6552
J. Phys. Chem. 1987, 91, 6552-6557
A Kfnetk Study of the Reaction Li -k N,O: Temperature Range 363-900 K
Non-Arrhenius Behavior over the
John M.C . Plane Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida 33149- 1098 (Received: May I , 1987; In Final Form: July 13, 1987)
A kinetic study is presented of the reaction between lithium atoms and nitrous oxide over the temperature range 363-900
K, using a new experimental system. Li atoms are produced in an excess of NzO and He bath gas by pulsed photolysis of either LiI or LiCl vapor. The concentration of the metal atoms is then monitored in real time by the technique of laser-induced fluorescence of Li atoms at X = 670.7 nm using a pulsed nitrogen-pumped dye laser and box-car integration of the fluorescence signal. Second-order rate constants for the title reaction have been measured at T = 363, 41 1, 474, 545, 600, 647, 700, 800, and 900 K. When this data is plotted in the standard Arrhenius form, a strong departure from linearity above 600 K is evident with an activation energy increasing with temperature. The best analytical description of this temperaturedependence over the temperature range studied is given by k l ( T ) = (2.4 0.5) X 10-llT1/Zexp(-(1468 f 137)/T) + (7.9 4.7) X 10-10T1/2exp(-(4157 f 540)/T). The first term of this expression describes a low-temperature Arrhenius behavior similar to that observed by other workers for the analogous reaction of sodium atoms. We interpret the form of the second term as describing the participation in the reaction at temperatures above 600 K of highly vibrationally excited NzO, which enables the reaction to proceed by a close-range charge-transfer mechanism. This significantly enhances the reaction cross section. A simple two-channel model is discussed which accounts for the observed temperature dependence.
*
Introduction The reactions of group IA and IIA (groups 1 and 2)47 metal atoms with NzO is a class of reactions that has received much attention for a variety of reasons. One area of interest has arisen from the fact that these reactions are usually highly exothermic and the metal oxide product is often formed in excited states, giving This property has been rise to strong chemilumine~cence.~~~~~~~~ exploited as a spectroscopic marker in molecular beam studies of these reaction^.*^^^^^ There has been some disagreement over the chemiluminescent yields of certain of these reactions studied in molecular beams, which has resulted from widely differing estimates of the total reaction cross sections.2a,b Against the background of the present work, it should be noted that accurate measurement of the thermal rate constants over a broad temperature range permits an independent experimental determination of the absolute reaction cross section and such studies therefore complement work with molecular beams. Another area of interest has been the observation that the oxygen-abstraction reactions of metal atoms with oxidants like NzO or COzare important in combustion processes: the critical influence of the alkali elements and their oxides and hydroxides in high-temperature systems has long been known and ~ t u d i e d . ~ , ~ Furthermore, there has been an interest in the construction of a chemical COzlaser based on CO-NzO combustion catalyzed by Na metal vapor through an NaO intermediate: which prompted an early study of the reaction N a + NZO.’ Finally, the oxides of lithium, sodium, and potassium are thought to play an important role in the chemistry of these alkali metals in the upper atmosphere at about 90 km,where the source of the metal atoms is ablation from meteorite^.^,^ The origin of the component of the nightglow a t 589 nm arising from D-line emission from Na(2P) atoms was first postulated by Chapmanlo (1) Pfeifer, J.; Gole, J. L. J. Chem. Phys. 1984, 80, 565. (2) (a) Wren, D. J.; Menzinger, M. J. Chem. Phys. 1975,63,4557; Discuss. Faraday 1979,67,97. (b) Dickson, R.; George, S. M.; Zare, R. N . J. Chem. Phys. 1977,67, 1024. Cox, J. W.; Dagdigian, P. J. J. Chem. Phys. 1983, 79, 5351. (3) Gonzalez Urena, A. Adu. Chem. Phys. 1987, 65, 213. (4) Jensen, D. E.; Jones, G. A. Combust. Flame 1978, 32, 1. (5) Husain, D.; Plane, J. M. C.;Chen, Cong Xiang J. Chem. Soc., Faraday Trans. 2 1985, 81, 561. (6) Fenimore, C. P.; Kelso, J. R. J . Am. Chem. SOC.1950, 72, 5045. (7) Walker, R. E.; Creeden, J. E. Combust. Flame 1973, 22, 39. (8) Thomas, L.; Isherwood, M. C.; Bowman, M. R. J. Atmos. Terr. Phys. 1983, 45, 587. (9) Swider, W. J . Geophys. Res. 1986, 91, 6742.
c.
*
to result from the reaction of NaO with 0 atoms. The metal oxides are also central to the processes which are thought to govern the distribution of these metals between the free atoms and sink compounds such as the superoxides and hydroxide^.^,^ In order to study reactions of the alkali metal oxides which are of atmospheric interest, the reaction between alkali atoms and N z O is a particularly convenient method for preparing the metal oxides cleanIy.11J2 There are thus several important reasons for measuring the thermal rate coefficients of this class of reactions over as wide a temperature range as possible. Here we present an investigation of the reaction Li + NzO LiO Nz (1)
-
+
from near room temperature (363 K) up to the decomposition temperature of N 2 0 in our stainless steel reactor ( T > 950 K). To the best of our knowledge, no previous studies of this reaction have been reported. By contrast, the reaction Na + NzO has been studied by a number of investigators using different techniques. These have included diffusion flames,13 flash photolysis and time-resolved resonance absorption spectro~copy,’~ and fast flow tubes employing resonance fluorescence d e t e c t i ~ n . ~ JOnly ~ J ~ the study by Husain and Marshall14 has involved measurements at over 600 K. A major advantage of the new experimental system that is described in this paper is the ability to measure reaction 1 over a broad temperature range (540 K) by a single experimental technique, an important consideration when making a detailed investigation of the temperature dependence of a reaction. In the case of reaction 1 there is the opportunity to observe the effect on the thermal rate coefficient of vibrational excitation in the reactants: above 600 K, N 2 0 becomes significantly populated (>43%) in its low-frequency bending mode.I6 The effect of vibrationally excited reactants on the rates of reactions of this type has recently been discussed and reviewed by Fontijn and Zellner.” ~
~~
~
~ _ _ _ _
(10) Chapman, S. Astrophys. J . 1939, 900, 309. (1 1) Plane, J. M. C.; Husain, D. J . Chem. SOC.,Faraday Trans. 2 1986, 82, 2047. (12) Ager 111, J. W.; Talcott, C. L.; Howard, C. J. J . Chem. Phys. 1986, 85, 5584. (13) Bawn, C. E. H.; Evans, A. G. Trans. Faraday SOC.1937, 33, 1571. (14) Husain, D.; Marshall, P. Combust. Flame 1985, 60, 8 1. (15) Silver, J. A.; Kolb, C. E. J . Phys. Chem. 1986, 90, 3262. (16) Herzberg, G. Molecular Spectra and Molecular Structure II. In-
frared and Raman Spectra of Polyatomic Molecules; Van Nostrand Reinhold: New York, 1945.
0022-3654/87/2091-6552$01.50/0 0 1987 American Chemical Society
The Li
,
+ N 2 0 Reaction
The Journal of Physical Chemistry, Vol. 91, No. 26, 1987 6553
BOX-CAR A V E K A G I N G SYSTES
I
LIF Signal Charging
Unl
Flash Lamp
Pulse 1 Delay Generator
-
pre-triggez Cati"g
A known mixture of N20in He is flowed from the gas-handling line to the reactor, where it enters the vessel through a side arm as shown in Figure 1. The concentration of N 2 0 in the flow is accurately metered by mixing two flows, one of pure H e and the second of N,O/He, at controlled flow rates (MKS Model 247B). The N,O/He mixture is made up in an all-glass vacuum system, and all pressures are measured with an independently calibrated capacitance manometer (MKS Barratron Model 226A- 1). The total pressure in the reaction vessel is controlled by a needle valve on the exit line to the pump, so that, by altering the total mass flow from the gas-handling line, or the extent to which this needle valve is open, the residetlce time of the gas mixture in the reactor can be altered while maintaining a constant total reactor pressure. Typically, the total mass flow rate was varied from 50 to 100 sccm, so that the average residence time in the central chamber ranged from about 5 to 20 s. The flow entering the side arm then entrains LiCl or LiI vapor which is in equilibrium above a sample of the solid/molten salt either contained in a tantalum boat or on the wall of the side arm, before flowing into the central chamber. This section of the side arm is independently heated by a heating element wound around the stainless tube, which can heat and maintain the temperature of the sample of the lithium salt up to 900 K. When the central chamber is at a temperature below about 500 K, then essentially all the lithium halide vapor flowing into the chamber will condense on the walls.20 In order to maintain a reasonable concentration of the vapor in the middle of the chamber, where it provides the photolytic precursor of lithium atoms, the temperature of the side arm is kept at 850 K (pLiI = 1.8 X l O I 5 cm-320)and the gas flow through the reactor is sufficiently rapid that about 0.005% of the lithium iodide vapor (assuming a sticking coefficient of unity on the side arm and reactor walls and a rough estimate of the diffusion coefficient of LiI in H e taken from ref 12) reaches the reaction volume and is sufficient for the flash photolysis/LIF experiment. The lithium halide vapor is photolyzed by a low-powered flashlamp (EG&G, Model FX193U), which has a sapphire end-window allowing transmission in the vacuum ultraviolet, and is characterized according to the manufacturer by a black-body temperature of 16 000 K. We have coupled this flashlamp to a 10-pF fast-discharge storage capacitor, permitting a maximum discharge energy (at 1 kV) of 5 J. The maximum pulse energy was only used in the low-temperature experiments when little of the precursor was available in the center of the reactor. For work above 600 K, a flashlamp discharge energy of less than 1 J was required. The half-width of the light pulse from this lamp is about 15 ps, which makes it suitable for carrying out kinetic studies after about 100 ps. The output from the flashlamp is collected into a parallel beam by a Suprasil lens (f=2.5 cm)at the focal distance in front of it and is then loosely focused into the middle of the central chamber by a second Suprasil lens (f = 20 cm) on the end of the reactor side arm (see Figure 1). Both LiI and LiCl have large photolysis cross sections above 200 nm,21so that vacuum optics are not required. The lithium atoms resulting from the photolysis of the lithium halide vapor are then monitored by the LIF technique at X = 670.7 nm (Li(2PJ)-Li(2S1/2),gA,, = 1.2 X lo8 s - I ~ ~ ) , using a nitrogen-pumped dye laser as the probe (Laser Science Inc, Model VSL-337). This dye laser system has a stated output of about 15 pJ, resolution 0.01 nm, and pulse width 3 ns. The dye that was used in the present work is DCM (Laser Science Inc). The laser beam is expanded to a radius of about 3 mm in the reactor, in order to avoid the possibility of any saturation effects. The
i "'1 U High Volrage
Fover Supply
Figure 1. Experimental arrangement for studying the reaction Li + N20 by the method of time-resolved laser-induced fluorescence of Li atoms at X = 671 nm (Li(*P,)-Li(*S,,,)), follawing pulsed photolysis of lithium halide vapor in an excess of N20and He; L1, L2: Suprasil lenses, f = 2.5 and 20 cm; F1,F2: main and side-arm furnaces; P photomultiplier and gating circuit; R: stainless steel reactor; E: ground glass end-windows set at the Brewster angle.
Experimental Section Reaction 1 has been investigated by the technique of timeresolved laser-induced fluorescence spectroscopy of Li atoms a t 671 nm (Li(22PJ)-Li(22Sl,2)), following the pulsed photolysis of LiI or LiCl vapor in an excess of N20 and H e bath gas. This is an extension of an earlier technique in which the concentration of the alkali metal atoms was followed by resonance absorption s p e c t r o s ~ o p y . ~ ~ JThe * J ~experimental arrangement is shown in Figure 1. Since this is a newly constructed apparatus, a fairly detailed description follows. The reaction vessel is fashioned out of stainless steel (304) to facilitate working at high temperatures and to present a relatively inert surface to the hot reagent gases. It comprises a central cylindrical chamber with its axis vertical ( r = 3 cm; 1 = 8 cm) with an arm directly above it to provide an optical coupling for measuring the LIF signal from the center of the chamber below. The central chamber is also at the intersection of a stainless steel cross (tube radius = 0.9 cm) in the horizontal. The two orthogonal pairs of tubes enter the central chamber half-way along the vertical side of the cylinder. One pair of opposite arms provides an optical axis for the probe laser, with ground glass windows set at the Brewster angle and a series of baffles inserted inside the pair of steel tubes to exclude scattered laser light from the central chamber. The other two arms provide an optical coupling for the flash lamp that is used to photolyze lithium halide vapor in the central chamber, and as an exit for the gas flow to the pump. The reactor is enclosed in a furnace which can heat the vessel and about half the length of the side arms to over 1200 K. The temperature of the gas in the reaction volume in the middle of the central chamber is monitored by a permanently inserted chromel/alumel thermocouple whose tip is about 1 cm below the paths of the flash lamp and probe laser. Once the selected temperature has been reached, the temperature controller (Omega Model 6100) maintains this temperature of the gas inside the reactor to within f5 OC. (17) Fontijn, A.; Zellner, R. Ih Reactions of Small Transienf Species; Fontijn, A., Clyne, M. A. A., Academic: London, 1983. (18) Davidovits, P. In Alkali Halide Vapours; Davidovits, P., McFadden, D. L., Eds.; Academic: New York, 1979. (19) Husain, D.; Plane, J. M. C. J . Chem. Sot., Faraday Trans. 2 1982, 78. 163, 1175.
LIF signal is collected in the vertical side a r m , w h e r e it passes
out of the reactor through a ground glass end-window and through (20) JANAF Thermochemical Tables, 3rd ed.;Chase, M. W., Jr., Davies, C. A., Downey, J. R., Jr., Frurip, D. J., McDonald, R. A., Syverud, A. N., J. Phys. Chem. R e j Dafa 1985, 14. (21) Brdhead, D. C.; Davidovits, P.; Edelstein, S. A. J. Chem. Phys. 1969, 51, 3601. (22) Corliss, C. H.; Bowman, W. R. "Experimental Transition Probabilities for Spectral Lines of Seventy Elements"; Natl. Bur. Stand. (US), Monogr. 53; US Government Printing Office: Washington, DC, 1962.
6554 The Journal of Physical Chemistry, Vol. 91, No. 26, 1987
I
200
I
I
400
,
I
600
,
Plane
800
( w c )
Figure 2. (a) Time-resolved decay of the LiF signal from Li atoms at X = 671 nm (Li(2P,)-Li(2SI,2))following pulsed photolysis of LiI vapor in He alone; [He] = 1.48 X ~ m - T~ = , 647 K. (b) Logarithm (base 10) of the LIF decay in (a). (c) Time-resolved decay of the LIF signal from Li atoms at X = 671 nm following pulsed photolysis of LiI vapor in N 2 0 and He; [N,O] = 8.04 X 10') cm-'; [He] = 1.48 X IOt8 ~ m - 7'~ =; 647 K. (d) Logarithm (base 10) of the LIF decay in (c).
an interference filter centered at 670 nm (Oriel Corp., fwhm = 10 nm), and is measured by a photomultiplier tube with a response rise time of 2.2 ns (Thorn EM1 Gencom Inc, Model 9816QB). The voltage at which the PMT was operated varied between 1.4 and 2.0 kV. This depended on the size of the LIF pulse, which increased at higher reactor temperatures and flashlamp energies and necessitated a reduction in the PMT gain in order to avoid saturation and a nonlinear response. The P M T and interference filter are maintained at under 25 OC by a flow of cooled dry air during the high-temperature experiments. The output from the PMT is terminated in a 2.2 kohm resistance in order to increase the apparent lifetime of the LIF pulse, from the lifetime of Li(zPr) of 27 nsZ2to about 3 pus. This signal is then input into the gated integrator of a box-car averager (Stanford Research Systems, Model SR250). The entire experiment is controlled by a pulse delay generator (Stanford Research Systems, Model DG535). With reference to Figure 1, a positive 5-V pulse lasting 60 ps is sent to a gating circuit in the PMT housing, which reduces the gain of the photomultiplier tube by a factor of lo3, and 14 ps after this gate is applied to the PMT, a trigger is sent to fire the flashlamp; 15 ps after the PMT gate has ended and the photomultiplier gain has been restored, a trigger is sent to the box-car. Thus, data acquisition can begin 75 ps after the start of the firing sequence. Generally because the tail effects from the flash at higher energy persist beyond this time interval, data acquisition was normally initiated at 105 ps after the flash. The laser firing is triggered by the box-car to coincide with the opening of the integrator gate as it is scanned to monitor the LIF signal at increasing time intervals after the flash lamp fires. The gate width was set at 3.5 pus, to allow for a 1.2 f 0.05 gs posttrigger delay in the laser firing. The shot-to-shot variability of the probe laser was sufficiently good that normalizing was not required. The preset delays scanned by the integrator ranged from 150 ps to 10 ms, depending on the lifetime of the Li atoms formed in the flash. Each scan was divided into 200 bins, and the scans were normally repeated once and
averaged to improve signal-to-noise. With the pulse/delay generator triggering the firing sequence at a repetition rate of 3 Hz, each kinetic decay could be taken in under 2 min. The averaged decays were then transferred to a microcomputer for a curve-fitting analysis and storage. Materials. Helium, 99.9999% pure (Matheson "Matheson Purity"), was without further purification. NzO, 99.99% pure (Matheson, Ultra High Purity), was degassed at 77 K before use. LiI and LiCl, 99% (Aldrich, anhydrous), were kept sealed under dry air in the dark before use, and then refluxed in the reactor side arm at 700 K for several hours prior to kinetic experiments, to remove traces of I2 or Cl,. Figure 2 illustrates examples of the decay of the LiF signal at X = 670.7 nm (Li(2Pr)-Li(2Sl,2)), generated by the pulsed photolysis of LiI in the presence of H e alone (Figure 2a) or in the presence of He and NzO (Figure 2c), demonstrating a tenfold increase in the decay rate in the presence of NzO. Since the signal-to-noise ratio of these decays is good and the scattered laser light signal is minimal, they can be satisfactorily fitted to the form A exp(-k't). To illustrate this, Figure parts b and d of 2 are log plots of the decays in parts a and c, respectively; their linearity demonstrates that these decays are described well by single exponentials. Under the conditions of the present study, in which the concentration of N20 W ~ always S well in excess of the concentration of Li resulting from the pulsed photolysis of lithium halide vapor, and in the absence of the possible interference from second-order kinetics which have been discussed by Husain and MarshallI4 and Ager et a1.,12 the loss of Li atoms may be described by the pseudo-first-order decay coefficient, k', where Na N 2 0 NaO N z (5)
+
-
+
The term km describes diffusion of the Li atoms out of the volume defined by the intersection of the beams from the flashlamp and
The Li
+ N 2 0 Reaction
1.6E4~
The Jotrrnal of Physical Chemistry, Vol. 91, No. 26, 1987 6555
.
TABLE I
(a)
1.4E4 o
1.2E4 A
cm3 molecule-I s-I
kl,
T = 363 K T = 600 K T = 900 K
1 .OE4
6000.0 6000.0
4000.0 2000.0 0.0 0.0
1.OE14
2.OE14
3.OE14
4.OE14
A 0
363 41 1 474 545 600 647 700 800 900 T/K
5.OE14 &BOO
[N20]/molecule c m - 3
1 .OE5
T, K
8.67 f 0.74 14.7 f 1.8 28.6 f 3.4 41.2 f 4.9 55.5 f 7.4 87.6 f 10 135 f 12 232 f 21 388 f 35
600
5yO
400
370
,
T=800 K T=700 K
.
T=474 K
\
L
( 1 /T)/K-'
Standard Arrhenius plot (In kl against 1/T) over the temperature range 363-900 K. Error bars depict 2a errors from leastsquares fits to the plots in Figure 3. The solid line is a best fit through the experimental data (see text). Figure 4.
. 0.0
2.OE14
4.OE14
6.OE14
found that the best least-squares fit to our data is given by a double-exponential expression
[N20]/molecule c m - 3
(a) Plots of the pseudo-first-orderrate coefficient (k') against [N,O] for T = 363,600, and 900 K P t d = 100 Torr in all cases. Solid lines are linear least-squares fits to the data. (b) Plots of k' against [N,O] for T = 41 1,474, 545,647,700, and 800 K; Ptotal = 100 Torr in all cases. Solid lines are linear least-squares fits to the data. Figure 3.
the laser. This volume is approximately cylindrical with a length equal to the width of the flash lamp beam (I = 1.9 cm) and radius equal to that of the expanded laser beam (r = 0.3 cm).In addition, this volume coincides with the limits of the field of view of the PMT. kdiais then approximately given by the "long time solution" of the diffusion equation for a cylinder23
kdiff= (a2/12+ 5.81/9)D(Li-He)/(p/atm)
(3)
Solution of this equation over the range of temperatures studied yields D(Li-He, 363 K < T < 900 K) = (0.45 f 0.16)(T/273 K)1.7*0.2cm2 s-' which is slightly greater than D(Na-He) a t corresponding temperatures, with a similar temperature d e p e n d e n ~ e . ' ~ - ~ ~ > ~ ~ When the dependence of k'on [N,O] is studied, the bath gas pressure is kept constant so that kdiashould appear as an intercept on a plot of k'against [N20]. Such plots are illustrated in Figure 3 for the nine temperatures at which reaction 1 was studied. At all temperatures, k' exhibits a clear linear dependence on [N20]. The slopes of these plots thus yield k , as a function of temperature, listed in Table I with 2a errors from a linear regression fit to each plot. Further experiments were carried out to demonstrate that k1( T ) is not a function of the bath gas pressure over the range 40-150 Torr. Figure 4 is a standard Arrhenius plot of the data contained in Table I. There is a linear section over the temperature range 363-600 K, after which there is a marked increase in activation energy of the reaction. Following Fontijn and Felder,26we have (23) Mitchell, A. C. G.; Zemansky, M. W. Resonance Radiation and Excited Atoms; Cambridge University Press: London, 1934. (24) Silver, J . A. J . Chem. Phys. 1984, 81, 5125. (25) Ager 111, J. W.; Howard, C. J. J . Chem. Phys. 1986, 85, 3469.
+
k l ( T ) = (2.4 f 0.5) X 10-11T1/2 exp(-(1468 f 137)/T) (7.9 f 4.7) X 10-10T1/2exp(-(4157 f 540)/T) (4) which is the solid curve depicted in Figure 4. This expression is the sum of two terms of the form which arise from simple collision the0ry.'~2~In order to retain some physical meaning in expression 4 rather than generate a purely analytical expression by using a full four-parameter fit,26 we have constrained the first term characterizing the low-temperature dependence of kl by using the best fitted threshold energy of 12.2 kJ mol-l between 363 and 600 K from Figure 4 (the difference between threshold energy in collision theory and Arrhenius activation energy is discussed in ref 17 and 27). In fact, a four-parameter fit to the data introduces only a slight statistical improvement,26 and all parameters are within the quoted (2u) errors given in (4) with the exception of the preexponential factor of the second term which is very sensitive to the fitting procedure and which should therefore largely be regarded as an analytical fitting parameter.
Discussion The present work represents the first measurement of reaction 1. The reaction has been studied over an extended temperature range and exhibits marked non-Arrhenius behavior above 600 K. Before we discuss this observation, a comparison should be made between the present work and studies on the analogous reaction of N a a t o m ~ ~ J ~ - ' ~ Na + N 2 0 N a O + N, (5)
-
Husain and Marshall14 and Ager et a1.12 both studied reaction 5 over an overlapping range in temperature below 500 K and obtained Arrhenius parameters. The activation energy obtained in the present work for reaction 1 below 500 K is 14.3 0.6 kJ mol-', which is very close to that obtained for reaction 5 by Ager et a1.12(14.1 0.7 kJ mol-') and slightly higher than the result of Husain and Marshall (12.5 f 0.6 kJ mol-').14 The A factor for reaction 1 is about 4.8 X lo-'' cm3 molecule-' s-' a t tem-
*
*
(26) Fontijn, A.; Felder, W. J . Chem. Phys. 1917, 67, 1561. (27) Smith, I. W. M. Kinetics and Dynamics of Elementary Gas Reactions; Butterworths: London, 1980.
6556 The Journal of Physical Chemistry, Vol. 91, No. 26, 1987 peratures below 500 K, corresponding to a reaction cross section of 41 A2. The measured A factors of reaction 5 range from 1.6 X to 4.6 X cm3 molecule-’ s-1,12,14 corresponding to a range in reaction cross section of 21-61 A2. Thus, the analogous reactions of Li and Na with NzO at temperatures below 500 K are characterized by very similar reaction cross sections and activation energies. Husain and Marshall14 also studied reaction 5 from 600 to 900 K and did not observe any significant non-Arrhenius effects. In view of the generally rather similar nature of the alkali metals, this contrast in behavior of Li and Na is surprising. We therefore carried out further investigations to determine if the discrepancy might be due to an experimental artifact in the present system at high temperature. Possible reactions which could affect this system include heterogeneous decomposition of N 2 0 to form N 2 and Oz, or reaction between NzO and solid or liquid alkali metal halide or !he gas-phase alkali metal halide dimers to yield the halogen diitomic and presumably an alkali metal oxide. We clearly observed the complete decomposition of N 2 0 a t 1000 K in our stainless steel reactor: the concentration of O2that results is too low28to compete with the diffusional removal of Li atoms and no increase in k’above kdia (see eq 2) is observed when N 2 0 is added to the reactor at 1000 K. Thus the decomposition of N 2 0 in the present system, if significant below 900 K, would lead to an underestimation of k l . To test for the decomposition of N 2 0 on hot quartz, which might have affected the experiments of Husain and Marshall14 who used a cylindrical quartz reactor, we passed N 2 0 through a quartz tube heated to 900 K before entry to the reactor and observed no effect on the measured rate of removal of Li atoms, implying that NzO is not decomposed rapidly on quartz at this temperature. This is in accord with other work on the decomposition of N20.z9 The reactions 2MX(s) + N2O M ~ O ( S+ ) Nz + X2 (6a) 4
M 2 W ) + Nz + Xz (6b) (MX)Ag) + NzO where M = Li, N a and X = I, C1 are all thermodynamically favorable at these elevated temperature^.^^ They could be an important source of error since the gas-phase reactions between the alkali metals and the halogen diatomics are extremely rapidem In the present system, we are able to rule out interference from reaction 6a at temperatures from 600 to 1000 K: the sample of the lithium salt over which the flow of N 2 0 in H e passes is independently heated to over 800 K in the side arm (see Figure l ) , so that the effects of reaction 6a producing I2 or C12 should be evident over the entire temperature range of the present study, particularly enhancing the reaction rate at low temperatures. In the case of reaction 6b, the steady-state concentrations of the alkali metal halide dimers flowing through the central chamber will be a function of their sticking coefficients on the walls of the chamber. The dimers will probably stick less efficiently at elevated temperatures so that their concentrations can become large enoughZofor reaction 6b to produce a significant quantity of halogen diatomic species. However, this process is unlikely to be occurring to a significant extent in this system since the production of I2 by reaction 6b (or (6a)) should in fact lead to a decrease in the observed rate coefficient at elevated temperatures. This is because 1, is mostly dissociated to atomic iodine (ca. 95% at T = 900 K20). The rate constant at 900 K for the recombination reaction Li + I He is about 1.5 X an6molecule-2 s-I, based on our experimental measurements and theoretical treatment of the analogous reactions of the lower alkalis;’ and so this reaction will not be important here. Since kl ( T = 900 K) is probably within a factor of 2 of the rate constant for the reaction Li + 12,30 +
+
(28) Kramer, S.D.;Lehmann, B. E.; Hurst, G . S.; Payne, M. G.;Young, J. P. J. Chem. Phys. 1-2, 76, 3614. (29) Loirat, H.; Caralp, F.; Font, W.; Schoenenberger, C. J . Phys. Chem. 1985, 89, 4586. (30) Maya, J.; Davidovits, P. J . Chem. Phys. 1974, 61, 1082. Silver, J. A. J . Chem. Phys. 1986,84,4718. (31) Plane, J. M. C.; Husain, D. J . Chem. Soc., Faraday Trans. 2 1986, 82, 897.
Plane the loss of N 2 0 to form mostly atomic I will lead to a decrease in the overall first-order decay of Li. We also observed no difference in k’when using Li or LiCl as a photolytic precursorfurther evidence that reactions 6a and 6b are not occurring to a significant extent here. Husain and MarshallI4 used NaI as a precursor in their study. It is possible that at high temperatures reaction 6a becomes rapid on a quartz substrate, so that a large fraction of the N 2 0 admitted to the cell reacts to form I/12.32 For the reasons given above, the observed rate of removal of N a would then be significantly slower and the apparent rate constant for reaction 5 underestimated. The unexpected divergence in the measured kinetic behavior of these two different reactions clearly requires further investigation. Non-Arrhenius Behavior. Reaction 1 exhibits substantial non-Arrhenius behavior, as illustrated in Figure 4. Fontijn and FelderZ6have shown, with respect to the reaction A1 + C02, that deviations from Arrhenius behavior of this scale cannot be explained realistically in terms of transition-state theory. The form of expression 4 suggests that at high temperatures a second reaction channel is opening. The nature of the two reaction channels is discussed below. The first term in expression 4 describes a reaction with a small activation barrier and a cross-section diameter (3.6 A) which is very similar to the mean of the hard-sphere diameters of Li (3.0 A)20and N 2 0 (4.6 A).33 The ground states of reactants and products of reaction 1 correlate on the basis of C, symmetry in the “least symmetrical complex” and the weak spin-orbit coupling
appro xi ma ti or^:^^ Li(2S1,z)+ NzO(XIZ+)
AI-
LiO(X211) + Nz(X’Zg+)
AH = -169.2 kJ mol-’
35936
(7)
which is consistent with the large reaction cross section. The second term in expression 4 must primarily be recognized as an analytical fit to the experimental data. That notwithstanding, we believe that the very large preexponential factor and the exponent possess a plausible physical interpretation. The size of the preexponential factor usually implies that an electron-jump mechanism3’ is operating, which requires consideration of the nature of the electron affinity of N 2 0 . This has been discussed in detail by B a r d ~ l e y . ~The ~ 211 state of N20- splits into a 2Ar state whose energy decreases with NzO bending angle (arising from the fact that in this 22-electron system an extra electron will enter the lowest unoccupied 3?r (loa) orbital, whose energy drops sharply with bending angle of the originally linear Nz038)and a ZA” state whose energy increases with bending angle. S C F c a l c ~ l a t i o n indicate s~~ that the minimum of the 2A’ state lies 0.39 eV below NzO(XIZ+),while the minimum of the 2A’r state lies about 1 eV above Nz(XIZ+). Thus the adiabatic electron affinity of N20(X22+)is positive when the N20-(2A’) state is formed. However, there is an energy barrier between these states representing the energy required to bend the molecule,38 which is reduced when NzO is already excited in its degenerate bending mode (vZ). Because the fundamental frequency of this mode is only 588 cm-’,16 the population of NzO(uz>O) becomes substantial at temperatures in excess of 600 K. This has been dramatically demonstrated by Chantry40 who observed about a thousandfold (32) Iodine production was observed after several minutes when very high pressures (30 Torr) were added to the quartz cell at high temperature; Marshall, P., Rensselaer Polytechnic Institute, New York, private communication. (33) Hirschfelder, J. 0.; Curtiss, C. F.; Bird, R. B. Molecular Theory of Gases and Liquids; Wiley: New York, 1954. (34) Husain, D.Ber. Bunsen-Ges. Phys. Chem. 1977, 81, 168. (35) Huber, K. P.;Herzberg, G. Molecular Spectra and Molecular Structure. IV. Constants ofDiatomic Molecules; Van Nostrand: New York, 1979. (36) Handbook ofphysics and Chemistry, 65th ed.;Weast, R. C., Ed.; CRC Press: Boca Raton, FL, 1985. (37) Herschbach, D.R. Ado. Chem. Phys. 1966, 10, 319. (38) Bardsley, J. N . J . Chem. Phys. 1969, 51, 3384. (39) Yarkony, D.R. J . Chem. Phys. 1983, 78, 6763.
The Li
+ N 2 0 Reaction
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The Journal of Physical Chemistry, Vol. 91, No. 26, 1987 6557
increase of the dissociative attachment rate of thermal electrons (e NzO Nz 0-) upon raising the vibrational temperature from 350 to 1000 K. Wren and Menzingerza observed a large enhancement of the chemiluminescence cross section for the reaction Ba NzO upon raising the vibrational temperature of the N 2 0 to 613 K. They explained this in terms of a close-range electron-transfer process which was permitted by the increased electron affinity of N20(u2>0). Interestingly, they estimated the activation energy describing the change in total beam attenuation cross section with temperature to be 12.1 f 1 kJ mol-’ below 700 K,Zawhich may be compared with an estimate for the activation energy of 23.4 f 7.9 kJ mol-’ from work on Ba NzO in diffusion flames between 923 and 1073 K.41 An analogous explanation was advanced to account for the strong non-Arrhenius behavior of the reaction A1 COz above 750 K.’7*26 We believe a similar process is occurring in reaction 1 at high temperatures. Thus, the second term in expression 4 should comprise the product of a rate coefficient describing the electron jump channel which will have a small temperature d e p e n d e n ~ e , ~ ~ and a Boltzmann factor describing the probability of an N 2 0 molecule having a sufficient degree of vibrational excitation to enable the electron-jump mechanism to occur. Inspection of the exponent in the second term of expression 4 indicates that a threshold excitation energy of 34.6 kJ mol-’ is required. This is very close to the energy required to promote NzO to the fifth level of its degenerate bending mode.I6 This may imply that if an N 2 0 molecule possesses at least this much vibrational energy in the bending mode, the degree of bending is sufficient for the molecule to have a positive vertical electron affinity. This is thought to be necessary for an electron jump to occur, particularly at reasonable internuclear distance^.^'*^^ Furthermore, the degeneracy of this mode increases as (uz + l ) , which will be a factor in the preexponential term: assuming the harmonic approximation for a doubly degenerate mode of fundamental frequency v,I6 the probability P(u21n) that the bending mode is excited to the nth or higher level is given by
+
+
+
+
+
P(uzln) = (n
+ 1 - n exp(-hv/kT))
~ 4 . exp(-423O/T), 3
exp(-nhv/kT)
T = 700-900 K, n = 5
(8a) (8b)
The preexponential factor in the second term of expression 4, when divided by the factor of 4.3 in expression 8b, becomes more physically reasonable as a rate coefficient. In terms of the electron-jump mechanism, the ionization energy of Li is 5.392 eV36and the electron affinity of vibrationally excited N 2 0 is likely to be less than 1 eV, so that a simple calculation balancing charge transfer against Coulombic attracti01-1~~ predicts a reaction cross section of about 34 A2,which is about the same as the hard-sphere collision cross section (see above). This is therefore more like the close-range charge-transfer mechanism discussed in the case of Ba NzOh (which has a similar ionization energy to Li36)than a long-range electron transfer commonly associated with the “harpoon m e c h a n i ~ m ” .However, ~~ there is no activation barrier to this chargetransfer reaction, and, given the small crossing radius of 3.7 A, the reaction can be expected to proceed on the lowest adiabatic surface with unit p r ~ b a b i l i t y . ~This ~ , ~ i~m p l i e ~that ~~,~~ the total reaction cross section will be determined by the orbiting criterion on this attractive surface. Beyond the curve-crossing radius the attractive forces will be almost entirely dispersive. The
+
(40) Chantry, P. J. J . Chem. Phys. 1969, 51, 3380. (41) Kashireninov, 0.E.; Kuznetsov, V. A,; Manelis, G. B. Russ. J. Phys. Chem. 1977, 51, 566. (42) Goldfield, E. M.; Gislason, E. A.; Sabelli, N. H. J . Chem. Phys. 1985, 82, 3179. (43) Grice, R. Adu. Chem. Phys. 1975, 30, 247. (44) Chamberlain, G . E.; Zorn, J. C. Phys. Reu. 1963, 129, 677.
effective potential Vcff is then given byz7 V,ff(r)= -cg/16 Eb2/rZ
+
(9)
where E is the collision energy and b the impact parameter, and r is the internuclear distance; c6 may be estimated from the London formula45and has a value of 5.9 X lo-’’ J A6 with values for the polarizabilities of Li and N 2 0 from ref 44 and 33, respectively, and the respective ionization energies from ref 36 and 20. Any collision which has sufficient energy to surmount the centrifugal barrier described in eq 9 is then assumed to undergo a charge transfer at close range. In the case of reaction 1, there are no restrictions on the maximum impact parameter arising from considerations of conservation of angular momentum in the exit ~ h a n n e l . The ~ rate coefficient is then given by27
k( T ) = T (2c6/ kBT ) ’ / 38( kBT/rp)’/21’( 2/ 3)
( 10)
where kB is the Boltzman constant and p the reduced mass. Equation 10 predicts a value for k(T=900 K) = 1.6 X cm3 molecule-’ s-I, which should be compared with our experimental value of 3.88 X cm3 molecule-’ s-’, reflecting the small population of NzO that possesses a sufficient degree of bending vibrational excitation at that temperature to undergo a chargetransfer reaction. A charge-transfer mechanism will involve an intermediate ion pair Li+(’S) and Nz0-(211,2A’ in Cs), which then rearranges to form the product^.^^,^' This ion pair correlates on a 2A’ and a *A” surface with the ground-state products LiO(X211) and N2(X1Zg+). Thus, the excited-state product LiO(A2Z+), which has been calculated46to lie 31.6 kJ mol-’ above LiO(X211) and is therefore exothermically accessible in reaction 1 does not correlate with the neutral reactants or an intermediate ion pair. From consideration of formal adiabatic correlations for either of these reaction channels, only the ground-state LiO(X211) will be formed in reaction 1. The two-channel model for reaction 1 which has been discussed above is clearly an oversimplification of the manner in which vibrational excitation of NzO will affect the rate of reaction 1. For instance, the symmetric stretch mode of NzO(vI) largely corresponds to an N-0 stretch and thus to the reaction coordinate. There is evidence2that excitation of the bending mode (u2), which can be in Fermi resonance with v1,16 is necessary to promote the enhancement in the reaction cross section which would be expected when the v1 mode is excited.2 In the absence of information on the reactivity of these vibrationally excited states of NzO the contribution of vibrational excitation with increasing temperature cannot be modelled in detail. The present model has been advanced to give a plausible and partially quantitative explanation for the striking non-Arrhenius behavior that has been observed for reaction 1. ,35936
Acknowledgment. This work was supported by funds from the University of Miami and under grant ATM-8616338 from the National Science Foundation. We thank Mr. P. Nilsson and Mr. D. Odum for generous technical assistance, and Drs. P. Marshall, E. Saltzman, and R. Zika and an anonymous reviewer for helpful advice and discussions. Registry No. Li, 7439-93-2; N20, 10024-97-2. (45) London, F. J . Phys. Chem. 1942, 46, 305. (46) Allison, J. N.; Cave, R. J.; Goddard 111, W. A. J . Phys. Chem. 1984, 88, 1262. (47) In this paper the periodic group notation in parentheses is in accord
with recent actions by IUPAC and ACS nomenclature committees. A and B notation is eliminated because of wide confusion. Groups IA and IIA become groups 1 and 2. The d-transition elements comprise groups 3 through 12, and the p-block elements comprise groups 13 through 18. (Note that the former Roman number designation is preserved in the last digit of the new numbering: e.g., 111 3 and 13.)
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