THEDECAY OF RADICALS IN NHa-02-N2 FLAMES
917
The Decay of Radicals in Ammonia-Oxygen-Nitrogen Flames by Melvin P. Nadler, Victor K. Wang, and Walter E. Kaskan Department of Chemistry, State University of New Yorlc at Binghamton, Binghamton, New Yorlc 13901 (Received August $6,1069)
Measurements have been made of the concentrations of OH and NH, and the relative concentrations of "2, in the flame gases from two fuel rich flat NHS-OrNz flames as a function of the distance from the burner surface. The technique involved the measurement of light absorption by an individual rotational level in the electronic ground state of each radical. [OH]was found to be at equilibrium,but [NH]was present in higher than equilibrium amounts. All three radicals decayed with flow downstream. Evidence is presented to show that during the decay, the reaction NH2 OH e NH HzO is in dynamic equilibrium. This equilibration allows the calculation of an fnumber for the NHs line. The implications of the findings for the analysis of the kinetics of radical decay are discussed.
+
+
Introduction Flames burning in H2-02-N2 or H2-CO-02-N2 are known to produce radical concentrations in excess of equilibrium amounts, which then decay by recombination a t measurable rates. I n the analysis of the kinetics of recombination, the concept of the equilibration of fast reactions has proven to be very useful. According to this concept, due originally to Bulewicz, James, and Sugden,l certain reactions which are fast relative to the recombination reactions are maintained in dynamic equilibrium during the recombination process. Hence radical concentrations may be quantitatively related to each other through thermochemical quantities, the equilibrium constants for the equilibrated reactions, and the kinetic analysis of recombination simplified considerably. A program of study of the flame gases from NHa02-N2flames has been initiated in this laboratory. The technique employed is the use of space resolved spectroscopic probing of stationary flat laminar premixed flames. I n view of the utility of the equilibration concept in other flames, it was felt that the first step should be a test of equilibration among the radicals in ammonia flames. Two earlier studies of ammonia flames are related to the present work. Fenimore and Jones2 studied low-pressure flames containing ammonia, using gas sampling techniques in the reaction zone and into the burned gases. They suggested that the reaction 3"
+H
2"
+ Hz
(1)
was equilibrated. They also noted that the NO which was formed in the reaction zones of their flames tended to react further if NH3 was present, presumably due to an incompletely specified reaction
NH2
+ NO +? +N2 eventually
(11)
and tended to not react further in lean flames where NH3 disappears more or less completely at the end of
the reaction zone. RiIacLean and Wagner3 made a similar experimental study of NHa-02 flames at reduced pressure, but in addition obtained measures of OH and N H by optical absorption. Their experimental findings resembled those of Fenimore and Jones, but led them to disagree with the suggested importance of reaction 11. Earlier experiments by one of us4had established that all three of the radicals, OH, NH, and NH2, could be observed in absorption in atmospheric pressure flames of the proper fuel-oxygen ratio. Since the H 2 0 concentration can be calculated with little error in such flames, it seemed feasible to test the reaction NH2
+ OH
4N H
+ HzO
(111) for equilibration. The oscillator strengths of both OH21:+-211 and NH3II3Z- are known5v6 so that OH and MH concentrations can be determined absolutely. The MH2 A-X oscillator strength is not accurately known, only an estimate having been reported,'so that only relative measurements of NH2 can be made. Equilibration of reaction I11 would be considered to be established insofar as the concentration function F3
exhibited the expected temperature dependence of the equilibrium constant K3, independent of the values of the radical concentrations. In this work only the (1) E. M. Bulewicz, C. G. James, and T. M. Sugden, Proc. Roy. Soc.,
A235, 89 (1956). (2) C . P. Fenimore and G. W. Jones, J . Phys. Chem., 65, 298 (1961).
(3) D. I. MacLean and H. G. Wagner, Eleventh Symposium (International) on Combustion, Combustion Institute, 1967,p 871. (4) Unpublished work of W. E. Kaakan, performed a t the General Electric Research Laboratory, Schenectady, N. Y . (5) D.M.Golden, F. P. Del Greco, and F. Kaufman, J . Chem. Phys., 39, 3034 (1963). (6) R. G. Bennett and F. W. Dalby, ibb!., 40, 1414 (1964): 32, 1716 (1960). (7) 0.Schnepp and K. Dressler, ibid., 32, 1682 (1960). Volume 74, Number 4 February 10, 1070
M. P. NADLER,V. K. WANG,AND W. E. KASKAN
918
L S O\ URCE \
BURNER
FLAME /
/
SPECTROMETER SLIT
Figure 1. Experimental arrangement, top view, not to scale (see text).
ratio of F3 to fz,an oscillator strength for NHz, can be determined. This paper describes the test of reaction 111 for equilibration in the flame gases from two fuel rich NHs-02-KZ flames burning at atmospheric pressure. Experimental Method A , Apparatus. The apparatus consisted of a gas handling system, the flat flame burner, and an optical system, depicted in Figure 1. Commerical gases in cylinders were used without purification. Metering was accomplished by the use of critical flow orifices. The flow through each orifice was calibrated using a wet-test meter and with the individual gases used, except for ammonia. For the ammonia orifice, the flow was measured using nitrogen and the ammonia flow was calculated from the nitrogen flow and the orifice equation. The specific heat of ammonia, as well as all other thermochemical data required in this work, was taken from the JANAF tables. The burner was a flat flame burner, whose surface was a 7.5 X 10 X 0.6-cm brass plate through which about 2000 0.i-cm holes were drilled in a regular array. The plate was mounted on a water cooled three-compartmented box in such a way that an inner section, 5 X 10 cm, was fed the desired iC”3-02-Nz mixture, and two outer 1.2 X 10-cm sections could be fed a shielding flow (see Figure 1). Since the flames used were fuel rich, the shielding flow was NZso as to prevent a diffusion flame from forming between ambient air and the still combustible flame gases. The area of the holes comprised about one-fourth of the burner surface. Even so, the flames were flat, homogeneous (to the eye) sheets rather than arrays of cones. This was presumably due to the fact that rather low gas velocities were employed, so that the combustible mixture “diffused” (in a hydrodynamic sense) around the edges of the holes to form a uniform stream before burning. A perforated, water-cooled brass plate was situated about an inch above the flame, in order to stabilize the flow of the hot The Journal of Physical Chemistry
gas stream. The burner plus stabilizing plate were moveable in the vertical direction, enabling the fixed optical system to observe the flame gases at varying distances from the burner surface. The optical system consisted of several light sources, a White multiple-pass system, and a 0.75 m SPEX Czerny-Turner grating spectrometer equipped with photoelectric recording. The sources were a 1000-W Hanovia 976C-1 high-pressure Xe arc lamp for providing a continuum in the uv and visible, and a tungsten strip filament lamp for sodium reversal measurements. Light from a source was directed into the multiplepass system as indicated in Figure 1. All of the mirrors were spherical, with 150-cm focal lengths. The burner was placed as near (about 15 cm) from mirror AI1 a t which the image is focused, in order to enhance the spacial resolution in the flame gases. To improve this resolution further, mirror R12 was stopped down in the vertical direction to a height of about 1 cm. The resulting spacial resolution was about 2 mm. Care was taken to make all beams parallel to the burner surface and equidistant from it in order to ensure that the entire gas volume sampled by the optical system was at the same stage of reaction. From 12 to 20 passes of the light beam over the burner were used, depending on the strength of absorption. B. Free Radical Measurements. The free radical measurements were made on the isolated spectral lines listed in Table I, by absorption on the Xe continuum. For OH and Tu”,the third order of a lOO-mm, 625 line/mm grating was employed, and for KH,, the second order of the same grating was used. The grating blaze was at 1 p . All measurements were made with straight 10-p entrance and exit slits, 5 mm long, giving a resolution of roughly 0.1 A. The NH2line, actually an unresolved doublet,s was chosen on the basis of its being the strongest feature which could be observed in flames in absorption out of the three strongest vibrational bands listed by Dressler and Ramsay.8 The strength of this line as observed in this work seemed anomalously high in comparison to intensities suggested by the above authors. Moreover, our spectrum showed additional weaker lines, some of which may be among the unassigned lines apparent in the photograph of Dressler and Ramsay. In order to ascertain that the line was properly identified, an Fe emission line at 5167.49 A was superposed on a scan of the absorption spectrum of NH2by reflecting light from a Westinghouse Fe hollow-cathode lamp from an inclined glass plate onto the slit. This provided an accurate wavelength calibration approximately 1 8 away from the RQo,4 line. By combining this with a measure of the dispersion, also from the Fe hollow cathode spectrum, a very satis(8) K, Dressler and D. A. Ramsay, Phil. Trans. Roy. Soc. London, A251, 583 (1969).
THEDECAY OF RADICALS IN NH8-O2-N2FLAMES
919
Table I 1 Wavelength, Speoies
Transition
OH NH
zz+
"2
A
3P
+
0-0 X, (0,12,0)
+ +
Line
pi5 P37
ZP, 0-0
3z-,
+
(O,O,O)
RQo.4
A
3 101 3385 5166
0.5
factory identification of the lines from RQo,4 through R&o,4 was made. This rather laborious procedure was necessitated by the fact that the dispersion of the combination spectrometer plus recorder varied by several per cent in consecutive scans over Fe lines, 30 A apart, and one could be sure of the identification only by obtaining a wavelength fix quite close to the desired line. There is no doubt that the NH2 line employed i s R&0,4, but it is possible that this rotational branch bends back so as to place a higher rotational line on top of R&0,4. Since the band has only been analyzed out to R&0,4, this point is obscure. In what follows, it is assumed that the '&0,4 line is not overlapped. The curve of growthg method was used to obtain concentrations from measurements of the absorption on a continuum. This method allows one to correct for that failure of Beer's law which occurs when the band pass of the spectrometer is wider than the absorption line width. A curve of growth is a log-log plot, for a particular value of the collision broadening parameter a,of the ordinate [(In ~)"*/AvD].!
(1
- e - "')dv = [(In ~)''*/IOAVD].!(10- I)dv
(2)
in which k, is the absorption coefficient at wave number v, 1 is the optical path, AVD is the full width at halfintensity of a Doppler line, Io is the incident intensity, and I is the transmitted intensity at v, against the abscissa N,f,l(ln 2)1'2/cnAv~in which N , is the number density of absorbers, fi is the line oscillator strength, and c is the velocity of light. The molecular data required for this method are the f numbers and the broadening parameters; only an estimate of the f number for NH2 was available,' so that parameter was assumed unknown initially. I n the last section of this paper a value for it will be deduced. For both OH and NH, individual line f numbers were calculated using an equation of the form fi = F
(--)si 2Ji
+1
(3)
in which F is the band oscillator strength, and S , is a rotational line strength. For OH, the S , were taken to be the A Kvalues of Dieke and Crosswhite,loas corrected by Learner,ll and FOHwas taken as 1.74 X For NH, S, were calculated from equations given by Budo,12
PIP - a 02
s
2 -0
0
0.1
Y
ni I
0.05
'0.02
0.01
2
5
20 CTAVD
Figure 2. Portion of curve of growth for NH.
which gave a value of 3.07 for the P37 line, and FNH was taken as 8.0 X 10-3.s The line broadening parameter, a, for OH was calculated from the data of Engleman,13 assuming the presence of only N2, H,, and HzO. These data have been verified in this laboratory under flame ~0nditions.l~ Broadening data for NH and NH2 were not available. Therefore portions of the curves of growth for both NH and NH2 were constructed by making absorption measurements at a single position in a single flame (Le., fixed N , ) at 4, 8, 12, 16, and 20 passes. The results for NH are shown in Figure 2 ; those for NH2 were similar. The deviation from a straight line (Beer's law) at high 1 is clearly apparent. These data could be fit by translation along the abscissa to a curve of growth with a collision broadening parameter a equal to approximately 1. This value of a has essentially no significance, since not nearly enough of the curve was con(9) s. S, Penner, "Quantitative Molecular Spectroscopy and Gas Emissivities," Addison-Wesley, Reading, Mass., 1959, Chapter 4. (10) G . H. Dieke and H. M. Crosswhite, J . Qciant. Spectrosc. Radiat. Transf.,2 , 97 (1962). (11) R. C. M. Learner, Proc. Roy. Soc., A269, 311 (1962). (12) A. Budo, 2.Physilc, 105,579 (1937). (13) R. Engleman, Jr., J. Quant. Spectrosc. Radiat. Transf., 9, 391 (1969). (14) M. P. Nadler and W. E. Kaskan, ibid., 10, 25 (1970).
Volums 74, Number 4 February 19, 1970
M. P. NADLER,V. K. WANG,AND W. E. KASKAN
920
structed to allow a reliable determination. However, it served the function of allowing the ordinate and therefore N,ft to be specified absolutely to within 10-20%. Then given .f$ from eq 3, N , could be determined. A similar procedure was followed for "2, except in this case only the product N d i was determined. The application of the procedures above gives N , (or N,ft), the concentration in the absorbing level. From these total concentrations NT of OH and N H were obtained from
NT
= 9
N iQr ,veEilkT (2J 1)
+
(4)
in which Q,,, is the rotation-vibration partition function, El is the energy of the absorbing state, and g is an electronic degeneracy of the ground state, having the value 4 for OH and 3 for NH. In the case of NH, the expression employed was
2t d.2
! 'I
d.4
d6
d.8
1!0
l!2
:4
1!6
Icm)
in which c = 2 is the symmetry number, and N is both the rotational quantum number without spin and the average of J , for the two unresolved levels which contribute to the absorption of RQo,4. The factor 4/3 arises because of the nuclear spin of the H atoms. Briefly it accounts for the fact that the measurement is made on a level in the ortho, or high statistical weight modification of NH2, but NT includes both modifications. The rotational part of Qr,v is the high temperature limiting form for an asymmetric rotor with neither nuclear nor electronic spin degeneracy. Molecular data for NHz came from the JANAF tables; those for N H and OH from Herzberg.l5 The experiments were conducted at atmospheric pressure. Temperatures were determined by sodium line reversal. Table I1 contains the essential data on the two flames studied, including Xa d i n e reversal temperatures, the nominal burned gas composition, assuming only Nz, Hz, and HzO as products, and the calculated temperature gradients (see below).
Figure 3. Data on concentrations as a function of 2, the distance from the burner, for flame 1.
0
T'2030' K [FLAME 1)
7.0
''L d4
d6
de
110Z k m i;2
02 i4
04
'
06
'
08
I'
IO
Figure 4. Data on behavior of Fa/fras a function of 2, the distance from the burner. Data for flame 2 displaced 1.2 crn for clarity. Dotted lines were drawn through points a t 0.5 cm and show expected temperature dependence of Ks.
Table I1 T
Rt
Flame no.
0.5 om, OK
om/seo
Vis, XNa
XHa
XHaO
dT/dz, OK/om
1 2
2033 2173
14.0 13.5
0.302 0.347
0.313 0,149
0.385 0.504
44 61
Results and Discussion A. Equilibration. Figure 3 shows the concentrations of the three radicals in flame 1. The results for flame 2 are simila,rboth in the trend of the values and in the actual concentrations. Figure 4 shows the funcThe Journal of Physical Chemistry
tion F8/fA as a function of distance from the burner for both flames. f4 is the oscillator strength of NHz R&o,4, to be discussed in more detail later. In Figure 4 the error bars indicate the uncertainty introduced by signa1 noise. Both relative and absolute error increase with distance from the burner because all three radicals are decaying and the absorption is decreasing. The data from flame 2 do not extend as far as those from flame 1 because the NH2 signal disappeared in the noise, typically 3%, beyond 1cm from the burner. (15) G. Herzberg, "Spectra of Diatomic Molecules," 2nd ed, D. Van Nostrand Co., Inc., 1950.
THEDECAY OF RADICALS IN NH3-OZ-N2 FLAMES Before interpreting these data in terms of equilibration, the temperature dependence of reaction I11 should be considered. This should be done not only because the measured temperatures of the two flames were different, but also because it is to be expected that the gases cool in the direction of flow through radiation by HzO, which is a major constituent. During preliminary experiments it was found that the measured reversal temperature decreased slightly with increasing distance from the burner, but the amount of decrease over the approximately 1-cm region of measurement was not much larger than the experimental uncertainty in the temperature determination, f15°K. Hence, temperatures were measured at only the one position of 0.5 cm in each case. I n addition, a temperature gradient was calculated using data on the total emissivity of water vapor,16 extrapolated to the totally transparent case, and the knowledge of the gas composition (assuming complete combustion to HzO, Hz, and N2), the heat capacity, and the hot gas velocity. The contribution of chemical heat loss from the deduced net reaction (to be discussed below) was only 20% of the heat loss by radiation. This method of calculating temperature gradients had been found previously to give results in good agreement (within 10%) with temperature gradients obtained by the use of fine silica coated thermocouples in lower temperature Hz-O2-Nz flames.” Given the temperature gradients, the straight lines in Figure 4 were drawn through the points a t 0.5 cm, a t which the temperatures were measured, to represent the variation of K 3 with distance. Two points can now be made. First, the upward drift of the experimental points with distance from the burner in each flame is in rough accord with the expected increase of Ka. Second, the ratio of the observed F3/f4values in the two flames at 0.5 cm is in good agreement with that calculated from the JANAF tables. The agreement displayed in Figure 4 between the behavior of the experimental function F3/f4 and the equilibrium constant K 3 is very strong evidence for the equilibration of reaction 111. I n the following it will be considered to have been established. The demonstration of equilibration has two immediate consequences. First, some statements can be made about the reactions occurring in the flame gases, and second, an f number for the observed transition in NHz can be calculated. These are discussed separately in the next two sections. B . Mechanism of Radical Decay. In the H2-02-N2 system, in which Nz is a nonreactive diluent, the reactions
+ H2 HzO + H H+ OH + 0 0 + Hz =OH +H
OH
0 2
(IV) (VI
(VI) have been shown to be equilibrated a t temperatures a t
921 least as low as 1500°K.*8 Other bimolecular reactions may occur between species, notably 20H
HzO
+0
(VW
but these are linear combinations of the complete linearly independent set IV-VI and can only serve to make more complete the equilibration of the entire system. The result of this equilibration is that in Hz-O2-N2 flames all of the radical concentrations, present initially at greater than equilibrium amounts, decay together. I n the flames discussed here, there is an interesting departure from this behavior in that the measured N H is in excess of the equilibrium, (and therefore “2) relative to Nz H2as final products, but the measured OH is the equilibrium value. Since the H2-02 system would on the basis of previous experience be equilibrated in these flames the finding that [OH]is the equilibrium value means that [HI, [0],and [O2]are also at equilibrium. Note here that Hzand HzO,being in excess, have essentially calculable concentrations whether or not the system is exactly a t equilibrium. Further evidence that OH is at equilibrium comes from the fact that the decay of OH agrees well with that which would be expected if OH were simply following the falling temperature, as calculated above. Hence, what is being observed is the decay of N-H species in an equilibrium Hz-OZsystem. Equilibration depends on the reaction in question being sufficiently fast in both directions, one criterion for which being that the activation energy in the endothermic direction not be too high. Sugdenlg has discussed this criterion and has suggested that reactions with activation energies less than 40-50 kcal/mol might be equilibrated at typical flame temperatures. Reaction 111 is a simple H atom transfer, for which the activation energy in the reverse direction should not be too different from its endothermicity of 26 kcal/mol. Its equilibration is thus not surprising. The same argument applies to two similar reactions
+
+ HEN + H~H NHz + 0 N H + OH NH~
(VIII) (IX)
In fact, given the equilibration of (111)-(IV), those of (VIII) and (IX) follow. But since (VIII) and (IX) are both simple H atom transfers, they both probably occur with a facility equal to that of (111)) and all three contribute to the equilibration of each. If these arguments are valid, then it is obvious that two other sets of reactions (16) W. H. McAdams, “Heat Transmission,” 3rd ed, MoGraw-Hill Book Go., Inc., New York, N. Y., 1954,pp 83,85. (17) W.E.Kaskan, Sixth Symposium (International) on Combustion, Reinhold Publishing Corp., New York, N. Y., 1957,p 134. (18) W.E.Kaskan, Combust. Flame, 3,49 (1959). (19) T. M. Sugden, Trans. Faraday soc., 52,1465 (1956),
Volume 74, Number 4 February 19,1070
M. P. NADLER,V. K. WANG,AND W. E. KASKAN
922 NH3 NH
+ OH (or H or 0)
+
NHz H20 (or H2 or OH)
+ OH (or H or 0)
N
(X)
+
H 2 0 (or Hz or OH)
(XI)
would be equilibrated, (X) more easily then (XI) on thermochemical grounds. Note that reaction X, with H and H2 as reaction partners, is the same as (I), postulated by Fenimore and Jones2 to be equilibrated. Again, as with reactions VI11 and IX, the equilibration of (X) and (XI) together with the previous reactions implies the equilibration of a set of hydrogen atom transfer reaction which can be represented by NH,
+ NH,
+ XH,+I
(XII)
but since these are simple H-atom transfers, they can be expected to occur and to contribute to the general equilibration of the system. The picture that emerges then for what is occurring in the flame gases of NH3-02-N2 flames is one of a radicalwith "2, catalyzed thermal decomposition of "3, NH, and K present in equilibrated amounts throughout. The only thing which is lacking is the set of reactions which convert the nitrogen in these species to the final products. At this point one can only speculate, especially since it is known that other species, principally NO, exist in these flames. Among the reactions which appear, qualitatively at least, to be capable of explaining the observed behavior are
+ N +N2 + H NH + 0 NO + H IS + NO N2 + 0 N + OH+ NO + H N + +NO + 0 NH
--+
--+
0 2
(XIII) (XW (XV) (XVI) (XVII)
These are all atom-transfer reactions which are very exothermic as written, and can thus be expected to be fast and irreversible. The proposed equilibration of reactions 11-XI1 suggests that the appropriate way to treat the kinetics of radical decay is through the use of the concentration function FN which represents the total nitrogen not yet in the form of NO or N2. For example if reactions 111-XVII comprised the entire mechanism, one could write (XVII)
in which the RI are the forward rates of (XII1)-(XVII), assumed irreversible. The only unknown concentration The Journal of Phpical Chemistry
in this equation is [NO]. Preliminary calculations, using suggested values for the rate constantsz0 for (XII1)-(XVII) and the dFN/dT which can be deduced from the data in this paper, result in a value for NO which appears consistent with previous work.1s2 The obvious conclusion to be drawn from the above considerations is that other species, especially NO, should be measured. Attempts at measurements of additional species are currently in progress. Even though the mechanism (111)-(XVII) is speculative, the point should be made that this mechanism appears to be at least in qualitative agreement with previous findings concerning the fate of the IS0 formed in the reaction Thus, in rich flames in which NH3 persists downstream, both the formation, through reactions XIV, XVI, and XVII, and the destruction, through (XV) of NO should occur. On the other hand, in lean flames the decay of FNwill be much more rapid, by reactions XIV, XVI, and XVII, due to the greatly increased concentrations of oxygen containing species. Once FN has become very small, so also will the rate of (XV) and the NO remaining will react further at only a very low rate. C. f Number for N H 2 RQo,4. Given the equilibration of reaction 111, F3 can be equated to K3 and a value of f4 deduced from the observed value of F3/f4 = K3/f4. This has been done for the datum at 0.5 cm in flame 1, which is a relatively reliable point in that the observed signals were relatively large, and also the temperature was measured directly. At the observed temperature of 2033"K, K3 = 2.32 X lo2 and K3/f4 = 5.8 X lo5leading to f4 = 4 X This is an entirely reasonable value, but depends on the thermochemical data used, and as pointed out previously, on the assumption that the RQo,4 is not overlapped by any other line. This line f number is of the same order of magnitude as that reported previ~usly,~ and also as those of the OH and NH lines used for observation in this work. It applies of course only to the RQo,4 line in the (0,12,0)(O,O,O) band. Inasmuch as the same ground state level of this transition is connected by optical transitions to a number of other vibrational levels in the upper electronic state, the total intensity of the electronic transition is probably an order of magnitude higher than indicated by f4. Given a set of relative line strengths for transitions of the type, NH2 A +- X, it would be possible t o deduce a band oscillator strength for "2. However, the authors are not aware of any such compilation. Acknowledgment. This work was supported by the National Science Foundation. (20) D. Gamin, Ed., "A Compendium of Evaluated and Estimated Rate Coefficients," National Bureau of Standards Report 9884, U. 8.Government Printing Office, Washington, D. C., 1968.
