880
J. Phys. Chem. 1981, 85,886-889
Blnary Systems of Trichloroethylene with Benzene, Toluene, p-Xylene, Carbon Tetrachloride, and Chloroform. 2. Vlscosltles at 303.15 K Jagan Nath" and S. N. Dubey' Chemistry Department, Gorakhpur University, Gorakhpur 27300 1, India (Received August 25, 1980)
Viscosities at 303.15 K have been measured for binary liquid mixtures of trichloroethylene (C2HC13)with benzene, toluene, p-xylene, carbon tetrachloride, and chloroform. The viscosity data have been analyzed in the light of absolute reaction rate and free volume theories of liquid viscosity, and it has been found that for the present mixtures the experimental viscosities are best reproduced by entropic and free volume corrections to ideal mixture viscosity. The enthalpic or free energy corrections to ideal mixture viscosity and the combination of free volume and reaction rate theories reproduce the experimental viscosities with the same degree of accuracy as that in the case of entropic or free-volume corrections for the systems C2HC13-CC14and C2HC13-CHC13only, whereas larger deviations are found for systems of CpHC13 with C6H6,C6H5CH3,and P-C~H,(CH~)~. The values of the quantity qE, which refer to the deviations from the rectilinear dependence of viscosity q of the mixture on mole fraction, have been calculated. Also the values of the parameter d have been calculated from the expression In q = x1 In q1 + x 2 In q2 + x1x2d, where q1 and q2 are the viscosities of pure components 1and 2, whose mole fractions in the mixture are represented by x1 and xp, respectively. The values of both qE and d show that the interaction of C2HC13becomes stronger with the aromatic hydrocarbon having an increased number of CH3 substituents attached to the aromatic ring. The slightly positive values of both qE and d for the system C2HC13-CHC13have been attributed to the formation of a weak hydrogen bond between CHC13 and C2HClB. The values of d for the systems C2HC13-C& and CpHCl3-CCl4indicate that C2HC13interacts with C6H6as strongly as it interacts with CCl,.
Introduction The measurements of excess volumes for binary mixtures of trichloroethylene (C2HC13)with benzene (C6H6), toluene (C6H5CH3),p-xylene (p-C&,(CH,),), carbon tetrachloride (CC14),and chloroform (CHC13) have been reported earlier.2p3 Quite r e ~ e n t l ythe , ~ measurements of ultrasonic velocities in, and adiabatic compressibilities, dielectric constants, and refractive indexes for, these mixtures have been made, and the results obtained have been discussed from the viewpoint of the existence of specific interaction between the components of the various mixtures. It has been indicated4that there exists specific interaction leading to the formation of complex species between C2HC13and the other component in the binary liquid mixtures Of C2HC13 with C&, C&CH3, P-CeH4(CH,),, CCl,, and CHC1,. Since the viscosity data for binary liquid mixtures are known5s6to shed light on the existence of specific interaction between the components, it was thought worthwhile to get further information concerning the formation of complex species in the binary liquid mixtures of C2HC13 with aromatics and halomethanes from viscosity data. Further, there is a current interest7to know to what extent the absolute reaction rate theory of Eyring and co-workers8 and the free volume theorye-ll of liquid viscosity can reproduce the viscosity (1)Chemistry Department, N.D. College, Barhalganj, Gorakhpur. (2)J. Nath and S. N. Dubey, J. Chem. Thermodyn., 11, 1163 (1979). (3)J. Nath and S. N. Dubey, J. Chem. Thermodyn., 12,399 (1980). (4)J. Nath and S. N. Dubey, J. Phys. Chem., 84,2166 (1980).This paper is treated as part 1. (5)L. Grunberg and A. H. Nissan, Nature (London),164,799 (1949). (6)R. J. Fort and W. R. Moore, Trans. Faraday SOC.,62,1112(1966). (7)V.A. Bloomfield and R. K. Dewan, J.Phys. Chem.,75,3113(1971). (8)S.Glasstone, K.J. Laidler, and H. Eyring, "The Theory of Rate Processes", McGraw-Hill, New York, 1941,Chapter 9. (9)A. K.Doolittle, J. Appl. Phys., 22, 1471 (1951);23, 236 (1952). (10)M.L.Williams, R. F. Landel, and J. D. Ferry, J.Am. Chem. SOC., 77,3701 (1955). 0022-385418 112085-0886$01.2510
data for binary mixtures of components of varying complexity. Hence, in the present program, the measurements of viscosities for binary liquid mixtures of C2HC13with eel,, and CHC13have been C6H6, C6H5CH3,p-C6H4(CH3)2, made a t 303.15 K, and the results obtained have been interpreted in this paper. Experimental Section The methods of purification of the various components and checking their purity have been described previously.2 The flow times of the pure liquids and their binary mixtures were measured a t 303.15 f 0.01 K by using the kinematic viscometer described by Tuan and Fuoe~.'~The viscometer was first calibrated by making measurements for liquids of known viscosities at 303.15 f 0.01 K, and the measurements of kinematic viscosities were then made for pure liquids and their mixtures studied in the present program. Kinematic viscosities were converted to dynamic viscosities by use of densities which for pure liquids were the same as reported earlier.2 The densities for mixtures were estimated from the densities of pure liquids and the measurements of excess volumes2 for their mixtures. Values of q thus estimated are accurate to fO.O1 mP. Results a n d Discussion The experimental values of the dynamic viscosities for various liquids and binary mixtures are given in column 2 of Table I, where x1 refers to the mole fraction of C2HCl3 The values of the viscosities for C6H6,C6H5CH3,and p C6H4(CH3)2 have been found to be 5.65,5.21, and 5.66 mP, respectively, which are in good agreement with the corresponding literature13 values 5.66, 5.23, and 5.68 mP, respectively, for the three liquids in the same order. (11)M.H.Cohen and D. Turnbull, J. Chem. Phys., 31,1164(1959). (12)D. F. T.Tuan and R. M. Fuoss, J. Phys. Chem., 67,1343 (1963). (13)J. Timmermans, "Physico-Chemical Constants of Pure Organic Compounds", Elsevier, Amsterdam, 1950.
0 1981 American Chemical Society
Binary Systems of Trichloroethylene
The Journal of Physical Chemistry, Vol. 85, No. 7, 1981 887
TABLE I: Values of Experimental and Calculated Viscosities (cP) and the Parameter d for the Various Liquid Mixtures at 303.15 K C,HCl ,-C6 H,
0.0000 0.1624 0.2635 0.3697 0.4701 0.6728 0.7735 0.8791 0.9429 1.0000
0.565 0.535 0.521 0.512 0.507 0.504 0.507 0.510 0.514 0.517
0.557 0.552 0.547 0.542 0.532 0.528 0.523 0.520
0.954 0.933 0.914 0.900 0.876 0.867 0.859 0.854
1.021 0.977 0.974 1.027 0.970 0.958 1.031 0.966 0.942 1.030 0.966 0.927 1.024 0.973 0.897 1.018 0.979 0.883 1.011 0.987 0.868 1.006 0.994 0.859
0.531 0.515 0.500 0.488 0.466 0.458 0.449 0.444
0.569 0.567 0.564 0.558 0.545 0.538 0.529 0.523
0.543 0.529 0.515 0.502 0.477 0.466 0.454 0.447
0.544 0.535 0.528 0.524 0.518 0.517 0.516 0.517
0.519 0.500 0.483 0.471 0.453 0.448 0.443 0.441
0.530 0.513 0.500 0.485 0.464 0.456 0.448 0.444
-0.30 -0.30 - 0.28 -0.27 -0.25 - 0.23 - 0.23 -0.20
0.0000 0.1548 0.2959 0.3989 0.4793 0.6444 0.7420 0.8706 0.9211 1.0000
0.521 0.520 0.519 0.515 0.515 0.515 0.518 0.520 0.519 0.517
0.520 0.520 0.519 0.519 0.518 0.518 0.518 0.517
1.014 1.027 1.035 1.042 1.051 1.056 1.060 1.062
0.995 0.991 0.989 0.988 0.989 0.991 0.995 0.997
0.527 0.534 0.537 0.541 0.544 0.547 0.549 0.549
0.517 0.515 0.513 0.513 0.512 0.513 0.515 0.515
0.525 0.529 0.531 0.534 0.538 0.542 0.546 0.548
0.524 0.526 0.527 0.527 0.526 0.524 0.522 0.519
0.531 0.540 0.545 0.549 0.553 0.554 0.553 0.551
0.528 0.536 0.539 0.543 0.547 0.549 0.550 0.550
-0.01 -0.01 -0.04 - 0.03 -0.03 0.00 0.04 0.04
0.0000 0.1527 0.2439 0.2805 0.3637 0.6212 0.6910 0.8094 1.0000
0.566 0.565 0.562 0.562 0.563 0.552 0.546 0.539 0.517
0.549 0.541 0.538 0.532 0.518 0.517 0.514
0.571 0.576 0.577 0.580 0.591 0.595 0.600
0.571 0.573 0.572 0.572 0.560 0.555 0.543
0.594 0.609 0.614 0.624 0.640 0.639 0.633
0.585 0.595 0.599 0.605 0.619 0.621 0.620
0.09 0.08 0.09 0.12 0.13 0.12 0.16
0.0000 0.2969 0.7481 0.7605 0.8498 0.9286 1.0000
0.845 0.699 0.555 0.551 0.539 0.526 0.517
0.731 0.585 0.582 0.557 0.535
0.728 0.581 0.579 0.553 0.531
0.728 0.585 0.582 0.557 0.535
0.724 0.581 0.579 0.553 0.531
0.726 0.581 0.579 0.553 0.531
- 0.21 - 0.28
0.0000 0.1451 0.2431 0.3368 0.4687 0.5793 0.6718 0.7912 0.8680 0.9526 1.0000
0.514 0.517 0.521 0.521 0.521 0.519 0.519 0.519 0.518 0.518 0.517
0.515 0.516 0.516 0.517 0.518 0.518 0.517 0.518 0.517
0.513 0.512 0.512 0.511 0.511 0.511 0.509 0.510 0.509
0.514 0.515 0.515 0.515 0.515 0.515 0.51 5 0.516 0.517
0.512 0.512 0.511 0.509 0.509 0.509 0.508 0.508 0.509
0.513 0.512 0.512 0.511 0.510 0.510 0.509 0.509 0.509
0.04 0.07 0.05 0.04 0.03 0.03 0.03 0.02 0.05
1.007 1.012 1.01 5 1.016 1.015 1.012 1.007 1.004
1.009 1.018 1.024 1.029 1.039 1.046 1.055 1.059
C,HCl,-p-C,H,(CH,),
0.558 0.554 0.552 0.548 0.535 0.532 0.526
1.041 1.064 1.073 1.092 1.142 1.152 1.167
0.984 0.977 0.975 0.970 0.968 0.971 0.978
1.023 1.034 1.037 1.043 1.047 1.043 1.032
1.024 1.040 1.046 1.059 1.105 1.119 1.141
0.581 0.589 0.592 0.598 0.611 0.613 0.614
C,HCl,-CCI,
0.730 0.585 0.582 0.557 0.535
0.995 0.994 0.994 0.993 0.992
1.002 1.000 1.000 1.000 1.000
0.997 1.000 1.000 1.000 1.000
0.997 0.994 0.994 0.993 0.992
0.726 0.581 0.579 0.553 0.531
-0.30 -0.25 -0.27
C,HCl,-CHCl,
0.514 0.515 0.515 0.515 0.516 0.516 0.516 0.517 0.517
0.997 0.994 0.992 0.989 0.987 0.987 0.985 0.984 0.984
1.001 1.001 1.002 1.003 1.003 1.003 1.002 1.002 1.000
1.000 0.998 1.000 0.995 1.000 0.994 1.000 0.992 0.999 0.990 0.999 0,990 0.999 0.987 0.999 0.986 1.000 0.984
One of the simple additive relations' to predict the mixture viscosity from the properties of pure components, when the interactions between the components are neglected, is eq 1,where x1 and x 2 are the mole fractions of In 7 = x1 In v1 x 2 In vz (1) components 1 and 2 in the binary mixture, and ql and v2 are the viscosities of the pure components. Two major semiempirical theories which can be used to predict liquid viscosity are the absolute reaction rate theory of Eyring and co-workerss and the free volume theory.*ll The absolute reaction rate theory relates the viscosity to the free energy required by a molecule to overcome the attractive force field of its neighbors, so that it can jump to a new equilibrium position, thus the deviation of the mixture viscosity from eq 1 being related to the free energy of mixing or the excess free energy. The free volume theory, on the other hand, relates the viscosity to the probability
+
0.512 0.512 0.511 0.509 0.509 0.509 0.508 0.509 0.509
of occurrence of an empty neighboring site into which a molecule can jump. Since, this probability is exponentially related to the free volume of the liquid, the deviation of mixture viscosity from eq 1 can be ascribed to the variations in the free volume of the solution. Combining the absolute reaction rate and the free volume theories of liquid viscosity, Bloomfield and Dewan' have obtained eq 2, where AHM is the enthalpy of mixing per mole of the AHM ASR In 7 = x1 In v1 + x2 In 92 - RT R
+-+
8-1
= In
vid
+ In vH + In 7s + In v v
X1
x2
81-1
82-1
)
(2) solution, ASR is the residual entropy per mole, R is the gas constant, T i s the absolute temperature, and v'l, uI2, and 8
888
The Journal of Physical Chemistty, Vol. 85,No. 7, 1987
Nath and Dubey
TABLE 11: Parameters for Pure Liquids at 303.15 K
103a, deg-'
y,
cal cm-3 deg-I
G P, cm3 mol-' T*,K P*,cal ~ m - ~ 89-95' 1.233b 0.292& 1.2975 69.33 4730 149 107.4'3 1.089' 0.278e 1.2694 84.63 5035 136 124.57' 1.038' 0.268f 1.2590 98.94 5165 129 97.68' 1. 240b 0.267b 1.2988 75.21 4718 137 81.18' 1.261' 0.286e 1.3028 62.31 4680 147 90.53' 1.193d 0.291f 70.19 4808 147 1.2898 a Based on densities reported in ref 2. Values obtained from the interpolation of the data tabulated in ref 15. ' Values computed from densities at three temperatures, the density data being taken from ref 13. Value obtained from A. Weissberger, E. S. Proskaur, J. A. Riddick, and E E. Toops, Jr., Tech. Org. Chem., 7, 206 (1955). e Values estimated liquid benzene toluene p-xylene carbon tetrachloride chloroform trichloroethylene
V, cm3 mol-'
from isothermal compressibility, k T , by using the relation y = f f / k T . Values of kT were obtained from R. Weast, "Handbook of Chemistry and Physics", Chemical Rubber Publishing Co., Cleveland, OH, 1971. Values estimated from isothermal compressibility which in turn was obtained from adiabatic compressibility reported in ref 4.
are the reduced volumes of component 1,component 2, and the mixture, respectively. Equation 2 takes into account the contributions to the mixture viscosity-from the ideal mixture viscosity obtained from eq 1and from enthalpic, entropic, and free volume corrections to the ideal behavior. In order to estimate the contributions to the mixture viscosity from AHM/(RT)and ASRJR in eq 2, we use Flory's equations14for A",and ASR, which can be written in the following form: M M = x1c1 1 - 1 + X 2 c 2 1 - i) 1 + xlcle2xl2
-(-
RT
Tl B1
0.2
.!
8
-'E
0.0
3
-0.2
w *
c-0.4
-(T2
fi2
BTIP1* (3)
*I
Figure 1. Plot of qEvs. mole fraction x , of CpHC13: (A) C2HCI3-CsHe; (0) C2HCI&H&H,; (0)C ~ H C I ~ - P C ~ H ~ ( C(V) H ~CpHCIa-CCI,; )~; (A) C,HCI3-CHCI3.
The parameter Cifor a component i is related to the characteristic pressure Pi*, the characteristic temperature Ti*,and the hard-core volume per mole Vi*of component i as described earlier.71~~ The characteristic parameters (see Ti*,and Vi*and the reduced temperature Table 11) Pi*, Ti and the reduced volume ciof the pure component i used in the calculations were obtained from the values (see Table 11) of the molal volume V, the thermal expansion coefficient a, and the thermal pressure coefficient y by using the methods described by Abe and F10ry.l~ The parameter &X12(characteristic of a system) used to calculate AH,/(RT) from eq 3, at all concentrations for each s stem, was estimated from the reduced excess volumes, 17 ,by using the experimental values2of the excess volumes for equimolal mixtures and by employing the relations described by Abe and F10ry.l~The values of v', the reduced volumes of mixtures, needed in eq 2-4 were also obtained from the relations of Abe and Flory15 by using the experimental data on excess volumes.2 The various terms in the viscosity expression defined in eq 2 have been recorded in columns 3-6 of Table I, whereas the values of the free energy contribution, defined s given in column 7. As has been pointed by q G = 7 7 ~ are out by Bloomfield and D e ~ a nit, ~is not clear whether the contributions of all terms to the mixture viscosity in eq 2 are equally important and should be considered together in computing q , and hence, in view of the absence of this information, we have tabulated in columns 8-11 the various combinations of the calculated contributions from various terms to V, combining them multiplicatively in accordance with the additive logarithmic relation in eq 2. The absolute reaction rate theory, which takes into account free energy corrections to the ideal mixture viscosity qid, corresponds to the multiplicative term VidtG, whereas the
x
(14)P.J. Flory, J. Am. Chem. SOC.,87,1833 (1965). (15)A. Abe and P. J. Flory, J . Am. Chem. SOC.,87, 1838 (1965).
free volume theory, which takes into account free volume corrections to the ideal mixture viscosity, corresponds to VidqV. Further MacedwLitovitz's theoryI6 which accounts for enthalpic and free volume corrections to ideal mixture viscosity corresponds to O i d l f m V , which is given in column 12 of Table I, whereas the values of the complete product V i d q m S V v are given in column 13. Table I shows that the experimental viscosities are best reproduced by either VidqS or VidVV for C2HC13-C6H6,C2HCl3--C6H5CH3,and C2HC13-p-C6H4(CH3)2.The viscosities reproduced by VidqC or VidVX are less satisfactory for these mixtures. Each Of VidqH, VidqS, VidVG, and fidVV predicts the mixture viscosities to the same degree of accuracy in the case Of C2HC13-CClk Though each Of VidqH, VidVS, VidvG, and Vidfv reproduces the experimental viscosities with the same degree of accuracy for C2HC13-CHC13as well, the percentage deviations of the calculated viscosities from the observed ones are much less in this case than in the case of C2HC13-CC14 Further, the complete product VidTjmSqV for all of the mixtures is very nearly equal to VidVH, which can be explained to be due to the fact that the entropy and the volume effects tend to cancel each other. MacedoLitovitz's theory16 (which corresponds to f i d q m v ) exhibits larger deviations in the case of C2HC13-C6H6,C2HCl,C6H5CH3,and C2HC13-p-C6H4(CH3)2.However, for C2HC13-CC14 and C2HC13-CHC13, this theory (or the term V i d V m V ) reproduces the values of 7 with the same order of accuracy as in the case of values obtained from VidqH, VidVG, Vid?lV, or VidqS. We shall now discuss the experimental viscosity data from the viewpoint of interactions between the components of various mixtures. The values (see Figure 1) of the quantity qE, which refers to the deviations from a rectilinear dependence6 of viscosity of the mixture on mole fraction, can be discussed from viewpoint of intermolecular (16)P.B.Macedo and T. A. Litovitz, J. Chem. Phys., 42,245(1965).
Binary Systems of Trichloroethylene
0.41
The Journal of Physical Chemistry, Vol. 85,
h
I
-0.4}
No. 7, 198 1 889
\
Figure 2. Plot of qE vs. VE for equimolal mixtures at 303.15 K: (1) C,HCI,-CeH,; (2) C2HCI3-C&l&H,; (3)C,HC13-p-C6H4(CH3)2.
interaction~.~J~ For systems where dispersion and dipolar forces are operating, the values of qE are found to be negative, whereas the existence of charge-transfer and hydrogen-bond interactions leading to the formation of complex species between the two components of the various binary systems tends to make the values of qE positive. For systems where all types of intermolecular forces are operating, the values of vE will be due to the contributions from all types of interactions. For mixtures of C2HC13with aromatics at any fixed mole fraction, qE has the sequence p-xylene > toluene > benzene This trend in the values of vE gives evidence in favor of increasing extent of specific interaction of C2HC13with aromatics having an increased number of CH3 substituents attached to the aromatic ring. The specific interaction between C2HC13and aromatics has been indicated4 to be the donor-acceptor-type interaction, the aromatic molecule acting as n-type sacrificial electron donor toward C2HC13. The negative values of qE for C2HCl3-C6H, may be explained to be due to the predominance of dispersion and dipole-induced dipole interactions over specific interaction which is believed to increase (as the viscosity data show) when the number of CH3 substituents attached to the aromatic ring is increased, since this results in the increase of ease of availability of T electrons of the aromatic ring. This fact further becomes quite evident (see Figure 2) when we examine the plot of qE vs. the excess volumes2 P for equimolal mixtures of C2HC1, with benzene, toluene, and p-xylene at 303.15 K. Figure 2 shows that the excess volumes decrease as the number of CH3 substituents attached to the aromatic ring increases, and these changes in VE quantitatively parallel the changes in qE. The slightly positive values of qE for C2HC1,-CHC13 can be explained to be due to the formation of a weak hydrogen bond, on account of interaction of the H atom of CHC13 with the 7r electrons of the ethylenic linkage of C2HC13. The negative values of qE for C,HC13-CC1, can be explained to be due to the predominance of dispersion and dipole-induced dipole interactions between the two componen ts. According to Grunberg and N i s ~ a nthe , ~ viscosity q of a binary mixture can be expressed by eq 5. In eq 5, the In 7 = x1 In q 1 + x2 In qz + xlx2d t 5) (17) R. K. Nigam and P. P. Singh, Indian J. Chem., 9, 691 (1971).
-30
I
-20
I
-10
0
I
I
I
I
I
IO
20
30
40
50
1 60
A b k,K
Figure 3. Plot of the mean valueof the parameter dvs. the difference (Abp, K) between the boiling point of the second component and of C,HCI, for the various systems: (1) C2HC13-C6H6; (2) C2HC13-C6H5CH3; (3)CZHC~S-P-CBH~(CH~)P
parameter d has been regarded as a measure of the strength of the interaction between the c ~ m p o n e n t s The .~~~ values of d calculated for the various mixtures from eq 5 by using the viscosity data in millipoise are given in the last column of Table I. The variation of d with composition is not large. The mean values of d for the systems C&C13-C&, C2HC13-CGHbCH3, C ~ H C ~ ~ - P - C ~ H ~ ( C H ~ ) ~ , C2HC1,-CC14, and C2HC13-CHC1, have been found to be -0.26, -0.005,0.11, -0.26, and 0.04, respectively. At any fixed composition, the variation of d with the strength of interaction is similar to that of qE, being negative in the case of systems in which the dispersion forces are predominant between the components, becoming less negative and then becoming positive as the strength of interaction increases. For the systems C2HC13-aromatics, in which the nature of the interaction between the components is believed to be the same, the mean values of d have the sequence p-xylene > toluene > benzene Fort and Moore,18Thacker and Rowlinson,lg and Reddy et alqmhave used the difference in boiling points of the two components as a measure of the strength of interaction. Figure 3, where the mean values of d for the systems C2HC13-aromatics have been plotted vs. the difference (Abp, K) in the boiling point of the second component and that of C2HC1,, shows that the values of d parallel the values of Abp. The slightly positive values of d for the system C2HC13-CHC13can be attributed to the formation of a weak H bond between CHC13 and C2HC13,as mentioned before in this paper. It is quite interesting to note that the values of d for the system CzHC13-C& are of the same order of magnitude as those for the system C2HC13-CC14, thus indicating that the strength of interaction between the components in the two systems is of the same order. Acknowledgment. We are extremely grateful to Professor R. P. Rastogi, Head of the Chemistry Department, Gorakhpur University, for encouragement during the course of this investigation. Thanks are also due to the University Grants Commission, New Delhi, for financial support. (18) R. J. Fort and W. R. Moore, Trans. Faraday SOC.,61,2102 (1965). (19) R. Thacker and J. S. Rowlinson, J. Chem. Phys., 21,2242 (1953). (20) K. C. Reddy, S. V. Subrahmanyam, and J. Bhimasenachar, Trans. Faraday SOC.,58, 2352 (1962).
