J. Phys. Chem. 1083, 87, 245-250
245
Thermogravitational Thermal Diffusion in Binary Mixtures of Chloroform .with Acetone, Benzene, Toluene, and Mesitylene Ning-Yuan Richard Mat and A. L. Beyerlein' Department of Chemistry and Geolcgy, Ctemson Unlverslty. Clemson, South Carolina 2963 7 (Received: July 6, 1982; I n Final Form: September 14, 1982)
Experimental thermogravitational thermal diffusion studies are reported on chloroform-benzene mixtures at 10, 15, 25, and 35 "C and on chloroform-acetone, chloroform-toluene, and chloroform-mesitylene mixtures at 25 "C. Thermal diffusion factors ( a )are calculated from the data on chloroform-benzene and chloroformacetone mixtures. For the chloroform-benzene derivative mixtures the produds avD (7and D being the viscosity and the diffusion coefficient, respectively) are evaluated. The thermal diffusion behavior for chloroform-acetone mixtures is consistentwith that obtained from a generalized form of the Baranowski et al. molecular association theory which assumes that the mixtures contain the 1:l chloroform-acetone complex and a considerably lesser amount of the 2:l complex. The maximum in the aqD products for the chloroform-benzene derivative mixtures at 0.3 chloroform mole fraction are best interpreted in terms of a van der Waals interaction between chloroform and benzene molecules and a coordination number of 2 (one chloroform molecule on each side of the benzene ring) rather than chloroform-benzene complex formation. The interaction energy between a chloroform and a benzene molecule is estimated from the temperature dependence of the chloroform-benzene thermal diffusion factor to be 1.1 kcal, which agrees well with Barker and Smith's estimate of 0.88 kcal.
Introduction In recent studies on methanol-benzene' and ethanoltoluene2 mixtures the thermal diffusion factor (defined such that it is positive for the less polar component diffusing in the direction of the temperature gradient) is found to increase gradually from negative values a t high alcohol concentrations to positive values as the alcohol concentration is decreased. It approaches a maximum and then gradually decreases at low alcohol concentrations ranging from 0.07 to 0.30 mole fraction. Johnson and Beyerlein' and Belton and Tyrrel12interpreted this concentration behavior in terms of the self-association of the alcohol component using either the molecular association theory of Baranowski et ala3or a modified form of this theory.' The same type of theory is also applicable to thermal diffusion in mixtures where there is association between the unlike components. The predicted thermal diffusion behavior for such mixtures differs considerably from mixtures studied in the earlier work1t2 where selfassociation has the dominant effect. It is the purpose of this work to experimentally characterize the thermal diffusion behavior of some chloroform mixtures where the molecular attraction between chloroform and the other component is much stronger than the molecular attraction between two chloroform molecules. These experimental results are also compared with theoretical predictions. The mixtures selected for investigation are chloroformacetone, chloroform-benzene, chloroform-toluene, and chloroform-mesitylene. The considerable amount of thermodynamic and spectroscopic data4-' on chloroform mixtures indicates that there is a significant degree of molecular attraction between chloroform and acetone, chloroform and benzene, and chloroform and benzene derivatives, whereas the self-interaction among chloroform molecules is too weak to affect thermal diffusion. Experimental Methods and Results The thermal diffusion behavior of the chloroform mixtures was investigated by employing a thermogravitational Graduate student completing portions of this work in partial fulfillment of the requirements for a Ph.D. degree.
thermal diffusion method described in detail in earlier ~ o r k . 'The ~ ~chemicals ~~ chloroform, benzene, and toluene were spectranalyzed reagent from Fisher Scientific Co. whose refractive indices at 20 "C (1.4452, 1.5006, 1.4956, respectively) agreed well with the literature values (1.4459, 1.5011, 1.4961).1° The mesitylene was certified reagent from Fisher Scientific Co. and the acetone was practical grade that was dried and distilled. The refractive indices of acetone and mesitylene at 20 O C are 1.3584 and 1.4988, respectively, which compare very well with literature values, 1.3588 and 1.4994.1° The thermal diffusion factors a for chloroform-benzene and chloroform-acetone mixtures are calculated from the thermogravitational thermal diffusion separations by using Horne and Bearman's equation" mLl
I P
-AB
W(1- w) 1-F
CY=
AW (1)
where 19 v2 - VI AW B=l/(@V) 1430 V A is a well-defined apparatus constantF9 D is the mutual diffusion coefficient, q is the viscosity, W is the weight fraction of chloroform, and A W designates the measured
F = -AB-
(1)Jung-Chen C. Johnson and A. L. Beyerlein, J. Phys. Chem., 82, 1430 (1978). (2) P. S. Belton and H. J. V. Tyrrell, Z. Naturforsch. A, 26,48 (1971). (3)B. Baranowski, A.E. deVries, A. Haring, and R. Paul, Adu. Chem. Phys., 16, 101 (1969). (4)R.D. Green.. 'Hvdronen - Bonding bv C-H GrOUDS". MacMillan. London, 1974. (5) J. A. Barker and F. Smith, J. Chem. Phys., 22, 375 (1954). (6) B. B. Howard. C. F. JumDer. and M. T. Emerson. J. Mol. Saectrosc., 10, 117 (1963). (7) C. F. Jumper, M. T. Emerson, and B. B. Howard, J. Chem. Phys., 35, 1911 (1961). (8)D. J. Stanford and A. L. Beyerlein, J.Chem. Phys., 58,4338(1973). (9)D. J. Stanford, Ph.D. Thesis, Clemson University, Clemson, SC, 1974,University Microfilms Order No. 74-30,062. (10)'Handbook of Chemistry and Physics", 60th ed., Chemical Rubber Publishing Co., Boca Raton, FL, 1980. (11)F. H. Home and R. J. Bearman, J. Chem. Phys., 49,2457(1968). I
.
I
0022~3654/83/2087-0245$01.50/0 0 1983 American Chemical Society
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The Journal of Physical Chemistry, Vol. 87, No. 2, 1983
TABLE I: Thermal Diffusion Factors vs. Mole Fraction for Chloroform-Acetone Mixtures at 25 "C a
acetone mole fraction
a
0.100 0.199 0.299 0.400 0.499 0.599
0.432 0.511 0.570 0.686 0.747 0.805
0.699 0.800 0.850 0,900 0.950 0.980
0.852 0.884 0.933 0.969 1.051 1.331
TABLE 11: Thermal Diffusion Factors vs. Benzene Mole Fraction for Chloroform-Benzene Mixtures at 10. 15. 25. and 35 "C
1 5 "C
benzene mole fraction
CI
benzene mole fraction
a
0.145 0.278 0.374 0.473 0.574 0.677 0.740 0.761 0.771 0.782 0.804 0.825 0,890 0.945 0.972
0.619 0.753 0.818 0.848 0.899 0.930 0.988 0.970 0.996 0.982 0.993 0.933 0.883 0.853 0.752
0.145 0.278 0.374 0.473 0.574 0.677 0.740 0.761 0.771 0.782 0.804 0.825 0.890 0.945 0.972
0.609 0.738 0.783 0.839 0.891 0.924 0.941 0.948 0.963 0.950 0.927 0.903 0.824 0.777 0.788
benzene mole fraction
a
benzene mole fraction
01
0.145 0.278 0.396 0.473 0.574 0.625 0.677 0.698 0.729 0.740 0.761 0.782 0.825 0.890 0.945
0.590 0.708 0.763 0.799 0.849 0.863 0.875 0.888 0.905 0.891 0.878 0.864 0.759 0.726 0.696
0.145 0.278 0.396 0.473 0.574 0.625 0.646 0.677 0.697 0.729 0.740 0.782 0.826 0.890 0.945
0.592 0.700 0.760 0.785 0.807 0.829 0.858 0.862 0.874 0.893 0.875 0.818 0.770 0.672 0.681
2 5 "C
TABLE 111: Products OrqD vs. Mole Fraction for Chloroform-Benzene Derivative Mixtures at 25 "C chloroform-toluene
ace to ne mole fraction
10 "C
Ma and Beyerlein
toluene mole fraction
10'aqD
mesitylene mole fraction
1O'aqD
0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.75 0.80 0.85 0.90 0.95
0.855 0.972 1.132 1.209 1.391 1.505 1.542 1.574 1.562 1.373 1.304 1.187
0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.75 0.80 0.85 0.90 0.95
0.934 1.051 1.178 1.197 1.285 1.473 1.533 1.438 1.450 1.328 1.210 1.078
CHLO'ROFO~M-
x 1.21
1.0
(12) National Research Council, 'International Critical Tables of Numerical Data, Physics, Chemistry, and Technology", Vol. 111, McGraw-Hill, New York, 1928. (13) J. Timmermans, "Physicochemical Constants of Binary Systems", Interscience, London, 1959. (14) P. A. Johnson and A. L. Babb, Chem. Reo., 56, 387 (1956).
1
0
0
g 1.0
**=*I I
I
I
I
3 5 "C
separation in chloroform weight fraction units. Equation 1presumes that a is positive when chloroform diffuses in a direction opposite to the temperature gradient. The specific volumes of the pure components Vi(i = 1designates chloroform and i = 2 designates the other component) and the thermal expansion coefficients @ for the mixture were estimated from density data in the "International Critical Tables"12 and the ideal mixing approximation for p. The specific volumes V of the mixture were obtained by interpolation on density data given in Timmermans.13 The product Dv was estimated at the desired temperatures by employing diffusion coefficient data of Johnson and Babb,14 viscosity data of Timmermans,13 and the pr~portionality'~ Dv 0: RT(1 + d In r / d In X) (2)
chloroform-mesitylene
e
l
.
1
I
I
I
I
I
I
0.2
0.4
0.6
0.8
i
1
1-X
Figure 1. avD product at 25 O C vs. benzene or benzene derivative mole fraction (1 - X ) on chloroform-mesitylene, chloroform-toluene, and chloroform-benzene mixtures.
where y and X are the rational activity coefficient and the mole fraction of chloroform, respectively. The required activity coefficient data were estimated from vapor pressure data.13 The thermal diffusion factors, which are averages of at least three measurements at each concentration, are given in Tables I and I1 for chloroform-acetone and chloroform-benzene mixtures. The estimated errors for the thermal diffusion factors given in this table range from about 4% at intermediate concentrations (between 0.2 and 0.8 chloroform mole fraction) to about 8% at extreme concentrations (0.05 or 0.95 chloroform mole fraction).I5 The thermal diffusion factors for chloroformbenzene mixtures are given as a function of temperature as well as a function of concentration. The temperaturedependence studies were motivated by the observation that the thermal diffusion factors of chloroform-benzene mixtures have a more complex concentration behavior than the thermal diffusion factors of the chloroform-acetone mixtures. Since no diffusion coefficient or viscosity data were available for toluene or mesitylene mixtures, avD was estimated, rather than the thermal diffusion factor a , by replacing B in the numerator of eq 1 with 1/ V and calculating B in the expression for F with diffusionI6 and vi~cosity'~ data on carbon tetrachloride-cyclohexane (15) Ning-Yuan Richard Ma, Ph.D. Thesis, Clemson University, Clemson, SC, 1982, will be available from University Microfilms, Ann Arbor, MI. (16) M. V. Kulkarni, G. F. Allen, and P. A. Lyons, J . Phys. Chem., 69, 2491 (1965).
The Journal of phvsical Chemistry, Vol. 87, No. 2, 1983 247
Thermogravitational Thermal Diffusion
mixtures. Since F is very small (less than 0.01), this approximate evaluation of F should introduce negligible error. The remaining auxiliary data V, P, and Vi were obtained directly or estimated from literature data12J3 using the ideal mixing approximation. The values obtained for aqD at 25 “C are presented as a function of mole fraction in Table III.’* Each entry in the table represents the average of three measurements. The aqD for chloroform-benzene derivative mixtures are compared with those for the chloroform-benzene mixtures in Figure 1. Interpretation of the Data in Terms of Molecular Association Theory. Previous form~1ations’~~J~ of the Baranowski et al. theory for thermal diffusion in mixtures with a chemical reaction have been presented for self-association reactions. In this section a more general formulation is derived that accounts for any combination of coupled association-dissociation reactions at local equilibrium. The coupled equilibria can be represented by the following generalized chemical equation:
X . For the general case where deviations from ideality are included in the formulation, KI is dependent on X , which is accounted for by the term (d In Kl/d In X ) V In X in eq
4. Solving eq 4 for V In X i in terms of V In T , V In X , and J yields a-2 Mi a-2 d In K j V In X i = C (A-’),=V In T + C (A-l)ij1=1 j=1 dlnx V In X - (A-l)i,a-l(J+ DTX(1 - X ) V In T ) ( 6 ) where the matrix A is given by
The gradient for the overall chloroform mole fraction is given by the equation
(I
C
uijaj
+0
j=1
vx
(3)
where the a, represent the monomers and various associated species in solution, a is the total number of species (monomers and associated species) in solution, and vij designates the stoichiometric proportion in which the species aj reacts in the association reaction designated by the subscript i (uij 0 for a reactant and vij > 0 for a product). The number of association reactions is necessarily a - 2. Equations that require the association reactions to be at equilibrium and the linear phenomenological equation for the chloroform diffusion flux form a linear set of equations in the gradients V In Xi1 a d In KI AH1 C uli V In X i = -V In T -V In X i=l RT d In X
+
a
X(1- X )
=
i-1
AfiV In X i
where
nixi - mixi Afi = CnjXj CmjXj the quantity ni is the number of chloroform molecules, and mi is the number of molecules of the other component in associated species i. The quantity Afi is the difference between the fraction of chloroform monomers that are in associated species i and the fraction of the monomers of the other component that are in this same associated species. Substitution of the expression for V In X i into eq 8, solving for V X / [ X ( 1 - X ) ] ,and identification of the coefficient to V In T with -a yields + %hem 1-r
aphyn
a=
n
2 XiDiV In Xi = -J - DTX(1- X ) V In T
i=l
(9)
(I
aphys
n
2 xiv In xi = o i=l
(4)
where the latter equation is obtained by differentiating E X i = 1. The quantities X i are the mole fractions of the monomers and various associated species. The quantity J is the center of mass chloroform diffusion flux, Di is a polynary diffusion coefficient, DT is a parameter characterizing thermal contributions to the diffusion flux, AHl is the enthalpy change for reaction 1, and K 1is given by
n Xi”” (I
Kl =
i=l
(5)
If the associated species behave ideally, Kl is the equilibrium constant for reaction 1 and is dependent on temperature but independent of the chloroform mole fraction (17) B.R. Hammond and R. H. Stokes, Tram. Faraday SOC., 52,781 (1956). (18)The value, 1.542 X IO-’, given in Table I11 for the a$ of chloroform-toluene mixtures at 1 - X = 0.7 differs from the value, 1.88 X given in N. Y. R. Ma’s thesis. The value given in this work is the result of a redeterminationof discontinuitiesin the interferometerreadings used to measure the separation AW. Methods for accounting for the discontinuities are described by F. H. Home and R. J. Bearman, J.Chem. Phys., 37, 2857 (1962), in ref 9, and in N. Y. R. Ma’s thesis. (19) B. Baranowski,A. Haring, and A. E. deVries, Physica, 32, 2201 (1966).
= D T X ( -~ X )
C Afi(A-’)i,a-l
i=l
(10)
The above equations represent the working relations for the interpretation of thermal diffusion factors in terms of association-dissociation equilibria. The quantity (Yphyn, called the “physical part” of a,is nearly independent of concentration. According to these equations the concentration dependence that characterizes a for mixtures with association-dissociation equilibria is contained in ache, called the “chemical part” of a. This latter contribution is dependent on the equilibrium constants K j and the enthalpies AHj for the various association-dissociation equilibria. The only assumption made in the derivation of the above equations is that the association reactions are at local chemical equilibrium. Since the Horne and Bearman equation (eq 1) is for a binary mixture, it requires that local chemical equilibrium also be assumed for the thermogravitational thermal diffusion experiment. In the utilization of eq 9-12 the following additional assumptions are made:
248
The Journal of Physical Chemistry, Vol. 87, No. 2, 1983
-
Ma and Beyerlein I
- T - - - T - r - l
I
I
I
I
1/11
1.ok
e ,, 0
Q.81
e
,
,
1
0.61 , /
I
0.8
1
0.6
-
I
0.4
d
I
0.2
I
X Figure 2. Sketch of predictions of molecular association theory for the chloroform mole fraction dependence of aphYs, am, and a assuming the association model nCHCI, A + (CHCl,),.A (lower graph n = 1 and upper graph n = 2).
+
(i) there is ideal mixing for the monomers and various associated species, i.e., r = 0; (ii) the polynary diffusion coefficients Di, the parameter DT, and AHi are independent of concentration. The assumption of local chemical equilibrium is believed to be valid for association by hydrogen bonding since such an association process is generally more rapid (10-7-10-9 s ) ~ O than the diffusion processes taking the association reactions away from equilibrium. However, a general verification of the accuracy of this assumption has not been obtained. The additional assumptions i and ii can only be validated by the succemful application of the above equations to a variety of systems. The first of these is a reasonable assumption if one conjectures that the nonideal behavior obtained with a twocomponent description is largely a result of molecular association and therefore should disappear in a description accounting for the various associated species. Assumption ii is reasonable in the context of assumption i, namely, that measured isothermal and thermal diffusion coefficients for nearly ideal binary mixture^^*^^-^^ have a weak concentration dependence. Assuming that the AHi are independent of concentration is consistent with experience regarding enthalpy changes for chemical reactions. Discussion and Conclusions. Figure 2 illustrates the predicted concentration dependence of achem and ffph for a binary chloroform mixture whose components ungrgo molecular association by a single reaction nCHC13 + A + (CHCl,),.A
I
(13)
where n may have values of 1or 2. Only the relative values of the polynary diffusion coefficients, i.e., D 1 / D z ,D3/D2, and DT/Dz,affect aphys and adem.The subscripts 1 , 2 , and 3 represent chloroform, the other mixture component, and the (CHC13),.A associated species, respectively. Figure 2 shows that, in general, aphys is nearly independent of concentration, which is as e ~ p e c t e d . ' ~For ~ n = 1 the calculated chemical contribution, archem, increases almost linearly with decreasing chloroform mole fraction. The rate of increase is most sensitive to the enthalpy change for the association and has only a weak dependence on the values (20)E.F.Caldin, "Fast Reactions in Solution",Wiley, New York, 1964. (21)T.G.Anderson and F. H. Home, J. Chem. Phys., 66,2831(1971). (22)J. C. R.Turner, B. D. Butler, and M. J. Story, Trans. Faraday Soc., 63,1906 (19673. (23)M.J. Story and J. C . R.Turner, Trans. Faraday Soc., 65,349 (1969).
0.2
0.4
I
I
0.6
0.8
1-x Figure 3. Comparison of the calculated and experimental a in chloroform-acetone mixtures. The calculated values are obtained by fitting the experimental data (0)to equations of molecular association theory assuming only a 1:l complex (dashed line) and assuming that 1:l and 2:l complexes are formed by a two-step reaction (solid line).
of the polynary diffusion coefficients or the association constants. For n = 2, "Ychem has a maximum in the neighborhood of 0.3 chloroform mole fraction. Slight shifts in the position of the maximum can be achieved by adjustment of the polynary diffusion coefficients. In the case where the following two-step equilibrium CHC13 + A + CHC13.A CHCl3.A
+ CHC13
(CHClJ2.A
(14
is involved in the formation of the 2:l chloroform complex (CHC13),.A,the maximum is retained if the 2:l complex is much more stable than the 1:l complex, i.e., K , C K2 where K , and K2 are equilibrium constants for the fust and second step, respectively. The position of the maximum ranges between 0 and 0.3 chloroform mole fraction depending on the ratio K 1 / K 2 . For K1 > K 2 the maximum disappears. For the chloroform-benzene derivative mixtu'res studied in this work aqD was calculated from the thermogravitational thermal diffusion separations because the diffusion coefficient data needed to calculate CY from experimental separations were not available. The concentration dependence contained in qD according to Hartley-Crank theory'* is given by (1 + d In y/a In X ) [ ( l - X ) / a C H C 1 , + X/uA]where uCHCI, and CTA are parameters related to molecular size. The factor (1- X ) / a C H C 1 , + X/uAgenerally has a weak linear dependence on chloroform mole fraction X. The factor 1 + d In y / a In X has a stronger concentration dependence but previous work',2 shows that its concentration dependence is still weaker than the a&em contribution to a. Thus, the contribution of (?,hem to cqD should not be dominated by the qD product and comparisons of the experimental aqD behavior with that expected from the theoretical predictions of (Ychem shown in Figure 2 should be useful. Figure 3 illustrates an increase in the thermal diffusion factor with decreasing chloroform concentration for chloroform-acetone mixtures. The increase is consistent with molecular association theory for a one-step equilibrium forming a 1:1 complex or a two-step equilibrium forming both 1:l and 2:l complexes with K 1 > K 2 . The thermal diffusion factors were fitted to theoretical calculations by the method of least squares for both association equilibrium models. Comparisons of experimental thermal dif-
1983 249
Thermogravitational Thermal Diffusion
fusion factors and the results of the least-squares calculations are illustrated in Figure 3. The experimental a at 0.98 acetone mole fraction was omitted in the calculations because it is believed that its large deviation from the calculated value may be the result of errors (about 16% at this extreme concentration) contributed by the calibration of the interferometersg used to measure the thermogravitational thermal diffusion separations. The least-squares calculations were performed with the association enthalpy fixed and the diffusion coefficient for the complex restricted to zero or positive values (same sign as the chloroform diffusion coefficient). The latter restriction is reasonable since the chloroform molecular mass is much greater than the molecular mass of the other component. Without these restrictions the root mean square (rms) deviation asymptotically approaches a minimum of about 0.030 with large negative values of the associated complex diffusion coefficient and small values of the association equilibrium constant. With these restrictions the rms deviation has a true minimum that is equal to about 0.035. Association equilibrium constants estimated by using literature values of the association enthalpy (range from -2 to -3 k ~ a 1 ) ~varied *~r~ from ~ 0.15 to 0.21. The calculations presented in Figure 3 for the one-step association model forming a 1:l complex are obtained by using -3 kcdB for the association enthalpy, 0.15 for the association equilibrium constant, and -2.0,0.0, and -1.82 for D1/D2,D3/D2,and DT/D2,respectively. For the two-step association model the calculations in Figure 3 assume values -2.46 and -2.34 kcal for the enthalpies of the first and second steps,% 1.48 for the ratio K1/K2,% 0.21 for K1, and -1.8, -0.4, 0.0, and -1.92 for D1jD2,D3jD2, D4/D2,and DT/D2,respectively. The calculations are not very sensitive to the relative diffusion parameters, and several combinations of values for these parameters yield comparable rms deviations. In contrast to this, a very small range of estimates are obtained for the association equilibrium constants of the 1:l complex. Therefore, comparisons of the estimates of the equilibriuin constants with other independent measurements provide a check on the accuracy of the theory as applied to thermal diffusion data. The estimated association equilibrium constant for the chloroform-acetone 1:l complex is in reasonable agreement with the value, 0.35, obtained from molar polarization measurements.26 It is however much smaller than the values obtained from NMR chemical shift^^>^' or thermodynamic data,4y24which range from 0.97 to 1.8. The equilibrium constants calculated from thermodynamic data are very likely overestimated because the calculations assume that the negative deviations from ideality are caused entirely by complex formation and contain negligible contributions from the intermolecular dipolar forces between acetone and chloroform. It is believed that the equilibrium constants calculated from NMR chemical shifts are also overestimated, because the calculations do not account for all the contributions to the solvent-induced chemical ~ h i f t . ~ Measurement ~,~~ of the association equilibrium constant by an NMR method which minimizes (24)A. Apelblat, A. Tamir, and M . Wagner, Fluid Phase Equilib., 4, 229 (1980). (25)For the least-squares calculations shown in Figure 3,the association enthalpies and the ratio K 1 / K 2are taken from ref 24. (26)S.Glasstone, Trans. Faraday Soc., 33,200 (1937). (27)C. M. Huggins, G. C. Pimentel, and J. N. Shoolery, J. Chem. Phys., 23,1244 (1955). (28)P. Laszlo, 'Progress in NMR Spectroscopy",Vol. 3,J. W. Emsley, J. Feeney, and L. H. Sutcliffe, Eds., Pergamon Press, New York, 1967, pp 231-402. (29)J. Homer, Appl. Spectrosc. Rev., 9, 1-132 (1975).
1 1.00.9
-
a: 0.8 0.7
-
0.6 -
1 association th&ry, which a&umes only that a 2:l chloroform-benzene associated species is formed, with experimental data on chloroform-benzene mixtures. The solM lines represent theory and the experimental data are for (0) 10, (0)15, (A)25, and (A)35 OC.
the unwanted contributions to the solvent-induced shift would be most helpful in judging the accuracy of molecular association theory for thermal diffusion. A suggested NMR technique would be to calculate the equilibrium constants from NMR data on acetone-chloroform-cyclohexane mixtures that are all obtained at the same dielectric constant. This would eliminate errors caused by a major portion30 (reaction field c o n t r i b u t i ~ n ~of ~ Jthe ~ ) solventinduced shift. Further minimization of solvent-induced shift contributions to the calculated equilibrium constants can be achieved by extrapolation of a sequence of such data to the dielectric constant of the inert solvent, cyclohexane. Such an NMR technique may prove to be difficult and tedious but should be possible with modern instrumentation. Figure 4 shows that the thermal diffusion factor for chloroform-benzene mixtures has a maximum at 0.3 chloroform mole fraction. Replacement of chloroform with carbon tetrachloride yields the nearly ideal carbon tetrachloride-benzene mixtures whose thermal diffusion factor is nearly independent of c ~ n c e n t r a t i o n .Thus, ~ ~ one can be reasonably certain that the concentration dependence of CY for chloroform-benzene mixtures is due tc the stronger intermolecular attraction between chloroform and benzene. This very surprising concentration dependence for CY is predicted from a molecular association theory which assumes that a 2:l chloroform-benzene complex is formed in a single step. The interpretation of these results in terms of a 2:l complex would however disagree with interpretations of a host of other independent thermodynamic and spectroscopic which for the most part suggest that at best a weak 1:l chloroform-benzene complex is formed. These considerations motivated additional studies on mixtures of chloroform and benzene derivatives (toluene and mesitylene) which also have been the subjects As is illustrated by the plots of previous of C Y ~inD Figure 1, these mixtures appear to have a thermal diffusion behavior almost identical with that of (30)L.G.Robinson and G . B. Savitsky,J.Magn. Reson., 2,269(1970). (31)A. D.Buckingham, Can. J. Chem., 38,300 (1960). (32)M. T a r e s , J. Am. Chem. Soc., 74,3375 (1952). (33)L. W. Reeves and W. G. Schneider, Can. J. Chem., 35,251(1957). (34)C. J. Creswell and A. L. Allred, J.Phys. Chem., 66,1469 (1962). (35)W. T. Huntress, J.Phys. Chem., 73,103 (1969). (36)J. Homer and A. Coupland, J. Chem. Soc., Faraday Trans. 2,74, 2218 (1978). (37)J. Homer and A. Coupland, J.Chem. SOC.,Faraday Tram. 2,74, 2187 (1978).
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The Journal of Physical Chemistry, Vol. 87, No. 2, 1983
chloroform-benzene mixtures. The only rationale for the maximum in the thermal diffusion factor that remains consistent with molecular association theory is that the interaction between chloroform and benzene is more like a strong van der Waals interaction rather than a long-lived hydrogen bond or donor-acceptor complex bond that can survive several molecular collisions. This conclusion is consistent with the very recent work of Homer and C ~ u p l a n d , who, ~ ~ ~ on ' the basis of a very extensive proton NMR study of chloroform-benzene-cyclohexane mixtures, concluded that no stable chloroform-benzene complexes are formed. The strongest intermolecular forces would be directed perpendicularly to the benzene ring causing a higher than average concentration of chloroform molecules on each side of the ring. The resulting symmetrical distribution of chloroform molecules about the benzene ring could be approximated by a molecular association model in which a 2:l associated species is formed in a single step. Thus, one obtains a very plausible explanation for the very striking correspondence between the experimental data and theoretical predictions assuming the single-step formation of a 2:l complex. Within the framework of this explanation the 21 complex in the association model would correspond to a maximum coordination number of 2 for chloroform molecules about the benzene ring rather than a formation of long-lived associated species. In view of the possibility that molecular association theory may correctly predict thermal diffusion behavior in mixtures with van der Waals like interactions, the temperature and concentration dependence of the chloroform-benzene thermal diffusion factors were fitted by least squares to theoretical predictions based on a singlestep formation of a 2:l complex. Comparisons of the calculations and the experimental data are shown in Figure 4. The scatter in the data is very evident on the expanded scale of Figure 4 that is designed to illustrate the temperature effect. The best estimate of the association en-
Ma and Beyerlein
thalpy obtained from the data is -2.2 f 1.0kcal. The large uncertainty in the association enthalpy reflects the large range of values for which comparable root mean square deviations (0.034.04)are obtained. Other results of the least-squares calculations are as follows: In K = 1107f T - 5.32,where K is the association equilibrium constant; DTf D 2= -615f T; D 1f D 2= -2.0;and D3f D2= -0.4. The result for the association enthalpy implies that the average energy for a chloroform-benzene interaction is 1.1 kcal, which is in good agreement with the value 0.88 kcal obtained by Barker and Smith5 from a statistical lattice model and heat of mixing data. Interaction energies in the range of 0.88-1.1 kcal are smaller than most long-lived hydrogen bond or donor-acceptor complex bond energies, which provides additional support for the view that the intermolecular forces between chloroform and benzene are primarily van der Waals forces. In summary, this work and earlier work1p2demonstrate that the thermal diffusion behavior for liquid mixtures with intermolecular interactions is very well characterized by molecular association theory. The interpretation of the chloroform-benzene thermal diffusion data in terms of van der Waals like interactions and a coordination number of two chloroform molecules about the benzene ring provides a very interesting method of applying equations of molecular association theory. At this point one can conclude that this explanation is only a plausible one. However, the striking correspondence obtained between theory and experiment demonstrates that this type of application of theory merits further investigation. Acknowledgement. We gratefully acknowledge the National Science Foundation for supporting this research under Grant CPE 8019544. Computer time provided by the Clemson University computer center is also acknowledged. Registry No. Chloroform, 67-66-3; acetone, 67-64-1; toluene, 108-88-3; benzene, 71-43-2; mesitylene, 108-67-8.
