J. Phys. Chem. 1980, 84, 3411-3417
number of cases fior which VOIP,,, is available, and the summation extends over all such cases. The value of u thus defined is 0.46,O.59, 1.55,0.97, and 1.25% for the 2s, 2p, 3d, 39, and 3p V(31P, respectively, of the type I11 atoms and 1.13, 1.69,4.04,0.79, and 1.27% for the 3s, 3p, 3d, 49, and 4p VOIP, respectively, of the type IV atoms. In conclusion, we must mention the fact that our VOIP formulas have been found to be very useful in evaluating E, of configurations for which direct empirical values are unknown for lack: of experimental spectroscopic data, in conformity with the expectation outlined in the Introduction. Detailed examples will be given e1~ewhere.l~ It should however be admitted that very few pieces of experimental data are available for the spectroscopic term values to either the pnx of the sp"-l type configuration.22 It is expected therefore that our VOIP formulas are yet to be improved for evaluating the average energy of a configuration of riuch a type, although our formulas are based on the best set of spectroscopic data available at present.
Acknowledgment. We are grateful to Professor Inga Fischer-Hjarmars of the University of Stockholm for reading an earlier draft of the present paper and giving several useful suggestions. Calculations reported in the present paper have been done by using a FACOM M190 at the Computer Center of Kyusliu University. We are grateful to the staff of the Center for their help in using the computer.
References and Notes (1) T. Anno and Y. Sakai, Theor. Chim. Acta, 18, 208 (1970). (2) T. Anno, Theor. Chim. Acta, 18, 223 (1970).
3411
(3)T. Anno and Y. Sakai, J. Chem. Phys., 56, 922 (1972). (4) In the presont paper, "atoms" often mean both neutral atoms and ions.
(5) T. Anno and Y. Sakai, J. Chem. Phys., 57, 4910 (1972);58, 5190 (1973). (6) See, for example, various review articles appearing in Mod. Theor. Chem., 4 (1977). (7) M. Wolfsberg and L. Helmholz, J. Chem. Phys., 20, 837 (1952);R. Hoffmann, !bid., 39, 1397 (1963). (8) R. Pariser and R. G. Parr, J. Chem. Phys., 21, 466,767 (1953);J. A. Popie, Trans. Faraday SOC.,49, 1375 (1953). (9)J. A. Pople and 0.A. Segai, J . Chem. Phys., 43, S136 (1965). IO) J. A. Popie, D. L. Beveridge, and P. A. Dobosh, J. Chem. Phys., 47, 2026 (1967). 11) N. C. Baird and M. J. S. Dewar, J. Chem. Phys., 50, 1262 (1969); M. J. S. Dewar and E. Haseibach, J. Am. Chem. SOC.,92, 590 (1970);R. C. Bingham, M. J. S. Dewar, and D. H. Lo, ibhf., 97, 1285 (1975). 12) See, for exalmple, varlous review articles appearing in Mod. Theor. Chem., 7-81 (1977). 13) J. C. Slateir, "Quantum Theory of Atomic Structure", Voi. 1, McGraw-HIii, New York, 1960,Chapter 14. 114) . . Y. Sakai and T. Anno. Mem. Fac. Sei.. Kvushu Univ.. Ser. C.. 12.. 137 (1980). Reprints are available upon'request to T. Anno. (15) Reference '13,pp 366-72. (16) C. E. Moore, Natl. Bur. SM.(U.S.),Circ., 1, 467 (1949). (17) T. Anno and H. Teruva. Theor. Chlm. Acta, 21. 127 11971). (18j T. Anno and H. Teruya, J. Chem. Phys., 52, 2840 (1970).' (19) L. J. RadzieinskC Jr., K. L. Andrew, V. Kaufman, and U. Liken, J. Opt. SOC.Am., 57 336 (1967)[Si]; Y. G. Toresson, Ark. Fys., 18, 389 (1961)[Si2']; W. C. Martin, J. Opt. SOC.Am., 49, 1071 (1959) P, PI]; L. J. Radzlemski, Jr., and V. Kaufman, bhf., 59 424 (1969)\a];A. Borgstrom, Ark. Fys., 38, 243 (1968)[ca2+j (20) In taking the weighted mean, each term is given a weight (2L 1x2s I),where Land S are the quantum numbers representingthe total
+
+
orbltai and h e total spin angular momentum, respectively, appropriate to the term. (21) Reference 13,pp 242-3. (22) In specifylng the electron conflguratiin, the core (K shell for the type 111 atoms and K and L shell for the type I V atoms) Is omitted for brevity; s or p stand for the inner (2sor 2p for the type 111 atoms and 3s or 31) for the type IV atoms) orbitals.
Reactive Channels of the CH302-CH302Reaction Charles S. Kan,+Jack 0. Calveit,*+ and John H. Shawt Depaartment of Chemistry and Department of Physics, The Ohio State University, Columbus, Ohio 432 10 (Received: July 22, f980; In Final Farm: August 25, 1980)
Kinetic studies of the products of the CH302-CH302reactions have been made by using long-path FT-IR spectroscopy. These allow an evaluation of the relative importance of the four suggested channels: 2CH302 '2CH30+ O2 (la); 2CH302 CH20+ CH30H+ O2 (lb); 2CH302 CH300CH3+ O2 (IC);2CH302 CH302H + (2HzOz(Id). The data from experiments at 25 "C give klb/kla = 1.32 f 0.16; klb/klc 1 7; kld h > 290 nm) 2CH3 + N2 (6) CH3 + 0 2 (+M) CHz02 (+M) (7) The photochemical decay of azomethane occurred with an apparent first-order rate constant of (1.2 f 0.1) X min-l, independent of initial azomethane and oxygen pressures. The infrared spectra derived during a typical experiment at high O2 pressure are shown in Figure 2. The initial spectrum of the azomethane (29.2 ppm)-oxygen (100 torr)-nitrogen (600 torr) mixture is labeled A; spectra after 10.2 (B) and 19.6 min of photolysis (C) are given as well. The spectra of the products in Figure 2C show formaldehyde (5.16 ppm), methanol (2.39 ppm), methyl hydroperoxide (2.14 ppm), formic acid (0.14 ppm), and CO (0.34 pprn). COz, and to some extent CO, desorbed from the cell wall as the photolysis lamps were turned on; hence the amounts of these compounds can be regarded only as upper limits to the homogeneous product yields. After subtraction of the identified products from spectrum C, the residual spectrum of some unknown product(s) resulted (see Figure 2D). The spectrum of an authentic sample of dimethyl peroxide is shown for comparison in Figure 2E. The time profiles of the various species are shown in Figure 3. It is not clear from the comparison of spectra D and E of Figure 2 what fraction, if any, of the unknown product is CH300CHB. Enlargements of the unknown spectrum and that for pure CH300CH3in the 940-1090-~m-~ region are shown in Figure 4, labeled A and F, respectively. The spectra do not match, yet a portion of the unknown may be CH300CH3. We have subtracted
-
-+
The Journal of Physical Chemistty, Vol. 84, No. 25, 1980 3413
Reactive Channels of ,the CH302-CH302 Reaction I
-
-
'
I
l
'
I
' 1
I
I,
1
I
I I
L
-I
%-I I E , 600
y
L
ti ,
1000
I "
--
14011
1800
2200
II, 3 J I 2600
I
3000
1 /A ,cm"
Figure 2. Fourier transform infrared spectra In the photolysls of azomethane-Op-N2 mixture at 25 O C (run 8, Table I): (A) inltlal azomethane; (B) reaction rnixture after 10.2 min of photolysls; (C) after 19.0 min of photolysis; (D) residual spectrum after subtraction of azomethane and other known products; (E)standard sample of dimethyl peroxide: absorptlon bands near 2350 cm-' are due to C02.
--
1
7 940
io00
970
1030
1060
1090
l / A ,cm-'
I
I
Flgure 4. (A) Fourier transform infrared spectra of the residual compound formed in atomethane-O,-N, mixture photolysls in the 9401090Gm-l region. (E%-E)Spectrum A mlnus 0.30, 0.42, 0.48, and 0.54 ppm of dimethyl percxkk, respectively. (F) Spectrum of pure dlmethyl peroxide.
pathways la, lb, tmd Id. Further experiments were carried out to test for the presence of the CH202product of reaction Id. In our recent study of the ozone-ethylene system, the form,ation of the CH202intermediate species was well establi~hed.~~ Thus the oxidation of SO2observed in the O3-CzH4-O2-SO2 system appears to originate in reaction 8. Recent unpublished work in our laboratory CHzO2 SO2 CH202S02(or CH20 + SO,; H2S04aerosol) (8) has shown that Cll3Oz and H02radicals do not oxidize SO2 significantly for thLe condition employed here. We observed also that CH202reach with CH20to form an unidentified unstable molecule X, perhaps HOCH20CH0,which reacts in a first-order process to give formic acid anhydride, presumably in reaction 10. There was no direct spectral evidence of the secondary ozonide formation which is indicated as an intermediate in reaction 9. I t is expected
+
T h e , min
Flgure 3. Time profiles of species involved in the photolysis of azomethane-02-N2 mixture at 25 O C (run 8,Table I): azomethane (squares); CH20 (circles),methanol (filled squares); formic acid (filled triangles); CO (filled circles). Simulation results are shown as lines; vertical dashed line, lamlps off.
from the unknown spectrum the contribution of 0.36,0.42, 0.48, and 0.54 ppm ad CH300CH3in the spectra labeled B-E, respectively. If we use the valley in the absorption a t 1045 cm-' as a guide to the CH300CH3maximum present in the experiment, we conclude that less than 0.36 ppm of CH300CH3 could be present in this product spectrum. However, judging from the shape of the total absorption band around 1030 cm-l, the CH300CH3contribution is probably much less than this. We conclude that Klb/klc L 7. We will consider later the possible chemical nature of the residual unknown species in the products. The Possible Reaction Channel I d . The observed products are in accord with the occurrence of the reaction
+
{4,>H3 -0-0
CH202 t CH20
+
x
(9)
X (HC0)20 + Hz (10) to be an intermediate of short lifetime which will lead to the unknown precursor to formic acid anhydride. We have taken advantage of these unique reactions to test for CH20zamong the CH302products. In one experiment, 30 ppm of azomethane, 100 ppm of SO2, 100 torr of 02, and 600 torr of N2 were photolyzed for 19.25 min. The +
3414
The Journal of Physical Chemistty, Vol. 84, No. 25, 1980
TABLE I: Photolysis of Azomethane-0,-N,
Kan et al.
Mixtures at 25 “C at Varied 0, Pressures
press. of reactants and products, ppm
C 600
time, min
MezNz initial
MezNz
0 2
final
CH,O
CH,OH
CH,O,H
HCO,H
co
19.3 19.6 19.5 19.3 19.4 19.6 19.6 19.6 19.5 19.5
50 50 100 150 300 5 50 6.6 X lo4 1.3 x 105 2.6 x 105 9.2 x 105
30.6 29.8 29.9 24.0 26.4 29.4 27.5 29.2 22.4 26.3
22.5 22.1 22.2 18.0 20.4 22.2 21.2 22.5 17.4 20.6
5.66 5.25 5.36 4.63 5.25 5.76 4.94 5.16 4.12 4.84
4.07 4.10 3.90 2.95 3.23 3.35 2.42 2.44 1.99 2.28
0.91 0.91 1.22 1.07 1.22 1.67 2.28 2.13 1.98 2.13
0.10 0.07 0.07 0.07 0.09 0.10 0.13 0.13 0.11 0.13
1.9 2.0 1.7 1.0 1.1 1.0 0.16 0.34 0.14 0.26
i
I 1000
1400
1800
1200
I / L ,cm-j
I 2000
~~
1 3000
~
I
C
3400
I
600
1000
I
I
1
1400
1800
2200
Flgure 5. (A) Fourier transform infrared spectrum of azomethaneS02-02-N2 mixture before photolysls. (8)Spectrum after 19.25 mln of photolysis. (C) Residual absorption after subtraction of known reactants and products.
resulting infrared spectrum of the products (Figure 5) showed the presence of the following (pprn): CH20, 5.4; CH30H,2.4; CH302H,2.3; HC02H, 0.13; CO, 0.30. There was no evidence of SO2oxidation in the system, and hence the presence of the CH202species in this system is not confirmed. In another experiment, 30 ppm of azomethane, 18 ppm of CH20, 100 torr of 02,and 600 torr of Nz were photolyzed for 10.4 min. The infrared spectrum of the products (Figure 6) showed the presence of the following species (pprn): CH20 (in excess of that added), 1.4; CH30H, 1.6; CH302H,1.2; HC02H, 0.75; CO, and an unidentified residual absorption at 1030 cm-l. There is no absorption at 1812, 1760, and 1090 cm-’ which are characteristic of (HC0)20, and the bands associated with the unknown precursor X at 1760, 1170, 1110, and 1050 cm-l are also absent. Again the experimental results indicate that CH202is not a significant product of the CH302-CH302 interaction. An additional series of experiments were carried out to study the mechanism of CH302Hgeneration in this system. Presumably it could arise either in reaction Id as Nangia and Benson suggested or through the disproportionation process 11 in experiments at low [02]where reaction 12 CH3O2 + CH30 CH302H+ CH20 (11) CH30 + O2 H 0 2 + CH20 (12) CH302 + H 0 2 CH302H+ 0, (13) is not the dominant fate of CH30, and in reaction 13 in experiments at high [O,]. The photolyses of azomethane
I 2600
3000
3400
I/X ,cm”
n-
,__ -_ - - __ _ - -_ - -_ -- - ---- -
6-
-
--
-
I
I
I
l l l l l l i
102
I
I , , , , , , ,
I
,
10’
1 , 1 1 1 1 1
t 0‘
I
, 1 1 1 1 1 1 ,
105
I
I
, t a t , t /
IO
oxygen,ppm
Flgure 7. Rate of methyl hydroperoxideformation as a function of P,$ circles, ex erlmental data; dotted curve, simulated results with kj3 = 1.3 X IO-’; dash-dot curve, simulated result with the value of k I 3 = 6.1 X om3 molecule-’ s-I.
in 02-N2 mixtures at varied [O,] were carried out to distinguish between these alternatives. The results are summarized in Table I. Note in Figure 7 the variation of the ratio of the initial rate of CH302Hformation to the initial azomethane pressure as a function of the pressure of 02. The ratio falls at low O2but reaches an essenti”aUyconstant min-l, at high O2pressures. Now value, (4.2 f 0.3) X if reaction Id were the sole fate of the CH3O2 radicals and the origin of CH302Hin this system, then no such O2effect
The Journal of Physical Chemistry, Vol. 84, No. 25, 7980 3415
Reactive Channels of the CH3O2-CH8O2Reaction
TABLE 11: Summary of the Mechanism and Rate Constants for the Simulation of'the Photolysis of Azomethane-0,-N, Mixtures at 25 "C reaction rate constantQ ref
--
CH,N=NCH, t hv + 2CH3 t N, CH, t 0, ( t M ) -+ CH,O, (tM) 2CH30, 2CH30 t 0, 2CH,O, CH,O t CH,OH t 0, CH,O + 0, CH,O t HO, CH30, + HQ, CH,O,H t 0, 2H0, H,O, + 0, CH30, + CH,O .+ CH,O,H t HCO CH,O, + CH,O CH,O,CH,O HO, t CH,O .+ (HO,CH,O) .+ O,CH,OH HO, t O,CH,OH .+ HO,CH,OH + 0, HO,CH,OH t hv (or wall) + HCO,H t H,O O,CH,OH - (HO,CH,O) -+ HO, t CH,O 2O,CH,OH .+ 2OCH,OH t 0, OCH,OH t 0, HCO,H t HO, CH,O t hu + H t HCO -+ H, t CO HCO + 0, --L HO, t CO H t 0, (tM)+ HO, (tM) 2CH,O + CH,OH t CH,O 2CH,O CH30,CH3 CH30 t CH,O, CH,O,H t CH,O CH,O + CH,O -+ CH,OH t HCO
(6)
2OX 2.2 x 1.6 x 2.1 x 6.1 X 1.3 X 3.6 X 3.4 x
(( l7a) ) (1b) (12) (13) (21) (2'7) (28) 1.0x (1'1) 2.0 x (16) 3.9 x (17) 1.5 (15) 1.2 x (19) 6.1 X (20) 4.2 X (22) 2.8 x (23) 5.6 x (24) 1.3 X (25) 2.5 X (30) 6.6 X (31) 6.8 X (11) 1.0 x (26) Rate constants in units of cm3 molecule-' s-l except for first-order steps in s-'. --f
+
-+
-+
-
I
-f
this work 3 4, this work 4, this work 26 this work 21 this work
10-4 lo-', 10-13
10-13
lo-'' lo-"
18 18 18 18 18 18 18 18 28, 29, 30 27 31 31 32 25
10-14 lo-', 1010-13
--f
-+
--f
a
10-5
lo-', lo-'' lo-" lo-" lo-'" 10-15
recent estimate OF kI3by Cox and Tyndall; when the latter I 7 estimate was used, the upper simulation curve in Figure 3,0/
0
i
,".
5
10
15
20
Ti me,m i n Flgure 8. Time profiles of the ratio [CH,0]/[CH30H] as a functlon of the Poz, Upper curve for high+,, experiments: 700 (circles), 200 (triangles), 100 (filled squares), and 50 (hexagons) torr. Lower curve for Iowa2experiments: 550 (diamonds), 300 (inverted triangles), 150 (filled hexagons), 100 (filled triangles), and 50 (squares, run 1; half-filled circles, run 2) ppm.
is anticipated. The variation seen is consistent with the formation of CH302Hin reactions 11and 13. At high [02J the CH30 radical reacts largely with O2 and reaction 13 would be favored for these conditions. The complete reaction sequence given in Table I1 was employed to simulate these results. The rate constants employed were derived from the current estimates in the literature in most cases. The dotted theoretical curve which matches the CH302H rate data quite well was obtained by using k13 = 1.3 X cm3 molecule-l s-l. This is a factor of 4 lower than the
7 was obtained; this shows the same product trend, but overshoots the RCHsO,H estimates. It is possible that the Cox and Tyndall use of the high values of the CH3O2 extinction coefficient reported by Parkes et al.23could lead to an underestimate of [CH302]values and an overestimate of k13. In any case the data support the more conventional pathways for CHB02Hformation in reactions 11and 13. Again no evidence is seen for the branching step Id, and we conclude that it is relatively unimportant compared to pathways l a and lb. The Possible Channels l a and l b . A new estimate of the branching ratio for processes l a and l b can be derived from the current data. We would anticipate that in the experiments with high [O,], the methoxy radical formed in reaction l a would react almost exclusively in reaction 12 to form CH20 and H 0 2 radicals. As a first approximation one might expect that for 50 < Po, < 700 torr, klb/kla 2[CH3OH]/([CH2O] - [CH,OH]) 1.58 f 0.14. However this is accurate only if no other processes produce or remove CH30€Iand CHzO. The presence of HCOzH and CO indicates that this condition is not met. We can account quantitatively for the HC02Hformation through the H02-CH20 interaction scheme of Su et al. (reactions 14-21).'8,24 Furthermore CH20 undergoes photolysis in HOz + CHzO (H02CH20) O2CHzOH (14) (H02CH20) HOZ CH2O (15) 0zCH20H HOz + O$H20H --* HOzCHzOH 0 2 (16) HOzCHzOH + hv HCOzH H2O (17) H02CHzOH+ wall H 2 0 + HC02H wall (18) 20zCII2OH 20CHzOH + 0 2 (19) OCHzOiH + 02 --* HCO2H + HOz (20) HOz + HOz --* H2Oz + 0 2 (21) our system and leads to CO, H2, and HOz radicals (reactions 22-25). If onlly reactions la, lb, 6 , 7 , and 11-25 occur CH2O + h~ H + HCO (22) --*H2+CO (23)
-
- - ++
-+
--
-+
-+
+
+
3416
The Journal of Physical Chemktty, Vol. 84, No. 25, 1980
HCO + 02 HOz + CO H + 02 (+M) HO2 (+M) +
+
Kan et al.
(24) (25)
in the system, then one expects klb/kla 2[CH30H]/ ([CHZO] [HCOZH] + [CO] - [CH,OH]) 1.39 f 0.09. There are further complications which show this picture to be incomplete as well. Note the time profile of the [CH20]/[CH30H] ratio at high [O,] plotted in Figure 8. Extrapolation of this ratio to zero time yields [CH,O]/ [CH,OH] N 2.5 f 0.2, with the rate of change of the ratio min-’ for the high-[O,] runs. equaling (2.0 f 1.2) X It is expected that side reactions forming or removing CHzO and CH30H would be unimportant at short times, so one may use this intercept to estimate klb/kla = 1.32 f 0.16. We believe this to be the best estimate of the branching ratio which is derivable from these data. It is in reasonable accord with the previous estimates, but should be somewhat more reliable. The origin of the decrease in [CH20]/[CH30H] with increasing photolysis times must be considered. Obviously it may result from processes which remove CHzO or form CH30H at the longer times. One such potential process cm3 molecule-l s-l as is reaction 26. If k26 N 1.0 x CH30 CH2O CH30H + CHO (26)
+
10 IO’
1oa
102
1‘ ‘ 0
10’
108
OXVGEN,ppm
Figure 8. Variation of the ratio [CH,O]/[CH,OH] wlth Po,. Circles, experimental data: dashed Ilne, the simulated resutl using the constants In Table 11.
t - - - - V I
-
+
has been or even if it is a factor of 100 times this value, then reaction 26 could not compete with reaction 12 for our high-[02] conditions. The two obvious pathways for CH20 reqoval, photodecomposition in reactions 22 and 23 and reaction with HOz in the reaction sequence 14-20, can account for only a decrease of 6.5 X min-l in the [CH20]/[CH30H] ratio with time. However there are two other reactions which we may consider as additional CH20 removal steps: CH302 CHzO CH3OBH HCO (27) CH3O2 + CH2O CH302CH20 (28) We can fit the [CHzO]/[CH30H]time dependence if kZ7 kzs N 3.4 X cm3 molecule-l s-l. The CO product observed can be used to set an upper limit on kZ7
