.2498 0.3007 0.3500 0.3997 0.4502 0.5011 0.5497 0.6007 0.6511 0.7010 0.7497 0.8005 0.8488 0.9003 0.9496 1.0000

−10.60 −10.74 −10.99 −11.23 −11.47 −11.76 −12.03 −12.24 −12.57 −12.83 −13.10 −13.40 −13.74 −13.99 −14.28 −14.65 −14.98 −15.40 −15.80 −16.16 −16.57

a

x2 is the mole fraction of second constituents. Standard uncertainties u are u(T) = 0.01 K, u(x2) = 0.0001 and the combined expanded uncertainties Uc are Uc(∂lnεr/∂T) = 0.00007 K−1 (level of confidence = 0.95).

the εEr = f(x2) presented in Figure 1. The largest difference from mole-fraction-weighted additivity of studied systems occurs in the case of significant differences in the type of alcohol and length of the chain. In this case, for mixtures of n-BuOH with t-BuOH, two extremes can be seen as minimum and maximum. It should be noted that the observed effects can also be associated with volumetric properties of the mixtures studied. Relative permittivity is largely due to the dipole density. Therefore, the effects of packaging can significantly affect the excess relative permittivity.

⎛ ∂ ln εr ⎞E ⎛ ∂ ln εr ⎞E ⎜ ⎟ (n‐BuOH) > ⎜ ⎟ (i‐BuOH) ⎝ ∂T ⎠ ⎝ ∂T ⎠ ⎛ ∂ ln εr ⎞E ⎛ ∂ ln εr ⎞E ⎟ (s‐BuOH) > ⎜ ⎟ (t ‐BuOH) >⎜ ⎝ ∂T ⎠ ⎝ ∂T ⎠

It clearly shows the dependence of a type of an alcohol and length of the carbon chain. The largest values of (∂lnεr/∂T)E are observed in the case of the unbranched primary alcohol, the smallest for the branched tertiary alcohol. The relationships (∂lnεr/∂T)E = f(x2) shown in Figure 2 remain similar in nature to 3168

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Table 6. Coefficients of the Redlich−Kister Equation and Their Standard Errors for Relative Static Permittivity Temperature Coefficient Excess Values (∂lnεr/∂T)E of Isomeric Butanol Mixtures at 298.15 K bi/K−1 b0·10

Δb0·10

b1·10

Δb1·104

2.48407 19.29158 39.99347 12.88000 50.81088 20.00207

0.44096 0.50176 3.1446 0.27813 0.41674 0.900862

3.23232 −0.21955 −37.2755 1.02024 −6.04061 2.98450

0.80586 0.91602 3.8171 0.50749 0.50571 1.64560

4

■

n-BuOH + i-BuOH n-BuOH + s-BuOH n-BuOH + t-BuOH i-BuOH + s-BuOH i-BuOH + t-BuOH s-BuOH + t-BuOH

4

4

AUTHOR INFORMATION

Corresponding Author

*Tel.: +48 426355846. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

Δb2·104

−90.8025

7.84020

−48.47030

1.03769

σ·104 0.202 0.176 0.668 0.117 0.155 0.036

(13) Sengwa, R. J.; Sankhla, S. Dielectric properties of binary and ternary mixtures of alcohols: Analysis of H-bonded interaction in complex systems. J. Non-Cryst. Solids 2007, 353, 4570−4574. (14) Sengwa, R. J.; Sankhla, S.; Shinyashiki, N. Dielectric parameters and hydrogen bond interaction study of binary alcohol mixtures. J. Solution Chem. 2008, 37, 137−153. (15) Sengwa, R. J.; Sankhla, S.; Khatri, V. Dielectric constant and molecular association in binary mixtures of N,N-dimethylethanolamine with alcohols and amides. Fluid Phase Equilib. 2009, 285, 50−53. (16) Sengwa, R. J.; Sankhla, S.; Khatri, V.; Choudhary, S. Static permittivity and molecular ineractions in binary mixtures of ethanolamine with alcohols and amides. Fluid Phase Equilib. 2010, 293, 137− 140. (17) Sengwa, R. J.; Khatri, V. Study of static permittivity and hydrogen bonded structures in amide−alcohol mixed solvents. Thermochim. Acta 2010, 506, 47−51. (18) Taniewska-Osińska, S.; Piekarska, A.; Bald, A.; Szejgis, A. Conductivity study of NaI solutions in n-propanol−n-butanol mixtures at 298.15 K. The effect of ion pairing on the standard dissolution enthalpies of NaI. J. Chem. Soc., Faraday Trans. 1 1989, 85, 3709−3715. (19) Taniewska-Osińska, S.; Piekarska, A.; Bald, A.; Szejgis, A. Electrical conductivity of NaI solutions in methanol−n-propanol and metanol i-propanol mixtures at 298.15 K. The effect of ion association on the standard dissolution enthalpies of NaI. Phys. Chem. Liq. 1990, 21, 217−230. (20) Chmielewska, A.; Ż urada, M.; Klimaszewski, K.; Bald, A. Dielectric properties of methanol mixtures with ethanol, isomers of propanol and butanol. J. Chem. Eng. Data 2009, 54, 801−806. (21) TRC Thermodynamic Tables; Thermodynamic Research Center, Texas A&M University: College Station, TX, 1994. (22) Iglesias, M.; Orge, B.; Canosa, J. M.; Rodriguez, A.; Dominguez, M.; Pineiro, M. M.; Tojo, J. Thermodynamic behaviour of mixtures containing methyl acetate, methanol, and 1-butanol at 298.15 K: Application of the ERAS model. Fluid Phase Equilib. 1998, 147, 285− 300. (23) Ogawa, H.; Murakami, S. Excess volumes, isentropic compressions, and isobaric heat capacities for methanol mixed with other alkanols at 25 °C. J. Solution Chem. 1987, 16, 315−326. (24) Riddick, J. A.; Bunger, W. B.; Sakano, T. K. Organic solvents: Physical properties and methods of purfication, 4th ed.; Wiley: New York, 1986. (25) Okano, T.; Ogawa, H.; Murakami, S. Molar excess volumes, isentropic compressions, and isobaric heat capacities of methanol− isomeric butanol systems at 298.15 K. Can. J. Chem. 1988, 66, 713−717. (26) Wisniak, J.; Tamir, A. Vapour−liquid equilibria of sec-butanol− isobutanol, sec-butanol−tert-butanol, and isobutanol−tert-butanol systems. J. Chem. Eng. Data 1975, 20, 388−391. (27) Canosa, J.; Rodriguez, A.; Orge, B.; Iglesias, M.; Tojo, J. Densities, refractive indices, and derived excess properties of the system metyl acetate + methanol + 2-butanol at 298.15 K. J. Chem. Eng. Data 1997, 42, 1121−1125. (28) Barthel, J. M. G.; Krienke, H.; Kunz, W. Physical chemistry of electrolyte solutions: Modern aspects; Topics in physical chemistry; Springer: New York, 1998; Vol. 5. (29) Abboud, J.-L. M.; Notario, R. Critical compilation of scales of solvent parameters; report to IUPAC Commission on Physical Organic

CONCLUSIONS The relative static permittivities of six binary mixtures of four isomeric butyl alcohols at (288.15, 293.15, 298.15, 303.15, and 308.15) K have been measured over the whole composition range. The relations of εr, εEr , (∂lnεr/∂T) and (∂lnεr/∂T)E values as the function of a composition for all the mixtures have been studied. It has been proved that the above values connected with the H-bond intermolecular interactions, as expected, depend on the carbon chain length of the mixture constituents and on the type of alcohol added (primary, secondary, or tertiary).

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b2·104

REFERENCES

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