GREEKLETTERS c
= energy dissipation rate in slurry per unit mass of
ip
= = = = = =
V
q p~ pp Pt
particle-free liquid, ergs/(g sec) porosity of carbon particles tortuosity factor, defined by eq 26 kinematic viscosity, cm*/sec eddy size, defined by eq 18 density of particle-free liquid, g/cma density of carbon particles, g/cma = density of solid Phase, true density, of carbon Particles, g/cma
Harriot, P., A.1.Ch.E. J . 8, 93 (1962). Kawazoe, K., Fukuda, Y., Kagaku Kogaku (Abr. Ed. Engl.) 3, 250 (1965). Levins, D. M., Glastonbury, J. R., Chem. Eng. Sci. 27,537 (1972). Misic, D. M., Smith, J. M., IND.ENG.CHEM., FUNDAM. 10, 380 (1971). Nagata, S., Yamamoto, K., Hashimoto, K., Naruse, Y., Kagaku Kogaku 24, 99 (1960). Satterfield, C. N., “Mass Transfer in Heterogeneous Catalysis,” M.I.T. Press, Cambridge, Mass., 1970. Schneider, P., Smith, J. M., A.I.Ch.E. J . 14, 886 (1968). Shinnar, R., Church, J. M., Ind. Eng. Chem. 52, 253 (1960). RECEIVED for review May 12, 1972 ACCEPTEDJanuary 12, 1973
literature Cited
Brian, P. L. T., Hales, H. B., A.Z.Ch.E. J . 15, 419 (1969). Brian, P. L. T.. Hales, H. B.. Sherwood. T. K.. A.Z.Ch.E. J . 15. 727’ (1969). ’ Calderbank, P. H., “Mixing, Theory and Practice,” Vol. 1, Chapter 6, Academic Press, New York, N. Y., 1966.
Acknowledgment is made to the Donors of The Petroleum Research Fun>, administered by the American Chemical Society, for the support of this work. Also, the gift of Filtrasorb by the Calgon Corporation is acknowledged.
Thermodynamics of Mixtures Containing Polar Liquids Jack Winnick University of Missouri, Columbia, M o . 66601
The partition function for polar liquids i s extended to mixtures using Scott’s two-fluid theory. The resulting expressions for the excess functions are tested against data for ten polar-polar and ten polar-nonpolar systems. One empirical mixture parameter i s required for each system. Its value i s set using an excess enthalpy datum. Good representation of the entire excess enthalpy and volume curves i s found for most systems, including those which are “cubic” in appearance. Excess entropy predictions are nearly always too high due to the degree of disorder assumed in the model.
R e c e n t l y a partition function was developed from a simple model of a pure nonpolar liquid (Winnick and Prausnitz, 1971a). Using a three-parameter theory of corresponding states, the partition function was generalized into a form which accurately correlated the volume and energy properties of nonpolar liquids ranging in complexity from argon t o high molecular weight paraffins and a giant siloxane. Two-fluid theory (Scott, 1956) was then utilized t o apply the partition function t o the description of nonpolar liquid mixtures (Winnick and Prausnitz, 1971b). Excess free energies, enthalpies, and volumes were calculated for a large number of mixtures of widely varying differences in component size and shape. Mixing rules required one empirical parameter, kI2,t h e deviation from the geometric-mean interaction energy. More recently, the pure-liquid theory was modified t o enable i t to describe polar liquids of simple structure (Winnick, 1972). The modification consisted of adding a reduced dipolar energy to the potential energy of each molecule in the liquid. For the eight species considered, no additional empiricism over t h a t required for nonpolar species was needed. It was found that the quantitative contribution of t h e polar energy of each was directly calculable and t h a t this contribution compared well with the theoretical value for cells formed of spherical molecules with point dipoles. The success of t h e above approach has prompted the present attempt a t describing excess properties of liquid mixtures containing polar components.
Theory
The configurational partition function for a pure polar liquid is
where
J ( p i ) = exp( -28.025exp(-4.84/Pf)
- 2.320/pi
+{}
(2)
and
Et
=
- [ L r i * / 8 i + mipi4/(Vi*)’RT]
(3)
For all pure components, mi = 1.0 x lo7 with units compatible with p , t h e standard dipole moment, in debyes, V* in cm3/mole, and RT in cal/mole. Here 8 is the molar volume reduced by a n empirically determined characteristic volume, V*. Similarly, p is the temperature reduced by a characteristic temperature, T*. The parameter, c, reflects the external degrees of freedom per molecule. The integration constant, {, is found from one vapor pressure datum but is not required in the treatment of mixtures. The characteristic energy, C*, is directly related t o the characteristic temperature Gi* = 9.008ciR2’i* Ind. Eng. Chern. Fundam., Vol. 12, No. 2, 1973
(4) 203
ETHANOL- WATER
a 0
A
H' H'
v'
6PxlO' 298.K 4 8 1 IO' 323.K 4.61 IOT 348.K
2 9 8 . ~ KISTER 1058 363.K NICHOLSON 1960 293.K
KURT2 l 9 S S
-
' 0 -
0
A
V'
298.K
FRANKS
I
H'
298.K
LAMA l 9 S S
196s
\
-2
-
/
H'
Y
>
-200;
0.2
0.4
0.6
0.8
-4
I3
HIO
Figure 1. Excess functions for water-acetone 0
Except for the term involving the dipole moment, p , in eq 3, the above equations and definitions are identical with those used to describe nonpolar liquids and mixtures (Winnick and Prausnitz, 1971a,b). The extension of the polar partition function to mixtures is handled in precisely the same manner as was done for nonpolar mixtures. For a binary mixture, Scott's two-fluid theory requires two types of cells: one wilh a component 1 molecule at its center, the other with a component 2 molecule a t its center. The configurational partition function for a mixture of mole fraction xtis
(5) where
E*,
=
- [C,,*/P,,
+ lWi,]
0.2
0.4
Mixing Rules
1.0
Figure 2. Excess functions for ethanol-water
N A is Avogadro's number. The packing factor, (, is assumed to be the same for all mixtures and thus does not need to be determined. The interaction probability for molecule j in either cell i o r j is dependent on its size
c 2
P, = x,.ldi
ZLUld
z=1
(9)
The parameter d is preassigned on the basis of shape (Winnick and Prausnitz, 1971b). For all mixtures considered here, d = 1.0. The pure component molecular diameter, u j , is assignable from V,*. The collision diameter of either cell is the interaction-probability-weighted average of the binary collision diameters 2
(6)
and Mi,is the coiitribution due to the polarity of either or both species. The excess thermodynamic properties are now found by standard techniques (e.g., Winnick and Prausnitz, 1971b) once the composition dependence of Vi,* and Vi,* are specified by the mixing rules. The third parameter, c l , is independent of composition since the external degrees of freedom of each molecule have been assumed constant.
0.8
0.8 %EtOH
ut,
=
C~ 3=1
3 ~ 1 5
The unlike collision diameter is assumed to be
The coordination number of each central molecule in its cell is assumed directly proportional to its surface area and inversely proportional to the surface area of each cell wall occupant 2
The same assumption of a semi-random mixture is made here as was made for nonpolar mixtures. T h a t is, the local mole fractions comprising both cells are the same. However, because molecules 1 and 2 are different sizes, the coordination numbers of their cells are different and are also functions of the overall mixture composition. Nonpolar Parameters
The characteristic volume and energy in the mixture are related to individual cell properties in precisely the same manner as for iionpolar mixtures
s,
= S t u i m Z i CP , U , , ~ 3=1
(12)
The cell characteristic energy, ,(E is the probability-weighted average of the binary interaction energies
All the above mixing rules are identical with those used for nonpolar mixtures. Additionally, we previously allowed one empirical parameter, k12, the deviation from the geometricmean unlike interaction energy €12
=
(€ll€zz)l'z(l -
k12)
(14)
However, in the present work it is assumed t h a t unlike dipole-dipole and dipole-induced dipole effects outweigh any 204
Ind. Eng. Chem. Fundarn., Vol. 12, No. 2, 1973
ACETONE -METHANOL
METHANOL- WATER
2 08. K
m!,
-saaJ ___ 0
.~.I~Io’
PA
0.2
0.8
0.8
1.0
0.2
XMrOH
Figure
effect of a deviation from the geometric-mean dispersive interaction energy, so that for all systems considered = 0.0
0.8
I
XACETONE
Figure 3. Excess functions for methanol-water
kl2
0.6
0.4
(15)
4. Excess functions for acetone-methanol
The polar species is component 1. The parameter, a2, is in the form of a molecular polarizability defined using the standard dielectric constant, e2
Dipole-Dipole Mixture Parameters
All thermodynamic excess properties of polar liquid mixtures can he calculated using the techniques described previously (Winnick and Prausnita, 1971b) once the terms, M i m in eq 6 are specified. It is assumed t h a t the contribution of dipolar interaction can be simply represented by a probabilityweighted average analogous to eq 13
c P@f
Excess Property Calculation
2
Mi.,
=
j-1
Equations 16, 17, and 19 are used with eq 20 to specify the terms M f , in the mixture partition function, eq 6. One empirical parameter, m12’,remains to be determined from binary data for each system.
(5
The excess Helmholtz energy, AE, is defined in eq 22 in
where
AE = Am Mil
= (1.0 X
10’)/~~~/(Vi.,*2RT)(i = 1,2)
(17)
2
2
z f A t - R T E xi:In x i i-1
(22)
I-1
terms of the configurational Helmholtz energy of the mixture, A , and those of the pure components, Ai. These configura-
and
dI12= m12~12~22/(V12*2RT)
(18)
where the theoretical unlike interaction energy (Bae and Reed, 1967) has been modified in a manner exactly analogous to t h a t for pure components (Winnick, 1972). The characteristic volume, Vlz*,is an “average” molecular volume defined by Vl2*
=
1 N*t[2 (UI,
+
UZ,)
I”
(19)
One empirical parameter, mlz, remains in the entire treatment. I t s value is expected to be about the same order as m for the pure components, 1.0 X lo7, in the absence of strong associating forces.
tional Helmholtz energies are in turn related to the corresponding configurational partition function
A m , i = -kT In
Qm,i
(23)
At low pressures the excess Gibbs energy is nearly identical with A E , so t h a t eq 22 is used to calculated GE. Similarly, the excess enthalpy is essentially equal to the excess internal energy, which is calculated in a manner analogous to that for the excess Helmholtz energy noting t h a t
Urn,*= kTZ(bIn Qm,t/’bT)
(24)
The excess volume, VE 2
VE
=
Vm-
ZiVi
(25)
2=1
Dipole-Induced Dipple Mixture Parameters
When one component is nonpolar, the interaction term, MI,, is no longer given by eq 18. Instead, the dipoleinduced dipole energy is obtained from the first term in t h e theoretical expression (Bae and Reed, 1967) for simple pairs. Here the polar molecule is assumed to be completely nonpolarizable.
MIZ= m 1 2 ‘ / ~ ~ ~ a ( ~ / ( V ~ ~ * ) ~ (20)
is calculated on the assumption that the equation of state for each component in the mixture has the same form as that for the pure component
The left side of eq 26 is negligible near atmospheric pressure. Ind. Eng. Chern. Fundarn., Vol. 12, No. 2, 1973
205
ETHANOL- ACETONE 2SB’K
Table 1. Excess Property Results 280-
Temp, m12
O K
X lo-’
HE
GE
VE
Poor Poor Poor Poor Poor Poor Poor Poor .
...
A. Polar-Polar Mixtures System Water-acetone Ethanol-water Methanol-water Acetone-methanol Ethanol-acetone Acetaldehydeethanol Chloroform-acetone Chloroformacetaldehyde Chloroformmethanol Chloroformethanol
298 363 298 323 348 298 298 298 298
2 92 2 68 52 4 8 45 3 1 1 25 0 45 -2 0
308 298
15 6 12 6
298
(17 0)
298
... Exc. I
.
.
... Good ...
Good Fair
Good Poor Good Good Poor . . . Poor Poor
...
Poor Poor Poor
-
Temp, O K
Exc. Exc. Exc. Exc. Exc. Exc. Exc. Exc. Good
m12’
X
HE
GE
B. Polar-Nonpolar Mixtures System Methyl chloride193 -0.25 Exc. . . . Exc. Good propane 213 -0.6 318 Good Poor Ethanol-n-hexane 3.6 Ethanol278 2.6 Good Poor cyclohexane Xethanol-carbon 293 Exc. Poor 3.9 tetrachloride Fair Poor Ethanol-carbon 318 2.6 tetrachloride Fair Poor Acetone-carbon 318 8.0 tetrachloride -1.2 Exc. Good Chloroform-carbon 298 tetrachloride Fair Fair -1.0 Ethanol-benzene 318 Poor Poor Chloroforma298 (1.0) ethanol Chloroforma298 (1.45) Poor Poor methanol a Assumed nonpolar.
VE
... ... ... Poor Exc. Fair .
..
0
0.2
0.4
0.6 %EtOH
0.8
I
Figure 5. Excess functions for ethanol-acetone
r
-
--
ACETALDEHYDE ETHANOL 298.K rn -2.0 a IO’
loool
Exc. Exc. Fair , ,
.
The mixture volume, V,, in eq 25 is then 2
V”, =
i=l
ziBrmVi,*
(27)
where each Vtm*must be determined from eq 7 , 9, 10, and 11 a t any mole fraction in exactly the same manner as was done for nonpolar mixtures (Winnick and Prausnitz, 1971b). The value of the packing parameter, & i s assumed t h e same in the mixtures as for the pure components and thus need not be determined. Results
Eighteen binary systems were tested. Of these, ten were mixtures containing two polar components. The other eight and two of the previous groups were comprised of a polar and a presumed nonpolar component. The fitting technique for each system consisted of determining the value of the parameter m12or 11112’ which provided the best overall fit of the excess enthalpy a t a given temperature. The enthalpy, rather than the Gibbs energy, was chosen for parameter determination in order that the parameter be more truly related to the interac206
Ind. Eng. Chern. Fundam., Vol. 12, No. 2, 1973
- 20010
0.2
0.4 0.8 0.8 %ACETALDEHYDE
I
Figure 6. Excess functions for acetaldehyde-ethanol
tion energy. The Gibbs energy is a combination of energy and entropy effects. If the parameter were fixed using GE and the HE prediction were in error the parameter value would thus have been compromised by the inaccuracy of the entropy calculation. After m12or m12’ was determined, the other excess properties were calculated directly. I n total, good results for the enthalpy of mixing were obtained for all but two polar-polar and five of the polar-nonpolar systems. The two polar-polar mixtures for Tthich poor results were obtained both contained chloroform, which has a relatively high polarizability and low dipole moment. For this reason, these two systems were also tested as being polarnonpolar. Where experimental data were available, excess volume prediction was generally satisfactory. However, 111 most cases
-
CHLOROFORM ACETONE 3OO.K
m',, H' V'
}
METHYL CHLORIDE- PROPANE -0.26~10' I93.K m:t= -O.6xlO4 213.K
{
16.eaio'
K
STAVELEY
1955
D
0
240
H' H' 0'
193.K 213.
213.
K
I
KAPPALLO 8 SCHAFER 1962 0
0 0
;200 8
\
R
=I60
I, (D
I20
00 -400.
40 0
0.2
0.4
0.6 XCHCl,
0.6
1.0
0
0
0.4
0.2
0.6
0.8
I 3
XMrCl
Figure 7. Excess functions for chloroform-acetone
Figure 9. Excess functions for methyl chloride-propane CHLOROFORM -ACETALDEHYDE 298.K
m,, 0
0
0.2
-
ETHANOL CYCLOHEXANE 278.K ml,=2.exi04 H' SCATCHARD 1964
-12.0a10'
XCHCA, 0.4 0.6
0.8
I,
A
-
-,. t
60
v'
3OO.K
SCATCHARD 1964
2ool
-a 0
-100
E
\ V
1 u
Y
"- -160
>
I
-2oc
-
1.0 0
260
-300
0
0.2
0.4
0.8 'EtOH
0.8
.LO
Figure 10. Excess functions for ethanol-n-hexane
Figure 8. Excess functions for chloroform-acetaldehyde
the calculated Gibbs energy was severely below experimental. The results are summarized in Table I. Polar Mixtures
The results for the polar liquid mixtures are shown in Figures 1-8. The two systems tested for which HE could not be reasonably fit with the one adjustable parameter, m12, were chloroform-methanol and chloroform-ethanol. For the other systems, t h e partitjon function successfully describes t h e excess enthalpy even in t h e cases where HE is highly asymmetrical (even "cubic") with composition. The temperature dependence of t h e HE was checked for two systems whose fit a t one temperature was good. For these systems, water-acetone and ethanol-water (Figures 1 and 2), the temperature dependence of HE mas qualitatively correct.
However, t o achieve quantitative fit a t increased temperatures the value of mI2 had to be decreased somewhat. Since positive values of mI2 indicate mutual attraction, this decrease with temperature is expected. The predicted excess volumes are compared with esperimental values where reliable data were fouiid. The results seem reasonable considering the simple arithmetic mean rule (eq 11) used for t h e unlike diameter. Honever, the calculated excess Gibbs energies for t h e polar systems were all considerably low. For example, the equimolar chloroformacetone prediction was -228 cal or about 100 cal below t h e measured value. The GE predictions are generally riot as poor for systems which show a lower degree of association. Thus, the excess entropy is in all cases lower than is predicted by the two-fluid model used. In other words, the associating solutions have a higher degree of order than that described by the semi-random mixture. Ind. Eng. Chem. Fundam., Vol. 12, No. 2, 1973
207
lCHLOROFORM ETHANOL-n-HEXANE 3I6.K
~~
CARBON TETRACHLORIDE 296.K
:,
m’,,.-1.2x104
m = 3.0x IO‘
r’
-
BROWN I 9 6 4
I
A
H’ V’
AOCOCK 1954 MCGLASHAN 1954
Q’
eo
’
fE
I \
0 V
I
0’ 0
0.2
0.4
0.6
0.6
1.0
XCHCIt
Figure 13. Excess functions for chloroform-carbon tetrachloride XETOH
Figure 1 1 . Excess functions for ethanol-cyclohexane
METHANOL- CARBON TETRACHLORIDE 293.K
m’,, 3.9~10‘ H’
v’
SCATCHARO 1952 l29E.K) PARASKEVOPOULOS 1362
100
-100
I
I
I
XM~OH
Figure 12. Excess functions for methanol-carbon chloride
tetra-
Polar-Nonpolar Mixtures
Five polar-nonpolar systems are shown in Figures 9-13. The cubic behavior of HE, when it appears, is reproduced as in the polar-polar system with the one empirical parameter, mlz’. I n addition, for those systems where a n unlike molecule repulsion is indicated by a negative value of m12’, a reasonable prediction of GE is obtained. These are methyl chloridepropane and chloroform-carbon tetrachloride. For these systems the SEcalculated from the semi-random model more closely approximates the true behavior. Fair fits of HE were obtained for the systems acetonecarbon tetrachloride and ethanol-carbon tetrachloride. The systems ethanol-chloroform and methanol-chloroform showed poor agreement between theory and experiment. While the cubic shapes of the HE curve of both systems were reproduced, as was not the case when both constituents were presumed polar (above), the magnitudes of the extrema were badly in error. The system ethanol-benzene shows a skewness in both GE and HE which was not reproduced by the theory. 208
!nd. Eng. Chem. Fundom., Vol. 12, No. 2, 1973
However, its excess volume, which is cubic, was predicted within 0.02 cm3/mole. Rowlinson (1958) has calculated the approximate contribution of the dipolar energy to GE for chloroform-carbon tetrachloride to be 8.5 cal. The present treatment yields 31 cal. This figure agrees more closely with the calculation of Prigogine (1957), but is no doubt too large. The reason for this is that no deviation has been allowed from the simple form for the dispersion energy, eq 14. If the parameter k12 in eq 14 is allowed to float, a nonpolar contribution to the equimolar GE of 17.5 cal can be obtained. This value, in agreement with that required by Rowlinson’s calculation of the polar contribution, yields a k12of 0.0040. This value for k12 is in excellent harmony with those obtained for carbon tetrachloride-benzene (0.0038) and carbon tetrachloridecyclohexane (0.0047) (Winnick and Prausnitz, 1971b), which must be the case (Rowlinson, 1958). Of course, if klz mere allowed to be nonzero, a new value for mlz’ would be obtained. I n the absence of rigorous calculations of the dipolar energy, a homomorphic nonpolar system must be selected (e.g., Blanks and Prausnitz, 1964) in order to fix klz. This selection is sometimes difficult (Maffiolo, et al., 1972). Furthermore, the percentage contribution of the “nonpolar” free energy will be much lower for the systems consisting of a t least one strongly polar component. T o provide a uniform treatment of all systems tested, k12 was always assumed to be zero. Conclusions
The semiempirical partition function for polar liquids has been extended to mixtures. For nearly all polar-polar mixtures tested, the excess enthalpy \vas successfully reproduced using only one empirical mixture parameter. The excess enthalpy, rather than the Gibbs energy, was used to fix this parameter because the enthalpy is more sensitive to the difference in the component molecules (e.g., Duncan and Hiza, 1972). Excess volume prediction showed qualitative agreement with experiment. Excess Gibbs energy predictions, made with the mixture parameter set by the excess enthalpy fit, were always in error due to incomplete entropy considerations. The effect of order in these polar mixtures must be incorporated into the theory if the excess Gibbs energy predictions are to be improved. However, the good fit of H E
indicates the energetic effects in solutions of simple molecules can be described by the partition function with the aid of one mixture parameter, the value of which is consistent with that for the pure component interaction (Winnick, 1972). The description of polar-nonpolar liquid mixture enthalpy is not quite so successful as that for polar-polar mixtures. However, for those systems with n-eakly repulsive unlike interaction energies (negative m12’,Table I), the excess Gibbs energy prediction agrees with experiment. These mixtures are much less ordered than those with strong mutual attraction. Thus, the semi-random theory used here accurately represented the excess entropy. The failure of both the polar-polar and 1)olar-nonpolar treatments for the chloroform-alcohol systems is due in part to the induction effect of’ each species on the other. T o include the 1-2 and the 2-1 induction effects as well as the permanent dipole interaction would require two additional terms, similar to 20, in eq 16. It is felt the extra empiricism involved is not justified a t this time. Acknowledgment
Joseph Kong helped with the calculations. literature Cited
Adcock, D. A,, McGlashan, 11.L., Proc. Roy. SOC.,Ser. A 226, 266 (1954). Bae, J. H., Reed, T. RI., 111, IND.ENG.CIXM.,FUSDIM.6, 67 (1967).
Blanks, R. E., Prausnitz, J. M., IND. ENG.CHEM.,FUNDAM. 3, 1 11964). Brown, I., Fock, W., Smith, F., Aust. J . Chem. 17, 1106 (1964). de Leew, H. L., 2. Phys. Chem. 77, 284 (1911). Duncan, A. G., Him, 31. J., IKD.EKG.CHEM.,FUNDAM. 11, 38 i1972). Franks,’F., Ives, D. J. G., Quart. Reu. Chem. SOC.20, 1 (1966). Hirobe, H., J . Fac. Sci. Tokzio Cniv. 1, 155 (1926). Jones, H. C., Bingham, E. C., Amer. Chem. J . 34, 481 (1906). Kappallo, W., Schafer, K., Z . Elektrochem. 66, .ill (1962). Kister, A. T., Waldnian, I). C., J . Phys. Chern. 62, 245 (1958). Kurtz, S. S., et al., J . Chem. Eng. Data 10, 330 (1965). Lama, 13. F., Lu, B. C., J . Chem. Eng. Data 10, 216 (1965). I‘Iaffiolo, G., Vidal, J., Iienon, H., IND.EKG.CHEM.,FUKDAM. 11, 100 (1972). RlcGlashan, 11.L., Prue, J. E., Sainsbury, I. E. J., Trans. Farad a y SOC.50, 1284 (1954). Xicholson, D. E., J . Chem. Eng. Data 5, 309 11960). Paraskevopoulos, Q. C., llissen, R. W., Trans. Faraday SOC.58, 869 (1962). Prigogine, I., “Molecular Theory of Solutions,” Chapter 14, North-Holland, Amsterdam, (1957). Rowlinson, J. S., Mol. Phys. 1, 414 (1935). Scatchard, G., ef al., J . Amer. Chem. SOC.74, 3721 (1952). Scatchard, G., Satkiewicx, G., J . Amer. Chem. SOC.86, 130 (19644). Scott, It. L., J . Chem. Phys. 25, 193 (1956). Stavely, L. A. K., Tupman, W. I., Hart, K. R., Trans. Faraday SOC.51, 323 (19%). Weast, It. C., “Handbook of Chemistry and Physics,” 50th ed: p D189, Chemical Rubber Co., Cleveland, 1969. Winnick, J., IND.ENG.CHEM.,FUKDLM. 11, 239 (1972). Winnick, J., Prausnitz, J. M., Chem. Eng. J . 2, 233 (1971a). Winnick, J., Prausnitz, J. AI., Chem. Eng. J . 2, 239 (1971b). RECEIVED for review May 17, 1972 ACCEPTED February 2, 1973 This work was carried out under the partial sponsorship of the Department of Defense (Project Themis).
Enthalpies of Mixing of Halogenated Methanes and Their Interpretation. 1. Dihalogenated Methanes Vittorio Ragaini, Cesare Giannini Zstitufo di Chimica Fisica, C-niversita di Xilano, Milan, Italy
Sergio Carra Zstituto d i Chiwiica E’isica e Spettroscopia, Cniversita di Bologna, Bologna, Italy
Enthalpies of mixing for binary mixtures of three dihalogenated methanes (CH2C12, CH2Br2, and CHAd at 2 5 ° C have been measured. The three systems show an endothermic behavior. The results of the excess enthalpies have been theoretically interpreted through the evaluation of the potential energy of the mixture following the procedure proposed by Hildebrand and Wood and employing the radial distribution function of hard spheres and a perturbing potential.
K n o w i e d g e of enthalpies of mixing of two or more liquids is important for many eiigineering calculations. Actually such data, for polar and noiipolar mixtures a t different cornpositions and temperatures, are not always easily available and therefore many attempts are in progress for the correlation or prediction of such thermodyiiamic data on the basis of theoretical (Rowlinson, 1969) or semiempirical models (Ahselineau and Reiion, 1970; Papadopoulos and Derr, 1959; Redlich, etal., 1959). In order to verify the therniodyiiamic behavior of mixtures of some halogenated hydrocarbons, a set of six biliary mix-
tures of halogenated methalies has been studied. I n this paper the experimental heats of mixiiig a t 25OC of dihalogenated methanes arid their interpretabion on the basis of intermolecular forces are reported. I n a subsequent paper (Ragaini and Carrh, 1973) the results for binary mixtures among CI12C12, CHC13, aiid CCl, \vi11 be given. The considered systems are: system 1, CH2C12-CH213r2; system 2, CH2C12-CHnIy; and system 3, CH21h-2-CH212. I11 the explored molar fraction field (0.1 5 z 5 0.9) the three systems show a n endothermic behavior, with maxima in H E which decrease in the folloiving order: system 2, about Ind. Eng. Chem. Fundam., Vol. 12, No. 2, 1973
209
