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Determination of the rate constant ratio for the reactions of the ethylperoxy radical with NO and NO2
Volume 168, number 1
CHEMICAL
PHYSICS LETTERS
20 April 1990
DETERMINATION OF THE RATE CONSTANT RATIO FOR THE REACTIONS OF THE ETHYLI’EROXY RADICAL WITH NO AND NO1 G. ELFERS, F. ZABEL
and ICH. BECKER
Physikalische Chemie, Fachbereich 9, Bergische Universitiit-Gesamthochschule Wuppertal, Gaussstrasse 24 D-5600 Wuppertal1, Federal Republic ofGermany Received 11 January 1990; in final form 5 February 1990
The thermal decomposition of ethyl peroxynitrate was studied in a 420 !2Dural glass reaction chamber in the presence of different initial [NO*]/ [NO] ratios. From an analysis of the data, the following rate constant ratios k2/kl for the reactions of C2H502radicals with NO (k,) and NOI (kz) were derived at different temperatures and total pressures: 0.81 kO.09 (255.6 R, 994 mbar), 0.50+0.04 (253.8 K, 100 mbar), 0.21 kO.05 (253.9 K, 10.2 mbar), and 0.43kO.05 (264.7 K, 101 mbar). Using literature values for k,, we derived kz from these ratios as a function of pressure. With the kz values from this work and literature values for the thermal decomposition rate constant of CzH,0zN02, the following expression was obtained by a third law analysis for the temperature dependence of the e@Jibrium constant of the reactions C2HJ02+N02~C2H,02N02: &=3.8x 10-z8 x exp( 10710K/T) cm3, Atmospheric implications of these results are discussed.
1. Introduction Ethane is the second most abundant hydrocarbon in the atmosphere and an important source of acetyl peroxynitrate (PAN), a typical oxidant present in the entire troposphere [ 11. The atmospheric degradation of ethane is initiated mainly via H atom abstraction by OH radicals or Cl atoms, leading to the formation of ethyl peroxy radicals. CZH502may react with either NO, N02, or other peroxy radicals. The rate constants for the reactions &H,Oz +NO-+C,H,O+NOt
(1)
and C2H50z +NOz =C~HSO~NOZ
(Z-2)
are not well established. Published values for k, [ 2,3 ] differ by a factor of 3, and the most recent CODATA compilation [4] states error limits of a factor of 2. Only one estimate of lc2exists in the literature [ 51, and error limits of a factor of 3 are estimated in the CODATA review [4] for this rate constant. Ethyl peroxynitrate, CzH,0zN02, is thermally unstable in the boundary layer but has a thermal lifetime of x 1 day in the upper troposphere [ 6 ] where it could act as a temporal reservoir for peroxy radicals and NO,. 14
As other loss processes for CZHS02N01 are probably slow, the actual lifetime of C2H502N02 in the upper troposphere will mainly depend on the rates of the competing reactions ( 1) and (2), i.e. on the ratio kzx PQllk,x [NOI. The rate constant ratio k,/k, is uncertain at the present time, as discussed above. Its value can be measured by following the decay of ethyl peroxynitrate in the presence of different [NO,] / [NO] ratios, as one of the consecutive reactions, i.e. reaction (2), leads to re-formation of CzHS02N02. In the present work, the ratio k2/kl was determined in this way at two temperatures, 254 and 265 K, and total pressures between 10 and 1000 mbar.
2. Experimental The experiments were performed in a temperature controlled ( - 25/ + 50”C) Duran glass reaction chamber of 420 IIvolume. The vessel is equipped with a built-in White mirror system for long-path IR absorption measurements with a Fourier-transform spectrometer (NICOLET 7 199 ) and surrounded by 24 fluorescence lamps for photolysis at wavelengths
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~300 nm. This apparatus has previously been described in more detail [ 71. Ethyl peroxynitrate was prepared in situ by photolyzing C12/C2H6/02/N02/N2 mixtures for 5- 10 min, according to the following mechanism: Cl2 +hv
+2Cl,
Cl+C2H6
-KzHS +HCl,
CzHs +W
+M)
42H502(
+W
+M) .
Care was taken to stop photolysis shortly before all the NO2 was consumed in order to avoid side reactions. Then the concentration of NO, was adjusted to the desired level by injecting additional NO2 in the dark. While the equilibrium of reactions (2) and ( -2) was maintained, the wall loss rate constant, k, of CzH502NOZ was measured by monitoring its IR absorption at 17 19 cm- *. Finally, NO was added using gas tight syringes. The decay of C2HSOzNOz accelerated due to reaction ( 1) competing with reaction (2). If one assumes quasistationary conditions for CZHSOl radicals, the relationship 1+ (b/h
I( [NO,]/ PI
1
(1)
can be derived, with kefl= -d(ln[C2H502NOZ])/dt-k,.
noise ratio. Temperatures were measured with a platinum resistance gauge extending about 25 cm into the reaction volume. Pressures were measured with capacitance manometers. Research grade &Ha, CIZ, 02, NZ, NO, and NOz were used.
3. Results and discussion
CzH502+NOz( +M)-KzHSOzN02(
k-J&=
20 April 1990
(II)
Although the [NOz ] / [ NO] ratio, and therefore kefl, may change with reaction time, & decreased only very slowly in most experiments thus exhibiting a well-defined slope in the plot of In [ C2H502N02 ] as a function of time. kerrwas determined for different initial [NOz]J [NO], ratios, and the ratio k2/kl was calculatedfromaplotk_,/k,,versus [NO,]/[NO] according to eq. (I). The concentrations of NO and NOZ were measured in each experiment as a function of time by long-path IR absorption. Effective IR absorption coefficients of NO and NO2 were determined as a function of temperature, total pressure, and partial pressure of NO or NO2 in separate experiments. Typically, 15 absorption spectra were consecutively measured in the kinetic experiments, with the total reaction times ranging from 2 to 10 min. Single ab-
sorption spectra were obtained by co-adding and averaging several interferograms for a better signal-to-
The ratios k_,/k,,from each experiment are plotted as a function of the effective [ NO2] / [NO ] ratios for different conditions in figs. 1a- 1c. Error bars of single data points correspond to 2g errors of the linear portions of In [ C2HS02N02] versus time plots. The straight lines are least-square fits of the experimental data points, in which the point ( [NO21 / [NO] =0, k_z/kea= 1) is weighted so that the line must pass through this point. The error limits attributed to the slope are la errors with each data point, including that for [NO,]/[NO]=O, being equally weighted. For the slope, la error limits are chosen instead of 20, because the statistical error is reduced by the inclusion of the point [NO,]/ [NO] =O. From the slopes of these plots, the ratios k,/k, are calculated according to eq. (I) and summarihed in table 1. The ratio k2/ k, is definitely pressure dependent in the 1O-l 000 mbar range. This result was expected, as (i ) the reaction rate constants of Ron + NO reactions seem to be pressure independent (see fig. 2) and (ii) reaction ( -2) is distinctively pressure dependent between 10 and 1000 mbar [6] and the same, therefore, must be valid for the reverse reaction (2). At 100 mbar, k,/k, shows a small negative temperature dependence which is virtually zero within the combinated error limits. This observation is also reasonable, as the rate constants of R02+N0 reactions are nearly temperature independent [4] and a small negative activation energy is to be expected for the recombination rate constant k2 in its fall-off region. Previous values of kl and k2 from the literature are subject to considerable uncertainty. From the k2 and k, values recommended in the most recent CODATA evaluation [ 41, a ratio k2/kl = (5 x 10-” cm3/s)/(8.9X lo-I2 cm’/s)=0.56 is derived for 1013 mbar, 298 K, with an overall uncertainty of a factor of 6. This may be compared with the present value 0.8 1 k 0.09 at 994 mbar, 25 5.6 K. Thus the er15
Volume 168, number 1
CHEMICAL PHYSICS LETTERS
20 April 1990
1.6
slope: 0.81t 0.09Hal
255.6 K 991 mbar
I 0.0
I
I
0.2
I
0.4 INO$INOI
%
I
I
0.6
0.8
1.0
I
2.0 $ 253.8K. 100 mbar
lbt
zy 1.5 Y
b 1.0
0
1
2
3
[NO2ll[NOl
Fig. 1. (a)-(c): Plots of k_,/bas
16
a function of the [NO,] / [NO] ratio for the reaction C2~s~z~02-rkproduc.
Volume 168,number 1
CHEMICALPHYSICSLETTERS ,
1.4
I
I
I
20 April 1990 I
I
slope; 0.21+0.05Ilo) z =a 1.2 z?
Fig. 1. Continued. Table 1 Rate constant ratios k2/k, fromplotsof k_Jk,
as a functionof
the [NO*]/ [ NO] ratios Data
T
PuOt
from
W)
(mbar)
k,lk, (loerror)
fig.
la lb
kza’ ( 1o-‘2
cm3/s) 255.6+0.6 253.82 1.4
1C
2x3.9+ 0.2
Id
264.7kO.5
994 +2
0.81 f0.09
7.2
loo
0.5o?r 0.04
4.5
f2
10.2_+0.1
101 f2
‘) From k,/k, withk,=8.9~
0.2 1+ 0.05
1.8
0.43 * 0.05
3.8
lo-l2 cm’/s.
ror limits for k2jk, could be considerably reduced in the present work. In addition, the pressure dependence of kJk, was measured for the pressure range which is of atmospheric interest showing that the pressure and temperature dependencies of k2/k, with increasing height above the ground are small and largely compensate each other. The reaction of methylperoxy radicals with NO, CH302 +NO-,CHsO+NOz
,
(3)
has been found to be nearly pressure and temperature independent between 240 and 360 K [4] and its rate constant at 10 13 mbar and 298 K is considered to be well known (( 7.6+ 1.9) x lo-‘* cm3/s [ 41). Rate constants for reaction (3) and other R02 +NO reactions at room temperature are collected in fig. 2. The rate constants for R&H5 and i-C3H7 from Basco and Adachi [2,9] are probably low due to interference by nitrate products disturbing the UV monitoring of R02 radicals (see discussion in ref. [8 ] ). If one omits the values of Basco and Ada&i, the value of Plumb et al. [ 31
k, x 8.9x lo-” cm3/s is considered to be an appropriate one to estimate k2 as a function of pressure from the k2/kl ratios of the present work. The results thus obtained for k2 are included in table I and compared in fig_ 3 with other rate constants from the literature for the reactions ROz + NO,+ products. The pressure dependence of k2 clearly fits to the pressure dependencies observed for R = H [ 4 1, CH, [ 8 1, CX, with X=Cl and/or F [12], and CH&O [13]. As the pressure dependence of k2 and of the rate constant k_* for the reverse reaction must be the same, the experimentally determined reduced fall-off curve for k_2 from ref. [ 61 was fitted to the three data points for k2 derived from the present experiments (broken line in fig. 3). In this way, the following set of fall-off parameters is obtained for k2 in Troe’s notation [4,14] at 254 K: k,=l.OxlO-“cm3/s, kJ[N,]
=4.8x 1O-29cm6/s,
F,=O.3
(fromref. [6]) .
It should be kept in mind, however, that these values for k2 depend on the correct value of k,. With the k2 values from table 1 for a total pressure of 100 mbar and the corresponding values for k_2 derived from ref. [ 61, the equilibrium constants K,=k2/k_l=8.05x10-‘*cm3and 1.36~10-‘*cm~ are calculated at 253.8 K and 264.7 K, respectively. Since the temperature regime is too limited to deduce a reliable heat of reaction from van ‘t HOE’S relation, a third law procedure has been applied for this purpose. The entropy of reactions (2 ) and ( - 2) 17
Volume 168, number 1
CHEMICAL PHYSICS LETTERS
-10.5l
I
I
20 April 1990
I
I
I
CFCl2 , .CF3]6l ^_ a.,_,
I CH3C0 ]I 1
5
-11.0 c T
i-C3H7]51
R02+NO+RO+N02
16.5
110
175
ia0
19.0
la5
185
log (IMllcm-3l Fig. 2. Rate constants for the reactions ROs+NO+RO+NOa, R=H, CHs, CzH,, i-&H,, CF,, CFCI,, CF,Cl, CF3, and CH,CO at room temperature and different pressures (from the literature). 1 error limits, (1) ref. 181, (2) ref. [4], (3) ref. [3], (4) ref. [2], (5) ref. 191, (6) ref. [lo].
170
17.5
18.0
19.0
18.0
lg.5
log I]M]lcm’31 Fig. 3. Pressure dependencies of the rate constants for the reactions R0s+N02-rR02NOs, R=H, CHr, CsHs, CFs, CFCls, Ccl,, and CHrCO. Idata pointsfrom the present work at 254 K (see table I), broken line: tit to the data points with F,=O.3 (see text; $ ref. [ 111, 298K;fulllines:literaturedataatroomtemperature-(1)ref.[4],(2)ref.[8],(3)ref.[5],(4)ref.[12],(5)ref.[13].
was assumed to be equal to the entropy change of the equivalent reaction CH30z +NO, =CH30,NOz. 18
(43-4)
AS&,8 = -160.2kJ/mol is calculatedusingK, (298 K)=2.53x lo-‘* cm3 and AH$98= -92.2 kJ/mol for reaction (4) from ref. [ 61. With this value for AS: and the above equilibrium constants for reac-
Volume168,number 1
CHEMICAL PHYSICSLETTERS
tion (2 ), - 9 1.Oand - 90.9 kJ/mol are obtained for AEIy at 253.8 and 264.7 IS, respectively. With the vibrational frequencies of C2HJ02N02 from ref. [ 6 ] and estimated frequencies for C2HS02, an average A@,298= -91.6 t- 3.7 kJ/mol is obtained for reaction (2), where the error limits mainly reflect the uncertainty of the heat of reaction (4). With MF.274 = - 91.3 kJ/mol and K, (253.8 K)=S.OS x lo-lo cm3, the relationship K, = 3.8 x 1O-” x exp ( 10710 K/T) cm’ results. Again, this expression depends on the correct value for k1 and changes proportionally to the deviation of kl from the presently applied value 8.9X lo-l2 cm’/s. A useful check on the consistency of the above analysis is the comparison of the present results for k2 with unpublished data of Bingemann and Zellner [ 141 who measured k,= (1.8kO.2) x lo-” cm3/s at 10.4 mbar and 298 K using a laser photolysis-laser absorption technique. The k2 value at their reaction conditions can be calculated using k_2 from ref. [ 61 and the above expression for the temperature dependence of &. The value k2= 1.30~ 10-Lz cm3/s results which is 44% lower than Bingemann and Zellner’s value. The agreement between both values is satisfactory considering the indirect method of deducing a room temperature value for /c2in the present work. The difference might be due to the long extrapolation of k,/k, from the experimental temperature range 254-265 K to 298 K. Alternatively, the value for k, used in the present analysis may be high by a corresponding amount. In the atmosphere, reaction (2) will not play any role close to the ground as it is reversible, the thermal lifetime of ethyl peroxynitrate being less than 1 s at 298 K [ 61. However, with increasing altitude, i.e. with decreasing temperature, the thermal lifetime of CzH502N02 increases and reaches 1: 1 day in the upper troposphere. Under these conditions, loss processes other than ( - 2 ) may be operative for CZHSOZN02(photolysis, reactions with OH or Cl), representing a potential sink for NO,.
4. Conclusions The ratios k2/kl determined in the present work are consistent with the pressure dependence previ-
20April 1990
ously observed for k_2 and with the most recent investigations on the rates of the individual reactions (1) and (2). Reactions (I) and (2) have approximately the same rate constants throughout the troposphere. As (2) is reversible at ambient temperatures, this reaction is important only in the upper troposphere where the recombination product CZHS02N02 may represent a temporal reservoir of NO, and, by loss reactions other than ( -2), a potential sink of NO,.
Acknowledgement Financial support by the Commission of the European Communities (CEC) under contract No. EV4V-0082-C is gratefully acknowledged. We thank R. Zellner for communication of results prior to publication.
References [ 11H.B. Singh and L.J.SaIas,Nature302(1983)326. [ 2] I-L Adachi and N. Basso, Chem. Phys. Letters 64 (1979) 431. [3] I.C. Plumb, K.R. Ryan, J.R. Steven and M.F.R. Mulcahy, Intern. J. Chem. Kinetics 14 (1982) 183. [4] R. Atkinson, D.L. Baulch, R.A. Cox, R.F. Hampson Jr., J.A. Kerr and J. Trot, J. Phys. Chem. Ref. Data 18 ( 1989) 88 1. [ 51 H. Adachi and N. Basco, Chem. Phys. Letters 67 (1979) 324. [6] F. Zabel, A. Rehner, K.H.Becker and E.H. Fink, J. Phys. Chem. 93 (1989) 5500. [ 71 I. Barnes, K.H. Becker, E.H. Fink, A. Reimer, F. Zabel and H.Niki,Chem.Phys.L.etters115 (1985) 1. [ 81 D.L.Baulch, R.A. Cox, R.F. Hampson Jr., J.A. Kerr, J.Troe andR.T.Watson, J. Phys. Chem. Ref. Data 13 (1984) 1259. [9] H. Adachi and N. Basco, Intern. J. Chem. Kinetics 14 (1982) 1243. [ lo] A.M. Dognon, F. Caralp and R. Lesclaux, J. Chim. Phys. 82 (1985) 349.’ [ 111 D. Bingemann and R. Zellner, private communication (1989). [ 121 F. Caralp, R. Lesclaux, M.-T. Rayez, J.-C. Rayez and W. Forst, J. Chem. Sot. Faraday Trans. II 84 (1988) 569. [ 131 I. Bridier, F. Caralp, R. Lesclaux, H. Loirat, M.-T. Rayez, B. Veyret, A. Reimer, F. Zabel and K.H. Becker, in preparation. [14]J.Troe,J.Phys.Chem.83 (1979) 114.
19
CHEMICAL
PHYSICS LETTERS
20 April 1990
DETERMINATION OF THE RATE CONSTANT RATIO FOR THE REACTIONS OF THE ETHYLI’EROXY RADICAL WITH NO AND NO1 G. ELFERS, F. ZABEL
and ICH. BECKER
Physikalische Chemie, Fachbereich 9, Bergische Universitiit-Gesamthochschule Wuppertal, Gaussstrasse 24 D-5600 Wuppertal1, Federal Republic ofGermany Received 11 January 1990; in final form 5 February 1990
The thermal decomposition of ethyl peroxynitrate was studied in a 420 !2Dural glass reaction chamber in the presence of different initial [NO*]/ [NO] ratios. From an analysis of the data, the following rate constant ratios k2/kl for the reactions of C2H502radicals with NO (k,) and NOI (kz) were derived at different temperatures and total pressures: 0.81 kO.09 (255.6 R, 994 mbar), 0.50+0.04 (253.8 K, 100 mbar), 0.21 kO.05 (253.9 K, 10.2 mbar), and 0.43kO.05 (264.7 K, 101 mbar). Using literature values for k,, we derived kz from these ratios as a function of pressure. With the kz values from this work and literature values for the thermal decomposition rate constant of CzH,0zN02, the following expression was obtained by a third law analysis for the temperature dependence of the e@Jibrium constant of the reactions C2HJ02+N02~C2H,02N02: &=3.8x 10-z8 x exp( 10710K/T) cm3, Atmospheric implications of these results are discussed.
1. Introduction Ethane is the second most abundant hydrocarbon in the atmosphere and an important source of acetyl peroxynitrate (PAN), a typical oxidant present in the entire troposphere [ 11. The atmospheric degradation of ethane is initiated mainly via H atom abstraction by OH radicals or Cl atoms, leading to the formation of ethyl peroxy radicals. CZH502may react with either NO, N02, or other peroxy radicals. The rate constants for the reactions &H,Oz +NO-+C,H,O+NOt
(1)
and C2H50z +NOz =C~HSO~NOZ
(Z-2)
are not well established. Published values for k, [ 2,3 ] differ by a factor of 3, and the most recent CODATA compilation [4] states error limits of a factor of 2. Only one estimate of lc2exists in the literature [ 51, and error limits of a factor of 3 are estimated in the CODATA review [4] for this rate constant. Ethyl peroxynitrate, CzH,0zN02, is thermally unstable in the boundary layer but has a thermal lifetime of x 1 day in the upper troposphere [ 6 ] where it could act as a temporal reservoir for peroxy radicals and NO,. 14
As other loss processes for CZHS02N01 are probably slow, the actual lifetime of C2H502N02 in the upper troposphere will mainly depend on the rates of the competing reactions ( 1) and (2), i.e. on the ratio kzx PQllk,x [NOI. The rate constant ratio k,/k, is uncertain at the present time, as discussed above. Its value can be measured by following the decay of ethyl peroxynitrate in the presence of different [NO,] / [NO] ratios, as one of the consecutive reactions, i.e. reaction (2), leads to re-formation of CzHS02N02. In the present work, the ratio k2/kl was determined in this way at two temperatures, 254 and 265 K, and total pressures between 10 and 1000 mbar.
2. Experimental The experiments were performed in a temperature controlled ( - 25/ + 50”C) Duran glass reaction chamber of 420 IIvolume. The vessel is equipped with a built-in White mirror system for long-path IR absorption measurements with a Fourier-transform spectrometer (NICOLET 7 199 ) and surrounded by 24 fluorescence lamps for photolysis at wavelengths
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~300 nm. This apparatus has previously been described in more detail [ 71. Ethyl peroxynitrate was prepared in situ by photolyzing C12/C2H6/02/N02/N2 mixtures for 5- 10 min, according to the following mechanism: Cl2 +hv
+2Cl,
Cl+C2H6
-KzHS +HCl,
CzHs +W
+M)
42H502(
+W
+M) .
Care was taken to stop photolysis shortly before all the NO2 was consumed in order to avoid side reactions. Then the concentration of NO, was adjusted to the desired level by injecting additional NO2 in the dark. While the equilibrium of reactions (2) and ( -2) was maintained, the wall loss rate constant, k, of CzH502NOZ was measured by monitoring its IR absorption at 17 19 cm- *. Finally, NO was added using gas tight syringes. The decay of C2HSOzNOz accelerated due to reaction ( 1) competing with reaction (2). If one assumes quasistationary conditions for CZHSOl radicals, the relationship 1+ (b/h
I( [NO,]/ PI
1
(1)
can be derived, with kefl= -d(ln[C2H502NOZ])/dt-k,.
noise ratio. Temperatures were measured with a platinum resistance gauge extending about 25 cm into the reaction volume. Pressures were measured with capacitance manometers. Research grade &Ha, CIZ, 02, NZ, NO, and NOz were used.
3. Results and discussion
CzH502+NOz( +M)-KzHSOzN02(
k-J&=
20 April 1990
(II)
Although the [NOz ] / [ NO] ratio, and therefore kefl, may change with reaction time, & decreased only very slowly in most experiments thus exhibiting a well-defined slope in the plot of In [ C2H502N02 ] as a function of time. kerrwas determined for different initial [NOz]J [NO], ratios, and the ratio k2/kl was calculatedfromaplotk_,/k,,versus [NO,]/[NO] according to eq. (I). The concentrations of NO and NOZ were measured in each experiment as a function of time by long-path IR absorption. Effective IR absorption coefficients of NO and NO2 were determined as a function of temperature, total pressure, and partial pressure of NO or NO2 in separate experiments. Typically, 15 absorption spectra were consecutively measured in the kinetic experiments, with the total reaction times ranging from 2 to 10 min. Single ab-
sorption spectra were obtained by co-adding and averaging several interferograms for a better signal-to-
The ratios k_,/k,,from each experiment are plotted as a function of the effective [ NO2] / [NO ] ratios for different conditions in figs. 1a- 1c. Error bars of single data points correspond to 2g errors of the linear portions of In [ C2HS02N02] versus time plots. The straight lines are least-square fits of the experimental data points, in which the point ( [NO21 / [NO] =0, k_z/kea= 1) is weighted so that the line must pass through this point. The error limits attributed to the slope are la errors with each data point, including that for [NO,]/[NO]=O, being equally weighted. For the slope, la error limits are chosen instead of 20, because the statistical error is reduced by the inclusion of the point [NO,]/ [NO] =O. From the slopes of these plots, the ratios k,/k, are calculated according to eq. (I) and summarihed in table 1. The ratio k2/ k, is definitely pressure dependent in the 1O-l 000 mbar range. This result was expected, as (i ) the reaction rate constants of Ron + NO reactions seem to be pressure independent (see fig. 2) and (ii) reaction ( -2) is distinctively pressure dependent between 10 and 1000 mbar [6] and the same, therefore, must be valid for the reverse reaction (2). At 100 mbar, k,/k, shows a small negative temperature dependence which is virtually zero within the combinated error limits. This observation is also reasonable, as the rate constants of R02+N0 reactions are nearly temperature independent [4] and a small negative activation energy is to be expected for the recombination rate constant k2 in its fall-off region. Previous values of kl and k2 from the literature are subject to considerable uncertainty. From the k2 and k, values recommended in the most recent CODATA evaluation [ 41, a ratio k2/kl = (5 x 10-” cm3/s)/(8.9X lo-I2 cm’/s)=0.56 is derived for 1013 mbar, 298 K, with an overall uncertainty of a factor of 6. This may be compared with the present value 0.8 1 k 0.09 at 994 mbar, 25 5.6 K. Thus the er15
Volume 168, number 1
CHEMICAL PHYSICS LETTERS
20 April 1990
1.6
slope: 0.81t 0.09Hal
255.6 K 991 mbar
I 0.0
I
I
0.2
I
0.4 INO$INOI
%
I
I
0.6
0.8
1.0
I
2.0 $ 253.8K. 100 mbar
lbt
zy 1.5 Y
b 1.0
0
1
2
3
[NO2ll[NOl
Fig. 1. (a)-(c): Plots of k_,/bas
16
a function of the [NO,] / [NO] ratio for the reaction C2~s~z~02-rkproduc.
Volume 168,number 1
CHEMICALPHYSICSLETTERS ,
1.4
I
I
I
20 April 1990 I
I
slope; 0.21+0.05Ilo) z =a 1.2 z?
Fig. 1. Continued. Table 1 Rate constant ratios k2/k, fromplotsof k_Jk,
as a functionof
the [NO*]/ [ NO] ratios Data
T
PuOt
from
W)
(mbar)
k,lk, (loerror)
fig.
la lb
kza’ ( 1o-‘2
cm3/s) 255.6+0.6 253.82 1.4
1C
2x3.9+ 0.2
Id
264.7kO.5
994 +2
0.81 f0.09
7.2
loo
0.5o?r 0.04
4.5
f2
10.2_+0.1
101 f2
‘) From k,/k, withk,=8.9~
0.2 1+ 0.05
1.8
0.43 * 0.05
3.8
lo-l2 cm’/s.
ror limits for k2jk, could be considerably reduced in the present work. In addition, the pressure dependence of kJk, was measured for the pressure range which is of atmospheric interest showing that the pressure and temperature dependencies of k2/k, with increasing height above the ground are small and largely compensate each other. The reaction of methylperoxy radicals with NO, CH302 +NO-,CHsO+NOz
,
(3)
has been found to be nearly pressure and temperature independent between 240 and 360 K [4] and its rate constant at 10 13 mbar and 298 K is considered to be well known (( 7.6+ 1.9) x lo-‘* cm3/s [ 41). Rate constants for reaction (3) and other R02 +NO reactions at room temperature are collected in fig. 2. The rate constants for R&H5 and i-C3H7 from Basco and Adachi [2,9] are probably low due to interference by nitrate products disturbing the UV monitoring of R02 radicals (see discussion in ref. [8 ] ). If one omits the values of Basco and Ada&i, the value of Plumb et al. [ 31
k, x 8.9x lo-” cm3/s is considered to be an appropriate one to estimate k2 as a function of pressure from the k2/kl ratios of the present work. The results thus obtained for k2 are included in table I and compared in fig_ 3 with other rate constants from the literature for the reactions ROz + NO,+ products. The pressure dependence of k2 clearly fits to the pressure dependencies observed for R = H [ 4 1, CH, [ 8 1, CX, with X=Cl and/or F [12], and CH&O [13]. As the pressure dependence of k2 and of the rate constant k_* for the reverse reaction must be the same, the experimentally determined reduced fall-off curve for k_2 from ref. [ 61 was fitted to the three data points for k2 derived from the present experiments (broken line in fig. 3). In this way, the following set of fall-off parameters is obtained for k2 in Troe’s notation [4,14] at 254 K: k,=l.OxlO-“cm3/s, kJ[N,]
=4.8x 1O-29cm6/s,
F,=O.3
(fromref. [6]) .
It should be kept in mind, however, that these values for k2 depend on the correct value of k,. With the k2 values from table 1 for a total pressure of 100 mbar and the corresponding values for k_2 derived from ref. [ 61, the equilibrium constants K,=k2/k_l=8.05x10-‘*cm3and 1.36~10-‘*cm~ are calculated at 253.8 K and 264.7 K, respectively. Since the temperature regime is too limited to deduce a reliable heat of reaction from van ‘t HOE’S relation, a third law procedure has been applied for this purpose. The entropy of reactions (2 ) and ( - 2) 17
Volume 168, number 1
CHEMICAL PHYSICS LETTERS
-10.5l
I
I
20 April 1990
I
I
I
CFCl2 , .CF3]6l ^_ a.,_,
I CH3C0 ]I 1
5
-11.0 c T
i-C3H7]51
R02+NO+RO+N02
16.5
110
175
ia0
19.0
la5
185
log (IMllcm-3l Fig. 2. Rate constants for the reactions ROs+NO+RO+NOa, R=H, CHs, CzH,, i-&H,, CF,, CFCI,, CF,Cl, CF3, and CH,CO at room temperature and different pressures (from the literature). 1 error limits, (1) ref. 181, (2) ref. [4], (3) ref. [3], (4) ref. [2], (5) ref. 191, (6) ref. [lo].
170
17.5
18.0
19.0
18.0
lg.5
log I]M]lcm’31 Fig. 3. Pressure dependencies of the rate constants for the reactions R0s+N02-rR02NOs, R=H, CHr, CsHs, CFs, CFCls, Ccl,, and CHrCO. Idata pointsfrom the present work at 254 K (see table I), broken line: tit to the data points with F,=O.3 (see text; $ ref. [ 111, 298K;fulllines:literaturedataatroomtemperature-(1)ref.[4],(2)ref.[8],(3)ref.[5],(4)ref.[12],(5)ref.[13].
was assumed to be equal to the entropy change of the equivalent reaction CH30z +NO, =CH30,NOz. 18
(43-4)
AS&,8 = -160.2kJ/mol is calculatedusingK, (298 K)=2.53x lo-‘* cm3 and AH$98= -92.2 kJ/mol for reaction (4) from ref. [ 61. With this value for AS: and the above equilibrium constants for reac-
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CHEMICAL PHYSICSLETTERS
tion (2 ), - 9 1.Oand - 90.9 kJ/mol are obtained for AEIy at 253.8 and 264.7 IS, respectively. With the vibrational frequencies of C2HJ02N02 from ref. [ 6 ] and estimated frequencies for C2HS02, an average A@,298= -91.6 t- 3.7 kJ/mol is obtained for reaction (2), where the error limits mainly reflect the uncertainty of the heat of reaction (4). With MF.274 = - 91.3 kJ/mol and K, (253.8 K)=S.OS x lo-lo cm3, the relationship K, = 3.8 x 1O-” x exp ( 10710 K/T) cm’ results. Again, this expression depends on the correct value for k1 and changes proportionally to the deviation of kl from the presently applied value 8.9X lo-l2 cm’/s. A useful check on the consistency of the above analysis is the comparison of the present results for k2 with unpublished data of Bingemann and Zellner [ 141 who measured k,= (1.8kO.2) x lo-” cm3/s at 10.4 mbar and 298 K using a laser photolysis-laser absorption technique. The k2 value at their reaction conditions can be calculated using k_2 from ref. [ 61 and the above expression for the temperature dependence of &. The value k2= 1.30~ 10-Lz cm3/s results which is 44% lower than Bingemann and Zellner’s value. The agreement between both values is satisfactory considering the indirect method of deducing a room temperature value for /c2in the present work. The difference might be due to the long extrapolation of k,/k, from the experimental temperature range 254-265 K to 298 K. Alternatively, the value for k, used in the present analysis may be high by a corresponding amount. In the atmosphere, reaction (2) will not play any role close to the ground as it is reversible, the thermal lifetime of ethyl peroxynitrate being less than 1 s at 298 K [ 61. However, with increasing altitude, i.e. with decreasing temperature, the thermal lifetime of CzH502N02 increases and reaches 1: 1 day in the upper troposphere. Under these conditions, loss processes other than ( - 2 ) may be operative for CZHSOZN02(photolysis, reactions with OH or Cl), representing a potential sink for NO,.
4. Conclusions The ratios k2/kl determined in the present work are consistent with the pressure dependence previ-
20April 1990
ously observed for k_2 and with the most recent investigations on the rates of the individual reactions (1) and (2). Reactions (I) and (2) have approximately the same rate constants throughout the troposphere. As (2) is reversible at ambient temperatures, this reaction is important only in the upper troposphere where the recombination product CZHS02N02 may represent a temporal reservoir of NO, and, by loss reactions other than ( -2), a potential sink of NO,.
Acknowledgement Financial support by the Commission of the European Communities (CEC) under contract No. EV4V-0082-C is gratefully acknowledged. We thank R. Zellner for communication of results prior to publication.
References [ 11H.B. Singh and L.J.SaIas,Nature302(1983)326. [ 2] I-L Adachi and N. Basso, Chem. Phys. Letters 64 (1979) 431. [3] I.C. Plumb, K.R. Ryan, J.R. Steven and M.F.R. Mulcahy, Intern. J. Chem. Kinetics 14 (1982) 183. [4] R. Atkinson, D.L. Baulch, R.A. Cox, R.F. Hampson Jr., J.A. Kerr and J. Trot, J. Phys. Chem. Ref. Data 18 ( 1989) 88 1. [ 51 H. Adachi and N. Basco, Chem. Phys. Letters 67 (1979) 324. [6] F. Zabel, A. Rehner, K.H.Becker and E.H. Fink, J. Phys. Chem. 93 (1989) 5500. [ 71 I. Barnes, K.H. Becker, E.H. Fink, A. Reimer, F. Zabel and H.Niki,Chem.Phys.L.etters115 (1985) 1. [ 81 D.L.Baulch, R.A. Cox, R.F. Hampson Jr., J.A. Kerr, J.Troe andR.T.Watson, J. Phys. Chem. Ref. Data 13 (1984) 1259. [9] H. Adachi and N. Basco, Intern. J. Chem. Kinetics 14 (1982) 1243. [ lo] A.M. Dognon, F. Caralp and R. Lesclaux, J. Chim. Phys. 82 (1985) 349.’ [ 111 D. Bingemann and R. Zellner, private communication (1989). [ 121 F. Caralp, R. Lesclaux, M.-T. Rayez, J.-C. Rayez and W. Forst, J. Chem. Sot. Faraday Trans. II 84 (1988) 569. [ 131 I. Bridier, F. Caralp, R. Lesclaux, H. Loirat, M.-T. Rayez, B. Veyret, A. Reimer, F. Zabel and K.H. Becker, in preparation. [14]J.Troe,J.Phys.Chem.83 (1979) 114.
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