Estimation of excess molar volumes and theoretical viscosities of binary mixtures of benzene + n-alkanes at 298.15 K

Int J Ind Chem (2016) 7:391–400 DOI 10.1007/s40090-016-0100-1 RESEARCH Estimation of excess molar volumes and theoretical viscosities of binary mixtures of benzene + n-alkanes at 298.15 K Omer El-Amin Ahmed Adam1,3 • Akl M. Awwad2 Received: 27 July 2015 / Accepted: 21 September 2016 / Published online: 30 September 2016 Ó The Author(s) 2016. This article is published with open access at Springerlink.com Abstract Excess molar volumes, (VmE ), have been derived from the literature viscosity data for the binary mixtures of benzene with n-hexane, n-octane, n-decane, n-dodecane, ntetradecane, and n-hexadecane as a function of composition at 298.15 K and atmospheric pressure conditions. The VmE values were found to be positive over the entire composition range for all mixtures. Concentration dependence of VmE were fitted with Redlich–Kister polynomial equation to estimate the binary coefficients and standard errors. From density data, the partial molar volumes (Vm), partial molar volumes at infinite dilution 0 0; E (V m ), excess partial molar volumes at infinite dilution (V m ), and apparent molar volumes (V/), were calculated over the whole composition range as were the limiting apparent molar 0 volumes at infinite dilution (V / ) and excess apparent molar 0; E volumes at infinite dilution (V / ). Viscosity of the binary mixtures of benzene with n-alkanes were estimated using Kendall-Monroe, Frenkel, Hind et al., Katti-Chaudhri, Grunberg-Nissan, Wilke and Herráez et al. equations. The agreement between experimental and predicted values for all systems was found to be quite reasonable as evidenced from Electronic supplementary material The online version of this article (doi:10.1007/s40090-016-0100-1) contains supplementary material, which is available to authorized users. & Omer El-Amin Ahmed Adam 1 Chemistry Department, University of Kassala, P.O. Box 266, Kassala 31111, Sudan 2 Royal Scientific Society, P.O. Box 1438, Al-Jubaiha, Amman 11941, Jordan 3 Present Address: Chemistry Department, Faculty of Science and Arts in Baljurashi, Al baha University, P.O. Box 1988, Baljurashi 65635, Saudi Arabia computed standard deviation and average percentage deviation (APD). Wilke relation gives maximum deviations for all the systems in comparison to other methods employed. Other relations give comparatively good results. Keywords Density  Viscosity  Binary mixture  Excess molar volume  Molecular interactions  Viscosity deviation Introduction Excess thermodynamic properties and deviations of nonthermodynamic ones from ideal behavior of binary liquid mixtures are fundamental for the design of industrial equipment and for the interpretation of the liquid state, particularly when polar components are involved [1]. These quantities have the advantage of illustrating the sign and magnitude of the nonideality [2]. Volumetric properties of binary mixtures are complex properties because they depend not only on solute–solute, solvent–solvent and solute–solvent interactions, but also on the structural effects arising from interstitial accommodation due to the difference in molar volume and free volume between components present in the solution [3]. Partial molar properties are useful in providing information about solute–solvent interactions. This is because at infinite dilution, solute–solute interactions disappear. Of course this information is of great interest because it is composition independent. 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 well-known [4]. They are also employed in a large range of chemical processes [5]. 123 392 Int J Ind Chem (2016) 7:391–400 Properties such as viscosity or surface tension are required in many empirical equations for different operations such as mass and heat transfer processes. Determination of equations that modelize the mass transfer process requires knowledge of the density, viscosity, and surface tension of the liquid phase [6]. The measurement of viscosity reveals information about the molecular packing, molecular motion, and various types of intermolecular interactions as related to size, shape, and chemical nature of the component molecules [7]. In recent years, there has been considerable interest in theoretical and experimental investigations of the excess thermodynamic properties of binary mixtures [8, 9]. Generally, VmE can be considered as a result of three types of interactions between component molecules of liquid mixtures [10, 11]. (1) Physical interactions consisting mainly of dispersion forces or weak dipole–dipole interaction making a positive contribution, (2) chemical or specific interactions, which include charge transfer, H-bonding and other complex formation interactions, resulting in a negative contribution, and (3) 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 negative contribution. In a previous work by Akl et al. [12], results of density and viscosity measurement were determined for binary mixtures of benzene ? n-alkanes at 298.15 K and atmospheric pressure. Excess molar volumes (VmE , excess molar viscosities (D lng), and excess molar activation energies, (DG*E) were calculated. The effect of orientational order of n-alkane on solution molar volumes and viscosities is investigated as well as the adequacy of the absolute rate and free volume theories to predict solution viscosities. For longer n-alkane DG*E and D lng are positive and associated with the orientational order. In the present work, the data of density and viscosity reported in the literature [12] have been used to evaluate the excess molar volume (VmE ) along with other derived parameters, such as partial molar volumes at infinite dilu0 0 Theoretical analysis Excess molar volume Excess molar volumes (VmE ), were calculated for the binary mixtures of benzene with n-hexane, n-octane, n-decane, ndodecane, n-tetradecane, and n-hexadecane using viscosity data by a correlation proposed by Singh [13]. According to the relation, the deviations in viscosity, Dg, and excess molar volumes, VmE , are related to each other as: Dg ¼ K  VmE where, K is a fitting parameter. The values of K for the investigated mixtures were evaluated using the experimentally reported Dg and VmE data [12] (Table 1). From the experimental Dg data, VmE values at the whole mole fraction range were calculated at 298.15 K and results were presented in Table 2. Figures 1, 2, 3 show that VmE values calculated from viscosity data are positive over the entire composition range for all investigated mixtures and follow the sequence: n-hexane \ noctane \ n-decane \ n-dodecane \ n-tetradecane \ n-hexadecane. VmE v (...truncated)