153 Acta Chim. Slov. 1998, 45(2), pp. 153-160 (Received 25.5.1998) EXCESS MOLAR VOLUMES OF BINARY LIQUID MIXTURES OF CYCLOHEXANE - CARBON TETRACHLORIDE AND TOLUENE - BENZENE AT VARIOUS TEMPERATURES A.Petek, V.Doleček Faculty of Chemistry and Chemical Engineering, University of Maribor, Smetanova 17, 2000 Maribor, Slovenia Abstract: Excess molar volumes of binary mixtures of cyclohexane - carbon tetrachloride at 288.15, 293.15, 298.15 K and of toluene - benzene at 293.15, 298.15, 308.15 K have been determined using a vibrating tube densimeter. Flory's theory of liquid mixture has been applied to calculate the excess enthalpy of cyclohexane -carbon tetrachloride at 298,15 K; the calculated value for the equimolar mixture is in fairly good agreement with experimental results. INTRODUCTION Excess molar volumes of binary mixtures of cyclohexane - carbon tetrachloride and toluene - benzene are presented in this paper. The toluene - benzene system which forms nearly ideal solutions has been used as reference system. The aim of our work was to calculate the excess enthalpy from measured excess volumes, using the statistical Flory's theory of liquid mixtures [ 1 ]. Flory has developed an approach which relates the excess properties of a mixture to measurable macroscopic properties of pure liquid components by a partition function. This theory has been very useful in predicting the thermodynamic properties of binary mixtures of nonpolar 154 molecules such as hydrocarbons (normal, branched, cyclic and aromatic) and halocarbons [2,3]. In this work we use this approach to the mixture of cyclohexane - carbon tetrachloride with a moderate polarity. EXPERIMENTAL Cyclohexane (Kemika, Zagreb), carbon tetrachloride (Carlo Erba), toluene (Kemika) and benzene (Riedel - de Haen), with p.a. stated purity, were used without further purification. The investigation of sources of errors in \^ by Lepory et al. [4] showed namely, that purity of substances was not a crucial factor in \^measurements. Densities were measured, using a vibrating tube densimeter A.Paar DMA 60/602, at 288.15, 293.15, 298.15 and 308.15 K. Temperature control of the cell was ± 5-10-3 0C. Before each series of measurements, the instrument was calibrated with doubly distilled water and dry air at atmospheric pressure. The density d, of any liquid relative to the density of pure water dw , is given by d = dw + k (f-fw ) (1) where k is the characteristic of a particular oscillator. J2 and J^w are vibration periods of the tube, filled with liquid and with water, respectively. The determined densities [5,6] are accurate to at least ± 10-5 g cm-3 . For pure cyclohexane, benzene, toluene and carbon tetrachloride they agreed well with literature values [7-10,12-14]. The mixtures were prepared by weight. The values of \^ determined from density measurements are accurate within ±0.0005 cm3 mol-1. RESULTS AND DISCUSION Excess molar volumes \^ of binary mixtures of cyclohexane (1)- carbon tetrachloride (2) and toluene (1) - benzene (2) were calculated from the corresponding density measurements using the equation \^ (cm3 mot1) = XiMi (dm' - di') + XiMi (dm' - d2~') (2) where xt is the molar fraction of component i, and dm and df are the densities of the mixture and pure component i, respectively. M are the molar masses of the pure components. The obtained results are listed in Table 1 and Table 2. 155 Table 1: Densities and excess molar volumes Ve of binary mixtures of toluene(1) - benzene(2) at 293.15, 298.15 and 308.15 K 293.15 K 298.15 K 308.15 K X 2 d Ve (g cm-3 ) (cm3 mol-1 ) X2 d Ve (g cm-3 ) (cm3 mol-1 ) X2 d Ve (g cm-3 ) ( cm3 mol-1 ) 0.00000 0.86685 0.0000 0.00000 0.86223 0.0000 0.00000 0.85299 0.0000 0.10676 0.86771 0.0280 0.09093 0.86291 0.0238 0.07520 0.85346 0.0209 0.16292 0.86818 0.0421 0.16471 0.86349 0.0415 0.24456 0.85459 0.0645 0.23090 0.86876 0.0593 0.23253 0.86403 0.0585 0.26568 0.85461 0.0851 0.29499 0.86937 0.0696 0.24830 0.86416 0.0621 0.28276 0.85486 0.0736 0.34447 0.86987 0.0752 0.29065 0.86456 0.0662 0.31242 0.85507 0.0809 0.38214 0.87027 0.0779 0.33250 0.86494 0.0728 0.37459 0.85559 0.0875 0.40612 0.87050 0.0828 0.37787 0.86536 0.0797 0.40639 0.85587 0.0898 0.45288 0.87099 0.0882 0.41849 0.86578 0.0814 0.47647 0.85652 0.0922 0.48365 0.87135 0.0880 0.48448 0.86647 0.0849 0.59077 0.85766 0.0910 0.51775 0.87175 0.0882 0.52499 0.86691 0.0861 0.59490 0.85770 0.0912 0.54412 0.87202 0.0931 0.57627 0.86751 0.0837 0.68986 0.85876 0.0817 0.58951 0.87264 0.0851 0.59444 0.86772 0.0835 0.73848 0.85933 0.0755 0.65377 0.87346 0.0820 0.63416 0.86821 0.0801 0.75586 0.85955 0.0717 0.75732 0.87492 0.0667 0.69181 0.86894 0.0746 0.80325 0.86016 0.0612 0.81199 0.87572 0.0580 0.73162 0.86947 0.0689 0.85483 0.86082 0.0515 0.86405 0.87641 0.0588 0.79248 0.87032 0.0577 0.90854 0.86159 0.0341 0.90216 0.87717 0.0339 0.85753 0.87128 0.0425 0.95616 0.86229 0.0182 0.94521 0.87777 0.0338 0.89630 0.87187 0.0328 1.00000 0.86298 0.0000 1.00000 0.87888 0.0000 0.95441 0.87282 0.0132 1.00000 0.87356 0.0000 Table 2: Densities and excess molar volumes Ve of binary mixtures of cyclohexane(1) - carbon tetrachloride(2) at 288.15, 293.15 and 298.15 K 288.15 K 293.15 K 298.15 K X 2 d Ve (g cm-3 ) (cm3 mol-1 ) X2 d Ve (g cm-3 ) (cm3 mol-1 ) X2 d Ve (g cm-3 ) ( cm3 mol-1 ) 1.00000 1.60374 0.000 1.00000 1.59311 0.000 1.00000 1.58427 0.000 0.95162 1.55895 0.035 0.95243 1.55008 -0.008 0.95118 1.53959 0.039 0.89768 1.50984 0.063 0.89964 1.50223 0.026 0.89982 1.49347 0.062 0.85224 1.46883 0.096 0.85152 1.45925 0.051 0.84930 1.44861 0.088 0.80115 1.42346 0.121 0.79943 1.41332 0.077 0.79976 1.40527 0.106 0.69971 1.33524 0.154 0.69900 1.32651 0.116 0.70118 1.32036 0.156 0.59972 1.25030 0.191 0.59972 1.24271 0.156 0.59743 1.23358 0.174 0.49878 1.16713 0.179 0.49878 1.16003 0.150 0.49892 1.15360 0.146 0.39881 1.08633 0.192 0.40045 1.08070 0.198 0.40045 1.07416 0.235 0.30000 1.00839 0.190 0.30077 1.00295 0.160 0.29962 0.99606 0.187 0.20020 0.93158 0.166 0.15004 0.88850 0.099 0.20087 0.92094 0.168 0.14949 0.89325 0.145 0.09949 0.85101 0.067 0.15021 0.88361 0.086 0.10266 0.85857 0.081 0.05004 0.81477 0.028 0.10291 0.84864 0.064 0.04667 0.81738 0.023 0.00000 0.77838 0.000 0.04739 0.80818 0.019 0.00000 0.78320 0.000 0.00000 0.77386 0.000 156 Each set of experimental results as fitted to the Redlich - Kister equation [11] n \^ (cm3 mot1) = X1X2 2^i Ai (1 - 2 X2/ (3) z=0 Values of coefficients^, are listed in Table 3, together with the standard deviation of the fit, aV1, defined as where N is the number of data points and « is the number of coefficients. Table 3: Coefficients^, and standard deviation ol^ of equation (3) T (K) Ao Ai A2 A3 cV1 (cm3 mot1) cyclohexane-carbon tetrachloride 288.15 293.15 298.15 0.7967 0.6903 0.8129 0.2549 0.2970 0.5045 0.1356 -0.2709 -0.1836 -0.1290 -0.1113 -0.8788 0.013 0.012 0.022 toluene-benzene 293.15 298.15 308.15 0.3535 0.3465 0.3770 -0.0356 -0.0291 -0.0092 -0.0218 -0.0491 -0.0211 -0.0320 0.0090 -0.0867 0.0052 0.0012 0.0167 The \^ of both mixtures are positive throughout. However, they are significantly smaller for toluene-benzene mixture, which is nearly ideal solution, than for the cyclohexane-carbon tetrachloride system. Positive values can be explained by the predominance of expansion in volume, caused by the loss of dipolar association and difference in size and shape of component molecules, over contraction in volumes, due to the dipole-dipole and dipole-induced dipole interactions. Ocon, Tojo, Espada [12] have determined \^ of cyclohexane-carbon tetrachloride at 293.15 K. Our results for this mixture at 293.15 K are compared with literature ones in Fig.1; it can be seen, that our values are higher in a part of the curve (X2 = 0.4-0.5). The reason may be in additional purification of chemicals [12]. iV = I(Cx p-^1)2 /(N-n) 157 0.2 -i 0.15 0.05 ¦ Series 1 -----Series2 Series3 X, Fig.1: Experimental V for cyclohexane-carbon tetrachloride at 293.15 K ( series 1); Ocon, Tojo, Espada (series 3); calculated values based upon equ. 3 (series 2) Analysis in terms of the Flory theory The interaction parameter %12 in Flory's theory can be calculated from experimental excess volume data and should be used further to obtain HE. Details were given by Flory (1965) and Abe, Flory (1965). Symbols in the following equations have their usual meaning and are explained at the end of the text: V (v0) 0 \7/3 (t-t0)(x1 V 1*+x2 V 2*), (4/3)-(v0)1/3 HE=X 1 P 1* V 1*(1/v1-1/v)+X2P2*V2(1/v2-1/v)+X 1 V 1*®2Xu~ where v 0 = O1 v1 + 02 v2, T-- v,1/3-1 = o1 p1* t1+®2 p2*t ^p1*+^2p2*-^©2x12 a T 3(1 + «i T) ' X V O1 =1-09 =-------* 1-1------* 2 X 1 V 1+X 2 V 2 (5) (6) (7) (8) (9) (10) The key quantity of the theory, the interchange energy parameter %12, was fitted to equimolar experimental values of VE for cyclohexane-carbon tetrachloride at 298.15 K. The resulting %12 was used to calculate HE , along with the pure component parameters 158 (ai from Wood, Gray [14] and yi from Holder, Whalley [15] ) as given in Table 4. Comparison between calculated and experimental (Adcock and McGlashan [16] ) excess enthalpy, and TSE is given in Table 5. Table 4: The parameters of pure liquid component used in Flory's theory component c-C6H12 CCl4 Vi (cm3/ mol) 108.75 97.08 « r103 (K 1 ) 1.217 1.229 Yi(J/cm3K) 1.067 1.143 ~ 1.2904 1.2927 ~ 0.06314 0.06345 P*(J /cm3) 532 569 V* (cm3/ mol) 84.28 75.10 ti * (K) 4720 4697 *i 0.5288 0.4712 ®i 0.5192 0.4808 Table 5: Calculated (Flory's theory) and experimental HE (X=0.5) and TSE (X=0.5) values for the cyclohexane-carbon tetrachloride system, at 298.15 K X12 HE (J/mol) calc. exp. T SE (J/mol) calc. exp. 7.9 167 149 78.3 46.5 From Table 5 it can be seen, that the theory predicts HE reasonably well, even though the calculated value exceeds the experimental by 12%. The agreement in excess entropy is worse; but it is well known, that Flory's theory can not provide a better conformity for a moderate polarity of molecules. 159 LIST OF SYMBOLS HE excess molar enthalpy P* characteristic pressure of pure component T* characteristic temperature of pure component Ti reduced temperature of component I Ve excess molar volume Vi molar volume of pure component V* characteristic volume of pure component vi reduced volume of pure component X2 mole fraction of component 2 Q2 site fraction of component 2 F2 segment fraction of component 2 g thermal pressure coefficient a thermal volume coefficient c 12 interaction parameter REFERENCES 1. PJ.Flory, J. Am. Chem. Soc. 1965, 87, 1833-1838 2. A.Abe, PJ.Flory, J. Am. Chem. Soc. 1965, 87, 1838-1846 3. R.Battino, Chem. Reviews, 1971, 71, 5-31 4. L.Lepori, M.Mengheri, V.Mollica, J. Phys. Chem. 1983, 87, 3520-3525 5. V.Hrženjak, Diplomsko delo 1995, FKKT Maribor, 1-33 6. K.Frece, Diplomsko delo 1991, FKKT Maribor, 1-45 7. M.Akl Awwad, A.Kifah Jabra, Fluid Phase Equii. 1989, 47, 95-102 8. P.Berti, L.Lepori, E.Matteoli, Fluid Phase Equil. 1989, 44, 285-294 9. D.V.SJain, N.S.Dhar, Fluid Phase Equil. 1990, 58, 173-180 10. W.Riddick, W.B.Bunger, Organic Solvents 1970, John Wiley, NY 11. O.Redlich, AKister, Ind. Eng. Chem. 1948, 40, 345-348 160 12. J.Ocon, G.Tojo, L.Espada, An. Chini. 1969, 65, 633-639 13. O.Kiyohara, G.C.Benson, J. Chem. Thermodyn. 1977, 9, 807-809 14. S.E.Wood, J.A.Gray, J. Am. Chem. Soc. 1952, 74, 3729-3733 15. G.A.Holder, E.Whalley, Trans. Faraday Soc. 1962, 58, 2095 16. D.S.Adcock, M.L.McGlashan, Proc. Roy. Soc. 1954, London, A226, 266-282 Povzetek: Z gostotomerom smo izmerili gostote raztopin cikloheksana z ogljikovim tetrakloridom pri 288,15, 293,15 in 298,15 K ter raztopin toluena z benzenom pri 293,15, 298,15 in 308,15 K in iz njih izračunali presežne molske volumne. S pomočjo Flory-jeve teorije za raztopine smo za sistem cikloheksan-ogljikov tetraklorid pri 298,15 K izračunali presežno molsko entalpijo; izračunana vrednost za ekvimolarno mešanico se relativno dobro ujema z experimentalno določeno.