J. CHEM. SOC. FARADAY TRANS., 1994, 90(8), 1083-1088 Excess Volumes of the Ternary Mixtures Butylamine-Cyclohexane- Benzene and Tributylamine-Cyclohexane-Benzene S. L. OswaI* and S. G. Patel Department of Chemistry, South Gujarat University, Swat395 007, India Excess volumes of the ternary mixtures butylamin-yclohexane-benzene and tributylamine-cyclohexane-benzene at 298.15, 303.15 and 313.15 K have been investigated from density measurements using a vibrating densitometer. A number of empirical equations predicting ternary mixture properties from the composite binary parameters have been examined. Furthermore, the Prigogin-Flory-Patterson theory has been extended for ternary mixtures and is applied to the present ternary mixtures. Experimental excess molar volumes, VE, are required when classical thermodynamics is to be used to relate and to compute the equilibrium properties of liquid mixtures.They are of particular importance for both the testing of existing theories and the development of new theories of mixtures. ' Theoretical predictions of VE of non-ideal binary liquid mixtures are more or less satisfactory for determining the sign and approximate magnitude. However, for ternary mix- tures the predictive approach is much more complex and unreliable.2 Rastogi3 has shown that the results of empirical correlations of sets of binary and ternary experimental data may be valuable for interpreting the interactions between the molecules in such systems. A number of researchers2-, have proposed empirical equations to predict excess thermodyna- mic properties for ternary mixtures from the results of corre- sponding binaries.However, experimental measurements of VE for ternary mixtures are scarce, making it difficult to test the predicting ability of these various equations. In a previous paper" we have published VE values of binary mixtures of triethylamine and tributylamine with alkanes and alkylamine at three temperatures. In continua- tion of this work, this paper provides VE values of two ternary mixtures, butylamine(l)-cyclohexane(2)-benzene(3) and tributylamine(l)-cyclohexane(2)-benzene(3) and of the corresponding binary mixtures at 298.15, 303.15 and 313.15 K. The present values of VE for ternary mixtures are com- pared with those obtained from the different empirical expressions due to Redlich-Kister; Tsao-Smith,' Kohler,6 Ja~ob-Fitzner,~ Rastogi et ~l.,~and Lark et aL9 employing the binary mixture data, as well as with those predicted by the Prigogine-Flory-Patterson (PFP) statistical theory.' '-14 Experimental Material Butylamine (C4H,NH2) and tributylamine [(C,H,),N] of Fluka (puriss grade), and cyclohexane (C6HI2) and benzene (C6H6) of BDH (AnalaR grade) were used in this work.C,H,NH2 and (C4H,),N were refluxed over Na and then distilled using a fractionating column.'5 C6H12 and C6H6 were purified by standard procedures as recommended by Riddick et all6 The purities of the liquids were checked by measuring their densities, p, and refractive indices, n,.The values obtained for p and n, are compared with the literature in Table 1. The purities of the liquid (as tested by gas-liquid chromatographic analysis) were better than 99.7 mol% for C6H1, and C6H6 and 99 mol% for C4H,NH2 and (C,H,),N. Thrice-distilled water and dehumidified air were used for densitometer calibration. Mixture Preparation All the mixtures were prepared by mixing weighed amounts of pure liquids in air-tight, narrow-mouth stoppered bottles. A Mettler (AE 163,Switzerland) balance with a precision of 1 x lo-' g was used for the purpose. Proper care was taken to minimize evaporation of the components. Hence, the pos- sible error in the mole fraction is estimated to be lower than +2 x 10-4. Density Measurements The densities of pure liquids, binary mixtures and ternary mixtures were measured with an Anton-Paar model DMA 60/602 vibrating tube densitometer, thermostatted at the desired temperature within f0.01K using a HetoBirkeroad ultrathermoset together with a digital thermometer as described elsewhere." Water and air were chosen as cali- brating fluids, since they span a wide range and their den- sities are known to a high level of precision.'6*21 The precision of p measured is estimated to be better than kO.02 kg m-,.The VE values covering the complete composition range were calculated from the molar masses, M, and the densities, p, of the pure liquids and mixtures. The estimated error in VE for all systems was smaller than +6 x lo-, m3 mol-'.Results and Discussion The experimental VE values at different mole fractions of the four binary mixtures C4H,NH2-C6H, 2, C4H,NH2-C6H6, Table 1 Density and refractive index of pure liquids at 298.15 K densityhg m-liquid exp. lit. C,H,NH, 733.35 733.08" 734.52' (C,H,),N 774.23 773.78" 774.306 C6H12 773.90 773.85f C6H6 873.62 873.6Sf refractive index exp. lit. 1.3977 1.3987b 1.4267 1.4265' 1.4268' 1.4262 1.4253b 1.4978 1.4979' a Ref. 15; 'ref. 16; ref. 17; ref. 18; ref. 19; ref. 20. 1084 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 2 Excess molar volume, VE, for binary mixtures at 298.15, (C4Hg)3N<,H12 and (C,Hg)3N-C,H, at 298.15, 303.15 and 303.15 and 313.15 K 313.15 K are reported in Table 2.A variable-degree polynomial of the form X1 298.15 303.15 313.15 C4H9NH&6H 12 0.1098 0.428 0.435 0.445 was fitted to each binary mixture at each temperature by the 0.1980 0.657 0.668 0.684 0.3883 0.847 0.876 0.889 least-squares method. 0.4834 0.837 0.859 0.877 The parameters A,, of eqn. (1) and the standard deviations, 0.5922 0.757 0.77 1 0.797 a,? are given in Table 3. Table 3 also lists the required 0.8112 0.454 0.464 0.488 parameters, A,, of eqn. (1) for the binary mixture 0.8919 0.273 0.282 0.290 cyclohexane-benzene at 298.15, 303.15 and 313.15 K, taken from the literature.20.22 C4H9NH 246H6 0.0974 0.059 0.050 0.042 Fig. 1 and 2 show VEplotted against x1 for the first com- 0.1974 0.128 0.122 0.08 1 ponent and the VE curves calculated from the smoothing 0.3596 0.226 0.22 1 0.224 equations.0.4787 0.25 1 0.255 0.264 VE values for C,H9NH,-C,H12, C,HgNH2-C,H6,0.5902 0.269 0.270 0.273 0.7984 0.2 13 0.205 0.202 (C,H,),N-C,H,, and (C4Hg),N-C6H, at 298.15 K have 0.9042 0.137 0.132 0.127 been measured earlier.15*23.24 Our results on VE for equi- molar mixtures of these systems are within 5% of the liter- (C4H9)3N-C6H120.1012 0.185 0.183 0.182 ature values, except for the value for (C,H9)3N-C,H12 0.2089 0.283 0.275 0.272 reported by Phuong-Nguyen et aL2, For the latter mixture, 0.4001 0.311 0.302 0.283 VE at xi = 0.5 reported by Phuong-Nguyen et al. is 0.5116 0.277 0.265 0.263 0.389 x lop6 m3 mol-', while Letcher" reports0.5868 0.254 0.245 0.224 0.280 x lo-, m3 mol-'.Our VE value of 0.284 x lo-, m3 0.7953 0.152 0.138 0.124 mol-is very close to that of Letcher.0.9021 0.086 0.073 0.067 Inspection of Table 2 and Fig. 1 and 2 shows that VEfor (c4H9)3N-C gH 6 all the mixtures is positive. VE for C,~gNH,-C,Hl, and 0.1084 0.338 0.348 0.361 (C,Hg)3N-C,H, increases with rise in temperature, while the 0.2016 0.496 0.51 1 0.532 0.2272 0.516 0.540 0.560 0.3639 0.584 0.622 0.647 0.4013 0.573 0.593 0.634 t 6 is defined as 0.4593 0.580 0.608 0.4986 0.544 0.574 0.605 0.6007 0.496 0.53 1 0.565 0.7001 0.414 0.463 0.498 0.7956 0.328 0.373 0.408 0.9003 0.186 0.228 0.250 where n and m,respectively, are number of experimental points and number of coefficients used in eqn. (1). Table 3 Parameters, A,, of the smoothing equation [eqn.(l)] and standard deviations, 6,along with HE (exp), X,,,, and Xi,YE for the equimolar mixture T/K Ad A1 A2 a A3 6' Ht/J mol-' Xij, '/J cm- Xi,yEc/J cm-j C4H9NH2-C6H12 298.15 3.31 15 0.9095 0.6480 0.0065 303.15 3.3969 0.9062 0.6366 0.01 13 1 131d 60.7 50.4 313.15 3.4822 0.8900 0.6781 0.0070 298.15 1.0417 -0.5O44 0.1 147 0.0109 C4H gNH 2-C6H 6 303.15 1.0500 -0.5200 -0.01 82 0.0109 584' 32.5 20.3 313.15 1.0787 -0.5337 -0.1725 0.01 20 298.15 1.1342 0.6670 0.5751 (C4H9)3N-C6H120.0025 303.15 1.0939 0.6526 0.5044 0.0045 151' 5.2 4.9 313.15 1.0357 0.7678 0.5297 0.0059 298.15 2.1874 0.9001 0.9692 (C,H,),N-C,H,0.0043 303.15 2.2889 0.7103 1.263 1 0.0034 775 27.0 13.8 313.15 2.4383 0.6526 1.3246 0.0086 298.15 2.6164 -0.1030 0.0272 0.0010 C6H12-C6H6B 303.15 2.6273 -0.1027 0.0465 0.0017 0.0003 8008 40.6 39.3 313.15 2.6487 0.1086 0.0566 0.0037- 'Units: lo6m3 mol-'.Obtained from HE(exp). Obtained from VE(exp). Ref. 27. Ref. 24. Ref. 28. Ref. 20 and 22. * Ref. 29. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 u.I 0.6 0.5 r I-0 0.4 E (DI 0.3 1 L 0.2 0.1 0.0 0.0 0.2 0.4 0.6 0.8 1.o XI Fig. 2 Excess volumes for (a) (C,H,),N-C,H,, and (b) (C,H,),N-C,H, at 298.15 (O), 303.15 (A) and 313.15 K (0).Solid curves represent eqn. (1). XI Fig. 1 Excess volumes for (a) C,H,NH2-C,H,, and (b) Solid (C,H,),N-C6H,,-C,H6 and at 298.15, 303.15 and 313.15 KC,H,NH,-C,H, at 298.15 (O),303.15 (A) and 313.15 K (0).curves represent eqn. (1). are presented in Tables 4 and 5. reverse is the case for (C,H,),N-C,H,, . The variation of VE Correlation of VfZ3 with Empirical Equations with temperature for C,H,NH,-benzene is very small and no If the interactions in a ternary i-j-k mixture are assumed to definite trend is observed. The different magnitudes of posi- be closely dependent on the interactions in the constituent tive VE suggest that the effects of size, shape and chemical i-j, j-k and i-k mixtures, it should be possible to evaluate nature of the molecules involved predominate. thermodynamic excess molar volumes for a ternary mixture The experimental excess molar volumes, Vf.,,,for the of non-electrolytes, when the corresponding volumes for ternary mixtures C,H,NH,-C6H,,-C,H6 and binary i-j,j-k and i-k mixtures are known.Table 4 Excess molar volumes, VE, for C,H,NH2 (x,)<,H12 (x,)<,H, (x3) at 298.15, 303.15 and 313.15 K, along with VFFp at 303.15 K; ijVE = VE -VEPFP VE/lO-, m3 mol-' 0.1231 0.2230 0.517 0.524 0.529 0.690 -0.166 0.573 -0.049 0.2509 0.1903 0.556 0.560 0.570 0.792 -0.232 0.601 -0.041 0.3834 0.1577 0.545 0.556 0.572 0.819 -0.263 0.587 -0.03 1 0.5154 0.1231 0.492 0.502 0.533 0.767 -0.265 0.531 -0.029 0.6501 0.0889 0.395 0.396 0.433 0.641 -0.245 0.432 -0.036 0.7842 0.0548 0.302 0.312 0.324 0.446 -0.112 0.295 0.017 0.9252 0.0190 0.141 0.148 0.158 0.171 -0.023 0.111 0.037 0.1218 0.4347 0.745 0.748 0.754 0.898 -0.150 0.770 -0.022 0.2640 0.3687 0.773 0.822 0.847 1.002 -0.180 0.8 15 0.007 0.3931 0.3039 0.767 0.792 0.875 1.013 -0.221 0.792 0.000 0.6642 0.1682 0.542 0.534 0.576 0.759 -0.225 0.568 -0.034 0.8444 0.0772 0.303 0.325 0.345 0.406 -0.083 0.300 0.025 0.9280 0.0360 0.152 0.160 0.174 0.198 -0.038 0.145 0.015 0.1350 0.6479 0.714 0.720 0.738 0.836 -0.055 0.728 -0.008 0.2716 0.5455 0.834 0.849 0.857 1.024 -0.175 0.854 -0.005 0.4065 0.4445 0.830 0.848 0.893 1.082 -0.234 0.882 -0.034 0.5399 0.3446 0.747 0.788 0.836 1.020 -0.232 0.820 -0.032 0.6694 0.2476 0.619 0.631 0.684 0.851 -0.220 0.677 -0.046 0.8004 0.1495 0.404 0.415 0.467 0.580 -0.165 0.460 -0.045 0.9225 0.0580 0.185 0.188 0.195 0.247 -0.059 0.195 -0.007 0.2457 0.3491 0.727 0.743 0.792 0.974 -0.232 0.792 -0.049 0.2461 0.2347 0.625 0.634 0.674 0.854 -0.220 0.667 -0.033 0.1556 0.2285 0.568 0.570 0.577 0.744 -0.174 0.605 -0.035 0.1685 0.6769 0.693 0.707 0.742 0.842 -0.135 0.722 -0.015 0.3139 0.0883 0.420 0.430 0.476 0.652 -0.222 0.436 -0.006 Xijis obtained from equimolar HE(exp). * Xijis obtained from equimolar VE(exp).1086 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 5 Excess molar volumes, VE, for (C4HJ3N (xl)+Hl, (x,)-C6H6 (x3) at 298.15, 303.15 and 313.15 K, along with VFFp at 303.15 K; 6VE = VE -VEPFP ~~ ~ 0.0272 0.2430 0.537 0.538 0.540 0.595 -0.057 0.542 -0.004 0.0676 0.2279 0.610 0.629 0.640 0.734 -0.105 0.614 0.01 5 0.2521 0.1868 0.682 0.695 0.719 0.910 -0.216 0.692 0.003 0.3648 0.1586 0.644 0.664 0.695 0.909 -0.246 0.672 -0.008 0.5110 0.1221 0.523 0.543 0.565 0.808 -0.265 0.584 -0.041 0.7022 0.0744 0.370 0.369 0.382 0.556 -0.187 0.398 -0.029 0.0578 0.4795 0.680 0.706 0.720 0.769 -0.061 0.700 0.006 0.1213 0.4004 0.695 0.711 0.751 0.840 -0.129 0.698 0.013 0.3154 0.3484 0.652 0.675 0.700 0.8 18 -0.143 0.659 0.016 0.4478 0.2810 0.572 0.580 0.588 0.734 -0.154 0.576 0.004 0.6103 0.1983 0.420 0.431 0.436 0.567 -0.137 0.437 -0.006 0.8375 0.0827 0.203 0.201 0.258 0.259 -0.058 0.195 -0.006 0.0649 0.701 1 0.552 0.572 0.568 0.580 -0.008 0.537 0.035 0.1334 0.6497 0.573 0.596 0.614 0.615 -0.019 0.552 0.044 0.2242 0.5816 0.565 0.587 0.599 0.623 -0.041 0.549 0.038 0.2744 0.5440 0.554 0.577 0.588 0.623 -0.016 0.538 0.039 0.0522 0.4778 0.685 0.678 0.674 0.765 -0.087 0.699 -0.021 0.1185 0.4445 0.673 0.702 0.711 0.818 -0.116 0.710 -0.008 0.5178 0.2072 0.486 0.489 0.557 0.718 -0.229 0.543 -0.054 0.4744 0.1241 0.602 0.610 0.626 0.849 -0.239 0.614 -0.004 0.4860 0.4101 0.385 0.389 0.433 0.485 -0.095 0.414 -0.025 X, is obtained from equimolar HE(exp); X, is obtained from equimolar VE(exp).The proposed Redlich and Kister expression4 for the Rastogi et id.* suggested a slightly different equation for excess Gibbs energy of ternary mixtures takes the form for estimating the excess molar volume of a ternary mixture predicting excess molar volumes : ~723= ~7 +2 ~!3+ ~73 (2) in which VF2, V:3 and VY3 represent the excess molar volumes, with xl, x2 and x3 the mole fractions of the ternary mixture calculated with eqn.(1) using the coefficients of Table where the values of Vt for binary mixtures are obtained in a 3. similar manner as for eqn. (4). The Tsao and Smith equation5 for predicting the excess The Jacob-Fitzner equation' is based on the binary data enthalpy of ternary mixtures takes the following form: at the composition nearest to the ternary composition, taking the form for the excess molar volume: where VE refer to the excess molar volumes for the binary mixtures at compositions xo, xy such that xp = xi for the 1-2 x1x3 v?3and 1-3 binary mixtures and x: = x2/(x2 + x3) for the 2-3 binary mixture.(xl + x2/2xx3 + x2/2) The Kohler equation6 for a ternary mixture is of the form: x2x3 v;3(x2 + x1/2xx3 + xl/2) (6) In this equation, VE refers to the excess molar volumes for the binary mixtures at compositions xo and xy, such that where V; is the excess molar volume of the binary mixtures x; = 1 -xj" = Xi/(Xi + Xi). at composition xp ,xy ,such that xi -xj = xo -xy . Table 6 Standard deviations between experimental VE and those obtained from the empirical equations [eqn. (2)-(7)] and PFP theory standard deviation T/K eqn. (2) eqn. (3) eqn-(4) eqn. (5) eqn. (6) eqn. (7) PFP theory butylamine-cyclohexane-benzene 298.15 0.023 0.126 0.029 0.161 0.023 0.104 303.15 0.023 0.120 0.027 0.170 0.023 0.112 0.187" 0.025b 313.15 0.025 0.104 0.028 0.190 0.025 0.128 tributylamine-cyclohexane-benzene 298.15 0.025 0.164 0.035 0.165 0.025 0.093 303.15 0.033 0.163 0.040 0.169 0.035 0.101 0.124" 0.02 1 313.15 0.029 0.154 0.034 0.180 0.029 0.112 " X, adjusted to equimolar HE(exp)ij.X, adjusted to equimolar VE(exp)ij. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 The equation proposed by Lark et a/.' for estimating the excess molar volumes for ternary mixtures is of the form -k [(n2)23 + (n3)231V;3 + [(%)i3 + (ni)i3lV?3 (7) where (ni)ii is the number of moles of component i in the binary mixture ij such that (r~,),~+ (n1)13 = xl, and x1 dis-tributes itself proportionally between components 1 and 2, i.e.and In order to compare the correlating ability of eqn. (2)-(7), the standard deviations, uybetween the experimental and pre- dicted VE for the ternary mixtures, have been calculated and are recorded in Table 6. Examination of Table 6 shows that eqn. (2), (4) and (6) due to Redlich-Kister, Kohler and Jacob-Fitzner gave similar values of u, while comparatively higher values of ts were obtained with the Rastogi et a!. Lark et al. and TsacAmith equations, the highest being for eqn. (5) of Rastogi et al.' Prigogine-Flory-Patterson Theory The statistical approach of PFP theory h as been 10-14925926 applied successfully to the excess thermodynamic properties of binary liquid mixtures.Here, an attempt is made to extend it to predicting the excess molar volumes of ternary mixtures. By analogy with binary rnixtures,l2 the excess volume for a ternary or higher component mixture is given by VFFp= V* V-1$iq) (8)(-i,j.k where Pand are the reduced volumes of the mixture and of the pure component i, and I/* is the characteristic volume of the mixture. The reduced volume, is related to the reduced temperature T T = ~p-= (PIP -1)/p4/3 (9)1 where T* is the characteristic temperature. The charactersitic volume, V*, temperature, T*, pressure, P*, and energy, U*, for a mixture can be calculated from the values of Flory's characteristic parameters of pure com-ponents applying the following combining rules' 2-'4 with the assumption that two-body interactions are predominant.V* = 1xi Vf (13)i,yk In eqn. (1l), Xijrepresents Flory's contact interaction energy parameter for the ij pair,12 which can be evaluated for each pair ij, jk and ik using either the experimental excess molar enthalpy, HE(exp), or the excess molar volume, VE(exp), of the corresponding pair. 1087 The relation used for Xij:HEfor the ij pair from the excess molar enthalpy, HE(exp)ij, in the notation of Patterson and Delmas14 is, (14) where the free-volume contribution to the excess enthalpy for the ij pair, Hf",ii, is estimated oia HF ij = UtCp,i,(Tu) -T",ij] (15)ci, j for the ij pair using the excess molar volume can be Xi,derived from26 where the free-volume and P* contributions to the excess molar volume for the ij pair are obtained by26 x {$i $j + ($i -djI21 (17) VE(P*)= Vz(q -QO(i-$j) (18) oycpand Tz are reduced quantities and can be evaluated from the appropriate relations with knowledge of c.Fur-thermore, &, Oi and $i, the segment fraction, surface fraction and contact energy fraction, respectively, for component i in the mixture are given by (19) i, j, k Bi = XiSiVf/ I 1xisiVf i. i,k $i = xiPi*Vf/ 1xiP? Vf (21) i, j, k here Si is the molecular surface-to-volume ratio of compone_nt i. Thus, from knowledge of the pure component values of Vf and Pf and the experimental values of either HE or VE for each pair ij, jk and ik,one can evaluate for the ternary mixture through the mixture P* and T*, using eqn.(10)-(18). This enables the excess molar volume for the ternary mixture to be estimated from eqn. (8). In the present work we have determined Xij,HEfrom the equimolar HE(exp)ij value, as well as Xii,VEfrom the equi- molar VE(exp)ii. Both of these values of Xijwere used to esti- mate the excess molar volume for the present ternary mixtures. The values of Flory's parameters for the pure components used are listed in Table 7, while Table 3 includes the values of equimolar HE(exp)ii, Xi,HE and Xij,YE for the composite binary mixtures. The VFFp values at 303.15 K obtained from Xij derived by using equimolar HE(exp) as well as VE(exp) are included in Tables 4 and 5 for comparison with the experimental VE. The difference 6VE (= VFxp-VFFp) at each composition is also given in Tables 4 and 5.The overall standard deviations, 0, between the experimental and theoretical VE for both approaches are included in Table 6. Inspection of Tables 4 and 5 shows that PFP theory always predicts the correct sign for VE at each composition for both ternary mixtures. The values for 6VE are in the range (-0.041 to -0.266) x m3 mol-', when VFFp is J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 7 Physical properties and Flory's parameters of the pure components component 0r/10-~K-' V V*/cm3mol-' C,/J K-' mol-'P*/J cmP3 T */K S/A -' cyclohexane 1.23 3 1.2975 84.33 benzene 1.233 1.2975 69.33 533 4730 0.93 158.1 623 4730 1.oo 136.8 but ylamine 1.319 1.3137 76.43 582 459 1 1.14 190.7 tributylamine 0.990 1.2491 192.35 448 5299 0.88 374.0 obtained from X, HE.On the other hand, when VFFpis calcu- lated using Xij,YE,6VE lies in the narrow range (-0.054 to 0.044) x m3 mol-l. Similarly, the overall standard devi- ations, 0, at 303.15 K are (0.187& 0.077) x m3 mol-' 7 8 9 K. T. Jacob and K. Fitzner, Thermochim. Acta, 1977,18, 197. R. P. Rastogi, J. Nath and S. S. Das, J. Chem. Eng. Data, 1977, 22, 249. €3. Lark, S. Kaur and S. Singh, Indian J. Chem. Sect. A, 1981,26, 197. and (0.124f0.080) x m3 mol-l, for C,H,NH,- 10 S. G. Pate1 and S. L. Oswal, J. Chem. SOC.,Faraday Trans., 1992, when HE(exp) is used to derive Xij, but they are only (0.025 f0.014) x m3 mol-' and (0.021 0.015) x m3 mol-', respectively, when X, is adjusted to the binary VE(exp) data.It may be concluded that the estimated V;,, values for the ternary mixture investigated are quite satisfactory when X, is adjusted to binary VE(exp) data, and are much better than those predicted using Xi.obtained through HE(exp). Further- VE(exp) data are also as good as those predicted by the empirical equations [eqn. (2), (4) and (6)], which also use C6H 12-C6H6 and (C,H,),N-C,H 1,-C,H,, respectively, more, the theoretical V,,,b values estimated through binary 11 12 13 14 15 16 17 18 19 88,2497. I. Prigogine, The Molecular Theory of Solutions, North Holland, Amsterdam, 1957. P. J. Flory, J. Am. Chem. SOC., 1965,87, 1833. A. Abe and P. J. Flory, J. Am. Chem. SOC., 1965,87, 1838. D. Patterson and G. Delmas, Discuss.Faraday SOC., 1970,49,98. T. M. Letcher, J. Chem. Thermodyn., 1972,4, 159; 551. J. A. Riddick, W. B. Bunger and T. K. Sakano, Organic Solvents: Physical Properties and Methods of Purijication, Wiley Inter- science, New York, 4th edn., 1986. A. Krisnaiah and P. R. Naidu, J. Pure Appl. Ultrason., 1987,9,2. C. Klofutar, S. Paljk and D. Krenser, J. Znorg. Nucl. Chem., 1975,37,1729. R. Philippe, G. Delmas and M. Couchen, Can. J. Chem., 1978, VE(exp) of the composite binary mixtures. 20 56,370. K. Tamura, K. Ohomuro and S. Murakami, J. Chem. Thm- One of us (S.G.P.) wishes to acknowledge the Government of Gujarat for the award of a research fellowship during the course of this work. 21 22 modyn., 1983, 15, 859. Handbook of Chemistry and Physics, ed. R. C. Weast, CRC Press, Boca Raton, 59th edn., 1979. K. Tamura and S. Murakami, J. Chem. Thermodyn., 1984, 16, 33. 23 T. M. Letcher and J. W. Bayles, J. Chem. Eng. Data, 1971, 16, References 24 266. H. Phuong-Nguyen, €3. Riedl and G. Delmas, Can. J. Chem., 1 J. S. Rowlinson and F. L. Swinton, Liquids and Liquid Mixtures, Butterworth, London, 3rd edn., 1982. 2 G. L. Bertrand, W. E. Acree Jr. and T. E. Burchfield, J. Solution Chem., 1983,12,327. 3 R. P. Rastogi, J. Sci. Znd. Res., 1880,39,480. 4 0.Redlich and A. T. Kister, Znd. Eng. Chem., 1948,40,345. 5 C. S. Tsao and J. M. Smith, Chem. Eng. Prog. Symp. Ser., No. 7, 25 26 27 28 29 1983,61,1885. M. Costas and D. Patterson, J. Solution Chem., 1982,11, 807. B. Riedl and G. Delmas, Can. J. Chem., 1983,61,1876. J. Fernandez, I. Velasco and S. Otin, Znt. Data Ser., Sel. Data Mixtures, Ser. A(3),1990, 166; 167. A. S. Kertes and F. Grauer, J. Phys. Chem., 1973,77,3107. K. Elliot and C. J. Wormald, J. Chem. Thermodyn., 1976,8,881. 1953, 49, 107. 6 F. Kohler, Monatsh. Chem., 1960,91,738. Paper 3/06573A; Received 3rd November, 1993