NOTES
2028
cyclohexane at room temperature, corrected to 56.4 iVlc.p.s., vary from -80.0 to -81.0 C.P.S. depending on solvent. The discrepancy is partly the result of an unexpectedly large deuterium isotope effect and partly of the temperature dependenceL4of the cyclohexane shift, which was not noted in the earlier work.’ The isotope shift appears very clearly in the spectrum of a mixture of ODCH and ordinary cyclohexane a t room temperature. The broadened peak of the deuterated species lies 1.4 i 0.3 C.P.S. or 0.025 p.p.m. upfield from the sharp signal of the normal species. Similar but smaller deuterium effects havc been found in the proton spectra of substituted ethylenes, while shifts of comparable magnitude were reported for compounds of the type HD2CX compared with HaCX.16 The temperature dependence of the chemical shift was studied for ordinary cyclohexane a t about 30 vol. yo in carbon disulfide with tetramethylsilane as internal reference, over the range from 80 to -33”, in which the cyclohexane produces a single, sharp peak. The peak moves upfield linearly as the temperature is reduced, a t the rate of 0.011 0.004 c.p.s.jdeg. A similar temperature coefficient has since been reported14 for cyclohexane in a mixed solvent. Since the peak from ODCH is centered at -79.1 i 0.3 C.P.S.a t 3 5 O , the value of -77.0 C.P.S.for the average chemical shift at -95” is not unreasonable. Retmning to the analysis of the low-temperature spectrum, one readily findslO for the geminal H-H coupling constant J H H = 12.6 c.P.s., very near the value reported for methane.16 The difference in chemical shift between the axial and equatorial protons is 26.7 C.P.S. or 0.474 p.p.m. The uncertainty of this value is difficult to estimate but should not exceed 0.01 p.p.m. Although it is a little larger than the 0.455 p.p.m. reported by Jensen, et aL,l it lies quite significantly below the 0.525 p.p.m. estimated by Musher2 using the same data.17 The theoretical AB pattern calculated with these parameters is shown in Fig. lb. Extrapolating back to ordinary cyclohexane a t room temperature one finds that the “standard” shifts for axial and equatorial hydrogen should be -1.19 and - 1.66 p.p.m., respectively, although values differing
*
(13) G. V. D. Tiers, J. P h y s . Chem., 62, 1151 (1958). (14) J. L. Jungnickel, A n a l . Chem., 35, 1985 (1963). (15) E. I. Snyder, J. Phys. Chem., 67, 2873 (1963), and work cited there. (16) M. Karplus, D. H. Anderson, T. C. Farrar, and H. S. Gutowsky. J . Chem. P h y s . , 27, 597 (1957). (17) Since this study was completed, Professor F. 4.L. Anet has told us of unpublished work on cyclohexane-dii which yielded a value of 0.478 p.p.m. for this shift difference, in excellent agreement with our result. We wish to thank Professor Anet for this information.
T h e Journal
of
Physical Chemistru
by perhaps 0.02 p.p.m. from these might be obtained if a solvent other than carbon disulfide were used.
The Thermal Conductivity of Hydrogen-Helium Mixtures’
by Robert S. Hansen, Robert R. Frost, and James A. Murphy Institute for Atomic Research and Department of Chemistry, Iowa State University, A m e s , Iowa (Received February 19,1964)
The anomalous peaks recorded in a conventional gas Chromatograph on passage of a hydrogen sample with helium carrier gas have been discussed by Schmauch and Dinerstein2 and attributed to a minimum in the thermal conductivity of hydrogen-helium mixtures. However, the only published data concerning the variation of thermal conductivity of such mixtures with composition are due to Barua3; the data are insufficiently extensive to document a niinimuni and none is shown in Barua’s graphical presentation. It, therefore, seemed worthwhile to determine this variation in more detail, and also to investigate the possibility of representing it theoretically. Schmauch arid DinersteinZ have also shown that a simple model for heat transfer in the chromatograph thermal conductivity detector suggests that the bridge response should vary linearly with the reciprocal of the gas thermal conductivity. The measurements in the present work are based on this principle. The power supply, bridge circuit, and flow controller of a Research Specialties Co. 600 series gas chromatograph was used together with a four filament flow type detector modified by replacement of the two reference side filaments with 20-ohm precision resistors. Circuit response was monitored by a Moseley x-y recorder. The detector was immersed in an ice bath during all experiments. Gas mixtures were prepared in a previously evacuated vessel and displaced into the system with mercury, Commercially available hydrogen, helium, neon, methane, oxygen, nitrogen, and argon were used without further purification; with the exception of methane (99.0%), H2 (99.5%), and 0 2 (1) Contribution no. 1462. Work was performed in the Ames Laboratory of the U. S. Atomic Energy Commission. (2) L. J. Schmauch and R. A . Dinerstein, A n a l . Chem., 32, 343 (1960). (3) A. K. Barua, T n d i a n J. Phys., 34, 169 (1960).
2029
SOTES
1
.
0
,
i
-
1
1
I
I
400.-
390.'
w -1.0
\
.Pot-
\
- 3 .0.0 o L - - - - - - -5- 0- - d
I 25.0
10.0
Figure 1. Dependence of detector response on reciprocal of t,hermal conductivity.
(99.5%), all were specified to be at least 99.996% pure. Instrumental response was measured for a series of gases, and was found to vary linearly with the reciprocal of the gas thermal conductivity (these experiments were performed a t 25') as shown in Fig. 1. Yalues of i,herma,l conductivities at 300'K. were taken from Zemansky's Instruiiieiital response was, therefore, used to interpolate reciprocal thermal conductivities of hydrogen-helium mixtures between values for pure hydrogen and pure helium on a linear basis. Thermal conductivities of hydrogen (component 1)helium (component 2) mixtures were calculated a t 273.16'K. according to the method outlined by Hirscbfelder, Curtiss, and eq. 8.2-31, 8.2-35, 8.2-36, and 8.2-40, using values of paranieters selected from their tabulations. Parameter choices were. g1 o== 2.968 u2 = 2.576 A., g12 = (ul crz),'2 = 2.772 A , el/k = 33.3', e2/k = 10.22', ~ 1 2 / k= ( ~ ~ e Z ) " * /=k t8.4', 107(Xl),,,tl = 4040 cal./cm. sec. 'E;., 107(X2),,,tl = 3510 cal./cm. sec. "K. The equations were programmed for clomputer calculation and thermal conductivities calculated a t 0.02 mole fraction increments over the entire composition range. Experimental points were compared with the calculated curve in Fig. 2 . It is evident that values observed are always somewhat higher than theoretical, but the maximum deviation is 1% and the trend of results is very much in accord with theory. 4 definite minimum is evident at a hydrogen mole fraction of 0.13. Chromatographic behavior (using the conventional thermal conductivity detection instrumenta-
H.,
+
00
02 MOLE
04 0.6 FRACTION HYDROGEN
0.8
Figure 2. Dependence of thermal conductivity a t 0" of helium-hydrogen mixtures on composition. Curve is theoretical, points are experimental.
t,ion) can be, hence, siinply described in terms of the t'heoretical curve. If the peak hydrogen mole fraction is less than 0.13, a normal response will be obtained. If it is between 0.13 and 0.27, the response signal will be double peaked with an intervening minimum that' becomes more pronounced xyit'h increasing peak concent'ration; and when this concentration exceeds 0.27, a reversal in signal sign will result.
Acknowledgment. We are indebted t'o Thomas C. JIcGee for computer programming assist'ance. (4) M . W. Zemansky, "American Institute of Physics Handbook," D. E. Gray, Ed., 2nd Ed., hcGraw-Hill Book Co.. Kew York, N . Y . , 1963, pp. 4-81. ( 5 ) J. 0. Hirschfelder, C. F. Curtiss, and R. B. Bird, "Molecular Theory of Gases and Liquids," John Riley and Sons, Inc., New York, N. Y., 1954.
The Second Virial Coefficients of Carbon Disulfide by G . A. Bottoriiley and T. H. Spurling Department of Chemistry, Cnitersity of Western Austi alia, :Yedlands, Western Australia (Received February 15, 1584)
Waddington and co-workers' advocate carbon disulfide as a suitable reference substance for vapor-flow V o l u m e 68, iYumber 7
J u l y , 1964
