The Journal of Physical Chemistry, Vol. 83, No. 25, 1979 3207
Exchange Reaction between CIONOz and l5NO2
grant to J.E.S. (GM 13,116). References a n d Notes
M. Eigen, Angew. Chem., Int. Ed. Engl., 3, 1 (1964). G. Ilgenfritz, Ph.D. Thesis, University of Goettingen, 1966. M. Eigen and G. G. Hammes, J. Am. Chem. Soc., 82,5951 (1960). D. J. Lentz, J. E. C. Hutchins, and E. M. Eyring, J . Phys. Chem., 78, 1021 (1974). (10) M. C. Rose and J. E. Stuehr, J. Am. Chem. Soc., 90, 7205 (1968). (11) M. Dreyfus, "Proton and Ions Involved in Fast Dynamic Phenomena", P. Laszlo, Ed., Elsevier, New York, 1978, p 169. (12) G. C. Medeiros and G. J. Thomas, Jr., Biochem. Biophys. Acta, 238, l(1971). (6) (7) (8) (9)
(1) Most recent paper in this series: C.M. Frey and J. E. Stuehr, J . Am. Chem. Soc., 100, 139 (1978). sOc" 45' 486 (2) w' " Orndorff and F' w' Sherwood' J ' Am' (1923). (3) M. Eigen and L. DeMaeyer, Tech. Org. Chem., 8, 895 (1963). (4) The numbering system for A is based on the notation in scheme B. (5) M. Egen, W. Kruse, G. Maass, and L. DeMaeyer, Rog. React. Kinet., 2 (1964).
Pressure Dependence of the Exchange Reaction between CIONO:, and 15N02+ G. Schonle, H.-D. Knauth, and R. N. Schindler" Institut fur fhysikalische Chemie der Universitat Kid, 02300, Kiel, West Germany (Received March 2 f , 1979)
-
The kinetics of the reaction CIONOz + Nz C10 + NOz + Nz (-1) have been investigated at 313 and 333 K and total pressures from about 1 to 180 torr by infrared absorption measurements of C1015NOzformation in mixtures of C10N0z-'5N0z-Nz. No deviation from first-order [N,] dependence is observed for pressures 1120 = torr. The pressure dependence and the low order rate constant kl/cm3 mol-' exp(-11820/T) are in good agreement with the result of a former ClONO, decomposition study. Rate constants for the stratospheric relevant recombination reaction C10 + NO2 + Nz ClONOz + Nz (1)derived from this study by combination of klwith the known equilibrium constant for the reaction CIONOz = C10 + NOz are about three times smaller than the values obtained from discharge flow measurements. Possible reasons for the discrepancies are discussed.
-
Introduction Chlorine nitrate formation in the stratosphere is suggested to slow down ozone consumption by tying up chlorine photoproduced from chlorofluorocarbons. On the basis of model calculations the CIONOz production could interfere with the catalytic O3 destruction in both the chlorine and the nitrogen oxide cycles. The recommended rate constant for the formation of chlorine nitrate C10 NO2 (+ M) ClONOz (+ M) (1)
-
+
is based on three studies carried out in flow systems in the low pressure region of up to 6 torr of Nz. Zahniser et al.' followed the reaction by indirect detection of C10. Upon addition of NO to the flow system C10 was quantitatively converted to C1 which was detected by resonance fluorescence at 134.7 nm. Leu et ala2reported on measurements in a discharge flow mass spectrometer apparatus. Birks et ala3employed a similar technique in their investigations. No experimental values are available on the rate of recombination reaction 1 a t higher pressures where the reaction might be in its falloff region. Substantial deviations from first-order [MI dependence at pressures larger than 10 torr were predicted by two theoretical falloff studies4s5for reaction 1. Zellner's4 falloff calculations are based on weak-collision models6 by use of reduced Kassel integrals with low-pressure and highpressure limiting rate constants as reference points. These points are taken from experimental data'-3 and model calculations,' respectively. Application of RRKM theory in conjunction with a modified Gorin transition state by Smith and Golden5yielded a falloff of 35% at the highest stratospheric pressure of 50 torr and a representative stratospheric temperature of 220 K. N
'This paper is dedicated t o Professor Dr. W. Luttke, Gottingen. 0022-3654/79/2083-3297$01 .OO/O
The results of these calculations were not supported by a recent finding by Knauths who studied the thermal decomposition of ClONO, (reaction -1) in the presence of the OC1-scavenger NO. Deviation from the low-pressure region was found to be less than 5% at p(Nz) = 210 torr. At the highest pressure used, Le., p(NJ = 350 torr, a deviation of only 20% was observed. In the present work the rate of exchange of NOz was studied in the system C10N0z-15N0z-Nz as a function of reaction time, nitrogen pressure, and temperature. The formation of the product C1015NOzis described to result from a pathway consisting of (-1) followed by recombination reaction l a and direct exchange in a metathetical
-
+ 15N02(+ N,) ClONO, + l5NOZ
C10
C1015N02(+ N,)
C10'5N02 + NOz
(la) (2)
step (reaction 2). Following the rate of formation of the labeled product with IR spectroscopy as function of reaction time, we obtained data which allowed the calculation of rate constants for steps l a and 2. No deviation from the low-pressure value was observed for nitrogen pressures up to 120 torr. Experimental Section Chlorine nitrate was prepared and purified as described previo~sly.~ The labeled nitrogen dioxide (99 atom %) was supplied by Amersham-Buchler. It was purified by recrystallization to remove impurities of NO and Nz03. Messer-Griesheim Nz (99.99%) was dried with magnesium perchlorate and passed through oxisorb. Handling of all gases was performed on a standard high-vacuum line equipped with a Texas Instrument pressure gauge. The stopcocks were lubricated with a halocarbon product. The thermostated reaction cell as well as the reference cell were equipped with sealed-on Si 0 1979 American Chemical Society
3298
The Journal of Physical Chemistry, Vo/. 83, No. 25, 1979
windows which are transparent in the IR region of interest. The cells were directly connected to the vacuum manifold. All IR measurements were carried out with a PerkinElmer double-beam instrument, Model 325, equipped with an auxiliary recorder. The resolution of the spectrometer was 1 cm-l in our experiments. To follow the kinetics of the exchange reaction, we compensated for absorptions due to the parent compound. Pure samples in a pure system were very stable. No changes in the absorption could be detected over hours for the temperatures used. If traces of water were present HON02 was formed. The exchange reaction was observed either by repetitive scanning of the range 1800-1650 cm-l or by registration of the absorption at 1688.5 cm-l (P branch of the asymmetric NO stretching vibration in C1015N02)as function of time. The P branch of the unlabeled parent is located a t 1722 cm-l. Figure 1 illustrates the type of information obtained from each experiment (see Table I, run 15). The points are experimental values. It is apparent that the reaction reaches isotope exchange equilibrium. For the calculations described below data were taken from the plotted averaged line.
Schonle, Knauth, and Schindler A/%
'i/ I
*(+
I
I/
20
40
60
80
tlmin
100
Figure 1. Absorbance A at 1688.5 cm-' as function of reactlon time t for run 15 at 313 K. -Inz
I3l
*/@
Results To evaluate our experimental results the following mechanism is considered: ClONO2 (+ M) C10
+ 15N02(+ M) C10N02
-1
7C10 + NO2 (+ M)
__ la
-la
(-1,l)
C1015N02(+ M)
(la,-la)
+ 15N02& C1015N02+ NO2 -2
(2,-2)
Expressions -1,l and la,-la describe the thermally induced dissociation and recombination reactions for the unlabeled and the labeled chlorine nitrate, respectively. Since kinetic isotope effects can be neglected equal rate constants are used for equivalent reactions: kl = hla, kVl = k+,, h2 = k2. The assumption of a steady state for the intermediate C10 radical yields
0
I
10
20
,
I
30
LO
-
Urnin Figure 2. Plot of -In z (eq 8) vs. time t for runs 9,15 and 20 at 313 K.
to different collision efficiencies of C10N02, NO2, and N2 for (-1) in the low order range (see below). For an evaluation of the data according to eq 6 a calibration with labeled chlorine nitrate would be required. This can be by-passed by taking advantage of the absorption due to the product C1015N02after reaching isotope exchange equilibrium (see Figure 1). At equilibrium, i.e., z = 0, the C1015N02concentration can be expressed by
(3) with [l5NO2Ioand [C1ONO2lobeing the initial concentrations of 15N02and C10N02. Thus we obtain for the rate of C1015N02formation in the low pressure region d[C1015N02] dt
Thus with E being the extinction for C1015N02a t 1688.5 cm-' after different reaction times, and Eequil at equilibrium, respectively, -In z can be plotted as function of time according to
\
1
[15N02]o[C10N02]oX [15N02]o + [ClON02]0 V5N0210[C10N0210
Further substitution of [15N02]o+ [ClON02]0 z=1[C1015N02] [15N0210[C10N0210 yields
-d -In z dt
- -([15N0210
+
[c10N0210)(
UMI
[15N021o
+
h2
,r,
)
(6)
It should be noted that the term k-,[M] represents k-l,clo~oz[C10N02]o + k-l,~oz[15N02]0h-1,Nz[N2]according
+
These plots are given in Figure 2 for experiments 9, 15, and 20. Reasonable straight lines were obtained for all experiments with the slope given by
Tables I and I1 summarize the results for 22 experiments at 313 K and 24 experiments at 333 K, respectively. The next stex, is to calculate k-, of ea 9 for M being N, only. This con'stant will be denoted k l l , ~ The ~ . relative efficiencies of the different third bodies in our system, i.e.,
The Journal of Physical Chemistry, Vol. 83, No. 25, 1979 3299
Exchange Reaction between CIONOPand I5NO2
TABLE I: Initial Pressures of ISNO,, ClONO,, and N, and the Graphically Determined Values of m for All Runs at 313 Ka ([N21 f
m i ( r 5 ~ 0 t~ 1a ~ [ ~ ~ ~ ~ ~ , ~ , ) i run
['5N021,
6 7 8 9 11 12 14 15 19 20 21 50 51 52 53 55 56 75 76 71 78 I9
0.496 0.527 0.488 0.198 0.198 0.188 1.054 0.517 0.265 0.553 0.689 0.501 0.532 0.529 0.493 0.514 0.465 0.529 0.529 0.514 0.514 0.535
Pressures in torr, m in min-'
[N,1
/C1ONO,I0 3.991 3.544 2.763 1.473 1.621 1.217 3.015 2.330 4.153 3.093 2.243 5.227 4.172 3.251 2.604 1.661 1.331 1.799 1.438 1.156 0.923 0.736
13.86
0 12.68
0 11.00 8.26 6.84 5.28
0 13.91
10.11 124.00 98.97 77.14 61.78 39.42 31.58 182.77 146.04 117.38 93.80 74.73
m
[C1ONO,I,)
0.160 0.065 0.096 0.031 0.090 0.057 0.046 0.049 0.143 0.103 0.054 0.850 0.640 0.372 0.247 0.119 0.083 0.464 0.289 0.247 0.158 0.127
0.0357 0.0159 0.0295 0.0187 0.0493 0.0404 0.0112 0.0172 b.0323 0.0282 0.0185 0.1484 0.1361 0.0979 0.0798 0.0548 0.0461 0.1993 0.1469 0.1478 0.1100
[1
5 ~ 0 ~ 1
54.8 22.4 44.8 24.8 82.9 65.6 16.0 25.3 52.3 43.8 25.6 282.2 212.2 166.2 142.8 87.5 77.4 356.6 284.9 235.9 188.5 144.4
0.1000
, 01 = 3.3.
Figure 3. Pressure dependence of the rate of the exchange reaction plotted according to eq 11.
besides Nz also CIONOz and NOz, are taken into account by the expressions a = ~-I,c~oNo~/~-I,N~ (loa)
P
=
~-I,NO~/~-I,N~
(lob)
Thus we obtain m [N21 + 4C1ON0zlo = k-l,Nz [15N02]o+ [ClONOZ]o [15N0210 k-l,NzP + kZ (11) If m/([15N02]o+ [CIONOz]o)is plotted against the dimensionless parameter ([NJ + a[ClONOZlo)/[15N0z10a straight line should be obtained, the slope of which directly gives the wanted rate constant k-1,N2. The intercept allows the determination of k2. Values of a = 3.3 and P = 1.65 are taken from the literature.1° With these values, we can plot eq 11 (Figure 3). Data of ([N2] + a[ClONO,],)/ [15N02Joare included in the tables. For the temperature of 313 K a good linear dependence is obtained for experiments with nitrogen pressures up to 120 torr. A slight deviation is observed for runs 50,75, and 76 (points A in Figure 3). If the results of the latter three = runs are omitted (see Discussion) one obtains klNz (198.0 f 4.7) cm3 mol-l s-l and kz 5 736 cm3 mol-l sL1. A larger scatter was observed in the experiments a t 333 K. This was particularly the case for the experiments 57, 58,
+
2.7
-
I
I
2,8
2,9
1
1
3,O
3,l
1 3.2
103~-'/~-1 Flgure 4. Arrhenius plot from the results of this work (+) and the values given by ref 8 (0).
66, and 70. In these runs T ~ was / ~C10 s. Under these conditions the time required to reach thermal equilibrium cannot be neglected. Also, side reactions in the not yet homogeneously mixed system will contribute to the deviation (see Discussion). All runs with [C10N02], > 2 torr were omitted for the evaluation of the rate constants at 333 K. From the remaining experiments we obtain k-1,N2 = (2041 f 49) cm3 mol-I s-l and kz I5534 cm3 mol-l s-l. One should be reminded that reactions -1 and 2 are of different order. Thus under typical conditions contributions of reaction 2 to the overall exchange process are a few percent only. For instance, in run 71 a contribution of 2% is calculated. In the most unfavorable case, i.e., run 18 at [N,] = 1.4 torr, this contribution is 25%. Figure 4 shows an Arrhenius plot with the data of the present study together with data from ref 8. Good agreement was reached between these two groups of
3300
Schonle, Knauth, and Schindler
The Journal of Physical Chemistry, Vol. 83, No. 25, 1979
TABLE 11: Initial Pressures of 5N0,,ClONO,, and N, and the Graphically Determined Values of m for All Runs a t 333 Ka
run 16 17 18 22 24 25 26 57 58 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 a
115N021 0.874 0.812 0.573 1.312 0.935 0.807 0.809 0.519 0.519 0.475 0.514 0.514 0.514 0.493 0.506 0.522 0.505 0.522 0.481 0.514 0.519 0.496 0.475 0.514
[N, I 2.88 1.94 1.38 7.35 5.09 4.25 3.16 97.59 78.7 2 51.70 41.80 33.15 26.65 21.49 17.27 76.60 61.90 49.95 39.52 68.91 55.81 45.05 36.46 29.36
[CION02 1 0 1.272 0.855 0.606 1.633 1.132 0.945 0.703 4.941 3.985 2.618 2.116 1.678 1.349 1.088 0.874 5.187 4.191 3.382 2.676 2.166 1.754 1.416 1.146 0.923
m 0.115 0.073 0.058 0.192 0.136 0.121 0.067 5.718 3.982 1.886 1.610 0.971 0.737 0.522 0.399 4.500 2.811 2.044 1.793 2.155 1.573 1.180 0.797 0.613
.
(tN*1 t a [CIONO, l o ) /
m / ( [I5N0,1 t [ClONO,],) 0.0536 0.0435 0.0488 0.0652 0.0659 0.0690 0.0441 1.0472 0.8840 0.6097 0.6121 0.4431 0.3955 0.3302 0.2889 0.7883 0.5986 0.5237 0.5680 0.8040 0.6921 0.6172 0.4913 0.4263
[I 5
~
0
~
1
8.15 5.90 5.93 9.75 9.47 9.17 6.80 219.7 177.2 127.1 95.1 15.4 60.6 50.9 39.9 180.0 150.2 117.4 100.8 148.1 118.8 100.3 84.7 63.1
Pressures in torr, m in min", a. = 3.3.
TABLE 111: Enthalpy and Entropy Values for NO,, C10, and ClONO, at 298 K Taken from Literature AH"f,
kJ mol-'
NO 2 33.18' ' 33.10'2
c10 3 '
'
101.84" 101.21'2 101.63'4*'5
TABLE IV: Rate Constants and Arrhenius Expressions for Reactions 1 and -1
ClONO, 26.4
i
k , *N,/10-33 cm6 s-' 313.15 333.15 K K
So, J
mol- K'
239.95'' 239.9112
9 1 3
226.52'' 226.5612 225.02"
k l,N,/10-' cm3 s-'
O.B93I6
302.4617
measurements. The resulting Arrhenius parameters for reaction -1 from the rate constants of both studies are EA = (98.3 k 0.9) k J mol-l and A = 1018.7*0.1 cm3 mo1-ls-l.
Discussion Rate Constant. From the rate constants k-1,N2for the dissociation process given in the preceding section we can calculate rate constants for the recombination reaction using the equilibrium condition K = k + N /kl,Nz: The equilibrium constant K is related to thermodynamic data of NOz, OC1, and CIONOz by -RT In K = ( m f o N O z + M?OCL - AHf'CION02) T(SoN02+ s o O C l - SOCION02) For the calculation of K the data given in Table I11 were + AHfOoc1 used. The maximal error in AHr' = A€€f0~o2 - AHfoC10N02 should not exceed 1.7 k J mol-l. The uncertainty limits are taken from literature (see Table 111). The entropy data are known from spectroscopic measurements with fair accuracy. Their contribution to the error should be less than abQut 20%. Thus the maximum error in K should not exceed a factor of about 2 at 313 K. With K mol ~ m a -t 313 ~ and 333 and 1.52 X = 1.34 X K, respectively, the calculated rate constants for the recombination can be given (Table IV). For comparison rate constants obtained from data reported by others are also included. There exists close agreement between the results obtained in flow experiments on one side and the data obtained in static experiments on the other side. In the former the rate of C10 disappearance was used to calculate the rate constant kl. In the latter experiments the rate
ref
41b
37'
a
40'
35b
8
0.82, exp(- 11820/T) 1.33. exp(- 1198 O / T)
6.2, exp( 950iT) 3.69, exp( 1150/T) 4.40, exp( 1087/T)
129
107
1
145
116
2
142
115
3
a This work. constant.
Calculated by use of the equilibrium
of CIONOz disappearance and C1015NOzformation were used to calculate lzl with the help of the equilibrium constant K. Before discussing possible reasons for this apparent discrepancy a brief estimation of the experimental errors in the present study will be given. Due to the finite slit width in the absorption measurements deviation from Lambert-Beer's law is to be expected. From extensive calibration runs with C10N02 it was found that this deviation results in a 2% decrease in the value of m for the pressure range used in the present experiments. If this correction is applied our rate constants are to be reduced by 2 % . Another factor of concern might be the ratio a given in (loa). The value 8 does not enter into the calculation of k-l,Nz. For the determination of the rate constant, a = 3.3 was used. To check how critically I t - 1 , ~ ~ depends on a this parameter was varied between 0 and 100. For 0 < a C 10, k-l,Nz changes by 10% only. Best fit with the experimental data a t 313 K was obtained for a = 3.1. For a > 10 the rate constant decreases sharply. The statistical error of about 3% given in the measured rate constants corresponds to the standard deviation in the slope of Figure 4. All these considerations indicate that
Exchange Reaction between CIONOPand I5NO2 I a i k , /cm3s1)
16
17
18
’’
---. 20 lg([N21/cm-?
Flgure 5. Pressure dependence of the recombination reaction at 300 K. Data from this work (-) and Knauth’s results’ (- - -) are compared and with calculated with values taken from flow experimentsi3 falloff curves4 (--) adapted to the results of ref 1-3. (-.-.-e)
experimental errors in the determination of k-l do not contribute significantly to the discrepancy observed. The predominant source of disagreement might be the high uncertainty in the equilibrium constant K. If K were reduced by a factor of 3 the two sets of experimental values would concur. However, such a reduction in K can hardly be deduced from known thermodynamic data, although a factor of
