J. Phys. Chem. 1992, 96, 1296-1301
1296
reaction rate predictions for CH,CH,Cl and CH2ClCH2C1.
kl is shown in Figure 4. The results indicate that the revised SAR expression largely corrects for the original overestimate of the magnitude of kl. The revised model also accurately predicts the temperature dependence of kl and is thus recommended for extrapolation to higher combustion temperatures. These revised group factors do not significantly affect the temperaturedependent
Acknowledgment. The partial support of this work by the National Foundation (Grant CBT 8900750) is Patefully Registry No. Hydroxyl, 3352-57-6; 1,1,2-trichloroethane, 79-00-5.
A Kinetlc Investigation of the Reaction Mg('S) 382-893 Kt
+ N,O over the Temperature Range
John M. C. Plane,* School of Environmental Sciences, University of East Anglia, Norwich, NR4 7TJ. U.K.
Chia-Fu Nien, and B. Rajasekhar Rosenstiel School of Marine and Atmospheric Science and the Department of Chemistry, University of Miami, 4600 Rickenbacker Causeway, Miami, Florida 331 49 (Received: August 27, 1991)
This reaction was studied by two techniques. At temperatures below 650 K, where the reaction is extremely slow, a novel static-flow method was used to measure the rate coefficient relative to the diffusion coefficient of Mg('S) atoms in N2 These measurements were complemented at higher temperatures by employing a two-laser pulseprobe technique to determine absolute rate coeficients; Mg atoms were produced in an excess of N20and N2bath gas by the pulsed multiphoton (193.3 nm)disoociation of MgO and then monitored by timeresolved laser-indud fluorescence spectroscopy at 285.21 nm (Mg(31P1-31S)). The dependence of the rate coefficient is given by k(382 K 4 T 4 893 K) = (6.8 f 1.6) X lo-" exp[-(39.6 1.0) kJ moI-'/RT] an3molecule-I s-', where the quoted uncertainty is 2a. This result is discussed in terms of the reaction o c c u h g both adiabatically and via a nonadiabatic spin transition from the 1'A' to the 13A' surface. Lastly, a comparison is made with the analogous reactions of other group 2 metal atoms.
Introduction The reaction
study, Kashireninov et al.5 estimated the activation energy of reaction 1 to be 27.6 9.2 kJ mol-', later corrected to 48.0 f 8.4 kJ mol-'? This is in good agreement with a recent flow-tube study by Vinckier and Christiaen~,'~ who investigated reaction 1 from 470 to 925 K and obtained an activation energy of 42.6 f 2.9 kJ mol-'. By contrast, in another flow-tube study Meinzer et a1.16 found an activation energy of only 30.1 f 1.6 kJ mol-', although over a lower temperature range (325-450 K). These later estimates of the activation energY&lSJ6 appear to be consistent with a molecular beam studylo which revealed sharp reaction thresholds at 28.8 and 38.4 kJ mol-'. Finally, these experimental observations are in general accord with an ab initio study of reaction 1 by Yarkony? which indicated that there is a significant barrier on the lowest singlet ('A') surface.
*
Mg('S)
+ N20
+
MgO
+ N2
(1)
is one of the class of reactions between group 2 metals and N 2 0 that is of both theoretical and practical interest. These reactions tend to be highly exothermic, so that the metal oxide product is often formed in excited states and this can give rise to strong chemiluminescence. An important theoretical challenge has been to understand the branching ratios for the nascent production of the accessible product electronic states, which involve multiple A major practical interest in these potential energy types of reactions has been as a means of producing large concentrations of metal atoms in excited states, through the further reaction between the metal oxide and CO,ea and the development of chemical lasers? Reaction 1 has been studied by a variety of experimental techniques, including molecular beams,*.*-' diffusion flames,H and flow-tube reactor^.^^-^^ It became apparent from the earliest of these investigations that the reaction is very slow. Indeed, Bourguignon et a1.12did not observe any reaction between Mg('S) and N 2 0at room temperature in a fast flow tube, in accord with a singlmllision molecular beam study of Dagdigians who failed to observe the formation of either the X ' P , a3n, or A'II states of MgO. However, in a later beam study with a much improved detection sensitivity? MgO(X'E+) was detected by laser induced fluorescence (LIF). Breckenridge and Umemoto" also observed the very slow formation of MgO(X'Z+) in a flow tube at 520 K and estimated that reaction 1 has an activation barrier of 60-80 kJ mol-'. More recently, Busener et aI.l4 generated MgO(XlZ+) by mixing Mg vapor and N 2 0 at 1100 K. In a diffusion flame
'
* To whom correspondence should be add&.
The experimental work w a carried out at the Rosenstiel School of Marine and Atmospheric Science, University of Miami.
(1) Alexander, M. H.; Dagdigian, P. J. Chem. Phys. 1978,33, 13. (2) Yarkony, D. R. J . Chem. Phys. 1983, 78,6763. (3) Bourguignon, B.; Rostas, J.; Taieb, G.; Gargoura, M. A.; McCombie, J. Loser Chem. 1986, 6, 15. (4) Bernard, D. J.; Slafer, W. D.; Hccht, J. J. Chem. Phys. l9l7,66, 1012. (5) Kashireninov, 0. E.; Kuznetsov, V. A.; Manelis, G. B. Zh. Fiz. Khim. 1911, 51, 958; Russ. J. Phys. Chem. 1977, 51, 566. (6) Kashininov, 0.E.; Manelis, G. B.; Repka, L. F. Zh. Fir. Khim. 1982, 56, 1030; Rum. J . Phys. Chem. 1982.56, 630. (7) Fenimore, C. P.; Kelso, J. R. J . Am. Chem. Soc. 1950, 72, 5045. (8) Dagdigian, P. J. J . Chem. Phys. 1982, 76, 5375. (9) Cox, J. W.; Dagdigian, P. J. J . Phys. Chem. 1984,88, 2455. (10) Costes, M.; Naulin, C.; Dorthe, G.; Moudden, Z. h e r Chem. 1990, 10, 367. Naulin, C.; Costes, M.; Moudden, Z.; Dorthc, G. J. Phys. Chem. 1991,95, 8244. (1 1) Naulin, C.; Costes, M.; Moudden, Z.; Dorthe, G . Chem. Phys. Lett., in press. (1 2) Bourguignon, B.; Rostas, J.; Taieb, G. J. Ch" Phys. 1982,77,2979. (13) Breckenridge, W. H.; Umemoto, H. J . Phys. Chem. 1983,87,1804. (14) Busener, H.; Heinrich, F.; Hew, A. Chem. Phys. 1987, 112, 139. (15) Vinckier. C.; Christiaens, P. Presented at the Eleventh International Symposium on Gas Kinetics, Assissi, Italy, Sept 1990; paper D1. (16) Meinzer, R. A,; Michels, H. H.;Tripodi, R. Inst. Phys. Conf. Ser. 1985, 72, 193.
0022-3654/92/2096-1296$03.00/00 1992 American Chemical Society
The Mg('S)
+ N 2 0 Reaction
The Journal of Physical Chemistry, Vol. 96, No. 3, 1992 1297
Naulin et al." have shown in a crossed molecular beam study that, at a relative translational energy of the reactants of 0.9 eV, MgO is produced from reaction 1 in the X ' P , a311, and A'II states. Thus, the reaction is nonadiabatic with respect to spin multiplicity. In fact, this nonadiabaticity has also been demonstrated for the reaction Mg(",) N20 MgO(X1Z+,a311,A111) N2 (2) where the ratio of MgO(X12+)/MgO(a311)is 0.77 f 0.22, even greater than the ratio of 0.23 which is predicted statistically.8 Reaction 2 has also been studied by a variety of techniques, d the total though with marked disagreement. Dagdigian8m scattering reaction cross section, um, to be 33.6 f 4.6 A2 for a beam of MgCP) atoms impinging upon a low pressure of N 2 0 at room temperature. Taieb and Broidal' in a fast flow-tube study obtained k2(300 K) = 2.5 X lW1cm3molecule-' s-l, which yields a reaction cross section, a, of about 3.7 A2 from simple collision theory.18 Since um includes both reactive and nonreactive scattering, and the effective colliiional temperature in the beam study was probably around 500 K,19 these results may well be in accord with each other, and are also consistent with the theoretical prediction of Yarkony2 that there is no appreciable barrier on the triplet (1 jA') potential surface. However, two other studies found that reaction 2 is appreciably slower. Bourguignon et al.12 obtained k2(300 K) = 2.2 X cm3 molecule-' s-' from a flow-tube study, and Husain and coworkers,2°.21in a time-resolved laser pumping experiment, determined that reaction 2 had an activation energy of 41.3 f 5.3 U mol-', yielding k2(300 K) = 1.7 X lo-'' cm3 molecule-' s-l, or u, = 3 X lo4 A2. These large discrepancies have not been accounted for. In this study we will report measurements of kl over a significant temperature range, in order to determine the Arrhenius parameters accurately and resolve the current uncertainty in the activation energy of reaction 1. In fact, because the reaction is very slow below 650 K,a new experimental technique had to developed for measuring klin the range l@17-1&14cm3molecule-' s-l. The results obtained, in conjunction with other work on reactions 1 and 2, will then be used to examine the role of nonadiabatic transitions between the singlet and triplet potential energy surfaces which characterize the Mg N20 system. In addition, we will address the discrepancies in the different studies8J2*17*20.21 of reaction 2 referred to above. Finally, the trend in reactivity of the group 2 metals with N 2 0 will be discussed.
+
-
+
+
Experimental Section Reaction 1 was investigated by two techniques. In the temperature range 382-609 K,a new static-flow (SF)method was employed, in which kl was determined relative to the diffusion coefficient of Mg in N2. Between 780 and 893 K,reaction 1 was studied by timaresolved laser-induced fluorescence spectroscopy of Mg atoms following the pulsed photolysis of MgO vapor in an excess of N 2 0 and N2 bath gas (the PLP-LIF method). Both experimental methods employed the same stainleas steel reactor, which has been described in detail Briefly, the reactor consisted of a central cylindrical reaction chamber where the reaction was studied, which was enclosed in a furnace and could be heated to over 900 K. This chamber was at the intersection of four horizontal side arms which were mutually orthogonal. One pair of opposite (Le., collinear) side arms provided the optical coupling for the Mg resonance lamp (SF method) or the lasers (PLP-LIF method) into and out of the central chamber, as well as the means by which flows of N20, diluted in N2, entered the chamber. The third side arm was independently heated to (17) Taieb, G.; Broida, H. P. J. Chem. Phys. 1976, 65, 2914. (18) Smith, I. W. M. Kinetics and Dynamics of Elementary Gas Reactions; Butterworths, London, 1980. (19) Nien, C.-F.; Plane, J. M. C. J . Chem. Phys. 1991, 94, 7193. (20) Humin, D.; Schifino, J. J. Chem. Soc., Faraday Trans. 2 1982, 78, 2083. (21) Humin, D.; Roberts,G. J . Chem. Soc., Faraday Trans. 2 1986,82, 395. (22) Plane, J. M. C. J. Phys. Chem. 1987, 91, 6552.
act as a heat-pipe source of Mg vapor, and the fourth side arm served as an exit for the gas flows to the pump. A fifth vertical side arm provided the coupling for the photomultiplier tube (Thorn EM1 Gencom Inc., Model 9816QB), which monitored the fluorescence signal at 285.21 nm (Mg(3lP)-Mg(3'S)) after passing through an interference filter centered at 285 nm (Microcoatings, Model ML3-285, fwhm = 10 nm). Magnesium metal chips were placed in a tantalum boat in the heat pipe, which was then heated to between 600 and 700 K,so that the concentration of Mg vapor in equilibrium above the solid metal ranged from 1.9 X loL2to 1.1 X 1014atoms cm-3.23 The vapor was entrained in a flow of N2 and carried into the central chamber. When the central chamber was cooler than about 550 K,a significant fraction of this Mg vapor was lost through deposition onto the wall of the heat pipe at the junction with the central chamber. Under these conditions, the heat pipe was run at temperatures closer to 700 K,in order to compensate for this loss and to ensure that sufficient Mg vapor reached the chamber. Once the heat-pipe temperature was set, it was maintained to within i l K,being monitored by an internal thermocouple in contact with the Mg metal. For the SF technique, the Mg vapor in the central chamber was observed by resonance fluorescence at 285.21 nm. A Mg hollow-cathode lamp was focused into the center of the chamber, and a fast photon-counting system (Thorn EM1 Model Aped-I1 emitter-follower and EG&G Ortec ACE-MCS multichannel scaler) was then employed to detect the fluorescence signal. A variable flow of carrier gas through the heat pipe was employed to vary the Mg concentration in the central chamber; this was used to ensure that the fluorescence signal was linearly proportional to the Mg mcentration. It was found that some care was required to limit this amcentration so that the Mg vapor remained optically thin. The steady-state concentration of Mg in the chamber is a balance between input from the heat pipe, reaction with N 2 0 in the gas phase, and deposition onto the walls of the chamber. For an experimental run, the input of Mg vapor and the rate of deposition were kept constant by fming the flow conditions, Le., pmsure, total flow, and turnover (residence) time in the chamber. The steady-state Mg atom concentration in the center of the chamber was then measured as a function of e x w s N 2 0 concentration, relative to the Mg concentration in the absence of N20. Hence, kl was determined relative to diffusion of Mg to the chamber walls. For the PLP-LIF techniq~e,2~ Mg vapor from the heat pipe was mixed with a large excess of N 2 0 in the central chamber, so that, at temperatures above 700 K,all the Mg was rapidly converted to MgO vapor through reaction 1, with no significant loss of N20. Some of this MgO would have formed gas-phase clusters," although short turnover times of the gas mixture in the central chamber were employed (less than about 500 ms) in order to minimize the loss of MgO due to cluster formation and condensation on the reactor walls. This mixture of monomers and clusters was then photolyzed using an ArF excimer laser (Questek, Model 2110, pulse energy 40-70 mJ). The excimer beam was shaped by a system of lenses and a pinhole, and then focused into the reactor. The resulting Mg('S) atoms were probed at 285.21 nm (Mg(3lP1)-Mg(3lS)) using a nitrogen-pumped dye laser M (Laser Science Inc., Model VSL-337; laser dye 1.5 X Rhodamine 6G in methanol, bandwidth = 0.01 nm), frequencydoubled with a BBO crystal ( h a d Corp.). In these experiments, the excimer and dye lasers were arranged to be collinear. The diameter of the dye laser was carefully maintained to be about 80% that of the excimer using a beam expander. The timeresolved LIF signal was then recorded using a gated integrator (Stanford Research System, Model SR250) interfaced to a microcomputer. Mstaiab. Nitrogen, 99.9995% purity (Liquid Carbonic), was used without further purification. N20,99.99% pure (Matheson, (23) JANAF Thermochemical Tables, 3rd 4.;Chase, Jr., M. W., hvies, C. A., Downey, Jr., J. R.,Frurip, D. J., McDonald, R. A., Syverud, A. N., Eds. J . Phys. Chem. Ref. Data 1985, 14. (24) Ziemann, P. J.; Castleman, Jr., A. W. J. Chem. Phys. 1991,94,718. (25) Plane, J. M. C.; Nien, C.-F. J . Phys. Chem. 1990, 94, 5255.
1298 The Journal of Physical Chemistry, Vol. 96, No. 3, 1992
Ultra High Purity), was degassed at 77 K before use. Mg metal chips, 99.95+% (Aldrich), were heated in the heat pipe at 600 K for about an hour prior to kinetic experiments.
Plane et al. 300.
(a)
0382 K a442 K A510 K
Resulk3 Tbe Static-FlowTedudque. This method was designed to study the gas-phase reaction of a refractory species that is slow cm3 molecule-' s-'), so that diffusional loss to the walls of the reactor can be made comparable to chemical loss in the gas phase. In the present system, the steady-state concentration of Mg vapor in the central chamber, [Mg],, is given by d[MgI /dr F - kl IN201 [Mglss - kdiff[Mglss= 0 (3) where F is the rate of input of Mg vapor from the heat pipe and kdin is the rate of diffusional loss of Mg vapor by deposition onto the walls of the chamber. Use of eq 3 assumes that two conditions are met: first, that the loss of Mg vapor by pumping into the exit side arm of the reactor is much smaller than either chemical reaction or deposition on the walls, and second, that the Mg vapor is well mixed in the central chamber. Both of these conditions were met by ensuring that the turnover time in the central chamber was at least a factor of 20 longer than l/kdiff. Assuming that the mass accommodation coefficient of Mg atoms on the chamber walls is greater than about 0.5, kafi is described by the solution of the master diffusion equation for cylindrical geometery26 kdfi = [(*/02 + (2.41/r)21D(Mg-N2)/p
(4)
where the cylinder has dimensions 1 and r, p is the pressure, and D(Mg-N2) is the binary diffusion coefficient of Mg in N2 (the mixture of N 2 0 in N2 is too dilute for diffusion of Mg in N 2 0 to be significant in this experiment). The central chamber is cylindrical (r = 3 cm and 1 = 8 cm), and we have assumed that the holes in the chamber walls where the side arms are attached, which are only 4.8% of the total surface area of the cylinder, do not significantly affect the applicability of eq 4. D(Mg-N2) does not appear to have been measured, and so we estimated this by comparison with the binary diffusion coefficient of Na in N2,which has been determined recently by three group^^^"^ who are in good agreement. Silver27and Ager and Howard%used fast flow-tube 17)(T/ reactors to obtain D(Na-N2,320-698 K) = (165 300)'.79*0.02cm2 Torr s-l, and D(Na-N2,300 K) = (144 f 14) cm2 Torr s-l, respectively. Husain et al.29 obtained D(Nacm2Torr s-' using N2,570-1016 K) = (132 f 44)(T/300)'.52M.25 the flash photolysis/timemlved resonance absorption technique. Combining the individual measurements of D(Na-N2) from these studies, we obtain D(Na-N2,300-700 K) = (155 21)(T/ 300)(1.67*0.27) cm2 Torr s-l, where the stated uncertainty is 2u. The ratio of D(Mg-N2)/D(Na-N2) was then calculated using Chapman-Enslcog theory,mwhere the binary diffusion coefficient is given, to first order, by D12/(cm2Torr s-') = 1.997[p(M1 + M2)/2M1M2]lI2/ [ U ~ ~ ~ ( Q ~ ~ T12*))] ('*')*( (5)
*
*
where M 1and M2 are the molecular masses of the two species in amu; TI2*is the reduced temperature kT/t12; Q12('*')*(T12*) is the reduced collision integral;30and we have assumed that the interaction between species 1 and 2 is described by the two-parameter Lennard-Jones potential, = 4el2[(~12/r)'~ - (.~/r)~l
(6) In order to calculate eI2 and u12for Mg or Na interacting with N2, we applied the combination rules,3o namely, u12= (ull + u22)/2 and c12 = (cIIe22)1/2, Values of u l l and e l l for Mg or Na V12W
(26) Mitchell, A. C. G.; Zemansky, M. W. Resonance Radiation and Excited Aroms; Cambridge University Press: London, 1934. (27) Silver, J. A. J . Chem. Phys. 1984. 81, 5125. (28) Ager,, J. W.,111; Howard, C. J. J . Chem. Phys. 1986, 85, 3469. (29) Husain, D.; Marshall, P.; Plane, J. M.C. J. Chem. Soc., Faraday Trans. 2 1985,81, 301. (30) Hirschfelder, J. 0.;Curtiss, C. F.; Bird, R. B. Molecular Theory of Gases and Liquids; Wiley: New York, 1954.
A547 K
0 609 K 100
[NzO]
/
molecules cm-3
/
molecules cm-3
A893 K (6.4 torr)
00
50E15
[N20]
1.OE16
1 .' 116
Figure 1. (a) The SF method: plots of the pseudo-first-order rate coefficient k', defined as kdi&([Mglo/[Mgjar)- l), against [N,O] (see text); [N2] ranged from (1.6 - 10) X 10'' ~ m - ~(b) . The PLP-LIF method: plots of the pseudo-fust-order rate coefficient k'against [NzO]; the pressure of the Nz bath gas is indicated in parentheses at each temperature. The solid lines in (a) and (b) are linear regression curves through the data at each temperature.
were derived from spectroscopic data on the metal dimers Na2 and Mg2,23and uzzand eu for N2 were obtained from second virial coefficient meas~rements.~~ This yields u12= 3.63 and 3.27 A, and e12/k = 204 and 782 K, for Mg and Na, respectively. D12 was then calculated using eq 5 for each of the metals, and the experimental value of D(Na-N2) was then multiplied by the ratio D( Mg-N2) /D(Na-N2) to obtain D( Mg-N2). If [Mglois the steady-state Mg concentration in the absence of N20, Le., when the input flow from the heat pipe is balanced only by deposition onto the chamber walls, and if the total flow and pressure are kept constant while the N 2 0 concentration is varied, it follows from eq 3 that [MglO/ [Mglsa = kl [N201/kdiff + (7) Hence, a plot of kdin([Mgl0/[Mg], - 1) versus [N20] should be linear, passing through the origin with a slope of k l . Such plots are illustrated in Figure la. The linear regression lines, fitted to the data at each temperature, all pass through the origin within their 2u uncertainties. The resulting values of kl are listed in Table I, along with the pressures in the central chamber at which each kl was measured. The values of D(Mg-N2), calculated at each experimental temperature, are also given in Table I. The quoted uncertainties of klinclude both the 2u uncertainties from the linear regression fits to the plots in Figure la, and the uncertainties of kdp At the temperature extremes at which the SF method was employed, Le., 382 and 609 K, kl was determined over a range of pressure. Inspection of Table I demonstrates that k, is independent of pressure, as expected. We believe that this, together with the form of the plots in Figure la, establishes that eqs 3,4, and 7 correctly characterize the competition between gas-phase chemical reaction and diffusion-controlled deposition, upon which the SF technique is based. The lower temperature limit of the SF method resulted from kl being so slow below 382 K that two problems arose when attempting to measure kl relative to kdm,since these terms need to be of comparable magnitude. First, very large concentrations
+ N 2 0 Reaction
The Mg(lS)
1"he Journal of Physical Chemistry, Vol. 96, No. 3, 1992 1299
TABLE I: Experimental Determinations of k(Mg + N20)as a
T / K
Function of 7" ~~
~
1E-11
The Static-Flow Method
1000
700
500 0
25.5 30.0 35.0 40.0 12.8 10.0 11.7 10.0 15.0 20.0 25.0
382 382 382 382 442 510 547 609 609 609 609
T/K 780 780 830 893
354 354 354 354 440 541 598 697 697 697 697
** 2323 23 * 234678 97 133 133 133
* 133
2.31 0.20 2.76 0.25 3.02 0.35 2.81 0.27 9.32 f 1.18 57.4 10.4 106 19 352 f 83 388 108 290 78 382 108
* *
The Pulsed Laser Photolysis/LIF Method press./Torr k/ lo-" cm3 molecule-' s-' 7.2 1.14 0.04 10.0 0.980 f 0.058 12.1 2.63 0.01 6.4 3.37 0.19
*
"Quoted uncertainty is 2a. bkdirris then equal to 0.800D(MgN2)/p, from eq 4.
of N 2 0 had to be employed, in which case the N20/N2mixture in the reactor was no longer dilute enough for diffusion of Mg through N 2 0 to be ignored. Second, we attempted to use higher pressures in the reactor in order to decrease kdm,but found that this caused too large a fraction of the Mg vapor to be lost through deposition on the cool walls of the heat pipe, close to the entrance of the cold central chamber. The upper temperature limit was caused by the background scattered light signal, arising from black-body radiation from the hot reactor surface, becoming substantially larger than the Mg atom resonance fluorescence signal, even though the interference filter has a transmission/ blocking factor of about 3000: 1. The PLP-LIFMethod. The yield of Mg atoms from the photolysis of MgO vapor, measured by LIF at 285.21 nm about 5 ps after the excimer laser pulse, was shown to have an approximately quadratic dependence on the excimer laser fluence. This indicates that at least a two-photon process is occurring. Furthermore, we observed Mg(3lP-3lS) emission at 285.21 nm during the excimer laser pulse itself, indicating that Mg(3lP) is a nascent photolysis product. Assuming that singlet spin multiplicity is preserved during the photodissociation, then the process M o o= MgO(XIZ+) Mg(3lP) O(lD) 944 25 kJ m o P 23 (8) requires the absorption of at least two 193.3 nm photons (1240 kJ mol-'). We have previously observed identical behavior for the photolysis of both CaO and BaO at 193 nm.1992sThe O(lD) will be quenched very rapidly by the relatively large concentration of N20,31and a small proportion will be physically quenched to O('P).19 We assume that the production of other excited states of Mg (e.g. 3PJ)was not important in this experiment. Such states would only interfere in the Mg(lS) kinetics if they were slowly quenched to the ground state. However, chemical reaction of excited Mg atoms with N 2 0 is more likely than quenching,8J2J8*20s21 and, indeed, we did not observe the production of Mg(lS) at longer times after the excimer laser pulse. Under the conditions of the present study, where the concentration of NzO was always well in excess of the concentration of Mg atoms resulting from the pulsed photolysis of MgO vapor, the loss of Mg atoms should be d d b e d by the pseudo-fmt-order decay coefficient, k', where k' kdifn ki[NzO] (9) +
+
+
(31) Heidner, R. F.; Humin, D. Inr. J . Chem. Kinet. 1973, 5, 819. (32) Futerko. P. M.;Fontijn, A. J. Chem. Phys., submitted for publication. (33) Fontijn, A,; Zellner, R. In Reacrions of Small Transienr Species; Fontijn, A., Clyne, M.A. A., as.Academic: ; London, 1983.
Kashireninov et aI
m
3
Vinckier and Christioens 1E-16
300,
This work (relative method)
0 This work (PLP/LIF method)
1E-12 ~
400
- Meinzer et aI
\
I300 The Journal of Physical Chemistry, Vol. 96, No. 3, 1992
Plane et al.
product statesDare shown to scale (with the exception of the Mg+ + N20-(22+) surface); the energies of the intermediate chargetransfer complexes and various surface crossings are qualitative. Note, however, that Yarkony2 has calculated that the bent charge-transfer complex Mg+-N20-(2A') lies in a shallow local minimum on the 1'A' surface, 59.7 kJ mol-' below the reactants. All the surfaces of the incoming reactants are wumed to undergo avoided crossings with the relevant ionic surfaces. There is evi d e m 2 that these crossings tend to occur close to the transition-state region, not as shown in Figure 3, where we have s e p arated the crossings for the sake of clarity. Consider the singlet surfaces first. The lowest 'A' surface of the incoming reactants will undergo an avoided crossing with the 'A' surface arising from Mg('P1) N20, and then undergo a second avoided crossing between the ionic charge-transfer intermediates and the products. A completely adiabatic reaction under C, symmetry will thus proceed along the lowest 'A' athbatic Nz. In surface, correlating Mg('S) + N20 with Mfl(XIZ+) surface correlates MgCP,) N20 a similar fashion, the lowest with MgO(a311) + N2. However, as we have seen in the IntroFigure 3. Adiabatic correlation diagram under C, symmetry of the duction, reactions 1 and 2 both produce the X'Z+,a311, and A'II reaction between Mg and N,O,including an intermediate chargetransfer states of Mg08J1so that these reactions must be nonadiabatic complex. The relative energies of the reactants and the products are with respect to spin. Bourguignon et aL3 have argued that the shown to scale. All energies are taken from ref 23. Crwing points where transition from the 13A' to the 1'A' surface may m r through nonadiabatic spin transitions can occur are circled. surface crossing in the entrance channel, as well as through with the diffusion flame study of Kashireninov et a l . S v 6 is also much spin-orbit interaction in the charge-transfer complex or exit better than in the cases of the analogous reactions of Ca25and Channel, where the singlet and triplet forms are likely to be close Ba.19 As we stated p r e v i ~ u s l y , the ' ~ ~diffusion ~~ flame technique in energy ( F i e 3). In terms of reaction 1, the triplet channel n d y relies on the extraction of the rate constant by modeling will be indistinguishable kinetically unless there is a probability a complex set of reactions. Because kl is so much slower than of the nonadiabatic transition occurring in the entrance channel the analogous reactions of Ca and Ba (see below), reaction 1 is w and affecting the reaction energy barrier. consideration of F probably rate-determining in the diffusion flame and kl can 3 indicates that the barriers of the triplet and singlet paths in the therefore be determined by this method. entrance channel for reaction 1 will be determined by the energetic There is also good agreement between the present study and accessibilities of the Mg(3P,) and Mg(lPl) states, respectively. that of Meinzer et a1.I6 over the overlapping temperature range This predicts that the barrier of the triplet path will be lower. (382-450 K), although those workers obtained a smaller activation In fact, Costes et al.1° have established that reaction 1 has cm3 energy (30.1 kJ mol-') and preexponential term (5.1 X threshold energies at 28.8 and 38.4 kJ mol-', which they concluded molecule-' s-I). Indeed, a combination of the different studies are the barriers for reaction on the lowest 3A' and 'A' surfaces, illustrated in Figure 2 suggests that there may be curvature in respectively. Such a dual-path model for the reactions between the Arrhenius plot of reaction 1, as in the case of Ca + N20.25 the group 2 atoms and N20has also recently been put forward Inspection of eq 10 reveals that the preexponential term is about by Futerko and F ~ n t i j n .From ~ ~ simple collision theory,18*33 the a factor of 2 smaller than would be expected for a simple bimoactivation energy measured over the temperature range Tl to T2 lecular reaction. This could be explained if there is slight nonis equal to the energy barrier plus 0.5RT12,where R is the gas Arrhenius curvature over our experimental temperature range (see constant and T12= (T1T2)1/2.Thus, the activation energies below) * corresponding to reaction along the triplet and singlet paths'O The ab initio study of Yarkony2 showed that reaction 1 is should be about 31.2 and 40.8 kJ mol-', respectively. The acfavored by near-collinear attack of the Mg atom on the oxygen tivation energy of 39.6 f 1.6 kJ mol-' determined in this study end of the N20. This leads to a short-range charge transfer from therefore largely describes reaction on the singlet surface, whereas the Mg to the lowest unoccupied 3a (loa) orbital of N20, forming the activation energy of 30.1 f 1.6 kJ mol-' measured by Meinzer the initially linear (211) state of N20-.34 This charge transfer et a1.16 may reflect the dominance of the triplet path at lower is the crucial step for successful reaction: because of the small temperatures. If k1(Q is expressed as the sum of two Arrhenius electron affinity of N 2 0 (the adiabatic affinity is 0.39 eV and the terms representing the two reaction paths, with activation energia vertical electron affinity is neguriue2) and the relatively large calculated from the threshold energies'O (see above), then a fit ionization energy of Mg('S) (7.65 eV39, this reaction cannot to the data from our study yields proceed by an electron capture or "harpoon" m e c h a n i ~ m . ~ . ~ ~ J ~kl(382 . ~ ~ K < T < 893 K) In fact, in a collinear collision there is poor spatial overlap between exp[-(31.2 kJ mol-')/RT] (8,3?,6J) X (8.5?#) X the Mg 3s orbital and the 3a orbital of N20, so that the probability lo-'' exp[-(40.8 kJ mol-')/RT] cm3 molecule-' s-' (11) of a charge transfer is very smallF5 However, mixing the Mg('S) with the excited 'P1 state increases the orbital overlap between This fit is somewhat better than the single Arrhenius fit in eq 10 the reactants and hence facilitates the charge transfer. Figure ( x 2 = 1203 and 2280, respectively). The point here is that while 3 is a correlation diagram for the Mg + N20system, indicating there is no evidence of curvature in our experimental data, and the low-lying singlet and triplet surfaces which connect the thus no reason for recommending eq 11 over eq 10, the dual-path reactants and products through the intermediate charge-transfer is certainly compatible with our data. According to mode110*32 complexes. This diagram is based on our previous work on Ca this model, the preexponential factor of the first Arrhenius term + N20?5 Yarkony's theoretical study? and on the study of in eq 11, which describes the triplet path, should contain a factor Bourguignon et al.3 The relative energies of the reactant and describing the probability of the nonadiabatic transition from the llA' to the 3A' surface in the entrance channel (Figure 3). This (34) Bardsley, J. N. J . Chem. Phys. 1969, 51, 3384. as the ratio of the first preexponential factor probability, ex@ (35) Handbook of Physics and Chemlsrry, 65th 4.Weast, ; R. C.,Ed.; to the sum of both preexponential factors in eq 11, is then 0.010 CRC Press: Boca Raton, FL, 1985. f 0.005, and is small enough so that significant curvature does (36) Levy, M. J . Phys. Chem. 1989, 93, 5195. not occuf in the Arrhcnius plot wer our experimental temperature (37) Jalink, H.; Harren, F.; Van den Ende, D.; Stoke, S. Chem. Phys. range. Dagdigiad has shown that the branching ratio for the 1986,108, 391.
+
+
+
+
The Mg('S)
+ N 2 0 Reaction
'he Journal of Physical Chemistry, Vol. 96, No. 3, 1992 1301 T / K
1 .DE-9
1000
500
400
300
r
250
"Y I
1.OE-10 c
-
'm
:-' .
1.OE-11 1.OE-12
I
l . O E - 1 3 W
_ . 0 1 .OE-3
2.OE-3
3.OE-3
4.OE-3
1/T (K-1)
Figure 4. Arrhenius plots over the temperature range 200-1000 K for the reactions of the group 2 metals with N20: Mg + N 2 0 (this study); Ca + N 2 0 (ref 25); Ba + N 2 0 (ref 19).
formation of Mg0(X1Z+)/Mg0(a311)in reaction 2 is 0.77 f 0.22, Le., the probability of the nonadiabatic transition from the 13A' to the 1'A' surface is 0.44 f 0.07. This higher probability is not inconsistent with our result above, so long as the most probable point for the transition is between the charge-transfer complexes, or in the exit channel (see Figure 3). In fact, non-Born-Oppenheimer interaction^^^ between the close-lying potential curves of MgO(X'Z+) and MgO(a311) are thought to enhance such transitions.s In the Introduction we described the discrepancy that exists concerning reaction 2. Husain and Roberts2' found an activation energy of 41.3 f 5.3 kJ mol-', which is, surprisingly, as large as the activation energy of reaction 1. By contrast, Yarkony's ab inito investigation2of the 13A' surface indicated an absence of a bamer for reaction 2, in accord with the MgO(a311) vibrational distribution obtained by Bourguignon et ale3and the large reaction cross section measured by Dagdigiana8 In the experiment of Husain and Roberts?' Mg vapor was mixed with a flow of N20/He in a slow flow through a heated reactor. Mg atoms were pumped to the 3P, state, and the subsequent reaction was monitored by both atomic Mg(3Pr1S) and molecular MgO(B'Z+-X'Z+) emission, thereby confirming that reaction 2 was being observed. The present study of reaction 1 demonstrates that in such a reactor, at temperatures in excess of 600 K, the Mg('S) vapor and N 2 0 would have reacted together rapidly compared to the residence time of the gas flow in the reactor. This removal of N 2 0 possibly explains why the values of k2 measured in that study2' were much slower than determined elsewhere.*J2J7 Figure 4 is an Arrhenius plot comparing the present study of reaction 1 with our previous work on the analogous reactions of CaZ5and Ba.I9 Reaction 1 is strikingly slower than the other reactions. We have argued above that the height of the reaction (38) Ikeda,T.; Wong, N. B.;Harris,D. 0.; Field, R. W. J. Mol. Spectrosc. 1977, 68, 452.
300
600
900
1200
Promotion Energy / kJmol-'
Figure 5. Plots of the reaction energy threshold versus promotion energy for the group 2 metal atoms + N20. The energy thresholds for the Mg reaction are from ref 10; otherwise, they are calculated by subtracting 0.5RT12 (see text for definition) from the experimental activation energies for Ca (ref 25) and Ba (ref 19). The promotion energy is defined in two ways: (m), the excitation energy of the lowest-lying triplet state, labeled (3), or lowest-lying excited singlet state, labeled (I), of the metal atom; (O), this electronic energy plus the ionization potential of the metal atom. These energies are taken from refs 23 and 35. For Ba, the singlet and triplet excitation energies are averaged.
energy barrier is determined by the energetic accessibility of the excited open-shell ID or 'P states of the metal atom. In addition, there is the small probability of a nonadiabatic spin transition onto the 13A' surface, where the height of the barrier is then determined by the accessibility of the excited 3D or 3P states. Following Futerko and Fontijn,32 we have correlated the energy barrier for each metal-N20 reaction against the promotion energy for that metal atom. This promotion energy was calculated in two ways. First, as the excitation energy of the metal atom to its lowest-lying singlet or triplet state; and second, as the sum of this excitation energy and the ionization potential of the metal atom. As illustrated in Figure 5 , the reaction barrier shows a strong correlation with both types of promotion energy. In particular, the lower energy barriers of the Mg and Ca reactions correlate well with their respective triplet promotion energies. Finally, we have discussed previo~sly'~3U5 the role of vibrational excitation of N20, in its low-frequency bending modes, in promoting these types of reactions. In the case of reaction 1, vibrationally-excited N 2 0 probably enhances mixing of the 'S and lP states of Mg, by reducing the symmetry of the favored collinear approach of the reactants,= and also facilitates the charge transfer from the Mg atom to the N20.22 However, any contributions to the activation energy from a Boltzmann term describing the equilibrium population of vibrationally-excitedN2OL9JUS will be overshadowed in this case by the large electronic barriers on both the singlet and triplet surfaces. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for support of this research. Registry NO. Mg, 7439-95-4; NZO, 10024-97-2.
