li’eb., 1963
315
KCYTB
ment is present as one or more pyridinates and addition of water converts the pyridinates to hydrates (in each case the solvate referred to is that which presumably activates the fluorescence). However, the spectral changes produced by adding relatively large quantities of water to pyridine solutions of chlorophylls are in marked contrast to those accompanying hydration of the pigment dissolved in benzene. Moreover, it is known that the absorption spectra of activated solutions of chlorophylls in benzene are independent of the nature of the activat0r.l The present data therefore demonstrate an interaction between chlorophylls and water which is distinct from the process of fluorescence ac tivation. Acknowledgment.-This investigation was made possible by a Research Grant (A-2733 C3) from the Ilivision of Arthritis and Metabolic Diseases of the United States Public Health Service. APPLICATION OF GESERALIZED QLASILATTICE THEORY TO HEAT OF PtlIXIKG D A T h FOR HYDROCARBON-HALOGES SUBSTITUTED HYDROCARBON SYST.ERIS BY J. B. OTT. J. R. GOATES.AND R. L. SNOW Department of Chemzstry, Brigham Young C’n,iaerszty. Provo, Ctah
Reeemed J u l y 2, 1962
It was the purpose of this investigation to determine how well a generalized quasi-lattice theory could describe the heats of mixing in hydrocarbon-halogen substituted hydrocarbon systems and to ascertain the magnitude of the energies of interaction that are required for a quasi-lattice interpretation of such systems. The very high heats of mixing and other related anomalies observed in hydrocarbon-perfluorohydrocarbon systemsl make them of special interest. Barker’s2#ageneralized quasi-lattice model that recognizes different types of sites on the same molecule was used in this study. To apply the theory, it is necessary to fix values for two types of parameters: (a) lattice constants that determine the number and types of contact points on each molecule, and (b) energies of interaction for all possible combinations of contact points. In previous ~ ~ we were r successful k ~ in ~describing ~ hydrocarbon-alcohol systems by assuming that each hydrocarbon tetrahedron occupied one site in a fourfold coordinated lattice. The same assignment was made in this study, and because of the similarity in size of the hydrocarbon and perfluorohydrocarbon tetrahedra, the latter was also assigned one site in the lattice. Each atom of chlorine and bromine was considered to occupy one site. The number of eontact points for each molecule was deduced from the structural formulas of the compounds. Type (I) is uscd to designate a contact point on a saturated hydrocarbon; (S), an aromatic hydrocarbon; (F), a perfluorohydrocarbon; and (Cl) and (Br) for contact points on chlorine and bromine atoms, respec(1) R.L. S c o t t , f . Phya. Chem,, 62, 136 (1958). ( 2 ) J. A. Barker, J . Chdm. Phya., 20, 1526 (3) J. A. Barker, zlizd., 21, 1391 (1963).
(1952).
(4) J. R. Goates, R.L. Snow, and M. R. Jam&, J . Phys. dhem., 65, 385 (1961). ( 5 ) J, Rh Goatds, Rh LASnow, and Jh B. O t t , ibid., 66, 1301 (l@32).
tbely. The number arid type of contact points assigned to each compound used in this study are: n-C6H14,14(1); n-C7H16, 16(I); i-CsH18, 18(I); Cy-CgH12, 12(I) ; CaH6, 12(s); COF14, 14(F); CiF16, 16(F); cC14, 12(C1); CzH4Cl2,4(I) and G(C1); C2H6Br, 5(I) and 3(Br); C2H4Br2, 4(I) and 6(Br). The interaction energy is defined as the energy change ia the quasichemical reaction 1/2(i-i) l/~(j-j) = i-j, where i and j represent the various types of contact points. The energies of interaction were fixed empirically at values ithat produced the best fit of experimental data taken from the literature. The average of the absolute values of the deviations a t mole fractions 0‘2, 0.4, 0.5, 0.6, and 0.8 was the criterion of best fit. The method of making the calculations has been described p r e v i o ~ s l y . The ~ ~ ~rather lengthy computations involved were made on an IBM-650 computer. Table I records tlhe empirically determined energies of interaction. The first three systems listed involved aromatic-aliphatic hydrocarbon type contacts only. The agreement among the three values, each determined from a different system, is fairly good. The average value of 70 cal./mole for the I-S interaction is in rough agreement with the 82 cal./mole value obtainedfor the same interaction from a study of alcoholhydrocarbon ~ y s t e r n s . ~The fourth system constitutes a test of the assumDtion that interactions between I type contact points on different kinds of molecules can be-assigned approximately zero energy The 5th-8th sysiems involve only a single (non-zero energy) type interaction in each system and allowed values for three different hydrocarbon-halogen interactions to be obtained. The discrepancy in the I-F values determined from the two different systems is rather large. The average value of 152 cal./mole, however, will reproduce the heat of mixing data to within 77” of the experimental values of both systems. The fact that a brainched chain hydrocarbon is involved in the 8th system may have something to do with the discrepancy. The theory is too crude and the data are too limited, however, to attempt to distinguish between normal and branched chain hydrocarbons. Systems 9-11 each involve two (non-zero energy) interactions, which 81-8assumed to be equal, allowing the values for four additional hydrocarbon-halogen interactions to be determined. The superscripts introduced at this point are used to distinguish between halogens that are from different types of molecules. For example, a chlorine in CCl, (Cl) has different properties than a chlorine in C2H4C12 (Cl”). In a similar manner a bromine in CzHsBr (Br’) is distinguished from one in CzH4Brz (Br”). Systems 11-15 are more complex in that three types of interactions had to be considered. Two out of the three constants required in each of these systems already had been determined by the study of the first ten systems. The remaining constant was then fixed a t the value that produced the best fit of the experimental data. Column four of Table I lists the one energy of interaction determined by a study of a given system; column three lists the assumptions made about the energy of the other interactions involved in that system. Of particular in1,erest is the comparison of the 14 cal./rnole 1 4 1 interaction and the approximately 150
+
516
NOTES
halogens. The experimental maximum value of 504 cal./mole could be obtained by assuming an I-F interaction energy of only 105 cal./mole. However, the curve was quite unsymmetrical with the maximum value occurring a t 0.62 mole fraction perfluorohexane. This resulted in a rather poor fit of the experimental data, the deviation being as much as 45% a t some composit ions. The high positive values shown in Table I for I-Cl”, I-Br’, and I-Br” are interesting. The halogens involved are connected to carbons that have attached hydrogens rather than other halogens as in the perhalohydrocarbons discussed above. This allows the halogen to take on a partial negative charge. One would expect that the repulsion between this partially charged halogen and the dissimilar saturated hydrocarbon site would contribute appreciably to the high interaction energy. Because of the way in which the quasi-lattice interaction energies are defined, however, one cannot separate such individual effects with the information available.
A 5 00
450
400
-
350
d 0
I .k
Vol. 67
300
0)
a. ul
.- 2 5 0 0)
TABLE I QUASI-LATTICE ENERQIES OF INTERACTIONS
L
0
0
u 200 System
cQ“%-ceHi4 6 CsHe%-CyHla 6 CeHerCJr-CeHiz 6 6 n-CeH14-)z-C&6 CCla-CeHe 7 CC1rCy-Ce,Hlz 7 n-CeF1d-n-C~H~4 8 n-C,Fiei-CBH18 8 ( CHzC1)~-cy-C&fl:! 9 (CHZBr)2-cy-C6H1210 (CHzC1)z-CsHe 9
m
.-
C
.-
150
I
* 0
c
Exptl. data Ref.
100
0
8
I 50
(CHzC1)z-CCld
9
CzH6Br-cy-C6Hlz 11 C2H6Br-CsHe 11
0
( CH2Br)z-CC14
- 50 0
.2
.4
.6
.8
1.0
M o l e F r a c t i o n o f C o m p o n e n t I. 1)Fig. 1.-Curve A, C6F14( 1)-cd&,(2); curve B, CZH~CL( CeHlz(2); curve c, C&3(1)-C&s(2); curve D, CzH4Brz(1)-CCl4(2); curve E, CC&(1)-CfiHIz(2); curve F, C2H4Br2( 1)-CCld(2); curve G, CzH,Br(l)-CsH6(2).
cal./mole average results obtained for I-F. The interesting point is that the quasi-lattice theory is able to account for the high (over 500 cal./mole maximum) heat of mixing in hydrocarbon-perfluorohydrocarbon systems with such a reasonably low interaction energy as 150 cal./mole. While this is large compared to the 14 cal./mole for the perchlorohydrocarbon system, it is only about twice as large as an aliphatic-aromatic hydrocarbon interaction and only about one-third as large as I-Br’, I-Br”, and I-CI” interactions. Thus, when interpreted by quasi-lattice theory, the heats of mixing of perfluorohydrocarbons with aliphatic hydrocarbons do not seem abnormal. A n attempt also was made to fit the C&‘14-C6H14system by assuming that each fluorine occupies a site in therlattice as do the larger
12
Assumed energies of interaction, cal./mole
None None Sone None None None None Kone None None I-S = 70; I-C1” = 500 I-C1 = 14; I-C1” = 500 None I-S = 70; I-Br’ = 550 I-Br” = 480; I-C1 = 14
Calcd. energy of interaction, cal./mole
I-S = 68 I-S = 72 I-S = 71 1-1 = 1 s-c1 = 9 I-C1 = 14 I-F = 171 I-F = 134 I-Cl” = 500 I-Br” = 480 s-C1”
=
91
C1-C1” = 236 I-Br’ = 550 S-Br’
=
68
C1-Br” = 213
The high energy of interaction of I-C1” and I-Br’ is seen to decrease by almost an order of magnitude when the hydrocarbon is changed to an aromatic compound. A dipole-induced dipole attraction between the partially negative halogen and the aromatic ring prescmably makes a major contribution to this decrease. The data for the first four systems in Table I are at 20’; all others are at 25’. Previous ~ o r on k ~the temperature dependence of the interaction energies indicates that they change by only 1-2% for each ten degree temperature change. Figure 1 shows the extent of agreement obtained between theory and experiment for seven representative examples of the 15 systems investigated. The theory (6) A. R. Mathieson a n d J. C. J. Thynne, J . Chem. SOC.,3706 (1956). (7) J. R. Goates, R. J. Sullivan, a n d J. B. Ott, J . Phgs. Chem., 63, 569 (1959). (8) A. G. Williamson a n d R. L. Scott, ibad., 66,275 (19Gl). (9) K.Amaya and R. Fujishiro. Bull. Chem. SOC.Japan, 31, 90 (1956). (IO) E. Baud, Bull. 8oc. chzm. P a ~ i Is V , 17, 329 (1916). (11) R. Anderson, unpublished doctoral dissertation, Dept. of Chemical Engineering, University of Cal’lfornia, 1963. (12) H. Hirobe, J . Fur. Sci., Tokyo. 1, 155 (1925).
NOTES
Feb., 1963 is represented by the solid lines and the experimental data by the circles and triangles. Inasmuch as only one adjustable parameter was used to make the fit in each system, the agreement is fairly good, The poorest fits were obtained with the systems C2HL&--CSH12 and C2H4Brz-C6Hl2. The quasi-lattice theory predicted curves skewed slightly toward the low concentrations of the halogen compounds while the experimental data were almost symmetrical in both systems. The average of the deviations (absolute values) a t the five mole fractions of 0.2, 0.4, 0.5, 0.6, and 0.8 is less than 10% in both systems. It seems reasonable to expect that the self-consistent set of interaction energies that produced the curves of Fig. 1 could be used to make estimates about heats of mixing in other systems in which the same type of interactions operate. For example, the experimental heat of mixing a t the equal mole fraction composition of C6H6CH3-CC14is $3 cal./mole.13 The calculated value made on the assumption that the eleven aromatic and three aliphatic contacts on toluene have the same properties as those in benzene and cyclohexane, respectively, is -4 cal./mole. In view of the assumptions made, the agreement seems satisfactory. Because the values of the energy parameters are not obtained by means that are independent of the theory, the agreement between theory and experiment shown in Fig. 1 does not necessarily constitute evidence in favor of a quasi-lattice model for liquids. The best that can be said of these empirical values is that they appear to be of correct sign and reasonable magnitude for the physical significance assigned to them in the theory. In spite of the shortcomings of the quasi-lattice model and the empiricism in the values of the energy parameters, the quasi-lattice theory does appear i o have value in (a) describing heat of mixing data with a limited number of adjustable parameters, and (b) allowing estimates of heats of mixing from a table of previously determined quasi-lattice constants. Acknowledgment.-The authors gratefully acknowledge the support given this project by the n’ational Science Foundation. (13) M. J. Tamres, J. A m . Chem. Soc., 74, 3375 (1952).
THE VAPOR PHASE VISCOSITIES, O F THE PENTAKES BY J. C. MCCOUBREY~ A N D N. M. SINGH Department of Chemzcal Engineering, Imperial CoZlege, London S.W. 7, England Received Julu 0, 106%
New self-consistent measurements have been made of the viscosities of the vapors of the isomeric pentanes and of cyclopentane in the capiliary flow constant volume apparatus previously described by McCoubrey and Singh2 using an air calibration and corrections as described there. The n-pentane was kindly provided by British Petroleum, (>99 mole %), the sample of igopentane was a pure sample kindly supplied by Shell Research, and (1) Research Department, Albright & Wilson (Mfg) Limited, Oldbury,
Nr. Birmingham. (2) J. C. McCoubrey and N. AI. Singh, Trans. Faraday SOC.,53, 877 (1957). (3) T. Titani, Bull. Chem. Soc. J a p a n , 4, 277 (1929).
517
the samples of neopentane and cyclopentane were standard samples obtained from the National Chemical Laboratory, Teddington. Viscosity measurements repofted below are in reasonable agreement with those of Titani3 and Lambert, et aL4 and represent consistent data over a wider range of temperatures than hitherto available. The results for cyclopentane disagree with those of McCoubrey, RilcCrea, and U b b e l ~ h d e and , ~ for this compound may be taken to supersede their results. TABLE I VISCOSITIES IPJ C.Q.S. UNITSFOR n-Pentane
T,O K .
x io’
302.5 330.5 371.5 40 1 440 469 474
712 771 863 928 1017 1085 1092
Isopentane
x 107 309 745 347 832 392 931 421 992 463.5 1084 T,
OK.
THE
PENTANES
Neopentane T , OK. II x 107
305 740 324.5 783 351 835 397 929 431.5 990 457.5 1050
Cyclopentane
T , OK.
x
101
297.5 756 334 847 343.5 861 398 973 403 982 423 1024 457 1104
The over-all accuracy of the viscosities is about 1% and the temperatures hare been rounded to the nearest half degree. A convenient method of representing the temperature dependence of viscosities is by means of the LennardJones 12 :6 intermolecular potential
where 4(r) is the intermolecular potential a t any distance, T , a is its minimum value, and u is the distance of closest approach for slow collisions. The equations relating viscosity to molecular mass, temperature, and to the constants of this intermolecular potential have beein discussed in detail by Hirschfelder, Curtiss, and Bird.6 Values of these (constants (T and B (usually expressed as a ratio of the Boltzmann constant k ) have been derived from the present experimental data by standard procedures and are given below. These constants are useful for extrapolating viscosity data. The physical significance of E and u is low since many lines of evidence can be used to show the inadequacy of the 12 :6 potential for molecules of these shapes. TABLE I1 Molecule
~CbHi2 Iso-CrHiz Neo-C5Hlz Cyclo-CsH~z
12:6 parameters e / h 3 OK.
A. 5.93 6.05 6.44 6.28 c,
300 250 191 190
The applicability of such a potential to viscosity measurements will probably be least for n-pentane and best for the fully branched and cyclic molecules, since such can be shown to be the case for other physical properties such as vapor pressures or gas imperfections.’ For this reason the apparent collision diameters should (4) J. D. Lambert, K J Cotton, M. W. Pailthorpe, A. M . Robinson. J. Scrivens, W. R. F. Vale. and R. hI. Young, Proc. Roy. Soc. (London), 8231, 280 (1955). ( 5 ) J. C. McCoubrey, J N. McCrea, and A. R. Ubbelohde, J . Chem. Soc.,
1961 (1951). (6) J. 0. Hirschfelder. 0.F. Cuitiss and R B Bird, “Molecular Theory of Gases and Liquids,” John Wiley and Sons, New York, N. Y., 1954. (7) K. S. Pitzer, J . Am. Chem. Soc.. 71, 3427 (1955).
