1537
METHYLENE REACTION R>ATES
Methylene Reaction Rates. Quantum Yields in the Diazomethane-Propane Photolysis System: Effects of Photolysis Time, Reactant Ratios, and Added Gases by Jerrg A . Bell Department of Chemistry, Simmons College, Boston, Massachusetts OW116 (Received January $6,1971) Publication costs assisted by the Petroleum Research h n d
Quantum yields have been measured for the production of the isomeric butanes in the photolysis of diazomethane-propane mixtures as functions of the CsHS/CHzNz ratio, total pressure, photolysis time, and added competitor gases, CH4, Yz, 02, Ar, and Xe. At C~H~/CHZNZ ratios above about 50, +(C4HlO) = 0.76; at lower ratios +(CdH,,,) decreases. Added gases decrease +(C4H10) by reacting with 'CHZand/or causing intersystem crossing to 3CHz. The results are all consistent with the following set of reactions and rate constants (cmSmolecule-' sec-1): CHzNz hv (405 nm) lCHz Nz,41 = 1.0 f 0.4 (1); lCHz C3HS + C4H10, (2); 'CHz C3Hs-+ 3CHz C3Hs, (2.4 =k 1.0) X lo-'' (3); 'CH2 CHzNz * CzH4 (6.3 f 1.7) X (4); lCHz CH4 CzHe*,(1.9 & 0.5) X 1O-l2 (ref 4); ICHZ CHI VHz Nz, (31 f 10) x (ref 4); lCHz Nz+ %H2 Nz, (0.5 =k 0.5) X 10-l2; 'CH2 Oz-+ "HZ CH4, (1.6 f 0.5) x 'CHZ Xe -+ ICHZ Ar * %Hz Ar, (0.8 i 0.3) X Oz (or other products), (4.0 f 1.0) X The results imply that the yield of T H Zin CHzNZ-CaH8systems is due T H z Xe, (1.8 & 0.6) X to reaction 3. Analysis of the isomeric hexane yields gives the ratio of the reaction rates for 3CHz C3HB -+ CH3 C3H7 ( k ~and ) T H 2 CHZNZ -+ CzH4 Nz ( k e ) ; ke/ks = 400 f 100, so a C H is~ efficientlyscavenged by CHzNz. Two reaction pathways are responsible for the isomeric pentane products: secondary lCH2 CdHIOreactions and, .probably, CtH5-forming reactions followed by CZH5 CaH,. Below 100 Torr total pressure the dissociation of C4H10*] formed initially in reaction 2, adds significantly to the yields of the pentanes and hexanes, products associated with the radical reactions following reaction 5. Comparison of these results with other studies of CHz reactions indicates that great care must be taken in assessing relative lCHz and V!Hz yields in the photodissociation of their precursors and the contributions of 'CHz and WH2 reactions to overall product yields.
+ +
+ +
+
-+
+
+
-+
+
+
+
+
+
+
+
+
Introduction Following the initial work of Frey and Kistiakowsky,l a number of other workers have studied systems in which they assume free methylene is produced in the presence of propaneO2 There appears to be substantial agreement among the various workers upon certain points: singlet methylene, CH2, inserts into the carbon-hydrogen bonds, favoring a secondary bond by a factor of 1.20 per bond; intersystem crossing from singlet to triplet methylene, TH2, can be collisionally induced; 3CH2 abstracts hydrogen atoms to form methyl and propyl radicals, favoring secondary abstraction by a factor between 12 and 20; V H 2 is much less reactive than TH2; both 'CH2 and 3CH2are produced (in varying ratios) by dissociation of photolytically excited precursors. There is still, however, some question as to whether or not triplet methylene inserts into carbon-hydrogen bonds and about the details of the formation of minor products, for example, the Csh y d r o ~ a r b o n s . ~ ~ ~ g ~ 3 This work on the diazomethane-propane system was begun to study some of these minor reactions. The serendipitous discovery that diazomethane was stable for relatively long periods (a few hours) in reaction vessels "seasoned" with diazirine led to an extensive investigation. The present analysis of the effects of
+ + +
-+
+ +
+ + +
+
photolysis time, reactant ratios, and added gases on the quantum yields, combined with other recent res u l t ~ gives , ~ ~ a~detailed ~ , ~ picture of the reaction mechanism and may serve to caution those of us trying to assess the relative yields of 'CH2 and 3CH2from the photodissociation of its precursors.
Experimental Section Materials. Fresh diazomethane (DM) was synthesized each day by mixing i n vacuo about 1 g of N methyl-N-nitroso-p-toluenesulfonamide,Eastman, with about 5 ml of degassed propylene glycol containing 4 or ti KOH pellets. The product was trapped at - 195' (1) H. M. Frey and G. B. Kistiakowsky, J . Amer. Chem. Soc., 79, 6373 (1957). (2) This is a leading, not an exhaustive, reference list of work to be referred to later in the paper: (a) G. Z. Whitten and B. S,Rabinovitch, J . Phys. Chem., 69, 4348 (1965); (b) M. L. Halberstadt and J. R. McNesby, J. Amer. Chem. Soc., 89, 3417 (1967); (e) S-Y. Ho and W. A . Noyes, Jr., ibid., 89, 5091 (1967); (d) D. F. Ring and B. S.Rabinovitch, Can. J . Chem., 46, 2436 (1968); (e) T. W. Eder and R. W. Carr, Jr., J . Chem. Phys., 53, 2258 (19VO); (f) A. K. Dhingra and R. D. Koob, J . Phys. Chem., 74, 4490 (1970); ( 9 )
C. J. Mitschele, Ph.D. Thesis, University of California, Riverside, Calif., 1967. (3) (a) D. C. Montagne and F. S. Rowland, J. Phys. Chem., 72, 3705 (1968); (b) T. W. Eder and R. W. Carr, Jr., ibid., 73, 2074
(1969). (4) W.Braun, A. M. Bass, and M. Pilling, J . Chem. Phys., 52, 5131 (1970).
The Journal of Physical Chemistry, Vol. 76, No. IO, 1971
JERRYA. BELL
1538 (liquid nitrogen), twice distilled from -SOo (Dry Icetrichloroethylene) to - 195", and held at - 195" until use. Propane (Pr), Matheson instrument grade containing about 0.017% ethane and a slightly larger amount of propylene (indeterminate by our analytical techniques), and xenon, Matheson research grade containing no detectable hydrocarbon impurities, were put through several freeze-pump-thaw cycles to remove more volatile gases (02). Oxygen, Linde industrial grade, methane, Matheson research grade, and Matheson counting gas mixture P-10, 0.10 methane and 0.90 argon, were used directly from their cylinders. Photolysis Procedure. All photolyses were carried out in 42.5-m1 cylindrical, detachable quartz cells with greaseless stopcocks. One cell was used for most of the results reported here, in order to keep all optical parts of the system as constant as possible. This cell had about 7 Torr of diazirine, the cyclic isomer of DM, stored in it for 6 months prior to its use in these experiments. Under the conditions of the experiments reported here, cells without such pretreatment gave erratic and useless results ascribable to rapid, nonphotolytic decomposition of DM. (Two months storage of diazirine followed by addition of propane and photolysis of the diazirine at 320 nm for 1hr produced the same conditioning effect. No shorter storage times were tried. Attempts to produce the same "poisoning" by using DM-100-Torr portions renewed every few hours-f ailed.) The sample cell was filled on the conventional highvacuum system used for DM synthesis and storage. To begin each experiment, the D M storage trap was warmed to -SO" and pumped briefly; the appropriate pressure of DM, measured on a mercury manometer, was allowed to fill a small volume and expand into the evacuated photolysis cell to give the desired initial amount. Other reactant gases were then expanded into the cell and the final total pressure in the cell measured with a mercury manometer after each addition. Mixing was assumed to take place as the expanding gas rushed into the cell; the order of addition of reactants (other than DM which could not be tested) made no detectable differencesin results. The photolysis lamp was a 200-W P E K super-highpressure mercury arc powered by a direct current supply. The light was passed through a Bausch and Lomb high-intensity monochromator, catalog no. 33-86-01 (entrance and exit slits, 3.3 and 2.0 mm; band pass, 6.6 nm), set at 405 nm and focused axially at the center of the photolysis cell. A selenium photocell and microammeter were used to monitor the light beam emerging from the cell to be sure the intensity remained constant within 501, during and between runs. Light fluxes were measured by ferrioxalate a ~ t i n o m e t r y . ~I n only a few cases were reactions carried beyond 20y0 depletion of the initial DM; l0-15yO was more typical. No more than 2% of the P r ever reacted, so its concentraThe Journal of Physkal Chemistry, Vol. 76,No. IO, 1971
tion was effectively constant for all runs. The light distribution was not uniform throughout the cell, but, due to the slit and cell geometries and focusing characteristics of the lens, probably was about twice as intense (per unit cross sectional area) on the axis in the center of the cell as at either end. Since almost no light is absorbed in the cell, less than 0.4% (Torr of DM) -l, the nonuniform distribution probably does not lead to any severe mixing effects. Analyses. All product analyses were done with a ' / 8 in. X 5 ft gas chromatographic column of 20% SF-96 on Chromosorb, run at 0" with Nz carrier gas, and a flame ionization detector and electrometer, Varian Aerograph Model 1200. The inlet system, stainless steel, Kovar, Teflon, and glass, caused the complete decomposition of the D M left in the product mixture to C2H4 and very small amounts of the C4H10 isomers. The product yields and ratios from this decomposition were quite reproducible. Analyses of unphotolyzed blank runs for all sets of reaction conditions were used to correct the observed C4H10 product yields for this extraneous source. Unfortunately, the large amount of C2H4 thus formed made it impossible reproducibly to determine the relatively small yields of CH4, CzH4, and C2HRfrom the photolysis. The chromatograph output was calibrated for almost all the identifiable products; those not calibrated directly were assumed to have the same sensitivity as their isomers. Calibrations were made with mixtures that reproduced typical reactant mixtures as nearly as possible, since the large excess of P r in all product mixtures altered the detector response. The response was also slightly dependent on the total pressure of sample injected, so all data were empirically corrected to the same injection conditions. Analyses were done at least in duplicate for all runs. Absolute yields and ratios are estimated to be good to &5%. Yields of C5 compounds, which are formed in small amounts and elute soon enough after P r to make their analysis on its tail very imprecise, and n-hexane, n-H, which is formed in very small amounts, are known less precisely, only to within 20%.
Results The major products of the reaction under all conditions were n-butane (n-B) and isobutane (i-B). CH4 which were not quantitatively determined, and c2&, were formed in much smaller amounts. CtH4 was formed in moderate amount a t low initial [PrI/[DMlo ratios, but also could not be determined quantitatively. Other products, never present in toto in amounts greater than about 10% of the total C4H10 product, were 2,3dimethylbutane (2,3DMB), 2-methylpentane (PMP), n-hexane (n-H), C4HR (isobutene and/or butene-1, ( 5 ) J. G. Calvert and J. N. Pitts, Jr., "Photochemistry," W h y , New York, N. Y . , 1966, pp 783-786.
1539
METHYLENE REACTION RATES
Table I: Yield Ratios in the DM-Pr Systeme [DMla,
Torr
1.8 1.8 1.8 1.8d 1.8d
WI/ DMlo
R(2,3DMB)bic x 102
R(c~H~)~ x 102
R(2MP)b'C x 108
R(Pl)b x 102
R(4MPl)b x 102
0.44 0.46 0.47 0.48 0.49
0.9 1.2 2.1 2.1 2.3
0.6 0.6 1.2 1.0 1.1
3.4 1.8 0.5
0.9 0.4 0.1
2.0 1.5 1.0 0.5
9.1 53
0.42 0.46
0.5 1.1
0.4 0.6
7.2 1.6
2.0 0.3
1.9 1.2
10 10
5.0 8.8
0.42 0.43
0.21 0.30
0.18 0.25
7.0 4.5
1.8 1.4
1.3 1.1
20 19
5.0 8.6
0.42 0.43
0.11 0.18
0.09 0.16
5.5 4.5
1.6 1.3
1.1
3.3 3.3
29 56 105 152 345
R(CB)'"
1.0
Values are 3 ~ 2 0 %except for E's less than 1 X IO-* where the error increases to about =t50%. Averages a Values are 3~0.01. for runs of 20 min or less. These yields are time dependent, Figure 5, but not enough data are available for all runs to extrapolate to A blank space indicates the yield was not detectable. Results of a single run. zero time, so averages are used in all cases.
which were not separated by our technique), isopentane (i-P), n-pentane (n-P), pentene-1 (Pl), 4-methylpentene-1 (4MP1), and two unidentified, very minor, products that eluted between 2MP and n-H. I n the longest runs a small amount of neopentane and traces of cyclopropane and 2-methylbutene-2 were also detected. All product yields are given as a ratio to [n-B], the yield of n-B, and labeled &(product) for ease in writing, e . g . , R(i-B) = [i-Bl/[n-B]. DM-Pr: Butanes. I n the pure DM-Pr system with [Pr]/[DM]o = 5 to 10, R(i-B) = 0.43 f 0.01. Figure 1 shows that this product yield ratio is invariant with photolysis time as [n-B] is monotonically increasing; about 50% of [Dhlr]~ has been reacted at the longest time shown. Similar results in relation to time are obtained for all the DM-Pr systems; R(i-B) does increase slightly, Table I, as [PI-]/[DRiIIo increases. Addition of small amounts of 0 2 , less than O.l[Pr], gives R(i-B) = 0.42 A 0.01 in all cases and also eliminates all products except the butanes and pentanes (see below). The effect of the O2 is presumably to intercept 3CH2, or the radical products of its reactions,2er6leaving only the products of 'CH2 insertion reactions. The O2 addition has no effect on (n-B], within analytical error. Assuming that the ratio of butanes formed as a result of 3CH2abstraction-recombination reactions (see mechanism below) in these systems is 4,2awe can calculate the fraction of the observed [n-B] that would result from the 'CH2 reaction in the above systems. In all cases more than 98% of the [n-B] arises from 'CH2 reaction. In the DM-Pr systems, therefore, all [n-B] was assumed to be the result of 'CH2 insertion. I n systems where 3CH2reactions contributed significantly to [n-B], the yield due to 'CH2 reaction was calculated as above. The [i-B] formed by 'CH, insertion was taken to be 0.42[n-B] in these cases.
4
F
0.4
.
t
1 ;0.2
t 0.02
:
3
.I
-
-
0.5
I -
0
0
I
0
0
0
I
I
10
20
0
0
I
I
I
I
40 50 60 Photolysis T i m e , Minutes
30
I
I
70
80
- 0.4
Figure 1. n-B yield, 0 , and yield ratios, R(i-B),0 ; R(2,3DMB), V; and R(2MP), A, as a function of 405 nm photolysis time for 10 Torr of DM with 88 Torr of Pr.
Figure 2 shows that [n-B]/ [DM]o is a linear function of photolysis time for short times, i.e., low conversions of DM. A large amount of data from other series at different [Pr]/ [DM]O and total pressures has been omitted from this plot in order to simplify it; the results are the same in all cases, a linear initial increase in [n-B]/ [DMIo. With these initial rates of formation, the total photon flux through the cell (3.32 X 10l6 photon see-'), and the amount of light absorbed per Torr DM initially present (with a decadic absorptivity = 3 1. mol-' em-' for DNl at 405 nm'), the quantum yield for formation of the C4H10 from 'CH2 may be calculated; +(C4H10)= 0.59 f 0.12 when [Pr]/[DMIo (6) (a) R. L. Russell and F. S. Rowland, J . Amer. Chem. Soc., 90, 1671 (1968); (b) F. S. Rowland, C. McKnight, and E. K. C. Lee Ber. Bunsenges. Phys. Chem., 7 2 , 236 (1968). (7) R. K. Brinton and D. H. Volman, J. Chem. Phys., 19, 1394 (1961). The Journal of Physical Chemi&ry, Vol. 76,No. 10, 1971
JERRY A. BELL 0
2.0
N
2 *”
1.5
m
I c
2
.M
1.0
c
d c 0 U
E 0.5 a.
I
I
10
20
I
I
I
I
40 50 60 Photolysis T i m e , Minutes
30
I
I
70
80
Figure 2. n-B yields as a function of 405 nm photolysis time: 10 Torr of DM, 88 Torr of Pr, 0; 1.8 Torr of DM, 101 Torr of Pr, +; and 1.8 Torr of DM, 191 Torr of Pr, 0.
8.8 and ~ ( C ~ H I=O 0.76 ) f 0.15 when [Pr]/[DM]o 1 50. The large error estimate arises mainly from the estimated uncertainty in the absorptivity of DM, not from scatter in the experimental data. At intermediate values of [Pr] : [DMIo, intermediate 4’s are obtained, but the experimental scatter is too large to tell exactly when the limit 0.76 is reached, although it is possible that a ratio of 30 is sufficient. DM-Pr: Pentanes. Figure 3 shows that Id(i-P) and R(n-P) increase linearly with photolysis time for [Pr]/[DR/I]o = ’8.8 and total pressure about 100 Torr, and that extrapolation back to zero time yields finite intercepts. Addition of O2reduces the relative pentane yields substantially, but they again show an increase with photolysis time that may be extrapolated back t o zero intercept at zero time. The rates of increase with time appear to be the same, within the considerable experimental error of these analyses, with or without
10
0
20
30 40 50 Photolysis Time, Minufes
60
70
80
Figure 3. CjHlz yield ratios as a function of 405 nm photolysis time and added 01,less than O.l[PrI, for 10 Torr of DM with 88 Torr of Pr: R(CP), +,O, and R(n-P), 0,0,Open symbols are runs with added 02.
=
02.
Figure 4 shows that R(i-P) behaves similarly for all [Pr]/[DM]o ratios as a function of photolysis time in systems with a total pressure of 100 Torr or greater. All other factors being equal, however, when the total pressure of the system is reduced below 100 Torr, R(CP) increases. Since the slope of the time dependence appears to be about the same at all total pressures, the increase must reflect a change in the mechanistic factor that gives rise t o the nonzero intercept at zero time. The butane yields in these lower pressure series are those expected on the basis of the [Pr]/[DM]o ratios and Figure 2. DM-Pr: Hezunes. Figure 1 shows R(2,3D;LIB) and R(2MP) as functions of photolysis time for [PI-]/ [DMjo = 8.8 at a total pressure of about 100 Torr. R(n-H) is not shown because its small yield and the large scatter in the analyses make interpretation imThe Journal of Physical Chemistry, Vol. 76, N o . 10, 1071
..
I I
I
h
-
:v
0.
A
so
0.5
0
10
20
30 40 50 60 Photolysis T i m e , Minutes
70
80
Figure 4. Yield ratios for i-P as a function of 405 nm photolysis time and mixture composition: 10 Torr of DM, 88 Torr of Pr, 0 ; 3.3 Torr of DM, 30 Torr of Pr, V; 1.8 Torr of Dill, 52 Torr of Pr, 0 ; 1.8 Torr of DM, 101 Torr of Pr, and 1.8 Torr of DM, 191 Torr of Pr, 0 . The line is the R(L;-P) line from Figure 3 without added 0 2 .
+;
possible. At relatively short photolysis times the yield ratios for the isomeric hexanes remain constant, but as the time increases and a substantial fraction of DM is depleted, the ratios increase somewhat. Figure 5 illustrates the striking increase in this trend as [Pr]/ [Dh/I]oincreases. Also we see that the initial values of R(2,3DMB) increase as [Pr]/ [Di\il:]oincreases; a plot, Figure 6 , of R(2,3Dl!tB),1 (extrapolated to zero time) us. [Pr]/[DNI]o is linear. The points at total pressure below 100 Torr are neglected, because they again show larger yields relative to the [Pr]/[DR!t]o ratios. The addition of small amounts of 0 2 eliminates all traces of
1541
METHYLENE REACTION RATES
,.*"
1 0
I
I
10
20
I
I
I
I
40 50 60 Photolysis T i m e , M i n u t e s
30
I
I
70
80
I
Figure 5 . Yield ratios for 2,3DMB as a function of 405 nm photolysis time and mixture composition: 20 Torr of DM, 100 Torr of Pr, A; 10 Torr of DM, 88 Torr of Pr, 0; 3.3 Torr of DM, 30 Torr of Pr, 7 ; 1.8 Torr of DM, 52 Torr of Pr, U; 1.8 Torr of DM, 101 Torr of Pr, e; and 1.8 Torr of DM, 191 Torr of Pr, 0. Dotted curves are the smooth extrapolations to zero photolysis time used in Figure 6.
[Pd/ [OM],
Figure 6. Yield ratios for 2,3DMB extrapolated to zero 405 nm photolysis time as a function of mixture composition. Symbols correspond to those in Figure 5 . The points that lie above the line are for runs at a total pressure less than 100 Torr.
the isomeric hexanes, and we can conclude that they are formed by radical and/or %H2 reactions. At pressures below about 100 Torr these radical and/or T H 2 reactions must be enhanced by some mechanism. The same mechanism is probably responsible for the similar increases in R(C5H12)'sat lower total pressures. Olefin Products. Table I presents product yield ratios for the three olefins formed in highest yield: C4H8 (isobutene and/or butene-1), PI, and 4MP1 (identified only by retention time and analogy with other workzd). Addition of small amounts of O2 eliminates all olefins. Yield ratios for olefin formation were somewhat erratic, so averages for runs with photolysis times less than 20 min were used in Table I. At long photol-
ysis times there is an apparent increase (10-20'3,) in the olefin yield ratios, but this may be an artifact resulting from the falloff of [n-B] at long times. As [Pr]/[DM]o is increased the yield of olefins decreases markedly; at ratios above about 200 they are no longer formed in detectable amounts. At pressures below about 100 Torr, there is again, as with the pentanes and hexanes, an increase in olefin yield ratios. There is some evidence from those [Pr]/[DMIoseries done at about 100 Torr and also at higher pressures that even at 100 Torr there may be slightly larger yield ratios than are expected. Unfortunately the analytical errors are too large to make an unequivocal assessment. DM-Pr-Other Gases. Since at [Pr]/[DM]o 1 50, qb(C4H10) is constant and attributable to lCH2, it seemed reasonable to add other gases to the DRf-Pr system as competitors with P r for lCH2 and hence to determine relative rates of 'CH2 reactions. CH4, Xe, and 0 2 were studied in this way by adding them in increasing amounts to the system [DMIO = 1.8 Torr, [Pr] = 100 Torr. [n-Bl/[n-B]~,the ratio of [n-B] with no added gas to that with added gas, 31, is shown in Figure 7 for 20-min photolyses as a function of [MI/ [Pr]. Table I1 gives R(i-B) and yields, Y(products), for the hydrocarbons formed in largest amounts in the DMPr-Xe system. In this series there is an increase in 3CHzcontribution to the C4H10 yields, reflected in the increasing R(i-B) with increasing [Xe]/ [Pr]. Using the assumptions cited previously, we can compute that the VH2 reaction has contributed about 6% of the [n-B] at the highest [Xe]/[Pr] used. This amount, and the corresponding corrections for other runs, was subtracted from the observed yield before Figure 7 was plotted in order that the [n-B] presented there should be wholly the result of lCH2reactions. For these competitive systems absolute yields (or quantities proportional thereto) are more meaningful than ratios to [ ~ - B ] M which , is reduced due to the competition. The values in Table I1 are Y(product) = R(product) ( [n-Blnl/[n-B]). The yields of 2,3DMB (perhaps 2RIP, but the results are ambiguous), C4Hs, and 4MP1 increase as [Xe]/[Pr] is increased. Within the experimental error of these analyses the yields of i-P and P1 appear unaffected by the addition of Xe. The CH4 series, Table 11,presents different problems. More than half the reactions of lCHz with CH4lead to the formation of CzH6*,much of which dissociates beupsetting fore collisional stabilization to yield CHSr4l8 the relative concentrations of radicals characteristic of VH2 reactions with Pr. More of the propyl radicals combine with the increased CH,, yielding more C4H10 by non-'CH2 reactions and reducing propyl-propyl reactions and, hence, the isomeric hexane yields, as Table I1 indicates. The ratio of isomeric C~H~O'S thus (8) J. A. Bell and G. B. Kistiakowsky, J . Amer. Chem. SOC., 84, 3417 (1962).
The Journal of Physical Chemistry, Vol. 76, No. 10,1971
JERRY A. BELL
1542 ~
~
~~
Table 11: Yield Ratios and Yields for the Systems [Pr]/[DM]o = 55 with Added Gases'
M
Xe
Ar
+ CH4'
N%
Y (Pl)b , d
Y (4MP1)h C
[MI/IPrl
R((-B)
Y(i-P)blc x 102
Y(2,3DMB)blc x 10%
Y(2MP)b'C x 10%
Y(CdHe)blc x 102
0 1.00 1.56 1.98 3.20
0.46 0.51 0.52 0.56 0.57
1.0 1.0 0.9 1.1 1.0
1.6 2.0 2.5 2.5 2.5
1.0 0.9 1.2 1.3 1.1
1.8 3.2 3.2 4.0 4.3
0.4 0.5 0.4 0.7 0.5
1.5 2.4 2.7 3.0 3.3
0 1.02 1.91 2.97
0.46 0.53 0.56 0.59
1.0 0.9 0.8 0.7
1.6 1.1 1.1 0.9
1.0 0.5 0.4 0.4
1.8 2.6 2.1 1.8
0.4 0.3 0.3 Trace
1.5 1.1 0.8 0.6
3.08
0.51
1.0
1.4
1.1
2.1
Of OQ
0.42 0.43 0.44
1.5 1.0 0.8
0.5 0.3 0.5
0.4 0.3 0.2
7.2 4.5 12.2
10.gh
'
x
io2
x
10%
1.5 2.0 1.4 1.3
2.0 1.1 2.6
' [DMlo = 1.8Torr; 20-minphotolyses at 405 nm. Yields, Y , are corrected values Y = R,b,d([n-B]3l/[n-B]), as explained in the text. 'Values are =k20%. Values are 2~50%. e 0.10CH4; 0.90Ar. [Pr]/[DM]o = 8.9; [DMIo= 3.3Torr. [Pr]/[DM]o = 8.8; [DMlo = 10Torr. [Pr]/[DM]o = 9.0; [DM]o = 3.3Torr.
formed will still, however, reflect the ratio of relative rates of 3CHzattack on primary and secondary bonds, so the technique for correcting observed [n-B] for 3CHz-reaction contributions should be valid; at [CH4]/ [Pr] = 3, the correction (reduction) is only 5%. Not only isomeric hexanes, but i-P, P1, and 4MP1 also decrease in yield as [CH,]/ [Pr] increases, although the change is not large for i-P and may not be a real effect. I n a blank photolysis run, DM-CH4 (no Pr), at a total pressure of 200 Torr, the major analyzable product was C4Hs (CI'S and CZ'S not analyxable). The yield was about 5 times the [C4Hs] in the DM-Pr-CH4 system, total pressure 200 Torr, with [Pr]/[CH,] = 1. [R(C4H8) = 11, but all the n-B could be attributed to DM decomposition in the gas chromatographic inlet system.] The rapid rate of CHa and 3CHz formation in the DM-CH4 system4 combined with their low reactivity toward CH, probably means that reactions with D M and, perhaps, radical-CHz reaction^^*^^ account for the enhanced yield of C4Hs. Time dependence studies on the [CH4]/[Pr] = 1 system were carried out to test whether rapid depletion of [DM] by such side reactions might cause lower yields of C4HlO that would lead to spurious values of [fi-B]/[n-B]~. The falloff in [n-B]/[DMIo in these runs exactly parallels that in the pure systems, so no significant amount of DNI is being destroyed by the side reactions. For the DM-Pr-OZ series the only detectable products were cZH4, i-B, n-B, and traces of i-P. One run was done using a counting-gas mixture of CH4 and Ar as the additive at a pressure of 313 Torr. The mixture contained 31 Torr of CH4 and 282 Torr of Ar, and had the same effect on [ ~ - B ] M as the addition of 100 Torr of CH4. Thus we can estimate that 69 Torr of CH4is as effective as 282 Torr of Ar in competiThe Journal of Phydcal Chemiatry, Vol. 76, N o . IO, 1071
'
tion with P r for 'CH, or that the rate of the CH4 reaction@) is 4.1 times that of the Ar reaction. The results of a single experiment done with 329 Torr of Nz added to 3.4 Torr of D3.I and 30.2 Torr of P r are given in Table 11. As a comparison, the yields for both a low and high pressure system with [PI-]/ [DM]o = 9 are also given. The changes observed with addition of NZcompared to the higher pressure DM-Pr system are qualitatively similar to those in the DMPr-Xe system. For this run with [N2]/[Pr] = 10.9, [n-B]/[n-B]x = 1.45.
Discussion Mechanism. A reaction mechanism consistent with previous work as well as this study is I2341
+ Nz C H z + Nz
CHzNz + 'CHz Id8
CHzNz-+
+ C3Hs kl+ n-CdHlo B i-C4Hla 'CH2 + C ~ H-%lCH2 + CsHs 3CHz + C3He lCH2 + CHZXZ-%- C2H4 + NZ 3CHz + C3Hs-% CHa + n-C3H7 3CHz+ CaHs2 CHa + i-C3H7 CZH4 + N2 %Hz + CHZNZ 'CH2
(1%) Ob) (24 (2b) (3)
(4)
(W (5b) (6)
(9) P.9. T.Lee, R. L. Russell, and F. 8. Rowland, Chem. Commun., 18 (1970). (10) H.M. Frey and R. Walsh, J . Chem. Soc., 2115 (1970).
1543
METHYLENE REACTION RATES 2CH3
5CZH6
+ n-C3H7 5 mC4HlO CH3 + i-C3H7 -% i-C4H10
and under these initial conditions, eq 13 reduces to
CH3
2n-CaH7 n-C3H7
Since [C4H10] = 1.42[n-B] and ks = 1.42k2a7we have
zq C6H14 (n-H)
+ i-C3H7 2C6H14 (2MP)
2i-CaH7 -%
(2,3DMB)
+ ~ C + HM ~ 'CH2 + M other products C H 2 + O2 + other products ~ C H n,f ~
kll
I, is the absorbed light intensity per unit concentration of DM per unit time and 41 and 43 are, respectively, the quantum yields for 'CH2 and C H z production in the initial photodissociation. The steady state concentration of 'CHZ is
The yield of n-B is unaffected by the addition of small amounts of 02,less than 0.1 [Pr], but all radical recombination products, reactions 7 and 9, are eliminated; R(i-B)is constant, 0.42, under these conditions. Thus, the contribution of reaction 5a, followed by 8a, to the [n-B], in t,he absence of 34, is negligible, and we have d [n-B]/dt = kza [ 'CH2],, [Pr]
The slopes, A, of the lines in Figure 2 are equal to (d[n-B]/dt)/ [DMIo; for two different sets of reaction conditions we can write
(14) We can choose for condition (A), [Pr]/[DA4]o = 8.8, but condition (B) is a problem, since the higher slope in Figure 2 is a limit that may be reached when [Pr]/ [DM]o E;: 30. Using (14) with XA/XB = 0.77 and ([pr]/[DM]o)~= 30 gives (kz k3)/k4 = 0.25; with ([pr]/[DM]o)~= 50, the rate constant ratio = 0.30. Thus the reactions of 'CH2 with D M are about 3 to 4 times as fast as with Pr. At [Pr]/[DM] 2 50, a t least 94% of all 'CH2 reacts with Pr, so (12) may be written approximately as
+
+
The ratio k2/(k2 k3) may be estimated from information available in the literature. For reactions 10a and 10b with M = CH4, Braun, et uLJ4 have and klob = measured klOa = (1.6 f 0.5) X (1.9 f 0.5) X 10-l2 cm3 molecule-' sec-', where reaction 10b refers to 'CH2
+ CHI +C2Ha*
(C2Ha* may either be collisionally stabilized or dissociate to give 2CH3.) The ratios k2a/klOb = 2.33 and k2b/klOb = 1.00 were derived by Halberstadt and McNesby.2b Thus k2 = k2a k2b = (2.33 1.00). (1.9 X 10-l2) = (6.3 f 1.7) X 10-l2 cm3 molecule-' sec-l. Carr has suggested that the rate constants for the intersystem crossing reactions 3 and 10a are approximately proportional to the polarizabilities of the 'CH2 collision partners.2e I n the range of polarizabilities for cm3, and Pr, 63 X cm3, CHI, Q! = 27 X his intersystem crossing rate constants increase about a factor of 2 for a threefold change in polarizability. (Relative rather than absolute values are cited here, because our absolute values do not agree with Carr's.) Thus we can estimate that ks = (2/3)(63/27)kloa = (1.5)(1.6 X 10-l2) = (2.4 f 1.0) X 10-l2 cm3 molek3) = 6.3/(6.3 2.4) = cule-' sec-1 and kzl(k2 0.73 i 0.20. Comparison with (15) indicates that 41 = 1.0 f 0.4; we shall assume that t$l is unity in further data analyses. Further evidence, but not unequivocal proof, of the validity of the assumptions made to obtain kz and ks is obtained from the competitive reaction systems, DMPr-M. The mechanism predicts that [ ~ - B ] M[DMIo / for competitive systems, [Pr]/[DM]o 2 50, will be related to [n-B]/ [DMIo,their pure counterparts, under constant, short-photolysis-time conditions, by the equation
+
+
+
+
where both [n-B]'s represent the yields due to reaction 2a. Figure 7 shows the straight-line relationships obtained and Table I11 gives values for klo/(kz Ic3) derived from the slopes of the lines. The rate conk10b)/(k2 Stant ratio for CH4, 0.37 0.08, is4 (kloa k3) and, using the rate constants above, we calculate this ratio to be 0.40 f 0.16, in excellent agreement with the measured value. This agreement gives us confidence in the conclusion
+
*
+
+
Th.e Journal of Physical Chemktry, Vol. 76,No.10,1971
1544
JERRY A. BELL ~~
~
Table 111: Rate Constant Ratios Determined or Assumed in This Study Value
Notes
0.76 f 0.15 0.73 f 0.20
Assumes $1 = 1 Assumes absolute values for k's; see text From [n-B]/[DMl0 falloff Assumes absolute values for k's Reference 2b From relative [n-B]at different [Pr]/[DM10 Figure 7 Figure 7 Assumes absolute values for k's Figure 7 See text Ar is "4 as effective as CHa; see text From 2,3DMB yields
Ratio
kzl(kz
+ k3)
kS/(kZ
+ k3)
kZa/k2b
ka/(ka
+ k3) + +
k10(Xe)/(k2 k 3 ) kio(CHa)/(kz k3)
+
0.39 f 0.10 0.28 =k 0.10 3.6
2.33 0.6
0.21 f 0.06 0.37 =k 0.08 0.40 0.16
*
kio(Oz)/(kz ka) kiO(Nz)/(k2 k3) klo(Ar)/(kz f IC3)
0.46 f 0.09 0.06 f 0.06 0.09 f 0.03
k6/kS
(4.0 f 1.9) x 102
+
Comparisons with Other Work klo(Ar)/k,o(CH4) 0.25 f 0.05 This work Ratio of absolute rate con0.18 stants measured by Braun, et al., ref 4 k d X e )/kz 0.29 This work 0.047 Cam, ref 2e5 kro(Oz)/kz 0.63 This work 0.46 Cam, ref 2ea kio(Nz)/kz 0.08 This work 0.048 Cam, ref 2e" kdAr)/kz 0.12 This work 0,030 Carr, ref 2ea 0.024, 0.033 Koob, ref 2f6 a Ketene photolyzed at 313 nm. The data analysis used assumes k3 = klo. *Vacuum ultraviolet photolysis of Pr at 123.6 and 147 nm. The figures given assume that the quantum yield for CHZproduction is unity for 'CHZ. klo(Ar)/(kz k3) is obtained directly and is 0.014 and 0.013 at the two wavelengths investigated.
+
that the photodissociation of D M yields 'CH2, with a quantum yield of unity, which, at [Pr]/[DMIo 2 50, all reacts with P r either to form C4HI0(70-80% of total CH2) or to be deactivated to 3CH2(20-30% of total CH2.) At lower [Pr]/[DMl0, reaction 4 with led = (3.6 f: 0.5) (ICz A k3) = (3.1 * 1.0) X cm3 molecule-' sec-' has to be taken into account. Assuming 4, = 1, we can use eq 12, revised to include all butanes, to calculate 4(C4H10) = 0.55 f 0.20 for [Pr]/[DM]o = 8.8, which agrees very well with the experimental value 0.59 f 0.12. To explain why the butane yield is not a function of [Pr]/[DMIo for ratios from 50 to 345, we must assume that reaction 6 is much faster than reaction 5, so that almost all the C H 2 is removed by reaction with DM. The data for CeHI4yields confirm this assumption and The Journal of Physical Chemistry, Vol. 76, No. IO, 1971
M/[Pd
Figure 7. Relative n-B yields as a function of added competitor gases for 20 min, 405 nm photolyses of 1.8 Torr of DM with 100 Torr of Pr: Xe, 0; CHI, 0 ; 02,A.
provide an estimate for k6/ks. For pure DM-Pr systems the above mechanism predicts
where we have assumed k6 [DIM] >> ks [Pr] and, $8, the quantum yield for 3CHzproduction, is equal to zero. The mechanism indicates that a constant ratio of CH3, n-C3H7, and i-CaH7 will be produced and, therefore, that a fixed fraction, f, of each of these radicals will disappear by each of the reactions 7-9. (That this assumption is not completely true is indicated by the R(2,3DMB)/R(2N!P) results from Table I, which show a variation with [Pr]/ [DMIo, presumably because of side reactions with Dhl and radicals derived therefrom.2d This effect is small, however, and will be neglected.) Thus the rate of formation of any radical recombination product will be a fixed fraction of the rate of radical production, reaction 5 , e.g. fk~[~CH2],,[Prl = kgc[i-C3H7I2
(18)
Assuming that kBb = 4ksa (secondary hydrogen abstraction favored by a factor of 12) and that the disproportionation-combination rate constant ratio is 0.6,2d we get f = 0.1 in this case. (Disproportionation is not included in the mechanistic scheme explicitly since none of the disproportion products, CH4, C3He, and CaHs, could be analyzed quantitatively in these experiments, but its effects have to be accounted for here.) We get, therefore
where f?(2,3DMB)o is the yield ratio a t the initial reaction conditions, extrapolated for the higher [PrI/
METHYLENE REACTION RATES
1545
[DNI],, as shown in Figure 5. Combining this expression with (17) yields
Figure 6 is a plot of R(2,3DABB)o us. [Pr]/[DM]o. combined with f = The slope of the line, 1.6 X 0.1 and k3/k2& = 0.54, gives k6/k6 = 3.0 X Another method of analyzing the 2,3DMB data is possible; at higher [Pr]/ [DRI],, combination of (12a) and (17) gives
ie., [3CH2],, is constant a t constant light intensity. Combining (20) with (18) and integrating, we obtain
that of the butanes formed by lCH2 insertion. If, as assumed previously, this yield represents about 10% of the overall yield of radical reactions following 3CHz attack on Pr, then the C H 2 reactions account for 16% of the products, in agreement with the prediction. Similar arguments can be made for systems with added gases, in which the [3CHz],,/ [‘CH2],, ratio is increased; the results are consistent with the above relative reactivity of 3CH2toward D l I and Pr. Analysis of the [n-B]/[DM], falloff shown in Figure 2 provides further evidence for the mechanism and rate constants derived above. The depletion of D M at [Pr]/[DM] 2 50 is almost entirely a result of reactions l a and 6 -d[DM]/dt = I a [ D M ]
+ k6[3CH2]sa[DR!I] (22)
Combining (20) and (22) and integrating gives [OM], = [DRI],, exp(-It)
assuming that [Pr] is constant, an assumption valid within much better than 1%. A plot of [2,3Dn!IB]/ [Dh!I]o, the total number of molecules of 2,3DMB produced per Torr of DM initially present, us. photolysis time is presented in Figure 8 for [Pr] = 191 Torr = 2.7 X lozomolecules. I , is 8.6 X sec-’ or 11.9 X l O I 3 photons sec-I (Torr of DM)-’. The slope of the line in Figure 8 is 1.34 X 10l2molecules sec-1 (Torr of DM),,-l and, combining this value with the constants already calculated or assumed, we get ks/& = 2.1 X which agrees satisfactorily with the results of the previous paragraph. Using all the data, we estimatekelk6 5 (2.5 X 1.2) X At [Pr]/[DM], = 345, only about 1/2 the 3CH2 reacts with Pr. Since about 20% of the total CH2 is 3CH2,approximately 10-15% of the products of CH2 P r reactions should be the result of 3CH2reactions. The yield of 2,3DMB in this system is about 1.6%
+
5
30
‘e
-
x
1
20 Phololysis
Time,
30
40
Minutes
Figure 8. Absolute yields of 2,3DMB as a function of 405 nm photolysis time for 1.8 Torr pf DM with 191 Torr of Pr.
(23)
where
By substituting (23) into (13a), integrating the resulting equation, and fitting the observed [n-B ]/ [DMIo us. t data to the integrated equation, we can calculate I , (1.2 A 0.2) X sec-’; I / I , = (1.2 X 10-4)/(8.6 ka) = 0.39 f 0.10, X = 1.39. Thus k3/(kZ which may be compared to the value 0.28 0.10 derived from the rate constants themselves. I n the runs with [Pr]/[DRI]o = 8.8, the falloff in [n-B]/ [DM], is somewhat faster, reflecting the contribution of reaction 4 to the depletion of DM. Competitive Systems. In the systems with added gases, the increased fraction of 3CH2reacts mainly with DM and depletes it faster than in pure systems, thus decreasing the rate of light absorption faster than in the pure systems. Since this means a lower rate of n-B production, the effect could lead to spurious results for the competitive systems because the conclusions are based on analyses of the reductions in n-B yields. I n the DM-Pr-02 system, no trouble should arise since the 3CH2presumably reacts with OS, reaction 11, and is removed before it can react with DM.6 (If anything, the [n-B] should be slightly enhanced, since DM is not being depleted as rapidly, but, a t the largest [02]/ [Pr], the enhancement would be only about 2%.) For the highest [Xe]/[Pr] used, we can use the rate constants already derived to calculate that 20% of the initial DM will have disappeared, compared with 13% in the absence of Xe under the same conditions. Very crudely, then, the average amount of DM present during the photolysis will be decreased from 0.93[DM]o to 0.90’ [DM],. Such an effect is within the experimental error of the technique and, therefore, was neglected in the data analyses. The special case of the CH, systems was treated in the Results section.
+
The Journal of Physical Chemistry, Vol. 76,No. 10,1971
JERRY A. BELL
1546 We can calculate klo for Nz by using an appropriate modification of eq 16 to include reaction 4, which makes a significant contribution under the reaction conditions used, [Pr]/[DM]o = 8.9. The result is klo(Nz)/(kz k3) = 0.06 0.06 and lclo(Nz) = (5 f 5 ) X 10-13 em3 molecule-1 sec-l. (The large error limit reflects the great uncertainty involved in the analysis of only a single run.) lCHz probably undergoes reaction lOb4!l1
+
'CH2
+ Nz = CH2N2
I n the analysis of short-photolysis-time runs we assume a constant [DM], which is an average, but uncalculated, value. The reproduction of DM via reaction 10b will only make this average higher and hence could make the apparent effect of reaction 10 less than its true value. Time dependence studies need to be carried out in the DM-Pr-Nz system to judge the relative size of klOaand klOb. The results for other added gases have been previously discussed, and the results are given in Tables 111 and IV. The results for Ar relative to CH, are in moderately good agreement with those measured directly by Braun et aL4 Comparing our results with those of Carrj2"in Table 111, however, we note that, although the 0 2 and Nz results agree moderately well, for Ar and Xe our intersystem crossing rates relative to reactions with propane are 4-6 times as large. We see, Table IV, that our rate for Kz is only about l/z that obtained by Braun, et al. If the upper error limit for the NZ run represents the correct value, then our result agrees with Braun's but is almost 3 times as high as Carr's. (The complications due to reaction lob, reforming DM, probably make all Nz data a bit suspect.) It is disturbing to see this almost systematic discrepancy between the two sets of results in steady-state, low-intensity systems. For his data analysis Carr assumes k3 = kloe, which is probably not a very good assumption, since k3 = 1.5kloafor Xe, the most efficient gas, relative to Pr, that we used. Carr's technique involves reducing [Pr] as [M] is increased; removal of a more efficient lCH2 quencher tends to increase the contribution of 'CH2 to the reaction and to make the apparent effect of M less than the equal-efficiency assumption suggests. However, if this were a major defect of his analysis, it is difficult to see how the data could yield the straight-line plots presented. (In a different system, vacuum ultraviolet photolysis of Pr-Ar-02 systems, KoobZf finds kloa/kz = 0.024 and 0.033, in agreement with Carr.) More experiments are necessary to resolve this discrepancy.12 Pentanes. Since R(i-P) and R(n-P) increase linearly with photolysis time, it is evident that one mode for their formation is
The J o u T of~ Physical ~ ~ Chemistry, Vola76,No. 10,1072
+ ~-CQHIO i-C5HlZ lCHz + i-C4H10-+ neo-C5Hlz 'CHZ
+
(254
(254 With R(i-B) = 0.4 and secondary insertion favored by 1.2 per bond over primary insertion, this scheme predicts R(i-P)/R(n-P) = 1.4. The observed ratio, Figure 3, with added Oz, is about 1.6 h 0.5, which is reasonable agreement. The formation of neo-CbHlz, detected a t long photolysis times, is further confirmaTable IV:
'CHZ Reaction Rate Constants Rate constant, ems molecule-1 aec-1 X 1012
Reaction
+ +
'CHz CHd + CzHe* 'CHz CHd + 3CHz CH4 'CHz CaHs + n-CaHlo 'CHz C3Hs + i-CaH1o 'CHz CaHa + T!Hz C3Hs 'CHz CHzNz + CzHa Nz 'CHZ Oz -,3 C H ~ Oz (or other products) lCHz Xe + %HZ t- Xe 'CH2 Ar + G H z Ar
+
+ + + + +
+
+
+ 'CHz + Nz
+
+ +
+ 'CHz + Nz
(loa) (lob) (2%) (2b ) (3) (4) (10)
1 . 9 f 0.5a 1.6 f 0 . 5 a 4.4 f 1.2b 1.9 5 0 . 5 b 2 . 4 =t1 . O b 31 f 10" 4.0 f 1 . 0 ~
(loa) (loa)
1.8 f 0.6O 0.8 f 0 . 3 c 0.67 5 0.13" >0.5 f 0.50 0.90 f 0.20"
(104
a Values of Braun, et al., measured directly, ref 4. These are the values assumed in our data analysis; they are internally consistent with all the experimental results with $1 = 1. These values are derived from our assumed rate constants and the experimental ratios of rate constants, Table 111.
tion of this mechanism. When the yield of C4H10 is about 1% of the starting amount of Pr, the yield of CsH12 is about 0.5% of the C4H10, which is consistent with the very roughly equal rates of reaction of lCHz with C3Hsand C4H10. I n the absence of 0, there is obviously a second source of C6H12,which probably involves C H 2 or radicals, or both. As this source, RabinovitchZdhas suggested the reactions
+ CHzNz CzHs + C3H7
CH3
+CzH6
+ Nz
CsHiz
(26) (27)
The present results offer little clear evidence regarding this mechanism, although it seems quite plausible. Any clear dependence of R(i-P) on [ P ~ ] / [ D M ] ois hard to discern from Figure 4, although total pressure, below 100 Torr, has a large effect which is discussed (11) A. E. Shilov, A. A . Shteinman, and M. B. Tjabu, Tetrahedron Lett., 4177 (1968). (12) R. W. Cam, private communication, has suggested that 'CHz from diazomethane photolysis might be formed in a more highly energetic state than that from ketene. The density of final aCHz states could then be sufficiently large to account for the higher intersystem crossing rates observed in the diazomethane system.
1547
METHYLENE REACTION RATES below. Reactions 2 and 25 together imply that R(i-P) should be inversely proportional to [Pr] (as well as directly proportional to photolysis time when [Pi*] is constant). Assuming that reactions 1-10 determine the overall characteristics of the system and that (26) and (27) have little effect on radical steady-state concentrations, we see that the nearly constant [3CH2],,, eq 20, implies that [CH3],, and [C3H7Isaare proportional to [Pr]'/z and hence that [C2H5Iss is proportional to [DRT]. The rates of production of CsHlz and n-B are then, respectively, functions of [DRI][Pr]''z and of [DM], eq 13a, so that the contribution to the observed R(i-P) from reactions 26 and 27 should be proportional to [Pr]'/'. The observed R(i-P) will, therefore, be a complex function of [Pr] with decreasing and increasing terms whose contributions to the total vary as the photolysis proceeds. There is a slight bit of evidence from Figure 4 that the intercepts at zero time increase as [Pr] increases and that at longer photolysis times R(i-P) decreases at higher [Pr]. "'Hot" Butane. At pressures below about 100 Torr the mechanism (1)-(10) still seems to work for C4H10production, but it has to be modified to account for the sharp increase in relative yields of radical recombination products, Figures 4 and 6 and Table I. Reaction 2 accounts quantitatively for the production of C4H10 under all conditions studied. But it has been simplified and should be written 'CHz
+ C3H8 +C4H10*
C4Hlo* -% C4HlO C4Hlo* -% CH3
+ C3H7
(2c) (24
(and some 2C2H5) (2e)
At lower pressures reaction 2e can begin to compete with 2d, collisional stabilization, to act as a second source of radicals added to those from reaction 5. Since k6 is so much larger than k,, the yield of radicals from ( 5 ) is very small under most reaction conditions. Whitten and Rabinovitch2ahave found that wZa/kZe = 1 at 0.5 Torr and 1.5 Torr for n-B* and i-B*, respectively. At 50 Torr, therefore, about 1% of the initially formed C4HlO* would dissociate to produce radicals. The occurrence of 1% of (2e) relative to (2d) would be undetectable in the C4HlO yield, but would add very significantly to the radical concentrations and hence to their reactions. This hot butane effect on radical product yields is also observed in other results below about 70 Torr.2c,g At higher [Pr]/ [DMl0 ratios, R(2,3DRIB)/R(2R!IP) approaches a constant value, 2.2 + 0.5, for systems with and without added gases, presumably reflecting reactions 5 and 7-9 plus disproportionation. At lower [Pr]/ [DM IO ratios the &(2,3DMB)/R(2MP) ratio decreases, probably because of side reactions with DM. At low pressures, reaction 2e should alter the ratio [i-C3H7]/[n-C3H7] in favor of n-C3H7, but this
effect, if present, is masked by the side reactions, since the low pressure reactions were also carried out at relatively low [Pr]/ [DM IO. There is some evidence from the data presented in Table I that even at 100 Torr the yields of hexanes and olefins are a bit higher than expected. The analytical error is too large to make this certain but, to be on the safe side, one should probably use pressures above 100 Torr to eliminate hot-molecule effects. Olefin Production. Tables I and I1 show that olefin production is dependent on [Pr]/ [DRIlo and increases with decreasing total pressure below about 100 Torr. Olefin production is increased by the addition of "unreactive" gases, Xe and 1\72, which take part in reaction loa; the behavior is more complex with added CH4 because it reacts with 'CH2 to give C2H6* that dissociates to yield CHs in decreasing amounts as the total pressure increases. Clearly DM is involved directly in the olefin-forming reactions, but whether the reactions involve mainly G H 2 , 3CH2,or other radicals is very difficult to ascertain. Radicals must be involved at some stage, since, at low pressures where radical processes are enhanced by the small amount of CqHl0* dissociation, the yield of olefins increases. The formation of C4H8 (butene-1 probably) in DM photolysis systems with hydrocarbons is universal and probably, Table 11, involves 3CH2, CHI, and DM. (It was the largest analyzable product in the blank photolysis run with CH4 instead of Pr.) P1 production is little affected by increase in 3CH2and may be the result of 'CHZ, DM, and radical reactions. 4MPl follows trends closely similar to C4H8, except that its formation is definitely inhibited in the presence of CH4. Although the mechanisms for olefin formation remain obscure, their yields are low enough that they do not pose a major problem in interpreting the other results mechanistically. Implications f o r Other Systems. It now appears well established that 63/61, reaction 1, varies with precursor, DRI, ketene (K), or diazirine, and with photolysis wavelength for a given precursor. The conclusion reached here is that 63/41 = 0 and 6' = 1 for DR!I at 405 nm. A comparison of the results of this study with others in the literature indicates that a great deal of care in interpretation must be exercised as a result of differing rates for reactions 4 and 6 for the different precursors. Carr finds k4(K)/k2 = 0.9 and, thus, k4(K) = 5.7 X cm3 molecule-' sec-l for ketene at 313 nm and 760 Torr of total pressure,2e compared with k4 ( D X ) / k 2 = 5 from this work. Braun, et u Z . , ~ suggest that the sum of the rate constants for CH2 (multiplicity unspecified) I< reactions, not including intersystem crossing, lies between 1 X 10-l2 and 5 X 10-l2 cm3 molecule-' sec-' which compares favorably with this estimate for kh(1i). Equation 12a should hold for I< at a [Pr]/[K] ratio '/5 as large as the [Pr]/[DRI]
+
The Journal of Physical Chemistry, Vol. 76, No. 10,1971
JERRY A. BELL
1548 = 50 necessary for DN. If all CH2 is initially formed as ‘CH2,then the maximum possible yield of C4H10from reaction 2 is k z / ( k 2 k3) = 0.73 A 0.20. Analysis of Noyes’ data,20Table V, for K-Pr a t 280 nm and 200 Torr of total pressure indicates a C4H10yield (corrected for T H z reaction) that is 0.66 of the total CH2 (based on CO yield). It is conceivable, therefore, that a large fraction of all the C H 2product in this system is a result of reactions 3 and 5-9 and that 43 is close to zero for I< at 280 nm.13 Looking at “singlet” and “triplet” products without also doing relative quantum yield studies may, therefore, lead to spurious conclusions regarding 43/41,
+
Table V : Data for the K-Pr System a t 280 nm. Yields Relative t o CO” Total pressure, Torr
[Prl/ [Kla
[CaHiol
R(I-B)
[CzH41
[CzHel
[CHal
196 200
5 10
0.576 0.728
0.548 0,505
0.131 0.064
0.059 0.049
0.008 0.006
a
Ho and Noyes, ref 2c.
A further implication of the small kq(Ii)/lc2 is that the reaction lCH2
+ CH2C0+ 3CH2+ CH2C0
(28)
may be very important in I< systems. We x-ould expect, on the basis of C a d s polarizability correlation,2e that this reaction would be relatively important compared with (3). I< has a = 44 X cm3, based on molar refractions, and a total polarizability 159 X cm3 when its permanent dipole is taken into account;14 it should be at least as effective as Xe in inducing intersystem crossing in CH2. Disregarding reaction 28 might lead to serious errors in assessing &/$I. On a molecule-for-molecule basis, the reactivities of olefins and saturated hydrocarbons toward ‘CH2 are c~mparable,’~ so reaction 28 may, under some conditions, be an important source of 3CHzin the Kolefin systems often used to assess $3/41.20,3b For DnI we find k6/h;6 = 400, but the corresponding ratio for I< must be much lower. For [Pr]/[D31lo = 9, we find the R(i-B) = 0.42 f 0.01 characteristic of the lCHz reaction. I n systems with [Pr]/[K] = 10 photolyzed at 280 or 313 nm, the observed R(i-B) = 0.53,201gwhich implies a large C H 2 contribution via reactions 5 and 8. Using Koyes’ results, Table V,2c we can estimate k , ( K ) / k 6 . The CO yield, corrected for the nonphotolytic production by reactions analogous to (4) and (6)) is equal to the total amount of CH, produced upon photolysis. The sum of the yields of CH4, CzH4,C4H10,and twice C2H6should, given the mechanism we have been using, equal the CH2 yield, The Journal of Physical Chemistry, Vol. 76, X o . 10, 1971
but in all cases the sum is slightly less. We assume that this “lost” CH3 is lost via V H z reactions with I< (an assumption that can only make the apparent reactivity with K larger than its true value). The amount of singlet product, C2H4 C4Hlo,is calculated by using R(i-B) to correct the observed C4H10yields for 3CHz reaction and then using lc4(K)/k2 to compute C2H4 from reaction 4. The yields of C2H, and CeHlo from T H 2reactions are obtained by subtracting the amounts computed for ‘CH2 reactions from the totals. The yield of C2H4from 3CH2plus the “lost” CH2is taken to be proportional to the rate of 3CH2reaction with K. The sum of the yields of CH4, twice C2H6, and the C4Hlo from %H2 is taken as proportional to the rate of 3CHzreaction with Pr. Combined \\ith [Pr]/[K],, these relative rates give k6(I
