J. Phys. Chem. 1984,88, 1566-1571
1566
effects are evident from the plotting positions of their corresponding log krelvs. c* values which are far above the slope of the lines, when projected in Figure 1. In conclusion, the present findings confirm Maccoll's theory on the heterolytic nature of the transition state for alkyl halide pyrolyses in the gas phase.24
substituents. This means that, as the latter group destabilizes the reaction center in the transition state, the hydrogen adjacent to Z (Scheme I) may become more acidic and thus assist the leaving chlorine atom. Such a phenomenon sometimes may cause a nearly or slightly higher pyrolysis rate with respect to the unsubstituted ethyl chloride. Consequently, this interpretation about the inflection point at u*(CH3) = 0.00 into two slopes accounts for the belief that slight alteration in the polarity of the transition state results from changes of electronic transmission at the carbon reaction center.'%25 Table IV lists several polar substituents in /+substituted ethyl chloride which have been found to enhance these eliminations by their resonance effect or through anchimeric assistance. These
Kinetics of the Reaction HO,
+ NO2 + M
Acknowledgment. We are grateful to the Consejo Nacional de Investigaciones Cientificas y Tecnoldgicas (CONICIT) for their support (Project No. 51.78.31, S1-1072). Registry No. c-C5H9CH2CH2C1, 84226-36-8; c-C6HI,CH2CH2C1, 1073-61-6; CHS(CH2)5Cl, 544-10-5; CHSCH2CH(CH,)CHZCH2Cl, 62016-93-7; (CH,),CHCH2CH2CH2Cl, 62016-94-8.
+
H0,N02
+M
Stanley P. Sander* and Mary E. Petersont Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91 109 (Received: June 14, 1983)
-
The flash photolysis/ultraviolet absorption technique was used to measure the rate constants for the reaction H 0 2 + NO2 + M H 0 2 N 0 2+ M over the pressure range 50-700 torr and temperature range 229-362 K using He, 02,and N2 as diluent gases. The data were fit to the expression derived by Troe and co-workers for describing the pressure and temperature dependence of reactions in the falloff region. By combining these data with recent measurements of the rate constant for H 0 2 N 0 2thermal decomposition values of 73.8 f 2 eu for the standard entropy and -12.6 f 2 kcal mol-' for the standard enthalpy of formation of H0,N02 were obtained. A significant enhancement in the rate constant was observed when water vapor was added to the system.
HO2N02
Introduction The reaction H02
+ NO2 + M -,HO2N02 + M
(1) has been studied by a variety of techniques and is known to produce pernitric acid ( H 0 2 N 0 2 ) as the primary product.'-" Like other termolecular reactions involving NO2 studied in our l a b o r a t ~ r y , ~reaction ~ J ~ 1 is pressure dependent and in the falloff region between second- and third-order kinetics in the 100-700-torr pressure range. Since pernitric acid is expected to form in the troposphere and stratosphere and may participate in a photochemical cycle which catalytically destroys odd-hydrogen radicals, detailed kinetic measurements are needed.I4 These measurements should also include the effects of other species such as water which are present in the atmosphere and may affect the reaction mechanism. Before kinetic data were available, reaction 1 was thought to produce H O N O and O2 with rate constant estimates ranging between and cm3 molecule-' s-'. Using static photolysis, Simonaitis and Heicklen showed that a long-lived reaction product was formed which thermally regenerated NO2 and were the first to suggest that H 0 2 N 0 2might be f ~ r m e d .Verification ~ of this finding came from the studies of Niki et a1.: Hanst and Gay, Jr.,5 and Levine et a1.,6 who observed H02N02by FTIR spectroscopy. Howard performed the first direct study of reaction 1 using discharge flow/laser magnetic resonance (DF/LMR) in the third-order (0.5-3 torr) pressure range at 298 K.' Termolecular rate constants for M = He, N2, and O2were measured, and the reaction channel forming H O N O was found to be insignificantly slow ( k < 1 X cm3 molecule-' s-l). Further FTIR studies using H 0 2 N 0 2synthesized directlyss9and by in situ photochemistrylo complemented the direct study of reaction 1 by measuring the rate constant for the thermal decomposition of H02N02: t Present address: Oregon Graduate Center, Beaverton, Oregon 97006.
0022-3654/84/2088- 1566$01.50/0
+M
+
HOz
+ NO2 + M
(2)
Cox and Patrick measured k l in the transition regime (40-600 torr) using molecular modulation spectrometry and obtained the UV absorption spectrum of HO2NO2." However, the kinetic measurements were made at only one temperature, 283 K. In the present study, absolute measurements of kl have been made using the flash photolysis/ultraviolet absorption (FP/UV) technique. Rate constants were measured over the following ranges of conditions: total pressure from 50 to 700 torr with He, 02,and N 2 as diluent gases, temperature from 229 to 362 K with N2 as the diluent gas at constant total pressures of 100 and 700 torr, and added water vapor from 263 to 298 K at a constant pressure of 350 torr of N2. Pseudo-first-order conditions were (1) R. Simonaitis and J. Heicklen, J . Phys. Chem., 78, 653 (1974). (2) R. A. Cox and R. G. Derwent, J . Photochem., 4, 139 (1975). (3) R. Simonaitis and J. Heicklen, J . Phys. Chem., 80, 1 (1976). (4) H. Niki, P. D. Maker, C. M. Savage, and L. P. Breitenbach, Chem. Phys. Leu., 45, 564 (1977). (5) P. L. Hanst and B. W. Gay, Jr., Environ. Sci. Technol., 11, 1105
(1977).
( 6 ) S. Z. Levine, W. M. Uselman, W. H. Chan, J. G. Calvert, and J. H. Shaw, Chem. Phys. Lerr., 48, 528 (1977). (7) C. J. Howard, J . Chem. Phys., 67, 5258 (1977). (8) R. A. Graham, A. M. Winer, and J. N. Pitts, Jr., Chem. Phys. Lett., 51, 215 (1977). (9) R. A. Graham, A. M. Winer, and J. N. Pit& Jr., J . Chem. Phys., 68, 4505 - ..(1978). ,-(10) W. M. Uselman, S . Z. Levine, W. H. Chan, J. G. Calvert, and J. H. Shaw, Chem. Phys. Lett., 58, 437 (1978). (11) R. A. Cox and K. Patrick, Inr. J . Chem. Kinet., 11, 635 (1979). (12) S . P. Sander and R. T. Watson, J . Phys. Chem., 84, 1664 (1980). (13) S . P. Sander, G. W. Ray, and R. T. Watson, J . Phys. Chem., 85, 199 (1981). (14) National Research Council, "Causes and Effects of Stratospheric Ozone Reduction: An Update", National Academy Press, Washington, DC, 1982. - I
0 1984 American Chemical Society
Kinetics of the Reaction HOz
+ NOz + M
-+
HOzNOz + M
The Journal of Physical Chemistry, Vol. 88, No. 8, 1984 1567
used with [NO,] >> [HO,],. The data were fit to the expression derived by Troe and co-workers for describing the pressure and temperature dependence of rate constants in the falloff region.l6,I7 This permitted the limiting low-pressure (k,) and high-pressure ( k , ) rate constants and their temperature dependences to be estimated. For the first time, a significant enhancement of k l was observed when water vapor was added to the system. The implications for atmospheric chemistry of both the water vapor effect and the new falloff parameters derived from this study will be discussed.
Experimental Section The flash photolysis system has been described in detail prev i o ~ s l y . ’ ~A~ ’collinear ~ Pyrex flash lamp/reaction cell about 1 m long and 2.5 cm in diameter was used in this study. HOz radicals were monitored by UV absorption at 229.4 nm. This wavelength was selected to coincide with a minimum in the NOz absorption spectrum. Eight-pass White Cell optics were used to achieve an absorption path length of about 800 cm. Absorption signals accumulated from about 100 flashes were averaged and processed by a computer. The temperature was controlled by circulating methanol (229-298 K) or ethylene glycol (3 17-362 K) through the cell’s jacket. Flash energy (10-ps duration, 0.1 H z repetition rate) was generally set at 518 J per flash. The flash lamp filter cell was filled with a Cl,-Brz mixture which, at equilibrium, contained 60 torr of BrCl and 200 torr of Cl,. BrC1, which has an absorption band centered at 370 nm, absorbed a fraction of the light which would have otherwise resulted in NO, photolysis. At 518-5 flash energy, NO, photolysis was limited to about 0.2% per flash as indicated by monitoring the disappearance of NOz at 400 nm. This was low enough to avoid complications due to the reaction of HOz with photolytically produced NO. H 0 , radicals were produced by photolyzing mixtures of Cl,, C H 3 0 H , and 0, at wavelengths longer than 300 nm: Cl,
+ hv
-
2C1
(A
> 300 nm)
O
P
A P
O P
[k](molecules cmd1 x 10-l~ Figure 1. Plots of k’ = kl[N02]vs. [NO,] a t 298 K for total N, pressures of 100, 350, and 700 torr. Adherence to first-order kinetics is indicated by the linearity of these plots and their small y intercepts. The dependence of k l on pressure is also indicated.
(3)
C1 + CH3OH HC1+ C H 2 0 H k4 = 6.3 X lo-” cm3 molecule-’ s-I (ref 19)
(4)
CHZOH + 0, HOZ + H C H O k5 = 2 X cm3 molecule-’ s-l (ref 20)
(5)
+
+
Reagents flowed continuously through the reaction cell with a residence time shorter than the flash repetition frequency to avoid the buildup of reaction products. The ranges of reagent concentrations were (in molecules cmT3)as follows: [Cl,], 4-12 X lOI5; [CH30H], 2-5 X lOI5; [O,], 2-4 X lOI7; [NO,], 3-40 X lOI4. Initial HOz concentrations were varied over the range 1-4 X l O I 3 molecules ~ m - resulting ~, in initial analytical beam absorptions of 2-10%. Absorption signals could generally be followed for 3-5 l / e times, depending on the initial HOZconcentration. In runs with added water vapor, a bubbler immersed in a thermostated bath was inserted into the carrier gas line. Water vapor pressures were calculated by assuming that the bubbler achieved complete saturation. This has been verified in a previous study.I5 Reagents and carrier gases had the following stated purities: Cl,, 99.96%; 02,99.99%; He and N,, 99.999%. C H 3 0 H (Fisher (15) S. P. Sander, M. Peterson, R. T. Watson, and R. Patrick, J . Phys. Chem., 86, 1236 (1982). (16) K. Luther and J. Troe, paper presented at the 17th International Symposium on Combustion, Leeds, England, Aug 1978. (17) J. Troe, J. Phys. Chem., 83, 114 (1979). (18) R. T. Watson, S. P. Sander, and Y . L. Yung, J . Phys. Chem., 83, 2936 (1979). (19) J. V. Michael, D. F. Nava, W. A. Payne, and L. J. Stief, J . Chem. Phvs.. 70. 3652 (19791. 120) H. E. Ridford, Chem. Phys. Lett., 71, 195 (1980). (21) W. B. DeMore, Ed., “Chemical Kinetics and Photochemical Data for Use in Stratospheric Modeling, Evaluation No. 5”, J.P.L. Publication 82-57, Pasadena, CA, 1982. (22) S. W. Benson, ‘Thermochemical Kinetics”, Wiley, New York, 1976.
0.00 y 0
I
m
I
400
I
600
I
800
PRESSURE (Torr1
Figure 2. Plots of k , vs. total pressure of He, 02,and N, at 298 K. The solid lines are fits to the data using eq I.
Spectral Grade) was degassed several times at 77 K before use. NOZ-O2mixtures were made by reacting small amounts of NO (Matheson C.P. Grade, 99.0% purity) with a large excess of 0, and allowing sufficient time (>1 day) for conversion. N z 0 4 corrections were negligible.
Results The reaction between H 0 , radicals and NO, was studied as a function of total pressure (50-700 torr), diluent gas (M = He, N,, O,), temperature (229-362 K), and water vapor (0-15.9 torr). The study was performed using pseudo-first-order conditions with the ratio [NO,]/[HO,]o ranging from 10 to 300. Plots of In (HO, signal) vs. time were linear over the entire range of experimental conditions. A residual absorption was present after the reaction was completed, the magnitude of which averaged about 30% of the initial HOz absorption. At 229.4 nm, the cross sections of H02and H 0 , N 0 2 are 2.4 X lo-’* and 8.1 X cmz molecule-’, respectively. The residual absorption is therefore consistent with the reaction product being HO,NO,, since the ratio aH02N02/aH02 is 0.34 at 229.4 nm and stoichiometric conversion of H 0 2 to H02N02is expected. As shown in an earlier paper,’, the residual
1568 The Journal of Physical Chemistry, Vol. 88, No. 8, 1984 TABLE 1: Rate Constants for the HO, Reaction at 298 K
pres-
+ NO, + M
1 o i 3 k ,n I c1n3 niolecule-'
sure, torr 50 100 200 350 500 700
Sander and Peterson
M=
M=N,
H C ~
M=O,
3.05 i 0.53 ( I O ) 2.50 * 0.11 (10) 2.76 t 0.19 (22) 4.62 i 0.37 (10) 3.74 i 0.31 (10) 4.33 i 0.18 (21) 6.45 * 0.49 (32) 6.63 i 0.40 ( I O ) 5.38 i 0.20 (25) 9.44 i- 0.70 (12) 7.84 i 0.32 (10) 6.37 i 0.22 (27) 11.2 i 0.50 ( 1 1 ) 10.3 i 0.40 (10) 7.35 * 0.52 (25) 13.2 i 0.80 ( 1 1 ) 12.6 i- 0.80 (4)
X
i
Numbers of runs are in parentheses. Quoted uncertainties are Corrected for the con-
l o and do not include systematic errors. tribution from M = 0,.
TABLE 11: Rate Constants for the HO, over the Range 229-362 K
+ NO, + N ,
Reaction
1Oi3k, cm3 molecule-' s-' temp, K 36 2 338 317 298 217 246 229
p = 100 torr 1.88 i 0.26 2.69 i 0.19 3.35 i 0.24 4.62 i 0.37 5.24 i 0.43 7.26 i- 0.83 9.23 i 0.91
(IO) (11)
(11) (IO) (11) (10)
(IO)
Numbers of runs are in parentheses
30.0 I
p = 700 torr
6.93 i 0.81 ( I O ) 9.13 f 0.83 (10) 12.3 i 1.1 (12) 13.2 i 0.80 (1 1) 16.3 i 1.4 (9) 25.1 i 2.0 ( I O ) 27.6 ? 2.5 (18)
1
I
5.a
5.40
5-80
6.a)
Ln T
Figure 3. Dependence of k l on temperature at 100 and 700 torr total pressure of N2. The solid lines are fits to the data using eq I and the parameters in Table IV.
Quoted uncertainties
are l a .
absorption does not affect the first-order rate constant analysis if the transmitted light intensity at long reaction times is used as the reference intensity (lo). The pressure dependence of reaction 1 at 298 K was studied between 100 and 700 torr for M = H e and between 50 and 700 torr for M = N2and 02. The lowest pressure that could be used was determined by the diffusional loss of HOz to the cell walls. Conditions were adjusted so that the first-order reactive loss was always at least 10 times larger than the first-order diffusional loss. Plots of k' = kl [NO,] vs. [NO2] were linear with negligibly small y intercepts (Figure 1). Figure 2 shows some of the k'vs. [NOz] data for M = N 2 at 298 K. The rate constants for each diluent gas and total pressure were obtained from the slopes of these plots and are given in Table I. Figure 2 shows the rate constant curves along with the computer fits to the theoretical falloff expression (see Discussion). As expected from the unimolecular decomposition studies on H02N02,8-10reaction 1 is in the falloff region in the 50-700-torr pressure range with collision efficiencies increasing in the order H e < Oz < N2. The temperature dependence of reaction 1 was measured between 229 and 362 K at total pressures of 100 and 700 torr of Nz.The results are plotted in the form In k vs. In T in Figure 3 and listed in Table 11. The rate constants vary inversely with temperature with a slightly stronger dependence being observed at 100 torr than at 700 torr. The addition of water vapor to the reactant mixture had a substantial effect on the measured rate constants. In Figure 4 and Table I11 we show the data obtained by varying the water vapor pressure at temperatures between 275 and 298 K. k , appears to vary linearly with added water vapor. The water vapor dependence increases with decreasing temperature; the effective third-order rate constant with water as the third body increases from 1.0 X to 1.6 X cm6 molecule-2 s-l as the temperature is reduced from 298 to 275 K. Discussion Secondary Reactions. Under the conditions employed in this study, the characteristic time for H 0 2 formation is less than 15 p s , making its formation always much more rapid than its loss (7 >lo0 p s ) . The apparent absence of secondary H 0 2 reactions was indicated by the adherence to first-order kinetics over wide variations in initial [ HOz] and other reagent concentrations.
0.M 0.0
5.0
15.0
10.0
20.0
H20 PRESSURE (Torr)
Figure 4. Dependence of k , on the pressure of added water vapor at a constant total pressure of 350 torr of N I . Measurements were made at temperatures of 275 K (0),286 K (+), and 298 K (0). TABLE 111: Rate Constants for the HO,
Reaction with Added H,O temp, K
H*O pressure, torr
298
0.0
286
5.4 9.6 12.8 15.9 0.0 3.3 6.6 0.0 2.3 4.5
27 5
+ NO, + N,
1 0 i * k , cm3 ~
molecule?
SKI
0.944 i 0.07 1.08 i 0.10 1.27 t 0.1 1 1.31 i 0.10 1.58 i 0.14 1.29 i 0.09 1.46 ?: 0.12 1.59 * 0.16 1.51 i 0.14 1.65 f 0.16 1.76 i 0.16
kIII,b cm6
molecule-z s-' i .o x i 0-30
i .3 x 10-30
1 . 6 x 10-30
M = 350 torr of N,. Effective third-order rate constant for HO, + NO, + H,O at 350 torr of N,.
The highest temperature that could be employed in this study was limited by the thermal decomposition of H02N02,reaction
+ NO, + M
Kinetics of the Reaction HO, TABLE 1%':
Falloff Parameters for the HO,
-
HO,N02
+ NO,
The Journal of Physical Chemistry, Vol. 88, No. 8, 1984 1569
t M Reaction
Y-'
1031k,300,cmb
M = He
M = N,
M = 0,
10'2k_300, cm3 molecule-' S K '
I
1.00 i 0.25
this work" this workb
1.2
2.09 i 0.52 2.5 t 0.6 2.3 i 0.6
1.51 i 0.38 2.3 t 0.6 2.1 i 0.6
3.6 i 0.9 4.2 -r 1.0
ref
a
+M
i
0.3
Results of curve fits to He, N,, and 0, data.
m
Fc
0.56 0.56
k i.
0.1 0.1
-0.2 -0.2
i i
n
1.0 1.0
4.6 4.6
i
1.0
+ 1.0
Results of curve fits to N, and 0, data only
2, which regenerates HO,. In the worst case ( T = 362 K, [NO2] = 8 X loL4molecules ~ m - ~the ) , ratio k l [ N O 2 ] / k Z is about 20, indicating that decomposition of H 0 2 N 0 2is still much slower than its production. Therefore, no corrections for this effect were necessary. Falloff Parameters. Troe and co-workers have shown that the rate constant falloff curves of addition reactions can be described by the following e x p r e s s i ~ n : ' ~ . ~ ~
where k,( T ) = kO3O0( T/300)-", the low-pressure limiting rate constant, k,(T) = km3O0( T/3O0ym, the high-pressure limiting rate constant, and N = 0.75-1.27 log F,. This expression incorporates both the pressure and temperature dependence of k and is particularly useful for atmospheric modeling studies where rate constants must be calculated as a function of altitude. Equation I uses five parameters: kO3O0,km3Oo(the low- and high-pressure limiting rate constants at 300 K), n, m, and F,. As in previous ~ t u d i e s , ' ~these , ' ~ parameters have been derived by fitting the experimental data to eq I. Several constraints limit the choice of parameter values. First, while falloff curves for the systems with different diluent gases will have different ko values, all must reach the same high-pressure limit, k,. Second, uncertainties in the predicted values of m and n can be reduced by measuring the temperature dependence of k at more than one value of total pressure. These parameters must be the same for each isobaric temperature plot. Because the temperature dependence data were collected at constant pressure rather than constant number density, the data were fitted by using nonlinear least squares to a modified form of eq I in which the substitution
[MI = P/RT has been made. The best-fit parameters are listed in Table IV. Two sets of parameters are reported, one which optimizes the simultaneous fit to the He, N,, and 0, data and the other which considers only the N , and 0, data. While the differences between these two sets amount to only about lo%, the best fit fo the Nz/Oz parameters are the preferred values for atmospheric modeling calculations. There are two direct experimental studies of reaction 1 with which to compare our data. Howard measured kl using the discharge flow/laser magnetic resonance technique at room temperature in the 0.5-3-torr pressure range and obtained ko for M = He, N2, O,, and NO,.' As indicated in Table IV, these results overlap with those of the current study within the error limits of the two measurements. The largest discrepancy is for M = 02, where the difference is about 25%. The excellent agreement for all three diluent gases confirms the validity of extrapolating our flash photolysis data from the falloff region to the termolecular region. The other direct study with which our data may be compared is that of Cox and Patrick," who measured k , using molecular modulation at 283 K in the range 40-600 torr of N1. We did not measure the rate constant at this temperature but can compare our results with theirs using interpolated values calculated from eq 1. The data plotted in Figure 5 indicate that the measurements from this study are about 40-60% higher than the Cox and Patrick results over the entire pressure range. While there is no obvious explanation for this discrepancy, corrections were made in the Cox and Patrick study to account for depletion of NO, along the reactor length. This results in an underestimation
-THIS WORK + -1-
COX AND P A T R I C K
BALDWIN AND GOLDEN
PRESSURE (torr1
Figure 5. Comparison of experimental and theoretical falloff curves for the H 0 2 NOz N2 reaction at 283 K. The experimental results are from Cox and Patrick (ref 11) and this work. The theoretical curve is from the RRKM calculation of Baldwin and Golden (ref 23) using k , and Kq from this study.
+
+
of the rate constant which may partially account for the observed difference. Also shown for comparison in Figure 5 is the predicted falloff curve from the RRKM calculation of Baldwin and G0lden.2~ In plotting this curve, the equilibrium constant obtained in this study was used to calculate k , from the theoretical values of k2 interpolated to 283 K. The predicted curve falls about 20% lower than the curve predicted from our data, which is remarkably good agreement considering the uncertainties in the parameters required for the calculation. Thermodynamics. The rate constant data obtained in this study may be combined with data on the thermal decomposition of HOzNOzto obtain the equilibrium constant for the reaction pair
HOz
I + NO2 + M 7 H02N02 + M
as well as the standard entropy and enthalpy of formation of H 0 2 N 0 2 . As indicated in Table IV, the extrapolated rate constant for reaction 1 in the low-pressure limit for M = N, is k , = (2.3 f 0.6)
X
10-31(T/300)-46 cm6 molecule-2 s-]
The rate constant may also be expressed in Arrhenius form as
kl = 3.0
X
exp(2510/RT) cm6 molecule-2 s-l
For the reverse reaction Graham et aL9 obtained the following expression for k z in the low-pressure limit (p < 7 torr of NJ:
kz = 5.2 X
exp(-19900/RT) cm3 molecule-' s-l
Combining these data lead to the values -37.9 eu and -23.0 kcal ~
(23) A. C. Baldwin and D. M. Golden, J . Phys. Chem., 82, 644 (1978). (24) C. J. Howard, J . Am. Chem. SOC.,102, 6937 (1980). (25) D.L. Baulch, R. A. Cox, P. J. Crutzen, R. F. Hampson, Jr., J. A. Kerr, J. Troe, and R. T. Watson, J . Phys. Chem. ReJ Data, 11, 327 (1982).
1570 The Journal of Physical Chemistry, Vol. 88, No. 8, 1984
Sander and Peterson
TABLE V: Kinetic and Thermodynamic Quantities for the Reaction 1
+ NO, + M f
HO,
+M
HO,NO,
2
S~,,,,(HO,NO,), A H ~ ~ , , , , ( H O , N O , )I ~01% I=, cm3 eu kcal mol'' molecule-' SKI
ref 9
s- '
cm3 molecule-'
K,,, 1.68 x
-10.8
71.2 A 9 76.2
1l a 21b 23c 25d this workf
10-15,4,-,
rxp(l1980/T)
21.5 2.33 x I O - 2 7 exp(10870/T)
5 5 4 . 2 i- 1
71.6 -13 I 5 -12.6 2
*
73.8 i 2
25 0.14 7.2
5.79 x
exp(11 280/T)
Molecular modulation-UV absorption study at 283 K . Evaluation based on data from ref 9 and this work. R R K M calcu1ation;A factors based on analogous reactions. Evaluation based on data from ref 9 and 26. e Static photolysis/I:TIR study; data on reaction 1 bascd on results from ref 7. f See test for discussion. Based on AHfOlor,values for NO, and HO, from ref 22 and 24, respectively. NO2 reaction as for the H 0 2 disproportionation, however. In the latter reaction at 298 K, 16 torr of water approximately doubles the reaction rate while for the reaction with NO2, the enhancement is only about 50%. The temperature dependence of the water vapor effect is also smaller for the HOz + NO2 reaction. A dependence of 1600/T is observed for the third-order process HOz NO2 H20 HO2NO2 H20while 2800/ T is observed for the HOz H0, H 2 0-+ HzO, 0, H,O reaction over the same temperature ranges3' The explanation that has been proposed for the water vapor dependence supposes that HOz and water are in rapid equilibrium with a hydrogen-bonded c o m p l e ~ : ~ ~ ! ~ ~
+
+ +
-+
+
+ +
K
HO2 + HzO
I
A
-23
2
1
1
I
I
3
4
5
6
NOz can react with both complexed and uncomplexed HOz:
+ NO, + M + NO2 + M
HOz 7
HOyH,O
Ln PRESSURE (torr)
Figure 6. Plots of k l / k 2 = Kq vs. total pressure at 261.2 and 277.7 K. k , values are from this study, computed from eq I, while the k2 values
are experimental points from Graham et al. (ref 9). The independence of this ratio with total pressure shows the excellent consistency between the falloff curves measured for the forward and reverse reactions. mol-' for the standard entropy and enthalpy change of reaction 1, respectively. These quantities may be used to obtain the kinetic and thermodynamic quantities listed in Table V. This table also compares the values obtained by other groups. While there appears to be a reasonable consensus on the HO2NO2enthalpy of formation, estimates and measurements of the standard entropy vary widely. This leads to large differences in the computed high-pressure A factors and the expressions given for the equilibrium constant. At a temperature of 220 K, which is typical of the stratosphere at 24-km altitude, the values of the equilibrium constants in Table V vary by more than a factor of 10. An excellent check on the consistency of the measurements by different groups of the forward and reverse rate constants can be made by computing the ratio k l / k 2= Kq as a function of pressure. The ratio should be pressure independent. For this calculation, k2 values were taken from the Graham et al. study in which measurements were made over the pressure range 10-760 torr in N, at 261.2 K and separately in Nzand 0, at 277.7 K. Corresponding values of k , were computed from eq I by using the parameters listed in Table IV. A plot of kl/kz appears in Figure 6 and shows that while the individual values of k, and k2 vary by more than 20, the average deviation from the mean of the ratio k , / k z is only about 10%. Thus, there is excellent consistency between the falloff curves measured by Graham et al. and ourselves for the reverse and forward reactions, respectively. Effect of Water Vapor. The enhancement of the rate constant when water vapor is added has also been observed in the HOz + H0, r e a c t i ~ n . ' ~ The ~ ~ ~effect - ~ ~ is not as large for the H 0 2
+
(26) E. J. Hamilton, Jr., J. Chem. Phys., 63, 3682 (1975)
H02*H20
+
-+
HOzNO2
H02NOZ
+M
+ HZO + M
(1) (6)
Since complexed HOz appears to have very nearly the same UV cross section as the uncomplexed f ~ r m , ~the ~ observed ,'~ kinetic decay is that of the sum of the two species concentrations and the appropriate rate equation is
Assuming that complexation is a rapid equilibrium, then
Substituting dW021 dt
d[H0*43201 dt -(kl + ~G,K[HZol)[H021[NO21 = -kobsd[H021 [N021 +
The slopes of the lines in Figure 4 are therefore given by k6K. Lii et aL30have obtained values of K from experiments between 298 and 373 K although these estimates are subject to large uncertainties. At 298 K, Kwas determined to be (3 A 2) X lo-'' cm3 molecule-', which leads to a value of 3.3 X cm3 molecule-' s-l for kg. This is substantially larger than the rate constant obtained for the reaction of uncomplexed HOz with NO,, kl = 9.4 X cm3 molecule-' s-l, under the same conditions of pressure and temperature (350 torr of N,, 298 K). This is con(27) (28) (29) (30) (1981). (31)
E. J. Hamilton, Jr., and R.-R. Lii, In?. J . Chem. Kinet., 9,875 (1977). R. A. Cox and J. P. Burrows, J . Phys. Chem., 83, 2560 (1979). W. B. DeMore, J . Phys. Chem., 83, 1113 (1979). R.-R.Lii, M. C. Sauer, Jr., and S. Gordon, J . Phys. Chem., 85,2833 C. Kircher and S. P. Sander, in preparation.
1571
J. Phys. Chem. 1984,88, 1571-1575
+ NO2 + M O H + HO2N02 O H + HO2 HO2
sistent with the observations of Lii et al., who noted that the reactions HOyH20 + HO2 H202 + 0 2 + H2O -+
net:
and HOyH20
+ H02mH20
4
H202
+ 0 2 + 2H20
were significantly faster than the reaction between uncomplexed H 0 2 radicals. The likely explanation for this effect has to do with the relative stability of the Lindemann intermediate formed by complexed H02. As suggested by Thrush and T ~ n d a 1 1the , ~ ~intermediate formed by the reaction of H02.H20 with NO2 (or H 0 2 ) will be more stable with respect to redissociation than the uncomplexed intermediate because of the larger number of vibrational modes available for energy disposal. This results in an enhancement in the overall forward rate constant. The magnitude of the water vapor effect in both the H 0 2 H 0 2 and H 0 2 NO2 reactions apparently rules out the explanation that H 2 0 is simply acting as an efficient vibrational quencher. At 350 torr of N 2 at 298 K, the ratio kl(M = H20)/kl(M = N2) is about 20 while the same ratio for the H 0 2 H 0 2 reaction is 74. Since the N 2 collisional efficiency is usually 0.3 or greater, enhancements of this magnitude cannot be attributed solely to more rapid quenching. This apparent stabilization of the intermediate by complexed H02 suggests that other H 0 2 reactions such as H 0 2 O3and H 0 2 C10 which produce long-lived (>10-l2 s) intermediates may also show a water vapor dependence. htmospheric Implications. The H 0 2 + NO2 reaction takes which destroys dd-hydrogen (Hex) part in an atmospheric radicals:
+
+
+
+
+
(32) B. A. Thrush and G. S. Tyndall, Chem. Phys. Lett., 92,232 (1982). (33) R. D. Hudson et al., Eds., "The Stratosphere 1981: Theory and Measurements", WMO Global Research and Monitoring Project Report No. 11, World Meteorological Organization, Geneva, Switzerland, 1982. (34) L. Froidevaux, private communication.
+M H2O + 0 2 + NO2
-
+
H02NO2
H2O
(1) (7)
+0 2
Because reaction 7 is much slower than reaction 1 throughout most of the upper troposphere and lower stratosphere, the O H + H 0 2 N 0 2reaction is the rate-limiting step in the cycle. However, since the formation of H 0 2 N 0 2by reaction 1 and its destruction by photolysis are nearly in equilibrium, the H02N02mixing ratio is strongly influenced by k l . Since [H02N02]enters into the rate of reaction 7 , accurate values of k , are required for modeling purposes particularly since the above cycle dominates the loss of HO, throughout most of the troposphere and lower stratosphere. While the enhancement of the H 0 2 + NO2 reaction rate by water vapor observed in this study is substantial, the effect on the integrated HO, loss rate in the atmosphere is small. Using typical atmospheric conditions of temperature, pressure, and relative humidity, one can calculate the contribution of the water vapor effect to the overall rate as a function of altitude. The water vapor increases k l by 17% at the surface, but the rapid thermal decomposition of H 0 2 N 0 2at surface temperatures minimizes the effect of the O H H 0 2 N 0 2reaction. At higher altitudes, O H H 0 2 N 0 2increases in importance, but the water vapor enhancement of k , rapidly disappears due to the falling water vapor concentration. The net effect is therefore fairly small. 14933334
+
+
Acknowledgment. The research described in this paper was carried Out by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. We thank L. Froidevaux and Y. Yung for the use of results from their 1-d atmospheric model. Registry No. H02N02,26404-66-0; C12, 7782-50-5; CH30H, 6756-1; 02,7782-44-7; H02, 3170-83-0; NO2, 10102-44-0; N2,7727-37-9; He, 7440-59-7; H20, 7732-18-5.
Formation of Metastables and Dissociative Trapping in High-Energy Molecule-Surface Collisions Ron Elber and R. B. Gerber* Department of Physical Chemistry and The Fritz Haber Research Center f o r Molecular Dynamics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel (Received: June 14, 1983; In Final Form: August 19, 1983)
Dissociation of diatomic molecules in high-energy impact on a solid surface is studied by classical trajectory calculations for systems in the parameter regime E >> D 2. B where E is the collision energy and D and B are respectively the molecular and the atom-surface binding energies. The calculations are for model of I2 colliding with a smooth surface. The main results are as follows: (1) Dissociative trapping, corresponding to the reaction I2 + surface 1.-surface + I, remains appreciable even for E / B = 10, decreasing only slowly with energy. (2) The velocity distribution of I atom fragments is doubly peaked, the structure of the low-velocity peak reflecting the effect of dissociation trapping. (3) A substantial fraction (-5%) of the scattered I2 molecules emerge as metastables, in a rotational predissociation state, indicative of efficient translational-rotational energy transfer with large changes of angular momentum in the collision. (4) The average rotational excitation energy of the nondissociated molecules is higher than the vibrational one. Several experiments are suggested in light of these results.
-
1. Introduction
Dissociation dynamics in molecular impact on solid surfaces has been the topic of intensive research efforts in recent years. Experimentally, molecular beam scattering techniques have yielded increasingly detailed information on such processes.' Important (1) See, for instance, M. Balooch, M. J. Cardillo, D. R. Miller, and R. E. Stickney, Surf.Sci. 46,358 (1974); S. T. Ceyer and G. A. Somorjai, Annu. Rev. Phys. Chem., 28, 477 (1977); M. Salmeron, R. J. Gale, and G. A. Somorjai, J . Chem. Phys., 67,5324 (1977); 70,2087 (1979); S. L. Bernasek, Adc. Chem. Phys., 41, 477 (1980).
0022-3654/84/2088-1571$01.50/0
insight has been obtained also from theoretical studies employing classical trajectory simulation^.^-^ Many of the theoretical in(2) J. H. McCreery and G. Wolken, J. Chem. Phys , 64, 2845 (1976); Phys, Lett,, jg, 478 (1976), (3) A. Gelb and M. J. Cardillo, Surf. Sci., 75, 199 (1978) (4) G. C. Tantardini and M. Simonetta, Surf.Sci., 105, 512 (1981). ( 5 ) A. B. Elkowitz, J. H. McCreery, and G. Wolken, J . Chem. Phys., 17, 423 (1976). (6) A. Diebold and G. Wolken, Surf. Sci., 82, 245 (1979). (7) G. F. Tantardini and M. Simonetta, Chem. Phys. Lett., 87,420 (1982).
0 1984 American Chemical Society
