COMMUNICATIONS TO THE EDITOR
light of Holtzmark’s theory of line broadening which does not predict splitting at all6 Even if one discounts this early theory as inapplicable at high densities, it is difficult to maintain the Stark splitting hypothesis when the double band is observed a t densities as low as those employed in the Hg-C3F8 system. At present, we feel that the short wavelength component of the band observed in C3F8and, by analogy, that in C3Hs, is related to the “violet bands’’ observed in the spectrum of Hg and alkali metals perturbed by a wide variety of gases at low pressures.’ For Hg perturbed by argon, de Kluvier* and Robing have shown that these bands, initially quite weak, approach and eventually exceed the intensity of the principal line as the density increases. At densities near the critical density of argon, two peaks of approximately equal intensity are observed. At higher densities, near that of the solid, the principal line is replaced by the appearance of a second satellite, and at 6 kbars pressure where the argon density is near that of a close-packed solid, a double peak is again observed and is due wholly to the satellites. It is this latter spectrum that Robinson2 compared to the spectrum of Hg in neopentane. On the other hand, Gunning assigns the bands in hydrocarbons as R and S which are Robin’s terms for the principal line and the S, satellite, respectively. Our results are in accord with Gunning’s assignment; we find no evidence for more than two bands in the density ranges employed. We see, then, no compelling reason to invoke exclusively high density properties of the solvent to explain the observation of a double band in solutions of Hg. Our results in C3F8 supplement Robin’s results in argon in indicating the connection between the high and low density satellite bands. Only if there appear additional satellites at higher C3F8densities will there be a possibility for explanations such as those listed by Gunning. Even if this is observed, as it is in argon, we feel that the known increase in satellite band intensity with density and the fact that more than one satellite is observed a t low densities are strong indications that the exclusively high density interpretations are superfluous. We are currently investigating further the analogy between the Hg spectra in hydro- and fluorocarbon solvents over a wider density range. A more complete and detailed discussion of the subjects presented here, (6) R.G.Breene, “The Shift and Shape of Spectral Lines,” Pergamon Press Inc., New York, N. Y.,1961, Chapter 4. (7) S. Ch’en and M. Takeo, Rev. Mod. Phys., 29, 64 (1957). (8) H.de Kluvier, Discussions Faraday SOC.,22, 80 (1956). (9) J. Robin and S. Robin, Compt. Rend., 233, 928 (1951).
601
along with the results of experiments now in progress, will be submitted for publication in the near future.
Acknowledgment. Acknowledgment is made to the Union Carbide Corporation and to the Atomic Energy Commission for support of this research. JAMES D. LEAR JAMES E. STURM
DEPARTMENT OF CHEMISTRY LEHIGHUNIVERSITY BETHLEHEM, PENNSYLVANIA RECEIVED DECEMBER 6, 1965
Self-Diffusion in Cyclohexane-Benzene Solutions
Sir: Solutions of cyclohexane and benzene have been the subject of a recent diffusion study by Rodwin, Harpst, and Lyons.’ This system is of considerable interest because it is well characterized with regard to thermodynamic variables. Rodwin, Harpst, and Lyons’ chose to phrase their discussion in terms of an equation213which can be written as
D
=
&(x&
-k XbDC)
(1)
where D is the mutual diffusion coefficient, x is the mole fraction, D band D,are the self-diffusion coefficients,and
Q
=
( b In z,f,/b In 5,)
(2)
The subscripts c and b refer to cyclohexane and benzene. Rodwin, Harpst, and Lyons obtained D, and Db by means of an extrapolation procedure and compared measured D values with D values calculated by means of eq 1. In this note we wish to report the results of selfdiffusion studies in C&,-C& solutions and CeDeC6Hl2 solutions by proton magnetic resonance spinecho methods. These results provide a test of eq 1 that does not depend upon the extrapolations previously‘ employed. Solutions were prepared from benzene and cyclohexane of about 99% isotopic purity. The solutions were examined by high resolution nmr and it was found that exchange did not occur. The spin-echo self-diff usion technique has been described previously. All measurements were made a t 25”. We expect an *v6
(1) L. Rodwin, J. A. Harpst, and P. A. Lyons, J. Phys. Chem., 69, 2783 (1965). (2) G. S. Hartley and J. Crank, Trans. Faraday SOC.,45, 801 (1949). (3) R. M.Barrer, J . Phys. Chem., 61, 178 (1957). (4) H.Y.Carr and E. M. Purcell, Phys. Rev., 94, 630 (1954). (5) D. C. Douglass and D. W. McCall, J . Phys. Chem., 62, 1102 (1958).
Volume 70, Number 3 February 1966
602
COMMUNICATIONS TO THE
EDITOR
Table I
:-
’
[ : : , I
BE111_:,SE,F
0
- CYCLOHEXANE,
A
- MUTUAL (
1.2
,
D~FFU,SION,
SELF DIFFUSION
7
DIFFUSION R O D W I N , HARPST 8 LYONS’
I. 0
0
0.1
0.2 0.3 0.4 0.5 0.6 0:7 0.0 MOLE FRACTION CYCLOHEXANE
0.9
1.0
Figure 1. The concentration dependence of self-diffusion coefficients in benzene-cyclohexane solutions, 25”.
1.88 1.86 1.83 1.81 1.79 1.79 1.80 1.84 1.90 1.99 2.10
1.88 1.85 1.79 1.72 1.66 1.63 1.64 1.68 1.78 1.90 2.09
1.88 1.86 1.83 1.79 1.77 1.78 1.80 1.83 1.90 1.98 2.09
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
in terms of the “density defect.” These quantities are roughly proportional to one another although the “density defect” is about an order of magnitude smaller than the (‘viscosityd e f e ~ t . ” ~
Acknowledgment. We are indebted to D. C. Douglass and B. Ottar for stimulating discussions of this work. absolute accuracy of better than 5% with the pure liquids but the errors can be expected to be greater in solutions dilute in protons. This is particularly true in dilute solutions of CaH6 in CBDIP. The results are shown in Figure 1 together with the mutual diffusion results of Rodwin, Harpst, and Lyons.’ It is clear that the spin-echo results (which are absolute and have not been adjusted to fit the tracer data) exhibit the correct limiting behavior, i.e. lim D = D,
(6) R. J. Bearman, J . Phys. Chem., 65, 1961 (1961). (7) J. D.Birkett and P. A. Lyons, ibid., 69, 2782 (1965). (8) J. A. Dixon and W. Schiessler, ibid., 58, 430 (1954).
(9) NOTEADDED IN PROOF. Rodwin, Harpst, and Lyons’ do not suggest that the parameters they have deduced ( L e . , those corresponding to our Db and D,) are self-diffusion coefficients. This interpretation has been made by Bearman.6 Dr. Bearman has called our attention to a recent tracer diffusion study of this system by D. A. Collins and H. Watts, Australian J. Chem., 17, 516 (1964). We have benefited greatly from comments contributed by Professor P. A. Lyons and Professor R. J. Bearman. BELLTELEPHONE LABORATORIES HILL, N i w JERSEY MURRAY
zo+o
and
DAVIDW. MCCALL ERNESTW. ANDERSON
RECEIVED DECEMBER 14, 1965
Table I shows a comparison of experimental D values with D values calculated from eq 1. It is clear that the agreement is poor. Bearmad has discussed eq 1 from a theoretical viewpoint and casts some doubt upon the general validity of the relation. Thus, the discrepancies observed are not too surprising. A simple equation that describes the data well is
D
= (ZcDb
+
ZbDc)P/(ZbVb
+
Z c d
(4)
Heats of Mixing of Benzene with Hexafluorobenzene, Pentafluorobenzene, and 1,2,4,5-Tetrafluorobenzene’
Sir: As part of our research program on fluorocarbon solutions, we have measured the molar heat of mixing (ie., the molar excess enthalpy RE)for each of the
+
+
+
where 7 is the solution viscosity. Table I also contains D values computed from eq 4. The agreement is well
Systems CeHa CeFa, CsHa CaFsH, and CeH6 1,2,4,5-tetrafluorobenxeneover a wide mole fraction
within experimental error. We have not corrected the viscosities for the isotope effect.'^^ Equation 4 can be regarded as the simplest mixture formula corrected for the “viscosity defect,” [l r1/(xCrlc4- Z b v b ) ] . The discussion could also be phrased
(1). Contribution No. 1905 from the Department of Chemistry, University of California, Los Angeles, Calif. This work was supported in part by the U. 8. Atomic Energy Commission and in part by the University Grants Committee, New Zealand (Postgraduate Scholarship in Science to D. V. F.).
The Journal of Phyeical Chemietrl
