Thermodynamic excess properties of binary mixtures of methanol + pyridine, methanol + benzene, and pyridine + benzene at several temperatures and atmospheric pressure

ABSTRACT This work reports experimental densities and sound speeds at (293.15, 298.15, 303.15, 308.15, and 313.15) K and viscosities at 298.15 K for the binary liquid mixtures methanol + pyridine, methanol + benzene, and pyridine + benzene over the entire range of compositions and atmospheric pressure. The excess properties, namely the excess molar volume , excess isentropic compressibility , and excess Gibbs energy for activation of viscous flow G* E were calculated from experimental data and are fitted to Redlich-Kister polynomials. The results obtained were discussed in terms of molecular interactions between the mixing components and structural effects.


Introduction
This article presents an extension to our previous works on thermodynamic and transport properties of binary mixtures of alkanols with various organic and non-organic compounds [1] [2][3][4]. Alkanols and aromatic compounds treated separately or in mixtures find applications in everyday life and various chemical and industrial processes. Methanol, either alone or blended with water, is a promising material serving as a fuel additive for improving engine performance and emission characteristics [5,6]. Methanol + benzene mixtures are used to separate heavy crude oil into various fractions [7]. Also, significantly higher conversion and oil yield are achieved when raw mined coal is thermally pre-treated with a methanol + benzene mixture [8]. Pyridine alone or combined with methanol is also widely used as a denaturing additive to ethanol. However, extensive production and everyday use of organic substances is inevitably associated with environmental pollution. Environmental engineers designing separation processes and process equipment need information on various thermodynamic and transport properties of involved organic substances and their mixtures. Therefore, studying the thermodynamic and transport properties of organic substances and their mixtures, covering the entire composition ranges and at different temperatures, is of great practical importance. It will also contribute to the fundamental understanding of complex molecular interaction between components of the mixture and, thus, to a better understanding of the liquid state theory.
Here, we present experimental densities and sound speeds u from 293.15 to 313.15 K at 5 K intervals, viscosities η at 298.15 K for the methanol + pyridine, methanol + benzene, and pyridine + benzene mixtures covering the entire mole fraction ranges. The related

Experimental section
Methanol (≥99.8%), benzene (≥99.7%), and pyridine (≥99.5%) were supplied by Sigma-Aldrich. The purity of these chemicals was ascertained by measuring their physical properties and comparing them with literature values (see Table 1). Since the agreement is good, no further purification was made. Sixteen mixtures of methanol + pyridine, 20 mixtures of methanol + benzene, and 20 mixtures of pyridine + benzene have been prepared to cover the whole mole fraction range. The details of the preparation and storage of mixtures were reported in our earlier papers [3,29]. The mole fraction uncertainty of the studied mixtures was estimated to be within ±0.0001.
Densities, ρ, and speed of sound, u, of pure liquids and liquid mixtures were measured at T = (293. 15, 298.15, 303.15, 308.15, and 313.15) K by using a density and speed of sound analyser model DSA5000M. The apparatus was calibrated periodically with ultrapure water and dry air. The density and sound speed standard uncertainties supplied by the manufacturer are ±5 × 10 −6 g·m −3 and ±0.1 m·s −1 , respectively. A calibrated Cannon-Fenske viscometer was used to determine the dynamic viscosities, η, of pure liquids and liquid mixtures. Before making the flow-time measurements, the viscometer with the test liquid was allowed to stand for 30 min in a water bath at 298.15 ± 0.04 K. A digital stopwatch with a readability of ±0.01 s was used for flow-time measurements. The reported viscosities are average values over five independent measurements.
Excess molar volumes, V E m , were calculated from density data by the following relation: where ρ is the density of the mixture; x i , M i , and ρ i are the mole fraction, molar mass, and density of the pure component i, respectively. Excess isentropic compressibilities, κ E S , were evaluated from the difference between experimental isentropic compressibility, κ s , and ideal isentropic compressibility, κ id S [30] where κ S was determined from the experimental density ρ and sound speed u using the Newton-Laplace equation: κ S ¼ ρ À 1 u À 2 ; The ideal isentropic compressibility κ id S was evaluated using the following expression suggested by Benson and Kiyohara [31]: Table 3. Density ρ and sound speed u of x methanol + (1-x) benzene mixtures at temperature T. where x i is the mole fraction of component i, and ϕ i denotes the volume fraction of component i in the mixture. T denotes the absolute temperature, and V m;i , κ S;i , α i , and C p;i are respectively the molar volume, isentropic compressibility, isobaric thermal expansivity, and isobaric molar heat capacity of the pure component i. The isobaric thermal expansivity was obtained from its definition α i ¼ À ρ À 1 @ρ=@T ð Þ p [30], while the isobaric molar heat capacities were taken from the literature [28,[32][33][34], see Table S1 in the supporting information.
The authors used the following equation for the calculation of excess Gibbs energy of activation for viscous flow G* E [35]: Table 4. Density ρ and sound speed u of x pyridine + (1-x) benzene mixtures at temperature T. η and V m is the mixture's dynamic viscosity and molar volume, respectively, and η i and V m,i are the dynamic viscosity and molar volume of the pure component i, respectively. R is the universal gas constant, and T is the absolute temperature. The combined expanded uncertainties at a 95% confidence level (k = 2) for the derived thermodynamic properties were estimated at U(V E m ) = 0.009 cm −3 ‧mol −1 , U(κ E S ) = 1.0 TPa −1 , U(G* E ) = 9 J‧mol −1 . Thermodynamic excess properties, V E m , κ E S , and G* E of the studied mixtures are presented graphically in Figures 1 to 3. The supplementary information also reports these data in Tables S2 to S5. The values of the excess properties were fitted at each temperature with a smoothing polynomial of the Redlich-Kister type [9]: where Y is the thermodynamic property to be fitted, x 1 and x 2 are the mole fractions of components 1 and 2, respectively, B j are the fitting parameters, and p is the polynomial order, which was optimised by using the F-test [36]. Table 6 lists the fitting parameters B j and the corresponding standard deviations σ(Y). The solid lines in Figures 1 to 3 refer to values calculated with equation (5) by using the corresponding fitting parameters in Table 6. Results indicate a good agreement between experimental and fitted lines generated using an optimal number of parameters, with σ (Y) better than the expanded uncertainties of the corresponding excess properties.
The V E m values of methanol + pyridine and pyridine + benzene are negative over the entire composition ranges at each investigated temperature. The V E m data of the methanol + benzene system exhibit a sine-like dependence with composition, with positive values in the benzene-rich region, and negative values in the methanol-rich region. The dependence of κ E S with temperature and mole fraction is similar to that of V E m for all studied mixtures. On the contrary, the G* E data seem to exhibit the opposite behaviour to that of V E m . The V E m and κ E S values increase when the temperature rises for the x methanol + (1-x) benzene system. The only exception is for the κ E S property for which a negative temperature coefficient is observed in the region 0 < x < ~0.1. Contrary to the methanol + benzene system, a decrease of V E m and κ E S is observed when the temperature rises for other systems under study.
The observed changes in excess properties can be interpreted qualitatively by considering the various interactions between component molecules in the mixtures. London-type weak dispersion interactions, which are likely to be operative in every case, should make positive contributions to V E m and κ E S , but a negative contribution to G* E . The dissociation of a component that is associated in the pure state should make the mixture flow more easily (G* E <0) and increase the volume and compressibility (V E m and κ E S >0). Strong specific interactions, such as complex formation, dipole-induced dipole and dipole-dipole interactions, and hydrogen bonding between unlike molecules, reduce the distances between molecules in the mixture, thus reducing volume and compressibility (V E m and κ E S <0) but increasing the viscosity (G* E >0). The magnitudes of the contributions made by these different interaction types will vary with both the components and the composition of the mixture [37]. Interstitial arrangement due to differences in sizes and shape of molecules is also expected to influence considerably the resulting excess properties.
Considering the above, then the positive values of V E m and κ E S in the benzene-rich region of the methanol + benzene system (see Figures 1 and 2) can be attributed mainly to the breaking of hydrogen bonding of methanol as the methanol molecules are added to a large amount of benzene. The negative V E m and κ E S values in the methanol-rich region suggest that complex formation occurred through π···HO bonding between the π-electron cloud of the aromatic ring of benzene and the OH group of methanol. Interstitial accommodation of benzene molecules into the remaining hydrogen-bonded methanol structure should make an additional negative contribution to V E m and κ E S . Table 6. Fitted parameters B j and standard deviations of the fit σ(Y) a for representation with Redlich-Kister polynomial of property Y for methanol + pyridine, methanol + benzene, and pyridine + benzene mixtures at temperature T.
; N is the number of experimental data points; exp refers to experimental data, cal refers to data calculated by equation (5).
The negative V E m and κ E S values for the methanol + pyridine system can be attributed to the formation of complexes by cross-associated N···HO and π···HO interactions [2,3]. The temperature dependence of V E m is, however, negative for this system, suggesting that complex formation is not the major contributor to the negative excess molar volume since this contribution is expected to decrease with increasing temperature [17]. Formation of tightly packed structures due to different sizes and shapes of component molecules, facilitated by π···HO and N···HO type interactions, is believed to be the primary factor contributing to the negative V E m values. The same kind of behaviour for excess molar volume has been observed in our recent study on ethanol + pyridine mixtures [3] and by Kijevčanin et al. [38] for the binary mixtures of pyridine with mono-and polyalcohols.
A similar planar conformation of pyridine and benzene molecules, facilitated by π···H interactions between the partial positive charge of H -in the position para with N -of pyridine with π electrons of aromatic rings [2], favours the formation of tightly packed structures leading to negative V E m and κ E S values in the pyridine + benzene system. The negative temperature dependence of V E m observed for this system appears to support this conclusion.
The positive values observed for the G* E of the methanol + pyridine system suggests that N···HO and π···HO specific interactions are more important than the breaking of the selfassociations in methanol. Comparing the G* E results for the present methanol + pyridine mixture with results reported by Zeqiraj et al. [2] for the ethanol + pyridine system, it can be seen that the G* E becomes negative when methanol is replaced by ethanol. This observation suggests that the dissociation of ethanol should contribute more to the resulting G* E than the strong-specific interactions between component molecules in mixtures of pyridine with ethanol. The negative G* E values in the benzene-rich region of the methanol + benzene system are indicative of the dissociation of methanol structures. In contrast, the π···HO interactions and perhaps molecular size differences may account for positive values of G* E in the methanol-rich region. These findings agree with the conclusions of Fort and Moore [39] about the behaviour of binary systems in which at least one of the components exhibits association. Table 7 summarises the thermodynamic properties V E m , κ E S , and G* E of studied systems at equimolar composition (x = 0.5) as they compare to the data extracted from the currently published literature [2,[10][11][12][13][14][15][16][17][18][19]. A reasonable agreement is observed between the data of this work and the literature. To the best of our knowledge, κ E S data for methanol + pyridine and pyridine + benzene are not available in the literature for comparison in the temperature range studied here.

Conclusions
This paper reports a combined experimental study of density, sound speed, viscosity, and their related thermodynamic excess properties V E m , κ E S , and G* E , for methanol, pyridine, and benzene and their binary mixtures essential for various chemical and industrial processes. Redlich-Kister polynomial provided a statistically significant mathematical representation of V E m , κ E S , and G* E data with an optimal number of parameters and standard deviations better than the experimental uncertainties.
From the kind of behaviour observed in the studied mixtures, we get a clear idea of the types of interactions between the mixing components and of the effect of temperature on the interactions and, thus, on the resulting macroscopic properties. In the future, the authors of this work will also extend this study to include the ternary systems containing pyridine, benzene, and linear and branched alkanols.

Disclosure statement
No potential conflict of interest was reported by the authors.