NOTES
3086
ring opening and crack as alkanes, which give essentially no cyclic products. Figure 1 shows the distribution by carbon number of the products from cracking an alkane, n-hexadecane,z and three cycloalkanes of increasing ring size, hexamethylcyclohexane, cyclododecane, and cyclopentadecane. Table I shows the reaction conditions and product composition. The product distribution from cyclododecane and cyclopentadecane, as determined from a combination of gas chromatographic and mass spectrometric analyses, is unusual in that: (1) the moles of cycloalkanes in the product from cracking equal the moles of cycloalkane that cracked-thus, no rings are lost in the cracking process; ( 2 ) the predominant cyclic products are alkylcyclopentanes and alkylcyclohexanes having seven or eight carbons; (3) the predominant alkane products are isobutane and isopentane; (4) no evidence for cycloheptanes through cycloundecanes is found in the mass spectrometric analysis of the product from cracking; (5) essentially no methane, no ethane, and only a small amount of propane are produced in cracking. This product distribution is quite similar to that obtained from the paring reaction of hexamethylcyclohexane (Fig. 1B). This suggests that cyclododecane and cyclopentadecane undergo a rapid ring contraction on the surface of the catalyst to form alkylcyclopentanes and alkylcyclohexanes. Some of these cycloalkanes are desorbed before they crack and appear as isomers as shown in Table I. The remaining isomers Table I: Reaction Conditions and Product Composition
________Reactant-------
Temp., “C. Pressure, a t m . Residence time, sec.’ First-order rate constant (cracking only), 8ec. -1 Conversion, total 5% Conversion, cracking % Product (moles/100 mole8 of reactant) CI-CS alkanes Ca-G isoalkanes Ca-C? unbranched alkanes Ca-Cla alkanes i-C16 alkanes CS-CII cycloalkanes C U cycloalkanes C I cycloalkanes ~ Reactant
nHexadecane
Hexamethylcyclohexane
Cyclododecane
Cyclopentadecane
290 82 7 6
2 34 82 146
296 82 16 6
291 82 15.5
0 088 51 4 48 7
0 125 100 87 5
The apparatus, procedure, and methods of analysis uscd have been discussed previously.’ In the present experiments, the catalyst was nickel sulfide (5.37& Ni) on commercial silica-alumina, the pressure was 82 atni., and the molal ratio of hydrogen to reactant was -10. Nost of the experiments were performed in duplicate or triplicate with reproducibility within 10%. Chemicals. n-Hexadecane was obtained from Humphrey-Wilkinson (99% pure). Only one peak was observed in gas chromatographic analysis. The cyclododecane contained no impurities detectable by gas chromatographic analysis. The boiling ~ point was 160”at 100 mm; n z 01.4504. Cyclopentadecane was obtained by reduction of cyclopentadecanone (Aldrich) 9S.6yo pure by gas chromatographic analysis. The melting point was 62.8-63.4 ”. Acknowledgments. The authors gratefully acknowledge the contributions of Mr, C . F. Spencer in the mass spectrometric analysis of the products and of kIr. J. Abell for assistance in obtaining the cyclododecane and cyclopentadecane.
0.192 98.5 94.9
(2) Data from R. F. Sullivan of this labolators. (3) D. J. Cram and G. S. Hammond, “Organic Chemistry,” 2nd Ed.: McGraw-Hi11 Book Co., New York, N Y , 1964, p. 161.
7 1 67 3 8 9
8 4 86 5 9 9 11 2
Diffusion Potential in Molten SaltaSystems
97 7
1.7 91.5 1.4
.., ...
82 1 12.5
96 4 6 Zb
...
2 6
...
...
3 6b 1 6
a Apparent time of hydrocarbon in volume occupied b y catalyst; calculated assuming no conversion and perfect gas Mainly cyclopentane and law for hydrogen and vapor. cyclohexane rings.
The Journal of Phyaical Chemiatrv
Experimental
0.164 97.4 91.0
12.1 89.2 13.1 26.2 2.7
48.6
undergo selective cracking a t a slower rate. The mechanism of this cracking reaction has been described previously. The behavior of the cyclopentadecane is of interest because the ring strain present in medium-size rings containing 8-14 carbons has largely disappeared in rings containing 15 or more carbons (“Rings containing 15 or more carbons are folded in nearly random stacks and resemble open-chain compounds3”). It is concluded that as the ring size is increased, cycloalkanes containing up to 15 ring carbons still behave as cycloalkanes rather than as unbranched alkanes in hydrocracking.
by I. G. Murgulescu and D. I. hlarchidan Institute of Physical Chemistry, Bucharest 9,Romania (Received J u n e 1 , 1964)
In our previous worksl-a we have shown that the diffusion potential is nil in the concentration cells of the type
NOTES
3087
+
1
hfel jnle,x,[ lATelX,(zl) ~ e ~ ~ , Mel ( x ~ ) for the following binary melts: AgCl KC1, AgBr KBr, AgBr NaBr, AgBr LiBr, AgBr PbBrz, AgXOs LiKOa, PbClz 4- XC1. At the separation limit between the molten salts, no use of diaphragms was made. For the diffusion potential, we have taken as valid the relation, used for aqueous electrolytes,* of the form
+
+
+ +
e =
nF
JAB
(tl
d In al
+
+ tz d In a%)
+
(1)
By substituting the activity uzas a function of a],with the aid of the Gibbs-Duhem equation, there results
In virtue of the fact that the diffusion potential E is nil, we can write zzt, - %It2 = 0 (3) From relation 3 there results that the transport numbers of the two cations are variable and proportional to the molecular fractions of the corresponding salts. In a note publisheld in this journa1,j Berlin and his collaborators ascribe to us the statement that the mobilities or the transport numbers should remain constant all along the concentration range as used in the cell. This statement is not to be found in our works, and on the other hand the fact that the diffusion potential vanishes does not imply any direct conclusion as to the individual mobilities of the ions. (1) I. G. Murgulescu and I>. I. Marchidan, Z h . Fiz. Khtm., 34, 2534 (1 960). (2) I. G. Murgulescu and D. I. Marchidan, Bev. Chim. Acad. Rep. Populaire Roumaine, 5 , 17 (1960). (3) I. G. Murgulescu and 11. I. Marchidan, ibid., 5 , 299 (1960). (4) (a) K. Jellinek, “Lehrbuch der physikalischen Chemie,” I11 Band, Stuttgart, 1930, p. 780; (b) E. A. Guggenheim, “Thermodynamics,” 1957, p. 396. (5) A. Berlin, F. MBnBs, S. Forcheri, and C. Monfrini, J . Phya. Chem., 67, 2505 (1963).
are well known for flow in cylindrical tubes in the limit of low pressures (Knudsen flow) and of high pressures (Poiseuille flow) ; however, the intermediate (slip flow) regime is not well u n d e r ~ t o o d . ~In many of the recent theoretical treatments, the authors make use of Knudsen’s original data5 to relate their results to experiments. In this note, further experiments of this kind are reported; it will be seen that these data show features not present in previous work. Flow experiments were performed by measuring the time dependence of the pressure differences between two containers of known volume connected by twentyfive stainless steel tubes of length 10.000 cm. and i.d. 0.015 cm. The pressure differences were read to an accuracy of 3 X mm. by means of a differential capacitance nianonieter coupled to a chart recorder. Data have been obtained for helium, neon, and argon at a number of temperatures and a t pressures corresponding to a tube diameter to mean free path ratio ranging from 0.002 to 15. Flow rates are given in terms of the number of molecules passing through unit area of the tube in unit time, for unit gradient in the gas density. IF this quantity is denoted by D , one can calculate a dimensionless flow rate D* = D/av, where a = tube radius and V = average molecular speed. These rates are plotted in Fig. 1-3 as a function of a/X, where X = kinetic theory mean free path. It is most convenient to compute X from the viscosity of the gas
I I
2.4
D*
I
1 o THIS WORK
I
Fe Fe
I
H2 1288.5 IHe,Ne,t A L L
/
/ -
POlSEUl LL E
*8w KNUDSEN
Low Pressure Flow of Gases
0 0
by H. J. M. Hanley and W. A. Steele Whitmore Laboratory, Department of Chemistru, The Pennsylvania State University, University Park, Pennsylvania (Received June 4, 1964)
The isothermal flow of gases a t low pressures has been a subject of interest, both theoretically and experimentally, for some tinie.1-3 Theoretical equat,ions
I
I
I
I
5
10
15
20
oiA
Figure 1. Flow data for various workers. (1) W. G. Pollard and R. D. Present, Phys. Rev., 73, 762 (1948). (2) D. S. Scott and IF. A. L Dullien, A I.Ch.E. J . , 8,293 (1962). (3) 0. Gherman, Soviet P h y s . JETP,34, 1016 (1958). (4) S. A. Schaaf, “Handbuch der physik,” Band VIII/P, SpringerVerlag, Berlin, 1963. (5) M.Knudsen, Ann. Physik, 2 8 , 75 (1909).
Volume 58, Number 10 October, is64
