Research Article  Open Access
Arvind R. Mahajan, Sunil R. Mirgane, "Excess Molar Volumes and Viscosities for the Binary Mixtures of nOctane, nDecane, nDodecane, and nTetradecane with Octan2ol at 298.15 K", Journal of Thermodynamics, vol. 2013, Article ID 571918, 11 pages, 2013. https://doi.org/10.1155/2013/571918
Excess Molar Volumes and Viscosities for the Binary Mixtures of nOctane, nDecane, nDodecane, and nTetradecane with Octan2ol at 298.15 K
Abstract
Experimental values of densities (ρ) and viscosities (η) in the binary mixtures of noctane, ndecane, ndodecane, and ntetradecane with octan2ol are presented over the whole range of mixture composition at K. From these data, excess molar volume (), deviations in viscosity , and excess Gibbs free energy of activation have been calculated. These results were fitted to RedlichKister polynomial equations to estimate the binary coefficients and standard errors. JouybanAcree model is used to correlate the experimental values of density and viscosity at K. The values of have been analyzed using PrigogineFloryPatterson (PFP) theory. The results of the viscosity composition are discussed in the light of various viscosity equations suggested by GrunbergNissan, Tamara and Kurata, Hind et al., Katti and Chaudhri, Heric, Heric and Brewer, and McAllister multibody model. The values of have also been analyzed using Bloomfield and Dewan model. The experiments on the constituted binaries are analyzed to discuss the nature and strength of intermolecular interactions in these mixtures.
1. Introduction
Density and viscosity data for liquid mixtures are important from practical and theoretical points of view. Experimental measurements of these properties for binary mixtures have gained much importance in many chemical industries and engineering disciplines [1]. Experimental liquid viscosities of pure hydrocarbons and their mixtures are needed for the design of chemical processes where heat and mass transfer and fluid mechanics are important. Prediction of the liquid behavior of hydrocarbon mixture viscosities is not yet possible within the experimental uncertainty. Therefore, experimental measurements are needed to understand the fundamental behavior of this property and then to develop new models [2]. Alkanes are important series of homologous, nonpolar, and organic solvents. They have often been used in the study of solute dynamics because their physicochemical properties as a function of chain length are wellknown [3]. They are also employed in a large range of chemical processes [4]. The physicochemical properties play an important role in the understanding of several industrial processes. Properties such as viscosity or surface tension are required in many empirical equations for different operations such as mass and heat transfer processes. For example, it is necessary to know the mass transfer coefficient to design gasliquid contactors. To determine the equations that modelize the mass transfer process requires knowledge of the density, viscosity, and surface tension of the liquid phase [5].
Viscosities and excess molar volumes of binary mixtures of methylbenzene [6] and methylcyclohexane [7] with octan2ol at K are only reported. To the best of our knowledge, the properties of the binary mixtures of octane, decane, dodecane, and tetradecane with octan2ol have not been reported earlier.
In the present paper, we report density and viscosity data for the binary mixtures of noctane, decane, dodecane, and tetradecane with octan2ol K. This work will also provide a test of various semiempirical equations to correlate viscosity of binary mixtures. The types of used relations are Tamara and Kurata, Heric, Heric and Brewer, Hind et al., Katti and Chaudhri, and McAllister multibody model.
2. Experimental
Chemicals used in the present study were of analytical grade and supplied by S.D. Fine Chemicals Pvt Ltd. Mumbai with quoted mass fraction purities: noctane (>0.99), decane (99.6), dodecane (99.8), and tetradecane (99.7). Octan2ol (purity 99.3) was supplied by EMerck. Prior to use, all liquids were stored over 0.4 nm molecular sieves to reduce the water content and were degassed. The binary mixtures of varying composition were prepared by mass in special airtight bottles. The masses were recorded on a Mettler balance to an accuracy of g. Care was taken to avoid evaporation and contamination during mixing. The estimated uncertainty in mole fraction was .
The densities of the solutions were measured using a single capillary pycnometer made up of borosil glass with a bulb of 8 cm^{3}, and capillary with internal diameter of 0.1 cm was chosen for the present work. The detailed pertaining to calibration, experimental set up, and operational procedure has been previously described [6–10]. An average of triplicate measurement was taken in to account. The reproducibility of density measurement was g/cm^{3}.
The dynamic viscosities were measured using an Ubbelohde suspended level viscometer [6–10] calibrated with conductivity water. 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 reproducible to 0.05 s were obtained, and the results were averaged. Since all flow times were greater than 300 s and capillary radius (0.1 mm) was far less than its length (50 to 60) mm, the kinetic energy and end corrections, respectively, were found to be negligible. The uncertainties in dynamic viscosities are of the order of 0.003 mPa·s.
The purity of the samples and accuracy of data were checked by comparing the measured densities and viscosities of the pure compounds with the literature values, which are given in Table 1. Thus, our results are in good agreement with those listed in the literature.
 
[39], ^{b}[37], ^{c}[48], ^{d}[42], ^{e}[41], ^{f}[38], ^{g}[38], ^{h}[6]. 
3. Results and Discussion
Experimental values of densities and viscosities of mixtures at 298.15 K are listed as a function of mole fraction in Table 2. The density values have been used to calculate excess molar volumes using the following equation: where is the densities of the mixture and , , , and , , are the mole fractions, the molecular weights, and the densities of pure components 1 and 2, respectively.

The variation in excess molar volumes, with mole fraction of the binary mixtures of octane, decane, dodecane, and ntetradecane with octan2ol at = 298.15 K, is displayed in Figure 1. The curve for the mixture of octane and octan2ol is sigmoidal and tends to change to positive values at higher mole fractions of octane while values for decane, dodecane, and tetradecane with octan2ol mixtures show positive deviation over the entire composition range.
Generally, can be considered as arising from three types of interactions between component molecules of liquid mixtures [11–13]: physical interactions consisting of mainly of dispersion forces or weak dipoledipole interaction making a +ve contribution, hereby the contraction volume and compressibility of the mixtures, chemical or specific interactions, which include charge transfer, forming of Hbonds and other complex forming interactions, resulting in a −ve contribution, and structural contribution due to differences in size and shape of the component molecules of the mixtures, due to fitting of component molecules into each other’s structure, hereby reducing the volume and compressibility of the mixtures, resulting in a −ve contribution.
The large positive values (Figure 1) for decane, dodecane, and ntetradecane with octan2ol mixture are attributed to the breaking up of threedimensional Hbonded network of octan2ol due to the addition of solute, which is not compensated by the weak interactions between unlike molecules. The exhibits an inversion in sign in the mixtures (octane + 2octanol). The values of are negative in the lower region of due to interstitial accommodation is more as compared to the declustering of 1octanol molecules and beyond as the amount of octane increases in the mixture, due to dispersion forces, thereby making a positive contribution to .
The viscosity deviations were calculated using where is the viscosities of the mixture and , and , are the mole fraction and the viscosities of pure components 1 and 2, respectively.
Figure 2 depicts the variation of with mole fraction of the binary mixtures of noctane, decane, dodecane, and tetradecane with octan2ol at = 298.15 K.
The deviations viscosity may be generally explained by considering the following factors [14]. The difference in size and shape of the component molecules and the loss of dipolar association to a decrease in viscosity; specific interactions between unlike molecules such as Hbond formation and charge transfer complexes may cause increase in viscosity in mixtures rather than in pure component. The former effect produces negative in excess viscosity, and latter effect produces positive in excess viscosity. Positive values of are indicative of strong interactions whereas negative values indicate weaker interactions [15].
The negative deviations in viscosity support the main factor of breaking of the selfassociated alcohols and weak interactions between unlike molecules. The negative values viscosity deviation decreases in the following sequence: octane decane dodecane tetradecane.
Excess Gibbs free energies of activation of viscous flow for binary mixtures can be calculated as where is the molar volume of the mixture, is the molar volume of the pure component, is the gas constant, is the absolute temperature, and is the dynamic viscosity of the mixture, respectively. is the dynamic viscosity of the pure component and the mole fraction in component. The values of all binary systems are shown in Table 2. The values of for all binary mixtures are negative over entire mole fraction. According to Meyer et al. [16], negative values of correspond to the existence of solutesolute association.
The excess molar volumes and deviations in viscosity were fitted to Redlich and Kister [17] equation of the type where is either or and is the degree of polynomial. Coefficient was obtained by fitting (5) to experimental results using a leastsquares regression method. In each case, the optimum number of coefficients is ascertained from an examination of the variation in standard deviation .
was calculated using the relation where is the number of data points and is the number of coefficients. The calculated values of the coefficients along with the standard deviations are given in Table 3.

4. Theoretical Analysis
4.1. Semiempirical Models for Analyzing Viscosity of Liquid Mixtures
Several empirical and semiempirical relations have been used to represent the dependence of viscosity on concentration of components in binary liquid mixtures, and these are classified according to the number of adjustable parameters used to account for the deviation from some average [18, 19]. We will consider here some of the most commonly used semiempirical models for analyzing viscosity of liquid mixtures based on one, two, and three parameters. An attempt has been made to check the suitability of equations for experimental data fits by taking into account the number of empirical adjustment coefficients.
The equation of GrunbergNissan, Tamara and Kurata Hind et al., and Katti and Chaudhri has one adjustable parameter.
GruenbergNissan provided the following empirical equation containing one adjustable parameter [20]. The equation is where may be regarded as a parameter proportional to the interchange energy also an approximate measure of the strength of the interaction between the components.
The oneparameter equation due to Tamura and Kurata [21] gave the equation of the form where and are the volume fractions of components 1 and 2, respectively; is Tamura and Kurata constant.
Hind et al. [22] proposed the following equation: where is attributed to unlike pair interactions.
Katti and Chaudhri [23] derived the following equation where is an interaction term and is the molar volume of pure component .
Heric [24] expression is where is a term representing departure from a noninteracting system and is the interaction parameter. Either or can be expressed as a linear function of composition:
From an initial guess of the values of coefficients and , the values of are computed.
Heric and Brewer [25] equation is and are molecular weights of components 1 and 2, and and are interaction parameters, and other terms involved have their usual meaning. and are parameters, which can be calculated from the leastsquares method.
McAllister’s multibody interaction model [26] was widely used to correlate kinematic viscosity data. The twoparameter McAllister equation based on Eyring’s [27] theory of absolute reaction rates has taken into account interaction of both like and unlike molecules by twodimensional threebody model. The threebody interaction model is And fourbody model was given by where , , , , and are interaction parameters and and are the molecular mass and kinematic viscosity of pure component , respectively.
The correlating ability of each of (6)–(14) was tested as well as their adjustable parameters and standard deviations : where represents the number of data points and is the number of numerical coefficients given in Table 4. The interaction parameter is negative for binary systems. Nigam and Mahl [28] concluded from the study of binary mixtures that if , and magnitude of both are large then strong specific interaction would be present; if , then weak specific interaction would be present; if , magnitude of both are large then the dispersion force would be dominant. According to Fort and Moore [29] and Ramamoorty and Varadachari [30], system exhibits strong interaction if the is positive; if it is negative they show weak interaction. On this basis, we can say that there is a weak interaction in the system studied.

Interaction parameter shows almost the same trend as that of . In fact, one could say that the parameters and exhibit almost similar behaviour, which is not unlikely in view of logarithmic nature of both equations.
Tamara and Kurata and Hind et al. represent the binary mixture satisfactory as compared to GruenbergNissan and Katti and Chaudhri. Use of three parameters equation reduces the values significantly below that of two parameters equation. From this study, it can be concluded that the correlating ability significantly improves for these nonideal systems as number of adjustable parameters is increased. From Table 4, it is clear that McAllister’s threebody interaction model is suitable for correlating the kinematic viscosities of the binary mixtures studied.
4.2. PrigogineFloryPatterson (PFP) Theory
The PrigogineFloryPatterson (PFP) theory [31–34] has been commonly employed to estimate and analyze excess thermodynamic functions theoretically. This theory has been described in details by Patterson and coworkers [35, 36]. According to PFP theory, can be separated into three factors: an interactional contribution, (int.) a free volume contribution, , and an internal pressure contribution, . The expression for these three contributions are given as : Thus, the excess molar volume is given as where , , and represent the contact energy fraction, surface site fraction, and characteristic pressure, respectively, and are calculated as
The details of the notations and terms used in (16)–(19) may be obtained from the literature [31–34, 37, 38]. The other parameters pertaining to pure liquids and the mixtures are obtained from the Flory theory [7, 31, 38] while α and values are taken from the literature [39–44]. The interaction parameter required for the calculation of using PFP theory has been derived by fitting the expression to the experimental equimolar value of for each system under study.
The values of , , three PFP contributions interactional, free volume, effect, and experimental and calculated (using PFP theory) values at near equimolar composition are presented in Table 5. Study of the data presented in Table 6 reveals that the interactional and free volume contributions are positive, whereas contributions are negative for all the three systems under investigation. For these binary mixtures, it is only the interactional contribution which dominates over the remaining two contributions. The contribution, which depends both on the differences of internal pressures and differences of reduced volumes of the components, has little significance for the studied binary mixtures as compared to the other two.


Furthermore, in order to check whether , derived from nearly equimolar values, can predict the correct composition dependence, has been calculated theoretically using over the entire composition range. The theoretically calculated values are plotted in Figure 1 for comparison with the experimental results. Figure 1 show that the PFP theory is quite successful in predicting the trend of the dependence of on composition for the present systems.
In order to perform a numerical comparison of the estimation capability of the PFP theory, we calculated the standard percentage deviations using the relation where represents the number of experimental data points.
4.3. Bloomfield and Dewan Model
There are different expressions available in the literature to calculate . Here, Bloomfield and Dewan [45] model have been applied to compare calculated values using experimental data for each binary mixture by the following relation: Bloomfield and Dewan [45] developed the expression from the combination of the theories of free volumes and absolute reaction rate where is the characteristic function of the free volume defined by and is the residual energy of mixing, calculated with the following expression [46]: where and are segment fractions defined by where and are in the ratio of respective molar core volumes and .
The excess energy can be obtained from the statistical theory of liquid mixtures proposed by Flory and coworkers [31, 32] and is given by where the various symbols used have their usual meanings.
Using the values from fitting values of and the values of the parameters for the pure liquid components, we have calculated and and finally , according to the Bloomfield and Dewan relationship, which is compared with the experimental data. Figure 3 shows that the good agreement between the estimated and experimental curves occurs for given binary systems.
4.4. Jouyban and Acree Model
Hasan et al. [6, 47, 48] has used this model for various binary system proposed a model for correlating the density and viscosity of liquid mixtures at various temperatures. The proposed equation is where , , and is density or viscosity of the mixture and solvents 1 and 2 at temperature , respectively, and are the volume fractions of solvents in case of density and mole fraction in case of viscosity, and are the model constants.
The correlating ability of the JouybanAcree model was tested by calculating the average percentage deviation (APD) between the experimental and calculated density and viscosity as where is the number of data points in each set. The optimum numbers of constants , in each case, were determined from the examination of the average percentage deviation value.
The constants calculated from the least square analysis are presented in Table 7 along with the average percentage deviation (APD). The proposed model provides reasonably accurate calculations for the density, viscosity, and ultrasonic velocity of binary liquid mixtures at 298.15 K, and the model could be used in data modeling.

5. Conclusions
The present paper is a continuing effort towards the understanding of the mixing behavior of binary liquid mixtures comprising of alkanes + octan2ol. Excess molar volumes and deviations in viscosity were calculated and fitted to the RedlichKister equation to test the quality of the experimental values. The negative deviations in viscosity support the main factor of breaking of the selfassociated alcohols and weak interactions between unlike molecules. Several empirical and semiempirical relations have been used to represent the dependence of viscosity on concentration of components in binary liquid mixtures. An attempt has been made to check the suitability of empirical and semiempirical relations for experimental viscosities data of alkanes + octan2ol fits by taking into account the number of empirical adjustment coefficients. Bloomfield and Dewan model and McAllister’s threebody interaction model are suitable for the above binary system. PFP theory is also quite successful in predicting the trend of the dependence of on composition for the present systems.
Acknowledgments
Authors are thankful to Prof B. R. Arbad, Dr. B. A. M. university for their valuable suggestions and discussion. Authors are also thankful to Principal Dr. R. S. Agarwal, J. E. S. College, Jalna for the facilities provided.
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Copyright © 2013 Arvind R. Mahajan and Sunil R. Mirgane. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.