G. Z. WHITTENAND B. S. RABINOVITCH
4348
The Chemically Activated Decomposition of n-Butane and of Isobutane
by G. Z. Whittenl and B. S. Rabinovitch Department of Chemistry, University of Washington, Seattle, Washington 98106
(Received J u l y $3, 1966)
kl
The unimolecular decomposition of n-butane and isobutane (n-CdHlo* + 2CzHr*; n-C4Hlo*-%- CHa. n-CaH,. ; .i'C4Hlo* "a, CHs. s-C3H7.), chemically activated by addition of methylene radicals to propane, has been studied a t 25" from 0.03 to 500 mm. in the presence and absence of oxygen. The pressure course of the principal products has been determined. The data have been solved by an iteration procedure for kl, kz, and ks, which are equal to the collision rate a t 0.25, 0.50, and 1.50 mm., respectively. Explanation of the products supports earlier findings (ref. 7 and 12) that triplet methylene can arise in diazomethane-substrate systems in relative amounts which increase with pressure up to 25-30% at high pressures, and that, as the proportion of triplet decreases, the methylene insertion rates into various C-H bonds approaches the statistical ratio. It is proposed that triplet methylene complicates the apparent insertion ratio by acting as the principal H-atom abstraction agent. RRKM calculations have been made which fit the observed decomposition rates and the model for which agrees with a value for ethyl recombination of -0.082. The data require minimum butane vibrational energy of 102.3 kcal. mole-1. Together with data on chemically activated cyclopropanes, ethane, and methane decompositions, this suggests that methylene radicals transport progressively less of their excess energy, acquired during genesis by diazomethane photolysis, into their combination products with olefins, with propane, with methane, and with hydrogen; the transported excesses are estimated as 20-25, 12, 9, and 0-2 kcal. respectively. This is explicable in terms of increasing inefficiency of methylene reaction along the series, with progressively increasing probability of collisional transfer of the excess energy.
+
+
other than thermal systems. Recently, Bell and Kistiakowsky6 have described the decomposition of The simple alkanes are notorious for their recalcichemically activated methane and ethane as produced trance toward yielding simple, accurate data for the rates of primary decomposition in thermal collisional (1) Weyerhaeuser Predoctoral Fellow. activation systems.2 The high temperatures which (2) (a) E. W. R. Steacie, "Atomic and Free Radical Reactions," prevail in such systems encourage abstraction and 2nd Ed., Reinhold Publishing Corp., New York, N. Y., 1954; (b) D. W. Setser and B. S. Rabinovitch, J . Chem. Phys., 40,2427 (1964); other secondary reactions which lead to complex B. S. Rabinovitch and D. W. Setser, Advan. Photochem., 3, 1 (1964) chain mechanisms and which obscure the primary [in Table XIV, under k,, change 5.57 and 5.45 to 7.6 and 7.5; in Table XIII, multiply k, by 21. rates. These systems have ill repaid the effort lavished (3) (a) G. B. Skinner and R. A. Ruehrwein, J . Phys. Chem., 63, on them and few reliable primary rate measurements 1736 (1959); (b) H. B. Palmer and T. J. Hirt, ibid., 67, 709 (1963). of this kind exist. With the aid of improvements in (4) (a) C. P. Quinn, Proc. Roy. SOC.(London), A275, 190 (1963); experimental and analytical technique, some progress (b) J. H. Purnell and C. P. Quinn, ibid., A270, 267 (1962); Can. J . Chem., 43, 721 (1965), where the possible existence of a molecular has been made very recently, particularly for the dedecomposition mechanism for butane is opposed; (c) A. Kupperman composition of methane, ethane14a and n-b~tane.~b?" and J. G. Larson, J . Chem. Phys., 33, 1264 (1960). Even for these examples, controversy has not been (5) R. W. Dexter and A. B. Trenwith, Proc. Chem. SOC.,392 (1964); I. Kudryavstseva, V. I. Vedeneev, and B. V. Pavlov, Russ. J . lacking with regard to fact as well as inter~retation.~-~ Y. Phys. Chem., 38, 530 (1964). Very few measurements of the decomposition rates (6) J. Bell and G. B. Kistiakowsky, J . Am. Chem. SOC., 84, 3417 (1962). of vibrationally excited alkanes have been made in
Introduction
The Journal of Physical Chemistru
CHEMICALLY ACTIVATED DECOMPOSITION OF n-BUTANE
by the addition of methylene radicals to hydrogen and methane, respectively CHh* 4CH3 H
+
C2Hs" +2CH3 A comparison of these data with the predictions of RRKM theory has been made and reasonable agreement has been obtained2b; extension of the theoretical tests to higher members was not possible and the desirability of accumulating further experimental information was noted. It was the purpose of the present research to make an experimental determination of the rates of decomposition of the two higher alkanes, n-butane and isobutane. Comparison with the lower members seemed of even greater interest since it has been found very recently for the analogous alkenes' that the decomposition of butene, or pentene, to give alkyl radical plus allyl radical proceeds through a much tighter activated complex than does the decomposition of the smaller member, propylene, to give H atom plus Chemically activated decomposition possesses some advantages over thermal activation systems. By the addition of methylene to propane, n-butane and isobutane were produced with enough excess vibrational energy to decompose by carbon-carbon rupture C3Hs
+ CHz('A1) --+ %-CdHlo*
4CH3
3. n-CaH,
--+ 2C2H5
+&CdH10* * CH,
4349
AND ISOBUTANE
warrant any corrections. Propane-l,1,1,3,3,3-ds was obtained from Merck Sharpe and Dohme, Montreal. It had 6% -d6 impurity. It contained 0.4% ethane and 0.003% butane as the principal impurities, and no methane. Oxygen was Air Reduction Co. tank grade and was used without purification. Nitric oxide was Matheson 98% purity. It was passed through silica gel at -78" several times and was then subjected to a number of freeze-pump-melt cycles at - 196". The purified solid was light blue in color. Apparatus and Procedure. A conventional vacuum system was used for gas handling. Small samples of DM were distilled into a volume of 0.96 cc. The average pressure of DM was 2 cm. so that the total amount of butanes formed was less than 1 pmole. The DM was admixed with propane and/or other gases. Runs were made in seasoned Pyrex bulbs. A G.E. AH-6 high-pressure, water-cooled mercury arc lamp (Pyrex jacket) was used as the light source for the photolysis. A combination of Dow Corning No. 5543 and 3389 filters centered the radiation proximate to the 4358-A. peak. A summary of the various experimental combinations employed is given in Table I.
Results and Interpretation of the Data Reaction products were normalized with respect to n-butane product and are plotted in Figure 1 to 4.
+ s-C~H~
The reactions were carried out at room temperature SO that abstraction and other unwanted secondary processes of the radical products were reduced. Oxygen and nitric oxide were also used, ostensibly as simple scavengers of free radicals at this temperature (but see later), in order to test the mechanism further. The species formed b y the various recombination and disproportionation reactions of the initial radical decomposition products have been investigated over a wide range of pressure. This systeni has been previously studied briefly,g but at pressures above those at which decomposition occurs.
Experimental Section Materials. Diazomethane (DM) was prepared by treating N,IS'-nitrosomethylurea with NOH solution and was xtored in a di-n-butyl phthalate matrix a t - 196". Propane was Matheson instrument grade and was used without further treatment. Gas chromatographic analysis indicated some butane (about 0.01%) and some ethane (about 0.00273, which were not sufficient Lo
0.0
'
.
, 0.I
I
I
I .o
IO
I
.. 100
I ( IO
P (mm) Figure 1. Plot of isobutane: butane ratio us. pressure; Solid pure ~ystem,0; oxygen added, 0 ; NO added, ciirves represent calculated fit, as in text; dashed curve assumes no decrease in abstraction a t lower pressures and rises t o 0.9 at 10-2 mm.
(7) F. H. Dorer and B. S. Rabinovitch, J . Phys. Chem., 69, 1952, 1964 (1965). (8) J. W.Simons, B. S. Rabinovitch, and F. H. Dorer, to be published. (9) H.M. Frey, Proc. Chem. SOC.,318 (1959); J . Am. Chem. Soc., 80, 5005 (1958).
Volume 69, Number 1.9 December 1966
4350
G. Z. WHITTENAND B. S. RABINOVITCH
I .2
Table I: Summary of Experimental Run Conditions Run no.
Pressure, mm.
Photolysis time, hr.
Propane/ DM
22 20 49 45 50 32 16
540 394 320 280 250 250 194 100 100 32.6 24.5 21.6 20.0 4.7 3.4 2.4 2.2 0.59 0.57 0.35 0.33 0.24 0.26 0.24 0.23 0.23 0.073 0.045 0.043 0.040 0.032
1 0.75 2 2 2 2 1 0.5 0.67 1 1 1 3 1 3 3 1 2 2 2 3 4 3 3 3 3 3 3 3 4 2
16.6 16.7 10.5 12.6 9.1 10.4 16.0 10.4 9.6 21.6 16.0 15.1 10.3 20.7 8.3 7.1 10.2 19.0 22.0 15.9 8.3 11.0 11.6 13.4 10.0 12.6 19.7 11.0 10.3 10.5 9.5
8 9 19 17 21 31 12 34 38 11 23 26 13 35 59 63 48 61 44 54 30 60 62
7 42 51 15 36
37 14 65
67 66 64 39 40 41
-
O2 added: 02/CHzX, 2 450 3 10.4 340 2 9.2 168 1 15.0 4.0 3 7.7 0.4 3 7.6 0.35 2 15 0.28 3 11.2 0.28 3 10.0 0.063 4 10.2 0,052 4 11.3 0.047 6 8.8 0 038 5 6.9 0.028 5 8.9 I
0
Reactor size, CC.
0.562 0.562 0.95 0.95 0.95 0.562 1.32 1.32 1.32 9.95 9.95 9.95 9.95 57.9 57.9 57.9 57.9 547 547 547 547 1000 1000 1000 1000 1000 5000 5000 5000 5000 5000 0.95 0.95 1.32 57.9 547
547 1000 1000 5000 5000 6000
5000 6000
NO added: NO/CH&n = 2 81 82
0.31 0.30
76 75 74
Runs with 1,l,lJ3,3,3-propane-de 0.30 3 13.0 0.24 5 8.9 0.22 4 8.3
78 79
3 4
12.5 9.7
1000 1000 1000 1000 1000
Runs with propane-&; O2 as above 10.6 1000 5.5 0.28 11.2 1000 3 0.25
The Journal of Physical Chemistry
00
0.2 0.
0.0
I
0.1
I
I
IO
1.0
: -
0
I
IO0
IO )O
P (mm)
Figure 2. Plots of ethane: butane and n-pentane:isopentane ratios os. pressure: e, for ethane; 0, for pentanes. Solid lines represent calculated fit; dashed line is ethane fit corrected as in text. ,
0.5
,
0.44
I
0%
0.3 0.2
0.I 0.0 0:i
1.0
I'O
IO0
I( 30
P (mm)
Figure 3. Plots of propylene: butane and isopentane: butane ratios us. pressure: propylene, 0; isopentane, 0 . Solid curve represents calculated fit for propylene, dashed curve is for isopentane.
In the presence of oxygen, isobutane and butane were the principal products at high pressure; their total yields were drastically reduced at lower pressures, as expected, since decomposition led to radical capture by oxygen with no return by recombination. Thus isobutane was wiped out (Figure 1) at 0.03 mm. as were other radical combination products-pentanes and hexanes. This appears surprising, since n-butane should also approach zero, until it is recalled that butane is an important product in the photolysis of pure DM in the presence of 02. Thus under our conditions, the proportions of the products CzH6 :C&: : n-CeHlo :i-CIH10 were found in blank experiments with DM ahd Dz to be on the average 1:575:2.5: 130:4, respectively (the quantitative precision in check experiments was poor, but was qualitatively consistent).IO Thus the main source of butane in the low(10) By contrast, the pure DM photolysis products were (average), 1: 0.67 :0.06 :0.008 :-0; the radical origin of the ethane is thus
evident.
CHEMICALLY
ACTIVATED DECOMPOSITIOK O F n-BUTANE
AND ISOBUTANE
4351
Q
0.08
.. . I
n
I
os
1.0
P (mm)
IO
100
1000
Figure 4. Plots of various hexane:butane ratios V S . pressure : n-hexane, 0 ; isohexane, 0 ; 2,3-dimethylbutane, 0 ; Solid sum of isohexane and 2,3-dimethylbutane, curves represent compute:r fit for n-hexane, isohexane, and the sum of isohexane and 2,3-dimethylbutane; the dashed curve is for 2,3-dimethylbutane.
.
pressure oxygen work below 0.1 mm. was the D M substrate itself, and the relative decline of isobutane to zero is only apparent. By contrast, the amounts of isobutane and butane above 0.1 mm. rise to values which are sufficiently large even in the presence of oxygen to be independent of the DM-related contributions and thus are significant. Ethylene and propylene were also formed in large relative amounts at low pressure in the oxygen system. The proportions to butane were 4 : l and -3:1, respectively, dropping t o 0.4:l for ethylene and to trace for propylene, a t high pressure. Evidently, the low-pressure ethylene :butane ratio represents DM reaction products in large part; the high propylene value is discussed later. Reaction Scheme. The present system can be largely accounted for by the reaction scheme CH2Nz--%CHz: CHz: $. C3I-1,
n-C4Hlo* '&c4$[10*
+ Nt
n-C4H10*
(1)
(2a)
+i-C4H10*
(2b)
C4HI0
(3)
*
-$GC4HIO
(4)
kl
n-C4H~o* +2CzHs. kz
-+CH3*
+ n-C3H7*
(5) (6)
Some CzH4 and CZH6 are also formed on diaaomethane photolysis, and this will be considered again later. Some abstraction by CHZwas evidenced by the occurrence of the various hexanes and propylene even at the highest pressure; these arise by recombination and disproportionation of n-propyl and isopropyl radicals (eq. 23-28). Also, ethyl radicals were evidently present at high pressure since n-pentane and isopentane were also formed (eq. 17-22). Analysis of the Data. Due to the complex nature of the above scheme and the scatter of some of the data, it was not practical analytically to derive values for kl, kz, and k3 directly from the experimental data. Instead an IBM 7094 computer was programmed to solve the steady-state equations with an assumed set of k values for reactions 3 through 28 and to plot the calculated products as a function of pressure. The assumed set of k values was optimized to give the best fit to the experimental results by trial combinations. 'Volume 69, Number 18 December 1966
4352
G. 2. WHITTENAND B. S. RABINOVITCH
The oxygen data helped to provide very strong conkZ)/k3. I n straints on the allowed values of (kl practice, as will be discussed later, this procedure turned out to be neither difficult nor arduous since the computational results were only a weak function of the rate constants for reactions 8 to 28, provided certain reasonable restrictions were observed ; in fact, this caIculational procedure provided clearer insights than would an analytical solution into the effect of various parameter changes on the amounts and pressure dependence of the various products. The program was written so as to include both H atom abstraction, with propyl radical formation, and also ethyl radical '5nput," so that the higher pressure data could be reproduced; the proportion of the abstraction reaction was also reduced at lower pressures for reasons discussed later. It will also be assumed, in anticipation of later discussion, that reactions 2a and 2b produced activated n-butane and isobutane in a slightly less than statistical 3 : 1 ratio. Then, at any pressure the Teelative amounts of ethyl, n-propyl, s-propyl, and methyl radicals which arose in the system were
+
The numbers 0.31 and 0.93 represent total H atom abstraction equal to 25% of the total product formation; abstraction was determined here from the pentane products to favor s-propyl formation by a net ratio of 3.0:l. The number 0.68 represents an amount of ethyl radical formation (15T0) necessary to fit the highpressure pentane products. The origin of all of this ethyl is not clear; it could arise by attack of methyl on diazomethane. Stabilized n-butane and isobutane (reactions 3 and 4) are then represented by
[n-C3H7.]in = [n-C3H7*]ss{ [CH2*]sS[k(lO)
+
[CzH6*lss[k(17> k(18) [n-C3H7*Iss[k(23)
+
+ k(13)] +
4-k(19)I 4k(26) J
+
[S-C3H7*] ~ ~ [ k ( 2 44-) k(27)]] (b) [s-C~H~. Jin
=
[S-C3H7*]SS{ [CH2*]8s[k(ll) -!- k(14) J
+
[CzHb'Iss[k(20)-k k(21) -k k(22)] -![n-C3H7*Is8 [k(24) k(27) ]
+
+
+ k(28)]]
Fs-CsH7- lss[Jc(25) [CH3
a
Iia
=
[CH3* Iss( [CH3Iss [k(8)]
+
+
(c)
[ C Z H ~ . ] S S [ ~ k(12)l ( ~ ~ ) -k
4-k(13) 1 4[s-CsH7*I~~[k(11) 4-k(14)I) (d)
[n-C3&* ISS[k(lO)
where k(n) represents the bimolecular rate constant for reaction n. The solutions were found by iteration. The first set was
+ + +
{ [C&L*]in/[k(15) k(16)]f1/* [n-C3H7. Jss(i) = { [n-C3H7.]in/[k(23) k(26)J]"a [s-ci"' lss(1) = { [ s - C ~ Hlin/[k(25) ~. k(28) J 1'' [CH,. Iss(1) = { [CHs. lin/k(8>]'la [C&Xi*]ss(~, =
The second set was calculated from the first; e.g., for ethyl one solves eq. a for the ith [C2H5.],,from the (i - 1) values of [C&* [n-C3H7.I,, [s-C3H7.Is8 and [CH3. Is8 [C2Hs*l s s ( i ) = -B
+ (B2+ G')''*
where
+ + +
B = { [CH3. l~~(z-1)[k(9) 4k(12) I [n-C3H7. ]ss(r-1) [k(17) k(18) k(19) I [s-C~H~. I s S ( i - 1 ) [k(20 k(21) k(22) 1 ]/2 [k(15)
+ W 6 )1
C == [C2I&*]in/[k(15) $- k(16)J
To obtain the steady-state values of the radical concentrations the following simultaneous quadratic equations were solved a t each pressure
Note that B and C are positive; only the positive root is possible. After 50 cycles the solutions had converged to closer than 1%. The steady-state values were then used to produce calculated results, such as the curves in Figures 1 through 4. Table I1 gives the values of kl, k2, and k3 and k(8) through k(28) which were used to obtain these particular calculated curves; the amount of abstraction was allowed to decline with pressure as pl(0.1 p ) . The fit of these curves to the data is best for n-hexane, for n- and isopentanes, for propylene, and for isobutane. The fit is correct
+
The Journal of Physical Chemistry
CHEMICALLY ACTIVAT~ED DECOMPOSITION O F n-BUTANE
Table 11: Rate Constants Used in Data Analysis Program'
kl = kz = k3 = k(8) = lc(9) = k(10) = le(l1) = k(12) = k(13) = k(14) = k(l5) = k(16) =
k(17) = k(18) = k(19) = k(20) = k(21) = k(22) = k(23) = k(24) = k(25) = k(26) = k(27) = k(28) =
0.50b 0.25b 1.50b 8.8" 14.0G 12.0 9.0 0.63 0.60 1.8 5.1° 0.66
9.5 0.75 0.55 7.5 3.23 1.5 4.0 6.0 2.5 0.56 2.4 1.6
a The rates of dispropoytionation are relative to the recombination rates and values have been taken primarily from ref. 11 and from S. W. Benson, Ann. Rev. Phys. Chem., 16, 397 (1965). kl, k2, and kt are expressed here in terms of pressure (mm.); Le., the rate of decomposition (hi) equals the rate of stabilization by collision ( w ) a t the pressure specified. All other rates simply appear as relative values since the calculated data are normalized to n-butane. ' Specific rates k ( 8 ) , k(9), and k ( l 5 ) were adjusted by the following expressions to allow for onset of fall-off in recombination a t lower pressures as governed by the constant in the denominator: k ( 8 ) = 8.8p/(0.5 p ) , k(9) = 14.0p/(0.06 p ) , k(15) = 5.lp/(0.01 p ) , where p is the pressure in millimeters.
+
+
+
with regard to pressure dependence, but somewhat off in magnitude, for ethane. This will be considered in the Discussion. Test for Molecular Decomposition. Some low-pressure work was also done with 1,1,1,3,3,3-propane-d6 in order to test for molecular elimination, since it was found that a considerable amount of propylene product (one-tenth in absolute amount of that produced in the pure system) still arose in the runs with added oxygen. If propylene and methane can arise from molecular elimination
-
C~HIO*
CH4
+ C3H6
then use of labeled propane in oxygen runs should allow a molecular decomposition methane product to be distinguished from any methane formed as a prsduct from DM photolysis. It is assumed that the deuteriobutanes would decompose by a molecular mechanism to give products such as
+ CD,CH=CD2 --+ CD4 + CHz=CDCHZD
CD3CH2CD&H2D5' +CH3D CD,CHCDa* +CHaD
I
CHs
+ CD,CH=CDz
*CDsH + CH2=CHCDs +CDI
+ CDZ=CHCHs
4353
AND ISOBUTANE
It is evident that CD4 and CD3H products could not arise in methane formed by some molecular process from DM; dideuteration would be the maximum extent of such deuteration of methane. I n actual fact, no methane could be detected in the oxygen system (the limit of sensitivity was -10% of the pure system amount) at a pressure (Table I) at which decomposition is virtually complete, so that on this basis no molecular decomposition to give propylene occurred. In the pure system, rupture of C-C bonds produces CDa, CH2D, and CH3 radicals, with the first preponderating. CD3 should give rise to a proportion of CD4 and CD3H products governed by the relative abstraction probabilities of secondaryH and primary-D from propane. For light propane, the secondary :primary abstraction ratio1' is '/a = 2.33; from primary-D, this ratio would be much higher. Methane was trapped in silica gel at -208" and analyzed on a mass spectrometer. The following relative amounts of methane were found CH4 5.0
CHaD 3.0
CHzDz 0.40
CHDs 2.4
CDI 1.0
The observed ratio 2.4 :1.0 suggests some small amount of molecular reaction. Although most of the methane product obviously has a free-radical origin, we conclude that the present data allow the possibility of a very minor or trace amount of a molecular process of this t~pe.~b$o Propylene product was reduced by still another factor of 5 when NO was used instead of 02. What propylene was left in the NO system was small enough to be explicable as DM photolysis product, as secondary reaction of methylene with ethylene, and a8 some other undetermined minor mechanism. Hence, there was no evidence of molecular elimination, and most of the propylene found in the presence of oxygen is conjectured as arising in the course of an oxidation chain sequence; in this sense, oxygen did not function entirely as an idealized radical getter.
Discussion Decomposition Rates: Fit os Data. The various alkyl radical rates of recombination, k(S)-k(28), are not known precisely, particularly for the higher alkyls; if they were, the corresponding average thermal unimolecular rate constants for decomposition of alkanes could, of course, be easily deduced, In the light of this, several sets of product data were calculated to test their dependence on these rates; for fixed values of kl, ICz, and ka, the values of k(S)-k(28) were varied ~~
(11) J. A. Kerr and A. F. Trotman-Dickenson, Progr. Reaction Kinetics, 1, 114 (1961).
Volume 68, Number 13 December 1066
4354
G. Z. WHITTENAND B. S. RABINOVITCH
widely. An interesting result was found: when rough obedience to the “rule of 211 (Le., kab/(kaakbb)1/2N 2 ) was required for alkyl radical combinations, the calculated data were virtually independent of the assumptions regarding k(8)-k(28). This requirement is well founded, particularly for alkyl radicakll Various combinations of the ratios of recombination rates for the series methyl-methyl :ethyl-ethyl :npropyl-n-propyl: and s-propyl-s-propyl, i.e., of k ( 8 ): k(15) : k ( 2 3 ):k(25), were used. The following extreme variation of rate ratios all gave similar calculated results, 8.8 : 5.1 :4.0:2.5, 1:1:1: 1, 4: 1:1:4, 1:4:4: 1, and 2.5: 4.0:5.1:8.8. Of these, the first set was used in Table I1 since it is considered to be the most reasonable. It is unnecessary to illustrate all of these calculated results with detailed figures. If the calculated solid line curves in Figures 1-4 were replaced by heavy brush strokes (and not all curves would have to be so broadened, nor a t all pressures) it would encompass virtually all of the variation. By contrast, a change in any single k(i) by only a factor of 2 made a significant change in a t least some of the calculated values. I n the same way, a change in any one of kl, ICz, or k3 by a factor of 2 changed the calculated relative product amounts substantially; also a uniform change of total rates at constant ratios, e.g., of the values of kl,k2, and kI while maintaining (kl k2)/k3 = constant, caused a marked and observable variation in the pressure at which characteristic changes in product amounts occurred. Various systematic combinations of the k $ were explored over a range of a factor of 10 to 100 in each. This method of data analysis led to the evaluation of the absolute and relative magnitudes of the unimolecular constants kl, kz, and ka to within a factor of 2 ; more consistent data could have produced better precision. Some error in the determination of the k z arises from the fact that the calculated fit of all of the product variations was not of uniform merit for all products. The ratio of (kl k z ) / k 3was weighted considerably by the oxygen data (the low isobutaneln-butane ratio found below 0.1 mm. was ignored as false for the reasons given above, and any attempt to fit that region caused the remainder of the fit to blow up completely). The ethane data could not be fitted much more closely without doing violence to the better agreement found for other products. The propylene, isobutane, pentanes, and hexanes were considered as the most crucial for optimization of fit in evaluation k1, kz, and ks. The total isohexane fit (Figure 4) is acceptable at pressures above 0.1 mm. but very poor below. The source of this discrepancy is not clear other than that the accuracy of determination of isohexane was less than
+
+
The Journal of Physical Chemistry
that for isobutane, isopentane, or propylene, which are closely related products; a more efficient recombination reaction than assumed for methyl radicals a t low pressures would remove part of the discrepancy. Actually, the ethane fit is better in two respects than first appears: first, the relative variation of ethane with pressure-which is important for the magnitude of kl-is correct (Figure 2); second, much of the discrepancy between the low-pressure experimental and calculated ratio to butane is explicable as follows. The low-pressure proportion of DM in the reaction mixture was -10% (Table I). Thus if 10% of the ethane product which is normally yielded by pure DM photolysislO arose, this would be an amount equal roughly to 5% of the DM used. But a t low pressures n-butane is only two-fifths to one-third of the total products, i.e., as little possibly as 33% of the DM. Thus the ethane formation directly from DM photolysis may reach 0.15 relative to the n-butane which, when added to the ethane calculated from the formal mechanism, puts the calculated ethane ratio up to 0.41 which is in better agreement with the data of Figure 2. Methylene Insertion Ratios. The measured relative amount of n-butane to isobutane at the high-pressure end was -2.5, which agrees with the work of F r e ~ . ~ It should be kept in mind that some pentanes and hexanes arise a t high pressures from radicals formed from propane by abstraction, say by methylene. The sec-propyl predominates in these products, so that combination with methyl gave additional butanes (especially iso-) such that the final calculated true insertion ratio becomes 2.7. This effect is probably present in many or most other gas phase systems; presumably, addition of 0 2 (which scavenges alkyl radicals) would alter the observed apparent insertion ratio. I n the present oxygen systems, the absolute amounts of butanes formed were reduced at high pressures. However, the ratio of n-butane to isobutane was substantially unchanged (Figure 1). The oxygen data were too few to verify the expected incre~se.~ Efects Due to Triplet Methylene. It has recently been shown that 20 to 30% of triplet methylene can be formed in ketene and DM systems at higher pressures, the percentage decreasing with lowering of system pressure.7~12 Nominally, little effect on the formation of the butanes in this system would be expected if, as is commonly believed, triplet radicals do not insert into carbon-hydrogen bonds. I n any case, (12) J. W. Simons and B. S. Rabinovitch, J . Phys. Chem., 68, 1322
(1964).
CHEMICALLY ACTIVATED DECOMPOSITION OF ~-BUTAPJE AND ISOBUTANE
any effects due to the presence of triplet methylene in this system would be most pronounced at the higher pressures. Actually, it was found that the calculated low-pressure isobutane ratio in the pure system was much too high and would not fit the experimental values unless the amount of abstraction (which gives rise predominantly to isopropyl radical and eventually to isobutane) was drastically reduced as low pressure (Figure 1). The sets of data in the figures were calculated on the assumlption that the abstraction reacp). tion decreased at lower pressures as pl(0.1 The constant, 0.1 mm., was subjected to variation. The optimum value used is lower than that found (>1 mm.) in our previous ~ o r kalthough , ~ ~ ~all~studies are in qualitative agreement regarding the effect of pressure. Since the reactions of such methylene species as are produced is independent of the mean time between collisions with substrate molecules, in a system of constant composition, it is plausible that reduction of abstraction at low pressures by methylene is associated with the reduced proportions of triplet CH2 at lower pressures and that virtually all H atom abstraction by methylene is due to the triplet species.13 As mentioned in a prior section, when account is taken of abstraction, the apparent insertion values are corrected in the direction of the statistical ratio. The effect of triplet methylene in altering insertion ratios away from the statistical value has already been noted.7 Virtually all old gas phase data in DM and ketene systems will bear correction of the apparent insertion ratios of C-H bonds of various types. Recently, Placzek and Rabinovitch14" offered an amplification of the "pressure-independent" formation of product alkenes which arise from triplet cyclopropanes upon reaction of triplet methylene with substrate alkenes15a; specifically considered was triplet state dimethylcyclopropane which, as pointed out earlier114b may be regarded as a triplet trimethylene diradical, I. Placzek and Rabinovitch proposed that the triplet
+
c-c-c-c I
*C I
c-c e-c \/
C I1
cyclopropane led by H migration steps on a triplet surface to relatively long-lived a,@ diradicals; these correspond to triplet state olefins that are known from Hg(3P1) photosensitization studies to be readily interceptible by collision.16 'This mechanism does still not explain the "pressure-independent" pentene-2 formation, unless CH3 migration15&or alternative diradical stahe, IIl5b90 is invoked. We consider it likely that some of the pressure-independent alkene products
4355
of triplet methylene with cis- or trans-butene-2 arise via H abstraction: allylic H abstraction, the most favored, leads to both cis- and trans-pentene-2 on CH, combination if the methallyl radical does not completely retain configuration, as is possible17; it should also lead to lesser amounts of 3-methylbutene-1, corresponding to a canonical methallyl radical structure, which is less fav0red.l' Abstraction of vinylic H leads to 2-methylbutene-2. Insofar as 2-methylbutene1 product is not explicable on this basis, support is still lent to the original interpretation of CvetanoviE and Duncan, and possibly that of Bell,15bas having relevance for some of the products. We are currently extending our investigations to higher pressures and liquid phase in an effort to discover the nature of the intersystem crossing mechanism leading to triplet methylene via the triplet precursor. Comparative absence of triplet methylene in liquid media studies of this typel8 could occur either because of specific ternary interactions which alter the effective rates of various processes or, quite possibly, because other collisional processes must be invoked. If so, the enhancement of triplet production in the gas phase with increase in pressure should eventually pass through a maximum at very high pressures. 18a Theoretical Calculations. The recombination of methyl radicals is known to occur at a rate very close to their singlet-state collision rate.lg This is usually accepted as signifying a very low activation energy for recombination. The critical energies for dissociation of alkanes into alkyl radicals may be taken as given by the heat of reaction at 0°K. If an Arrheniustype dissociation rate equation is evaluated from the equilibrium constant and the radical recombination (13) H. M. Frey and G. E. Kistiakowsky have independently come to the same conclusion (H. M. Frey, private communication). (14) (a) D. W. Placzek and B. S. Rabinovitch, Can. J . Chem., 43, 820 (1965); (b) D. W. Setser, B. S. Rabinovitch, and E. G. Spittler, J . Chem. Phys., 35, 1840 (1961). (15) (a) F. J. Duncan and R. J. Cvetanovid, J . Am. Chem. Soc., 84, 3593 (1962); (b) J. Bell, Progr. Phys. Org. Chem., 2, 45 (1964). (c) Although this same intermediate is believed to arise in the pentene-1 Hg(aPi)-photosensitized isomerization to l,2-dimethylcyclopropane,14a virtually no pentene-2 was formed in that process; this suggests the desirability of confirmatory evidence that this intermediate diradical is the precursor of the pentene-2 in the triplet methylene system, as proposed by Bell, (16) R. J. Cvetanovi; and L. C. Doyle, J . Chem. Phys., 37, 543 (1962). (17) R. F. Kubin, B. S. Rabinovitch, and D. W. Setser, ibid., 37, 937 (1962). (18) D. B. Richardson, M. C . Simmons, and I. Dvoretsky, J . Am. Chem. SOC.,83, 1934 (1961). (18a) NOTEADDEDIN PROOF.H abstraction by triplet methylene and the maximum suggested have now both been verified with cisbutene-2. (19) G. B. Kistiakowsky and E. K. Roberts, J . Chem. Phys., 21, 1637 (1953).
vobume 69, Number 18 December 1966
4356
G. Z. WHITTENAKD B. S. RABINOVITCH
rate, very large pre-exponential or' 'A" factors are obtained. The well-known Gorin treatment by absolute rate theory deals with these reactions as proceeding through a Ioose activated complex having free internal rotations. Such a model is fairly successful for the lower alkanes, methane, and ethane, but seems inappropriate in generalz0 When applied to n-butane decompositionzbit yields a frequency factor, 7.6 X lo1* sec.-l, which is too high by a factor of 4 3 a t 873"K., relative to a classical recombination rate of the radicals. For the present calculations, a loosened vibrational model rather than the loose model was used. For n-butane, a decomposition complex having lowered bending and torsional modes was constructed by fitting a calculated thermal pre-exponential factor, A , which was obtained by elimination between the ethyl radical-n-butane equilibrium constant a t room temperature and the recombination rate for ethyl radicals. Shepp and Kutschkezl have measured the recombination a t 50"; their value of 0.092 was adjusted to 0.082 for 25". The moments, frequencies, and cross sections used previously2b for ethyl radicals, plus the butane frequencies in Table I11 and the EO value in Table IV gave rise to a calculated A factor of 1.4 X lo1' sec.-I. To fit this, the adiabatic moment of inertia ratio was taken as 1.6 (as described for decomposition of butene'), and in the activated complex four bending and rocking frequencies were lowered to one-tenth of their value and three torsions to onesixth. This rather simplified description of frequency changes (Table 111, complex 1) can nevertheless provide realistic calculated values under the constraint that these changes have given the desired A value.2b This prescription for degree of loosening was applied to the construction of the other two complexes in Table 111. RRKM rate theory gives the well-known specific reaction rate expression for k E as
Table 111: Frequency Assignments (em. -1) for Molecules and Activated Complexes" -ButanebMolecule
Complex 1
Cornplex 2
1180 1152 972
115 97
118 115 97
1168 981
117 98
C-C-C bending
431 271
43 27
43
381 418
38 42
Torsion
225 194 102
38 32 16
38 32 16
203(2) 198
34(2) 33
1008 835
. ..
CH2, CHs bending
C-C stretch
kfd
= .JBIrn
(kEl
kE2
The Journal of Physical Chemistry
-
wf(E)dE
m,/Lmi (. kE1
+ + kE2
...
Table IV : Rate Constants and Energy Parameters
Reaction
Pressure, mm.
n-C4-+2C2
102
kexpti,
koaiodr
seo.-1
sec.-1
n-C4+ n-Cs
c+
10-9 102
+
10-2 102
Eo? kcal. mole-'
Emin,
kcal. mole-'
1 . 5 8 X lo8 81.5 102.3 1 . 4 X 108
7.0
x
107
1.21 x 108 4.96 X lo7 84.0 102.3 3.62 x 107 5.18 X lo8 81.6 1 0 3 . 9 *
4 . 2 X lo8 10-2
kElf(E)
791
a Only molecule frequencies which change in the complex are given; all other frequencies are assigned in footnotes b and c. J. H. Schachtschneider and R. G. Snyder, Spectrochim. Acta, 19, 117 (1963). R. G. Snyder and J. H. Schachtschneider, ibid.,21, 169 (1965).
i-C4"C s-CB
where I is an adiabatic partition function ratio and may include reaction path degeneracy considerations. ZP(Eyr)represents the total sum of vibration-rotation states at an energy E+ for the complex. Eo is the critical energy for reaction. N*(E) is the density of states for the molecule.22 The average observed rates for a competitive d e composition system such as butane are given by
...
,--Isobutanec---Molecule Complex
3.95
x
108
'An error of I kcal. in this quantity alters the calculated rate by a factor of ~ 2 . Based on AHfOo(n-butane)- AHr"o(sbutane) = 1.6 kcal. mole-I.
(20) H. S.Johnston and P. Goldfinger, J. Chem. Phys., 37,700 (1962). (21) A, Shepp and K. 0. Kutschke, ibid., 26, 1020 (1957). (22) The accuracy of the Haarhoff approximation as described by M. J. Pearson, B. S.Rabinovitch, and G. Z. Whitten [ibid., 42, 2470 (1965) (footnote 13)], has been overestimated somewhat: 3% should be changed t o 8% and 10,000 cm.-l to 20,000 em.+ in that reference.
CHEMICALLY ACTIVATED DECOMPOSITION O F n-BUTA.NE AND
where integration is over the range of the distribution function f (E). The appropriate representation of energy distribution functions for methylene systems has been discussed earlier.23 f(E) may simply be chosen to be a room temperature thermal spread, appropriate for the butane and isobutane molecules. k , was evaluated over a wide energy range. The required level of minimum energy, Emin,upon which f(E) is to be imposed was then found by trial to be 102.3 kcal. for n-butane in order to match k,l (calcd.) to kl (exptl.). The level of Eminfor isobutane is then 103.9 kcal., as governed by heats of formation. Excess Methylene Energy. Heats of formation a t 0°K. from the A.P.1.-W Tables (1952) were used, together with election of the values 102, 97, 97, and 93 kcal. mole-l for LY0(C-H) for methane, ethane, primary, and secondary propane, respectively. These gave the values shown in Table IV. Table I V summarizes the results of these calculations. The average internal energy of the formed n-butane, 2.6 = 104.9 kcal. calculated from f(E) is 102.3 mole-l. Taking AHfoo(CH2)= 87 kcal. mole-l for methylene,6 this gives a heat of reaction, Hoe, of 91.2 kcal. at 0°K. and an excess energy of 13.7 kcal. mole-l. Similar calculations yield AHoo = 83.5 and 27 kcal. excess for methylene in the dimethylcyclopropane isomerization system (using 7.0 k~a1.2~ for AHf"0, dimethylcyclopropane). I n the cyclopropane system, AHOo = 86 and 22 kcal. excess is found.24 Likewise, for ethane decomposition, AH', is 87.5 kcal. It has been found for ethanezb that at 90 kcal. the calculated rate is too low by a factor of 20 relative to the observed va1u.e6 to fit which an average of 98
+
4357
ISOBUTANE
kcal. is required for a bending vibration model. Thus 10.5 kcal. excess energy applies. Finally, aHoo = 103 kcal. and 1-3 kcal. excess for methane can be obtained.2b Any neglected energy distribution of the methylene formed in these photolysis systems, or error in AH,oo(CH2), cancels for relative comparisons. The average heat capacity of reactants a t 25" are only a few kcal. mole-1 and do not differ by more than 1-2 kcal. molew1. Hence the above excess energy quantities, if lower by 1-3 kcal. are the amounts transmitted by methylene into combination reactions. In conclusion, the high-frequency factors predicted for alkane decomposition seem to be justified. The rates given here, although accurate to only a factor of 2, can be fitted only by very loose-vibration complexes. The excess energy thereby predicted for the methylene seems quite reasonable when compared to related systems: the efficiency of C-H insertion is enhanced by the number of sites available per molecule, yet is not as efficient as addition to double bonds as in the cyclopropane systems; the amount of energy transmitted increases with reaction cross section; collisional transfer probability and loss of excess energy from the methylene increases inversely with reaction efficiency. Acknowledgment. This work was supported in part by the Petroleum Research Fund of the American Chemical Society and in part by the National Science Foundation. ~~
~~~~
(23) D. W. Setser and B. S. Rabinovitoh, Can. J . Chem., 40, 1425 (1962). (24) D. W. Setser, B. S. Rabinovitch, and J. W. Simons, J . Chem. Phgs., 40, 1751 (1964); 41, 800 (1964).
Volume 69, Number 18 December 1966
