H. SHAW, J. H. MENCZEL, AND S. TOBY
4180
Kinetics of Vibrationally Excited Ethane'
by H. Shaw, J. H. Menczel, and S . Toby School of Chemistry, Rutgers University, New BTUnSWkk, New Jersey 08908 (Received October 10, 1966)
The relaxation process of vibrationally excited ethane is explained in terms of RRKM theory. The photolysis of gaseous acetone was used to produce methyl radicals at 121, 216, and 298" over a 2000-fold pressure range. The photolysis of gaseous azomethane was used to produce methyl radicals at 100, 135, 150, and 180" over a 1000-fold pressure range. Deviations from a simple Lindemann mechanism become apparent when sources of methane, other than abstraction from acetone, are taken into consideration in the acetone photolysis, and the nonscavengeable ethane contribution is included in the mechanism for the photolysis of azomethane. Fairly good agreement is obtained with previously calculated values of rate constants using RRKllI theory with the strong collision formulation.
Introduction In 1952 Marcus2 predicted the pressure dependence of the decomposition of vibrationally excited ethane. He reformulated the Rice-Ramsperger-Kassel unimolecular theory3 (RRK), which is based on a classical statistical distribution of energy in the transition state, to include quantum restrictions. This improvement, generally referred to as R R I W theory, predicts that all vibrational degrees of freedom are involved in the energy distribution process. Kistiakowsky and Robe r t and ~ ~ Dodd and Steacie5 studied the effect of pressure on methyl radical dimerization in the photolysis of acetone. They could not see significant deviations from a simple Lindemann mechanism.6 Toby and Weiss7 studied the same effect using azomethane as the source of methyl radicals. They also found fair agreement with a simple Lindemann mechanism. Recently, secondary effects in the photochemistry of acetone and of azomethane were discovered. Shaw and Tobys discussed the contribution of methane, additional to that produced in the abstraction from acetone, in the photolysis of acetone. The contribution of nonscavengeable ethane in the photolysis of azomethane was evaluated by Toby and Nim~y.~ The cornmon features of the mechanism of both acetone and nzomethane which are pertinent to this paper are
The Journal of Physical Chemistry
CH3
+ A -% CHa + radical a
2CH3
C2H,* b
C&*
+A
CzH6
+A
The additional methane step in the acetone photolysis (which is important only at low pressures) can be represented'O as
A
+ wall -% CH, + CO + CH2(wall)
(&I,)
The nonscavengeable ethane in the azomethane photolysis may be accounted for by
A 5 C2&*
+ Nz
(4~1~)
(1) P,resented a t the Physical Chemistry Division, 152nd National Meeting of the American Chemical Society, New York, N. Y., Sept 1966. (2) R. A. Marcus, J . Chem. Phys., 20, 359 (1952). (3) L. S. Kassel, "Kinetics of Homogeneous Gas Reactions," Reinhold Publishing Corp., New York, N. Y., 1932. (4) G. B. Kistiakowsky and E. K. Roberts, J . Chem. Phys., 21, 1637 (1953). (5) R. E. Dodd and E. W. R. Steacie, Proc. Roy. SOC.(London), A223,283 (1954). (6) F. A. Lindemann, Trans. Faraday Soc., 17, 598 (1922). (7) 5. Toby and B. H. Weiss, J . Phvs. Chem.. 68, 2492 (1964). (8) H. Shaw and S. Toby, submitted for publication. (9) 5. Toby and J. Nimoy, J . Phys. Chem., 70, 867 (1966). (10) Note that &Isis denoted by X in ref 8.
4181
KINETICSOF VIBRATIONALLY EXCITED ETHANE
A common rate law can be derived from this mechanism
160
1
0
L
120
yl+-- kb
k3m
kc[A]
OBI.]
RE
40
(1)
where RM is the average rate of production of methane, REis the average rate of production of ethane, and [A] is the concentration of either acetone or azomethane. Equation 1 can be used for acetone by letting 4~ equal zero and can be used for azomethane by letting +c be zero. Equation 1 is formally correct whether we assume a simple Lindemann mechanism or the more sophisticated RRKM theory. In the latter case k b is not an equilibrium rate constant. That is, the population of energy states associated with vibrationally excited ethane is affected by reaction conditions, and k b is thus a function of pressure. A Lindemann-Hinshelwood plot can be used to distinguish between RRKRI theory and Lindemann theory." A plot of ac2 vs. [A]-' is a straight line when k b is an equilibrium rate constant while a saturation-type curve is predicted for k b based on RRKN theory. This work describes quantitative tests of the RRKAI theory for vibrationally excited ethane .
Experimental Section The experimental details for acetone photolysis are described in ref 8. A high-pressure mercury arc (Osram HBO-75W) was employed, the output being filtered to give mainly light a t 3130 A. Conventional high-vacuum techniques were used to purify acetone and separate product gases from unreacted acetone and low volatility products. The more volatile products (CO, CH,, and C2He)were analyzed chromatographically using a silica gel column a t 25". The experiments using azomethane were carried out on another vacuum system described in ref 9. Most experiments were done in the 3660-A region (Corning 7-37 filter), but a few were carried out using 3130-A light. A series of experiments was performed with a beam of light passing through the center of the photolysis cell only, using a suitable mask, to test for heterogeneous effects. The light-beam diameter was approximately 2.5 cm and the cell diameter was 5.9 cm. Results Experiments were done a t 121, 216, and 298" in the pressure range of 0.1-220 torr with acetone. In Figure 1 we show the Lindemann-Hinshelwood plot for this work. There is clear evidence that on applying the
--0
298O
0
78
a'
216O
0 0
0.02
0.01
"
0
' 4
'
*
8 IA1-1
"
"
"
'
.
12 16 20 24 X 10-4,1. mole-'.
"
28
"
32
Figure 1. Lindemann-Hinshelwood plot from photolysis of acetone: ae2 us. [A] -1.
correction for additional methane a Lindemann mechanism no longer explains the data. Similarly in Figure 2 we have plotted the data obtained in the photolysis of azomethane a t 100, 135, 150, and 180" for the range 0.3-200 torr. In this case there is good consistency with the acetone results. Other published data for acetone5 were treated in a similar fashion and the general shapes of the curves were as in Figure 1. It is interesting that the inclusion of the additional methane-producing step in the acetone photolysis a t low pressures removed the apparent discrepancy between the low-pressure photolysis of acetone and of azomethane, noted earlier.' Equation 1 can be rewritten making use of the Arrhenius plot for IC22/ka, for acetone8 in order to obtain an expression for the apparent decomposition rate constant k b
where D / S is the ratio of dissociation to stabilization for vibrationally excited ethane and w is the collision frequency. Equation 2 can also be applied to azomethane using the data reported by Toby and N i m ~ y . ~ The value of kb is proportional to the assumed collision diameter, and we have taken 5.3 A as the value for the ~~
~
(11) 5. W. Benson, "Foundations of Chemical Kinetics," McGrawHill Book Co., Inc., New York, N. Y., 1960.
Volume 71,Number 19 December 1967
4182
H. SHAW, J. H. MENCZEL, AND S. TOBY
0
0
f 120
150"
i
0
0
0 C
1
I
I
I
I1
2
4
0
0.1
1.0 Pressure, torr.
10
100
m
Figure 3. Test of R R K M theory for kb. Calculated'' values for 300" (dashed line) and limiting values (arrows) compared with data from acetone photolysis: 0, 298"; A, 216'; 0, 121'.
1 l10os O ~ l * o o
[Al-l X l O - 4 , 1 . mole-'.
Figure 2. Lindemann-Hinshelwood plot from photolysis of axomethane: cyc2 us. [A] -1; 0, 3660 A; 0,more monochromatic 3660 A (see text); A, 3130 A.
complex for both acetone and azomethane with vibrationally excited ethane. Setser and Rabinovitch12 have calculated the variation of S/D as a function of pressure using RRKM theory. They also calculated the limiting values for the rate constant k b at infinite pressure and at zero pressure. In Figure 3 we show our values of k b from experiments with acetone. These are compared with Setser Pnd Rabinovitch's calculated values at 300" and their calculated limiting rate constants. A similar plot for the azomethane experiments is shown in Figure 4. The temperature range here was much smaller and only two, representative curves are shown. In order to check on possible wavelength effects several of the azomethane runs at 150" were carried out with a 3130-A filter and also with a Corning 7-37 filter supplemented by a solution filter13 to give more monochromatic 3660-A radiation. No significant differences were seen as shown in Figure 2. In Figure 5 we show the effect of passing light through the center of the photolysis cell. The reaction volume was taken as the cell volume, light beam, and the effecThe Journal of Physical Chemistry
I
101
1
/C135O 0
0.1
1
10
100
m
Presaure, torr.
Figure 4. Test of R R K M theory for kb. Calculated" limiting values (arrows) compared with data from azomethane photolysis: 0, 180'; 0,135'. The calculated and experimental points at 180" have been displaced upward by a factor of 10 for clarity.
tive diffusion volume for methyl radicals,I4 and the function RMRE-"'[A]-'is plotted against azomethane pressure.
Discussion The development of unimolecular rate theory has evolved from Lindemann's original papers to RRK the01-y.~ The latter, although still useful for many systems, has been shown to be quite inadequate for the (12) D. W. Setser and B. S. Rabinovitch, J . Chem. Phys., 40, 2427 (1964). I t should be noted that their ks corresponds to our kb. (13) J. G. Calved and J. N. Pitts, Jr., "Photochemistry," John Wiley and Sons, Inc., New York, N. Y., 1966. (14) S. Toby, J . Phys. Chem., 64, 1575 (1960).
KINETICS OF VIBRATIONALLY EXCITED ETHANE
- \o
\ D '
a 0.6
4183
1.
\
I
I
6 10 Pressure, torr.
1 60
100
Figure 5. Effect of reduced light beam in azomethane photolysis at 150': RM/RE'/'[A]us. [A] ; reaction volume taken m cell volume, 0;light beam volume, 0 ; total radical diffusion volume, A ; unreduced light beam, 0.
ethane decomposition by Trenwith16 and by Benson and Kaugen.l6 The calculational difficulties in RRKM theory are more than compensated for by use of all vibrational degrees of freedom of the activated complex, rather than an empirical parameter. A thorough treatment of RRKM theory has been given by Rabinovitch and Setser." Inherent in their treatment is the strong collision formulation. l* It takes one collision of a complex molecule like acetone or azomethane to remove all of the excess vibrational energy. The average excess energy of vibrationally excited ethane is equivalent to the difference in potential energy between ethane and two methyl radicals a t the temperature of interest. The average excess energy is therefore approximately (8/2)RT. The energies removed per collision are therefore of the order of 4 kcal/ mole. The agreement between the calculated and observed values of kw shown in Figures 3 and 4 is very good. The agreement for k b m is only fair. The prediction of both low- and high-pressure limits is, however, well substantiated by experiment. The same effect is seen in experimental and theoretical values obtained by Placzek, Rabinovitch, and Dorerlg in studies of the decomposition of excited butyl radicals. The ratio k b m / k b O is a function of the distribution of energy for the excited ethane molecules. Our data yield values of kbm/kbO
of -45. This agrees with the calculated1' ratio of 39 a t 600" but not the 300" value of 19. The saturation-type curves of Figures 1 and 2 were also checked to determine whether heterogeneous effects could account for this deviation from Lindemann theory. Using simple collision theory, the rate of homogeneous stabilization of vibrationally excited ethane is equal to the rate of heterogeneous stabilization a t a pressure of 0.01 torr. Kennedy and Pritchard20 showed that this approximately predicted the inception of significant heterogeneous effects in the isomerization of cyclopropane. Benson and Spokes21also found that wall effects predominated a t pressures below 0.01 torr. Since the pressures used in this work were much greater than this value, heterogeneous effects are unlikely. Furthermore, if k b were independent of pressure and the cell wall were 100% efficient21 in deactivating vibrationally excited ethane, then calculation shows that lo4homogeneous collisions would be required for deactivation. We therefore discount heterogeneous effects. Figure 5 shows that in reduced-beam photolysis a t high pressures the curve obtained by assuming the reaction volume is the light beam volume (squares) approaches the curve for unmasked runs (filled circles). Thus radical diffusion outside the reduced beam is negligible above -100 torr. At the lowest pressures the curve assuming the reaction volume is the cell volume (open circles) merges with the curve for unmasked runs. Thus a t pressures below about 4 torr, methyl radicals can easily diffuse t o reach the cell wall. This, however, does not appear to introduce a significant heterogeneous component into the system.
Acknowledgment. We are very grateful to the National Science Foundation for the grant which supported this work. H. s. acknowledges with thanks a fellowship from the Allied Chemical Co. (15) A. B.Trenwith, Trans.Faraday SOC, 6 2 , 1538 (1966). (16) S.W.Benson and G. Haugen, J. Phys. Chem., 69,3898 (1965). (17) B . 8. Rabinovitch and D. W. Setser, Adcan. Photochem., 3, 1 (1964). (18) G. H. Kohlmaier and B. S. Rabinovitch, J . Chem. Phys., 3 8 , 1692,1709 (1963). (19) D. W. Placzek, B. S. Rabinovitch, and F. H. Dorer, ibid., 44,279(1966). (20) A. D. Kennedy and H. 0. Pritchard, J. Phys. Chem., 6 7 , 161 (1963). (21) S. W. Benson and G . N. Spokes, J. A m . Chem. SOC.,89, 2525 (1967).
Volume 71, Number 13 December 1967
