J . Phys. Chem. 1993,97, 12275-12281
CH
+ N2
12275
HCN2: Kinetic Study of the Addition Channel from 300 to 1100 K Laura J. Medburst,+Nancy L,Garland, and H. H,Nelson' Chemistry Division, Code 61 11, Naval Research Laboratory, Washington, DC 20375-5342 Received: July 12, 1993; In Final Form: September 16, 1993"
+
The reaction C H N2 e HCN2 has been studied using laser-induced-fluorescence detection of C H from 298 to 1075 K at 100 Torr total pressure. The experimental rate coefficient is fit by k = 44.0 X T5.3 cm3 s-' exp(-664.6/T). The pressure dependence was measured at 750 K, and the observed rate coefficient shows an increase from (3.2 f 1.8) X lO-Is cm3 s-l at 25 Torr to (8.0 f 1.8) X 10-15 cm3 s-l at 100 Torr. Transitionstate-theory modeling indicates that recent calculations of the structure of HCN2 [Manaa, M. R.; Yarkony, D. R. Chem. Phys. Lett. 1992, 188, 352; Martin, J. M. L.; Taylor, P. R. Chem. Phys. Lett. 1993, 209, 1431, which is datively bonded and stabilized by approximately 29 kcal mol-', are consistent with the data. temperatures (2' < 800 K), but at high temperatures (T> 2000 K) the energized complex can proceed directly to HCN N. The A persistent problem in hydrocarbon/air combustion is the simplest generalized reaction diagram for this system, in which formation of NO. N O produced in the postcombustion region the HCN + N (4S) channel is spin forbidden and requires a is adequately modeled by the Zeldovich mechanism. This crossing from a doublet to a quartet surface, is shown in Figure thermal mechanism is' 1. The changing mechanism with increasing temperature makes 0 N,+NO N this reaction interesting theoretically. Manaa and YarkonyloJl have calculated the geometry and energy of the minimum crossing N 0, -,NO 0 point and the minimum of the stabilized adduct for both a Cb and a datively bonded structure. A schematic of their results is NO formed in the flame front is referred to as prompt NO, and shown in Figure 2. This calculation predicts the binding energy its mechanism has been much more difficult to decipher. of the stabilized adduct HCN2 to be 22 kcal mol-' in the C2" Blauwens et a1.2 found its concentration to track with the geometry and the barrier for HCN + N production to be concentrationof CH and CH2 in a hydrocarbon/oxygen/nitrogen approximately 10 kcal mol-', assuming the barrier for HCN flame, and the currently accepted mechanism for prompt NO N production occurs at the crossing point for the two surfaces. formation is3 Other quantum calculations by Martin and TaylorI2 have predicted the minimum of the potential surface to be the datively C H N, -,H C N N bonded structure of Manaa and Yarkony with a binding energy of 29 kcal mol-'. Martin and Taylor's reaction surfaceis, however, HCN 0 + N C O H much more complicated with three doublet quartet crossingsand, most importantly, a barrier of approximately 70 kcal mol-I NCO H e N H CO between the dative and Czuadducts. This large barrier between the initially formed adduct and the CZ,geometry required for surface crossing to products was difficult to reconcile with the N H H N H, experimentally observed activation energy of 22 kcal mol-', and Martin and Taylor suggested that formation of HCN + N does N f OH NO H not occur through this reaction path. Recent calculations by Walch13 describe a different reaction path. He has calculated The initiation reaction in this mechanism, CH N2, has been the minimum-energy path to the C2u minimum of Manaa and the subject of many published kinetic studies."g Shock tube and Yarkony.lo He has found that it does not pass through the datively flame experiments conducted at temperatures of 2500 K and bonded structure, and there is a barrier of 18 kcal mol-' for above show normal Arrhenius behaviorG with an activation C2uadduct formation. Walch also calculates a barrier on the energy of -22 kcal mol-'. In studies at temperatures of 1000 quartet surface between the crossing point and the HCN + 4N K and below, the observed rate coefficientwas found to be pressure dependent at 298 K and todecrease with increasingtemperat~re.~,~ product of -22 kcal mol-'. Using a semiempirical QRRK calculation, Dean and BozzelliI4 found the stabilization energy This behavior has been explained with the following reaction to be 33 kcal mol-' and the barrier to HCN + N formation to scheme be 22 kcal mol-'. Transition-state-theory (TST) modeling of previous experimental however, has predicted the adduct to be stabilized by 50-70 kcal mol-' relative to CH + N2 and the barrier to HCN formation to be approximately 4 kcal mol-'. Because the recent quantum calculationsare at variance with the statistical modeling of the experimental data, many aspects of this reaction are still with the reaction occurring via an energized complex, which is unresolved. The stabilizationenergy of the adduct and the height collisionally stabilized to form the HCN2 adduct at lower of the barrier for HCN N production are still uncertain within a factor of 2. Consequently, the geometry of the adduct and the To whom correspondence should be addressed. doublet to quartet crossing point are still unknown. In this paper, t NRL/NRC Postdoctoral Research Associate. we present new experimentalmeasurements of the ratecoefficient Abstract published in Advance ACS Abstracts. November 1, 1993.
Introduction
+
+ +
+ +
+
+
+
+
+
+ +
+
+ + +
+
-
+
@
0022-3654/93/2097-12275.S04.00/0
0 1993 American Chemical Society
12276 The Journal of Physical Chemistry, Vol. 97,No. 47,1993
Medhurst et al, K N +
/-
Figure 1. Schematic of a simple potential that has been used to explain the reaction CH + N2 HCN + N(4S).
from 297 to 1075K a t 100Torr and a measurement of the pressure dependence of the rate coefficient at 750 K as well as results of TST modeling of these data. Our results will show that the quantum calculations for the geometry and stabilization energy ofthe datively bonded HCN2 areconsistent with theexperimental data.
HCN + q 4 S )
297 K
1 4
0.05
511 K
Experiment The majority of the measurements were performed in a hightemperature reactor based on the design of Fontijn.I5 Details of the apparatus are given elsewhere.16 In brief, gases enter the mullite reaction tube through an inlet in the bottomof the stainless steel cell. The reaction tube is heated by four banks of four silicon carbide rods, which are resistively heated. There are four small openings in the mullite tube for the probe laser beam, the photolysis laser beam, and fluorescence collection. A few experiments were performed in a stainless steel cell contained in a commercial convection oven. In both cases, CH is produced by excimer laser photolysis of CHBrzCl at 248 nm. The photolysis laser energy is approximately 40 mJ/pulse in the reaction cell. At the two highest temperatures, the CHBr2Cl was introduced into the reaction cell via a water-cooled inlet to prevent thermal decomposition of CHBrzCl prior to photolysis. Otherwise, all the gases were premixed and introduced together in the bottom of the cell. The reaction rate, -d[CH]/dt, was monitored by laser-induced fluorescence (LIF) on the B-X transition near 387 nm, using an excimer-pumped dye laser. This transition was chosen over the A-X transition at 433-435 nm to minimize interference from blackbody radiation at higher temperatures. The fluorescence was collected a t 90' to the counterpropagating photolysis and probe beams. A collimating-focusing lens pair imaged the signal onto a filtered (Corion P70-4004 for CH detection and Corion P10-4904 for A10 detection) photomultiplier tube (RCA 31000M). An acetone filter was used to discriminate against scattered photolysis light. The fluorescence signal was processed by a gated boxcar integrator and digitized and stored by a personal computer. The timing was controlled by a digital delay generator (SRS DG535), which triggered both lasers. All experiments were performed with argon buffer gas, and the CHBrzCI was previously diluted to 0.5% in argon. The gases (Air Products Industrial Grade; Ar, 99.997%; N2,99.998%) and CHBr2CI (Aldrich, 98%) were used without further purification. Some experiments were performed with Matheson research grade (99.9995%) N2. However, no difference in the observed rate coefficients was found between this and the other N2. The flow rates of the gases were determined by calibrated Tylan gas flow meters and flow controllers. The flow rates were 1.O-2.0 SLPM, which provided a compromise between thermal equilibrium of
K2D)
z:
0.00 0
10
Pressure
20
30
(torr)
Figure 3. Observed first-order rate coefficients versus [Nz] at 291,5 11, and 161 K.
the system and C H chemical lifetime. The pressure was measured by an MKS baratron. A thermocouple was inserted in the top of the high-temperature reaction cell to monitor the stability of the temperature during the kinetics experiments. However, reaction zone temperatures were determined by twice measuring the rotational spectra of AIOl7from 465 to 467 nm immediately preceding and succeeding the kinetics experiments. A10 was found to be superior to C H for temperature determination because its use resulted in a lower statistical uncertainty in the measured temperatures. Temperatures were measured directly by a thermocouple attached to the wall of the low-temperature, stainless steel cell and were constant to f l K.
Experimental Data and Analysis
In this experiment [CHI was measured as a function of time. The first-order rate coefficient, kl = 1/ T , was found from a linear least-squares fit to the log of the experimental data. The secondorder rate coefficient, kobs, is the slope of ~ / T C H versus N2 concentration. The results we obtain at 297,5 11, and 767 K are shown in Figure 3. Previous experiments on collisional energy transfer indicate that in some cases N2 is a more effective collider than argon while in other cases it is not.16 Since the stabilization of the adduct is a third-order process, plots of ~ / T C Hversus [Nz] should depart from linearity a t high concentrations of N2 if N2 is a more effective collider in this system. This was not observed in any of the secondorder plots like those in Figure 3. In the strong collision limit, the observed first-order rate coefficient can be described' as
where kd = kobs when no N2 is present, kjSCis the third-order rate coefficient, PT is the total pressure, BC is the collision
Kinetics of CH
+ N2 e HCN2 Reaction
The Journal of Physical Chemistry, Vol. 97, No. 47, 1993 12277
TABLE I: Temperature Dependence of Observed Rate Coefticients for the Reaction CH N2at 100 Torr Total Pressure
+
T f lu(K)
kob h la (10-14cm3s-l)
Tf l u ( K )
298 '2 324 10 415 h ' 2 429 f 20 482 f 38 511 f '2 527 f 15
41 * 8 20 4 9.0 2.4 18f5 6.0f 1.6 7.6 t 1.6 4.8 f 1.0
640 18 654 12 768 18 797 15 897 h 26 1008 f 30 1075 f 35
*
a
*
*
*
k0b* l a (lW14cm3s-1) 1.8 0.6 1.3 + 0.7 1.1 0.2 0.59 0.16 0.35 0.24 0.30 0.08 0.22 t 0.15
10.12
* * *
*
10-l~
Data from experimental apparatus 2.
10-l2
1
I
1
I
I
I
.
i
ii 0
w
A Thiswork
Berrnan&Lin
200
400
800
600
Total Pressure (torr)
-
Figure 5. Second-order rate coefficients, kob, versus pressure at 297 K. The triangles are our data, and the squares are data from Berman and Lin? The error bars represent 2u uncertainty in the measurement.
10-l~
7
'm
n
E s
4 10-14
Y
.C
+
a
10-l~
E
0.5
1.0
1.5
2.0
2.5
3.0
3.5
10~1-r (K") Figure 4. Second-order rate coefficients, kob.versus temperature at 100 Torr total pressure. The triangles are our data from the high-temperature reactor, the circles are our data from the convection oven, and the squares are data reported by Berman and Lin.' The line is a least-squares fit to our data with k = 44 X Ts.3 cm3 s-I exp[-664.6/T11. The error bars represent 2u uncertainty in the measurement.
A Thiswork
+
10-l~
0
efficiency, and x is the mole fraction of the bath gas. This expression can be rearranged to give
(k,- kd)/ [N,] = ~?PT(BC,,-I-(Bc,, - Bc,,)xN,) Berman and Lin show (kl - kd)/ [Nz] versus X N to ~ have zero slope at 297 K, which implies argon and nitrogen have the same collision efficiency within experimental error. Similarly, we could not find any difference in the collision efficiency of argon and nitrogen throughout the temperature range of this experiment. Our measured bimolecular rate coefficients as a function of temperature at 100 Torr total pressure are listed in Table I, and plotted in Arrhenius form in Figure 4 along with a nonlinear least-squares fit of kob = 44.0 X T-5.3cm3 s-I exp(-664,6/T) to our data, and the previous experimental results at 100 Torr.' There is reasonable agreement with the data of Berman and Lin at lower temperatures. There is, however, a small but significant differencein the slope of the two data sets. This differencepossibly arises from the uncertainty in the temperature measurement. To confirm our temperature measurements, some data points were taken in the convection oven apparatus, as indicated in Figure 4. As can be seen in Figure 4, the two sets of data from this lab are in agreement. Since kat. is smoothlydecreasing with increasing temperature, the temperature dependence of kob in Figure 4 is consistent with an addition-stabilization mechanism and does not show any evidence of dissociationto the products HCN + N. It also shows no evidence of a barrier to adduct formation, since that would produce a maximum in the temperature dependence. The pressure dependence of the observed rate coefficients at 297 K is shown in Figure 5 with the results of Berman and Lin, and
1
2
Berrnan&Lin Becker etal. Dean et ai. 3
1o3rr(~-') Figure 6. Second-order rate coefficients, kob, versus temperature. The triangles are our data, and the squares are data from Berman and Lin7 at 100Torr total pressure. The diamonds are shock tube results of Dean et al.,"and the circles aredata from Becker et a1.8 at 20Torr total pressure. The error bars represent 2u uncertainty in the measurement.
TABLE 11: Pressure Dependence of Observed Rate Coefficients for the Reaction CH + N2 at 298 K pressure (Torr)
( 1 0-13 cm3 s-I)
pressure (Torr)
10 50
0.56t 0.16 2.3 h 0.6
100 200
kob. f 1u
kob h l a
(
w3cm3 s-l) 4.4 h 1.0 5.8 h 1.8
our results are also listed in Table 11. Thesedata are alsoconsistent with an addition-stabilization mechanism. A summary of the recent experimental rate coefficients for the CH Nz system including our data and the results of Berman and Lin7 at 100 Torr, recent measurements at 20 Torr total pressure by Becker et al.? and the shock tube results of Dean et al.4 are shown in Figure 6. The shock tube data clearly show the presence of the higher-energy HCN + N channel. The HCN + N(4S)channel is 1 A 4 kcal mol-' endothermic, and the Arrhenius expression for the high-temperature channel is 7.31 X 10-l2cm3 s-l exp(-l1060/7'),4 which gives a barrier to reaction of 22 kcal mol-I. Therefore, the transition state for dissociation to HCN + N is not a simple fission transition state, since the barrier is much higher than the endothermicity. An apparent anomaly is evident in Figure 6; at 764 K the rate coefficient obtained by Becker et ala8at 20 Torr is greater than our value measured at 100Torr. This is not necessarily impossible;
+
12278
Medhurst et al.
The Journal of Physical Chemistry, Vol. 97, No. 47, 1993
0
ir
500
1
1
I
0
1
W
1'
A This work
Beckeretal.
0
10-l~
0
50
100
150
200
200
250
Total Pressure (torr) Figure 7. Second-order rate coefficients, koa,versus pressure at 750 f 40 K. The triangles are our data from the high-temperaturereactor, and the circle is data from Becker et a1.* The error bars represent 2a uncertainty in the measurement.
TABLE III: Pressure Dependence of Observed Rate Coefficients for the Reaction CH + Nz at 750 K pressure koa f l a pressure koa&l a (Torr) ( 10-15 cm3 s-I) (Torr) ( 1 ~ cm3 4 s-1) 3.2 f 1.8 5.1 f 1.6 7.5 f 3.2
25 37.5 50
100 200
8.1 & 1.8 8.0 f 2.2
We~tmoreland'~ has described several multichannel reactions, using a bimolecular QRRK theory, and the pressure dependence of the total rate can assume many forms. Assuming a potential like that in Figure 2, the addition-stabilization channel must increase with increasing pressure. For the total rate coefficient of stabilization plus product formation, kob,to decrease with increasing pressure, the rate of dissociationto HCN + N should be much greater than the rate of adduct stabilization, since the adduct stabilization increases linearly with pressure at this temperature and dissociation to HCN + N decreasesmore slowly. If the shock tube results, which are assumed to be only from the HCN N channel, are extrapolated to 760 K, the branching ratio of HCN N to HCN2 is approximately 0.03%. This is not large enough for kob to decrease with increasing pressure, and it can be seen from Figure 6 that the 20-Torr data of Becker et al. when extrapolated to higher temperatures do not agree with the results of Dean et aL4 To confirm this analysis, we measured the pressure dependence of this reaction at 750 K to determine the relative importance of the two reaction paths. Our measured rate coefficients are listed in Table I11 and shown plotted as a function of pressure along with the result of ref 8 in Figure 7. Our measured rate coefficient increases with increasingpressure from 25 to 100 Torr, in contrast with the result of Becker et al. The pressure dependence in Figure 7 clearly shows a linear increase below 50 Torr, which is associated with the addition-stabilization mechanism. The recent calculations by Martin and Taylor12 and Manaa and Yarkony" indicate that thereare twodeepminima, thedative and the CzUstructures shown in Figure 2. There is no barrier to formation of the dative adduct, but Walch13 has calculated an 18 kcal mol-I barrier for formation of the Cz, adduct. There is agreement among the three quantum calculations that the C2, structure is the minimum of the well which can dissociate to HCN + N. So it appears that there are at least two stabilized adducts possible, with only one leading to HCN + N. Therefore, the preceding argument is applicable to the C2, part of the potential. The dative adduct, which is probably the most important at these temperatures, should not access the HCN + N channel at all. Our observed rate coefficient in Figure 7 appears
+
+
1
I
I
a 300
I
I*
100 I
200
1 .# I
I
I
I
I
400
600
800
1000
1200
Temperature (K) Figure 8. Collisional energy-transfer parameter versus temperature, calculated from the bias-random-walk model.
to level off above approximately 100 Torr. This is probably the result of the relatively large uncertainty in the temperature since in our flow system it is difficult to maintain a constant high temperature at different pressures.
Transition-State-Theory Modeling Using transition-state theory, we have modeled the extended data set in order to compare with the quantum calculations of Manaa and Yarkony," Martin and Taylor,I2and also the previous RRKM models of the The model is that used in the UNIMOL program package by Gilbert, Jordan, and Smith.20 This is an RRKM treatment with a numerical solution to the master equation using a weak collision formalism. The master equation is
-kunig(t) = w l [ P ( c , c ' ) g(e') - P(e',t) g(e)] de' - &(e) g(t) where k,,i is the rate coefficient for unimolecular decomposition of the adduct, g(c) is the population of molecules with energy e, w is the Lennard-Jones collision frequency, P(c,d)is the probability that a collision transfers energy from t to d, and k(e) is the microscopic reaction rate coefficient, which is defined as
where Eo is the critical energy for the reaction, h is Planck's constant, p(E) is the density of states of the energized adduct, and p* (E+) is the density of states of the transition state for unimolecular decomposition. k(c) was calculated using the vibrational frequencies and rotational constants for a given geometry of the adduct and transition state. In this case a direct count method was used to determine the density of states. The bias-random-walkmode120was used for the probability of collisional energy transfer, P(e,e'). In this model, the energy is assumed to undergo a random walk in energy space during the collision. The energy-transfer parameter, hEdo,n, which was calculated by this method is shown in Figure 8 as a function of temperature. For all the TST calculations reported, this is the function used in solution of the master equation unless otherwise noted. Some calculations were performed with the exponential down model of collisional energy transfer, and no significant difference was found between the two functional forms used. All calculations were performed using orbital angular momentum conservation, and the solution to the master equation was obtained in the weak collision formalism by assuming the hard collision solution for g(c), the population function, calculating kuni, and iterating for the weak collision solution of g(c) and kuni.
Kinetics of C H loa1*
+ N2 F? HCNz Reaction I
I
I
The Journal of Physical Chemistry, Vol. 97, No. 47, 1993 12279 I
I
10-l~ r
'm P) v
10-l~
4
Y
10-l~
10-l8 0.5
I
1.0
I
I
I
I
1.5
2.0
2.5
3.0
i
3.5
1O ~ I T(K-')
Figure 9. Second-orderrate coefficients, kohl versus temperature. The triangles are our data from the high-temperaturereactor, and the circles are our data from the convection oven at 100 Torr total pressure. The error bars represent 2a uncertainty in the measurement. The lines are results of TST model calculations using parameters listed in Table IV: the solid line is the result using the parameters of Martin and Taylor" and AH = 29.19 kcal mol-', the dashed line is the result using the parameters of Berman and Lin7and AH = 57 kcal mo1-I and &??down = 350 cm-l, and the dotted line is the result using the parametersof Berman and Lin7and AH = 57 kcal mol-I and &??down from a biased-random-walk calculation as illustrated in Figure 8.
TABLE I V Parameters Used in the Transition-State-Theory Modeling Martin Berman parameter and Taylor1] and Lin7 29.19 57 EO(kcal mol-I) 3349 3130 adduct vib freq (cm-I) 1804 2102 1181 900 493 480
1252 1170
564 421
406 &)(adduct)(cm-I) BlD(adduct)(cm-I) Re (TS) (A) TS vib freq (cm-I), degeneracy
0.4056 11.63
700,l
0.3826 1.80 2733, 1 2330,l 100,l 75, 3
500, 1 0.06825 6.6352
0.2683 -
4.64 3200, 1 2400,l 800, 1
To determine k,,, the recombination rate coefficient, from the unimolecular dissociation rate, the relation k,, = Kqkuni was used with Kq calculated from the known vibrational frequencies and rotational constantsof CH andN2 and the assumedvibrational frequencies and rotational constants of HCN2. To begin simply with the addition-stabilization channel, we let k,, equal kob. The parameters used in the calculations are listed in Table IV. Martin and Taylor12 have calculated the vibrational frequencies and energy for stabilized HCN2 in the dative geometry shown in Figure 2, and they are listed in Table IV. The parameters for the transition states were varied to produce the best fit with the data. In another calculation, the parameters of Berman and Lin7 were used without modification, including the use of a constant, 350 cm-I, for the energy transfer. The values of Berman and Lin7 were also calculated with the same energy-transfer values as those used for Martin and Taylor12for a more direct comparison. Becker et a1.*used values essentially the same as those of Berman and Lin. Figure 9 summarizes the
temperature dependence results. The results we obtained using the parameters of Berman and Lin differ significantly from their results. At higher temperature our calculated values are more than a factor of 10 below their calculated values. The reason for this difference is most likely the different way collisional energy transfer was modeled in the two calculations. They used a strong collision formalism modified by applying Of, the collision efficiency. While inclusion of the collision efficiency greatly improves the results for a strong collision calculation, it has been shown that in the falloff region strong collision calculations using Bc are as much as a factor of 10 greater than trajectory calculations.20 Ironically, using a weak collision formalism improves the agreement of their parameters with our data. As can be seen in Figure 9, calculations using the results of Martin and Taylor are in excellent agreement with the data. However, the calculated adduct stabilization energies of Manaa and Yarkony (22 kcal mol-')Io and Dean and Bozzelli (33 kcal moi-')l4 are essentially in agreement with Martin and Taylor and could just as easily have been used. The most striking feature in Figure9 is therelativelygoodfit obtained with theverydifferent stabilization energy and assumptionsof Berman and Lin. Several things contribute to this. The assumption of a linear adduct means one rotation becomes a vibration, and consequently the density of states of the adduct is greatly reduced. A corresponding reduction in the density of states of the transition state is not effectively observed, since the low-frequency vibrations of the linear transition state of Berman and Lin also simulate rotations. A Morse potential was used for the separating fragments, where
Here V(r) is the potential, De is the dissociation energy, is the reduced mass of the separating fragments, and v is the vibrational frequency. The frequency corresponds to the reaction coordinate and therefore is the degree of freedom absent in the transition state. In these calculations /3 was varied to give the best fit to the data. The calculations were very sensitive to the value of /3 chosen. Berman and Lin have shown that if there were a barrier in the reaction path to adduct formation, k,, would go through a maximum in this temperature range. Since there is none, this is a simple fission transition state. The unimolecular reaction occurs by a lengtheningof the C-N bond, and the reaction coordinate is the C-N stretch. In the stabilized adduct, its frequency is approximately 1200 cm-I. As the bond lengthens, its vibrational frequency should decrease. The imaginary frequenciesdetermined from the best fit j3s are 367 cm-* for Martin and Taylor's parameters and 1495 cm-l for Berman and Lin. Given the respective transition-state geometries, the /3 used to fit Martin and Taylor's parameters is a more physically realistic value. There are, however, difficulties with the transition state used for the geometry of Martin and Taylor. The bond length and /3 both indicate a loose transition state, but the vibrational frequencies are still rather large. So it is unlikely that the real transition state is the one listed in Table IV, but rather one which has a very similar density of states. It does seem likely, however, that the stabilized adduct calculated by Martin and Taylor is quite close to the real adduct. The fit with experimental data is quite good, and the best fit transition state is also the most physically realistic one. The calculations of Manaa and Yarkony are also in agreement as to the stabilization energy and geometry of the adduct. The calculations of the pressure dependencies are presented in Figure 10. For the 297 K data, once again the values from Martin andTaylor give the best fit, but the parameter set used by Berman and Lin also gives an excellent fit to the data. For the 750 K
Medhurst et al.
12280 The Journal of Physical Chemistry, Vol. 97, No. 47, 1993
L
10-l~
h
r
v)
m
A Thiswork Benan8Lin
ii
-
10-l810-l~ -
-
lo-= -
6 B lomz4-
i
Y
Y
-
400
200
0
600
aoo
\\\
-Walch ,
0
1
2
3
IO~K(K-')
Total Pressure (torr)
Figure 11. TST model calculationsof kobusing the parameters of Wa1ch.I'
can approach unity.22 This assumption is certainly much more valid at lower temperature than at the combustion temperatures where the HCN N channel becomes important. Therefore, this calculation would be expected to result in rate coefficients larger than those experimentally observed. However, it is apparent from Figure 11 that the calculated rates are much lower than the experimental rates in Figure 6, and the solution to the master equation was unstable between 1000 and 2000 K. Part of this could be the use of the strong collision approximation in the RRKM calculation, which overestimates the rate of collisional stabilization compared to the rate of HCN N formation. However, it is unlikely that this is responsible for 4 orders of magnitude difference. Nonetheless, the TST model of Walch's parameters can still provide some insight into the reaction. The increase in the rate coefficient from 300 to 1000 K is mainly from formation of HCN2 in the C2" geometry. However, because of the 18 kcal mol-' barrier, the contribution of the CZ,adduct to the total rate is negligible, and this agrees with the TST calculations, which show the dative adduct formation to explain the ratein that temperature range. Above 2000 K, the calculated rate coefficient increases with approximately the same slope as the shock tube data although the absolute value calculated here is of course too low. Therefore, the simple description given in the introduction should be modified to
+
+
A Thiswork 0 Becker et al. L
0
4
50
100
150
200
250
Total Pressure (torr)
Figure 10. (a, top) Second-order rate coefficients, kob,versus pressure at 297 K. The triangles are our data from the high-temperaturereactor, and the squaresare data from Berman and Line7The error barsrepresent 2a uncertainty in the measurement. The lines are results of TST model calculations using parameters listed in Table IV: the solid line is the result using the parameters of Martin and Taylor,I1and the dashed line = 350 is the result using the parameters of Berman and Lin7with cm-l. (b, bottom) Second-order rate coefficients, kob, versus pressure at 750 f 40 K. The triangles are our data from the high-temperature reactor, and the circle is data from Becker et al.* The error bars represent 2u uncertainty in the measurement. The solid line is the result of TST model calculations using parameters of Martin and Taylor.Il
pressure dependence both parameter sets are in the low-pressure limit, so the shapes of the curves are identical; only the absolute values differ. Calculations of both the pressure dependence and the temperature dependence show that the experimental data below 1100 K are consistent with a dative adduct with a stabilization energy of -29 kcal mol-I. WalchI3 calculated the least energy path for HCN N production. HC approaches N2 in a cis geometry, in contrast to the trans approach which forms the dative adduct. There is a barrier of 18.2 kcal mol-] to CzUadduct formation, and the adduct is stabilized by 12.7 kcal mol-]. After crossing to the quartet surface, the molecule goes through a transition state for HCN N which is 22.8 kcal mol-l higher than the reactants. Figure 1 1 is an RRKM calculation of the total rate coefficient, using the values calculatedby Walch13with nothing varied. This calculation uses a chemical activation formalism in the strong collision approximation2' to calculate the ratio of HCN + N formation to HCN2 stabilization. The rate of HCNz stabilization was calculated by the same method described previously, and the sum of the two channels is shown in Figure 11. It has been argued that for a sufficiently long-lived complex the crossingprobability
+
+
Conclusions The reaction of CH + N2 at temperatures below 1100 K can be reasonablyexplained by formation and stabilization of datively bonded HCNz. The quantum calculations of Manaa and Yarkony'l and Martin and TaylorI2 provide a geometry and stabilization energy consistent with the experimentaldata. While it is not conclusive that this structure is correct, the combined evidence of two quantum calculations and the agreement with the experimental data supports a provisional assumption that the stabilized adduct is the datively bonded structure of Manaa and Yarkony. The minimum of the rate coefficient has not been seen experimentallyat any pressure, since the data of Becker et al. are not consistent with the present pressure dependencestudy at 750 K. The HCN + N channel probably does not go through the same activated complex as stabilized HCN2, in agreement with the recent calculation of Walch.I3 However, thecalculationsof Walch
Kinetics of CH
+ N2
HCN2 Reaction
do not appear to be consistent with the shock tube data. Some of the apparent discrepancy is the result of the simple RRKM model used in this work, However, it is also possible that the entrance channel barrier calculated by Walch is too high. Dean and BozzelliI4 calculate a similar overall barrier to HCN + N formation, but they assume a small barrier to adduct formation. Since formation of the adduct is very slow at temperatures greater than 1000 K and the concentration of CH is very low in the cooler parts of a premixed flame, the present results will have minimal impact on the calculated production of "prompt" N O in these flames. However, in diffusion flames where prompt NO can be more than two-thirds the NO formed,23this reaction could be more important.
Acknowledgment. We thank J. Bozzelli, P. Taylor, and J. Balla for supplying their results prior to publication, D. Yarkony, J. Bozzelli, P. Taylor, and T. Seidelman for helpful discussions, B. Williams for help with premixed flame calculations,and the Office of Naval Research for funding this work through the Naval Research Laboratory. References and Notes (1) Fenimore, C. P. Symp. (Inr.) Combust. [Proc.] 13th 1971, 373. (2) Blauwens, J.; Smets, B.; Peeters, J. Symp. (Inr.) Combust. [Proc.] 16th 1977, 1055. (3) Miller, J. A.; Bowman, C. T. Prog. E n e r a Combust. Sci. 1989, 15, 287.
The Journal of Physical Chemistry, Vol. 97,No. 47, 1993 12281 (4) Dean, A. J.; Hanson, R.K.;Bowman, C. T. Symp. (Int.) Combust. [Proc.] 23rd 1990, 259. (5) Lindackers, D.; Burmeister, M.; Roth, P. Symp. (Int.) Combust. [Proc.] 23rd 1990, 251. (6) Matsui, Y.; Nomaguchi, T. Combust. Flume 1978, 32. 205. (7) Berman, M. R.; Lin, M. C. J. Phys. Chem. 1983,87, 3933. ( 8 ) Bccker, K.H.; Engelhardt, B.; Geiger, H.; Kurtenbach, R.;Schrey, G.; Wiesen, P. Chem. Phys. Lett. 1992, 195, 322. (9) Balla, R. J.; Casleton, K. H.To be submitted to J. Phys. Chem. (10) Manaa. M. R.; Yarkony, D. R. J. Chem. Phys. 1991, 95, 1808. (11) Manaa, M. R.;Yarkony, D. R. Chem. Phys. Lett. 1992,188, 352. (12) Martin, J. M. L.; Taylor, P. R. Chem. Phys. Lett. 1993, 209, 143. (13) Walch, S.P. Chem. Phys. Lett. 1993, 208, 214. (14) BozzeUi,J. W.;Dean,A. M. Proceedingsofthe6th Toyoruconfercncc on Turbulence and Molecular Processes in Combustion;Elsevier: Japan, in press. (15) Marshall, P.; Fontijn, A. J . Chem. Phys. 1986,85, 2637. (16) Garland, N. L.; Stanton, C. T.; Fleming, J. W.; Baronavski, A. P.; Nelson, H. H. J . Phys. Chem. 1990, 94,4952. (17) Garland, N. L.; Douglass, C. H.; Nelson, H. H. J . Phys. Chem. 1992, 96, 8390. (18) Hippler, H.; Lindemann, L.; Tree, J. J . Chem. Phys. 1985,83,3906. Hippler, H.; Troe, J.; Wendelken, H. J. J. Chem. Phys. 1983, 78, 6709. (19) Westmoreland, P. R. PhD Thesis, Massachusetts Institute of Technology, 1986. (20) Gilbert, R.G.; Smith, S . C. Theory of Unimolecular Recombination Reactions; Blackwell Scientific Publication: Boston, 1990. (21) Robinson, P. J.; Holbrook, K. A. Unimolecular Reactions; Wiley-Interscience: New York, 1972. (22) Tully, J. C. J . Chem. Phys. 1974, 61, 61. (23) Drake, M. C.; Blint, R. J. Combust. Flume 1991, 83, 185.
