THERMODYNAMIC PROPERTIES OF LIQUIDS
371
The Thermodynamic Properties of Liquids, Including Solutions. I. Intermolecular Energies in Monotonic Liquids and Their Mixtures1 by Maurice L. Huggins Arcadia Institute for Scientific Research, 136 Northridge Lane, Woodside, California 94062
(Received July 7, 1969)
The intermolecular interaction energies in liquids, including solutions, can be related to the intermolecularly contacting surface areas of the segments of which the molecules are composed, to the contact energies per unit contact area (for each type of contact), and to an equilibrium constant, relating the contact areas of the different types to their contact energies. Equations based on these ideas can be used to deduce the magnitudes of the parameters involved from heat of vaporization and heat of mixing data. These parameters can then be used for other systems containing the same types of segments, to predict heats of vaporization, heat of mixing curves, and derived quantities. As simple examples, CCl,, SiC14,SnC14, TiCL, CeHe, c-CsH,z, and their mixtures are considered. Each of these substances is treated as monotonic: containing only one type of intermolecularly contacting group. Heat of mixing curves for pairs of these compounds conform quantitatively to the theoretical equations.
Introduction This series of papers is a result of an attempt to apply certain ideas, first developed for polymer solutions,2-6 to solutions in general. One aim is to deduce the parameters needed to relate the thermodynamic properties of polymer solutions to their composition from experimental data on liquids, including solutions, of low molecular weight. I n the process of developing and testing the theory, it soon became evident that it yields results for the low-molecularweight systems that are of considerable interest and use in themselves, without regard to their possible application to systems containing high-molecularweight components. This theory can be considered an extension and refinement of the theories of Hildebrand6J and Scatchard.* It also embodies some concepts related to those in the “quasi-chemical” treatment of Guggenheim,g further developed by Prigogine.lo It differs from these other treatments, however, in several important respects. These differences are responsible for the more quantitative agreement with experiment now obtained. Moreover, the new theory is much more readily applicable to systems containing molecules that contain segments that are chemically different. This first paper in the series deals with fundamental ideas and equations concerned with the cohesive energies in liquids and with the application of these ideas and equations to a few simple liquids and their mixtures.
Fundamental Ideas Interaction energies between pairs of atoms fall off quite rapidly, in general, as the interatomic distance
increases. By far the largest part of the intermolecular energy in a liquid comes from the interactions between pairs of atoms in adjacent molecules that are closest together. Moreover, in comparing different liquids of similar type or solutions of different concentrations, the sum of the intermolecular energies that are not due to close atom pair interactions changes but little. There is thus ample justification for concentrating attention on the close neighbor interactions, as the writer has done in other applications of the “s tructon” theory.’l-l The structure of any liquid, except perhaps one containing only monatomic molecules, is too coinplex and too little known to permit the calculation of the t,otal intermolecular energy by direct summation of the atom-to-atom interaction energies. Also, pres(1) Preliminary reports of the theory outlined in this paper have been presented at the 155th and 157th National .Meetings of the American Chemical Society, Ban Francisco, Calif., April 1968, and Minneapolis, Minn., April 1969 [see Polymer Preprints, 9, 558 (1968) and 10, 334 (1969)l and in a lecture at Kent State University [J. Paint Techno$.,41, 509 (1969)l. (2) M. L. Huggins, Ann. N . Y . Acad. Sci., 43, 1 (1942). (3) M. L. Huggins, J. Polgm. Sci., 16, 209 (1955). (4) M. L. Huggins, “Physical Chemistry of High Polymers,” John Wiley & Sons, Inc., New York. N. Y., 1958, Chapter 6. (5) M. L. Huggins, J . Amer. Chem. Soc., 86, 3535 (1964). (6) J. H. Hildebrand and R. L. Scott, “Solubility of Nonelectrolytes,” 3rd ed, Reinhold Publishing Corp., New York, N. Y., 1950. (7) J. H. Hildebrand and R. L. Scott, “Regular Solutions,” PrenticeHall, lnc., Edgewood Cliffs, N. J., 1962. (8) G. Scatchard, Chem. Rev., 8, 321 (1931). (9) E. A. Guggenheim, “Mixtures,” Clarendon Press, Oxford, 1952. (lo) I. Prigogine, “The Molecular Theory of Solutions,” NorthHolland Publishing Co., Amsterdam, 1957. (11) M. L. Huggins, J . Phys. Chem., 58, 1141 (1954). (12) M. L. Huggins, Bull. Chem. Soc. Jap., 28, 606 (1955). (13) M. L. Huggins, Macromolecules, 1, 184 (1968). (14) M. L. Huggins, Inorg. Chem., 7, 2108 (1968). Volume 7 4 , hiumber B January 22, 1970
MAURICE L. HUGGINS
372 ent knowledge of the dependence of these interaction energies on interatomic distances is, except for the interactions between simple ions116s16insufficient. Even in the very important case of H ** . H interactions, this is unfortunately true.17J8 For these reasons it is necessary to use a model, hoping that it will approximate sufficiently well the actual liquid and yet be simple enough to yield relationships that can be applied to experimental measurements on actual solutions. The model to be described appears to meet these requirements. Each molecule is considered to have a molecular surface, with the surfaces of neighboring molecules in mutual contact. If the molecules contain segments that are chemically different, such that different types of segments would be expected to interact differently with segments of other molecules, the molecular surface is considered to be composed of the segment surfaces of the component segments. For example, a normal alkane molecule is treated as consisting of two methyl segments and n - 2 methylene segments. Some of the molecular surfaces and segment surfaces do not contact other surfaces, but it seems reasonable to assume (except for molecules making intramolecular contacts, such &s those composed of long flexible chains) that for each segment type the average intermolecularly contacting segment surface area is constant at a given temperature, regardless of variations in the types and numbers of other segments. I n general, a segment surface can make contact with surfaces of segments of the same kind or of other kinds. It is assumed that for each kind of segmentsegment contact, the average contact energy per unit area of contact is constant at a given temperature, regardless of variations in the types and areas of other contacts. The relative contact areas of the different types should be such as to minimize the free energy. It is assumed, therefore, that the relative contact areas are . governed by one or more equilibrium constants, these constants being related in a n appropriate way to the interaction energies per unit contact area. With the foregoing assumptions one can derive equations relating the cohesive energy in a given system to the numbers of segments of the different types, the average intermolecularly contacting surface area for each type of segment-segment contact, and one or more equilibrium constants (if there are two or more kinds of segments). These equations can be tested against experiment. The parameters, once dctermined, should be applicable to many systems containing the same segments or segment-segment contacts. The experimentally determined dependence of the parameters on temperature and pressure should be useful in extending our knowledge of atomic and molecular interactions. Observed departures from the theoretical relationships deduced from the model will require theoretical or experimental explanation. The Journal of Physical Chemistry
Equations Let types of segments be designated by subscripts a, p , etc., and types of segment-segment contact by subscripts aa, ab, Po, etc. Let the intermolecularly
contacting surface areas in 1 mol of substance or mixture be designated by u,, uol etc. Let the average intermolecularly contacting surface area per mole (Avogadro's number) of single segments of the a (or p, etc.) type be designated by uaa (or upa, etc.). Let the average areas of intermolecular contact per mole for the different types of contact be designated by u,, uap1 upB, etc. Let the average energies per unit contact area for the different types of intermolecular contact be designated by e, a,@, app, etc. In general these energies are attraction energies, hence negative, in accordance with convention. (The unit area need not be specified, since the quantities obtained are either products of the form ue or ratios, such as up/u,.) If, in a given system, there is but one type of segment, hence only one type of contact, the total intermolecular energy (the negative of the cohesive energy) per mole is obviously
E = u,,~,,
= n , ~ , ~ e ~ ~ / 2
(1)
where n, is the number of a-type segments per molecule. If there are two types of segment, hence three types of contact
E =
umxeaa
u, =
-t u p p ~ p p4- ~ 2uaa
up = 2upp
+ +
n
p
~
a
~
(2)
gap
(3)
cap
(4)
The equilibrium constant, relating the contact areas of the three types, I define by the equation
K=
w2
______ 4a, upp
(5)
The 4 in the denominator is included to make K equal to 1 for perfect randomness of contact formation, with no preference for either of the two possibIe contact types as an (or p ) segment is added, hypothetically, to an equimolal mixture. The equilibrium constant can reasonably be related to the contact energies by an equation of the form (Y
K
=
A exp(-Ae/kT)
(6)
where A€ = 2 ~ , p - eaa
-~pp
(7)
(15) M. L. Huggins, J . Chem. Phys., 5 , 143 (1937). (16) M . L. Huggins and Y . Sakamoto, J . Phys. SOC.Jap. 12, 241 (1967). (17) M. L. Huggins, Makromol. Chem., 92, 260 (1966). (18) M. L. Huggins in "Structural Chemistry and Molecular Biology," A. Rich and N. Davidson, Ed., W. H. Freeman and Go., San Francisco, Calif., 1968, p 761.
THERMODYNAMIC PROPERTIES OF LIQUIDS If there are more than two segment types, more than one K is required. The K , A , k, and Ae constants in eq 5, 6, and 7 should then be given subscripts K,,, etc. The IC in eq 6 is not the Boltzmann constant, since its magnitude must depend on the choice of the unit of area and since the unit contact areas are not independent entities like gas molecules. The coefficient A is related to steric and other factors, in addition to Ae, affecting the relative amounts of the different types of contact. For present purposes no use need be made of eq 6; neither A nor k needs to be evaluated. The significance of A will, nevertheless, be briefly discussed at the end of the next section. Further discussion can well be postponed until after sufficient values of the temperature dependence of the solution parameters have been accumulated. From eq 3,4, and 5 one can readily deduce Q.8
=
-2(ua
+ ug)[l - (1 + Y)”~I K’
and
where
K‘ = 4
(i-
1)
and
373 simplicity, the latter procedure will be used here. Equation 1 then applies, with na = 1. The propriety of treating these substances as monotonic might be questioned, especially in the cases of Sn Clr and TiCL, since these compounds can add chloride ions and some organic chlorides to form complexes in which the coordination number of the metal ion is 6. Perhaps, in a mixture with CCl, for instance, Sn (or Ti) atoms “make contact” with some of the C1 (C) atoms. If so, the molecules can still be treated as monotonic, but the magnitudes of the u0Mcl1 and eaaS constants will be different from what they would be without the M * C1 contacts. The magnitude of the molal intermolecular energy, can be estimated hence also that of the product u,~,, from the standard heat of vaporization, AH,”, with the aid of the following equations
-
AH,” = AE,” AEv”
=
-Em01
interactions
+
CCL, SiC14, SnCI4, Tic14 and Their Mixtures As first examples the tetrachlorides of C, Si, Sn, and Ti will be considered. Each will be treated as a “monotonic” substance, containing only one kind of atom or group, with regard to intermolecular interactions. For our purpose, that group (“segment,” in the preceding theoretical development) might either be considered as a chlorine atom attached to an atom of C, Si, Sn, or Ti, or as the whole molecule. These two alternatives are equivalent, except that the UMCl, obtained by the latter procedure will be four times the UCI(M) obtained by the former procedure. For
AEinternal
+
(14) AEexternal
(15)
AVO is the molal volume of the ideal gas minus that of the liquid. E m o l interactions is the intermolecular energy in the liquid (the negative of the cohesive energy), designated in eq 1 merely as E. AEinternal, the difference between the energies of vibration and rotation of the atoms and groups within the molecules in the gaseous and liquid states, is probably close to zero. AEexternal is the difference between the energies of translation and rotation of the whole molecules in the gaseous state and the energies of vibration, torsion, and (in some cases) rotation of the whole molecules in the liquid state. These external energies in the liquid are difficult to estimate accurately. For the present I shall follow Bagley and co~vorkers~~ in putting AEexternal
Substitution of these equations into eq 2 for the molal interaction energy
+ PAV”
= -3RT/2
(16)
for molecular liquids of the sort dealt with here. This may well be inaccurate and have to be modified later, especially when dealing with more polar compounds. Fortunately, inaccuracies in the E values do not affect the accuracy of the treatment of heats of mixing, to be dealt with presently, or other solution properties. From the foregoing relationships, assumptions, and approximations
E
=
-AH,”
+ PAV” - 3RT/2
(17) Values of E , calculated by this equation for the liquids considered here, are listed in Table I. They may be in error by 1 kcal or more, but the differences between the values for different compounds are probably correct to within 0.1 or 0.2 kcal. Mixtures of pairs of these compounds can be treated, for present purposes, as ditonic systems, containing (19) E, B. Bagley, T. P. Nelson, J. W. Barlow, and S-A. Chen, submitted for publication. Volume 74,Number B January BB, 1970
374
MAURICE L. HUGGINS molar enthalpies (or energies) of the components, each multiplied by its mole fraction in the solution
Table I : Intermolecular Energies in the Pure Liquids Compound
12
Temp, OC
20 20 20 20 25 25 25
AHYO,
kcal/mol
7 . 83a’b 7.24a’b 9 .77a’a 8.80a8c 7 . 77a‘b 8. 102d 7 . 90Eid
PAT’’:
E,
kcal/mol
kaal/mol
0.58 0.58 0.58 0.58 0.59 0.590 0.590
-8.12 -7.53 -10.08 -9.11 -8.07 -8.40 -8.21
IP
=
H - ziHi - ~2Hz= E
- xlE1 - ~2E2 (18)
From eq 1, with nu = 1 for the pure compounds, and eq 13, with u, and uB equal to xluao and respectively
P = -(z~u,’
a F. D. Rossini, D. D. Wagman, W. H. Evans, S. Levine, and I. Jaffe, “Selected Values of Chemical Thermodynamic P r o p erties,” National Bureau of Standards, Circular 500, U. 5. Government Printing Office, Washington, D. C., 1952. D. D. Wagman, W. H. Evans, V. B. Parker, I. Halow, S. M. Bailey, and R. H. Schumm, “Selected Values of Chemical Thermodynamic Properties,” National Bureau of Standards, Technical Note 270-3, U. S. Government Printing Office, Washington, D. C., 1968. C. E. Wicks, “Thermodynamic Properties of 65 Elements-Their Oxides, Halides, Carbides and Nitrides,” Bureau of Mines Bulletin 605, U. S. Government Printing Office, Washington, D. C., 1963. “Selected Values of Physical and Thermodynamic Properties of Hydrocarbons and Related Compounds,” American Petroleum Institute Research Project 44, Tables 5p (1945) and 7p (1948). a Calculated from the densities of the liquid and the ideal gas a t 1 atm pressure.
just two types of “segments.” As with the pure compounds, it is convenient to take the segments as the same as the molecules, although one might validly take them as quarter molecules: a chlorine atom attached to a specified central atom. It would not be justified, however, to assume that a chlorine atom attached to one type of central atom (e.g., C) has the same intermolecularly contacting surface area and the same contact energies as a chlorine atom attached to another type of central atom (e.g., Si). The excess enthalpy per mole or molar heat of mixing, essentially equal to the molar energy change on mixing, is the difference between the actual enthalpy (or energy) of 1 mo€ of solution and the sum of the
+ x2upo)Ae K‘
or
where r =
(21)
upo/uao
If K is exactly 1, K‘ is zero and eq 20 reduces to
The heat of mixing thus depends on the concentration ( ~ 2 ) and on three parameters: K (or K‘), r, and the product uaoAe. From sufficiently accurate measurements of IP as a function of the composition of the solution, these three parameters can be determined. The accuracy of determination of the parameters can be increased if, as in the present instance, data are available (for a single temperature) for more pairwise mixtures than the number of segment types. Use can then be made of the additional requirement that the r values must be mutually consistent. Also, if data for a single mixture are available at a series of temperatures, it can reasonably be required that
Tabfe 11: Parameters for Mixtures“
aa”(rap
-
fad
Sic14 SnC14 Tic14 SnClr Tic14 Tic14 CClr CsHiz CeHn a
20.2 20.2 20.2 20.2 20.2 20.2 25 25 25
1.00 1.00 7.0 1.00
1.0 1.0 1.00 1.00 1.00
1.230 1.290 1.70 1.05 1.38 1.32 1.080 1.112 1.030
0.306 0.490 0.193 0.506 0.277 0.32 0.214 1.411 0.278
0.376 0.632 0.328 0.531 0.383 0.425 0.232 1.569 0.286
16.24 16.24 16.24 15.06 15.06 20.16 16.80 16.80 16.14
Units for the quantities in the last eight columns are kilocalories per mole.
The Journal of Physical Chemktry
15.06 20.16 18.22 20.16 18.22 18.22 16.14 16.42 16.42
14.09 15.69 13.38 16.89 13.96 16.83 15.76 15.07 15.90
17.33 20.23 22.75 17.71 19.33 22.19 17.02 16.77 16.38
2.15 0.55 2.86 -1.83 1.10 3.33 1.04 1.73 0.24
up”(cag
-
CPP)
-2.27 -0.07 -4.53 2.45 -1.11 -3.97 -0.88 -0.35 0.04
THERMODYNAMIC PROPERTIES OF LIQUIDS
375
70
50
60
40
50
I
I
I
I
I
I
I
I
I
30 ;E mole
40
20
30
10
20
0
AE
0
0.2
0.4
0.6
0.8
10
XP
+
Figure 2. Heats of mixing for CCl4 TiC14 a t 20.2'; data from ref 20. The curve represents eq 22 with the parameters of Table 11, columns 4,5, and 6.
10
0
0
0.2
0.4
0.6
1.0
0.8
XP
+
Figure 1. Heats of mixing for CCh I- SnClr (0) and CCh Sic14 (A) a t 20.2"; data from ref 20. The curves represent eq 22 with the parameters of Table 11, columns 5 and 6.
the values for each parameter lie on a smooth curve when plotted against the temperature. The parameter determinations are readily made with an electronic computer or a computing desk calculator such as the Hewbtt-Packard 9100A. Kolbe and Sackmann20have published heat of mixing data at 20.2" for the six pairwise mixtures obtainable from the chlorides of C, Si, Sn, and Ti. The parameters given in Table 11, columns 4-6, give good agreement with their data, apparently within the probable limits of experimental error, judged from the scatter of the data points about smooth curves (see Figures 14). The agreement is poorest for the Sic& TiCl.4 solutions, for which the experimental results seem to be relatively inaccurate. Neglecting possible systematic errors in the experimental results and assuming the other parameters to be exactly correct, the probable error in each of the values in eolumns 4-6 Is estimated to be a few units in the last decimal place shown, except for the solutions containing TiCL as a component. For these the probable error might be a few units in the next to the last decimal place. If the other parameters
+
are allowed to vary also, any one parameter value might be varied by perhaps ten times this "probable error," without spoiling the agreement unreasonably. With the additional requirement that the T values be consistent, the permissible variation is between these two extremes. The precision of the parameter determinations will, of course, increase as more and better data on these systems and on other systems Containing one or more of the same components become available. The figures in columns 7 to 13 of Table I1 were calculated from those in columns 5 and 6 and the E values in Table I by means of eq 1, 7, and 21. Because of the uncertainties in the E values, already discussed, the individual values in columns 8 to 11 may well be in error by 1kea1 or more. For comparing relative values, however, and for use in predicting uoAc values for other systems containing one of the same components, the values in these columns are given t o the second decimal place, ie., to 10 cal. It is to be expected that revisions of these figures will have to be made, as better experimental data are obtained and as more systems are treated. The dattt require that the equilibrium constant K be close to unity, even though u,"Ac and uaoAe are not zero, except for the solutions of TiC14 with ccb and perhaps for those of TiC14 with Sic14 and SnCl4. (The SiCL Tic14 data are such as to make a reliable
+
(20) A. Kolbe and H. Saokmann, 2.Phgs. Chem. (Frankfurt am Main), 31, 281 (1962).
Volume 74, Number 2 January 22, 1970
376 70
l
I
1
1
I
l
I
I
I
60
50
40 ;E
(3) 30 0
0.4
0.2
0
0.8
0.6
1.0
XZ
+
Figure 4. Heats of mixing for Sic14 TiClr at 20.2'; data from ref 20. The curve represents eq 22 with the parameters of Table 11, columns 5 and 6.
20
of molecules in contact only with molecules of the same type and for a mole of molecules in contact only with molecules of the other type. For most
10
I
0 0
0.2
0.4
0.6
I
I
I
I
I
I
I
I
1.0
08
28
XP
+
Figure 3. Heats of mixing for Sic14 SnCl4 (0) and SnCI4 TiC14 (A) at 20.2'; data from ref 20. The curves represent eq 22 with the parameters of Table 11, columns 5 and 6.
+ 24
+
determination of K impossible. The SnCla TlC14 data are satisfied as well by K and r parameters of 2.0 and 1.34, respectively, as by the 1.0 and 1.32 in the table. Increasing the r value would necessitate some adjustment of parameters for some of the other solutions.) This may a t first seem surprising. Formally, it may be interpreted as indicating a value of the factor A , in eq 6, different from unity. This factor must allow for the fact that the unit areas of segment surface do not behave independently with regard to making contacts with other segment surfaces, since all the unit areas of each segment surface are connected together. The shapes of the segment surfaces must also be involved, as well as other factors. Perhaps more important is the fact that the difference between the interaction energies of a given segment type for contacts with like and unlike segments is, in the examples being considered, oi the order of magnitude of the gas constant times the absolute temperature, roughly 0.6 kcal/mol. Illustrating this, columns 12 and 13 of Table I1 show the differences between the average intermolecular energy for a mole The Journal of Phyakal Chemistrg
20
16 A E
12
8
4
0 0
0.2
0.4
0.6 X2
+
0.8
1.0
Figure 5. Heats of mixing for CeHB CC14 a t 25'; data from ref 21. The curve represents eq 22 with the parameters of Table 11, columns 5 and 6.
THERMODYNAMIC PROPERTIES O F
LIQUIDS
377
of the solutions the values in these columns are not more than a few times RT, indicating that changes in intermolecular contacts take place quite readily, hence frequently. However, column 13 shows relatively large negative values for the solutions of Tic14 with CCld and SnC14. This means that Tic14 molecules attract CCL and SnCl4 molecules considerably more strongly than they attract other TiCL molecules. It will be interesting to see if accurate data for the Sic& TiCL system will lead to a similar result. It thus seems likely that, except for the solutions of TiCL with CC14 (and possibly those of TiCL with SiCL and SnC14), the magnitudes of the differences in oontact energies for the different types are insufficient to prevent practically perfect random mixing of the molecules. This does not, of course, lead to athermal mixing. These solutions appear to be “regular” solutions, in the Hildebraiid sensea6J
+
Benzene, Cyclohexane, and Their Mixtures with Each Other and with Carbon Tetrachloride As further examples, C6H6,c-C~HE,and their solutions with each other and with
cc14 will be considered.
35
30
25
20 E;
15
10
l
l
I
0
I
0.2
I
I
I
0.4
I 0.6
1
I
I
0.8
l
l
l
l
l
l
l
I50
TiE
mole
50
0 0
02
0.4
0.6
08
10
x2
+
Figure 7. Heats of mixing for CeHs C-CBHI~ at 25’; data from ref 24. The curve represents eq 22 with the parameters of Table 11, columns 5 and 6.
Again, each of these will be treated as monotonic. One might, alternatively, treat benzene and cyclohexane molecules each as ditonic, their central cores making contact directly with hydrogen or chlorine atoms of other molecules, but for our present purpose this is not necessary. Each molecule as a whole can be considered as a single “segment.” For pure benzene and pure cyclohexane the magnitudes of the intermolecular energy, per mole, and so of the u,~,, products can be estimated as was done for the tetrachlorides. Making the same assumptions and approximations, the E values listed in Table I are obtained. Heats of mixing of solutions of benzene and carbon tetrachloride at 25” have been reported by a number of groups of researchers. The older data have been carefully reviewed and compared with their own new data by Larkin and McGlashan.21 Their data appear to be the most accurate that cover a wide range of composition. They will be used here. It should be noted, however, that the true values are probably a little higher (about 0.2 cal/mol for an equimolar mixture), as noted by Larkin, Fenby, Gilman, and Scottzz and at the conclusion of the Larkin-McGlashan paper. One suspects that the data used here for the C6H6 C6Hl2 and ccl4 C6H12 solutions are also slightly in error, perhaps by a similar amount. For all three mixtures the data are here used as published, with the realization that the magnitudes of the parameters, especially the uaoAe parameters, and other quantities
+
5
0
200
+
x2
+
C-C~HIZ at 25’; data Figure 6. Heats of mixing for CClr from ref 23. The curve represents eq 22 with the parameters of Table 11, columns 5 and 6.
(21) J. A. Larkin and M. L. McGlashan, J . Chem. Soe., 3425 (1961). (22) J. A. Larkin, D. V. Fenby, T. S. Gilman, and R. L. Scott, J. Phys. Chem., 70, 1959 (1966). Volume 74, Number S January W ,1070
MAURICE L. HUCGINS
378 derived from them may have to be modified slightly later. For the ccI4 CeH12system heats of mixing reported by Adcock and McGlashan2*and for the CsH8 CsH12 system those published by Peiia and Martin24 are used. It may be noted that Perk is a former collaborator of McGlashan. The parameters obtained for the three systems, by equations and procedures like those used for the mixtures of tetrachlorides, are included in Table 11. The close agreement with the individual data points is shown in Figures 5-7. For each of these three systems, as with most of the tetrachloride mixtures, a value of K equal to unity, corresponding to a regular solution, is found to yield satisfactory agreement. Mutually consistent values of r are obtained. As shown in columns 12 and 13, the energy differences for different types of close neighbors are quite small.
+
+
Summary and Conclusion A new theory for the molecular interaction energies in pure liquids and liquid solutions has been described. Equations have been presented for liquids containing only one or two chemically different types of molecules or segments. Some of the parameters can be deter-
The Journal of Physkal ChmiStru
mined, roughly, from heats of vaporization; others, more accurately, from heats of mixing. According to the theory, the parameters should be transferable from one system to others (at the same temperature) containing the same segments or combinations of segments. This has been tested with regard to mixtures of two monotonic substances at different concentrations and with regard to the relative contacting surface areas of different segment types. Quantitative agreement with accurate heat-of-mixing data has been obtained. Extensions and further applications of the theory will be presented in future papers.
Acknowledgment. I n the development of this theory I have had discussions with many other scientists. For their comments and suggestions I am very grateful. I also want to acknowledge my great indebtedness to the experimenters who have provided, in the scientific literature, the excellent data that I have used, and am using, to test my theory and various tentative hypotheses. (23) D. S. Adcock and M. L. McGlashan, Proc. Roy. Soc., Ser. A , 226, 266 (1954). (24) M.D.Peiia and F. F. Martin, An. Real SOC.I s p a n . Fis. Quim., Ser. E , 59, 323 (1963).
