Thermophysical Properties of Binary Liquid Systems of Ethanoic Acid , Propanoic Acid , and Butanoic Acid with Benzene or Acetophenone

The density (ρ), viscosity (η), and surface tension (σ) of binary mixtures of carboxylic acids (CAs) (ethanoic acid (EA), propanoic acid (PA), butanoic acid (BA)) + benzene (BEN) or acetophenone (ACT) have been measured at 298.15, 308.15, and 318.15 K. From the experimental results, excess values of molar volume (V), viscosity (η), Gibb’s free energy for the activation of low (G), and surface tension (σ) were evaluated and fitted to a Redlich-Kister type of equation. The parameter “d” of Grunberg and Nissan expression has also been calculated. From the sign and magnitude of V, η, G, σ, and “d” values, it is concluded that specific interactions are present in CA+ACT system and these interactions are absent in CA + BENmixtures. Various viscosity and surface tension models have been used to test the consistency of the data.


Introduction
Studies on thermophysical properties of binary liquid mixtures containing carboxylic acids are not extensive [1][2][3].In view of this, we have undertaken studies on binary mixtures of carboxylic acids (CAs), namely, ethanoic acid (EA), propanoic acid (PA), and butanoic acid (BA) which are self-associated solvents, with a nonpolar solvent benzene (BEN) and polar acetophenone (ACT).These acids exist as cyclic dimers in the pure state.However, trimers also exist which are formed because of strong interactions between ring dimers and monomers [4][5][6].
The excess properties   ,   ,   ,   , and Grunberg and Nissan parameter "" computed from the experimental data (density (), viscosity (), and surface tension) ()) of binary mixtures of carboxylic acids (EA, PA, BA) with benzene and acetophenone have been determined.Benzene interacts with acid through Vander Waal's or London dispersion forces and acetophenone forms chemical aggregates with acid through hydrogen bonding.The results are used to theoretically justify the validity of various viscosity and surface tension models.The main thrust of the investigation is to correlate the experimental data in terms of the interacting components of the mixtures and to stress the factors affecting these interactions.

Experimental Section
Ethanoic acid, propanoic acid, butanoic acid, benzene, and acetophenone were purified by the standard methods described in the literature [7].Ethanoic acid (BDH, 99% assay) was washed with a calculated amount of acetic anhydride for about 10 h and was subjected to fractional distillation.Propanoic acid and butanoic acid (E.Merck, 99% assay) were dried over anhydrous sodium sulfate for two days and the samples were distilled over potassium permanganate.Benzene (E.Merck, 98.4% assay) was dried by keeping over anhydrous calcium chloride for six to eight hours and then fractionally distilled.Acetophenone (Merck, 99% assay) was also dried by keeping it over anhydrous calcium chloride for two days and distilled at reduced pressure.The purity of all the components was checked by comparing their experimental densities with that of the literature values [7].For each run, a fresh liquid mixture was prepared on a mass basis (precision of 1 × 10 −5 g).The purity of each component with respect to the corresponding literature value is recorded in Table 1.Densities () of the pure components and their mixtures were measured with a density meter (AP, DMA-48) calibrated at each temperature with ethanol and 1,2-dichloroethane.The densities were measured with an accuracy of 1 × 10 −1 kg⋅m −3 .
Viscosities () were determined using a modified Ubbelohde viscometer [8].At each temperature, the viscometer was calibrated against the known viscosities of benzene and carbon tetrachloride [9].The viscometer constants at each temperature were determined from the following where  and  are the temperature-dependent constants.At a particular temperature, an average value of the five consistently measured efflux times  and the densities were used to calculate viscosity.The accuracy of the viscosity measurements is in the order of ±0.0013 mPa⋅s.Surface tension () of the pure components and their mixtures was determined by the differential capillary rise method [7], using (2).The difference Δℎ in the liquid levels in two capillaries was measured with a cathetometer reading to 0.05 mm with a vernier constant of 0.01 mm.The surface tension values are accurate to within ±0.02 mN⋅m −1 .Consider where , ℎ 1 and ℎ 2 are the heights of liquids in capillaries 1 and 2,  1 and  2 are the radii of the capillaries, and  is the acceleration due to gravity (=9.80 m s −2 ), respectively.The constants , , and  of (2) were determined by measuring the Δℎ for two test liquids (benzene, ethyl ethanoate) of known  and  at 298.15 K.The constant  was separately determined by noting the height of the test liquid in one of the capillaries.The corresponding radius  2 of the capillary was determined from the measured weight of the mercury column of known length.The constants (, , and ) were assumed to be temperature independent.For each mixture of the respective systems and pure components, Δℎ was recorded at three different temperatures over the entire composition range.
All the measurements were made at a constant temperature that was maintained with the help of a circulating type ultra cryostat (type MK 70, MLW, Germany) within ±0.02 ∘ C.

Results
Experimental densities of pure components and their literature values at 298.15 K are given in Table 1.Experimental values of , , and  were fitted to (3) using nonlinear regression technique [10].The computed coefficients of (3) and standard errors are listed in Table 3.
Equation (3) fits the experimental data within the average uncertainty in the temperature range of 298.15 K-318.15K and Based on the regular solution theory [11], Grunberg and Nissan proposed an empirical expression for viscosities of real mixtures: where  1 and  2 refer to the dynamic viscosities of the pure liquid components 1 and 2, respectively,  1 and  2 are the mole fractions of components 1 and 2, respectively, in the mixture, and "" is a parameter which denotes the measure of strength of interaction between the two components.The values of "" are reported in Table 2.
From the experimental data, excess molar properties, namely;   ,   ,   , and   were calculated [12] from the following expressions: (mN where  1 and  1 are the molecular weight and density of the carboxylic acids.The same symbols with subscript 2 refer to BEN or ACT, respectively. 1 ,  2 , and  mix are the molar volumes and  1 ,  2 , and  mix are the surface tension of the 1st, and 2nd components and mixture, respectively.Graphical representations of   ,   ,   , and   as a function of the mole fraction ( 1 ) of CA are given in Figures 1-8, respectively.Each of these functions,  =   ,   ,   and   , has been fitted to the Redlich-Kister relation [13]: where   ,  1 , and  2 are adjustable parameters and have been evaluated by the method of least squares.The value of Temp.Temp.these parameters along with standard deviation is reported in Table 4.
where  is the total number of experimental points.Stevanovic et al. [14] have recently compared the available correlation models for liquid mixture viscosities of organic compounds.Amongst the available correlations for predicting the binary liquid mixture viscosity, the present experimental binary viscosity data was fitted to the following five correlations.
McAllister's [15] model: where  12 and  21 are interaction parameters.Heric [16] model: where  12 is a deviation function given by Here,  12 and  21 are interaction parameters.Auslander [17] model: where  12 ,  21 , and  21 are parameters representing binary interactions.Teja and Rice [18] model: where   =  2/3  /(    ) 1/2 for  = 1 or 2 component or the mixture 1 must be evaluated at a temperature ( 1 / mix ) and  2 at a temperature ( 2 / mix ). is the system temperature and  12 is an adjustable interaction parameter having a value unity.The interaction parameter has been shown to be  independent of temperature and composition [19,20].The subscript  indicates a reduced quantity.Kubendran et al. model [21]: where  12 ,  12 , and  12 are binary interaction constants.The observed data on surface tension of binary mixtures was fitted to the following models available in the literature.
Zihao and Jufu model [22]: where  12 and  21 are interaction parameters.Rice and Teja model [23]: where Φ  =  2/3  /  for  = 1 or 2 component or the mixture Here,  1 is to be evaluated at a temperature =  ( 1 / mix ) and  2 at a temperature = ( 2 / mix ). is the system temperature and  12 is an adjustable interaction parameter having a value around unity.The interaction parameter has been shown to be independent of temperature and composition [19,20].The subscript  indicates a reduced quantity.9)     Empirical two-constant model [24]: where   and   are binary interaction parameters.The model parameters of (11), and ( 13)-( 21) were determined using nonlinear regression technique and the estimated values are reported in Table 5.

Discussion
The values of   as illustrated in Figures 1 and 2 are positive for the entire concentration range at all the three temperatures for the systems EA + BEN, PA + BEN, and BA + BEN and negative for the remaining three systems.About 5% more negative or less positive   values at higher temperatures for all the systems may be due to increased population of acid monomers to enter into the heterointermolecular interactions.
The positive and negative   values may be explained by considering the following three steps equilibria accompanying the mixing process as proposed by Lark and Banipal [2]: ⇐⇒ 2, where  and  denote a dimer and a monomer of the acid under question.The first process is accompanied with a large volume increase in the right direction; the second is isochoric; that is, the volume of the dimer is assumed to be equal to twice the value of the monomer [4,5]; the third step is accompanied with large contraction in case of ACT and expansion in case of BEN.So the addition of ACT or BEN to anyone of the acids first creates monomers by the first two steps resulting in expansion.In the third step, stronger heteromolecular dipoledipole interactions result in the observed negative   in case of CA + ACT and positive   values in the case of CA + BEN system due to induced dipole-dipole interactions.Therefore, the third step is accompanied with contraction in volume in case of ACT and expansion in case of BEN.
The pK  values of EA, PA, and BA are 4.76, 4.88, and 4.82, respectively.It is expected that the order of dimerization constants of various acids would increase in the same order.The increasing dimerization constant would lead to a smaller number of available monomers and thus to a smaller volume increase as described by (22).However, the observed order of   for the CA + BEN system is as follows: BA > PA > EA (Table 6).This shows that in case of BEN there are strong acid-solvent interactions which govern the magnitude and sign of   , which increases as the inductive effect of alkyl chain of the acid as is also observed by Lark et al. [25].Similar results were also obtained by Venkateswarlu and Raman [26] as the positive excess volumes of 1,2-dichloroethane and 1,2-dibromoethane with three acids observe the following order: BA > PA > EA, which is the same as discussed above; that is, the increase in chain length of acid contributes to the decrease in excess volume.The large negative   values in the case of CA + ACT mixture arise due to depolymerization of acid accompanied with strong hydrogen-bonded heterocomplex formation.However, in CA + ACT system, the   values follow the order PA > BA > EA as was also observed by Lark et al. [25] in CA + MEOH system.
The data presented in Figures 3 and 4 reveal that excess viscosity (  ) is positive for the systems EA + ACT, PA + ACT, and BA + ACT, and is negative for the systems EA + BEN, PA + BEN, and BA + BEN at 298.15 K.The algebraic positive values of   may be represented in the following order: PA + ACT > EA + ACT > BA + ACT > BA + BEN > PA + BEN > EA + BEN.The sign and magnitude of   depend on the combined effect of the factors such as molecular size, shape, and intermolecular forces.The positive value of   for the CA + ACT system suggests that the viscosity of the mixture is higher than that of the pure components and hence the fluidity of the mixture is low.This indicates the presence of a specific interaction such as the formation of chargetransfer complex between unlike molecules.The negative value of   in the systems EA + BEN, PA + BEN, and BA + BEN suggests the mutual loss of a specific interaction in like molecules that outweigh the specific interaction between unlike molecules.The positive values of   increase with the increase in temperature in all these systems.The   values almost observe the similar trend as observed by   as shown in Figures 5 and 6.
The variation of Grunberg and Nissan parameter "" with composition of a particular mixture is not large.The values of "" are negative for CA + BEN system and positive for CA + ACT system for most of the concentration range.The positive values of "" for CA + ACT system show that CA forms an intermolecular complex with ACT in the liquid phase.The values of "" increase with the increase in temperature in all the systems showing that the interactions between the components increase with the increase in temperature.Even the negative values of "" for CA + BEN system change      According to Hildebrand [27], free volume is necessary for flow and then shrinkage on mixing (which would reduce the free volume) would be associated with increase in viscosity of the system.If  is defined as /  , where  is the experimental viscosity of the mixture and   is the ideal viscosity, calculated using then this quantity could be related to free volume (  ) of the solution according to Stairs [28] by the following equation: According to (26), a plot of  −1 versus   should be linear.However, when  −1 is plotted against   , a nonlinear plot was obtained in the present study.However, when ln  is plotted against   , a single straight line with a nonzero intercept was obtained in Figure 9.This type of result is not unexpected, because the expression for   takes into account both viscosity and volume.Also, in all these systems, positive   and negative   and vice versa have been observed for most of the concentration range.This behaviour was also observed by Palepu et al. [29] in binary mixtures ochlorophenol with substituted anilines.
From the literature, no clear cut theoretical basis has been proposed for the prediction of nonideal behaviour of the binary mixtures in terms of their   values.However, recently, Papaioannou and Panayiotou [30] have correlated the sign of   values with   values and the deviations from Raoult's law.Their observation reveals the following.
(1) Corresponding to the positive enthalpies of mixing (  ), positive volume of mixing (  ) and positive deviations from Raoult's law,   values, have been observed to be negative.
(2) Corresponding to the negative enthalpies of mixing (  ), negative volume of mixing (  ) and negative deviations from Raoult's law,   values have, been observed to be positive.As shown in Figures 7 and  8, the excess surface tension (  ) values are negative for CA + BEN system and are positive for CA + ACT system.The positive values of excess surface tension (  ) increase with the rise in temperature in all systems.The negative value of   in CA + BEN system is due to the predominance of the following factors: homopolymer complex formation and the tendency of the component with lower surface tension to be adsorbed at the interface.But in CA + ACT system complex formed are block copolymer [CA]  [ACT]  and also dipole-dipole interactions between carboxylic functional group of CA and carbonyl group of ACT in the bulk phase rather than in the interface.
The interaction parameters of various models used can change with temperature but not with composition, but the interaction parameter  12 in Rice and Teja and Teja and Rice models, based on the theory of corresponding states, has been shown to be independent of temperature and composition [19,20].It is observed that the models of McAllister, Auslander, and Teja and Rice fit the experimental viscosity data very well as compared to the Heric and Krishnan and Laddha models.Surface tension data is well predicted by the empirical two-parameter model [21] as well as by Rice and Teja model.The Zihao & Jufu model, based on the work of Hildebrand & Scott [31], also predicts satisfactory results for the systems studied.

Table 2 :
Mole fraction of first component  1 , density, viscosity, and surface tension for various systems.

Table 4 :
Coefficients of (9) and standard deviation (SD) determined by the method of least squares.

Table 5 :
Interaction parameter/parameters for various models and standard deviation (SD) determined by least square method.

Table 6 :
Comparison of excess volume   cm 3 mol −1 of equimolar mixture at 298.15 K.