1492
J. N. BRADLEY AND M. A. FREND
branched nonane isomers interconvert freely between forms which do and do not contain quaternary carbons. The manner in which the third tertiary carbon facilitates the ionic isomerization is obscure. That the triply branched octanes crack a t a rate comparable to their interconversion is consistent with the observations of Condon.' However, it is surprising that the triply branched nonane isomers interconvert with negligible cracking. This anomaly may be tentatively explained if one assumes that the equilibrium distribution among the isomeric ions is similar to the equilibrium distribution of the corresponding paraffins. From the API data 2,2,4-trimethylpentane is most abundant in the triply branched octane equilibrium
distribution. Hence for the triply branched octane system the most abundant carbonium ion would be the 2,2,4-trimethylpentyl ion. I n this ion the charged tertiary carbon is P to the quaternary carbon and rapid cracking is to be expected. For the triply branched nonane system the dominant ion would be the stable 2,2,5-trimethylhexyl ion.
Acknowledgment. The author wishes to thank David Benn for his skilled assistance in performing the experimental work described above and George Kramer for helpful discussions. (7) F. E. Condon, J . Amer. Chem. Soc., 73, 3938 (1951).
Single-Pulse Shock Tube Studies of Hydrocarbon Pyrolysis. 11. The Pyrolysis of Ethane by J. N . Bradleg* and M. A. Frend Department of Chemistry, UniEersity of Essex, Colchester, Essex, England
(Received January 4, 1971)
Publication costs borne completely by The Jounal of Physical Chemistry
The pyrolysis of ethane in an argon diluent has been studied over the temperature range 1220-1660'K using a single-pulse shock tube technique. In agreement with previous work, the reaction shows a complex temperature dependence, the activation energy falling almost to zero at the highest temperatures. The transition in kinetic behavior is accompanied by a change in product distribution. Numerical integration of the kinetic equations shows that the behavior cannot be explained in terms either of the falloff characteristics of the unimolecular reactions involved or of inhibition by the products of reaction. The only explanation which has been found to reproduce both the observed kinetics of reaction and the product distribution is the participation of an alternative decomposition step for the ethyl radical, C2HS+ C2H3 HZ, followed by reactions of the vinyl radical, including CzH3 + C2H2 H.
+
+
Introduction The kinetics of the thermal decomposition of ethane have been studied extensively and, although there has been some controversy over the orders of reaction of the separate steps and over the involvement of surface processes, there appears to be qualitative agreement on the basic reaction mechanism, at least below 1000°K. During a program of investigations1r2on the pyrolysis of higher molecular weight hydrocarbons, it mas found that some pyrolyses displayed normal linear Arrhenius behavior over a wide range of temperatures while others showed very marked departures from an Arrhenius temperature dependence, accompanied by correspondingly pronounced transitions in product distribution. As previous shock tube s t ~ d i e s ~had -~ The Journal of Physical Chemistry, Vol. '76,N o . 10, 1971
suggested similar behavior for ethane, it was decided to reexamine this reaction at temperatures above 1000'1 0 or IRe (A,) j ) and the element,s of 1 {lo, Table V.
11,
. . . , I k f T are given in
Table V : Coefficients for Gear's Method k
1
lj
1 1 0 0 0 0
16
0
10
I, lz
la 14
3
4
6
6
6/11 11/11 6/11
24/50 50/50
1/11
10/50 1/50 0 0
120/274 274/274 225/274 85/274 15/274 1/274 0
720/1764 1764/1764 1624/1764 735/1764 175/1764 21/1764 1/1764
2
2/3
3/3 1/3 0 0 0 0
35/50
0 0 0
The iteration is terminated when
Ijy,("+l)
-
l1/1
IY7L'"+1'1
I
is comparable with the relative accuracy of the number representation, 11 1 I being interpreted as the element of largest magnitude for computational convenience, though another norm could be substituted. The Jacobian bf/by is evaluated only when the iterat,ion has not effectively converged after a small number (3, on
-
1501
IGNITION OF AROMATIC HYDROCARBON-OXYGEN MIXTURES empirical grounds) of iterations. It may either be calculated exactly if appropriate code has been generated by the user or by an automatic differentiation package, or alternatively each column af/by, may be approximated numerically by
+
{f(xfl, Yn 6%) - f ( x n 1 Yfl)}/6 for some suitable 6, where the j t h element of el is unity and the remainder zero. A continuing failure to converge is countered by reducing lhl. The step-length may also be reduced by the error cont,rol procedure, which ensures that IIYn(")
is effected by simply multiplying the i t h vector element (i = 1, , . . , k ) of a, by e'. The integration commences with IC = 1, and k is successively increased to 5 by unit steps, the stability region for lc = 6 being unsatisfactory. The additional vector element in a, required a t each increase is calculated by approximating h k +1
(k
+ I)!
yn(k+l)
by
- Y n ( o ) l l / l l Y f l ( Y 5 Ihlv
where q is the maximum relative error which the user will tolerate over a unit interval in x. Failure of this test results in repetition of the step with Ihj decreased, while otherwise the probable effect of increasing Ih is assessed on the assumption that the local error behaves likes h L f l . Xote that changing h by a factor e
I
Whenever h or lc are changed, no increase in either is permitted for at least k st,eps to allow the resulting perturbation to decay. Further theoretical details are contained in ref 8 and an ALGOL program is available from Dr. J. Oliver, Computing Centre, University of Essex.
Ignition of Aromatic Hydrocarbon-Oxygen Mixtures by Shock Waves by H a j i m e M i y a m a Basic Research Laboratories, Toray Laboratories, Inc., Tebiro, Kamakura, J a p a n
(Received December $1, 1970)
Publicatwn costs borne completely by The Journal of Physical Chemistry
Induction periods T for the oxidation of various hydrocarbons were measured by using shock-tube technique. The following linear relationships were obtained between log T [ O ~and ] l/T, where T is temperature behini the reflected shock wave: log 7 [ 0 2 ] = (9300 f 28O)lT - (7.00 f 0.77) for benzene, log 7 [ 0 2 ] = (10,360 f 310)/T - (7.22 * 0.21) for toluene, log 7[02]= (8880 f 260)/T - (6.29 f 0.20) for o-xylene, log ~ [ 0 2=] (8920 310)/T - (6.24 i 0.24) for m-xylene, log 7[02] = (8420 =k 310)/T - (5.98 i: 0.23) for p-xylene, log 7[02] = (6840 =t240)lT - (5.33 0.17) for ethylbenzene, log 7[02] = (9660 f 390)/T - (7.52 f 0.17) for propylbenzene, and log 7[02]= (12,200 f 530)/T - (8.72 f 0.23) for l13,5-trimethylbenzene. Here T is expressed in seconds, [02] in moles per liter, and T is degrees Kelvin.
*
*
Induction periods for the oxidation of aromatic hydrocarbons a t high temperatures were measured by Xullins' in the range 750-1100" by injecting the fuel into a hot air stream. Also, a t higher temperatures, Kogarko and Borisov2 measured induction periods for 3% benzene-97% air mixtures in shock wave and obtained the relationship =
10-13.6
exp (- 26,00O/T) (1) where 7 is induction period in seconds and T is shock temperature in degrees Kelvin. However, no data are available for other aromatics at higher temperatures. It is expected that aromatics having different substitu-
ents such as methyl, et'hyl, and propyl may give different expressions for 7 values depending on the kind, number, and position of the substihents in a benzene ring. Therefore, in the present st'udy, we measured induction periods for benzene-, toluene-, o-xylene-, rn-xylene-, p-xylene-, ethylbenzene-, propylbenzene-, and 1,3,5-trimethylbenzene-oxygen-argonmixtures.
Experimental Section A shock tube consisting of a 2.4-m long driver section (1) B. P. Mullina, Fuel, 32, 363 (1953). (2) 8. M . Kogarko and A. A . Borisov, Bull. Acad. Sei. U S S R , N o . 8 , 1255 (1960). The Journal of Physical Chemistru, Val. 76, No. 10, 1971
