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Molar excess volumes of ternary mixtures of nonelectrolytes
Nuid Phase Equilibria, Elsevier
Science
18 (lY84) 333-344
Publishers
MOLAR EXCESS VOLUMES NONELECTROLYTES P.P. SINGH
Department (Received
*, R.K.
NIGAM,
of Chemistry, January
333
B.V., Amsterdam
-
OF TERNARY
S.P. SHARMA
Muharshi Dayanand
6th, 1984;
Printed
accepted
in final
in The Netherlands
MIXTURES
and SADHNA
AGGARWAL
lJniuersit_y, Rohtak form
OF
May 22nd.
(India) 1984)
ABSTRACT Singh, P.P., Nigam, ternary mixtures
R.K., Sharma, of nonelectrolytes.
S.P.
and
Aggarwal,
S., 1984.
Fluid Phose Equilibria,
Molar
excess
volumes
of
18: 333-344.
Molar excess volumes [Fk of methylenebromide( i) + pyridine( j) + P-picoline (k), cyclohexane( i ) + pyridine( j)+ &picoline( k), benzene( i ) + toluene( j) + 1,2-dichloroethane( k), benzene(i) + o-xylene( j) + 1,2-dichloroethane( k) and benzene( i) + p-xylene( j) + 1.2dichloroethane( k) mixtures have been determined dilatometrically at 298.15 K. The data have been examined and it is found coefficients molecular these
in terms of Sanchez and Lacombe theory and the graph-theoretical that they are described well by the latter. Self- and cross-volume
vJk, I& interactions
approach, interaction
and the values utilised to study and VJkk, etc., have also been evaluated between the j th and k th molecular species in the presence of the i th in
i + j + k mixtures.
INTRODUCTION
In a binary i +j mixture, i - i andj -j contacts in the pure components i andj are replaced by i -j contacts in the mixture. If interactions in a ternary i +j + k mixture are assumed to be closely dependent on the interactions in the constituent i +j, j + k and k + i mixtures, it should be possible to evaluate thermodynamic excess functions for ternary mixtures of nonelectrolytes when the corresponding functions for the binary i +j, j + k and k + i mixtures are known, Singh and Sharma (1983) recently employed a graph-theoretical approach that utilises connectivity parameters of the third degree, 3<,, to describe successfully the molar excess volumes V” of ternary mixtures of nonheterocyclic nonelectrolytes. Furthermore, the Lacombe and Sanchez (1976a,b) theory of fluid mixtures also suggests that the thermodynamic properties of ternary mixtures of nonelectrolytes are determinable from the corresponding * Author
to whom
0378-3812/84/$03.00
correspondence
should
0 1984 Elsevier
be addressed.
Science Publishers
B.V.
334
properties of the constituent binary mixtures. This prompted us to study further the molar excess volumes rFk of some ternary mixtures of nonelectrolytes and analyse the data in terms of (i) the graph-theoretical approach and (ii) the Lacombe and Sanchez theory of fluid mixtures. EXPERIMENTAL
Materials and methods Benzene, toluene, o- and p-xylene, pyridine, cyclohexane and &picoline (all B.D.H., Analar Grade) were purified by standard procedures (Vogel, 1978a, b, c). Methylenebromide. however,, was obtained from two different sources. One sample (Sojuzchimexport, Moscow) was purified by shaking with 5% sodium carbonate solution, followed by washing with distilled water, drying over anhydrous calcium chloride and then fractional distillation. The other sample of methylenebromide was synthesised from bromoform in the manner suggested by Vogel (Vogel, 1978d), and was finally purified by the same method as described above. These two samples of methylenebromide were stored in two separate amber-coloured bottles for subsequent use. The purity of the purified samples was checked by measuring their densities at 298.15 + 0.01 K, and these agreed well with the corresponding literature values, as is evident from Table 1. Molar excess volumes r,“k were determined in a dilatometer similar to that used by Brown and Smith (1962), the only difference being that there were now three limbs for the three components. The temperature of the water bath was controlled to within less than 50.01 K by means of a toluene regulator, and the change in level of the liquid in the dilatometer capillary was measured by a cathetometer that could be read to &O.OOI cm. Further,
TABLE
1
Densities
of purified
Compound
liquids
at 298.15 K
Density
Reference
(g cmp3)
Experimental
Literature
Methylenebromide Pyridine P-Picoline
2.45844 0.9778 0.95231
2.45849 0.9782 _
Timmermans (1950) Rochdestwensky et al. (1935) _
Cyclohexane Toluene o-Xylene Benzene p-Xylene 1,2-Dichloroethane
0.77389 0.86224 0.87588 0.87366 0.85665 1.24535
0.77389 0.86220 0.87583 0.87370 0.8567 1.24530
Forziati Forziati Forziati Singh et Williams Coulson
et al. (1946) et al. (1946) et al. (1946) al. (1968) and Krchma et al. (1948)
(1927)
335 TABLE
2
Comparison of V,,k values measured for various i + j + k ternary mixtures at 298.15 K, with corresponding V, ._, values evaluated from graph theory and Lacombe and Sanchez theory ’ (all LY’Sare in cm 1: molV’)
-r,
qFk(cm3
x1
Exp. Methyfenehromide(i)
+ pyridine(i)
mol-‘) Graph theory
Lacombe
and Sanchez theory
+ p - picoiine(k)
298..15 K = - 2.8705( - 9.1500), LY,~= -- 0.7340( - 4.8449). Q, = -- 36.2644( - 4.7321) 0.0018;7 0.064 0.095 (0.058) 0.283 0.050% 0.1149 0.8241 0.495 (0.071) 0.318 0.120 0.556 (0.099) 0.144 0.1306 0.4851 0.150 0.574 (0.073) 0.309 0.1309 0.7309 0.136 0.631 (0.098) 0.269 0.1646 0.6159 0.170 0.283 (0.151) 0.144 0.2068 0.1500 0.184 0.143 (1.007) 0.191 0.2141 0.184 0.0545 0.3141 0.3154 0.4031 0.4313
0.1618
0.5390 0.6419 0.7755 0.8066
0.3511 0.2861 0.1143 0.1011
0.8578 0.9317 0.9585
0.0931 0.0421 0.0217
Pyridine
(i) + j3 -picoline
0.5038 0.0765 0.2406
0.249 0.254 0.200 0.310 0.302 0.288 0.243 0.218 0.169 0.089 0.058
0.334 (0.200)
0.164
0.726 0.213 0.486 0.681
(0.147) (0.239) (0.216) (0.172)
0.204 0.116 0.164 0.176
0.607 (0.159) 0.294 (0.167)
0.208 0.238
0.264 0.239 0.115 0.062
0.218 0.3Q5 0.369 0.401
(j) + cyclohexane
(0.151) (0.107) (0.061) (0.042)
(k)
298.15
K = - 0.734 ( - 4.8449), (Y,k = - 7.8838 ( - 7.7793), Q, = -- 2.2118 (0.0) 0.108 (0.043) - 3.067 o.o:
0.2107
0.3293 0.3470 0.5284
0.0898 0.6238 0.2172 0.0432
0.594 0.621
0.401 (0.093) 0.420 (0.045)
0.115 0.360 0.211
0.0733
0.124
0.140 0.440 0.423 0.302
0.7901 0.8297
(0.118) (0.095) (0.024) (0.039)
- 1 .OOl - 1.451 1.559 0.274 0.799 1.1’74
336 TABLE 2 (continued) x,
x,
ryA (cm” mol-I) &P.
Graph theory
Lacombe and Sanchez theory
Benzene (i) + tofuene fj) + 1,2 - dichloroethane (k) 298.15 K 0.0?54 cy = - 2.2712 0.2215 (- 10.4352), 0.165a,, = - 0.323 168.1757 (- 2.2769), 0.117 IY~,= 4.5523 ( - 6.8100) (0.239) 0.0993 0.7957 0.111 0.457(0.151) 0.242
0.1079 0.1288 0.2238 0.2304 0.2936 0.2977 0.4661 0.6075 0.7303 0.8368 0.8396 0.8865 0.9071
0.2122 0.8030 0.1509 0.4799 0.5734 0.2799 0.0847 0.3341 0.0685 0.0832 0.0625 0.0685 0.0600
0.187 0.065 0.217 0.180 0.134 0.221 0.240 0.115 0.161 0.085 0.095 0.055 0.043
0.569(0.233) 0.106 0.538(0.066) 0.280 1.056(0.204) 0.080 0.961(0.191) 0.218 1.081(0.113) 0.252 1.238(0.210) 0.143 1.653(0.158) 0.038 1.355(0.062) -2.312 1.415(0.090) 0.097 0.051(0.973) 0.163 0.029tO.692) 0.201 0.023(0.577) 0.141 0.047(0.949) 0.152
Benzene(i)+ o-xylene (j) + 1,2-dichloroethane (k) 298.15K = -1.8315(-7.0882), a,, 0.&8 0.0898 0.181 0.1071 0.7500 0.193 0.1108 0.1847 0.274 0.1231 0.6186 0.274 0.2103 0.6679 0.244 0.2807 0.0652 0.255 0.3644 0.4932 0.312 0.2465 0.3732 0.346 0.3176 0.3953 0.351 0.0390 0.256 0.5146 0.5855 0.3157 0.284 0.7419 0.0616 0.199 0.8472 0.0928 0.134 0.8674 0.0526 0.117 0.8755 0.0730 0.112 0.8773 0.0400 0.108 0.9084 0.0616 0.083
aA, = -4.5523(-6.8100) 11.1328 (-2.1479), 0.204 0.088(0.233) 0.419 0.177(0.188) 0.263 0.141(0.348) 0.388 0.202(0.287) 0.197 0.288(0.188) 0.168 0.176(0.201) 0.386 0.407(0.216) 0.306 0.275(0.259) 0.331 0.373(0.276) 0.171 0.217(0.150) 0.378 0.46X(0.173) 0.079 0.240(0.109) 0.160 0.263(0.078) 0.136 0.189(0.063) 0.157 0.221(0.064) 0.129 0.163(0.056) 0.164 0.187(0.049)
337
X,
V,TA(cm3 mol-‘)
XI
Exp.
Lacombe
Graph theory
and Sanchez theory
Benzene (i) + p - xylene 0) + I,2 -dichIoroethane (k)
298.15K o.ok3= -2.1233 0.6737 (-8.5266), 0.191 (Y,~ = -28.9924 0.183 (-2.2635),a,,= 0.335 -4.5523(-6.8100) (0.252) 0.0819 0.3216 0.285 0.174(0.373) 0.234 0.0871 0.7933 0.126 0.262(0.167) 0.330 0.1070 0.3341 0.292 0.211(0.366) 0.244 0.1091 0.0618 0.164 0.143(0.168) 0.083 0.1802 0.4086 0.293 0.321(0.326) 0.273 0.4264 0.4763 0.242 0.626(0.152) 0.343 0.5090 0.2519 0.279 0.567(0.198) 0.250 0.5586 0.0856 0.268 0.447(0.164) 0.055 0.8020 0.0940 0.154 0.401(0.081) 0.235 0.8323 0.0774 0.135 0.354(0.069) 0.209 0.8440 0.0800 0.131 0.349(0.064) 0.229 0.8578 0.7740 0.114 0.334(0.059) 0.221 0.8860 0.0615 0.094 0.280(0.047) 0.221 0.9020 0.0480 0.082 0.238(0.041) 0.185 y.,“, values in parentheses are those calculated from the graph theoretical approach in which 3c values for the constituent moieties were evaluated from 8 considerations of the respective molecular graphs.
in order to ensure that the liquid in the capillary stem had the same composition as the bulk solution on mixing, after mixing the components the dilatometer was placed in a cold bath so that there was a minimum amount of liquid in the capillary and then replaced in the experimental water bath. This process was repeated two or three times. The uncertainty in the measured v$ values is - 0.55% at the most. RESULTS
The F,“k data for the various ternary i +j + k mixtures as a function of composition at 298.15 K are recorded in Table 2. These data were expressed (Singh and Sharma, 1983) as
0) [Ita~kb-xJ]+x;x,xkj i:A:;k(x,-xk)y]
+x*x/,
n=O
n-o
where X, and xj are the mole fractions of the i th and j th components i +j + k mixture, and Ayj (n = O-2), etc., are parameters characteristic
in the of the
338
binary i + j, etc. mixtures. evaluated by fitting
i
The A:+
(x+c,)“A;,
-xx/xk
1
(xi - xk)Ayk
TABLE
II
/x,xixk
(n = O-2)
I
parameters
I
(x,-x,)A.:;
;
in eqn. (1) were
n=o
data to
3
Values of Ayj (n = O-2), etc., parameters in eqn. (1) for various i + j, j + k and k + i binary mixtures, together with An,k (n = O-2) p arameters for i + ,j + k mixtures and standard deviations a(
Parameters n=O
Methylenebromide (i)+ pyridine ( j)+ P-picoline (k) Pyridine (i) + P-picoline ( j) + cyclohexane (k) Benzene ( i) + toluene ( j) + 1,2-dichloroethane (k) Benzene (i) + o-xylene ( j)+ 1,2-dichloroethane (k) Benzene (i) + p-xylene ( j) + 1,2-dichloroethane (k) Methylenebromide (i)+ pyridine ( j) Methylenebromide (i)+ /3-picoline (j) Pyridine (i) + P-picoline ( j) Pyridine (i) + cyclohexane (k) P-Picoline ( j)+ cyclohexane (k) Benzene (i) + toluene ( j) a Benzene (i) + 1,2-dichloroethane ( j) b Benzene( i ) + o-xylene ( j) a o-Xylene ( j) + 1,2-dichloroethane (k b, Benzene (i) + p-xylene ( j) ’ p-Xylene ( j) + 1,2-dichloroethane (k) Toluene ( j)+ l,Zdichloroethane (k) b a Nigam et al. (1979). b Singh and Sharma (1983).
e (Y,“,) (cm3 mol-‘)
Ayj, AyJk, etc. n=l
n=2
- 0.7807
1.1055
- 39.9144
0.001
- 1.4904
10.4610
86.3290
0.002
- 0.1570
- 0.7538
20.0000
0.001
0.2715
- 1.2838
0.4110
0.0004
14.4241
0.002 0.0018
- 0.1220
- 2.58
1.2200
0.0900
0.0380
1.3800
0.3580
- 0.1440
0.003
0.1560 2.200 2.4400 0.3360 0.907
0.0120 - 1.0110 - 1.2500 Q.0001 - 0.045
- 0.1000 - 0.2060 0.6750 - 0.1313 0.134
0.0007 0.0014 0.0026 0.0005 0.002
1.0600 1.166
0.0500 -0.33
- 0.1875 - 0.085
0.001 0.003
0.8400 1.013
0.1625 - 0.422
-0.1875 - 0.01
0.001 0.003
0.665
- 0.208
- 0.057
0.002
339
by the method of least squares, and are recorded standard deviations a( I,$,“,) defined as
in Table 3 together
with
where WI is the number of data points and p the number of adjustable parameters in eqn. (1). The parameters A:,, A,yk and Ayk, etc., for the i + j, j + k and k + i binary mixtures were taken from the literature (Nigam et al., 1979; Singh and Sharma, 1983). DISCUSSION
We are unaware of any previous l?f; data with which to compare the present results for i +j + k mixtures. The q,,E data for the ternary mixtures were first analysed (Singh and Sharma, 1983) using the Lacombe and Sanchez (1976a,b) theory of classical fluids and their mixtures. However, it was observed that the right-hand side of the equation of state (eqn. (34a) in Lacombe and Sanchez, 1976(b) varied from 0.010 to 0.051 for the various binary mixtures. Since the i + j, j + k and i -I- k mixtures thus do not satisfy the equation of state for binary mixtures, it follows that the resulting i +j + k ternary mixture would also not satisfy the equation of state. Thus y.fk values evaluated in the manner originally proposed by Lacombe and Sanchez, 1976(b) would not compare well with the corresponding experimental values. The equation of state for a ternary mixture has been shown (Singh and Sharma, 1983) to be given by
= 4 [CR.H.S.
of the equation
of state for i + j, j + k and i + k mixtures]
where 3, jk and cTjk have the same significance as explained earlier (Singh and Sharma, 1983). Once this equation of state for a ternary mixture has been established, pZjk and hence q$ for the mixture at any composition and temperature can be evaluated readily. yk values thus obtained for the various ternary mixtures are recorded in Table 2, where they are also compared with the corresponding experimental values. Examination of Table 2, however, reveals that while the KY, values calculated at 298.15 K compare well with the corresponding experimental values for benzene (i) + o-xylene ( j) + 1,2-dichloroethane (k) and benzene (i) + p-xylene ( j) + 1,2-d’KZ hl oroethane (k) mixtures, the same is not true of the remaining ternary mixtures. In some cases even the sign is not predicted correctly. A possible reason for this failure may be the assumption that the
340
right-hand side of eqn. (11) for the i +j, j + k and i + k binary mixtures comprising the i +j + k mixture is constant over the entire range of x,, x, and xk at the given temperature. Nevertheless, the theory makes a significant theoretical attempt to evaluate yFk data for ternary mixtures of nonelectrolytes from a knowledge of their binary interaction coefficients. The yyk data for the various ternary mixtures were then analysed (Singh and Sharma, 1983) in terms of the graph-theoretical approach (Singh et al., 1981). yFk according to this approach is given by
(4 where CX,,~is a constant characteristic of the i +j + k mixture and is assumed to be independent of composition, and xi, etc., are the mole fractions of the ith, etc., components in the mixture. The term 3
where S,, S,, S, and a,, etc., denote the degrees of the 1th, m th, n th and oth, etc., vertices of the graph for the ith molecule (Graovac et al., 1977) and were evaluated in the manner described earlier (Singh et al., 1981). Evaluation of vTk for a ternary mixture thus requires a knowledge of (Y;,~ for the mixture. The latter was shown (Singh and Sharma, 1983) to be given bY a
(6)
a,j+aJk+a,k]
so that eqn. (4) reduces
to
(7) Thus, from a knowledge of the binary interaction coefficients (Y,~,tiJk and CQ for the i +j, j + k and i + k binary mixtures, rFk for a ternary i +j + k mixture can be evaluated readily if 3,$i parameters for the constituent molecules are known. Since pyridine and /3-picoline undergo reactions that are characteristic of the aromatic ring (disregarding the basic nature of these compounds for the present analysis), and as their molar volumes are almost the same ( - 10% lower) as those of benzene and toluene, the 3[i parameters for pyridine and P-picoline were taken as those for benzene and toluene, respectively (Singh et al., 1981). However, such an approach can be highly restrictive, and Singh (1983) has recently advocated the use of 6” (valence 6, which reflects explicitly the valency of the atoms forming the bonds) rather than S to evaluate 3,$iin calculating HE and VE for binary mixtures of nonelectrolytes. In the present analysis we thus evaluated ‘6, parameters for the constituent
341
molecules of the ternary mixtures using both these approaches and then utilised both sets of results to calculate vFk data for the mixtures. The yyk values thus obtained are recorded in Table 2 ( vFA values obtained from eqn. (4) using 3c, parameters evaluated from 6 are enclosed in parentheses), where they are also compared with the corresponding experimental values. Examination of Table 2 reveals that although the calculated r,“,(S) values predict the signs of the experimental v$ values correctly, the quantitative agreement is dictated by xi, xi and xk for all except the pyridine (i) + /3picoline (j) + cyclohexane(k) mixture. For the latter mixture, the V,Tk(6) values compare reasonably well with the corresponding experimental values. The failure of this approach (Singh, 1983) in describing the yyk data for all except the pyridine (i) + /I-picoline ( j) + cyclohexane (k) mixture may be attributed to the involvement of either the T-electron clouds of pyridine, /3-picoline and the aromatic hydrocarbons, or of the atoms in them, or both, with methylenebromide or 1,2-dichloroethane in the corresponding i +j + k mixtures. This would mean that when the r-electron clouds of pyridine, P-picoline or aromatic hydrocarbons are involved in molecular interactions in ternary mixtures with methylenebromide or 1,2-dichloroethane, it is the C-C skeleton rather than the valency of an individual atom in the molecular “graph” that determines the r,“, value. In such a case y,“,( 6) values should describe the experimental V;yAdata for the mixture well. On the other hand, when (depending upon xi, xi, xk) individual atoms in a molecule are involved in molecular interactions, y,“k values evaluated from eqn. (4) employing 6’ considerations for the constituent molecules should be more appropriate. When both of these factors are involved in molecular interactions, each will make a contribution (depending upon its relative magnitude) to the measured V,,“kvalues. The present r,:. (T = 298.15 K, xixi) data were next utilised (Singh and Sharma, 1983) to evaluate, via the Mayer-McMillan formalism (Desnoyers et al., 1976), y.kr f& and y.kk volume interaction coefficients for thejth and k th moieties of i +j + k mixtures in the presence of the i th species. These coefficients at 298.15 K are recorded in Table 4. Examination of Table 4 reveals that while the yik interaction coefficients for 1,2-dichloroethane (k) with toluene, o-xylene and p-xylene (j) in the presence of benzene vary as o-xylene < p-xylene < toluene, the V+ interaction coefficients for pyridine (j) with /3-picoline (k) in the presence of methylenebromide and cyclohexane in methylenebromide ( i ) + pyridine ( j) + /3-picoline (k) and cyclohexane (i) + pyridine ( j) + P-picoline (k) mixtures at 298.15 K vary as methylenebromide < cyclohexane. The variation of the l/;k interaction coefficients for 1,2-dichloroethane with toluene, o-xylene and p-xylene in the presence of benzene is understandable, since preliminary NMR studies (Singh and Sharma, 1984) of benzene + 1,2-dichloroethane
342
mixtures have suggested the presence molecular complex having the following w \
Cl
of a 1 : l-contact, geometry:
charge-transfer
CL
/,
c-c
/
\
‘\
/’
Ii \
,
63
Such a scheme of molecular interactions would suggest that the presence of two -CH, substituents in the aromatic ring should cause xylene to interact more strongly with 1,2-dichloroethane. However, there would also be increased steric repulsion between the bulky CH, substituents on xylene and the chlorine atom of 1,2-dichloroethane. Again, the presence of benzene in 1,2-dichloroethane + xylene mixtures should also give rise to weak repulsive interactions between benzene and xylene. In order to minimise steric repulsion between its -CH, substituents and the chlorine atom of 1,2-dichloroethane on the one hand and benzene on the other, the xylene molecule may orient itself in such a way that its -CH, substituents lie farther away from the chlorine atom of 1,2-dichloroethane. In that event it would be the r-electron-donating ability of the aromatic hydrocarbon that would determine the extent of molecular interaction with 1,2-dichloroethane. This would mean that in the presence of benzene, o-xylene, p-xylene and toluene would interact with 1,2-dichloroethane in the order o-xylene > p-xylene > toluene. The & coefficients at 298.15 K for benzene (i) + toluene (j) + 1,2dichloroethane, benzene (i) + p-xylene ( j) + 1,2-dichloroethane (k) and benzene (i) + o-xylene ( j) + 1,2-dichloroethane (k) mixtures indeed support this conjecture.
TABLE
4
Self- and cross-volume
interaction
coefficients
at 298.15 K v/,k 4.5531
V/kk 1.0476
3.26
3.66
VIk - 4.3943
7.48
8.35
- 1.4026
0.9482
0.1667
P-picoline (k) Benzene (i)+ toluene (j)+
0.685
2.32
0.1972
- 0.1293
0.0912
1,2-dichloroethane (k) Benzene (i)+ o-xylene ( j)+
2.34
2.32
-0.2177
- 0.0342
0.2095
1,2-dichloroethane (k) Benzene (i) + p-xylene ( j) +
2.105
2.32
- 0.0587
- 0.1652
0.2667
Vkk
System Methylenebromide
(i)+
pyridine ( j) + P-picoline Cyclohexane (i) + pyridine
1,2-dichloroethane
(k)
(k)
( j)+
343
Again, preliminary NMR studies of methylenebromide + fi-picoline mixtures (Singh and Sharma, 1984) have indicated that the methylenebromide protons are de-shielded in the presence of /?-picoline. This suggests the presence of the following 1 : 1 molecular complex in this mixture: The addition of pyridine to methylenebromide + /3-picoline mixtures should then cause pyridine to approach either the electron-deficient end of /?-picoline or the proton of methylenebromide. Such a scheme of molecular interaction would suggest that pyridine should interact more strongly with P-picoline in the presence of methylenebromide than in the presence of cyclohexane. The v/k coefficients for methylenebromide (i) + pyridine( j) + /3-picoline (k) and cyclohexane (i) + pyridine ( j) + &picoline (k) mixtures fully support such a conjecture. Further, since in cyclohexane ( i) + pyridine ( j) + P-picoline (k) mixtures it is the individual atoms in the various molecular moieties which are involved in molecular interactions, it appears that any approach that takes into consideration the valency of individual atoms in a moiety should be successful in describing <:A data for these mixtures. The fact that the r/;yk data for this mixture as evaluated from eqn. (4), in which 3< values of the constituent moieties were evaluated utilising 6” considerations, compare well with the corresponding experimental values lends further support to the qualitative treatment of v-Fk data in terms of the graph-theoretical approach. ACKNOWLEDGEMENT
One of us (S.P.S.) thanks Senior Research Fellowship.
the C.S.I.R.,
New Delhi,
for the award
LIST OF SYMBOLS
xi, etc. Ayj,
etc.
m
P VE yjj
V <:k
'kk
mole fraction of i adjustable parameters (eqn. (1)) number of data points number of parameters in eqn. (1) molar excess volume (cm3 mol-l) self-interaction coefficients between j, j or k, k volume interaction coefficients between j and k volume interaction coefficients between j, j and k volume interaction coefficients between j, k and k connectivity parameter of third degree for i
of a
344
REFERENCES Brown, I. and Smith, F., 1962. Volume changes on mixing. I. Alcohol + benzene solutions. Aust. J. Chem., 15: 1-6. Coulson, E.A., Hales, J.L. and Herington, E.F.G., 1948. Fraction distillation. II. Dilute solutions of thiophene in C,H, as test mixtures and a comparison with mixtures of C,H, and C,H,Cl,. Trans. Faraday Sot., 44: 636-642.. Desnoyers, J.E., Perron, G., Avedikian, L. and Morel, J.P., 1976. Enthalpies of the urea-tertbutanol-water system at 25 ‘C. J. Solution Chem., 5: 631-640. Forziati, A.F., Glasgow, A.R., Jr., Willingham, C.B. and Rossini, F.D., 1946. Purification and properties of 29 paraffin, 4 alkylcyclopentane, 10 alkylcyclohexane and 8 alkylbenzene hydrocarbons. J. Res., Natl. Bur. Stand. (U.S.), 36: 129-139. Graovac, A., Gutman, I. and Trinajstic, N., 1977. Topological Approach to the Chemistry of Conjugated Molecules. Lecture Notes in Chemistry, Vol. 4, Springer, Berlin. Kier, L.B., 1980, in S.H. Yalkowski, A.A. Sinkula and SC. Valvani (Eds.), Physical Chemical Properties of Drugs. Dekker, New York, Chap. 9, 277-318. Lacombe, R.H. and Sanchez, I.C., 1976a. An elementary molecular theory of classical fluids: pure fluids. J. Phys. Chem., 80: 2352-2362. Lacombe, R.H. and Sanchez, I.C., 1976b. Statistical thermodynamics of fluid mixtures. J. Phys. Chem., 80: 2568-2580. Nigam, R.K., Singh, P.P., Ruchi, M. and Singh, M., 1979. Excess volumes of mixing of 1,2-dichloroethane and aromatic hydrocarbons. Thermochim. Acta, 34: 275-280. Rochdestwensky, M., Pukirew, A. and Maslova, M., 1935. Pyridine from pyridine bases. Trans. Inst. Pure Chem. Reagents (Moscow), 14: 58-61. Singh, P.P., 1983. Topological aspects of the effect of temperature and pressure on the thermodynamics of binary mixtures of nonelectrolytes. Thermochim. Acta, 66: 37-73. Singh, P.P. and Sharma, V.K., 1983. Thermodynamics of ternary mixtures of non-electrolytes: molar excess volumes. Can. J. Chem., 61: 2321-2328. Singh, P.P. and Sharma, S.P., 1984. Thermodynamics of binary mixtures of non-electrolytes. Indian J. Chem., in press. Singh, J., Pflug, H.D. and Benson, G.C., 1968. Molar excess enthalpies and volumes of benzene isomeric xylene systems at 25 O. J. Phys. Chem., 72: 1939-1944. Singh, P.P., Nigam, R.K., Singh, KC. and Sharma, V.K., 1981. Topological aspects of the thermodynamics of binary mixtures of non-electrolytes. Thermochim. Acta, 46: 175-190. Timmermans, J., 1950. Physico-Chemical Constants of Pure Organic Compounds. Elsevier, Amsterdam, p. 216. Vogel, A.I., 1978. Textbook of Practical Organic Chemistry. 41h edn. English Language Book Society/Longmans, London. a) 266 b) 267 c) 277 d) 3’d edn. p. 300. Williams, J.W. and Krchma, I.J., 1927. The dielectric constants of binary mixtures. II. The electric moments of certain organic molecules in benzene solution. J. Am. Chem. Sot., 49: 1676-1686.
Science
18 (lY84) 333-344
Publishers
MOLAR EXCESS VOLUMES NONELECTROLYTES P.P. SINGH
Department (Received
*, R.K.
NIGAM,
of Chemistry, January
333
B.V., Amsterdam
-
OF TERNARY
S.P. SHARMA
Muharshi Dayanand
6th, 1984;
Printed
accepted
in final
in The Netherlands
MIXTURES
and SADHNA
AGGARWAL
lJniuersit_y, Rohtak form
OF
May 22nd.
(India) 1984)
ABSTRACT Singh, P.P., Nigam, ternary mixtures
R.K., Sharma, of nonelectrolytes.
S.P.
and
Aggarwal,
S., 1984.
Fluid Phose Equilibria,
Molar
excess
volumes
of
18: 333-344.
Molar excess volumes [Fk of methylenebromide( i) + pyridine( j) + P-picoline (k), cyclohexane( i ) + pyridine( j)+ &picoline( k), benzene( i ) + toluene( j) + 1,2-dichloroethane( k), benzene(i) + o-xylene( j) + 1,2-dichloroethane( k) and benzene( i) + p-xylene( j) + 1.2dichloroethane( k) mixtures have been determined dilatometrically at 298.15 K. The data have been examined and it is found coefficients molecular these
in terms of Sanchez and Lacombe theory and the graph-theoretical that they are described well by the latter. Self- and cross-volume
vJk, I& interactions
approach, interaction
and the values utilised to study and VJkk, etc., have also been evaluated between the j th and k th molecular species in the presence of the i th in
i + j + k mixtures.
INTRODUCTION
In a binary i +j mixture, i - i andj -j contacts in the pure components i andj are replaced by i -j contacts in the mixture. If interactions in a ternary i +j + k mixture are assumed to be closely dependent on the interactions in the constituent i +j, j + k and k + i mixtures, it should be possible to evaluate thermodynamic excess functions for ternary mixtures of nonelectrolytes when the corresponding functions for the binary i +j, j + k and k + i mixtures are known, Singh and Sharma (1983) recently employed a graph-theoretical approach that utilises connectivity parameters of the third degree, 3<,, to describe successfully the molar excess volumes V” of ternary mixtures of nonheterocyclic nonelectrolytes. Furthermore, the Lacombe and Sanchez (1976a,b) theory of fluid mixtures also suggests that the thermodynamic properties of ternary mixtures of nonelectrolytes are determinable from the corresponding * Author
to whom
0378-3812/84/$03.00
correspondence
should
0 1984 Elsevier
be addressed.
Science Publishers
B.V.
334
properties of the constituent binary mixtures. This prompted us to study further the molar excess volumes rFk of some ternary mixtures of nonelectrolytes and analyse the data in terms of (i) the graph-theoretical approach and (ii) the Lacombe and Sanchez theory of fluid mixtures. EXPERIMENTAL
Materials and methods Benzene, toluene, o- and p-xylene, pyridine, cyclohexane and &picoline (all B.D.H., Analar Grade) were purified by standard procedures (Vogel, 1978a, b, c). Methylenebromide. however,, was obtained from two different sources. One sample (Sojuzchimexport, Moscow) was purified by shaking with 5% sodium carbonate solution, followed by washing with distilled water, drying over anhydrous calcium chloride and then fractional distillation. The other sample of methylenebromide was synthesised from bromoform in the manner suggested by Vogel (Vogel, 1978d), and was finally purified by the same method as described above. These two samples of methylenebromide were stored in two separate amber-coloured bottles for subsequent use. The purity of the purified samples was checked by measuring their densities at 298.15 + 0.01 K, and these agreed well with the corresponding literature values, as is evident from Table 1. Molar excess volumes r,“k were determined in a dilatometer similar to that used by Brown and Smith (1962), the only difference being that there were now three limbs for the three components. The temperature of the water bath was controlled to within less than 50.01 K by means of a toluene regulator, and the change in level of the liquid in the dilatometer capillary was measured by a cathetometer that could be read to &O.OOI cm. Further,
TABLE
1
Densities
of purified
Compound
liquids
at 298.15 K
Density
Reference
(g cmp3)
Experimental
Literature
Methylenebromide Pyridine P-Picoline
2.45844 0.9778 0.95231
2.45849 0.9782 _
Timmermans (1950) Rochdestwensky et al. (1935) _
Cyclohexane Toluene o-Xylene Benzene p-Xylene 1,2-Dichloroethane
0.77389 0.86224 0.87588 0.87366 0.85665 1.24535
0.77389 0.86220 0.87583 0.87370 0.8567 1.24530
Forziati Forziati Forziati Singh et Williams Coulson
et al. (1946) et al. (1946) et al. (1946) al. (1968) and Krchma et al. (1948)
(1927)
335 TABLE
2
Comparison of V,,k values measured for various i + j + k ternary mixtures at 298.15 K, with corresponding V, ._, values evaluated from graph theory and Lacombe and Sanchez theory ’ (all LY’Sare in cm 1: molV’)
-r,
qFk(cm3
x1
Exp. Methyfenehromide(i)
+ pyridine(i)
mol-‘) Graph theory
Lacombe
and Sanchez theory
+ p - picoiine(k)
298..15 K = - 2.8705( - 9.1500), LY,~= -- 0.7340( - 4.8449). Q, = -- 36.2644( - 4.7321) 0.0018;7 0.064 0.095 (0.058) 0.283 0.050% 0.1149 0.8241 0.495 (0.071) 0.318 0.120 0.556 (0.099) 0.144 0.1306 0.4851 0.150 0.574 (0.073) 0.309 0.1309 0.7309 0.136 0.631 (0.098) 0.269 0.1646 0.6159 0.170 0.283 (0.151) 0.144 0.2068 0.1500 0.184 0.143 (1.007) 0.191 0.2141 0.184 0.0545 0.3141 0.3154 0.4031 0.4313
0.1618
0.5390 0.6419 0.7755 0.8066
0.3511 0.2861 0.1143 0.1011
0.8578 0.9317 0.9585
0.0931 0.0421 0.0217
Pyridine
(i) + j3 -picoline
0.5038 0.0765 0.2406
0.249 0.254 0.200 0.310 0.302 0.288 0.243 0.218 0.169 0.089 0.058
0.334 (0.200)
0.164
0.726 0.213 0.486 0.681
(0.147) (0.239) (0.216) (0.172)
0.204 0.116 0.164 0.176
0.607 (0.159) 0.294 (0.167)
0.208 0.238
0.264 0.239 0.115 0.062
0.218 0.3Q5 0.369 0.401
(j) + cyclohexane
(0.151) (0.107) (0.061) (0.042)
(k)
298.15
K = - 0.734 ( - 4.8449), (Y,k = - 7.8838 ( - 7.7793), Q, = -- 2.2118 (0.0) 0.108 (0.043) - 3.067 o.o:
0.2107
0.3293 0.3470 0.5284
0.0898 0.6238 0.2172 0.0432
0.594 0.621
0.401 (0.093) 0.420 (0.045)
0.115 0.360 0.211
0.0733
0.124
0.140 0.440 0.423 0.302
0.7901 0.8297
(0.118) (0.095) (0.024) (0.039)
- 1 .OOl - 1.451 1.559 0.274 0.799 1.1’74
336 TABLE 2 (continued) x,
x,
ryA (cm” mol-I) &P.
Graph theory
Lacombe and Sanchez theory
Benzene (i) + tofuene fj) + 1,2 - dichloroethane (k) 298.15 K 0.0?54 cy = - 2.2712 0.2215 (- 10.4352), 0.165a,, = - 0.323 168.1757 (- 2.2769), 0.117 IY~,= 4.5523 ( - 6.8100) (0.239) 0.0993 0.7957 0.111 0.457(0.151) 0.242
0.1079 0.1288 0.2238 0.2304 0.2936 0.2977 0.4661 0.6075 0.7303 0.8368 0.8396 0.8865 0.9071
0.2122 0.8030 0.1509 0.4799 0.5734 0.2799 0.0847 0.3341 0.0685 0.0832 0.0625 0.0685 0.0600
0.187 0.065 0.217 0.180 0.134 0.221 0.240 0.115 0.161 0.085 0.095 0.055 0.043
0.569(0.233) 0.106 0.538(0.066) 0.280 1.056(0.204) 0.080 0.961(0.191) 0.218 1.081(0.113) 0.252 1.238(0.210) 0.143 1.653(0.158) 0.038 1.355(0.062) -2.312 1.415(0.090) 0.097 0.051(0.973) 0.163 0.029tO.692) 0.201 0.023(0.577) 0.141 0.047(0.949) 0.152
Benzene(i)+ o-xylene (j) + 1,2-dichloroethane (k) 298.15K = -1.8315(-7.0882), a,, 0.&8 0.0898 0.181 0.1071 0.7500 0.193 0.1108 0.1847 0.274 0.1231 0.6186 0.274 0.2103 0.6679 0.244 0.2807 0.0652 0.255 0.3644 0.4932 0.312 0.2465 0.3732 0.346 0.3176 0.3953 0.351 0.0390 0.256 0.5146 0.5855 0.3157 0.284 0.7419 0.0616 0.199 0.8472 0.0928 0.134 0.8674 0.0526 0.117 0.8755 0.0730 0.112 0.8773 0.0400 0.108 0.9084 0.0616 0.083
aA, = -4.5523(-6.8100) 11.1328 (-2.1479), 0.204 0.088(0.233) 0.419 0.177(0.188) 0.263 0.141(0.348) 0.388 0.202(0.287) 0.197 0.288(0.188) 0.168 0.176(0.201) 0.386 0.407(0.216) 0.306 0.275(0.259) 0.331 0.373(0.276) 0.171 0.217(0.150) 0.378 0.46X(0.173) 0.079 0.240(0.109) 0.160 0.263(0.078) 0.136 0.189(0.063) 0.157 0.221(0.064) 0.129 0.163(0.056) 0.164 0.187(0.049)
337
X,
V,TA(cm3 mol-‘)
XI
Exp.
Lacombe
Graph theory
and Sanchez theory
Benzene (i) + p - xylene 0) + I,2 -dichIoroethane (k)
298.15K o.ok3= -2.1233 0.6737 (-8.5266), 0.191 (Y,~ = -28.9924 0.183 (-2.2635),a,,= 0.335 -4.5523(-6.8100) (0.252) 0.0819 0.3216 0.285 0.174(0.373) 0.234 0.0871 0.7933 0.126 0.262(0.167) 0.330 0.1070 0.3341 0.292 0.211(0.366) 0.244 0.1091 0.0618 0.164 0.143(0.168) 0.083 0.1802 0.4086 0.293 0.321(0.326) 0.273 0.4264 0.4763 0.242 0.626(0.152) 0.343 0.5090 0.2519 0.279 0.567(0.198) 0.250 0.5586 0.0856 0.268 0.447(0.164) 0.055 0.8020 0.0940 0.154 0.401(0.081) 0.235 0.8323 0.0774 0.135 0.354(0.069) 0.209 0.8440 0.0800 0.131 0.349(0.064) 0.229 0.8578 0.7740 0.114 0.334(0.059) 0.221 0.8860 0.0615 0.094 0.280(0.047) 0.221 0.9020 0.0480 0.082 0.238(0.041) 0.185 y.,“, values in parentheses are those calculated from the graph theoretical approach in which 3c values for the constituent moieties were evaluated from 8 considerations of the respective molecular graphs.
in order to ensure that the liquid in the capillary stem had the same composition as the bulk solution on mixing, after mixing the components the dilatometer was placed in a cold bath so that there was a minimum amount of liquid in the capillary and then replaced in the experimental water bath. This process was repeated two or three times. The uncertainty in the measured v$ values is - 0.55% at the most. RESULTS
The F,“k data for the various ternary i +j + k mixtures as a function of composition at 298.15 K are recorded in Table 2. These data were expressed (Singh and Sharma, 1983) as
0) [Ita~kb-xJ]+x;x,xkj i:A:;k(x,-xk)y]
+x*x/,
n=O
n-o
where X, and xj are the mole fractions of the i th and j th components i +j + k mixture, and Ayj (n = O-2), etc., are parameters characteristic
in the of the
338
binary i + j, etc. mixtures. evaluated by fitting
i
The A:+
(x+c,)“A;,
-xx/xk
1
(xi - xk)Ayk
TABLE
II
/x,xixk
(n = O-2)
I
parameters
I
(x,-x,)A.:;
;
in eqn. (1) were
n=o
data to
3
Values of Ayj (n = O-2), etc., parameters in eqn. (1) for various i + j, j + k and k + i binary mixtures, together with An,k (n = O-2) p arameters for i + ,j + k mixtures and standard deviations a(
Parameters n=O
Methylenebromide (i)+ pyridine ( j)+ P-picoline (k) Pyridine (i) + P-picoline ( j) + cyclohexane (k) Benzene ( i) + toluene ( j) + 1,2-dichloroethane (k) Benzene (i) + o-xylene ( j)+ 1,2-dichloroethane (k) Benzene (i) + p-xylene ( j) + 1,2-dichloroethane (k) Methylenebromide (i)+ pyridine ( j) Methylenebromide (i)+ /3-picoline (j) Pyridine (i) + P-picoline ( j) Pyridine (i) + cyclohexane (k) P-Picoline ( j)+ cyclohexane (k) Benzene (i) + toluene ( j) a Benzene (i) + 1,2-dichloroethane ( j) b Benzene( i ) + o-xylene ( j) a o-Xylene ( j) + 1,2-dichloroethane (k b, Benzene (i) + p-xylene ( j) ’ p-Xylene ( j) + 1,2-dichloroethane (k) Toluene ( j)+ l,Zdichloroethane (k) b a Nigam et al. (1979). b Singh and Sharma (1983).
e (Y,“,) (cm3 mol-‘)
Ayj, AyJk, etc. n=l
n=2
- 0.7807
1.1055
- 39.9144
0.001
- 1.4904
10.4610
86.3290
0.002
- 0.1570
- 0.7538
20.0000
0.001
0.2715
- 1.2838
0.4110
0.0004
14.4241
0.002 0.0018
- 0.1220
- 2.58
1.2200
0.0900
0.0380
1.3800
0.3580
- 0.1440
0.003
0.1560 2.200 2.4400 0.3360 0.907
0.0120 - 1.0110 - 1.2500 Q.0001 - 0.045
- 0.1000 - 0.2060 0.6750 - 0.1313 0.134
0.0007 0.0014 0.0026 0.0005 0.002
1.0600 1.166
0.0500 -0.33
- 0.1875 - 0.085
0.001 0.003
0.8400 1.013
0.1625 - 0.422
-0.1875 - 0.01
0.001 0.003
0.665
- 0.208
- 0.057
0.002
339
by the method of least squares, and are recorded standard deviations a( I,$,“,) defined as
in Table 3 together
with
where WI is the number of data points and p the number of adjustable parameters in eqn. (1). The parameters A:,, A,yk and Ayk, etc., for the i + j, j + k and k + i binary mixtures were taken from the literature (Nigam et al., 1979; Singh and Sharma, 1983). DISCUSSION
We are unaware of any previous l?f; data with which to compare the present results for i +j + k mixtures. The q,,E data for the ternary mixtures were first analysed (Singh and Sharma, 1983) using the Lacombe and Sanchez (1976a,b) theory of classical fluids and their mixtures. However, it was observed that the right-hand side of the equation of state (eqn. (34a) in Lacombe and Sanchez, 1976(b) varied from 0.010 to 0.051 for the various binary mixtures. Since the i + j, j + k and i -I- k mixtures thus do not satisfy the equation of state for binary mixtures, it follows that the resulting i +j + k ternary mixture would also not satisfy the equation of state. Thus y.fk values evaluated in the manner originally proposed by Lacombe and Sanchez, 1976(b) would not compare well with the corresponding experimental values. The equation of state for a ternary mixture has been shown (Singh and Sharma, 1983) to be given by
= 4 [CR.H.S.
of the equation
of state for i + j, j + k and i + k mixtures]
where 3, jk and cTjk have the same significance as explained earlier (Singh and Sharma, 1983). Once this equation of state for a ternary mixture has been established, pZjk and hence q$ for the mixture at any composition and temperature can be evaluated readily. yk values thus obtained for the various ternary mixtures are recorded in Table 2, where they are also compared with the corresponding experimental values. Examination of Table 2, however, reveals that while the KY, values calculated at 298.15 K compare well with the corresponding experimental values for benzene (i) + o-xylene ( j) + 1,2-dichloroethane (k) and benzene (i) + p-xylene ( j) + 1,2-d’KZ hl oroethane (k) mixtures, the same is not true of the remaining ternary mixtures. In some cases even the sign is not predicted correctly. A possible reason for this failure may be the assumption that the
340
right-hand side of eqn. (11) for the i +j, j + k and i + k binary mixtures comprising the i +j + k mixture is constant over the entire range of x,, x, and xk at the given temperature. Nevertheless, the theory makes a significant theoretical attempt to evaluate yFk data for ternary mixtures of nonelectrolytes from a knowledge of their binary interaction coefficients. The yyk data for the various ternary mixtures were then analysed (Singh and Sharma, 1983) in terms of the graph-theoretical approach (Singh et al., 1981). yFk according to this approach is given by
(4 where CX,,~is a constant characteristic of the i +j + k mixture and is assumed to be independent of composition, and xi, etc., are the mole fractions of the ith, etc., components in the mixture. The term 3
where S,, S,, S, and a,, etc., denote the degrees of the 1th, m th, n th and oth, etc., vertices of the graph for the ith molecule (Graovac et al., 1977) and were evaluated in the manner described earlier (Singh et al., 1981). Evaluation of vTk for a ternary mixture thus requires a knowledge of (Y;,~ for the mixture. The latter was shown (Singh and Sharma, 1983) to be given bY a
(6)
a,j+aJk+a,k]
so that eqn. (4) reduces
to
(7) Thus, from a knowledge of the binary interaction coefficients (Y,~,tiJk and CQ for the i +j, j + k and i + k binary mixtures, rFk for a ternary i +j + k mixture can be evaluated readily if 3,$i parameters for the constituent molecules are known. Since pyridine and /3-picoline undergo reactions that are characteristic of the aromatic ring (disregarding the basic nature of these compounds for the present analysis), and as their molar volumes are almost the same ( - 10% lower) as those of benzene and toluene, the 3[i parameters for pyridine and P-picoline were taken as those for benzene and toluene, respectively (Singh et al., 1981). However, such an approach can be highly restrictive, and Singh (1983) has recently advocated the use of 6” (valence 6, which reflects explicitly the valency of the atoms forming the bonds) rather than S to evaluate 3,$iin calculating HE and VE for binary mixtures of nonelectrolytes. In the present analysis we thus evaluated ‘6, parameters for the constituent
341
molecules of the ternary mixtures using both these approaches and then utilised both sets of results to calculate vFk data for the mixtures. The yyk values thus obtained are recorded in Table 2 ( vFA values obtained from eqn. (4) using 3c, parameters evaluated from 6 are enclosed in parentheses), where they are also compared with the corresponding experimental values. Examination of Table 2 reveals that although the calculated r,“,(S) values predict the signs of the experimental v$ values correctly, the quantitative agreement is dictated by xi, xi and xk for all except the pyridine (i) + /3picoline (j) + cyclohexane(k) mixture. For the latter mixture, the V,Tk(6) values compare reasonably well with the corresponding experimental values. The failure of this approach (Singh, 1983) in describing the yyk data for all except the pyridine (i) + /I-picoline ( j) + cyclohexane (k) mixture may be attributed to the involvement of either the T-electron clouds of pyridine, /3-picoline and the aromatic hydrocarbons, or of the atoms in them, or both, with methylenebromide or 1,2-dichloroethane in the corresponding i +j + k mixtures. This would mean that when the r-electron clouds of pyridine, P-picoline or aromatic hydrocarbons are involved in molecular interactions in ternary mixtures with methylenebromide or 1,2-dichloroethane, it is the C-C skeleton rather than the valency of an individual atom in the molecular “graph” that determines the r,“, value. In such a case y,“,( 6) values should describe the experimental V;yAdata for the mixture well. On the other hand, when (depending upon xi, xi, xk) individual atoms in a molecule are involved in molecular interactions, y,“k values evaluated from eqn. (4) employing 6’ considerations for the constituent molecules should be more appropriate. When both of these factors are involved in molecular interactions, each will make a contribution (depending upon its relative magnitude) to the measured V,,“kvalues. The present r,:. (T = 298.15 K, xixi) data were next utilised (Singh and Sharma, 1983) to evaluate, via the Mayer-McMillan formalism (Desnoyers et al., 1976), y.kr f& and y.kk volume interaction coefficients for thejth and k th moieties of i +j + k mixtures in the presence of the i th species. These coefficients at 298.15 K are recorded in Table 4. Examination of Table 4 reveals that while the yik interaction coefficients for 1,2-dichloroethane (k) with toluene, o-xylene and p-xylene (j) in the presence of benzene vary as o-xylene < p-xylene < toluene, the V+ interaction coefficients for pyridine (j) with /3-picoline (k) in the presence of methylenebromide and cyclohexane in methylenebromide ( i ) + pyridine ( j) + /3-picoline (k) and cyclohexane (i) + pyridine ( j) + P-picoline (k) mixtures at 298.15 K vary as methylenebromide < cyclohexane. The variation of the l/;k interaction coefficients for 1,2-dichloroethane with toluene, o-xylene and p-xylene in the presence of benzene is understandable, since preliminary NMR studies (Singh and Sharma, 1984) of benzene + 1,2-dichloroethane
342
mixtures have suggested the presence molecular complex having the following w \
Cl
of a 1 : l-contact, geometry:
charge-transfer
CL
/,
c-c
/
\
‘\
/’
Ii \
,
63
Such a scheme of molecular interactions would suggest that the presence of two -CH, substituents in the aromatic ring should cause xylene to interact more strongly with 1,2-dichloroethane. However, there would also be increased steric repulsion between the bulky CH, substituents on xylene and the chlorine atom of 1,2-dichloroethane. Again, the presence of benzene in 1,2-dichloroethane + xylene mixtures should also give rise to weak repulsive interactions between benzene and xylene. In order to minimise steric repulsion between its -CH, substituents and the chlorine atom of 1,2-dichloroethane on the one hand and benzene on the other, the xylene molecule may orient itself in such a way that its -CH, substituents lie farther away from the chlorine atom of 1,2-dichloroethane. In that event it would be the r-electron-donating ability of the aromatic hydrocarbon that would determine the extent of molecular interaction with 1,2-dichloroethane. This would mean that in the presence of benzene, o-xylene, p-xylene and toluene would interact with 1,2-dichloroethane in the order o-xylene > p-xylene > toluene. The & coefficients at 298.15 K for benzene (i) + toluene (j) + 1,2dichloroethane, benzene (i) + p-xylene ( j) + 1,2-dichloroethane (k) and benzene (i) + o-xylene ( j) + 1,2-dichloroethane (k) mixtures indeed support this conjecture.
TABLE
4
Self- and cross-volume
interaction
coefficients
at 298.15 K v/,k 4.5531
V/kk 1.0476
3.26
3.66
VIk - 4.3943
7.48
8.35
- 1.4026
0.9482
0.1667
P-picoline (k) Benzene (i)+ toluene (j)+
0.685
2.32
0.1972
- 0.1293
0.0912
1,2-dichloroethane (k) Benzene (i)+ o-xylene ( j)+
2.34
2.32
-0.2177
- 0.0342
0.2095
1,2-dichloroethane (k) Benzene (i) + p-xylene ( j) +
2.105
2.32
- 0.0587
- 0.1652
0.2667
Vkk
System Methylenebromide
(i)+
pyridine ( j) + P-picoline Cyclohexane (i) + pyridine
1,2-dichloroethane
(k)
(k)
( j)+
343
Again, preliminary NMR studies of methylenebromide + fi-picoline mixtures (Singh and Sharma, 1984) have indicated that the methylenebromide protons are de-shielded in the presence of /?-picoline. This suggests the presence of the following 1 : 1 molecular complex in this mixture: The addition of pyridine to methylenebromide + /3-picoline mixtures should then cause pyridine to approach either the electron-deficient end of /?-picoline or the proton of methylenebromide. Such a scheme of molecular interaction would suggest that pyridine should interact more strongly with P-picoline in the presence of methylenebromide than in the presence of cyclohexane. The v/k coefficients for methylenebromide (i) + pyridine( j) + /3-picoline (k) and cyclohexane (i) + pyridine ( j) + &picoline (k) mixtures fully support such a conjecture. Further, since in cyclohexane ( i) + pyridine ( j) + P-picoline (k) mixtures it is the individual atoms in the various molecular moieties which are involved in molecular interactions, it appears that any approach that takes into consideration the valency of individual atoms in a moiety should be successful in describing <:A data for these mixtures. The fact that the r/;yk data for this mixture as evaluated from eqn. (4), in which 3< values of the constituent moieties were evaluated utilising 6” considerations, compare well with the corresponding experimental values lends further support to the qualitative treatment of v-Fk data in terms of the graph-theoretical approach. ACKNOWLEDGEMENT
One of us (S.P.S.) thanks Senior Research Fellowship.
the C.S.I.R.,
New Delhi,
for the award
LIST OF SYMBOLS
xi, etc. Ayj,
etc.
m
P VE yjj
V <:k
'kk
mole fraction of i adjustable parameters (eqn. (1)) number of data points number of parameters in eqn. (1) molar excess volume (cm3 mol-l) self-interaction coefficients between j, j or k, k volume interaction coefficients between j and k volume interaction coefficients between j, j and k volume interaction coefficients between j, k and k connectivity parameter of third degree for i
of a
344
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