J. Phys. Chem. 1983, 87, 1804-1808
1804
should be evaluated: a logarithmic plot of [4(t--) 4(t)]/+(t+m) as a function of time leads to a slope given by ( k(E)) / $( t+-), or approximately k( ( E a c )/)$( t--..). With a suitable estimate of 4(t---), then h((Eac)) can be extracted. The usefulness of this approach for experiments like those in ref 6 is immediately evident. (Obviously, this approach is only applicable as long as the decay can be characterized by a single rate "constant" lz (E).)
lision efficiencies yc and energy transfer averages ( a E )has been made visible. The expressions derived appear to be most useful for a quick interpretation of experimental data. It should be emphasized that, whenever sufficiently detailed knowledge of the molecular parameters involved is available and when the measurements are of very high precision, a detailed master-equation analysis should follow the present analysis.
Conclusion In the present work, simple expressions for the yields of unimolecular reactions with nonthermal activations under time-dependent or time-independent observation have been derived. The relation between empirical col-
Acknowledgment. The author thanks R. G. Gilbert and K. Luther for their most valuable comments. Financial support of this work by the Deutsche Forschungsgemeinschaft (Sonderforschungsbereich "Photochemie mit Lasern") is gratefully acknowledged.
Reactions of Mg('S,), Mg(3P,), and Mg('P,) with Diatomic and Triatomic Oxidants W. H. Breckenrldge' and H. Umemoto Department of Chemistry, University of Utah, Salf Lake City, Utah 84 1 12 (Received: October 7, 1982)
Laser techniques have been utilized to study the reactions of ground-state Mg(3s3s1So)and excited Mg(3s3p3PJ) and Mg(3s3p'P1) atoms with the oxidants Oz, NO, NzO, COz, and SOz. Ground-state Mg('So) reacts only with N 2 0 at 520 K to produce MgO(XIB+),as expected thermochemically,but the reaction rate is very slow, consistent with theoretical predictions by Yarkony of an entrance-channel activation barrier. The reaction of Mg(lP1) with NzO produces excited MgO(B'Z+). In contrast, C 0 2 and SOz react with Mg('P,) to produce MgO(XIB+), with little or no production of MgO(B'Z+) or MgO(A'H). Reaction of Mg(3PJ)with O2produces MgO(XIZ+) but no MgO(A'H). The initial vibrational and rotational quantum state distribution of the MgO(X'Z+)resulting from the Mg(3PJ)/0zreaction, determined by a pump-probe laser technique, was very similar to that reported by Dagdigian from molecular beam experiments, and was much "colder" than predicted by statistical models.
Introduction The reactions of ground-state and electronically excited metal atoms with simple oxidant molecules in the gas phase have been studied by several Much of the original work was triggered by the possibility of electronic-transition chemical laser action, since many of the oxidation processes are sufficiently exothermic to produce several electronically excited states of the metal monoxide products. Research in this area has continued, for the most part because new experimental techniques for identification of state-resolved products have created the possibility of detailed characterization of processes with several possible exit channels. Theoretical advances in understanding the dynamics of reactions involving multiple potential energy surfaces have also contributed to the interest in these processes. We present here a study using laser techniques of the chemical reactions of ground-state Mg(3s3slS0)and excited Mg(3s3p 3PJ)and Mg(3s3p 'P1) with the simple oxidant molecules 02, NO, NzO, COz, and SOz. Experimental Section The experimental apparatus and laser system have been described previ~usly.~Briefly, magnesium vapor, pro~
~~
~~~~
(1) W. H. Breckenridge and H. Umemoto, Adu. Chem. Phys., 50, 325 (1982). (2) P. J. Dagdigian, J. Chem. Phys., 76, 5375 (1982), and references - therein. (3) J. W. Cox and P. J. Dagdigian, J . Phys. Chem., 86,3738 (1982), and references therein. 14) M. Menzinger, Adu. Chem. Phys.. 42, 1 (1980).
duced in a resistively heated alumina crucible, is entrained in a stream of helium gas. Oxidant gases are added to the magnesium/He vapor stream via a "shower-head'' stainless steel mixing device located just above the alumina crucible. The crucible and mixing device are located inside a stainless steel vessel with several ports for laser beam access and/or detection of fluorescence. Typical pressures for the experiments reported here were as follows: He, 17 torr; Mg vapor, 104-10-z torr; oxidant gases, 0.3-1.0 torr. The Mg(3s3p3PJ)and Mg(3s3p 'PJ states were excited in the gas stream by absorption of -6-11s pulses of dyelaser radiation. The third harmonic of a Molectron MY32 Nd:YAG laser was used to pump a Molectron DL-200 dye-laser head. For excitation of Mg('P1), the dye-laser output was frequency doubled by means of an angle-tuned ADP crystal to the 'So-'PI resonance transition at, 2852 A. For excitation of Mg(3Pl),the dye laser was tuned t o 4571 A, the highly forbidden 1S0-3P1transition. The temperature at the laser interaction region, measured with a thermocouple probe, was -425 K for the Mg('P,) studies. For the Mg(3PJ) studies, higher heater power was used to generate the maximum attainable concentration of Mg vapor, and the temperature for the Mg(3P,J)work was measured to be -520 K. Chemiluminescence from the reaction zone was dispersed with a Jobin-Yvon monochromator (resolution 60 A), and detected with an HTV R910 photomultiplier, the
-
-
-
( 5 ) W. H. Breckenridge and H. Umemoto, J . Chem. Phys., 77, 4464 (19821, and references therein.
0022-3654/83/2087-1804$01.50/00 1983 American Chemical Society
The Journal of Physical Chemistry, Vol. 87, No. 10, 1983
Reaction of Mg Atom with Oxidants
TABLE I : Spectroscopic Energies of Reaction, A E , " , for the Production of M g O ( X ' z + ) in the Reaction of the Three Lowest States of the Magnesium Atom with Various Oxidant Gases
TABLE 11: Electronic Excitation Energies ( u ~ of ) the Low-Lying States of the MgO Moleculea state
atomic state
oxidant
AE n o . kcal/mol
Mg('P,)
N2O
ClxD' A
-141.5 -62.2 -54.5 -48.7 -30.4 -103.9 -24.6 -16.9 -11.1 +7.2 -41.3 + 38.0 +45.7 t 51.5 + 69.8
d3A c3x+ BIZ+
0 2
CO, SO2
NO Mg(3PJ)
NZO 0, COZ
COz
3
a Bond dissociation energies were taken from ref 6 , 8 , and 9, atomic excitation energies from ref 1.
output of which was processed by a PAR 162/164 boxcar integrator. By adjusting the boxcar gate, detection of the fluorescence was limited to a period from 40 to 90 ns after the excitation of Mg('Pl). Detection of products was also accomplished by using a "pump-and-probe" laser technique. The Nd:YAG third-harmonic radiation in this case is split, one portion continuing to pump the dye laser for eventual excitation of Mg(3Pl) or Mg('P1). The other portion is spatially delayed a few nanoseconds and oscillates a second DL200 dye-laser head, which is scanned across wavelength regions in which products can be detected by laser-induced fluorescence. The laser-induced fluorescence was detected with an EM1 6256B photomultiplier, the output of which was processed by a PAR Model 162/164 boxcar integrator. A wide-band interference filter was used in the Mg(3PJ) experiments to isolate the MgO signal. Gases were used directly from the cylinders without purification. C02 (99.99%), SO2, and N20 were products of Matheson Co. The O2and NO gases were from Union Carbide Co., the helium gas (99.998%) from US.Welding.
Results The possible products of reactions of Mg('So), Mg(3PJ), and Mg('P1) with the oxidant gases studied are, of course, limited by the total energy available. Unfortunately, the bond strength of MgO(XIZ+)is still uncertain, but a value of 80.0 f 6.0 kcal/mol appears to be consistent with the latest experimental and theoretical results.6 (Note, however, that a very recent calculation' is consistent with a much lower value of 62 kcal/mol.) Shown in Table I are the values of moo for reaction of the three states of the Mg atom to produce ground-state MgO(X'Z+) and another fragment, calculated with this value of the MgO(X'Z+) dissociation energy. Shown in Table I1 are the excitation energies for the low-lying states of MgO. It can be seen (6) M. W. Chase, Jr., J. L. Curnutt, R. A. McDonald, and A. N. Syverud, J.Phys. Chem. Ref. Data, 7,793 (1978);N.S.Murthy and S. P. Bagare, J . Phys. B, 11, 623 (1978). (7)C. W.Bauschlicher,Jr., B. H. Lengsfield, 111, and B. Liu, J.Chem. Phys., 77,4084 (1982). (8)K.P.Huber and G. Herzberg, "MolecularSpectra and Molecular Structure. IV. Constanta of Diatomic Molecules", Van Nostrand-Reinhold, New York, 1979. (9)D. R. Stull and H. Prophet, Natl. Stand. Ref. Data Ser., Nutl. Bur. Stand., No. 37 (1971). (10)C.W.Bauschlicher, B. H. Lengsfield 111, D. M. Silver, and D. R. Yarkony, J . Chem. Phys., 74,2379 (1981).
1805
uoo, kcal/mol
--
85.7 85.1 84 81 57.2
state
(b3x+)
A1n a3n
Xlx
+
u o 0 , kcalimol
(- 1 8 ) 10.0 -7 0.0
Values are taken from ref 8 , except for the value for the b32+state, which is estimated from the theoretical work of ref 10.
from these tables that all of the gases are capable of reacting with Mg(3PJ)and Mg('Pl) to produce MgO(X'Z+), except perhaps for the case of NO reacting with Mg(3PJ). Indeed, there is sufficient energy in most cases to produce several excited states of MaO. In contrast, only N,O is capable of reacting with ground-state Mg('So) to-pro;duce MgO(X'Z+). Reaction of Mg('S,J with NzO. Consistent with the thermochemical calculations, only with NzO and groundstate magnesium vapor was MgO(X'Z+) detected by laser-induced fluorescence. No product MgO(XIZ+) was detected when magnesium vapor was mixed with 02,COz, SOz, or NO. The MgO spectra indicated a Boltzmann rotational quantum-state distribution consistent with the temperature of the vapor stream, as expected since the effective reaction time (determined by the flow rate) was milliseconds. However, the vibrational quantum-state distribution was much hotter, indicating that vibrational deactivation was inefficient under the experimental conditions. Reactions of Mg('Pl). Production of MgO(X'Z+). Strong LIF spectra of MgO(X'Z+) were detected when Mg('PJ was excited by the pump laser in the presence of C02 and SO2. Initial vibrational and rotational distributions of MgO(X'Z+) could be extracted from the spectra, and the results for C02 have been reported in detail e1sewhere.l' The yield of MgO(X'Z+) from the SO2 reaction was only -40% of that of the C 0 2reaction, but the initial vibrational and rotational quantum state distribution was quite similar to the COz case. No MgO(X'Z+) was detected when Mg('P1) was excited in the presence of O2 or NO. It was not possible to detect MgO(X'Z+) in the reaction of Mg('P1) with NzO because of the luminescence observed (see below). From estimates of the Mg('P1) vs. Mg(3PJ) concentrations in the Mg(3PJ)-02 experiments discussed below, it is possible to estimate conservatively that the yield of MgO(X'Z+) in the reaction of Mg('P,) with O2 is less than 10% of that observed in the Mg(3P~)-0zreaction. Production of MgO(B'Z+). When Mg('P,) was excited in the presence of N20, strong fluorescence was observed in the 4950-5050-A spectral region, which is due to the MgO(B'Z++X'Z+) transition. No such fluorescence was observed when Mg('Pl) was excited in the presence of any of the other oxidant gases. Unfortunately, the resolution of the monochromator was insufficient for extraction of the initial vibrational and rotational quantum state distributions of the MgO(B'Z+) product. Production of Other Excited States of MgO. Attempts to detect MgO(A'II) when Mg('P1) was excited in the presence of any of the oxidant gases were unsuccessful. No LIF signals were observed when the probe laser was scanned over the MgO(A'n+B'Z+) transition near 6060 A with exactly the same conditions for LIF detection of ~
(11)W.H. Breckenridge and H. Umemoto, J . Phys. Chem., 87,476 (1983).
1806
The Journal of Physical Chemistry, Vol. 87, No. 10, 1983
Breckenridge and Umemoto
MgO(X'2+) via MgO(B'Z+-+X'Z+) emission at -5000 A. The ratio of the transition moments for the B-X vs. the B-A transition has been measuredl2 to be 1.35 f 0.07. From the relative laser powers a t 6060 and 5000 A, it can therefore be estimated conservatively that the yield of MgO(A'II) is less than 40% of the yield of ground-state MgO(X'Z+) in the reaction of Mg('P1) with COz and SOz. (This estimate was made by taking into consideration the wider rotational structure of the B-A vs. the B-X vibrational bands.) Transitions for detection of MgO(a311)were beyond the accessible region of our dye-laser system, and the MgO(b3Z+)state has not yet been detected spectroscopically. When Mg('Pl) was excited in the presence of N20,luminescence was also observed in the 3800-A region. It is possible that this emission is due either to the MgO(CIC-+AIII) or MgO(D'A-+A'II) transitions (or possibly the c3Z+ a311transition), but the strength of the emission and the resolution of the monochromator were not sufficient for a definite assignment to be made. Production of Mg(3PJ). When Mg('P1) was excited in the presence of NO or Oz, Mg(3PJ) was detected by LIF of the 3PJ 'SI transitions in the 5168-5184-A region. Although t,he signals were more than an order of magnitude stronger than those detected for a variety of quenching gases (including COz and SOz), arguments presented earlier13indicate that production of Mg(3PJ) in the quenching of Mg('P,) by Oz and NO is a minor exit channel (branching ratio 50.1) even though the process is spin allowed for these nonsinglet ground-state molecules. Reaction o ~ M ~ ( ~with P J )0,. Excitation of Mg(3P,) by the pump laser is followed by rapid collisional intramultiplet relaxation by helium to form an essentially statistical (5:3:1) mixture of Mg(3Pz),Mg(3Pl),and Mg(3Po)multiplets. Because the multiplet spacings are so small (0.12 and 0.06 kcal/mol), the relaxation cross sections even for helium are extremely large. Equilibration of the J multiplets on the time scale of the pump-probe experiments was confirmed by LIF measurements of the individual 3PJ -* 3S1transitions. Thus, any reaction observed results from an equilibrated mixture of Mg(3P2,1,0) and not just the MgPP,) state initially pumped. When Mg(3PJ)was excited in the presence of 02,MgO(X'Z;') was observed as a product by laser-induced fluorescence. No MgO(X'Z+) was detected when Mg?PJ) was created in the preseiice of COz, SOz, or NO. Production of MgO(X'Z+) in the reaction of Mg(3PJ)with NzO could not be determined because of the presence of MgO(XIZ+)from the reaction of ground-state Mg('So) with N:,O. No fluorescent products were observed when Mg(3PJ)was produced in the presence of any of the oxidant gases, including NzO. Cox and Dagdigiad have also reported that no fluorescent excited MgO states are produced in the reaction of MgPPJ) with NzO. The MgO(X12+-+B'Z+)LIF spectra in the Mg(3PJ)/02 reaction were sufficiently strong for determination of the initial vibrational and rotational quantum states of MgO(X'Z+). Shown in Figure 1 is a typical experimental LIF spectrum of the MgO(X'2+) produced in the reaction of Mg("PJ) with 02.Because the laser bandwidth was not sufficient to resolve the rotational structure of MgO(X'Z'+B'Z') vibrational sequence bands (u" = u'), the initial distribution of MgO(X'Z+) vibrational and rotational states was determined by a trial-and-error procedure
in which the deviations between computer-simulated and experimental spectra were minimized. The simulation procedure was similar to that employed previ~usly.~J' The line positions of the B-X systems were calculated from the spectroscopic data of Lagerqvist and Uhler.I4 FranckCondon factors employed were the average of the values calculated by Ortenberg et al.15 and by Prasad.l6 The "best-fit" computer-simulated spectrum is shown in Figure 2. The initial rotational distribution of MgO(X'Z+, u=O) which resulted in the "best-fit" spectrum of the 0,O band at -5005 8, is shown in Figure 3 (circles). This distribution is very similar to a Boltzmann distribution with an effective "temperature" of 1400 K. Similar initial rotational distributions were assumed for simulation of the other vibrational bands. The "best-fit" initial vi-
(12) T. Ikeda, N. B. Wong, D. 0. Harris, and R. W. Field, J . Mol. Spectrosc., 68, 452 (1977). (13) W. H. Breckenridge and H. Umemoto, J . Chem. Phys., 75, 698 (1981).
(14) A. Lagerqvist and U. Uhler, Ark. Fys., 1, 459 (1949). (15) F. S. Ortenberg, V. B.Glasko, and A. B. Dmitriev, Sou. Astron. (Engl. Transl.),8, 258 (1964). (16) K. Prasad, Proc. Phys. SOC.,85, 810 (1965).
-
-
(0,O)
I
1
I
4970
4980
4990
Wavelength
5000
(i)
Figure 1. Typical experimental LIF spectrum (X'Z' produced in the reaction of Mg(3P,) with 02.
BIZ') of MgO
I
I
4970
-
4980
4990
Wavelength (
5000
A)
Figwe 2. "Best-fit'' computer simulation of spectra such as that shown in Figure 1. See text.
The Journal of Physical Chemlstry, Vol. 87, No. 10, 1983
Reaction of Mg Atom with Oxidants
6
Experimental e
*
e
e e
e
Phase-space
Prior
/
J
Flgure 3. Distribution of rotational quantum states J of MgO(X'Z+, Y =0) which yield the "best-fit'' computer simulation of the 0,O band at 5000-5010 A in Figure 2 (circles). Also shown are the distributions of MgO(X'Z+, v=O) rotational states for the Mg(3P,)-0, reaction predicted by information theory2' (squares)and phasaspace theory2' (triangles). Both of the statistical distributions have been converted to number density ones by dividing by the estimated velocity of the MgO(X'2') state."
TABLE 111: Relative Populations of Vibrational Levels of MgO(XIZ') Formed in the Reaction of M g ( 3 P ~with ) 0 , ,As Compared t o the Predictions of Statistical Models vibrational quantum no.
0 1 2 3
4 a
exptl
this work
1.oo 0.6 i 0.06 0.4 * 0.1 0.2 ?: 0.1
