Excess molar volumes and viscosities for the n-decane + 1-chlorodecane system at different temperatures

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1 Excess molar volumes and viscosities for the n-decane + 1-chlorodecane system at different temperatures MERCEDES E. F. DE RUIZ HOLGADO, CECILIA R. DE SCHAEFER, FRANCO DAVOLIO, AND MIGUEL KATZ' Ca'tedra de Fisicoquitnica, Instituto de Ingetlieria Quitnica, Faculrad de Cietzcias Esactas y Tecnologia, U.N. de Tucrrrna'n, Avda. Itldependencia 1800, S.M. de Tucurndn (4000). R. Argentina Received August 12, 1992 MERCEDES E. F. DE RUIZ HOLGADO, CECILIA R. DE SCHAEFER, FRANCO DAVOLIO, and MIGUEL KATZ. Can. J. Chem. 71, 790 (1993). Excess molar volumes, excess viscosities, and excess energies of activation for viscous flow have been determined for the n-decane + I-chlorodecane system at different temperatures, over the whole concentration range. The Prigogine- Flory-Patterson model for solution thermodynamics has been used to calculate the excess molar volumes. Grunberg and Nissan, McAllister, Teja and Rice, and Schrodt and Akel models have been used to calculate viscosity coefficients and these were compared with experimental data for the mixtures. MERCEDES E. F. DE RUIZ HOLGADO, CECILIA R. DE SCHAEFER, FRANCO DAVOLIO et MIGUEL KATZ. Can. J. Chem. 71, 790 (1993). OpCrant a diverses tempcratures et faisant varier la concentration sur I'ensemble des concentrations possibles, on a dcterminc les exccs de volumes molaires, de viscositcs et d'knergies d'activation de I'Ccoulement visqueux du systeme n-dtcane + I-chlorodCcane. On a utilisk la modele de Prigogine-Flory-Patterson de la thermodynamique des solutions pour calculer les exces de volume molaires. On a utilise les modkles de Grunberg et Nissan, de McAllister, de Teja et Rice et de Schrodt et Akel pour calculer les coefficients de viscositc et on a comparc ces valeurs aux donnces expcrimentales obtenues pour les melanges. [Traduit par la rcdaction] Introduction Excess molar volumes (ve) and excess viscosities of binary mixtures have been extensively studied from both theoretical and experimental points of view (1, 2). This work reports ve, and excess energies of activation for viscous flow (AG*~) for n-decane + 1-chlorodecane mixtures at , , , and K. An equation that reproduces the viscosity as a function of temperature and composition has been established for this system. Information could be obtained concerning the interaction between the mixed chemical species. The ve values were analyzed in terms of the Prigogine-Flory-Patterson model. The analysis shows the importance of the three contributions, AV,,,, AVp*, and AVF, to ve. Excess viscosities and energies of activation for viscous flow were used to calculate some thermodynamic parameters of activation. Some existing equations that calculate viscosities, viz., those of Grunberg and Nissan (3), McAllister (4), Teja and Rice (5), and Schrodt and Akel (6), have been compared, and this last equation showed the best agreement with experimental data. Experimental The methods used in our laboratory have been described previously (1, 2). Densities were determined with an AP digital densimeter, model DMA 45. A thermostatically controlled bath (constant to k0.01 K) was used. Calibration was carried out with air and doubly distilled water with an error of 20.1 kg m-'. All weighings were made on a Mettler H3 15 balance. Temperatures were read from calibrated thermometers. Viscosities of the pure components and of the mixtures were determined with a Schott-Gerate AVS 300 viscosimeter. The Ubbelohde viscosimeter tubes were calibrated and the temperature were maintained to k0.02 K with a Schott-Gerate CT 1450 temperature controller. The estimated error was mpa s. '~uthor to whom correspondence may be addressed n-decane Fluka (puriss.) and I-chlorodecane Schuchardt (puriss.) were distilled and only the middle fractions were collected. The binary mixtures were prepared by mixing weighed amounts of the pure liquids. Caution was taken to prevent evaporation. Results and discussion The experimental results for the pure components are reported in Table 1 together with literature values for comparison. The excess molar volumes were calculated with the following equation: [l] ve = x ~M~(~-' - + X~M,(~-' - p;') where x, and x, are the mole fractions of the components, MI and M2 are the molecular weights of the components 1 and 2, and p, p,, and p, are the densities of the solution and of the pure components. Excess viscosities were calculated from: where the additivity law in a logarithm form has been considered for the ideal mixture. The excess free energies of activation for viscous flow were obtained from the following equation: [3] AG*~ = RT(1n qv - x, In q,vl - x, In q,v,) where V, and V, are the molar volumes of the components and V is the molar volume of the solution: V = (xlm, + x2m2)ip. Tables 2 and 3 show the experimental values of densities and viscosities at four different temperatures. Each set of results was fitted with a Redlich-Kister equation of the type: [4] xe = x,(l - x,) C a,(l - 2x,)'-l n,= l

2 DE RUlZ HOLGADO ET AL TABLE 1. Densities and viscosities of the pure components K K K K Exp. Lit. Exp. Lit. Exp. Lit. Exp. Lit. Density, p X lo-) (kg m-)) " b Viscosity, -q (mpa s) ' " Density, p X (kg m-') ' Viscosity, -q (mpa s) "Reference 7. "Reference 8. 'Reference 9. TABLE 2. Experimental densities for the n-decane (1) + l-chlorodecane (2) system p x lo-) (kg m-)) X I K K K K where xe is ve or rle or AG*~; a, are the parameters obtained by a least-squares fitting procedure. In each case, the optimum number of coefficients are ascertained from an examination of the variation of the standard error u estimated with n (calculated with a VAX 11/780 computer): [51 u = [C (xfb,- ~~~,)'/(n,b, - n)ll'' The values adopted for the coefficients aj and the standard error estimates associated with the use of eq. [5] are summarized in Table 4. The viscosity of liquids varies with temperature according to the classical Andrade equation: where A and B are constants that depend on the nature of the liquids. The viscosity of liquid mixtures varies also with composition as: By using a multiple linear regression, an equation has been obtained which correlates T and x. For this system, the equation is TABLE 3. Experimental viscosities for the n-decane (1) + I-chlorodecane (2) system 3 (mpa s) with u = 0.02, where x, is the mole fraction of n-decane. The standard deviation of the logarithm of the viscosity coefficients has the form of eq. [5]. Figures 1, 2, and 3 show the experimental values of ve, rle, and AG*~, respectively. The continuous curves were calculated from eq. [4] using the adopted values for the coefficients. This system shows positive values of ve and negative values of rle. Several effects may contribute to the values of ve, such as breaking of liquid order on mixing, contribution due to the difference in size and shape of the components, difference in free volumes, and dipole-dipole interactions. The observed ve is a resultant contribution of the above effects. The positive values of ve indicate that the two former effects are dominant over the latter effects in this system (10, 1 l), implying that dispersion forces are dominant. The variation in the magnitude of ve with increasing temperature is found to be small. Generally, positive ve corresponds to negative rle, as in this case. The free energy AG*~ is considered a reliable means of detecting the interaction between molecules (12, 13). Positive values of AG*~ can be seen in binary systems where specific interactions between molecules take place. In this system, AG*~ is negative; thus we conclude again that dispersion forces are dominant. Molar excess volume can be calculated from the Prigogine-Flory-Patterson (PFP) theory (14). The original Prigogine-Flory theory includes three contributions in order

3 792 CAN. J. CHEM. VOL. 71, 1993 TABLE 4. Coefficients of eq. [4] and standard deviations determined by the method of least squares for the n-decane (1) + 1-chlorodecane (2) system fl x lo6 (m3 mol-i) rle (mpa s) AG*~ (J mol-i) "Reference 19. bfrom density measurements. 'Reference 20. TABLE 5. Equation of state parameters for the pure components at K 0.5 xi+ 1 FIG. 2. Excess viscosities for the n-decane (1) + 1-chlorodecane (2) system. Continuous curves were calculated from eq. [4]. FIG. 1. Excess molar volumes for the n-decane (1) + 1-chlorodecane (2) system. Continuous curves were calculated from eq. [41. to explain the thermodynamic behavior of the liquid mixtures: an interactional contribution (AV,,,), which is proportional to the interactional parameter X,,; the free volume contribution, which arises from the dependence of the re- duced volume upon the reduced temperature as a result of the difference between the degree of expansion of the two components (AV,); and the internal pressure contribution (AVp*), which depends on both the difference of characteristic pressures and on the reduced volumes of the components.

4 DE RUIZ HOLGADO ET AL. 793 Some new effects not treated in this theory have been discussed for molecules of different shape (15). The equation is = AVint - AVF + AVp, where is the reduced volume, V* is the characteristic volume, P* is the characteristic pressure, + is the contact energy fraction, C$ is the hard core volume fraction, and 8 is the surface site fraction. Heintz (16) introduced the so-called ERAS model, which combines the linear chain association model with Flory's equation of state theory. In this case, both components are not associated in the pure state and the chemical contribution is not taken into account. The various parameters involved in eq. [9] for the pure components (with subscript) and the mixture (without subscripts) are obtained from Flory's theory (17) and are shown in Table 5. The interactional contribution to ve contains the interaction parameter XI,, which is usually calculated using experimental values of the excess enthalpy HE. AS no values of HE are available for this system, XI, values were derived by fitting the theory to experimental values of ve for this system. The value of XI, obtained at K is x J rnp3 and, for equimolecular values, the three contributions are AVint = X AVF = 4.26 x lop4, and AVp* = 1.40 X with a calculated ve = x m3 mol-i. An analysis of each of the three contributions to ve shows that the interaction contribution is negative and small compared with the other two. The free volume contributions are positive and smaller than the internal pressure contribution. The total theoretical values are found to be in agreement with the experimental data, as shown in Fig. 4, with more error observed between x, 0.4 and 0.6. Different equations exist in the literature that can calculate viscosity coefficients for mixtures. Grunberg and Nissan (3) proposed an empirical equation to describe real mixtures: [lo] In -q = x, In -ql + X, In -q2 + xix28 where 8 reflects the nonideality of the system. The parameter 6 has usually been regarded as an approximate measure of the strength of the interaction between the components. However, it has been shown that in certain cases it can also be correlated with the difference in molecular volumes of the components and with the entropy of mixing (10). The values obtained for 6 at K for the system are summarized in Table 6 together with the percent error. The McAllister correlation (4) is based on a model proposed by Eyring et al. (18), which considers that interaction occurs between three bodies: [I 11 In v = x: In v, + xi In v, + xi In MI + xi In M2 - ln(x,m, + x2m,) + 3x7~~ In + 3x,xi In M, x:x2 In v,, + 3x,xi In v,, ( ) : 2 where v represents the kinematic viscosity (-q/p) and v,, and v,, are the interaction parameters obtained by a least-squares method. Table 6 gives these values with their percent error. We applied the comesponding states method of Teja and Rice (5) to calculate viscosities of the mixtures. These authors proposed the relation: where (r,) and (r,) refer to the properties of two reference fluids (in this case, the pure components) and w is the acentric factor. The values of < from eq. [12] were obtained from: [I31 < = V;/~/(T,M)"~ where Vc and T, are the critical volume and temperature, respectively. For mixtures, the pseudo-critical properties V,,, T,,, and w, of hypothetical substances that replace the pure fluids are defined (22). Values of (-q<)('" and (-q<)"" at the same reduced temperature have been calculated with + values, indicated in Table 6. Table 7 shows the parameters used for this application. Following the model of Schrodt and Akel (6), which is based upon Eyring's concept of fluid viscosity, the equation applying to mixtures (22), is where -q: = T~;V;/~N~, yr is the viscosity activity coefficient, and N, is Avogadro's number. Using a set of binary viscosity data, we found AG*~ values, and the viscosity activity coefficients were determined in this

5 CAN. 1. CHEM. VOL. 71, 1993 FIG. 3. Excess molar energies of activation for viscous flow for the rz-decane (I) + I-chlorodecane (2) system. Continuous curves were calculated from eq. [4]. FIG 4. Experimental and calculated excess molar volumes the n-decane (I) + I-chlorodecane (2) system at K. TABLE 7. Parameters for the pure components TABLE 6. Parameters of eqs. [lo], [l 11, [12], and [14] of the M V, X lo6 T, PC n-decane (1) + 1-chlorodecane (2) system at K Substance (g mol-i) (m') (K) (atm) w [lo] 6 = AD=0.21 n-decane " 617.6" 20.89" [I 11 v12 = 0.612; v,, = AD = Chloro- [I21 +=1 AD = 0.53 decane " " [I41 a = 0.30; 7,: = ; T,, = AD = 0.09 "Reference 2 1. case from equations like non-random two liquids' theory (NRTL) and related to AG:*~/RT. The parameters of the NRTL equations are also given in Table 6 together with the percent error defined as: Various thermodynamic properties of activation for viscous flow have been determined using Eyring's equation (ref. 18); for example: Over a short range of temperatures, the molar enthalpy of activation AH* and the molar entropy of activation AS:': are approximately constant. Using a least-squares method, the activation parameters hh"' and AS* were obtained and AG* was determined from the following equation: [17] AG* = &f* - TAS" The values obtained for AG2: vary between and J mol-'. They decrease with mole fraction of n-decane and increase with temperature. The values of &f:"t K vary from to J mol-i and ASs: varies from -49 to -55 J K-I mol-i. Only 1-chlorodecane is a polar molecule and qe is very small. This does not necessarily mean absence of interaction, but could imply that there is an interaction of the dipole-dipole induced type. Fort and Moore (1 1) and Nigam and Mahl (23) have reported that specific interactions are stronger in binary mixtures where qe and 6 are large and positive. In this system, both are negative and that means weak interactions. In regard to the values of AG*, the sign and magnitude are governed by the corresponding values of AH* and AS* according eq. [17]. A negative AS* indicates that the formation of an activated complex requires comparatively increased molecular order for an increase in its viscous flow. From the different equations that calculate viscosities of mixtures, the Schrodt and Akel model shows the best agreement with experimental data, since it presents the smallest deviation when compared with the other relations. for

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