J. Phys. Chem. 1983, 87,3694-3700
3694
Multistep Collisional Deactivation of Chemically Activated Dimethylcyclopropane I. Szll6gyl, L. Zalotal, T. B6rces; and F. MBrla Central Research Institute for Chemistry, Hungarian Academy of Sciences, H- 1025 Budapest, Hungary (Received: October 1, 1982; In Final Form: May 2, 1983)
The decomposition of chemically activated cis- and trans-dimethylcyclopropane formed by the photolysis of ketene (at 334 nm) or diazomethane (at 436 and 366 nm) in the presence of excess cis-butene-2and small amounts of oxygen was studied. Apparent fit-order decomposition rate coefficients for the chemicallyactivated molecules were measured and found to be pressure dependent over the extended pressure range from 0.1 to 40 kPa. The turnup observable at low pressure demonstrates the occurrence of multistep deactivation of the chemically activated molecules, while the pressure dependence at high pressure is indicative of a wide initial vibrational energy distribution of cis-dimethylcyclopropane. The theoretical approach used RRKM theory to calculate the energy-dependent decomposition rate coefficientsand assumed a stepladder model to describe collisional transition probabilities. The initial energy distributions of cis-dimethylcyclopropane were approximated by shifted Gaussian-type functions. The experimental results could be fit over the entire pressure range investigated with a theoretical model utilizing a collisional deactivation step size of about 14-22 kJ mol-' and initial energy distributions whose widths increased with increasing energy of the chemically activated molecules. It has been concluded that the wide distributions obtained in the diazomethane photolysis systems were mainly due to the dispersion originating from energy partitioning in the photolytic event producing singlet methylene.
Introduction Chemical activation has often been used to obtain species with nonequilibrium amounts of internal energy considerably in excess of the thermal energies. A common procedure is to produce chemically activated molecules by addition or insertion reactions of CH2(lA1). Partitioning of the released energy in the photolytic event yielding singlet methylene and partial relaxation of vibrational excitation of CH2(lAl) via unreactive collisions determine the energy distribution of the chemically activated molecules. Therefore, knowledge of the distribution of excess energy of CH2(lA1)formed in the widely used methylene sources is of prime importance. In this work we study the decomposition of chemically activated dimethylcyclopropane molecules formed with considerably different initial nonfixed energies in the reaction of singlet methylene and cis-butene-2. In previous studies of dimethylcyclopropane decomposition, experimental results were interpreted either in terms of singlestep collision ~tabilization'-~ of the chemically activated molecules or by utilizing multistep collisional deactivation models4s5with an average deactivation step size of about 50 kJ mol-'. The kinetics of vibrational energy relaxation of activated dimethylcyclopropane is being reinvestigated in this work with particular attention paid to the consequences that different initial energy distributions of the chemically activated molecules have on the rates of decomposition and stabilization. Experimental Section
Singlet methylene was formed in the presence of cisbutene-2 (CB2), 02,and the internal standard n-butane (NB) by the photolysis of ketene at 334 nm and by that of diazomethane at 436 and 366 nm. Reaction mixture (1) J. W. Simons and B. S. Rabinovitch, J . Phys. Chem., 68, 1322 (1964). (2) J. W. Simons and G. W. Taylor, J . Phys. Chem., 73, 1274 (1969). (3) W. L. Hase, R. J. Phillips, and J. W. Simons, Chem. Phys. Lett., 12, 161 (1971). ( 4 ) D. W. Setser, B. S. Rabinovitch, and J. W. Simons, J . Chem. Phys., 40, 1751 (1964). (5) J. D. Rynbrandt and B. S. Rabinovitch, J . Phys. Chem., 74, 1679 (1970).
0022-3654/83/2087-3694$0 1.50/0
compositions were CB2:NB:02:(methylene source) = 3.8:l:l:l and the pressure was varied from 0.1 to 40 kPa. Sample preparation and product handling were carried out on a conventional all-glass high-vacuum system employing greaseless stopcocks. Pressure measurements were made with an MKS Baratron (Type 170) pressure meter. Photolyses were performed at room temperature in well seasoned cyclindrical reactors equipped with quartz (Ultrasil) windows on both ends. A 83-cm3quartz reactor (5.0 cm X 4.6 cm i.d.) was used at pressures greater than 0.4 kP, and a 665-cm3 Pyrex reactor (40.0 cm X 4.6 cm i.d.) was employed at lower pressures. The photolysis systems consisted of a Philips HPK 125-W high-pressure mercury arc, lenses, filters, and the reactor. For 334-nm light a combinationloof NiSO, and naphthalene solutions and UG 11 glass filter was used while for 436-nm light a systemlo consiting of CuSO, and sodium nitrite solutions was applied. The 366-nm light was isolated by using 4-mm UG 11and 0.5" GG 18 glass filters (Zeiss, Jena). The intensity distributions of the above lamp-filter combinations were measured photoelectrically with a Zeiss monochromator and IP28 photomultiplier. Convoluting the measured radiant intensity distribution with the wavelength-dependent absorption coefficient of the methylene source and the quantum yield for singlet methylene formation, we found the distribution of the effective photolysis light: flight(X) €(A) @(A) dX(dE/dX). Literature data were used for the extinction coefficients of ketene6 and diazomethane.' In case of ketene photolysis, the quantum yield of singlet methylene formation was obtained by multiplying the yield of ketene decomposition8with the fraction of singlet methylene formation: 4('CHP)/[4(lCH2)+ 4(3CH,)]. On the other hand, in the narrow wavelength ranges occurring in the diazomethane photolyses, the quantum yields of singlet methylene formation were assumed to be constant. In this way, the (6) J. W. Rabalais, J. M. McDonald, V. Scherr, and S. P. McGlynn, Chem. Rev., 71, 73 (1971). (7) R. K. Brinton and D. H. Volman, J . Chem. Phys., 19,1394 (1951). (8) B. T. Conelly and G. B. Porter, Can. J. Chem., 36, 1640 (1958). (9) P. M. Kelley and W. L. Hase, Chem. Phys. Lett., 35, 37 (1975).
0 1983 American Chemical Society
Multistep Collisional Deactivation of Dimethylcyclopropane
The Journal of Physical Chemistry, Vol. 87, No. 19, 1983 3695
effective light distributions occurring in the ketene (K) and diazomethane (DM) photolysis experiments were determined. The distributions can be characterized by the following average energies, E, and standard deviations, sd, both expressed in kJ units. K(334 nm): E = 360.2, sd = 9.9; DM(436 nm): E = 274.3, sd = 0.5; DM(366 nm): E = 327.1, sd = 0.5. Following photolysis, a gas sample from the reaction mixture was analyzed on a H P 5750 type gas chromatograph equipped with FID. A 30-m squalane SCOT column at 280 K was used for routine analyses. Relative peak areas were determined with a H P 3370 type integrator. Calibration factors were assumed to be the same for all C5 products. Ketene was prepared by the pyrolysis of acetic anhydride" and was purified by repeated trap-to-trap distillation from 195 to 77 K. Diazomethane was prepared in vacuo by allowing N-methyl-N-nitroso-p-toluenesulfonamide to react with potassium hydroxide dissolved in ethylene glycol.12 After trap-to-trap distillation, the diazomethane was stored at 77 K for subsequent use.
Results Product Formation. As a result of the reactions occurring between singlet methylene and CB2 various reaction products are formed. Addition of CH2('Al) yields cis-dimethylcyclopropane (CDMC) and by subsequent isomerization trans-dimethylcyclopropane (TDMC), while insertion into the C-H bonds gives 2-methylbutene-2 (2MB2) and cis-pentene-2 (CP2). Pentenes are formed also by decomposition of the chemically activated dimethylcyclopropane molecules (see reactions 9 and l l ) . cis-Pentene-2 (CP2) or trans-pentene-2 (TP2)are formed if dimethylcyclopropane ring opening occurs by splitting of the bond between the two methyl-substituted C atoms. On the other hand, 2-methyl-butehg-1 (2MB1) or 2methyl-butene-2 (2MB2) are obtained if the ring is opened between an unsubstituted and a methyl-substituted C atom. Insertion of CH2('A1)into the C-H bonds of NB gives isopentane (IP) and n-pentane (NP). CH2XY + hv 'CH2* + XY (1)
---
- + + - - + -- - ----
TH2* 'CH2*
TH2*
+M
NB
'CH2
(2)
3CH2 M
(3)
IP
(4)
IP*
NP* NP 'CH2* CB2 P*
CDMC* CDMC* e TDMC* CDMC* P* -CDMC TDMC* P* -TDMC P* free radicals --+ -.+ - p
(5) (6) (7) (8, -8)
(9) (10) (11) (12) (13)
(14) In the above reaction scheme CHzXY is ketene and dia(IO) J. G. Calvert and J. N. Pitta, Jr., 'Photochemistry", Wiley, New York. 1966.DD 733-7. (11) H. M.'Frey and G. J. Kennedy, J. Chem. SOC.,Faraday Trans. I , 73, 164 (1977). (12) R. J. Wolf and W. L. Hase, J. Phys. Chem., 82, 1850 (1978).
1
5
i
CDMC
Flgure 1. The dependence of the relative product yields on overall pressure for the 334-nm ketene photolysis system. (The meaning of the symbols Is given in the text.)
---
zomethane, respectively, P stands for all pentene isomers, the symbol designates (collisional) stepwise deactivation, and the asterisk indicates excess vibrational energy. The scheme explains product formation as well as the change of the relative product yields with overall pressure, which is demonstrated for the 334-nm ketene photolysis system in Figure 1. Average Rate Coefficient. Collisional deactivations are expected to be multistep procesess as indicated in the reaction scheme; however, presentation and discussion of the experimental results is made more convenient by the introduction of a simpler approach. When a one-step deactivation model is used, an apparent average rate coefficient can be defined for the decomposition (structural isomerization) of the dimethylcyclopropanes RD ( k , ) = w(15) RS where w is the collision frequency, RD = RCD+ RTDdesignates the overall rate of decompositionfrom CDMC and TDMC into the pentene-2 isomers and the methyl-butenes, while RS = Rcs + RTSis the sum of the rates of formation of stabilized CDMC and TDMC. In the calculation of (k,) according to eq 15, the ratio of the rates of decomposition and stabilization at pressure P was obtained from dimethylcyclopropaneconcentrations (measured relative to that for the internal standard, which is not indicated here): (16) RD - = - - RD + RS 1 = ([CDMCI + [TDMCI), ([CDMC] + [TDMC]), RS RS Derivation of reliable kinetic data from analytical results, especially at the high pressure end of the pressure range, requires data evaluation to be carried out carefully. Determination of the RDIRSratio from stabilization product measurements is based on mass balance considerations. RD is obtained from the difference ([CDMC] + [TDMC]), - ([CDMC] + [TDMC])p which becomes small at high pressures and this results in some scatter of the calculated first-order rate coefficients. In addition, the limiting value ([CDMC] + [TDMC]), cannot be read simply from the ([CDMC] + [TDMC]) vs. P graph, since the extrapolated value appears to depend on the energy of the chemically activated molecules. If the results are analyzed in the form of reciprocal plots (i.e., ([CDMC] + [TDMC])-l vs. F ' ) , S-shaped curves are obtained. The S-shaped character is definitely evident only in the diazomethane photolysis systems; the curvature at high pressure appears to increase with the energy of the activated molecules. The limiting
3696
Szillgyi et al.
The Journal of Physical Chemistry, Vol. 87, No. 19, 1983 100
TABLE I: Lennard-Jones Parametersn and Effective Collision Diameters
a
Lennard-Jones parameters molecule ( e / h ) / K o / n m DMC CH,CO CH,N, NB CB2 0 2
320b 33OC 380d 325 259 113
0.54' 0.4V 0.447d 0.523 0.551 0.3433
A + M DMC + DMC; DMCT DMC + DMC+
sAMlnm
CH,CO CH,N, NB CB2
0,
0.644 0.648 0.682 0.682 0.502
!
--X-n
Data were taken from ref 13 and 14 except where indiEstimated from parameters for n-CsH,2and cated. Estimated Erom data f o r C,H, and ethylcyclopropane. Estimated from t h e parameters for methyl isocyanide. methyl isocyanide.
05
10
15 lo7/,
20
25
30
!
--.---_______
I 01
0001
1
I
I
0 01
01
1
IO
RSIRD
Flgure 3. (a) The 436-nm dlazomethane photolysis data, R D I R Svs. w-' plot: 0, experimental results; -, calculated curve, initial CDMC' distribution: shifted Gaussian function with ( E )= 492.6 kJ mol-' and u = 51.9 kJ mol-', ( A € ) = 14.6 kJ mol-'; -X-, calculated curve, initial CDMC' distribution: shifted Oaussian function with (E) = 504.2 kJ mol-' and u = 52.5 kJ mol-', ( A € ) = 25.1 kJ mol-'; ---, calculated curve, initial CDMC' distribution: 6 function at E = 475.1 kJ mol-', (A€) = 33.5 kJ mol-'; calculated curve, initial CDMC' distribution: 6 function at E = 455.2 kJ mor', (A€)= 14.6 kJ mol-'. (b) The 436-nm diazomethane photolysis data, (k,) vs. R S I R Dplot. Designations are given in (a).
1
12t
3'
3 C'
01
L
,
i
'0
io0
RStR3
Flgure 2. (a) The 334-nm ketene photolysis data, RDIRSvs. w-' plot: 0, experimental resub, -, calculated curve, lnithl CDMC' distribution: shifted Gaussian function with ( E ) = 439.2 kJ mol-' and u = 8.5 kJ mol-', ( A € ) = 14.6 kJ mol-'; -X-, calculated curve, initial CDMC' distribution: shifted Gaussian function with ( E ) = 448.3 kJ mol-' and u = 8.5 kJ mor', (A€)= 25.1 kJ mor'; ---, calculated curve, initial CDMC' distribution: 6 function at E = 444.8 kJ mol-', ( A € ) = 20.9 kJ mol-'. (b) The 334-nm ketene photolysis data, (k,) vs. RSIRDplot. Designations are given in (a).
value used for ([CDMC] + [TDMC]), in the calculation of the average first-order rate coefficient was derived from the reciprocal plot as the intercept of the tangent drawn at the inflection point. The effective collision diameter s, used in the calculation , ' ~multiof the collision frequency w, was ~ b t a i n e d ' ~by plying the Lennard-Jones hard-spheres diameter u by the square root of the collision integral Q2,2(T*). LennardJones parameters summarized in Table I were adopted. (13) J. 0. Hirschfelder, C. F. Curtiss, and R. B. Bird, 'Molecular Theory of Gases and Liquids", Wiley, New York, 1954. (14) 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).
Collision efficiency was taken to be 1for all colliders except O2 for which a value of 0.25 was assigned. Experimental Results. Experimental results are presented as points in Figures 2-4 for 334-nm ketene and 436and 366-nm diazomethanephotolysis systems, respectively. Data are given as plots of RD/RSvs. w-' in Figures 2a-4a, while an alternate method, eliminating the dependence of the results on the assumed collision diameters, is used in Figures 2b-4b. If strong collision hypothesis holds, the apparent rate coefficient (12,) would be constant and independent of the overall pressure provided that the chemically activated molecules can be treated as approximately monoenergetic species. The results show that this is not the case; the overall rate coefficients are pressure dependent more or less in the whole pressure range investigated. The turnup observable at low pressure (at greater w-l values in Figures 2a-4a or at smaller R S / R Dvalues in Figures 2b-4b) can be accepted as a proof that collisional deactivation of the chemically activated CDMC* and TDMC* molecules occurs by multistep processes. A curvature is apparent also at high pressure (at smaller u-' values in Figures 2a-4a or at greater R S / R Dvalues in Figures 2b-4b), at least in case of the diazomethane photolysis results. Different explanations have to be considered f o r this increase in the rate with increasing pressure. Rabinovitch and co-workers proved that a pressure dependence of (k,) due to the failure of intramolecular energy relaxation may become detectable under favorable
Multistep Collisional Deactivation of Dimethylcyclopropane 100
The Journal of Physical Chemistry, Vol. 87, No. 19, 1983 3697 a
I
i
60
6 4
"
001
01
IO
1
R
~
~
R
~
Flgure 4. (a) The 366-nm diazomethane photolysis data, RDIRSvs. o-'plot: 0,experimental results; -, calculated curve, initial CDMC' distribution: shifted Gaussian function with ( E ) = 504.1 kJ mol-' and 0 = 62.7 kJ mol-', ( A € ) = 14.6 kJ mol-'; ---, calculated curve, initial CDMC' distribution: 6 function at E = 477.0 kJ mol-', (A€) = 33.5 kJ mol-'. (b) The 366-nm diazomethane photolysis data, ( k , ) vs. R S I R Dplot. Designations are given in (a).
circumstances. Among the reactions of substances which are similar in structure and complexity to DMC, chemically activated hexafluoromethylcyclopropane-dzdecomposition was found15to show nonrandomized energy effects above about 90 kPa. The fast chemical reaction (E, N 200 kJ mol-') and the moderately slow internal energy flow (A N 6 X 10" s-'), which are characteristic for this system,15can explain the failure of the internal energy relaxation. However, in the reaction of chemically activated methylcyclopropane16at total pressure below 300 kPa and in the decomposition of activated dimethylcy~lobutane'~ up to 1500 kPa, where chemical reaction is much slower (E, 2 250 kJ mol-') and relaxation occurs a t a very high rate (A 5 X 10l2s-l), internal energy is essentially randomized prior to decomposition. Similar behavior is expected for CDMC and TDMC decomposition, thus nonrandomized energy effects are certainly not detectable at the moderately low pressure applied in this study. This conclusion is in full agreement with the theoretical predictions of B u n k e F made on the basis of the results of Monte Carlo calculations. The pressure dependence of the apparent fit-order rate coefficient of DMC* decomposition is rather similar to the effect observed by Richardson and S i m o n ~ in l ~the ~~~ (15) J. F. Meagher, K. J. Chao, J. R. Barker, and B. S. Rabinovitch, J. Phys. Chem., 78, 2535 (1974); B. S. Rabinovitch, J. F. Meagher, K. J. Chao, and J. R. Barker, J . Chem. Phys., 60, 2932 (1974). (16) J. N. Butler and G. B. Kistiakowsky, J. Am. Chem. SOC.,82, 759 (1960). (17) Fa-Mei Wang and B. S. Rabinovitch, Can. J . Chem., 54, 943 (1976). (18) Don L. Bunker, J. Chem. Phys., 40, 1946 (1964).
photolysis of diazomethane in the presence of cyclobutane as well as by Wolf and Hase12 in the study of chemically activated C3H8* and n-C4H10*formed by the 214-nm diazomethane photolysis in the presence of C2H, and C3H8, respectively. In these studies the pressure dependence was assumed to be the result of the wide initial energy distribution of the chemically activated molecules. In the following discussion we also explain the high-pressure turnup of the rate coefficient by the dispersion of the energy of chemically activated CDMC* a t the time of formation. Theoretical Model. The rate of dimethylcyclopropane decomposition as a function of overall pressure was studied theoretically by fitting initial energy distributions of CDMC* to the experimental plots of ( k a ) vs. R S / R Dand R D / R Svs. o-'. The theoretical approach used RRKM theory to calculate the microcanonicalrate coefficient k ( E ) for each energy level of CDMC and TDMC, and assumed a stepladder model to describe collisional transition probabilities. Initial CDMC* Distribution. The energy distribution of CDMC* in the K(334 nm) system was obtained by the application of the principle of microscopic reversibility to the reverse of the addition of singlet methylene to the double bond of CB2, as well as by "shifted" Gaussian type functions. For both DM systems, the vibrational energy distribution of the CDMC* a t the time of formation was approximated by "shifted" Gaussian type functions. In a few calculations the vibrational energy of CDMC* was represented by a 6 function in order to demonstrate the effect of broadening of the initial CDMC* energy distribution on the estimated average energy, ( E ) ,of chemically activated species, on the collisional deactivation step size, and on the calculated pressure dependence of the average decomposition rate coefficient, (ha). Transport Equations. The system of equations used to obtain steady-state populations and theoretical rates for decomposition and stabilization is given in terms of matrix formalism as
(a),
[w(I-PC) + IFT [o(I-PT)
+ IFD]NC - KTCP= R°Fc
+ IFc + I(rD]iV- KCTP= 0
(17)
KCTand PDare diagonal matrices with microscopic unimolecular rate coefficient elements for geometric isomerization and decomposition of CDMC, respectively, furthermore, KTc and FD are the same type of matrices for TDMC reactions. The rest of the symbols have the usual meaning.21 The PC and PTtransition probability matrices were constructed by assuming a stepladder model and by using a grain size of 185 cm-'. Rate Coefficients and Frequency Models. The microscopic unimolecular rate coefficients as a function of the internal energy were obtained from the RRKM expression.21 The sum of state and the density were calculated by a direct count method.22 For the sake of comparison we have adopted for CDMC and TDMC the frequency models used in a similar study by Rynbrandt and Rabin ~ v i t c hwhich ,~ agree well with the very recent data of During et aLZ3 The activated complex frequencies for cis (19) T. H. Richardson and J. W. Simons, Chem. Phys. Lett., 41,168 (1976). (20) T. H. Richardson and J. W. Simons, J. Am. Chem. Soc., 100,1062 (1978). (21) P. J. Robinson and K. A. Holbrook, "Unimolecular Reactions", Wiley-Interscience, London, 1972. (22) S. E. Stein and B. S. Rabinovitch, J . Chem. Phys., 58,2438 (1973). (23) J. D. During, A. B. Nease, and F. Milani-Nejad, J . Mol. Struct., 72, 57 (1981).
3698
The Journal of Physical Chemistry, Vol. 87, No. 19, 1983
Sziligyi et al.
TABLE 11: Thermochemical Data (Units: kJ mol-') species
AHf00
re f
Eth
species
AHfOO
ref
CH,CO CHJZ
-44.8 301 f 21 -113.8 0
a b
9.3 9.6 6.2 6.2
CHz( ' A , 1
4 2 6 . 0 % 6.0 14.6 t 4.2 19.7 t 6 . 5 1 5 . 5 I6 . 5
d
co NZ
C
CB2 CDMC TDMC
Eth
7.4 14.1 16.1 16.2
e
f g
Reference 28. ReferReference 25. Derived from a theoretical valuez6 and estimated lower and upper limits." ence 11, 29, and 3 0 . ' Reference 31. f Estimated by Simons and Taylor' using known heats of formation for cyclic compounds. Estimation of AHfo(CDMC) - AHf"(TDMC) = 4.2 from group additivity rules and by using a H f 0 ( C D M C )= 19.7.
trans isomerization and decomposition of the cyclopropanes were also taken from the work of Rynbrandt and R a b i n ~ v i t c h ;these ~ models were fit to the excellent thermal kinetic data of Flowers and F r e ~ .Finally, ~ ~ for the complex of CDMC CH2('Al) + CB2, a ring mode was taken as the reaction coordinate and two CH2 frequencies were lowered by about a factor of 2. The resulting grouped frequencies of the activated complex are (cm-') 3002 (lo), 1381 (9), 994 (9), 650 (21, 414 (4), 250 (2), free rotor (2). The critical energy Eowas estimated to be 426 kJ mol-' and (Z+ABc/ZABc)'/2 = 1.2 was assumed. Computational Results. Heats of formation presented in Table I1 were utilized in calculations of thermodynamic properties. With the exception of CH2N2,the heats of formation are known quite accurately. The heat of formation of 'CH, was the subject of longlasting controversy. After all, e ~ p e r i m e n t a l and ~ ' ~theoreti~alll*~~ ~~~~ values for AHom('CH2)seem to converge to 420-430 kJ mol-'. The thermochemicaldata given in Table I1 together with an assumed activation energy, E,,,(7) = 4.2 kJ mol-', for methylene addition to the double bond of CB2 give Emin = 425.9 kJ mol-' for the minimum possible nonfmed energy of CDMC* at the time of formation. The thermochemical data supply also lower and upper bounds for the average energy of reacting CDMC which the assumed CDMC distribution has to be consistent with. Calculated results are compared in Figures 2-4 with the experimental data. The functions used to represent the CDMC* distributions at the time of formation were shifted Gaussians and 6 functions. (Calculations for the K(334 nm) system with an energy distribution obtained by the application of the principle of detailed balance gave results similar to those based on Gaussian type functions with u = 2.) The Gaussian parameters (expressed in kJ mol-' units) were Em,= 439.6 and s = 10.2 as well as E, = 451.0 and s = 8.7 for the K(334 nm) system, E,, = 405.5 and s = 90.9 as well as E,, = 474.9 and s = 73.0 for the DM(436 nm) system, and finally E,, = 358.9 and s = 125.6 for the DM(366 nm) photolysis system. The initial CDMC* en-
-
(24)M. C. Flowers and H. M. Frey, Proc. Roy. SOC.London, Ser. A , 257, 122 (1960);260,424 (1961).
(25)R. L. Nuttal, A. H. Laufer, and M. V. Kilday, J. Chem. Thermodyn., 3, 167 (1971). (26)J. Lievin and G. Verhaegen, Theor. Chim. Acta, 42, 47 (1976). (27)J. C. Hassler and D. W. Setser, J . Am. Chem. Soc., 87, 3793 (1965). (28)D.D.Wagmen, W. H. Evans, I. Halow, V. B. Parker, S. M. Bailey, and R. H. Schumm, Natl. Bur. Stand. U.S.A., Tech. Note, No. 270-1 (1965). (29)R. K. Lengel and R. N. b e , J. Am. Chem. Soc., 100,7495(1978); D.Feldmann, K.Meier, H. Zacharias, and K. H.Welne, Chem. Phvs. Lett., 59, 171 (1978). (30)P. Saxe, H. F. Schaefer 111, and N. C. Handy, J. Phys. Chem., 85, 745 (1981):B. 0.Rooa and P. M. Sieebahn. J. Am. Chem. Soc.. 99.7716 (1977);L.B.Harding and W. A. Goadard 111, J. Chem. Phys.,' 67; 1777 (1977). (31)"Selected Values of Properties of Hydrocarbons and Related Compounds", American Petroleum Institute Project 44, Chemical Thermodynamic Properties Center, Texas A and M University, College Station, TX. (32)J. W. Simona and R. Curry, Chem. Phys. Lett., 38, 171 (1976).
TABLE 111: Average Initial CDMC* Energy ( E )and Energy Dispersion u , as well as Deactivation Step Size ( A E ) (Units: kJ mol-') distribution function
system K(334 n m )
(E)
Gaussian Gaussian detailed balance 6
DM(436 n m )
Gaussian Gaussian 6 6
DM(366 n m )
Gaussian 6
439.2 448.3 437.5 444.8 492.6 504.2 475.1 455.2 504.1 477.0
u
(AE)
8.5 8.5 8.3
14.6 25.1 14.3 20.9 14.6 25.1 33.5 14.6 14.6 33.5
51.9 52.5 62.7
ergy distributions used in the calculations were characterized by the average energy
(E) = CE f(E) dE
(18)
E,,
and energy dispersion u = ( C E2f(E) dE - [ C E f(E) dE]2)1/2 (19) E,"
Em
where E is the nonfixed energy, f(E) dE designates the energy distribution function of the initially formed CDMC* molecules, and summation is made from Emin. These characteristics together with the collisional deactivation step sizes are indicated in the legends of the figures and are summarized in Table 111. Initial CDMC* Energy Distribution and Deactivation Step Size. Results presented in the figures show that excellent fit of the low-pressure experimental turnup is obtained with a collisional deactivation step size of 14-22 kJ mol-' in computations where sufficiently wide initial CDMC* energy distributions, required by the high-pressure results, are used. Attempted fits with appropriate broad CDMC* energy distributions and larger ( AE)values suggest that step sizes above 25 kJ mol-' are incompatible with the experimental results (consider Figures 2 and 3). In some of the previous investigations which supplied information on the deactivation step size, narrow distributions, often 6 functions, were used to construct the energy distributions of the chemically activated molecules. Results in Figures 2-4 obtained with 6 functions and with broad Gaussians demonstrate the effect of the width of the distribution function on the best fit ( M )and ( E ) values. It may be seen from the figures that reasonably good agreement in the low-pressure turnup range can be attained with CDMC* distributions approximated by 6 functions; however, presumably too low CDMC* energies and considerably greater deactivation step sizes are required in such fits. These results indicate that the use of too narrow distributions for the activated species in the interpretation of chemical activation data may result in the underestimation of the average energies and may cause serious overestimation of the deactivation step sizes. Our deactivation step size is considerably smaller than ( 4 E ) = 47 k J mol-l reported previously5 for collisional
Multistep Collisional Deactivation of Dimethylcyclopropane
energy removal from CDMC* and TDMC* by CB2. A part of the difference (although not the whole) is certainly due to the more realistic energy distributions used in this work. The deactivation step size of 18 f 4 kJ mol-' is in line with most of the energy transfer results reported for chemically activated molecules of similar complexity formed in reactions of singlet methylene; i.e., ( AE) = 16-25 kJ mol-' ( AE) = 16-33 kJ mol-' for activated alkyl~yclopropanes,3~ and = 6-25 kJ mol-' for methylcyclobutane,'g~20~3* for higher alkylcyclobutanes.35 On the other hand, greater step sizes were also determined for highly excited molecules produced in 'CH2 reactions. Thus, ( AE) = 41.8 kJ mol-' has been obtained for the energy removing step size for methylcyclobutane-cyclobutane system.36 Deactivation step sizes for vibrationally highly excited polyatomic molecules were derived from systems which differ from the one used in this work. Thus, for instance, dehydrohalogenation studies of ethane derivatives formed by the combination of the appropriate methyl radical^,^'^^^ and investigations of systems produced by laser excitation and subsequent internal c o n v e r s i ~ nsupplied ~ ~ ~ ~ ~( AE) values (for bath gases similar to those used in this study) from 4 to 35 kJ mol-'. The quoted results show that despite considerable effort, our knowledge on the energy removing step size is not accurate enough. Reliable experimental results and careful reinterpretation of available data with due attention paid to the energy distribution of the activated molecules are definitely required. The kinetic results obtained in the high-pressure range carry information on the energy dispersion of CDMC* at the time of formation. Thermal Boltzmann distribution or similar distributions for the initial energies above Emin seems to be adequate for the K(334 nm) photolysis system. On the other hand, CDMC* is formed with very wide energy spread in diazomethane photolysis systems. The initial energy distributions can be characterized by "shifted" Gaussians. For both the DM(436 nm) and the DM(366 nm) systems the best-fit Gaussian parameter E , is smaller than Emin, which means that the actual distribution entering the calculations consists of monotonous decreasing population, above E-, with increasing energy. (It is to be pointed out that the final results are not too sensitive to the shape of the distribution as far as ( E ) and u are the same.) Interpretation of our results on the decomposition of chemically activated dimethylcyclopropanes definitely requires the use of distribution functions whose width increases with increasing initial energy of the activated molecules. This is in accordance with the expectation41 that the importance of the energy distribution diminishes as the ratio ( ( E )- Emin)/( ( E )- E,) decreases, where E , is the critical energy of the reaction and the remaining
(a)
(33)R. J. McCluskey and R. W. Carr, Jr., J.Phys. Chem., 82,2637 (1978). (34)R. J. McCluskey and R. W. Can, Jr., Znt. J. Chem. Kinet., 10,171 (1978). ' (35)R. J. McCluskey and R. W. Carr, Jr., J. Phys. Chem., 80, 1393 (1976);81,2045 (1977). (36)W. S.Kolln, M. Johnson. D. E. Peebles. and J. W. Simons. Chem. Phys. Lett., 65,85 (1979). (37)G.Richmond and D. W. Setaer, J. Phys. Chem., 84,2699(1980); P. J. Marcoux and D. W. Setaer, ibid., 82,97 (1978). (38)R. R. Pettijohn, G . W. Mutch, and J. W. Root, J.Phys. Chem., 79,1747,2077 (1975). (39)G.P.Smith and J. R. Barker, Chem. Phys. Lett., 78,253 (1981); M.J. Rossi and J. R. Barker, ibid., 85,21 (1982). (40)J. Troe and W. Wieters, J. Chem. Phys., 71, 3931 (1979);H. Hippler, J. 'hoe, and H. J. Wendelken, Chem. Phys. Lett., 84,257(1981); J. Troe, J. Chen. Phys., 77,3485 (1982). (41)P.Cadman, A. W. Kirk, and A. F. Trotman-Dickenson, J. Chem. SOC.,Faraday Trans. 1 , 72,996 (1976).
The Journal of Physical Chemistty, Vol. 87,No. 19, 1983 3699
TABLE IV: Excess Energies (in kJ mol-') of Reacting CH,( A, 1 K(334 nm) DM(436 nm) DM(366 nm)
11.8 158.4 211.2
3.6 57.0 68.5
0.31
0.36 0.32
symbols have the meaning already given. (The ratio is 0.06, 0.28, and 0.31 for the K(334 nm), DM(436 nm), and DM(366 nm) system, respectively.) We find that a simple correlation exists between the nonfixed initial CDMC* energy ( E ) and the energy dispersion B , which may be given roughly by the relationship ( E ) - Emin= 0.80 (20) The initial energy distributions and the deactivation step size derived above depend on the curvature of the ( k , ) vs. R S / R Dor the R D / R Svs. w-' plots at the high-pressure end of the pressure range. However, the high-pressure results in this work and in any other investigation which obtains RD from mass balance considerations may involve considerable experimental error. A rough estimation of the accuracy of ( E ) and ( AE) can be made as shown for the DM(436 nm) system below. The major source of the uncertainty of the high-pressure results is the error in the limiting vale ([CDMC] + [TDMC]), which we estimate to be about *8%. Computational results obtained with various CDMC* energy distributions show this to correspond to about f3.7% error in the average energy and about *27% error in the variance. Thus, for the DM(436 nm) system, ( E ) = 492.6 f 15.6 kJ mol-' and B = 51.9 f 13.9 kJ mol-'. Moreover, from the uncertainty of the width of the distribution one expects about *40% error limits for the deactivation step size, Le., (AE) = 14.6-20.6 kJ mol-' for the DM(436 nm) system. Energy of Reacting CH2('A1).From the nonfured energy of CDMC* at the time of formation, information may be gained about the vibrational energy of CH2('A1)at the time of reaction: (E('CH2))Ireact= (E(CDMC))Iinit+ A E O K
+ E,,
(21)
where AEoK is the difference in the zero-point energies of CDMC and 'CH2 + CB2, while E t h stands for the difference in the average thermal energies (E(CDMC)) IEans+rot - (E('CH2)) I$ans+rot (E(CB2)) t;ans+rot+vib Using AEoK+ E t h = -421.7 - 13.9 = -435.6 kJ mol-', one obtains the average vibrational energies given in the third column of Table IV. These energies of reacting CH2('A1) are compared with the energies released in the photolysis of CHzXY (see column two of Table IV) to obtain p, the fraction of excess energy possessed by singlet methylene as vibrational excitation at the time 'CH, reacts with CB2 giving CDMC. It may be seen that methylene, when it reacts, still carries about 30% of the energy released in the photolytic act. The considerable excess energy of reacting CH2(lAl) which increases in order of the extent of energy release in the three investigated systems may be best explained by assuming that deactivation of singlet methylene in collisions with heat bath molecules is very inefficient. Considering the rate coefficients and collisional frequencies we estimate, in our system at 13.3 kPa pressure, 5.4 X and 3.5 X s for the collisional and reactive lifetime of CH2(IA1),respectively. It follows from these data that singlet methylene suffers about 65 collisions before reaction occurs. The fact that reacting methylene is still hot shows
3700
J. Phys. Chem. 1983, 87,3700-3706
the average energy transferred in one collision to be small. The very wide spread in the energy of reacting methylene (which is practically the same as the initial energy dispersion for CDMC* given in Table 111) may originate either from energy partitioning between reaction products in the photolytic act or from energy transfer in collisions prior to reaction. Although probably both effects operate in our systems, the dispersion caused in energy partitioning is believed to be dominant. This is supported by the
increase in the spread with increasing energy release and by the inefficiency of collisional energy transfer. Further research is in progress to study energy partitioning in the photolytic production of CHZ('A1)and energy transfer in collisions between methylene and heat bath molecules. Registry No. cis-Dimethylcyclopropane,930-18-7;trans-dimethylcyclopropane, 2402-06-4;ketene, 463-51-4; diazomethane, 334-88-3; cis-2-butene,590-18-1; methylene, 2465-56-7.
Kinetics of NO Decomposition on Silica-Supported Rhodium Arthur A. Chlnt and Alexls T. Bell" Department of Chemlcal Englneering, Univerify of Caiifornia, Berkeley, California 94720 (Received: December IO, 1982)
Temperature programmed desorption (TPD) spectroscopy was used to study the desorption and decomposition of NO adsorbed on a Rh/SiOz catalyst. At room temperature, less than about 9% of the NO is adsorbed dissociatively, and hence associative adsorption predominates. Upon heating the catalyst, the adsorbed NO undergoes extensive decomposition to form Nz and Oz, as well as small amounts of NzO. The TPD spectra show two peaks for Nz, but only single peaks for NO, NzO,and Oz. It is suggested that the two N2 peaks are attributable to the following two processes: N, + NO, Nz + 0, + S and 2N, Nz + 2s. NzO is taken to be formed by the process N, + NO, NzO + 2s. Rate parameters for the elementary processes involved in NO desorption and decomposition were determined by forcing agreement between simulated and observed TPD spectra. The preexponential factor and activation energy for NO desorption determined this way are s-l and 23.7 kcal/mol, respectively. 1X
-
Introduction Temperature programmed desorption (TPD) spectroscopy can be used to elucidate the elementary processes occurring on the surface of a catalyst during the desorption and decomposition of an adsorbate.'-'l Relatively few efforts, however, have been made to apply this technique to the study of reactions which occur on supported metal catalysts or to use it as a basis for deducing the rate parameters for elementary surface reactions. In this paper we report on a study of the kinetics of NO desorption from, and decomposition on, a silica-supported Rh catalyst. TPD spectra were obtained by observing the composition of a helium stream passed through a shallow bed of catalyst as the catalyst temperature was raised in a linear fashion. The rate parameters for individual surface processes were determined by simulation of the observed TPD spectra. On single-crystal and polycrystalline Rh surfaces, NO adsorbs with a sticking coefficient near unity.lZ-l5 Dissociative adsorption predominates at low coverages but becomes less probable as the coverage increases. Infrared studies161s of NO adsorption on silica- and alumina-supported Rh suggest that at room temperature molecular adsorption of NO occurs preferentially. To date, all TPD studies of adsorbed NO have been carried out with unsupported Rh. In most cases, the primary products observed are NO, Nz, and 0212-15 The formation of N20 has also been observed in two of these in~estigations.'~J~ Desorption of NO occurs primarily from a single peak, the position of which is independent of coverage. This peak is observed only at high initial exposures. A t low initial coverages of NO, dissociation takes place before the desorption temperature is attained and 'Present address: Mobil Research and Development Corporation, Research Department, Paulsboro, NJ 08066.
-
-
consequently little, if any, NO desorbs from the surface. The principal nitrogen-containing product observed in all studies is Nz. This species desorbs from two states. A low-temperaturepeak appears at high initial coverages, the position of which is independent of coverage. A hightemperature peak is found at all coverages. The position of this peak shifts to lower temperatures with increasing initial NO coverage in a manner characteristic of secondorder kinetics. It is generally accepted that the high-temperature peak is due to the recombination of adsorbed nitrogen atoms, but there is disagreement as to the origin of the low-temperature peak. Where NzO is observed to form, it appears in a single peak, which is positioned in close proximity to the NO peak and the low-temperature Nz peak. The desorption of O2 occurs at significantly (1) Redhead, P. A. Vacuum 1962,12, 203. (2) Cvetanovic, R. J.; Amenomiya, Y. Adv. Catal. Related Subj. 1967,
17, 103. (3) Cvetanovic, R. J.; Amenomiya, Y. Catal. Reu. 1972, 6, 21. (4) Peterman, L.A. In "Adsorption-DesorptionPhenomena";Ricca, F., Ed.; Academic Press: New York, 1972. (5)Schmidt, L.D. Catal. Rev. 1974, 9, 115. (6) Smutek, M.; Cerny, S.; Buzek, F. Adv. Catal. Related Subj. 1975, 24, 343. (7) Madix, R. J. Catal. Rev. 1977, 15, 293. (8) Falconer, J. L.;Schwartz, J. A. Catal. Reu. Sci. Eng., in press. (9) Herz, R. K.; Kiela, J. B.; Marin, S. P. J. Catal. 1982, 73, 66. (10) Gorte, R.J. J . Catal. 1982, 75, 164. (11) Gorte, R. J.; Schmidt, L. D. Appl. Surf. Sci. 1979, 3, 381. (12) Campbell, C. T.; White, J. M. Appl. Surf. Sci. 1978, 1, 347. (13) Castner, D. G.; Sexton, B. A.; Somorjai, G. A. Surf. Sci. 1978, 71, 519. (14) Castner, D. G.; Somorjai, G. A. Surf. Sci. 1979, 83, 60. (15) Baird, R. J.; Ku, R. C.; Wynhlatt, P. Surf. Sci. 1980, 97,346. (16) Arai, H.;Tominaga, H. J . Catal. 1976,43, 131. (17) Savataky, B. J. Ph.D. Thesis, University of California, Berkeley, 1980. (18) Solymosi, F.;Sarkany, J. Appl. Surf. Sci. 1979, 3, 68.
0022-3654/83/2087-3700$01.50/00 1983 American Chemical Society
