XOTES
fune, 1963 of hexachloroethane must continue to rupture a t an appreciable rate, even in the post-pyrolysis zone, since it was demonstrated that p-xylylene does not accumulate to any appreciable amount until the pyrolyzate has cooled to about 700' a t a point 5 inches away from the pyrolysis zone of the furnace 6 Experimental The pyrolysis system shown in Fig. 1 of ref. 8 was modified to include a Rask containing a weighed amount of hexachloroethane (419 g.) which was located between manometer 11 and the furnace 10. The temperature of this flask was kept at 95'. The pyrolysis system was evacuated to 5 mm. pressure and p-xylene (672 @I.)was metered to the system a t the rate of 0.035 mole/ min. as described previously.8 The gas stream passed through the flask containing warm hexachloroethane into the pyrolysis furnace where co-pyrolysis occurred a t 1000" for an average residence time of 0.006 sec. The pyrolysate was collected in toluene (3.1) kept, a t -78'. At the end of the pyrolysis the resultant solution was warmed to room temperature and volatile components were removed by rapid evaporation a t 100' and 60 mm. pressure. A sample of the distillate was analyzed by means of a mass spectrometer and the presence of tetrachloroethylene and carbon tetrachloride in small amounts was detected. The residue (95 g . ) was stored at room temperature for several days. A small amount (2.1 g.) of needle-like crystals precipitated from the dark oil. These were removed by filtration and washed with hexane. The product was purified by vacuum sublimation a t 100' and subsequent recrystallization from methanol to give pure white needles of a,d-bis-trichloromethyl-p-xylene (also named p-bis(P,P,P-trichloroethy1)-benzene; m.p. 174-175') showing no depression with an authentic sample prepared and identified as described in a previous publication.6 The infrared spectrum of this product was identical with that reported earlier.@ The oily mother liquor was dissolved in hexane and the resultant solution was chilled to -78' to precipitate any additional a&-bis-trkhloromethyl-p-xylene or p-xylylene dichloride. No precipitate formed, however, and the hexane was separated by distillation a t atmospheric pressure and the residue was separated further by distillation a t 2.4 mm. to afford 5 major fractions: (1) 2 g., b.p. 70-90', (2) 20.2 g., b.p. 96-97', (3) 10.0 g., b.p. 120-135', (4)11.8 g., b.p. 135-150', and (5) 15 g., residue. Fraction 1 was mostly p-methylbenzyl chloride and fraction 2 was almost pure P,P-dichloro-p-methylstyrene4as indicated by infrared analysis. Fraction 2 was recrystallized from methanol to yield 15 g. of P,p-dichloro-p-methylstyrene in the form of white platelets (m.p. 32.5-33.5'). The third and fourth fractions were identified by infrared analysis as mixtures of 1,2-dip-tolylethane and alkylated diphenylmethanes. These were combined and dissolved in methanol. The solution was chilled t o -78" and 1,2-di-p-tolylethane (6 9.) crystallized from solution in the form of pearl-white platelets (m.p. 74-76°).9 Fraction 5 was a complex mixture of decomposition products containing phenyk and olefinic groups as indicated by infrared analysis and chlorine RS indicated by a qualitative test for halogen. (8) L. A. Errede and B. F. Landrum, J . A m . Chem. Soc., 79,4952 (1957). (9) L. A. Errede and J. P. Cassidy, zbad., 82, 3663 (1960).
ON THE CALCIJLATION OF THERMAL TRANSPIR-4TION BY GEORGEA. MILLER fiehool of Chemzstry, Georgzn Institute of Technology, Atlanta, Georgza Recezved November 8, 1969
On the basis of the fundamental studies of a number of Weber' developed his equation for the thermal transpiration of a gas along a closed cylindrical tube (1) J. C.Maxwell, Phal. Trans. Rog. SOC.,170, 231 (1879). ( 2 ) M. Kniidsen, A n n . P h y s z k , 28, 75 (1909); 31, 205 (1910). (3) G. Hettner, Z. Physzk, 27, 12 (1924). (4) M. Ceerny and G. Hettner, tbzd., 30, 268 (1924). (6) A. Sterntal, %bad.,39, 341 (1926). (6) T. Sexl, abzd., 62, 249 (1928).
(7) S. Weber, C o m m u n . Phys. Lab. Unzv. Leaden, No. 246b (1937).
1359
where P is the pressure, T is the absolute temperature, d is the inside diameter of the tube, X is the mean-freepath of the gas molecules, and the coefficients are given by the relations a
CY
n/128
p
E5
n/12
P =
-.
Q
g/h
+ gy)/(l + hY) h + P = 1 or (1
"4
N
1.25
Because thermal transpiration involves a transport phenomenon in a rarified gas, for which the usual meth6ds of kinetic theory fail, the derivation of equation l contains a number of approximations. I n particular a model is assumed in which the gas molecules are hard spheres of temperature dependent size, which undergo no specular reflection off the walls of the tube. Severtheless, in view of the difficulty of determinirig pressures in the important submillimeter range, the existing body of thermal transpiration data should be considered with the same degree of reservation as the theory. As pointed out by Weber, a useful approximate solution to equation 1 may be obtained by treating the left side as a quotient of finite differences. The solution may then be cast into one of several generalized forms in which a function of the temperature and pressure at the ends of the tube is obtained which is independent of the nature of the gas and the size of the tube. At present this approach is to be preferred not so much because the exact integration is tedious but because it permits data t o be combined on a single, generalized plot. I n this way it is indeed found difficult to reconcile sets of data from various sources with one another on the basis of any reasonable critique of the theory. The solution suggested here is A P 2T - 1 - (Pi/PZ) = AT P 1 - (Tl/T2)'/'-
d P 2T dT P
- - m y- - -
n=
1
+ BY +
' Tz
_____I
aY2
P
> Ti
(2)
where y is some mean value between y(P1, T1)and y(P2, T2). This solution is exact in the limits where the theory is exact according to the relations lim ( P 1 / P 2 )= (Tl/Tz)''z U+O
lim ( P p - P I ) = 0 u-+
m
The parameter y is calculated through the kinetic theory relation
XP
=
l~T/n(2)'/~rs2
where IC is the Boltzmann constant and n is the molecular hard sphere diameter. I n the usual experimental arrangement PP,Tz, and Ti, are known quantities and PI is to be calculated. The following convenient choice of y is made to avoid dependence on Pi
NOTES
1360 I
I 0
I 00
l
I
l
I
I
l
Vol. 67
l
I
I
I
I
I
1
I
I
h e 00
0
0
07
0
0
O % e 0
10.6
t
O
I - PJP2 I
%,"
0
0
0
- (TI/T2]''2
c
f 0.4
- 0.2
-
O
I
I
I
I
I
I
I
1
I
I
I
I
e 1
P%lW
Fig. 1.-A generalized plot of thermal transpiration data from various sources: (gas, TIITS) hydrogen and heliurn,'O 90/273'K.; helium and neon," 13.5,20.4,69,90/297"K.: helium and argon,1277, 195/297"K.; argon,l3 77, 193/3Ol0K.; krypton,14 78/299OK.: krypton,16 78/297"K.; neon, argon, xenon, and hydrogen,]< 7 7 , 90/299"K.
y = d/X = P z d ~ ( 2 ) ~ / ~ u ~ =, / k T
(Pzdu2/2.33T)X l o 3 (3) where Pa is in mm., disin mm., u is in 8.,and T = (2'1 f Td/2. The hard sphere diameter is based on the experimental value of the coefficient of viscosity at the average temperature, T . Values of o as a function of T have been tabulated for a l i m b e r of gases.* Alternately, u may be calculated from intermolecular force constants through the proper viscosity formulas. For the Lennard-Jones (12-6)potential the relation is
where the symbols have the usual meaning.9 (8) Landolt-Bornstein, "Zahlenwerte u n d Funktionen," Gections 13 241 and 13 242, Springer-Verlag, Berlin, 1950-1951. (9) J. 0. Hirschfelder, C. F. Curtiss, and R . B. Bird, "Molecular Theory of Gases and Liquids," John %ley a n d Sons, Inc., Neil- York, N. Y., 1954.
Figure 1 is the generalized plot of data for the inert gases and hydrogen from a number of sources.10-16 The scatter seems to lack any meaningful trends and, if anything, emphasizes the difficulty in measuring the thermal transpiration effect. However, certain sets of data points for hydrogen and helium (Weber and Schmidt), krypton (Rosenberg ; Rosenberg and Martell) , and xenon (Podgurski and Davis) fall consistently together. Another set for helium and neon (van Itterbeek and de Grande) deviate only at the lowest pressures. These four sets of data also agree reasonably well with equation 2 using Weber's approximate values for CY and (10) S. Weber a n d G. Schmidt, Commun. Phys. Lab. Univ. Leiden, No. 2460 (1937). (11) A . v a n Itterbeek a n d E. de Grande, P h y s i c a , 13, 289 (1947). (12) S . C. Liang, J . A p p l . Phys., 22, 148 (1951). (13) J. RI. Los and R. R. Fergusson, T r a n s . Faraday Soc., 48, 730 (1952). 114) A. J. Rosenberg. J . A n . Chem. S o c , , 78, 2929 (1956). (15) A. J. Rosenberg and C. 8. Martell, Jr., J . P h y s . Chem., 62, 457 (1968). (16) H. H. Podgurski and F. N. D a r i s , ibid., 66, 1343 (1961).
NOTES
June, 1963
6 , and setting g
= 2.5 and h = 2. The function II is insensitive to g and h within the limits set by Weber for these two coefficients. Furthermore, these four sets of data represent a combination of techniques of pressure measurement, namely, the Pirani gage, an adsorption technique, the McLeod gage, and a vapor pressure technique. An adjustment of a! and p has been made on the basis of these data alone. Values of p were first calculated wit,h a! = n/128 for each data point in the region y < 4. 'The average value of p so obtained was used to calculate an average value of a! for the data in the region y > 4. The calculation was repeated until consistent average values of the coefficients were obtained (Table I). The final form of equation 2 was
0 . 0 3 0 0 ~ ~ 0 . 2 4 5 ~ -~ 1 2y TABLE I THERMAL TRAKSPIRATION COSSTAKTS CALCULATED FROM DAT.A
Source
Gas
0.245) (Q = 2 . 5 ) ( h = 2) (2/ > 4 )
Ref. 10 Ref. 11 Ref. 14, 15 Ref. 16
Hz, He
,..
He, Ne Kr Xe
=
N
1.1 X 105/T2
X 103/2.33T)N 5.6 X 102/T
U2/UHe2
$?g
T
X 1O3,'/2.33T)?
a(me'
P H e = P(UHe2
(Ti
=
+ '5"4/2
T/128,
a
N
7/12,
gHe2 N
5X.2
The rather different relations generally used with the Liang e q ~ a t i o n ' ~are J ~ not of sufficient generality to apply if T Bdiffers appreciably from room temperature. The small correction factor for the Liang equation a t low pressuresls may be accounted for by the fact that p actually approaches unity only a t very low pressures.
THE C0UPLIh:G OF NJCLEAR SPINS OF PROTOi'r'S IT\' TWO '4LLEKES
P
(I
(p
C Y H ~=
(18) M. J. Bennett and F. C. Tompkins, T r a n s . F a i a d a y Soc., 53, 1136 (1957).
+ +
+
1361
( a = 0.0300) (Q = 2 . 5 ) (h = 2) (2/ < 4 )
0.181 .302 .262 ,234 ,245
0.0271 ,0322 .0306 Av. ,0300
It is seen from the selected values in Table XI that there is little choice between the fitted coefficients in equation 4 and the approximate values listed under
BY R. K. KULLNIG AND F. C. SACHOD Sterling-Winthrop Research I n s t i t u t e , Kensselaer, N e w Yorlz Recetzed October 1 7 , 1969
We have observed the coupling of nuclear spins of the allenic protons in 2,2-dimethyl-3,4-octadienal (I) and found the magnitude of the coupling constant ( J = 6.3 c.P.s.) in good agreement with the findings od previous investigators of alleiiic compound^.^-^ Un-
TABLEI1 SELECTED VALIJESOF THE GENERALIZED COORDINATES FOR THERMAL TRANSPIRATIOK Y
II
0.01 .02 .04 .OB5 .1 .2 .4 .65
1 .o 2 .O 4.0 6.5 10 20 40 65 100
a = n/128 p = T/l2 Q = 2.5 h = 2
0.993 ,985 ,971 .956 ,937 ,889 ,819 ,757 ,687 ,549 .375 ,252 ,158 ,061 ,0195 ,0082 ,0037
o = 0.0330
p
0.245 2.5 h = 2
= Q =
0.993 ,985 ,972 ,957 ,938 ,890 .823 ,761 ,693 .553 ,373 ,245 ,150 ,055 ,0169 ,0070 ,0031
n I
, 800
I 500
Ho+
equation 1. For the four preferred sets of data the average deviation of from values calculated with equation 4 is 0.016; in the region :L < y < 5, the average deviation is 0.022. Equations 3 and 4 may be used to estimate the thermal transpiration ratio, P I / P ~for , any gas for which the prerequisite viscosity dat'a are available. Over the entire pressure range the value of p has the limits 1 < p < 1.25. I€p is arbitrarily set a t unity, one obtains what is essentially Liang's empirical equation, 17 along with the following relations for Liang's coefficients ( 1 7 ) S . C . Liang, J . Phys. Chem., 57, 910 (1953).
400
300
200
too
0 CPS
Fig. 1.-Proton resonance spectrum of 2,2-dimethyl-3,4-octa dienal. Proton signal of CjH and C3H insert ( a )neat; insert (b' 20% solution in CCI,
fortunately, experiments which are suitable to determine the sign of the coupling constant are beyond the scope of the Varian A-60 spectrometer. The (1) The samples uere obtained from Eastman Chemical Products, Inc , Kinnswort Tennessee -. (2) E. R. Whipple, J. H. Goldstein, and W. E. Stewart, J . Am. Chem. Soc., 81. 4761 11959). , , ( 3 ) S. L. M a n a t t and D. 13. Elleman, ibid., 84, 1579 ( 1 9 6 2 ) . (4) E. I. Snyder and J. D Roberts, ibzd., 8 4 , 1682 ( 1 9 6 2 ) .
