RATEOF
June, 1961
THE
REACTION 0
RATE OF REACTION, 0
+ Hz
+ Hz
+
+
OH
013
+ H IN FLAMES
993
+ H, IY FLAMES
BY C. P. FENIMORE AND G. W. JONES General Electric Research Labaratory, Schenectady, N . Y . Received December 16, 1960
By probing low pressure flames of H ~ O Z - S ~ - N Z O and , using the ratios of rate constants previously determined in flames, we find that the rate constant for the reaction of oxygen atoms with hydrogen molecules is 2.5 f 0.4 X 108 1. mole-' sec-1 a t 1660°K. and 3.0 f 0.3 X 108 a t 1815". These values agree with a long extrapolation of Baldwin's results a t about 800"K., and combine with them to give k = 2.5 X lo9 1. mole-' sec.-l.
Introduction Of the three important bimolecular reactions in Hz-02 mixtures H
0
OH
+
k1 0 2
OH
+0
(1)
OH
+ €1
(2 )
k- 1
+ H2
+ H2
k2
k- 2 k3
H20
k-
+H
(3)
a
k11-4 and k 2 6 are moderately well known over a considerable range of temperature, but k-2 has not been measured above 820'K. and estimates of its value at high temperatures would be worthwhile. Measurement of kz in some H2-02-N2-Xz0 flames are reported in this paper. Nitrous oxide is included in the reactants because its irreversible decomposition in low pressure Hz-O2 flames allows the measurement of radical concentrations. It reacts chiefly by El + X'jzO +Kz + OH (4) M
+ NzO+ M +Nz + O 0 + KZ0 --+ 2NO
+
+
( 5) (6 ) ( 7)
0 s20 ---+ Nq 02 of which (4) is the fastest by far. It is assumed that no important reaction of oxygen atoms has been omitted, so that we can write out the expression for d[O]/dt due to the rhemical reactions above and solve the resulting expression for kz. Any consumption of oxygen atoms in the recombinations 20 M +0 2 M or 0 H M + OH M has been ignored, but these termolecular recombinations must be small compared to the reverse of reaction 1 which is included. Another simplification may as well be made from the start; it will always be possible to neglect the reverse of reaction 2 in the region where kq is evaluated, as will be shown, and to choose this region so that d [O]/dt is approximately zero. Then
+ +
h-2
=
-d[O]z/dt
+
+
+
+ ks[N,O] [AI] - d[N0]/2dt [Hzl LO1
and everything on the right side of this expression can be measured. The rates of change of [O,] and [KO] can be obtained by probing flat, one dimensional flames and (1) N. N. Semenov, Acta Physacocham., 20, 290 (1945). (2) R. R. Baldwin, Trans. Faraday Soc., 62, 1344 (1956). (3) G. L. Sohott and J. L. Klnsey, J . Chem. Phya., 29, 1177 (1958). (4) C.P.Fenimore and G. W. Jones, J . Phvs. Chem., 63,1154 (1959). (5) L.Avrsmanko and R. Lorentso, Zhur. Fiz. Khim., 24,207(1950). (6) C. P. Fenimore and G . W. Jones, J . Phys. Chem., 62,693 (1958).
correcting the traverses for diffusion. The composition traverses also allow estimates of k6[NzO][MI and [Hz]at any point. [O] can be estimated in two independent ways. First, since the nitric oxide formed in reaction G does not undergo appreciable decomposition, [O] can be obtained from d[NO]/dt = 2ks[O][Nz]
Second, it can also be estimated from thc three reactions 4 , 3 and 1 because -d[NzO]/dt= b [ H ] INz01 accounts for most of the decomposition of nitrous oxide and gives an estimate of [HI which can be substituted into d[HzO]/dt = &[OH] [Hz]
- k-E[HzO] [HI
to get [OH]. Both [HI and [OH] can then be substituted in -d[Oz]/dt
+ k7[01[X20]
=
ki[Hl[Ozl
-
k-i[OHl[Ol
to get [O]. In the last expression, the term in k7 can be omitted whenever d [NO]/dt is small compared to -d[Oz]/dt because k7 < 1 4 2 . Although the determination of [O] from reactions 4 , 3 and 1may seem involved, this method has two advantages over the simpler determination by reaction 6. It does not really depend on the separate values of k4, k,, k1 but only on their ratios; and since these constants were measured relative to one another in the temperature range in which me use them, the ratios are probably more accurate than the separate values. [ O ] from reaction G does of course depend on the separate value of k6. Also the reaction rates one uses in (4)) (3) and (1) are fairly large and can be tested for internal consistency. I n a region where d[O]/dt and d[OH]/dt are small, one should have -d[N20]/dt - 2d[Ot]/dt = d[HzO]/dt d[NO]/dl since oxygen must be conserved. This relation holds experimentally within lo%, and d [XO]/dl is a h a y s small compared to the three other terms in the equality. Therefore the three larger terms are a t least consistent among themselves. The small d[NO]/dt used in the determination of [ O ] via reaction 6 cannot be tested in the same way because it does not make a very significant contribution t o the conservation of oxygen or nitrogen. The values adopted for the rate constants are quoted in Table I. kl, k3, kd and le6 are correct relative to one another to perhaps 30%, and kl and k~ also agree within a factor of two with independent estimates in the literature. li5 is obtained from a correlation of much of the data on the pseudo-unimolecular, thermal decomposition of nitrous oxide.7 The limiting low pressure con-
+
7
C. 9. FENIMORE AND G. W. JONES
9 94
000%
O.!
e------
W
a
+ 4
g0.2
500
3 I-
c U 0 a (L
W
d = 0.1
000
C
, dt
,
'i
Vol. 65
calculated just as b e f ~ r e . The ~ flames were 60 to 70% nitrogen, and we first tried approximate DNO values appropriate t o binary SO-N2 mistures.lo These gave too great a correction holyever, and resulted in negative calculated values of d[NO]/dt in the early parts of some flames. After several trials in different runs, we eventually used DSO = 2.3 X
PE7 cm.2 set.-'
in all flames at 4 em. pressure of mercury. For other species, the diffusion coefficient was taken from DNO under the assumption that D n-as inversely proportional to the square root of the molecular weight. For other pressures, it wa5 assumed that D varied inversely with pressure. The value chosen for D N O is near the greatest value which did not overcorrect the nitric oxide traverse. The calculation of [ O ] by means of reaction 6 is considerably more sensitive t o changes in the diffusion coefficient than is the calculation tzu (4), (3) and (1). A smaller DNO decreases the maximum [O] as calculated from (6). Experimental
Fig. 1.-Traverses through a flame of reactant composition H2 0.66Nz0 1.81 air burnt at 2 cm. pressure of mercury with a mass flow of 2.32 X 10-3 g. cm.-2 sec.-l. Calculated reaction rates are plotted in the lower part of the graph.
The arrangement was the same as used before. It included a water-cooled, porous, flat flame burnerll of 31 .I cm.2 surface area mounted in a bell jar which was also equipped with a movable quartz probe (-0.1 mm. diam.), movable quartz coated thermocouple (made of butt-welded Pt-Pt, Rh wires 0.012 mm. diam.), pumps, and externally mounted cathetometer. The reactants were metered through critical flow orifices. Thermocouple readings were corrected for radiation" to get temperature traverses. Composition traverses of the stable components were obtained from mass spectrometric analyses of samples drawn through the quartz probe at critical flow rates.
stant list'ed is appropriate to initially pure nitrous oxide where [MI represent's initial [KZO]. If [MI represents the total concentration of a mixture of other gases, as it does in our flames, the
Determination of k2.-The upper half of Fig. 1 presents typical traverses through a flame burnt a t 2 cm. pressure. The lower part of the figure shows reaction rates calculated from the traverses. [0]as calculated from
ar
0.5 1.0 CM. DISTANCE FROM BURNER SURFACE.
+
+
[ 0 ] = dIN0]/2k61x&]dt
TARLE I BIMOLECCLAR R.4TE COXSTANTS" Rate constant, mole 1.-' sec.-l
Reaction
1 3 4 5 6
(j
x
2.5
1011 e-18'RT
x 1011
e-lOIRT
Ref.
4 6 4 7
4 X 1011 e-16.3'RT 4 x 1 0 1 2 e-5QIRT 1 x 1011 e-28!RT 8 rn kl < k6/2 9 a For reactions 1, 2 and 3, the rate constants for the reverse reactions can be obtained from the constants for the forward reactions and the equilibrium constants; kl/k-l = 35e-16.61RT,kglk-2 = 2e-3.01RT, k3/k-3 = 0.25e15.S'RT.
attains a maximum value of 6.0 x lop6 mole 1.p' at 0.8 to 0.95 em. from the burner surface. Calculating [O] in the alternate way descrihed above, we find that [HI
=
-d[P\'&] / k i [ 1201dt
is relatively constant through most of the flame. At a position 0.8 to 0.95 cm. from the burner surface, [HI = 1.4 x lopb mole 1 . ~ ~and ; then in turn, [OH] = 0.83 x from reaction 3 and [ O ] = 3.7 X lop6from reaction 1. The [0]obtained from reactions 4, 3 and 1 i q smaller by a factor of 1.6 than [0]calculated from pre-exponential factor of kL could be wrong by a factor of about two, and we will discuss this possi- reaction 6. A similar discrepancy orcurs in all bility later. For any use we make of k;, it. will the flames, by a factor of 3.6 in the worst case and be enough to knox t,hat a t the temperatures of 1.6 in the best, and always in the 5ense that [0] from reartion 6 is the larger. interest k 7 is smaller than k6. Since IO] from reaction G i h more sensiti1e t o a The diffusion corrections to get d[SO]/dt, change in the diffusion coefficient, me trust it less. -d[OZ]/dt, -d[N,O]/dt, d[H20]/dt from experimental composition traverses caused us some Other reasoiis for preferring the smaller [0]from trouble. With the diffusion coefficients DNO, reactions 4, 3 and 1 haye been given in the introDo1,etc., assumed the chemical reaction rates were duction; and lye lice the smaller [O] for estimating k2. (7) H. S. .Johnston, J . C'hem. PhUs., 19, 663 (1951). lcor the flame desciihed in Fig. 1. a t 0.8 t o 0.95 (8) C . P. Fenimore and G. TI'. Jones, 8th Combustion Syinposium at Pasadena, Calif., Sept. 1960. (9) F. Kaufnian, N. J . Clerri and R . E. Bowman, J . Chem. r h u s . , 26. 106 (19a6).
(10) -4 A. Westenbelg, Combustton and F l a m e , 1, 316 (1Yi7) (11) W. E. Kashan, "6th Sb niposium on Conihuition " Reinhold Publ. Corp., Neu E o r h , N P., 1957. I) I31
+ Hz
RATEO F THE REACTION O
June, 1961
cm. from the burner surface, the reverse of (2) is small compared to the forward reaction. This is apparent because the product of reaction partners for the forward process, [O][H2],is twenty times the product for the reverse, [OH][H]; but the equilibrium constant, kzlk-,, is of order unity. d[O]/dt is very small in the region 0.8 to 0.93 em. from the burner surface, so we substitute into h.2
=
-d[O]i/dt
+ ks[N20][ill] - d [ S 0 ] / 2 d t [01[Hzl
to get k2 = 2.8 X lo8 1. mole-' see.-' a t 1675°K. The term, k5[S20][M], is small compared to -d[O,]ldt and could have beem omitted in this example. Estimates of kg, obtained in a similar way in each flame, are listed in Table 11. The first four runs are fuel rich flames, the last two are fuel lean. The last column of Table I1 gives the percentage contribution of the term k5[N20][M] to the value of k,. If k5 were wrong, only runs no. 2 and 3 n-ould be affected.
-+
OH
k-2
kl
Run
P,LIII. 4
?' OK.
x
10-8,
[01 X 100, I mole-' mole 1 . - 1 set.-'
kj
term.a
%
3 0 -0 1 2 0 3 1 7 75 1830 6 1 8 33 1790 8 4 2 0 -0 1630 8 1 2 8 -0 3 7 1675 5 2 -0 3 0 2 8 1670 6 4 = Contribution of the term, kSINZO][MI, to the value deduced for kp if k5 is assumed to have the value in Table I. Actually k5 is eventually assumed to be 2.25 times larger than this value, see text, and the eventual values of h.2 in runs 2 and 3 are 3.3 and 2.6 X IO8, respectively. 1 2 3 4
18'25
As they stand, the first three runs in Table I1 average to k2 = 2.2 x 108 at about 1815°K. with a mean deviation of 26%. But k 5 is not known better than to a factor of about two, as was explained in the Introduction, and it is legitimate t o 1m-y the pre-exponential factor of l i b in order to get the best agreement in 12,. If k5 is multiplied by 2.25, the average deviation in k , decreases to only 8% and the average becomes identical with the only value of k , which is independent of 1%. Therefore we increase the h.5 given in Table I and accept li, = 3.0 =t 0.3 X lo8at 1815".
IN FLAMES
995
The last three runs give an average a t 1660°K. of kz = 2.5 =t 0.4 X los, independent of k5. Comparison with Other Work.-Baldwin2 dededuced from the low pressure limit of explosions in Hz-02-Nz mixtures that kz (or k3) = 2.0 X lo7 1. mole-' set.-' a t 793°K. The ambiguity arose because reactions 2 and 3 have an identical dependence on [Hg]; but since 2 X lo7 is only or 1/206 of the value expected for k3 from other work, it is probably k,. He also reported an activation energy of 9.2 kcal., but disclaimed much accuracy; for IC, was reproducible only within =t 12y0 at constant temperature, and the variation over the whole temperature range was 44%. Perhaps it is not unfair to suggest that his error might have been 1 3 kcal. If his estimate a t 793' is extrapolated to 1815", using 9.2 kcal. activation energy, it gives IC, = 5.4 x lo8 as compared to our observed 3 X lo8. This is good agreement. His and our estimates combine to h.2
TABLE I1 RSTIYATES OF
+H
= 2.5 X 109e-7.7'RT1. mole-' see.-'
and 7.7 is the same as 9.2 kcal. within the probable error of the latter. If the pre-exponential factor is taken proportional to part of the temperature dependence is ahsorbed by this factor, and E, becomes 6.4 rather than 7.7 kcal. In much the same way as Baldwin, but with less complete data and interpretations, Azatian and co-workers12found h-2 = 9 X 1O1O e-12.'/RT a t 840 to 930'K. from the lower explosion limits of CO-02 mixtures containing 0.76 to 8.0% added hydrogen. Their result extrapolates to twice Baldwin's estimate a t 793" and to ten times our estimate at 181.5'. It is not, possible to reconcile our measurements with those of Aaatian, et d., and still maiiitain an activation energy of 9 13 kral. NOTE ADDED I N PRooF.-Clyne and ThrushI3 reported just recently an estimate of kp = 1 2 X 10'0 e-9.2IRT 1. mole-' see.-' a t 409 to 733°K. by a very different method; 0 atoms were generated in known concentration by titrating N atoms with nitric oxide, and the decay of the 0 atoms when mixed with hydrogen was followed by the radiation S O emission. Their estimate of k2 is systefrom the 0 matically larger than the expression deduced in this paper by a factor of 2 to 3; but a disagreement of this order is perhaps within the error of any of the data.
+
(12) V 1 ' . Azatian, V. T' Toevodskii and A. B. Salbandian, Dokl A k a d . S a u k S S S R , 132, 864 (1960) (13) M. A A Clyne and B A Thrush, IYatuie 189, 135 (1961)
