R. P. RASTOGI, J. NATH,AND J. MISRA
2524
Thermodynamics of Weak Interactions in Liquid Mixtures. 11. Mixtures
of Carbon Tetrachloride, Benzene, o-Xylene, and rn-Xylene
by R. P. Rastogi, Jagan Nath, and J. Misra Chemistry Departmenl, Gorakhpur University, Gorakhpur (U.P.), India
(Received December 21 1966)
Volume changes on mixing and heats of mixing have been measured for carbon tetrachlorideo-xylene, carbon tetrachloride-m-xylene, benzene-0-xylene, and benzene-m-xylene at different temperatures. The total vapor pressures for mixtures of carbon tetrachloride with o-xylene and m-xylene have also been measured at 0” and the values of GE have been derived from these. The results for VE, HE,GE, and TSE have been analyzed in the light of current theories of solutions, especially those of Prigogine and Flory. Analysis shows that the contributions of the dipolar effects due to xylenes to the excess functions are small. The inversion of sign in the case of volume of mixing for carbon tetrachlorideo-xylene with increasing concentration of carbon tetrachloride is not predicted by any theory. Quantitative and sometimes qualitative agreement between theories and experiment is poor. An examination of the partial molal volumes of carbon tetrachloride a t high dilution in the aromatics indicates the increasing tendency of interaction with the aromatic hydrocarbons as the number of CH3 substituents in the ring is increased. The measurements of dielectric constants and molar polarizations for mixtures of carbon tetrachloride with 0- and m-xylenes have also been made. It is concluded that specific interaction exists between aromatics and carbon tetrachloride.
plexes of carbon tetrabromide with all the three xylenes Introduction have been reported.? It is clear that the ionization Recently,’ it has been pointed out that the stability potentialS of the aromatics would favor the increasing of the new species formed from carbon tetrachloride interaction of aromatics with carbon tetrachloride, and aromatics will be favored by the increasing numas the number of CH3 substituents in the benzene ber of CH, substituents in the benzene ring and the ring is increased, because we expect the Lewis acidview has been supported from measurements of therbase type of interaction to be present in these systems, modynamic properties2 and dielectric constants2 of binary mixtures of carbon tetrachloride with benzene, toluene, and p-xylene. Recent measurements of heats (1) J. H. Hildebrand and R. L. Scott, “Regular Solutions,” Prenticeof mixing of mixtures of carbon tetrachloride with Hall, Inc., Englewood Cliffs, N. J., 1962. (2) R. P.Rastogi, J. Nath, and J. Misra, J. Phys. Chem., 71, 1277 methyl-substituted pyridines have also been interpreted (1967). in terms of increasing interaction of carbon tetrachlo(3) K. W. Morcom and D. N. Travers, Trans. Faraday Soc., 6 2 , ride with pyridine derivatives, as the number of CH3 2063 (1966). substituents in the base molecule is increased.a The (4) R. Anderson and J. M. Prausnitz, J. Chem. Phys., 39, 1225 (1963). evaluation of the equilibrium constants for the forma(5) I. D. Watson and A. G. Williamson, J . Sci. Ind. Res. (India), tion of l :l species of carbon tetrachloride with benzene 24, 615 (1965). and mesitylene from spectrophotometric measurements (6) J. B. Ott, J. R. Goates, and A. H. Budge, J. Phys. Chem., 66, also gives evidence in support of this b e h a ~ i o r . ~ , ~1387 (1962). (7) J. E. Clark and R. V. Luthy, Ind. Eng. Chem., 47, 250 (1955). However, the solid-liquid equilibrium studiese do not (8) L. J. Andrews and R. M. Keefer, “hlolecular Complexes in show the existence of any such species of carbon Organic Chemistry,” Holden-Day, Inc., Amsterdam, The Nethertetrachloride with 0- and m-xylenes,6 though the comlands, 1964, p 28. The Journal of Physical Chemistry
2525
THERMODYNAMICS OF WEAKINTERACTIONS I N LIQUID MIXTURES
Table I: Excess Volumes for Various Systems -Carbon tetrachlorideo-xyleneMole fraction VE, of CClr cc/mole
. -Carbon
tetrachloride-m-xyleneMole fraction VE, of CClr cc/mole
Temp, 10" 0.1343 +0.009 0.2318 $0.013 0.3527 +0.012 0.5111 -0.002 0,8247 -0.013 0.8612 -0.008 0.9067 -0.006
Temp, 10" 0.2058 0.048 0.3058 0.074 0.4478 0.094 0.5675 0,098 0.5994 0.093 0.6900 0,086 0.8812 0.028
Temp, 20" 0.1256 +o, 009 0,1803 + O . 016 0,2803 +O. 014 0,5317 -0.003 0.8115 -0.013 0.8667 -0,011 0.9051 -0.008
Temp, 20" 0,1657 0.036 0.3195 0,076 0.4103 0.094 0.4301 0.099 0.5314 0,099 0.8040 0.060 0.8456 0.044
Temp, 30 0.1794 +0.010 0.2319 +0.015 0.2596 0,015 0.3025 +0.014 0.3639 $0.008 0.4055 +0.003 0.5312 -0.005 0.6138 -0.008 0,7310 -0.012 0.7578 -0.015 0.7800 -0.013 0.8390 -0,009
Temp, 30" 0.2172 0.052 0.3085 0.082 0.4213 0.097 0.5134 0,100 0.5975 0.096 0.6423 0.095 0.7433 0.073 0.8700 0.032
O
+
the aromatic hydrocarbon acting as the electron donor and the carbon tetrachloride as the electron acceptor. Hence, it was thought worthwhile to undertake the investigation of the thermodynamic properties and dielectric constants of mixtures of carbon tetrachloride with 0- and m-xylenes and to see if these give any information at all regarding the interaction between the two components of the mixtures in each case. The values of HE and VE for mixtures of benzene with oand m-xylenes have also been measured.
Experimental Section Materials and Their PuriJicalim. (i) Benzene and carbon tetrachloride were purified in a similar manner as described earlier.2 (ii) +Xylene and m-xylene, obtained from the British Drug Houses, were freed from thiophene as described earlier.g The -samples so obtained were washed with water followed by subsequent washings with sodium carbonate solution and distilled water. These were then throughly dried over anhy-
-Benzene-o-xylenMole fraction of o-xylene
--Benzene-m-xyleneMole fraction VE, of m-xylene cc/mole
c
VE, cc/mole
Temp, 30" 0.1466 0.086 0.2560 0.161 0.4523 0.220 0.5511 0.219 0.6822 0.183 0.7433 0.143 0.8607 0.086
Temp, 30" 0.0750 0.051 0.1244 0,098 0.2000 0.160 0.2700 0.202 0.4630 0.269 0.4737 0.273 0.5929 0.245 0.7732 0.138 0.8651 0,074
drous calcium chloride and distilled fractionally several times. Experimental Procedure. (i) Volume of Mixing. The dilatometric mixing vessel used during the present investigation was essentially the same as described It consisted of two glass bulbs separated earlier.2~10~11 by a bent glass tubing and a glass capillary (having a uniform bore) which was attached to one of the bulbs. The liquids to be mixed were placed in the two bulbs and separated by means of mercury in the bent tubing. The mixing of the liquids was brought about by tilting the vessel and the change in volume on mixing was ascertained by following the position of the liquid meniscus in the capillary with a cathetometer (least
(9) R. P. Rastogi and R. K . Nigam, Tram. Faraday Soc., 55, 2005 (1959). (10) R. P. Rastogi and J. Nath, Indian. J . Chem., in press. (11) J. Nath, Ph.D. Thesis, Gorakhpur University, 1965.
Volume 71, Number 8
J u l y 1967
R. P. RASTOGI, J. NATH, AND J. MISRA
2526
Table 11 : Heats of Mixing for Various Systems -Carbon t e t r a c h l o r i d ~ o - x y l e n ~ Mole HE, fraction of cc14 cal/mole
-Carbon tetrachloride-m-xyleneMole fraction HE, of c c h cal/mole
-Benzenw-xylenMole fraction of o-xylene
HE, oal/mole
-Benzens-m-xylene---. Mole fraction of m-xylene
HE, cal/mole
Temp, 10" 0.4495 -3.9 0.5758 -4.8
Temp, 10" 0.4364 4.9 0.4982 5.0 0.5632 4.3
Temp, 20" 0.3151 23.1 0.4436 28.5 0.5545 28.8 0.6501 23.6
Temp, 20" 0.3208 20.3 0.4088 24.1 0.5676 26.1 0.7006 21.7
Temp, 20' 0.2755 -2.7 0.5261 -5.3 0.7562 -3.2
Temp, 20" 0.3157 4.1 0.4297 5.4 0.4819 5.7 0.5757 4.8
Temp, 30" 0.1522 -1.3 0.4300 -3.3 0,4944 -4.8 0.5573 -5.1 0.6774 -3.9
Temp, 30" 0.2250 3.4 0.4495 6.3 0.4948 6.4 0.5239 5.7 0.5694 5.3 0.6675 4.3
Temp, 30" 0.1211 9.2 0.3086 20.4 0.4243 24.4 0.4891 27.7 0.5533 26.3 0.6907 21.7 0,8326 11.5
Temp, 30" 0.3035 19.3 0.3361 18.0 0.4240 21.8 0.5490 24.9 0.7222 20.0 0.8365 12.8
~
count = =kO.OOl cm). The results are given in Table I. (ii) Heats of Mixing. The mixing device for these measurements has been described earlier.2J0J1 The liquids were confined over mercury in two bells separated by means of a stopcock. The mixing device was dipped in mercury contained in a triple-walled vacuum jacket and the mixing was brought about a t constant temperature by opening the stopcock mechanically from the outside. The temperature changes on mixing were ascertained with a ten-junction copper-constantan thermopile as described elsewhere.2,10,11 The results are given in Table 11. (iii) Vapor Pressure. The equilibrium still used for the present measurements was connected to the manometer and the vacuum line by a three-way stopcock as described earlier.* A cold trap was placed between the stopcock and the vacuum system. The vapor pressures were measured with a cathetometer which could read correct to zkO.001 cm. The measured heights were corrected to the standard gravity. The results are given in Table 111. (iv) Dielectric Constants. These measurements were made with a Dekameter, Type DK 03, Wissenschaftlich-Technische Werkstiitten, Germany. The cell used (Type MFLlIS) had a capacity of about 10 cc. The temperature a t 30" was kept constant by circulating the water around the cell from a thermostat maintained a t the required temperature regulated to better than 10.01". The results are given in Table IV. The Journal o j Physical Chemistry
~~~
~~
~~~
~
Table 111: Total Vapor Pressures for Various Systems at 0" o-Xylene-carbon tetrachloride Mole Total vapor pressure, fraction of CCI4 om
0.0000
0.2510 0.4649 0.6492 0.8126 1.0000
0.132 0.790 1.475 2.128 2.708 3.345
m-Xylene-aarbon tetrachloride Mole Total vapor fraction pressure, of CCl4 cm
0.0000
0.2806 0.4715 0.6640 0,8089 1.0000
0.135 0.900 1.532 2.194 2.700 3.345
(v) Refractive Index. The refractive indices were measured with a Carl Zeiss refractometer, Model No. 13232. The temperature a t 30" was maintained by circulating water around the prisms from a thermostat.
Discussion Volume of Mixing. The values of VE for o-xylenecarbon tetrachloride, m-xylene-carbon tetrachloride, m-xylene-benzene, and o-xylene-benzene have been plotted against mole fraction in Figures 1and 2. The data have been fitted by equations given in Table V. X A denotes the mole fraction of carbon tetrachloride in mixtures with 0- and m-xylenes and x B that of benzene in mixtures with 0- and m-xylenes. The data show a positive temperature coefficient of VE for m-xylene-carbon tetrachloride. However,
THERMODYNAMICS OF WEAKINTERACTIONS IN LIQUIDMIXTURES
2527
Table IV : Dielectric Constants and Molar Polarizations for Various Systems a t 30" Mole fraction of cc14
Dielectric constant
Density, g/cc
PI?, cc
Carbon Tetrachloride-u-Xylene, PAD= 72.558cc
0.0000 0.0771 0.1775 0.2726 0.3704 0.4607 0.5584 0.6473 0.7271 0.8054 0.8780 0.9527 1.0000
2.578 2.561 2.538 2.506 2.477 2.451 2.418 2.389 2.347 2.312 2.277 2.246 2.218
0.8716 0.9157 0.9754 1.0341 1.0971 1.1677 1.2259 1.2906 1.3523 1.4123 1.4712 1.5339 1.5748
41.835 40.965 39.787 38.445 37.209 36.049 34.745 33.529 32.266 31.103 29.971 28.946 28.201
Carbon Tetrachloride-mXylene, PAD= 67.742cc 0.0000
0.1075 0.1847 0.2817 0.3725 0.4591 0.5624 0.6512 0,7327 0.8063 0.8826 0.9349 1.0000
2.355 2.346 2.337 2.327 2.317 2.305 2,293 2.281 2.270 2.257 2.243 2.231 2.218
0.8555 0.9177 0.9641 1.0247 1.0834 1.1427 1.2163 1.2827 1 ,3462 1.4059 1 ,4704 1.5161 1.5748
38.534 37.511 36.734 35.758 34.853 33.925 32.885 31.964 31.112 30.327 29.528 28.922 28.201
1 Figure 1. Excess volumes for ( I ) o-xylene-carbon tetrachloride: 0, experimental point; -, curve calculated from the equation (Table V); (11) mxylene-carbon tetrachloride: 0,experimental point; -, curve calculated from the equation (Table V).
0.28
024
0.20
Table V : Equations for Excess Volume of Mixing
-2
3
0%
1
v"
o*t2
UI-
> 0.00
I.04
o*oe e
the values are practically independent of temperature for a-xylene-carbon tetrachloride. Inversion of sign occurs for o-xylene-carbon tetrachloride with the increasing concentration of carbon tetrachloride.
0
'L '4 *b * 8. MOLE FRACTION M: BENZENE.
1.0
Figure 2. Excess volumes for ( I ) benzene-o-xylene: 0, experimental point; , curve calculated from the equation (Table V); (11) benzene-xylene: 0 , experimental point; , curve calculated from the equation (Table V).
----- -
V o l u m 71, Number 8 July 1967
R. P. RASTOGI, J. NATH,AND J. MISRA
2528
perature dependent for the lntter three systems while this is not so for the first system. The data have been fitted by the equations given in Table VI. The values of dHE/dT for equimolal mixtures have also been included in Table VI. Vapor Pressure. The vapor pressures of the mixtures have been fitted by the equation of the type’*
P= pAsAe1 [ ( I-zA)*/RT][B’
-kB’(1-4ZA)
1 - [(PA - vAA)(P-PA)/RTlj
) fB’(3-4ZA)lPB(1 - x,)e r ( ~ A * / R T[Bo
+
[@B - vB)(P- PB)/RTI I
(1)
Figure 3. Heats of mixing for (I) o-xylene-carbon tetrachloride: 0, experimental point; -, curve calculated from the equation (Table VI); (11) m-xylene-carbon tetrachloride: 0,experimental point; , curve calculated from the equation (Table VI).
-
where PA and P B refer to the vapor pressures of carbon tetrachloride and the aromatic hydrocarbon in the pure state, respectively, VA and V B are the corresponding molal volumes, and P A and P B are the second virial coefficients. Bo and B’ are the constants. The values of the molal volumes needed were found by making use of the density datal3 and those of the second virial coefficients were calculated by using the Berthelot relati0n~~8’6 =
[9RT0 -128P,
27RTC3] 64P,T2
(2)
where the subscript c refers t o the critical values. The values of the constants Bo and B’ were evaluated from eq 1 and were substituted in eq 312 t o get the values of the excess Gibbs free energy of mixing GE. The values of GE obtained in this manner have
GE =
-d Y
J-
r $0.0
0.0
0
‘2
.4
‘6
*a
(4
MOLE FRACTION OF BENZENE.
Figure 4. Heats of mixing for (I) benzene-o-xylene: 0, experimental point; , curve calculated from the equation (Table VI); (11) benzene-mxylene: 0,experimental point; -, curve calculated from the equation (Table VI).
------
Heats of Mixing. The values of HE for o-xylenecarbon tetrachloride, m-xylene-carbon tetrachloride, m-xylene-benzene, and o-xylene-benzene have been plotted in Figures 3 and 4. The heat of mixing is temThe Journal of .Physical Chembtru
Z A ( ~-
+ B’(1 -
ZA)[BO
&A)]
(3)
been plotted in Figure 5 and have been fitted by equations given in Table VII. The values of TSE have also been calculated by using the relationship GE = HE - TSE from measurements of HE and GE (calculated from vapor pressure data) and the values so obtained have also been plotted in Figure 5 . The equations in Tables V, VI, and VI1 have been fitted t o the experimental data by the method of averages. Dielectric Constants. The values of PI2 (Table IV), the molar polarizations of mixtures of carbon tetrachloride with o-xylene and m-xylene, have been cal(12) G. Scatchard, G. M. Kavanagh, and L. B. Ticknor, J . A m . Chem. SOC.,74, 3715 (1952). (13) J. Timmermans, “Physico-Chemical Constants of Pure Organic Compounds,” Elsevier Publishing Co., Amsterdam, The Netherlands, 1950. (14) G. Scatchard and L. B. Ticknor, J . Am. Chem. SOC.,74, 3724 (1952). (15) J. 0.Hirschfelder, C. F. Curtiss, and R. B. Bird, “Molecular Theory of Gases and Liquids,” John Wiley and Sons, Inc., New York, N. Y., 1954,p 252.
2529
THERMODYNAMICS OF WEAKINTERACTIONS IN LIQUID MIXTURES
Table VI:
Equations for Heats of Mixing dHe/dT, oal/mole Equation
System
a
eCgH4(CH3)z-CCla m-Ce,H4( CH3 )z-Cch CsHs-o-C&(CJ&)z
H E
CgHe,-m-CgH4( CH3)Z
H E
H E
H E
-
deg
10.05(~~ - ZB)'] = ~~z~[-4+ 3 .0,22642' 6 - (3.8-I-0.01681')(~~ - ZB) (-717.9 - 2.27332')(~~ - ZB)'] = ~A~B[447.2 - 1.12782'+ (0.43452'- 131.5)(~A- ZB) (4.50302'- 1411.9)(~A- %E)'] = zAz~[362.6 - 0.88082' + (125.4- 0.3672T)(~~ - ZB) -k (-572.05 + 1.8175T)(Z~- Ze)']
HE"=
Z A Z B [ - ~ ~ . ~1 0 . 4 ( ~ ~ZB)-k
+ +
. . I
0.056 -0.28 -0.22
is in units of calories per mole.
Table VII: Equations for Excess Gibbs Free Energy System
@CgH4(CH3)r-CCla m-CsH4(CHa )z-CCla a
Equation fitting the data
ZA(I- ~ ~ ) [ - 1 7524.4(1 - kA)] GE = z~(1- ~~)[-146.1 7,7(1 - 2zA)]
GE4=
GE is in units of calories per mole.
culated by the method of Earp and GlasstonelGand have been plotted in Figures 6 and 7, respectively. The densities of the mixtures needed for the evaluation of molar polarization were derived from the experimental values of VE for the respective systems. P A D , the molar polarization of the species AD formed from A (acceptor) and D (donor), was also estimated in a similar manner as described by these workers. l8 The lattice model theories" are unable to explain the values of the excess functions obtained in this investigation, for these predict no volume change on mixing, Le., VE = 0, whereas we find that VE = 0.103 and -0.001 cc/mole for mixtures of carbon tetrachloride with m-xylene and o-xylene, respectively, for equimolal mixtures. Also we find that VE = 0.224 and 0.269 cc/mole at 30" for equimolal mixtures of benzene with o-xylene and m-xylene, respectively. The conformal solution theoriesls also do not explain the results, because these do not predict the inversion of sign of the excess functions and we have HE > 0, VE > 0, GE (at 0") < 0, and TSE > 0 for carbon tetrachloride-m-xylene and HE < 0, GE < 0, and TSE > 0 for carbon tetrachloride-o-xylene. The signs of HE and VE for mixtures of benzene with o-xylene and m-xylene are in agreement with the conformal solution theories. The cell model theorieP and the average potential model theorieslE of liquid mixtures predict inversion of sign of excess functions. According to the refined theory of Prigogine and co-workers, l9 VEcalcd,
Figure 5. Excess Gibbs energy and TSE for I: tetrachloride; 11, -, o-xylene-carbon tetrachloride. The curves for GE are those calculated from the equations (Table VII) for the respective systems.
_ - - - _,-mxylene-carbon
and GEoalcd were evaluated by making use of the expressions given earlier.2s1g The excess entropy SEcalcd was evaluated from the expressi~n'~ HEcalcd,
(16) D. P. Earp and S. Glasstone, J. Chem. SOC.,1709 (1935). (17) E. A. Guggenheim, "Mixtures," Oxford University Press,
London, 1952. (18) I. Prigogine, "Molecular Theory of Solutions," North-Holland Publishing Co., Amsterdam, The Netherlands, 1957. (19) I. Prigogine, A. Bellemans, and A. E. Chwoles, J. Chem. Phys., 24, 518 (1956).
Volume 71, Number 8
July 1967
R. P. RASTOGI, J. NATH,AND J. MISRA
2530
sE = ZAZB(CAA(-20
+
+ 9p2) +
'/~(TCAA' CAA)[e2 -
3/462
3/2kp[6(2~-
+ 66(1 +
22B)]
+
"t
+ + 5pl)
(4) The values of the parameters 6, p, and 6 for the mixtures were calculated in a similar manner as described earlier.1&20 The quantities A, Y*, CAA, ~ A A , VAA, VAA', and VAA" have the same significance as described earlier.19~20V A A , VAA', and VAAf t were calculated in a similar manner as described previously.2 ZB)
'/26
36
u
0
- 3 4 -
2
a
32
-
30
-
Table VIII: Parameters for Pure Components OC
CClk
CsH6
O-CsHc(CHs)n
. .. ...
1.015 0.915
1,1467 1.0375
1.1317 1.044
0 0 0 30 0 30
1.000 0.96 3700 0.000 7530 97.688 94.210 0.1171
...
... ... ...
89.956
... ... ... ...
30
0.0000
Temp,
Parameter
x Y*
TCAA,cal CAA', cal/deg - ~ A A , cal/mole VAA,cc/mole VAA',cc/mole deg VAA", cc/mole deg2
, . .
...
...
...
0.0005
...
...
*8
1'0
36
32
'2
*4
*0
MOLE FRACTION OF CARBON TETRACHLORIDE ,
Figure 6. Molar polarization us. mole fraction of carbon tetrachloride in the system o-xylene-carbon tetrachloride a t 30'.
The Journal of Physical Chemistry
...
...
U
6
0
...
38
3
r
...
4.0
-
m-CsHk(CHs)r
0.1111
42
t- ' s
I *2
MOLE.
-4-
*6
*8
(.o
FRACTION OF CARBON T€TRAcHLORIDL.
Figure 7. Molar polarization us. mole fraction of carbon tetrachloride in the system m-xylene-carbon tetrachloride a t 30".
These have been recorded in Table VIII. Table I X contains values of VE for carbon tetrachloride-oxylene a t mole fractions of carbon tetrachloride equal to 0.2, 0.5, and 0.8, whereas the values for the other systems are for equimolal mixtures. A comparison of the calculated and the experimental values of VE in Table IX shows that these agree in sign in most of the cases, although the agreement as regards the magnitude is not very good. The inversion of sign of VE for o-xylene-carbon tetrachloride is not predicted by this theory. The values of TSEoalodand TSEobsd for o-xylene-carbon tetrachloride are 50.7 and 38.4 cal/mole, respectively, whereas the corresponding values for m-xylene-carbon tetrachloride are 60.9 and 40.9 cal/mole, respectively, for equimolal mixtures a t 0". The values of HE&d for equimolal mixtures of carbon tetrachloride with o-xylene and m-xylene are 178.3 and 204.4 cal/mole, whereas the corresponding values of HEobsd are -4.7 and 4.4 caI/moIe at 0". Values of GEoalcd for the systems o-xylene-carbon tetrachloride and m-xylene-carbon tetrachloride are 127.2 and 143.2 cal/mole, respectively, whereas the corresponding experimental values are -43.1 and -36.5 cal/mole, respectively, at 0". We give below the results of the excess functions calculated on the basis of the recent theory of Flory2' (20) R. P. Rastogi and K. T. Rama Varma, J. Chem. Soc., 2257 (1957). (21) P. 3. Flory, J. A m . Chem. Soc., 87, 1833 (1965).
THERMODYNAMICS OF WEAKINTERACTIONS IN LIQUIDMIXTURES
Table IX : Comparison of Calculated and Observed Values of Excess Volumes for Various Systems System
ZA
~-CaHa(CHs)z-cCla
0.2000
m-CsH4(CHs)z-CCl, CGHB-O-C~H~( CHI)? CsHe+CsH4(CHI)2
0.5000 0.8000 0.5000 0.5000 0,5000
Temp, "C
VEoalod,
VEobsdv
cc/mole
cc/mole
30 30 30 30 30 30
0.980 $1.527 $0.975 1.739 3.507 3.809
$0.016 -0.001 -0.011 0.103 0,224 0.269
and compare these results with the experimentally determined quantities. The values of V, the molal volume, and CY, the coefficient of thermal expansion for carbon tetrachloride at 30", are the same as given previously.2 V for benzene at 30" was calculated from the density data, whereas CY was obtained from the interpolation of the values reported earlier.22 The values of CY for o-xylene at 30" were obtained from molal volume data (calculated from densities) at different temperatures in a similar manner as described earlier.2 The value of y, the thermal pressure coefficient (Table X) for benzene and carbon tetrachloride, is either the same as reported previously2 or as obtained by the interpolation of earlier data.22 The value of y for o-xylene was obtained by making use of the relationshipZ2y = a / k T where kT is the isothermal compressibility. Since reliable data for k T of o-xylene could not be obtained, it was calculated from adiabatic compressibilityz3 k , which in turn is related to the isothermal compressibility by the expressionz4
where C,
=
C, - TVa,y,
(6)
C, refers to the heat capacity per mole at constant pressure at the temperature T. The value of y, at the required temperature was obtained by calculating the temperature derivative of the analytical expression fitted from the vapor pressure data a t different temperatures. The values of y, so obtained were substituted in expression 6 to get c,. The value of C, used in the present analysis was taken from Timmermans' data.la Further kT so obtained was used to calculate y for o-xylene (Table X). The parameters 0, T*, V*, and P * for pure components (Table X) were calculated in a similar manner as described by FloryZ1and by Abe and Flory.22 According to this theory, VEcalcd and HEcslCd were eval-
2531
uated in a similar manner as described earlier.2 Also the excess entropy SE (equated to SR, the residual entropy for the present case) was obtained from the expressionsz2
sR=
-3(NlPl*Vl*Fl/T) In [(G,'" - 1 ) / ( ~ '-/ ~I)]
= -3(NzP2*Vz*Fz/T) X
- I)/(Z?'~ - I ) ] (7)
In
The values of d used to calculate SRfrom the above equation were derived from the experimental values of VE. Since no reliable data for the isothermal compressibility of m-xylene could be obtained, calculations of the excess functions for the systems containing mxylene as one of the components have not been done. HEcalod and TSEcalcd obtained from this theory are -24.4 and -21.4 cal/mole, respectively, for equimolal mixtures of o-xylene-carbon tetrachloride at 30°, whereas the corresponding observed quantities are -4.4 (at 30") and 38.4 (at 0') cal/mole, respectively. HEcalcd and HEo,bsd for equimolal mixtures of benzene and o-xylene are - 18.1 and 26.5 cal/mole, respectively, at 30'. The calculated and observed values of VE for o-xylene-carbon tetrachloride and benzene-oxylene have been compared in Table XI. The values of VEobsd included are those obtained from the respective equations given in Table V. The analysis shows that the theory of Flory is also not in accord with the experimental data. The failure of the various theories of solutions to predict the excess functions correctly may be partly attributed to the fact that the specific interaction between carbon tetrachloride and the aromatics is not taken into account in theories. Since o-xylene and m-xylene are polar, it may appear that the contribution of dipolar effects to the excess functions may be significant. The permanent dipolar contributions to the excess functions of a mixture containing a component B with a permanent dipole and a nonpolar component A can be represented by the expressions'* GpE
HpE
=
=
+
'/3zAXBr{ - h A A [ 1 '/26 - %Bp] 3/2C~~T6 - zAkT(1 - '/26 - 3 p ) / '/32AzBr( (-2hAA (1
+
'/26
(8)
+ TCAA) x
- 3 2 ~ p )- 3/zTC~~6 zAkT(1
-
'/26
- 3p)]
(9)
(22) A. Abe and P. J. Flory, J. A m . Chem. s o c . , 8 7 , 1838 (1965). (23) W. Brzostowski, Bull. Acad. Polon. Sei., Ser. Sci., Chim., 13,
501 (1965). (24) J. S. Rowlinson, "Liquids and Liquid Mixtures," Butterworth and Co. Ltd., London, 1959.
Volume 7 1 , .\'umber
8
July 1967
R. P. RASTOGI, J. NATH,AND J. MISRA
2532
Table X : Parameters for Pure Liquids a t 30' V, Liquid
CClr CeHs o-CsHd CHa )z
a X 108,
cc mole-'
deg -1
97.688 89.956 121.808
1.240 1,234 0.885
Y,
cc-1
cal deg-1
CC14+CeHa( CHI )z
Temp,
VEcsiod.
VEobsdt'
OC
cc/mole
cc/mole
0.1000
30
-0.043 -0.127 -0.139 -0.186 -0.150 -0.149 -0.147 -0.145 -0.075 -0.112
+O. 013
0.3000 0.4000 0,5000 0.6000 0,7000 0.8000 0.9000 0.5000
CsHs-+CsHd(CHs), a
30
V*, cc mole-1
T*, OK
P*, cal mole-'
75.23 69.34 99.30
5101 4727 5646
134 148 117
1.2986 1.2974 1.2266
so obtained were substituted in the formula PB = ~ B / ( € F ~ B * Y B B * ~ ) "to ~ get PB where p B is the electric moment of the aromatic hydrocarbon. Further F was obtained from r = P B 4 / p B B o , where F B B 0 is related to l the reduced temperature of B by T'BB= r F ~ ~ o ($JBB). For the present analysis T ' B B has been equated with T'BB', since $BB has small values.ls The parameters of the pure components are given in Table XII, whereas the values of the excess functions obtained on account of these considerations are given in Table XIII. The contribution due to inductive forces (Table XIII) to the excess functions has been estimated by using the relationshipsI8 yBB*
ZA
0.2000
V
0.263 0.291 0.257
Table XI: Comparison of Calculated and Observed Excess Volumes for Various Systems Syetem
I
$0.016 $0.012 $0.006
-0.001 -0.007 -0.011 -0.011 -0.007 +0.224
+
E
Estimated from Table V.
Gp
+
= ~ A Z B { ( ~ ~ A A '/&T)['Y
('/d
+
(1 VpE
=
2/3ZAZBr{ ('/4VAA
TVAA')[l '/48[2ZBVAA
+ '/d -
3PB))
+
[')'
SpE =
+
(11)
+
+
+ '/Zk) x [ y + ('/d +
VpE =
n:AZB(
[Y
p,
D.
cc
ex
CClr ... 10.5' o-CsH4(CHs), 0.58' . . . ?~~-csH~(cHa)i 0.46b . . . ref 18.
y*,
1014,
A
ergs
~4
x lo4
6.62' 4.38" . . . 7.15 5.02 3.3 7.20 4.95 1.3
YBB x 106
... 24.5 9.5
' C. P. Smyth, J . Am. Chem. SOC.,46, 2151
(1924). ~~
The Journal of Physical Chemistry
+ 2VAA')
- ('/ZVAA
+ ('/d +
x
3p)('/ZXAYAB
+
3~rnpl
+
- ZBYm)
5/4TVAA'6(ZA?'
f
rm))
(15)
The parameters TAB, YBB, and ym were obtained as given below.I8 The values of EAA', YAA', EBB', and ~ B B O obtained from the relations EAA* = EAA'[~ yAA* = y A A o [ l
$JBB(T) 1, and
Table XI1 : Parameters for the Pure Components
carbon
(13)
-ZAZB(2CAA
$JAA(T)],
Hydro-
ZABYm]
3p)('/ZZATAB
'/2ZB)]]
x io",
+
- ZBYm)
3P('/ZZAYAB
ZA)
The parameter I' was obtained as follows. The values of EAA* and YAA* (Table XII), the coordinates of the minimum in the potential energy curve for carbon tetrachloride, were used to evaluate EBB* and YBB* for o-xylene and m-xylene from the relationsT8(1 6) = ~BB*/€AA* and (1 p ) 3 = (YBB*/~AA*)'; EBB* and
' See
+
(12)
- ZBym) 2ZAZBCAAa(Ym - ZAYBB) 1 (14)
+ 3 / 2 ~ ( 1+ I + ~ T V A A '+( ~
aA
x
= ~/~zAzB(~AA TcAA)
(10)
+
- ZBYm) 1 TCAA)6(Ym - ZAYBB)]
3p)('/ZZA?'AB (hAA
H,"
+
YBB*
=
+
YBB'
+
+ + ~PBB(T) 1, respectively, and#^^ -T/d',
#AA(T)],
[1
EBB*
=
EBBo[l
where +AA = ~ A A= 0,$BB = 2/31?, = were used to evaluate CAB' and TAB' from EAB' = (EAA' X EBB^)^" and TAB' = '/Z(YAA' YBB'). The superscript degree refers to the unperturbed quantities. The various parameters have the same significance as described by Prigogine.18 As an approximation, we have obtained €AB' from the geometric mean of the corresponding quantities for components A and B. Further TAB and YBB, obtained from TAB = C Y A ~ B ' /
+
THERMODYNAMICS OF WEAKINTERACTIONS IN LIQUIDMIXTURES
2533
Table XIII: Dipolar and Inductive Contributions to the Excess Functions
104
Gal/ mole
Dipole-UpE, TSpE, cal/ cal/ mole mole
7.1 4.4
0.79 0.30
2.58 0.81
GpE, System CClr-o-CeH4(CHa)~ CClr-rn-CaH~(CHs)i
Temp, 'C
TAB X
0 0
1.58 0.50
,
GpE,
VpE, cc/ mole
eel/ mole
0,007 0,003
-1.89 -1.33
and Y B B = # B B / 2 , respectively, where is the polarizability of component A, were used to calculate y and ym by making use of the relationships y = TAB - YBB and ym = ' / ~ Y A B - Y R B . The contributions to the excess functions on account of the inductive effects are also included in Table XIII. The total contribution of dipolar and inductive effects to the excess functions is negligible as compared to the contribution due to interactions discussed below. This is at once clear when the values from Figures 8 and 9 are compared with the values given in Table XIII. The experimental values show that the values of VE are greater for carbon tetrachloride-m-xylene as compared to those for carbon tetrachloride-o-xylene. We also find that HE > 0 for carbon tetrachloride-mxylene whereas HE < 0 for carbon tetrachloride-oxylene. This indicates that the tendency of the formation of new species with carbon tetrachloride is more displayed by o-xylene than by m-xylene. The values
Inductive------? TSpE* eel/ eel/ mole mole
UpE,
-2.47 -1.85
-0.94 -1.54
+ inductiv-
-Dipolar
VpEs cc/
GpE, eel/
HpE, cal/
mole
mole
mole
-0.014 -0,010
-1.1 0.11 1.03 1.04
TSpE, cal/ mole
0.64 -1.04
VpE, cc/ mole
-0.007 -0.007
yABo6~ABo CYA
I
Figure 8. Ionization potential of the aromatics us. Vinteraotion: 1, benzene; 2, toluene; 3, mxylene; 4, o-xylene; 5, p-xylene.
86
32
'I
Figure 9. Ionization potential of the aromatics us. HEinteraotian: 1, benzene; 2, toluene; 3, m-xylene; 4, o-xylene; 5, p-xylene.
of VE become negative at a higher concentration of carbon tetrachloride. However, when we compare these values with our earlier study,2 we find that the values of VE for equimolal mixtures with carbon tetrachloride are in the sequence m-xylene > p-xylene > benzene > o-xylene > toluene. Similarly the values of HE for equimolal mixtures of carbon tetrachloride with each of the above aromatics are in the sequence benzene > toluene > m-xylene > o-xylene > p-xylene. The heats of mixing of carbon tetrachloride with these aromatics indicate a trend of the increasing basicity of the hydrocarbons as the number of CH3 substituents in the benzene ring is increased and hence the increasing tendency of interaction of carbon tetrachloride with the hydrocarbons. The departure of the systematic behavior in the values of VE for mixtures of carbon tetrachloride with aromatics having an increasing number of CH3 substituentsin the ring may be due to the size effect. As the size of the benzene and carbon tetrachloride molecules are nearly idenVolume 71,Number 8 July 1967
R. P. RASTOGI, J. NATH,AND J. MISRA
2534
tical, we can have an estimate of the nonideality caused by the successive addition of CHs substituents in the benzene ring by making corresponding measurements for mixtures of each of these methylbenzenes with benzene. We may thus write VEobsd = VEsize effect E VEinteraction and H obsd = H E s i z e effect HEinteraotion where VEsize effeot for o-xylene-carbon tetrachloride is taken equal to VEobsd for mixtures of o-xylene and benzene, since benzene and carbon tetrachloride have approximately the same molal volumes. The values of VEinteraotion obtained by taking this effect into account show a definite trend with the increasing number of CH, substituents in the ring. The trend of these excess functions with the increasing basicity of the aromatics becomes more evident when we plot the ionization potentials8 of the aromatic hydrocarbons against HEintoraction and VEinteraction for equimolal mixtures of these systems (Figures 8 and 9). The above arguments get more support when we calculate the partial molal volumes of carbon tetrachloride at high dilutions in the aromatics. The values of V A - VAo, where ?A is the partial molal volume of carbon tetrachloride and V A O is the molal volume of pure carbon tetrachloride, obtained from the experimental measurements are given in Table XIV.
+
+
Table XIV: Values of ( VA - VA") for CCl4 a t Mole Fraction = 0.04 in Aromatics a t 30" (PA
x
vA')
108, cc/mole
Solvent
Benzene" Tolueneb 0- X y 1ene m-Xylene pXyleneb 'See ref 10 and 11.
-
-5.3 -2.0 $0.6
+1.4 +0.9
* See ref 2.
The increase in the values of (PA - VA') when the number of CH3 substituents in the aromatic ring is increased again shows a systematic trend. This trend in the values of (VA - VAo)for carbon tetrachloride in aromatics is similar to that of the values of ( PA VAo) for iodine in the aromatics.' The plot (Figure 10) of the ionization potential of the aromatics against ( V A - VAo)also signifies a similar behavior which is further supported when we plot the ionization potentials of the aromatics against the values of GE (at 0 " ) of mixtures of these hydrocarbons with carbon tetrachloride. The Journal of Physical Chemistry
Figure 10. Ionization potential of the aromatics us. ( PA - VA"): 1, benzene; 2, toluene; 3, m-xylene; 4, o-xylene; 5, p-xylene. (Subscript A has been put equal to 1.)
The values of PA, the apparent molar polarizations of carbon tetrachloride, calculated by the method described elsewhere, l 6 in the case of o-xylene-carbon tetrachloride and m-xylene-carbon tetrachloride when plotted against mole fraction of carbon tetrachloride show a tendency to increase as the concentration of carbon tetrachloride in the two cases is decreased. This indicates the existence of new species of carbon tetrachloride with the aromatics in the two systems. The values of Plz when plotted against mole fraction (Figures 6 and 7) in the systems o-xylene-carbon tetrachloride and m-xylene-carbon tetrachloride show positive deviations from the mixture law. The excess molar polarization may be attributed to the formation of a bond between the two species. The values of P A D (Table IV), the molar polarizations of the species AD, together with those of the molar refractions for AD (taken to be equal to the sum of the molar refractions of each of the components) mere used to have an idea about the electric moments of the new species by the method described else~vhere.~5But no reliable information could be drawn from these values, since
(25) S. Glasstone, "Textbook of Physical Chemistry," Macmillan and Co. Ltd., London, 1956.
THERMODYNAMICS OF WEAKINTERACTIONS IN LIQUIDMIXTURES
these were not found to be much different from the sum of the moments of the components.26 For the systems under consideration, the real trend in H E and VE due to specific interaction is masked by size effects. Even the sign of heat of mixing becomes positive in carbon tetrachloride-m-xylene. A correct picture emerges only when this is taken into account. The analysis shows that specific interactions do exist between the hydrocarbons and carbon tetrachloride. It is interesting to note that the phase diagram6does not give any evidence of complex formation for these systems. It is easy to give an explanation if we assume that the solid complex is formed by the lattice rearrangement. The new lattice probably has only a very small energy difference as compared to the original ones. The lattice is maintained intact by specific interactions which are quite weak. New crystalline
2535
rearrangement is facilitated when the species have similar size. The differences in size lead to lattice distortions. When these distortions predominate over specific interactions, a new lattice rearrangement does not appear and consequently no new species is detectable by phase diagram. It seems that geometrical factorse may be responsible for the instability of the new species formed between carbon tetrachloride and xylenes, especially 0- and m-xylenes, since the center of symmetry would be much different as compared to benzene or toluene.
Acknowledgment. Thanks are due to the Council of Scientific and Industrial Research (India) for supporting the investigation. (26) See footnote b of Table XII.
Volume 7 1 , Number 8 July 1967
