KINETICS OF V~BRATIONALLY HOTPROPANE
607
Kinetics of Vibrationally Hot Propane Produced by Methylene Insertion into Ethane1
by F. B. Growcock, W. L. Hase, and J. W. Simons* Chemistry Department, New Mexico State University, Las Cruces, New Mexico 88001
(Received September 19, 1971)
Publication costs borne completely by The Journal of Physical Chemistry
T h e reaction of !thane with excited singlet state methylene radicals produced via t h e photolysis of diazomethane a t 4358 A, yields chemically activated propane with a n average energy of 119.4 2.0 kcal/inol. T h e measured decomposition rate coefficient for the energized propane is (4.7 f 1.2) X 108 sec-I. This rate is correlated by RRKM and absolute rate theory calculations with thermal A factors in the range 101e.7-1017,2 sec-’ and radical recombination rate coefficients in the range 2.2 x 109-5.8X lo9 1. mol-’ sec-’, which a r e CSHS. A dilemma of possubstantially lower than estimates of experimental recombination rates for CHa sible theoretical significance exists.
*
+
Introduction Pyrolysis studies of propane have shown that the primary reaction in the decomposition of propane is C-C bond rupture giving methyl and ethyl radical^.^-^ However, quantitative measurements of rate parameters in the thermal studies have suffered from surface reactions and complicating secondary reactions which accompany the primary process. Chemical activation provides a technique for studying unimolecular reactions at low temperatures, which minimizes these complicating processes. Chemically activated propane may be produced by radical and atom comb i n a t i o n ~ ~and - ~ by singlet methylene i n ~ e r t i o n . ~ - ’ ~ Recent studies of the decomposition rates of chemically activated alkanes (C4-C6)have shown via RRKM theory and absolute rate theory that correlations of these decomposition rates with estimated radical recombination rates are barely possible, even though the extremes oi high critical energies for decomposition, “tight” radical models, and free-internal-rotor activated complex models are used.l1tz2 In the case of n-CeHlo + 2CzH5 the correlation was not possible. An extension of these previous studies to the chemically activated propane molecule is of interest. Estimates of the CHa CzH5 recombination rate are more reliable than for the larger radicals, and fewer adjustments in complex and radical models are possible. Diazomethane was photolyzed at 4358 A to yield excited ‘CH2, which inserts into the C-H bonds of ethane to yield “hot” propane. The decomposition of excited propane in this system can be measured unambiguously with the aid of oxygen as a triplet and doublet radical scavenger13 and an internal standard to monitor total reaction. l 4 The excitation energy, E*, of the “hot” propane can be determined by addition of cis-2-butene and determining E” for “hot” cis-
+
1,2-dimethylcyclopropane15in a propane bath. The addition of cis-2-butene serves as ah E” monitor. Experimental Technique
Procedure. Approximately 15% oxygen was added to 2: 1 :0.6 ethane-n-butane-diazomethane mixtures. These were photolyzed a t pressures ranging from 0.8 to 107 cm Hg for 2-6 hr, depending on total pressure. A summary of the reactant concentrations is given in Table I. In the E* monitor system ethane-cis-2-butene-isobutane-diazomethane mixtures in ratios of 2:0.5 :0.5: 0.6 with -15% added oxygen were photolyzed a t pressures ranging from 0.2 to 171 cm for 3-14 hr. Several (1) The National Science Foundation is gratefully acknowledged for financial support. (2) (a) D . A. Leathard and J. H. Purnell, Proc. Roy. SOC.Ser. A., 305, 517 (1968); (b) D. A. Leathard and J. H. Purnell, ibid., 306, 553 (1968). (3) K. J. Laidler, N. H. Sagert, and B.W. Wojciechowski, ibid., 270, 242 (1962). (4) K. J. Laidler, et al., ibid., 270, 254 (1962). (5) E. W. R. Steacie and D . S. Dewar, J . Chem. Phys., 8,571 (1940). (6) E. Gorin, W. Kauzman, J. Walter, and H. Eyring, {bid., 7, 633 (1939). (7) B. S. Rabinovitch and D. W. Setser, Advan. Photochem., 3, 1 (1964). (8) R. L. Johnson, W. L. Hase, and J. W. Simons, J. Chem. Phys., 5 2 , 3911 (1970). (9) G. Z. Whitten and B. S. Rabinovitoh, J . Phys. Chem., 69, 4348 (1965). (10) J. W. Simons, C. J. Mazac, and G. W. Taylor, ibbd., 72, 749 (1968). (11) W. L. Hase and J. W. Simons, J. Chem. Phys., 54, 1277 (1971). (12) W. L. Hase, R. L. Johnson, and J. W. Simons, Int. J. Chem. Kinet., 4, 1 (1972). (13) S. G. Lias and P. Ausloos, J. Chem. Phys., 43, 2748 (1965). (14) F. H. Dorer and B. S. Rabinovitch, J . Phys. Chem., 69, 1973 (1965). (15) J. W. Simons and G. W. Taylor, ibid., 73, 1274 (1969). The Journal of Physical Chemistry, Vol. 76, No. 4, 1979
F. B. GROWCOCK, W. L. HASE,AND J. W. SIMONS
608
Table I : Ethane*-Butane-Diazomethane-Oxygen
System
[IPlb PCzEe'
5.18 4.65 4.78 6.36 6.61 7.39 7.72 10.14 15.03 15.4 20.9 33.9 40.9 61.5 93.3 105.5 127.1 260.45 346.5 370.0 709.0 914,O
Pn-CrElO
PCHzNz
2.58 2.21 2.32 2.99 3.11 3.49 3.19 4.70 6.78 7.30 9.10 16.6 20.1 28.4 41.9 47.6 59.3 137.3 156.9 173.2 365.0 449.0
1.35 1.37 1.37 1.81 1.81 2.08 2.09 2.72 3.79 4.50 5.40 8.90 12.7 22.8 24.2 25.3 36.2 70.85 85.5 94.5 210 7 266.0 I
'/4POz
[CsHsl
0.35 0.384 0.551 0.447 0,532 0.48 0.50 0.74 0.936 1.195 1.34 2.46 3.18 5.05 9.12 6.11 10.15 17.8 23.1 10.43 44.5 64.0
2.73 2.94 3.36 2.44 2.60 2.41 2.37 2.04 1.71 1.51 1.47 1.20 1.25 1.02 0.831 0.854 0.979 0,786 0.. 733 0.897 0.788 0.836
a All pressures are in units of Torr. Product ratios are molar and are normalized by the reactant ratio.
experiments were performed where ethane: (cis-2-butene isobutane) was 3:1, but the product ratios did not vary with this change. The total product yield was less than 1% in all cases, so that secondary reactions were negligible. The data for this system are reported in Table 11. Materials. Matheson lecture-bottle ethane and nbutane were purified by gas chromatography and vacuum distillation at 77"K, and analyses showed them to be relatively free of impurities (less than 1%). Diazomethane was prepared by the reaction of N-methyl-Nnitroso-p-toluenesulfonamide with an anhydrous saturated solution of NaOH in lJ4-butanediol and was stored in di-n-butyl phthalate at liquid nitrogen temperature. The nitrogen impurity in commercial-grade Linde oxygen was reduced by distillation at 77°K. Analysis by glpc of the purified 0 2 showed only trace impurities. Isobutane and cis-&butene were Matheson CP grade and were purified by glpc and vacuum distillation. Apparatus. All gas-handling was performed in a standard high-vacuum system using greaseless stopcocks. Reaction products were analyzed on an Aerograph 90-P3 gas chromatograph which used a thermistor detector. The photolysis radiation was that from a Hanovia No. 6738, 500-W medium-pressure mercury arc lamp which employed No. 7-56(5850) and No. 3-73(3389) Esco Products glass filters to isolate the 4358-A band. Analyses. All product amounts were determined by
+
The Journal of Physical Chemistry, Val. 76,N o . 4, 1972
glpc analyses after the product mixture was vacuum distilled at 77°K to rid the reaction vessel of O2 and other noncondensables. The condensables from tho ethane n-butane experimental runs were passed through a 25 ft dibutyl phthalate-firebrick column with a 4 ft attachment of didecyl phthalate on firebrick. The oxygenated products did not come off the column; the only products observed with retention times greater than n-C4Hlo were isopentane and n-pentane. The condensables from the ethane-cis-2-butene-isobutane monitor system were first passed through a 25 ft column of AgNOa on firebrick to separate Cq and Cg olefins from the system, for these species interfered with analyses of cis- and trans-1,2-dimethylcyclopropane(CDMC and TDMC). The eluents were subsequently trapped and passed through the first column mentioned above. The dibutyl phthalate column was calibrated periodically to determine the sensitivity of the detector toward reactant and product molecules. The absolute sensitivities of the products cancelled out in the determination of the rate contants, and only their ratio was needed for calculation of the high-pressure intercepts. Samples of the reactants were also checked periodically to reaffirm the absence of impurities. In addition, dark reactions at several pressures for both the propane and E* monitor systems were run and analyzed to show that no interfering products were present. The effective pressure of O2 was taken to be '/4 its actual value, as the collisional deactivation efficiency of O2 was taken to be about 0.25.16 Any error resulting from this choice has a negligiblc effcct on the total collision frequency. The collision diameters used for all reactant species were those obtained from the application of a LennardJones potential to their transport properties. l7v1* These lead to collision frequencies of W C ~ H = ~ (1.95 X 107pCeHe, un-C4Hlo = (2.12 x 1 0 7 ) ~ ~u C-H~ z N z~ = ~ ~ ~ , (1.85 x ~ ~ ' ) P Candwo, H ~ N= ~ ,(1.41 x 1O7)O.25PoZ.The collision frequencies for the species present in the E* monitor system are uCZHa = (2.08 X 10')PCeHe, ui-C4H10 = (2.07 x 1 0 7 ) ~ ~uCtS.2-C4H8 - ~ ~ ~ ~ = ~(2.14 , x 107). Pcis-2-C4Hs, WCHzivz = (1.92 x 1O7)PCHgNz, and ~ O Z= (1.53 X 1O7)0.25Po,.
+
Experimental Results Unimolecular Decomposition of C3HB* from V H Z 4C2HB. The major primary processes in this system are the two insertion reactions given by reactions 1-2'. (16) G. H. Kohlmaier and B. 9. Rabinovitch, J . Chem. Phys., 38, 1709 (1963); J. D. Rynbrandt and B. S. Rabinovitch, J . Phys. Chem., 74, 1679 (1970). (17) J. 0. Hirschfelder, C. F. Curtiss, and R. B. Bird, "Molecular Theory of Gases and Liquids," Wiley, New York, N. Y., 1954. (18) S. C. Chan, B. S. Rabinovitch, J. T. Bryant, L. D. Spicer, T. Fujimoto, Y. N . Lin, and S. P. Pavlou, J . Phys. Chem., 74, 3160 (1970).
KINETICSO F VIBRATIONALLY HOTPROPANE
609
Table I1 : Ethane-cis-2-Butene-Isobutane-Diazomethane-Oxygen System
892 110.2 99.3 84.0 60.85 39.5 30.9 14.79 14.40 4.71 4.69 4.09 3$39 2.76 2.21 1.98 1.71 1.54 5
224 39.8 22.7 28.8 14.04 10.1 7.10 3.54 3.47 1.17 1.13 1.035 1.23 0.516 0.505 0,662 0.3473 0.545
234 13.2 22.8 9.29 13.81 10.1 7.30 3.45 3.40 1.15 1.09 1.095 0.421 0.509 0.534 0.287 0.3473 0,1734
All pressures are in units of Torr.
'CH2
+ 'CIIZ + n-CJHlo
(2)
n-ChHlz*
(2')
+ CzHj
1.49 1.54 1.37 1.68
...
5.94 4.68 3.38 2.93 1.82 1.38 0.94 0.99 0.94
... ...
1.62 1.74
...
2.42 2.64 2.71 2.88 3.65 3.64 3.81 4.55 4.26
...
0.87 0.55 0.78 0.60 0.72
The expression has been normalized by the reactant ratio.
2 50-
(3)
CaHs* A C3H8 (4) where k3 is the average rate constant for decomposition and w is the collision frequency. H atom split-off i-C3H7 or H n-C3H7are of from C3H8" to form H minor importance; they occur at a rate of less than 1% compared to CH3 split-off, as can be derived from the differences in activation energies and A factors.Za A steady-state treatment of reactions 1-4 for C3Hx* gives
PPI [CzHel ___ - -lei_ k3 [CBRX] [n-CJIio] w
... 7.66
3 00-
An asterisk denotes a species in the ground electronic state with excess vibrational-internal rotational energy. The pentanes are collisionally stabilized. Isopentane (IP) is formed a t an average energy of 121.5 kcal/mol above the ground state12 and, a t the lowest pressure used (0.8 cm), only 1.3% of the excited isopentane decomposed. By utilizing O2 as a scavenger for triplet and doublet radicals, the large number of radical recombination products that would have been formed were eliminated. The excited propane formed from (1) can undergo reactions 3 and 4
+
1708.2 198.35 181.43 149.7 112.3 74.22 56.77 26.65 26.87 8.71 8.639 7.26 6.204 4.551 4.039 3.454 2.9133 2.760
(1)
C3H8*
' C l l ~ n-CdH~o-% i-CsHlz*
C3H8*-% CHI
66.2 7.45 7.63 5.68 4.14 2.82 2.26 0.893 1.192 0.36 0.349 0.30 0.248 0.155 0.1794 0.146 0.1067 0.1006
All product ratios are molar.
b
+ CzHe A
292 27.7 29.0 21.9 19.43 11.7 9.21 3.98 4.41 1.32 1.38 0.74 0,915 0.611 0.611 0.379 0.402 0.401
+
+ kz-
ki
(1)
A plot of [IP]/[C~HB], normalized to the reactant ratio, us. 1/w should be linear from which the average uni-
2 00/ P CIHe
CJH8 ".%HI0 150-
05
100
200
300 4 0 0 5 0 0 $ 0 0 7 0 0 800 9 0 0 1000 / I O
x
lo3,TORR-'
eo:,
Figure 1. Plot of [IP]/[C3H8] vs. l/Ptotal X lo4for the 4358 photolysis of CHzNzin the C2H6-n-C4HI0systems, where the ratio [IP]/[CaH8] has been normalized to a reactant ratio of 1.0 and Ptotalis in units of Torr. The collision frequency of C3He* for each experimental point has been calculated with the following collision dia?eters a t 300'K: CzHs, 5.23A; n-CaH~o, 6.73A; CHzN2, 5.45A; and 02,3.60A. The line through the data points was drawn to give the intercept obtained from a least-squares analysis and an approximate fit to the other points.
molecular rate constant for decomposition, k3, can be obtained. Figure 1 depicts a plot of eq I. A leastsquares regression analysis of the data points gives k3 = (4.7 f 0.5) X loxsec-', or 26.8 Torr, and the highpressure intercept kz/lcl = 0.89 & 0.07 for 90% confidence limits. This value for the intercept, combined with kz/k2' = 0.90 (determined by Simons, et aZ.'o), gives a value for the relative reactivities of ethane and k2')/lc1 = 1.89. This value is in n-butane: (k2
+
The Journal of Physical Chemistry, Val. 76. No. I , 1971
6 10
F. B. GROWCOCK, W. L. HASE,AND J. W. SIMONS
excellent agreement with the value of 1.88 determined by Halberstadt and McNesby.19 E* Monitor System. The E* monitor was used to determine the amount of excess energy carried by singlet methylene, E*( 'CH2), into the chemically activated insertion product, C$HS*. This value has been determined for CH2N2-cis-2-butenephotolyses at 4358 b, but the average energy of the methylene radical might be expected to be lower in this system which contains -50% ethane, due to an increased fraction of unreactive collisions.evll I n the monitor system, cis-2butene and isobutane were substituted for n-butane t o measure the geometric and structural,rate constants of chemically activated cis-1,2-dimethylcyclopropane. This substitution did not affect the fraction of unreactive collisions, since the intrinsic reactivities of nbutane, isobutane, and cis-2-butene are nearly the same." The reactions of interest in the E* monitor system are the following
+ 'CH2 IP* cis-2-butene + 'CH2 -% CDMC* CDMC*
(6)
+
-%pentenes"
+ k,
k,
h x
[IP1
+ [TDMC]
(11)
[cis-2-butenel [i-C4Hio]
k,ks 1 -k6
80 0
I20 0
100 0
I
140 0
I
160 0
1800
200
TORR
Figure 2. Plot of [CDRIIC]/[TDMC] us. Ptotsl for the 4338 photolysis of CHzNz in the E* monitor system, where Ptotsl is in units of Torr. The collision frequency of CDil,IC* for each data point was Calculated with the following c2llision diameters a t 300' K : cis-2-CaHs, 6.69 A; 2-C4H10, 6.56 A; CH2N2, 5.45 A; Os, 3.60 .&. The line drawn through the data points is an approximate fit which gives the intercept from a least-squares calculation.
s.ooc
t 1.000
(11)
Application of the steady-state assumption to all activated species gives [CDMC]
S0,O
?OTAL+
(10)
Applying the steady-state assumption to TDMC" yields16
= - + -k,'
40.0
(9)
-% pentenes*
w
,
I
200
(8)
TDMC* -% TDMC
[CDMC] [TDMC]
i
(7)
TDMC*
CDMC* -% CDMC TDMC*
8.00
(5)
i-C4&0
CDMC*
10.00~
+g k5
(111)
Data for this E* monitor system can be found in Table 11. Plots of the data for eq I1 and 111 are shown in Figures 2 and 3, respectively, where unit collisional deactivation efficiency for ethane is assumed. Leastsquares regression analyses on the data in Figures 2 and 3 yield kg = (5.74 f 0.18) X 108 sec-' and k, = (1.14 0.11) X 108 sec-1 for 90% confidence limits. This gives a ratio of the geometric to the structural rate constant, k,/k,, of 5.03, which is lower than previous values.15 Simons and Taylor obtained a value for k g
*
The Journal of Physical Chemistry, Vol. 76,No. 4, 107.2
2.000
3,000
+
[TDMC]) vs. l/Ptotaifor Figure 3. Plot of [IP]/( [CMDC] the 4358 A photolysis of CH2Nz in the E* monitor system, [TDMC]) has been where the r&io [IP]/([CDMC] normalized to a reactant ratio of 1.0 and Ptotnlis in units of Torr. The collision frequency of CDMC* for each experimental point was calculated with the collision diameters given in the Figure 2 caption. The line drawn through the data points is an approximate fit that gives the intercept calculated by a least-squares analysis.
+
of 5.5 x 10s sec-1, in good agreement with our oyn, for diazomethane-cis-2-butene photolyses at 4358 A.16 Their value for k , was somewhat lower (0.68 X los sec-l) than ours, but is probably within the expcrimental uncertainties. These results indicate that methylene does not lose more energy by virtue of unreactive collisions with ethane than with larger hydrocarbons, This conclusion would be altered for a collisional deactivation efficiency of ethane less than one, but an efficiency significantly less than one for (19) M.L. Halberstadt and J. R. MoNesby, J. Amer. Chem. SOC.,
89, 3417 (1967).
KINETICSOF VIBRATIONALLY HOTPROPANE
611
ethane is unexpected. An efficiency as low as 0.7018 would affect E* and k g values in compensating ways. The average excitation energy of the propane molecule is given by
propane molecule was taken from Schachtschneider and Snyder,31along with the two torsional frequencies measured by Weiss and L e r ~ i . This ~ ~ structure gave a calculated entropy of propane at 400°K equal to 69.98 eu. The entropy of propane has been experi-(E*) = AHto0(C3Hs)- AHro"(CzHs) mentally determined to be 70.37 eu.zo This small discrepancy has a negligible effect on these calculations. [AHf,"('CH2) 4- E*('CH2) I - E t h (IV) Activated complex models were constructed accordThe values for AHf,' (C3H8) and AHi,"(C2Hs) were ing to a format previously followed for hydrocarobtained from ref 20, Eth was calculated to be 2.2 bons:7*8g12lengthening of the C-C reaction coordinate kcal/mol, and [AHfo0( 'CH2) E*( 'CH2) ] was taken and lowering of four frequencies, including methyl rocks, from reference 15. The values combine to give (E*) = methylene racks, and a skeletal bend. The propane 119.5 kcal/mol. activated complexes were constructed by lowering two methyl rocks, one methylene rock, and one skeletal Theoretical Calculations bend by a constant factor, until the calculated rate, RRKM theory provides an accurate description of was the same as the experimental decomposition unimolecular decomposition p r o c e ~ s e s . ~ The ~~~-~~ rate (ha). RRKM theory expression for the specific decomposition The C-C stretch a t 924 cm-l was taken as the rerate of a molecule a t the energy E* is action coordinate. The following is a description of f+ five activated complex models that were used: (I) both torsions treated ?s free rotors; rupturing C-C bond extended to 2.0 A; all external rotors adiabatic; (11) same as (I),but the external rotor along the figure where .Zf*f,,+=o P(ev,*) is the sum of all the active viaxis treated as active in both the complex and the brational-internal rotational energy eigenstates of the molecule; (111) both torsions treatedo as free rotors; activated complex up to the energy e * ; N(evr*) is the rupturing C-C bond extended to 3.0 A; one external number of eigenstates per unit energy of the active rotor active in complex and molecule; (IV) both degrees of freedom of the molecule at the energy E*, h torsions treatedo as vibrators; rupturing C-C bond is Planck's constant, d is the reaction path degeneracy, extended to 3.0 A; one external rotor active in complex and Zo*/.Zo*is the ratio of the product of the adiabatic and molecule; (111') same as (111), but eo raised to partition functions in the complex to those in the 84.6 kcal/mol, molecule. A more accurate treatment of adiabatic Radical Structures. The methyl radical structure rotationsZ1,22only slightly alters the calculated results was taken from experimental infrared work.33 from eq V. The structure of the ethyl radical has not been deFor the methylene-ethane system, the distribution termined, but the barrier to internal rotation, although function for the chemically activated propane is quite (20). American Petroleum Institute Research Project No. 44, CarThus the experimental rate narrow relative to ( E *). negie Institute of Technology, Pittsburgh, Pa., 1944-1952. constant k3 may be closely approximated by the (21) R. A. Marcus, J . Chem. Phys., 43, 2658 (1965). specific rate constant at the average energy (E*). (22) E. V. Waage and B. S. Rabinovitch, Chem. Rev., 70, 377 (1970). This is the same procedure that was used in determining (23) R. A. Marcus and 0. K. Rice, J . Phys. Colloid. Chem., 55, 894 (1951). AHf,"('CHz)] and would the quantity [E*('CH2) (24) G. Z. Whitten and B. 8. Rabinovitch, J . Chem. Phys., 41, 1883 in effect cancel any errors resulting from equating (1964). lqE+)with k3. The densities of the vibrational-internal (25) D. C. Tardy, B. S. Rabinovitch, and G. Z. Whitten, ibid., 48, 1427 (1968). rotational eigenstates and the corresponding sums for (26) S. Gl;sstone, K. J. Laidler, and H. Eyring, "The Theory of Rate the states of the various activated complex structures Processes, McGraw-Hill, New York, N. Y., 1941. were calculated using an accurate a p p r o ~ i m a t i o n . ~ ~ * (27) ~ 6 S. W. Benson, "Thermochemical Kinetics. Methods for the Estimation of Thermochemical Data and Rate Parameters," Wiley, The computations were done on an IBM-360 computer. New York, N. Y., 1968. Arrhenius A factors and activation energies were calculated from absolute rate theory expressions.26 (28) J. A. Kerr, Chem. Rev., 66, 465 (1966). (29) H. L. Johnston, L. Savedoff, and J. Belzer, "Contributions to the The critical energy was calculated from the C-C bond Thermodynamic Functions bv a Planck-Einstein Oscillator in One Degree of Freedom," Office df Naval Research, Department of the dissociation energy,27,28 and was found to have a value Navy, Washington, D. C., 1949. Of 82'6 2'o kcal/mol* The thermodynamic functions (30) D. R. Herschbach, H. S. Johnston, K. S. Pitser, and R. E. were calculated with the aid of oscillator tables,29and Powell, J . Chem. Phus., 25,736 (1956). the reduced moments of inertia for the free internal (31) J. H. Schachtschneider and R. G. Snyder, Spectrochim. Acta, 19, 117 (1963). rotors were computed using a technique for unsym(32) S. Weiss and G. E. Leroi, ibid., Part A , 25, 1759 (1969). metrical tops.30 (33) D. E. Milligan and M. E. Jacox, J . Chem. Phys., 47, 5146 Activated Complex Structures. The structure of the (1967).
+
+
*
The Journal of Physical Chemistry, Vol. 76, No. 4, 1978
612
F. B. GROWCOCK, W. L. HASE,AND J. W. SIMONS
approximately 3.0 kcal/mol in ethane, 27 may be rather small.'* The structural model used was taken from previous studies,34and consisted of a five-member set of geometrically averaged frequencies based on the vibrational frequencies of the ethane molecule. Since the barrier to internal rotation about the bond adjacent to the unpaired electron is not known, the torsion in the ethyl radical was treated as both a vibrator (289 cm-1, the same as the torsional frequency in ethane) and a free rotor in the CH3 CzHs recombination rate calculations. A complete description of the two radical structures is given in Table 111.
+
Table I11 : CHa
+ C2H6 Radical Recombination Rates Models" Methyl radical
3100 (2) 2930 1230 (2) 611
= 49.4 eu In (QT/IV)= 20.41 eub E t h y l radical
2960 ( 5 ) 1155 (2) 993 820 (2) 289 or F.R.
Free rotor (eu)
S",oo 62.34 In ( & T / N ) 26.18
289 om-1
(4
61.48 25.67
Ratesc Torsion as Complex
289 cm-l vibrator
I I1 I11 IV 111'
2.20 x 109 3.02 x 109 3.32 x 109 6.50 X 108 5.82 x 109
Torsion as F.R.
1.34 1.84 2.01 3.93 3.51
x x x x x
109 109 109 108 109
a All frequencies are in cm-'. b (QT,") is the total partition function. All rates are given in 1. mol-lsec-l and are calculated l d C z H d l N I , where EO by k , = (kT/h)(&r* l i V ) / [ & d C H ~ ) l N[ Q for recombination was taken t o be zero.
Calculational Results Complex models adjusted to give calculated values for k ( ~ *in ) agreement with the experimental decomposition rate (k3) are presented in Table IV. The torsions in the molecule were treated as free rotors in all the calculations, since the excitation energy is quite high. In the thermal calculations it was more reasonable to treat these torsions in the molecule as vibrations: 216 cm-1 and 271 cm-1. The A factors and activation energies for the activated complex are given in Table IV. The A factors for a critical energy of 82.6 kcal/mol range from 5.5 X 10l6 t o 9.1 X 1016 sec-l, and are approximately twice as large for a critical energy of 84.6 kcal/mol. The pyrolysis of C3Hs has been studied, but not extenThe Journal of Physical Chemistry, Vol. 76, N o . 4, 1978
~ i v e l y no ; ~Arrhenius ~~ parameters have been measured. Rabinovitch and Setser calculated a thermal Arrhenius A factor at 873°K of 9.07 X 1017 sec-1 on the basis of a Gorin-type complex model.7 Leathard and Purnell estimated the decomposition A factor at S0O"K to be 2.14 X 1017 sec-I, allegedly on the basis of a radical recombination rate at 800°K of 2.0 X 10'0 1. mol-' sec-1.2a This estimate is approximately 4 times too small, since it is actually based on an A factor for recombination at 80OoK of 2 X 1O1O 1. mol-' sec-1, ;.e., the Arrhenius activation energy, E,,, for recombination was taken to be exactly zero. An activated complex consistent with these Arrhenius parameters for recombination gives negative values of the critical energy, Eo,, for recombination. Theoretically, the minimum value of E o r is zero. Tsang35 estimated the thermal Arrhenius parameters for propane pyrolysis from shocktube studies of other hydrocarbons t o be A = 2.5 X 10l6sec-l and E', = 81.3 kcal/mol at 300°K. TrotmanDickenson had earlier estimated the A factor at 600°K to be 4 X 10'7 with an activation energy of 82.0 kcal/ mol.ae The Arrhenius parameters estimated by Tsang are slightly lower than our values, while the A factor of Rabinovitch and Setser7 is an order of magnitude larger than our values. Trotman-Dickenson's A factor is an estimate, and its absolute value can only be regarded as precise to within an order of magnitude. Recombination rate calculations of CH3 CZH5 using the activated complex models derived from this work are given in Table 111. Taking an external rotor active, cases 11, 111, 111', and IV, in both the complex and the molecule decreases the calculated rate of decomposition as expected, and the resultant loosened complex gives a 50% larger recombination rate. Thynne37 determined a recombination rate of CH3 C2Hs t o be 5.0 X 101O 1. mol-' sec-'. Recombination of CH, CzHjcan be approximated from ~ A = R ~ ( ~ A A ~ B B )where ~ " , ~ log ~ ~ C A A = 10.34 for CH, -k CH3 CSHj. Thus, AB = and log i&B = 10.4 for CzHb 4.68 X 1Olo 1. mol-l se4-l. It is clear from Table 111 that complex models consistent with the decomposition rate for propane (this work) cannot give arecombination rate for CH3 CzH5 as large as 4.7 X 101O 1. mol-' sec-l. The most favorable case gives approximately oneeighth of this magnitude, while more reasonable cases give approximately one-twentieth of this value for the recombination rate. These results clearly demonstrate that no reasonable adjustments will give complexes that correlate the decomposition and recombination rates for the propane system.
+
+
+
+
+
(34) W. L. Hase, Ph.D. Dissertation, New NIexico State University, 1970. (35) W. Tsang, Int. J . Chem. Kinet., 1, 245 (1969). (36) A. F. Trotman-Dickenson, "Gas Kinetics," Butterworth, London, England, 1955. (37) J. C. J. Thynne, Trans. Faraday SOC.,58, 676 (1962). (38) H. M. Frey and R. Walsh, Chem. Rev.,69, 103 (1969).
613
KINETICS OF VIBRATIONALLY HOTPROPANE Table IV : Complex Models Description of mode
C-C stretch CH3 rock CHI rock C-C-C bend CH2, CHa rock CH3 torsion CHs torsion I,, x 1040, g cma I,, X 1040, g cm2 ( I J J E ) x 10116, ga cm5 Thermal A factors, sec-l b Eo,kcal/mol E,, kcal/molb
MoleauleC
Model I
924 cm-l 1151 903 382 747 F.R. (271) F.R. (216)
Model I1
Model I11
Model 111'
Model I V
...
...
...
...
...
228 181 77 149 F.R. F.R. 5.02 4.78 4.41
200 163 69 135 F.R. 5.02 4.78 4.41
241 196 84 163 F.R. F.R. 5.07 5.02 15.5
247 202 86 168 21.6 76"
203 162 70 135 F.R. F.R. 5.07 5.02 15.5
8 . 5 5 X 10l6
8 . 3 6 X 10'8
82.6 85.2
82.6 85.1
5.55
x
F.R..
10'6
82.6 85.1
...
*..
15.5 9.10
x
1015
1.75
x
1017
84.6 87.3
82.6 86.0
a Low-frequency torsion of complex I V was taken to be the frequency that would generate an equivalent entropy to that of a free Arrhenius parameters were calculated a t 700'K. c The moments of inertia of the propane molecule were taken t o b e ? I , = rotor. 1.11 X g cm2; I , = 9.72 X 10-3Qg cm2; I , = 3.01 X 10-88 g cm2.
The ability of complex 111 to explain the experimental decomposition rate data for activated propane isopropyl radical combination produced by H atom was tested. The average rate constant for decomposition, k,, is defined in terms of the amount of decomposition, D,and the amount of collisional stabilization,
+
s 7 n m
1.
where w is the collision frequency, and f(Evr)is a thermal energy distribution function for the associated propane and is of the form7
where the prime is a symbol for the reverse decomposition process, and Zvr* is the vibrational-rotational partition function ior the active degrees of freedom in the molecule. The structural model used for the isopropyl radical was the same as that of Rabinovitch and Setser.' By taking the minimum energy of the complex to be 9.4 kcal/mol, the average energy of the complex was computed to be 11.7 kcal/mol at 25', and the average energy of the activated propane to be 94.3 kcal/mol, which are identical with Rabinovitch and Setser's values. These calculations with complex 111 yield calculated low- and high-pressure rate constants, respectively, of k,, = 3.47 X lo5 sec-l and IC, = 5.49 X lo5 sec-l. For complexes I, 11, IV, and
111' these values would be multiplied by factors of 1.24, 1.11, 0.614, and 0.524, respectively. The ratio k,,/k,, = 1.55 is rather small, indicating a relatively narrow thermal spread for association of H isopropyl radical (-10 kcal/mol). Rabinovitch and Setser7 calculated values for k,, and k,, which are about 50 times higher than our calculations. Experimentally, Avrahami and Kebarle found k a = 6.3 X lo6 at 25°.ae Heller and Gordon40 experimentally found k a , to be 3.3 X 106 sec-1 at 55" which compares with our calculated value of 1.05 X lo6 sec-l at 85'. At 25' Falconer, et al.,41 found the decomposition rate constant e~~ to be 6.6 X 106 sec-l, and Darwent and S t e a ~ i found 3.6 X 106 sec-1, which was corrected to -1 X lo6 by Setser and R a b i n ~ v i t c h . ~With the exception of Avrahami and Kebarle's value, the agreement between these experimental results and calculations based on the complex models presented here is within experimental error and strongly supports the models. Reliable unimolecular decomposition data for propane would provide a further means of testing the complex models and activation energies used in this work. The thermal unimolecular specific rate constant, as given by RRKM theory including centrifugal distortion, was cal~ulated.~~*~~,~~ Table V gives values of kuni as a function of pressure at three different temperatures using complex 111. Calculation of the Arrhenius parameters from the high-
+
(39) M. Avrahami and P. Kebarle, Can. J . Chem., 41, 339 (1963). (40) C. A. Heller and A. 8. Gordon, J . Phys. Chem., 64, 390 (1960). (41) W. E. Falconer, B. 5. Rabinovitch, and R. J. Cvetanovic, J . Chem. Phys., 39, 40 (1963). (42) B. deB. Darwent and E. W. R. Steacie, ibid., 16, 381 (1948). (43) E. V. Waage and B. S. Rabinovitch, ibid., 52, 5581 (1970). The Journal of Physical Chemistry, Vol. 76, No.
1972
F. B. GROWCOCK, W. L. HASE,AND J. W. SIMONS
614
Table V : Thermal Unimolecular Fall-Off Calculations for Propane Decompositionazb Temp, OK
600 700
800
b
------------------
I -
1010
100
10s
10'
108
10'
Pressure, Top108
lo4
------102
101
--------------10
10-1
10-2
lo-*
10-4
Multiplier
4 . 5 4 2 . 2 8 0.78 10-16 sec-l 22.05 22.05 22.05 22.05 22.05 22.05 22.04 21.84 21.62 21.03 18.90 14.43 8 . 3 1 3 . 3 7 0 . 9 5 lo-" see -1 46.50 46.50 46.50 46.50 46.50 46.50 46.48 46.10 45.40 42.55 35.16 22.90 10.83 3 . 6 4 0 . 8 7 lo-* see-' 8.24
8.24
8.24
8.24
8.24
8.24
8.24
8.24
8.12
7.94
7.51
6.52
a The Lennard-Jones collision diameters for propane at 600,700, and 800'K were calculated to be 5.3\5, 5.24, and 5.14 d, respectively. The vibrational frequencies of propane were grouped together: 2925 (8); 1406 (9); 1005 (6); 747; 382; 271; 216.
pressure results at various temperatures gave the same activation energy as absolute rate theory calculations, and an A factor that was only 4% lower.
Conclusion It was shown previously that, by taking extremes of activated complex and radical structures and high critical energies for decomposition, it was barely possible to correlate chemical activation decomposition rates with estimated radical recombination rates for most larger alkanes.8t11.12 The correlations were based on RRKM and absolute rate theories. I n the present case of chemically activated propane decomposition, where fewer adjustments in complex and radical strucCzH6 recombination ture are possible and the CHI rate can be better estimated (from measurements of
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The Journal of Physical Chemistry, Vol. 76, N o . 4, 1079
+
+
CH3 CH3 and C2H6 CzHa), it is shown that the most favorable adjustments cannot satisfactorily correlate the decomposition and recombination rates. Clearly an important dilemma exists here which may have theoretical significance. A study of chemically activated ethane (1CH2 CH,), which is in progress, should provide some important information, since in this case there are no reasonable adjustments in complex and radical structures that could improve the correlation of decomposition and recombination rates, and the recombination rate is reliably known. An excellent discussion of some aspects of the ethane problem has appeared recently.44
+
(44) E. V. Waage and B. S. Rabinovitch, Znt. J. Chem. Kinet., 3 , 105
(1971).
