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The dissociation of hydrogen peroxide and its role in the hydrogen-oxygen reaction
103
ROLE OF HYDROGEN PEROXIDE
2
THE DISSOCIATION OF HYDROGEN PEROXIDE AND ITS ROLE IN THE HYDROGEN-OXYGEN REACTION By R. R. B A L D W I N , P. D O R A N AND L. MAYOR Although H~O2 had been detected as a reaction product in both the photochemical reaction ~, 2 and thermal reaction 3' 4 between H2 and O2, its importance as a reaction intermediate was not realized until many years later. Thus, as recently as 1946, Hinshelwood and Willbourn 5 interpreted their results on the slow reaction in KCl-coated vessels at 570°C by adding reactions ( l l a ) and an initiation process no to the reactions (1) to (5a) used to describe the second limit. OH
+
H~
H20
+ H
(1)
H
+
O~ = OH
+ 0
(2)
O
+
H~ = OH
+ H
(3)
H
+O~+M
+M
(4)
=
=HO~ surface
HO2 = 1I-I20 -+- ~-O2 (5a)
HO2
+
H2 = H20
+ OH.
If it is assumed that H202 is ultimately decomposed to tt20 and 0~, the alternative reaction (11) is kinetically equivalent to (lla).
(11)
This mechanism gives the rate expression: d[H20]
dt
Ano
1
(i)
2k2
]C51a[H2]
]c~[M]
ks~ + knjH2]
H02 + H202 = H20 -Jr- 02 + OH.
where the value of A (between 1.5 and 2) is dependent on minor details of the reaction scheme. The variation of rate with mixture composition suggested that no cc [H~][M], and this was interpreted as indicating that dissociation of hydrogen was the initiation process. In a paper given at the first postwar Combustion Symposium at Wisconsin in 1948, Lewis and von Elbe 6 showed that the rate of dissociation of hydrogen is too slow by a factor of 10'3 to account for the observed rate. This confirms their earlier conclusion 7 that initiation must occur through dissociation of a compound with a much lower
(6)
If (6) is the predominant reaction of H202 and dissociation by (7) is relatively infrequent, then the initiation rate becomes proportional to [H2][M']. H202 + M ' = 2 0 H -4- M ' .
(7)
Occurrence of (6), however, would require the homogeneous decomposition of H~O2 to be a chain reaction [through the reaction sequence (7), (15) and (6)] with an order either 2 or 1.5, depending on whether the chain termination process was the surface removal of HO2 [reactions (5) or (5a)], or the gas phase process (10). O H + H202 :
(lla)
HO2 + H2 = H202 + H.
dissociation energy than I-I~, namely, H202. They suggest that H~O2 reaches a stationary concentration as a result of its formation by reaction (11) and removal by (6).
H20
--~ HO2
(15)
surface
1 HO2 -= ~H202 + !Oo 2 . 2HO2 = H202
+ 02.
(5) (10)
The constant percentage decomposition over a 10-fold range of H202 concentration found by Baldwin and Brattan s confirms previous views 9, 10, 1, that the reaction order is unity, and reaction (6) is thus excluded. If an expression similar to (i) is applicable to KCl-coated vessels, then high average chain lengths will be obtained only when the ratio of chain branching to chain breaking is nearly unity, i.e., when the denominator of (i) is significantly less than unity. Its value is then extremely sensitive to the constants used in evaluating the variation of k4[M] and ks~ with mixture composition; the latter was obtained 12 from third limit studies by assuming first, that the limit is isothermal, and second, that HO~ radicals are destroyed efficiently in KCl-coated vessels (i.e., ks~ cc 1/P). I t is unlikely that either of these assumptions are justified. All these points add to the difficulty of interpreting the slow reaction data in KCIcoated vessels.
104
CHEMICAL KINETICS
Clear demonstration of the importance of H~O2 as an intermediate in the slow reaction was given by Baldwin and Mayor} 3, 14 who were particularly fortunate in discovering that a boricacid surface which had been aged by repeated tests becomes extremely inert toward both HO~ and H~02. This inertness toward H~02, necessitated by the kinetic features of the reaction, has been confirmed by studies of H202 decomposition in such vessels. 8 The main mode of formation of H202 is directly from HO2 radicals, and there is convincing evidence that this occurs through the gas phase process (10) in aged boricadd-coated vessels. Since H202 mainly undergoes reaction (7), it may be regarded as a rather unreactive chain center (actually equivalent to two centers, since it is formed from two centers and dissociates to give two centers). A straight chain is thus set up by the reaction sequence:
H (4)) HO2 (10)) ½H2 O2 (7)) OH (1)) H. Superimposed on this straight chain is linear branching through reactions (2) and (3), and in the absence of termination reactions, the reaction would be explosive. Analysis of the variation of rate with mixture composition and total pressure shows that the termination reactions are: H + H202 = H20 + O H OH +H20~
= H20 + H O 2 .
(14) (15)
Since H202 may be regarded as a chain center, the mechanism is thus of the linear-branching, selftermination type, represented by the equation: dn/dt = no 4- chn -- D n 2
(ii)
and if the initiation rate no is negligible at maximum rate, as suggested by the markedly autocatalytic nature of the pressure-time curve, the concentration of centers at maximum rate is given by n = dp/D. One striking advantage of the aged boric-acidcoated vessels is that the reaction proceeds quite rapidly at 500°C, whereas temperatures of about 560°C are necessary to get reasonable rates in KCl-coated vessels of moderate diameter. At these lower temperatures, the induction period is of quite long duration, varying from minutes at 470°C to about 10 sec at 540°C. By sampling the reaction mixture at various stages during the induction period, Baldwin and Mayor showed that the concentration of H202 rose during the induction period, reached a maximum value at
maximum rate, and decreased beyond the point of maximum rate. This demonstration of the importance of H202 would be impossible in KC1coated vessels, first, because of the difficulty of extracting H202 without loss due to surface decomposition, and second, because at the temperature of 560°C or higher necessary to get reasonable reaction rates, the maximum H~02 concentration would be reached almost instantaneously. Introduction of reaction (6) into the reaction scheme for aged boric-acid-coated vessels gives kinetic expressions entirely inconsistent with the experimental results, and the first convincing evidence against this reaction, later confirmed by the peroxide decomposition studies, is thus obtained. A detailed examination of the variation of rate with mixture composition shows that it is necessary to include a small contribution from reaction (11), and the final mechanism, involving reactions (1) to (4), (7), (10), (11), (14) and (15) gives a rate expression: R - d[H~O] _ 2k7 [H202] [M'I G dt where [H2 02] =
kl k2[HJ[O2] (1 +/~k4[M]/k2) k14 kl[HJ + k15 k4[Oj [M] (1 - ~)
k n [ H j (1 4- k2/k4[M]) = (2k10 R)~
G = h[O~][M] + k~[O~] + k~jH~O~] k4[Oj[M]
- k2[Oj - k~4[H2Oj
By a careful examination of the variation of rate over a wide range of mixture compositions, the following values of rate constant ratios at 500°C (in mm Hg, min units) can be deduced: kl k2 tcT/k4 k15 = 0.120, kl k14/k4 k15 = 700, k11/(k10) ½ = 1.1 X 10 -3. Since the term G, which can be readily evaluated knowing kl k14/k4 k15, is only slightly greater than unity, the reaction rate is effectively the dissociation rate of H202. Determination of the maximum H20~ concentration by sampling and analysis permits the absolute value of k7 to be determined. Tests with three quite different mixtures gave values of 0.069, 0.052 and 0.075 mm Hg-imin -1. Since high values would be expected
ROLE OF HYDROGEN PEROXIDE
because of loss of H 2 Q both by decomposition and adsorption during sampling, the agreement with the value of 0.046 obtained by direct study s of the decomposition of H~02 provides convincing support for the mechanism. From /~7 = 0.046 and k2/k4 = 18.5 mm Hg (M = H2) at 500°C, k ~ / k ~ = 268. If this difference between/ct4 and k2 is attributed entirely to activation energy difference, then (E2 - E,4) = 8.6 kcal/mole. The best value of k2 is probably that obtained from first linfit studies, '5 giving/c2 = 3.4 X 10-~5 and /~4 = 9.1 X 10-13 in (molecules/era 3) ' sec-1 units at 500°C. The above value of k2 corresponds to unit steric factor and an activation energy of 19.8 kcal/mole, or if the activation energy of (2) is taken as equal to its endothermicity (16.2 kcal/mole), then a steric factor of 0.10 is required. Depending on which of these alternatives is adopted k14 varies from 1.33 × 10-9 e -ll,200/RT to 1.28 × 10-1° e-v,6°°jRr (molecules/cn?) -1 sec-1. From the values of kl k14/k4 k15 , k:/k4 and k14/k2, kl~/kl = 7.1 at 500°C. This is consistent with a value of approx 6 obtained from a stud5~ of the decomposition of H202 at 440°C in the presence of H2. No reliable figures for k~ appear to be available. At temperatures of about 360°C in aged boricacid-coated vessels, the decomposition of H202 is a first-order heterogeneous reaction, s with a somewhat variable velocity constant, a typical value for a 6-mm diameter tube being 0.018 sec -1. Allowing for temperature (from the activation energy of the heterogeneous reaction) and diameter, this would correspond to k~ = 0.016 for a 15-mm diameter vessel at 500°C. Since the slow H.o/O: reaction showed no diameter dependence, surface destruction of H202 must be small compared to gas phase termination, i.e., k,[H202] < ~k14[H][H.~O2]. From the values of k , , k~4, quoted, [HI > 10-5 mm Hg. This does not seem unreasonable. Although the mechanism of the slow reaction between H2 and 02 in aged boric-acid-coated vessels may now be regarded as firmly established, there are two points not conclusively settled by the slow reaction studies. First, the reaction between H atoms and H202 can be written either as (14) or (14a): H + H~O~o = H2 + HO.,.
(14a)
The choice of (14) is based on small differences between the kinetic expressions obtained with the two alternative reactions. The second limit
105
studies,,~. 16 described briefly below, provide more convincing evidence for the occurrence of (14). Final confirmation is provided by studies of the decomposition of H202 in the presence of H2, when a marked increase in the decomposition rate is found, s This is explained by the chain sequence (7), (1) and (14), the chains eventually being terminated by reaction (15). If (14a) occurs, however, no chain reaction is possible.
O + H-.O2 = H20 + 02.
(13)
The second point not fully resolved by slow reaction studies is the nature of the second termination reaction, (15) and (13) giving similar kinetic features. Detailed analysis of the slow reaction data gives some support for (15) rather than (13). At the temperature of 440°C used to study the H~OgH2 system, (13) cannot occur, since H + 02 = OH + 0 would be negligible compared to (4) and (14), even in the presence of 0.5 mm HgO 2present either as reaction product or as impurity. The concentration of O atoms must thus be negligible, and if (15) does not occur readily, then (4) or (14a) must be the termination reaction. Neither of these reactions provides a satisfactory account of the kinetic features, and (15) is the only termination reaction capable of explaining the experimental results. Support is provided by the agreement of the values of k l J k l obtained from studies of the H2/02 reaction, and from peroxide decomposition studies in the presence of H2. Since the velocity constant for peroxide decomposition at 500°C implies a half-life time of about 1 sec at 500 mm Hg, it seems a little surprising that induction periods varying from 20 to 90 seconds are obtained in the slow reaction between H2 and 02 at this temperature. This is explained by the proposed mechanism, since the dissociation of peroxide merely continues the chain, and branching occurs only when the H atom undergoes reaction (2). Since under the experimental conditions, the rates of (4), which continues the chain, and (2) are in the ratio of 15-25:1, the long induction periods can be understood. The mechanism thus accounts both for the magnitude of the induction periods and for their variation with experimental factors. ~4 Elimination of (6) requires reconsideration of the mechanism of the slow reaction between H2 and 0~ in salt-coated vessels. For a surface that is efficient in destroying H~.02, k~ = 23 D i d 2 for a cylindrical vessel of diameter d. With the
106
CHEMICAL KINETICS
Stefan-MaxwelW ,18 relation for D with ~u2o2 = ao2 = 3.62A, aN2 = 3.92A, ks = 0.82 see-~ for a 5 em diameter vessel at 560°C and 760 mm Hg (M = N2). Under the same conditions, kr[M'] = 2.3 see -1, so that the ratio of dissociation to surface destruction of H202 would be about 3:1. Assuming the value previously quoted for kt4 of 1.28 X 10 -1° e -7'8°°lRT (molecules/ema)-~ see-', k7[M'][H2021 = k14[H][H2021 at 560°C and 760 mm Hg (M' = N2) when [H] = 1.5 × 10-4 mm Hg, which is a feasible value. Removal of H202 by OH also appears likely, particularly in view of the increased concentration of OH resulting from reaction (7), and it thus seems probable that reactions (7), (14), (15) and surface destruction all play a part in controlling the concentration of H~O2. Removal by OH would account for the high order with respect to hydrogen, but a detailed analysis is required before a precise mechanism can be given.
face in KCl-coated vessels. The H202, having evaporated into the gas phase, is assumed to undergo either reaction (6) in large vessels, or reaction (8) in small vessels, this change accounting for the slight decrease in the limit as the vessel diameter decreases. A variety of evidence,16, 19 however, makes it doubtful whether HO2 radicals will survive on a KCl-eoated surface, and evidence against reaction (6) has already been given; moreover, alternative explanations of the small changes in limit with vessel diameter arc available (15). H+02+H202
(iii)
They interpreted this equation by introducing the quadratic branching reaction:
Lewis and yon Elbe 7 were the first to allocate a significant role to H202 at the second limit. They assumed HO2 = ½H202 -4- ½02 at the surI
(8)
3/[ = A + g/[o2] ½.
T h e Second L i m i t
fOOl
= H20+05+OH
A more important influence of H202 at the second limit was suggested by Egerton and Warren,2° who found that the limit in boric-acidcoated vessels rose markedly at low mole fractions of O2, according to the relation:
'
H + HO2 = 2OH.
(9)
In a reaction with quadratic branching (Fn2), '
'
'
OO
80 ,O
B 60
M
I
A ,O
40
2%
I
, rMM'I/3 ,2
I
,6
I
2o
I
24
Fro. 1. Second limits in fresh and aged boric-acid-coated vessels 500°C. Mole fraction H2 = 0.28. A, aged coating (selection of points) ; B, fresh coating. X, 51-mm diameter; @, 36 mm; A, 24 mm; 27, 15 mm.
107
ROLE OF HYDROGEN PEROXIDE
explosion is possible even if the net branching factor q5 is negative provided 4n0 F > ¢2. The initiation rate no thus affects the explosion boundary, and Egerton and Warren suggested that the initiation reaction was the unimoleeular firstorder dissociation of I-I202 produced in equilibrium concentration by reactions (5) and (6). Reaction (6) has now been eliminated, and the dissociation of It202 shown to be bimolecular (or, more strictly, unimolecular second order), but Baldwin, Doran and Mayor '6 showed that their own observations on the limit in aged boricacid-coated vessels could be accommodated by adding reaction (9) to the mechanism for the slow reaction in these vessels. Their complete mechanism involves reaction (1) to (4), (7), (8), (10), (14) and (15); reaction (11), which plays some part in the slow reaction, is unimportant at temperatures of 500 ° and below. If (15) is neglected, a cubic equation is obtained for the center concentration. Expressing the condition for three real solutions, and making iustifiable approximations, the limit is given by:
[M]
2k2 + /c4
/27k2 k7 ]c~[M][M']'~ l/a
\
4k~ l~,-ok,4[02~ /
(iv)
I
I
I
1
500°C 8O
60
48o"c
M
40 460°C
0
I 8
I
I 1/^16
I 2.,4
"
A plot of [M] against ([M][M']/[O~}) m over a wide range of mole fractions of 02 shows only slight curvature (Fig. 1A), and if allowance is made first for the occurrence of (15) to the exLent indicated by slow reaction studies, and second for the approximations made in obtaining solution (iv), a precise interpretation is obtained of the variation of limit with mixture composition} 6 Two difficulties arise with this mechanism: (1) It is strictly applicable only to the limit in aged boric-acid-coated vessels. In a 51-ram diameter cylindrical vessel (20 cm long), the limits at 500°C in both freshly coated and aged vessels are little different, suggesting that exactly the same mechanism operates. As shown in Figure 1, however, the limit rises significantly in freshly coated vessels as the vessel diameter decreases, whereas in aged vessels the limit, as required by (iv), is independent of diameter. Figure 2 gives the limits obtained with both fresh and aged boric-acid-coated vessels over the temperature range of 440 to 500 ° using relatively fast withdr/~wal rates. ~ The limits are higher with
a freshly coated surface and this difference persists, increasing as a percentage, down to 440°C; this is surprising, because lower limits due to increased surface termination might have been expected in the fresh vessels at the lower temperatures. (2) Quite long induction periods (30 to 120 see) are observed in the slow reaction at 500°C in aged boric-acid-coated vessels, and these increase markedly as the temperature is reduced. i t seems doubtful therefore, whether there is sufficient time for H202 to reach its equilibrium concentration when rapid manipulation proeedures are adopted to determine the second limit at temperatures below 480°C. An alternative mechanism can thus be suggested in which the peroxide plays no part. Such a mechanism, involving reactions (1) to (4), (5a) and (8), gives
The withdrawal rates used corresponded to 3 to 8 mm Hg/sec over the range of 150 to 130 mm Hg; the rate will fall off at lower pressures, being
roughly proportional to p,-1.5, the exact exponent depending on the particular capillary used to control the withdrawal rate.
FIG. 2. Variation of second limit with temperature in fresh and aged boric-acid-coated vessels, with the use of rapid withdrawal rates. Mole fraction H~ = 0.28. E), Fresh coating; X, aged vessel.
108
CHEMICAL KINETICS
the limit expression: [M] 1/2 = (2~'2/~'4)';2 + ('no Z'~//~'4~'~[O21)1/~. Because /c5 is diameter dependent, the initiation process no nmst be a surface process to account for the limit being effectively independent of diameter. Although it is possible to interpret the variation of M with mixture composition at 500°C by assuming arbitrary values of p and q in the expression no oc[ It2]~[02] g, the mechanism has a number of unsatisfactory features which have been fully discussed elsewhere.I6 Ileplaeement of (5a) by (10) now requires a gas phase initiation and no reaction satisfying the experimental results can be found. To examine further the role of H202 at the
5 0 0 °C.
second limit in aged boric-acid-coated vessels, tests were carried out in which the manipulation time was deliberately varied. Figure 3 shows the results of tests over the range of 440-500°C in which the evacuation with rapid withdrawal rates was interrupted for various times at a pressure about 20 mm Hg above the limit obtained with no interruption. At 500°C, the limit decreases as the time of interruption is increased. This can be attributed to water formation, and, as would be expected, the effect increases with increasing mole fraction of 0.2 • At 480°C, however, there is an initial rise in the limit, which then falls as the interruption time is further increased. The rise in the limit increases as the mole fraction of 02 decreases, whereas the subsequent fall
75-
480°C"
,oo I
L
,
0o f
0
, 3
, 8
~ -,~251 9 0 TIME IN
t
12
24
36
MINUTES.
FIG. 3. Effect of interrupted withdrawal on second limit. Mole fraction H2 = 0.28. Mole fraction of O2: )<, 0.72; Q, 0.28; A, 0.10; V, 0.025.
109
ROLE OF HYDROGEN PEROXIDE
increases as the mole fraction of 02 increases. The rise in the limit becomes more marked as the temperature decreases to 460 and 440°C, whereas the time to obtain the maximum limit increases. Further tests showed that somewhat higher limits than those indicated in Figure 3 could be obtained at 480 and 460°C either by using moderate withdrawal rates and interrupting the evacuation for the optimum period, or by using extremely slow withdrawal rates without interruption. The latter method could be used only with mixtures of low oxygen content, since with mixture of high oxygen content, complete suppression of explosion resulted from the use of slow withdrawal rates. At 440°C, the maximum limit at low mote fractions of 02 could be obtained only by the use of the slowest withdrawal rates together with interruption periods of at least 15 minutes. All these observations are described in detail elsewhere. ~ The rise in limit with increased manipulation time can be attributed only to the build-up of some relative unreactive intermediate and H.~02 is the only possibility. Since the rise in the limit is most marked at low mole fractions of O : , it is clearly associated with the third term in (iii). Convincing evidence of the role played by H202 is thus provided. Even with rapid manipulation and fast withdrawal rates, the limit rises slightly as the mole fraction of 0.~ decreases, even at 440°C in aged boric-acid-coated vessels. Since the third body coefficient in reaction (4) is less for O2 than for N~, this can be attributed only to some contribution from quadratic branching. The slow build-up of peroxide indicated by Figure 3 suggests that initiation by H20.~ might be negligible when very rapid manipulation is used at 440°C. It is possible, therefore, that this residual quadratic branching is due to a surface initiation which at higher temperatures becomes relatively unimportant compared to initiation by H~O2. Figure 2 shows that higher limits are obtained in freshly coated vessels than in aged vessels, particularly at the low temperatures. This can be explained by assuming that the surface initiation is faster in fresh boric-acid-coated vessels. This would also explain why at 500°C, the limits in fresh vessels are higher than in aged vessels, and increase as the vessel diameter decreases.
Acknowledgments We wish to thank the Preston Education Committee for a grant to L. M. and the Depart-
ment of Scientific and Industrial Research for a grant to P. D. Grants from the Royal Society, Imperial Chemical Industries, Ltd., and Shell Research, Ltd., are gratefully acknowledged. Part of this work was sponsored by the United States Air Research and Development Command under Contract No. A F 61(052)-62. REFERENCES 1. MARSHALL, A. L.: J. Physic. Chem., 30, 34, 1078 (1926). 2. BATES, J. R., AND SALLEY, D. J.: J. Am. Chem. Soc., 55, 110 (1933). 3. PEASE, R. N.: J. Am. Chem. Soc., 52, 5106 (1930). 4. HOLT R. B. AND OLDENBERG, O.: J. Chem.
Phys., 17, 1091 (1949). 5. HINSHELSVOOD, C. N., AND WILLBOURN, A. H.:
Proc. Roy. Soc. (London), A185, 369 (1946). 6. LEWIS, B., AND VON ELBE, G.: Third Symposium on Combustion, Flame, and Explosion Phenomena, p. 484. The Williams & Wilkins Company, Baltimore, 1949. 7. LEWIS, B., AND VON ELBE, G.: J. Chem. Phys., 10, 366 (1942). 8. BALDWIN, R. R., AND BRATTAN, D.: Eighth Symposium (International) on Combustion, p. 110. The Williams & Wilkins Company, Baltimore, 1962. 9. GIG[TERE, P. A., AND LIU, J. D. : Can. J. Chem., 35, 283 (1957). 10. FORST, W.: Can. J. Chem., 36, 1308 (1958). 11. HOARE, D. E., PROTHERO, J. B. AND WALSH, A. D.: Trans. Faraday Soc., 55, 548 (1959). 12. ]-~INSHELWOOD, C. N. AND WILLBOURN, A. H. :
Proc. Roy. (1946).
Soc.
(London),
A185,
353
13. BALDWIN, R. R., AND MAYOR, L.: Seventh
14. 15. 16. 17.
Symposium (International) on Combustion. Butterworth & Company, Ltd., London, 1958. BALDWIN, R. R., AND MAYOR, L.: Trans. Faraday Soc., 56, 80, 102 (1960). BALDWIN, R. R.: Trans. Faraday Soc., 52, 1344 (1956). BALDWIN,R. R., DORAN, P., AND MAYOR, L.: Trans. Faraday Soc., 56, 93 (1960). STEFANJ.: Wien. Sitzber., 63, 63 (1871); 65, 323 (1872).
18. MAXWELL, J. C. : Collected scientific papers I,
p. 393; II, p. 57, 345. 19. WALSH, A. D.: Seventh Symposium (International) on Combustion. Butterworth & Company, Ltd., London, 1958. 20. EGERTON, A., AND WARREN, D. R.: Proc. Roy. Soc. (London), A204, 465 (1951). 21. BALDWIN, R. R., AND DORAN, P.: Accepted
for publication, Trans. Faraday Soc., 1961.
ROLE OF HYDROGEN PEROXIDE
2
THE DISSOCIATION OF HYDROGEN PEROXIDE AND ITS ROLE IN THE HYDROGEN-OXYGEN REACTION By R. R. B A L D W I N , P. D O R A N AND L. MAYOR Although H~O2 had been detected as a reaction product in both the photochemical reaction ~, 2 and thermal reaction 3' 4 between H2 and O2, its importance as a reaction intermediate was not realized until many years later. Thus, as recently as 1946, Hinshelwood and Willbourn 5 interpreted their results on the slow reaction in KCl-coated vessels at 570°C by adding reactions ( l l a ) and an initiation process no to the reactions (1) to (5a) used to describe the second limit. OH
+
H~
H20
+ H
(1)
H
+
O~ = OH
+ 0
(2)
O
+
H~ = OH
+ H
(3)
H
+O~+M
+M
(4)
=
=HO~ surface
HO2 = 1I-I20 -+- ~-O2 (5a)
HO2
+
H2 = H20
+ OH.
If it is assumed that H202 is ultimately decomposed to tt20 and 0~, the alternative reaction (11) is kinetically equivalent to (lla).
(11)
This mechanism gives the rate expression: d[H20]
dt
Ano
1
(i)
2k2
]C51a[H2]
]c~[M]
ks~ + knjH2]
H02 + H202 = H20 -Jr- 02 + OH.
where the value of A (between 1.5 and 2) is dependent on minor details of the reaction scheme. The variation of rate with mixture composition suggested that no cc [H~][M], and this was interpreted as indicating that dissociation of hydrogen was the initiation process. In a paper given at the first postwar Combustion Symposium at Wisconsin in 1948, Lewis and von Elbe 6 showed that the rate of dissociation of hydrogen is too slow by a factor of 10'3 to account for the observed rate. This confirms their earlier conclusion 7 that initiation must occur through dissociation of a compound with a much lower
(6)
If (6) is the predominant reaction of H202 and dissociation by (7) is relatively infrequent, then the initiation rate becomes proportional to [H2][M']. H202 + M ' = 2 0 H -4- M ' .
(7)
Occurrence of (6), however, would require the homogeneous decomposition of H~O2 to be a chain reaction [through the reaction sequence (7), (15) and (6)] with an order either 2 or 1.5, depending on whether the chain termination process was the surface removal of HO2 [reactions (5) or (5a)], or the gas phase process (10). O H + H202 :
(lla)
HO2 + H2 = H202 + H.
dissociation energy than I-I~, namely, H202. They suggest that H~O2 reaches a stationary concentration as a result of its formation by reaction (11) and removal by (6).
H20
--~ HO2
(15)
surface
1 HO2 -= ~H202 + !Oo 2 . 2HO2 = H202
+ 02.
(5) (10)
The constant percentage decomposition over a 10-fold range of H202 concentration found by Baldwin and Brattan s confirms previous views 9, 10, 1, that the reaction order is unity, and reaction (6) is thus excluded. If an expression similar to (i) is applicable to KCl-coated vessels, then high average chain lengths will be obtained only when the ratio of chain branching to chain breaking is nearly unity, i.e., when the denominator of (i) is significantly less than unity. Its value is then extremely sensitive to the constants used in evaluating the variation of k4[M] and ks~ with mixture composition; the latter was obtained 12 from third limit studies by assuming first, that the limit is isothermal, and second, that HO~ radicals are destroyed efficiently in KCl-coated vessels (i.e., ks~ cc 1/P). I t is unlikely that either of these assumptions are justified. All these points add to the difficulty of interpreting the slow reaction data in KCIcoated vessels.
104
CHEMICAL KINETICS
Clear demonstration of the importance of H~O2 as an intermediate in the slow reaction was given by Baldwin and Mayor} 3, 14 who were particularly fortunate in discovering that a boricacid surface which had been aged by repeated tests becomes extremely inert toward both HO~ and H~02. This inertness toward H~02, necessitated by the kinetic features of the reaction, has been confirmed by studies of H202 decomposition in such vessels. 8 The main mode of formation of H202 is directly from HO2 radicals, and there is convincing evidence that this occurs through the gas phase process (10) in aged boricadd-coated vessels. Since H202 mainly undergoes reaction (7), it may be regarded as a rather unreactive chain center (actually equivalent to two centers, since it is formed from two centers and dissociates to give two centers). A straight chain is thus set up by the reaction sequence:
H (4)) HO2 (10)) ½H2 O2 (7)) OH (1)) H. Superimposed on this straight chain is linear branching through reactions (2) and (3), and in the absence of termination reactions, the reaction would be explosive. Analysis of the variation of rate with mixture composition and total pressure shows that the termination reactions are: H + H202 = H20 + O H OH +H20~
= H20 + H O 2 .
(14) (15)
Since H202 may be regarded as a chain center, the mechanism is thus of the linear-branching, selftermination type, represented by the equation: dn/dt = no 4- chn -- D n 2
(ii)
and if the initiation rate no is negligible at maximum rate, as suggested by the markedly autocatalytic nature of the pressure-time curve, the concentration of centers at maximum rate is given by n = dp/D. One striking advantage of the aged boric-acidcoated vessels is that the reaction proceeds quite rapidly at 500°C, whereas temperatures of about 560°C are necessary to get reasonable rates in KCl-coated vessels of moderate diameter. At these lower temperatures, the induction period is of quite long duration, varying from minutes at 470°C to about 10 sec at 540°C. By sampling the reaction mixture at various stages during the induction period, Baldwin and Mayor showed that the concentration of H202 rose during the induction period, reached a maximum value at
maximum rate, and decreased beyond the point of maximum rate. This demonstration of the importance of H202 would be impossible in KC1coated vessels, first, because of the difficulty of extracting H202 without loss due to surface decomposition, and second, because at the temperature of 560°C or higher necessary to get reasonable reaction rates, the maximum H~02 concentration would be reached almost instantaneously. Introduction of reaction (6) into the reaction scheme for aged boric-acid-coated vessels gives kinetic expressions entirely inconsistent with the experimental results, and the first convincing evidence against this reaction, later confirmed by the peroxide decomposition studies, is thus obtained. A detailed examination of the variation of rate with mixture composition shows that it is necessary to include a small contribution from reaction (11), and the final mechanism, involving reactions (1) to (4), (7), (10), (11), (14) and (15) gives a rate expression: R - d[H~O] _ 2k7 [H202] [M'I G dt where [H2 02] =
kl k2[HJ[O2] (1 +/~k4[M]/k2) k14 kl[HJ + k15 k4[Oj [M] (1 - ~)
k n [ H j (1 4- k2/k4[M]) = (2k10 R)~
G = h[O~][M] + k~[O~] + k~jH~O~] k4[Oj[M]
- k2[Oj - k~4[H2Oj
By a careful examination of the variation of rate over a wide range of mixture compositions, the following values of rate constant ratios at 500°C (in mm Hg, min units) can be deduced: kl k2 tcT/k4 k15 = 0.120, kl k14/k4 k15 = 700, k11/(k10) ½ = 1.1 X 10 -3. Since the term G, which can be readily evaluated knowing kl k14/k4 k15, is only slightly greater than unity, the reaction rate is effectively the dissociation rate of H202. Determination of the maximum H20~ concentration by sampling and analysis permits the absolute value of k7 to be determined. Tests with three quite different mixtures gave values of 0.069, 0.052 and 0.075 mm Hg-imin -1. Since high values would be expected
ROLE OF HYDROGEN PEROXIDE
because of loss of H 2 Q both by decomposition and adsorption during sampling, the agreement with the value of 0.046 obtained by direct study s of the decomposition of H~02 provides convincing support for the mechanism. From /~7 = 0.046 and k2/k4 = 18.5 mm Hg (M = H2) at 500°C, k ~ / k ~ = 268. If this difference between/ct4 and k2 is attributed entirely to activation energy difference, then (E2 - E,4) = 8.6 kcal/mole. The best value of k2 is probably that obtained from first linfit studies, '5 giving/c2 = 3.4 X 10-~5 and /~4 = 9.1 X 10-13 in (molecules/era 3) ' sec-1 units at 500°C. The above value of k2 corresponds to unit steric factor and an activation energy of 19.8 kcal/mole, or if the activation energy of (2) is taken as equal to its endothermicity (16.2 kcal/mole), then a steric factor of 0.10 is required. Depending on which of these alternatives is adopted k14 varies from 1.33 × 10-9 e -ll,200/RT to 1.28 × 10-1° e-v,6°°jRr (molecules/cn?) -1 sec-1. From the values of kl k14/k4 k15 , k:/k4 and k14/k2, kl~/kl = 7.1 at 500°C. This is consistent with a value of approx 6 obtained from a stud5~ of the decomposition of H202 at 440°C in the presence of H2. No reliable figures for k~ appear to be available. At temperatures of about 360°C in aged boricacid-coated vessels, the decomposition of H202 is a first-order heterogeneous reaction, s with a somewhat variable velocity constant, a typical value for a 6-mm diameter tube being 0.018 sec -1. Allowing for temperature (from the activation energy of the heterogeneous reaction) and diameter, this would correspond to k~ = 0.016 for a 15-mm diameter vessel at 500°C. Since the slow H.o/O: reaction showed no diameter dependence, surface destruction of H202 must be small compared to gas phase termination, i.e., k,[H202] < ~k14[H][H.~O2]. From the values of k , , k~4, quoted, [HI > 10-5 mm Hg. This does not seem unreasonable. Although the mechanism of the slow reaction between H2 and 02 in aged boric-acid-coated vessels may now be regarded as firmly established, there are two points not conclusively settled by the slow reaction studies. First, the reaction between H atoms and H202 can be written either as (14) or (14a): H + H~O~o = H2 + HO.,.
(14a)
The choice of (14) is based on small differences between the kinetic expressions obtained with the two alternative reactions. The second limit
105
studies,,~. 16 described briefly below, provide more convincing evidence for the occurrence of (14). Final confirmation is provided by studies of the decomposition of H202 in the presence of H2, when a marked increase in the decomposition rate is found, s This is explained by the chain sequence (7), (1) and (14), the chains eventually being terminated by reaction (15). If (14a) occurs, however, no chain reaction is possible.
O + H-.O2 = H20 + 02.
(13)
The second point not fully resolved by slow reaction studies is the nature of the second termination reaction, (15) and (13) giving similar kinetic features. Detailed analysis of the slow reaction data gives some support for (15) rather than (13). At the temperature of 440°C used to study the H~OgH2 system, (13) cannot occur, since H + 02 = OH + 0 would be negligible compared to (4) and (14), even in the presence of 0.5 mm HgO 2present either as reaction product or as impurity. The concentration of O atoms must thus be negligible, and if (15) does not occur readily, then (4) or (14a) must be the termination reaction. Neither of these reactions provides a satisfactory account of the kinetic features, and (15) is the only termination reaction capable of explaining the experimental results. Support is provided by the agreement of the values of k l J k l obtained from studies of the H2/02 reaction, and from peroxide decomposition studies in the presence of H2. Since the velocity constant for peroxide decomposition at 500°C implies a half-life time of about 1 sec at 500 mm Hg, it seems a little surprising that induction periods varying from 20 to 90 seconds are obtained in the slow reaction between H2 and 02 at this temperature. This is explained by the proposed mechanism, since the dissociation of peroxide merely continues the chain, and branching occurs only when the H atom undergoes reaction (2). Since under the experimental conditions, the rates of (4), which continues the chain, and (2) are in the ratio of 15-25:1, the long induction periods can be understood. The mechanism thus accounts both for the magnitude of the induction periods and for their variation with experimental factors. ~4 Elimination of (6) requires reconsideration of the mechanism of the slow reaction between H2 and 0~ in salt-coated vessels. For a surface that is efficient in destroying H~.02, k~ = 23 D i d 2 for a cylindrical vessel of diameter d. With the
106
CHEMICAL KINETICS
Stefan-MaxwelW ,18 relation for D with ~u2o2 = ao2 = 3.62A, aN2 = 3.92A, ks = 0.82 see-~ for a 5 em diameter vessel at 560°C and 760 mm Hg (M = N2). Under the same conditions, kr[M'] = 2.3 see -1, so that the ratio of dissociation to surface destruction of H202 would be about 3:1. Assuming the value previously quoted for kt4 of 1.28 X 10 -1° e -7'8°°lRT (molecules/ema)-~ see-', k7[M'][H2021 = k14[H][H2021 at 560°C and 760 mm Hg (M' = N2) when [H] = 1.5 × 10-4 mm Hg, which is a feasible value. Removal of H202 by OH also appears likely, particularly in view of the increased concentration of OH resulting from reaction (7), and it thus seems probable that reactions (7), (14), (15) and surface destruction all play a part in controlling the concentration of H~O2. Removal by OH would account for the high order with respect to hydrogen, but a detailed analysis is required before a precise mechanism can be given.
face in KCl-coated vessels. The H202, having evaporated into the gas phase, is assumed to undergo either reaction (6) in large vessels, or reaction (8) in small vessels, this change accounting for the slight decrease in the limit as the vessel diameter decreases. A variety of evidence,16, 19 however, makes it doubtful whether HO2 radicals will survive on a KCl-eoated surface, and evidence against reaction (6) has already been given; moreover, alternative explanations of the small changes in limit with vessel diameter arc available (15). H+02+H202
(iii)
They interpreted this equation by introducing the quadratic branching reaction:
Lewis and yon Elbe 7 were the first to allocate a significant role to H202 at the second limit. They assumed HO2 = ½H202 -4- ½02 at the surI
(8)
3/[ = A + g/[o2] ½.
T h e Second L i m i t
fOOl
= H20+05+OH
A more important influence of H202 at the second limit was suggested by Egerton and Warren,2° who found that the limit in boric-acidcoated vessels rose markedly at low mole fractions of O2, according to the relation:
'
H + HO2 = 2OH.
(9)
In a reaction with quadratic branching (Fn2), '
'
'
OO
80 ,O
B 60
M
I
A ,O
40
2%
I
, rMM'I/3 ,2
I
,6
I
2o
I
24
Fro. 1. Second limits in fresh and aged boric-acid-coated vessels 500°C. Mole fraction H2 = 0.28. A, aged coating (selection of points) ; B, fresh coating. X, 51-mm diameter; @, 36 mm; A, 24 mm; 27, 15 mm.
107
ROLE OF HYDROGEN PEROXIDE
explosion is possible even if the net branching factor q5 is negative provided 4n0 F > ¢2. The initiation rate no thus affects the explosion boundary, and Egerton and Warren suggested that the initiation reaction was the unimoleeular firstorder dissociation of I-I202 produced in equilibrium concentration by reactions (5) and (6). Reaction (6) has now been eliminated, and the dissociation of It202 shown to be bimolecular (or, more strictly, unimolecular second order), but Baldwin, Doran and Mayor '6 showed that their own observations on the limit in aged boricacid-coated vessels could be accommodated by adding reaction (9) to the mechanism for the slow reaction in these vessels. Their complete mechanism involves reaction (1) to (4), (7), (8), (10), (14) and (15); reaction (11), which plays some part in the slow reaction, is unimportant at temperatures of 500 ° and below. If (15) is neglected, a cubic equation is obtained for the center concentration. Expressing the condition for three real solutions, and making iustifiable approximations, the limit is given by:
[M]
2k2 + /c4
/27k2 k7 ]c~[M][M']'~ l/a
\
4k~ l~,-ok,4[02~ /
(iv)
I
I
I
1
500°C 8O
60
48o"c
M
40 460°C
0
I 8
I
I 1/^16
I 2.,4
"
A plot of [M] against ([M][M']/[O~}) m over a wide range of mole fractions of 02 shows only slight curvature (Fig. 1A), and if allowance is made first for the occurrence of (15) to the exLent indicated by slow reaction studies, and second for the approximations made in obtaining solution (iv), a precise interpretation is obtained of the variation of limit with mixture composition} 6 Two difficulties arise with this mechanism: (1) It is strictly applicable only to the limit in aged boric-acid-coated vessels. In a 51-ram diameter cylindrical vessel (20 cm long), the limits at 500°C in both freshly coated and aged vessels are little different, suggesting that exactly the same mechanism operates. As shown in Figure 1, however, the limit rises significantly in freshly coated vessels as the vessel diameter decreases, whereas in aged vessels the limit, as required by (iv), is independent of diameter. Figure 2 gives the limits obtained with both fresh and aged boric-acid-coated vessels over the temperature range of 440 to 500 ° using relatively fast withdr/~wal rates. ~ The limits are higher with
a freshly coated surface and this difference persists, increasing as a percentage, down to 440°C; this is surprising, because lower limits due to increased surface termination might have been expected in the fresh vessels at the lower temperatures. (2) Quite long induction periods (30 to 120 see) are observed in the slow reaction at 500°C in aged boric-acid-coated vessels, and these increase markedly as the temperature is reduced. i t seems doubtful therefore, whether there is sufficient time for H202 to reach its equilibrium concentration when rapid manipulation proeedures are adopted to determine the second limit at temperatures below 480°C. An alternative mechanism can thus be suggested in which the peroxide plays no part. Such a mechanism, involving reactions (1) to (4), (5a) and (8), gives
The withdrawal rates used corresponded to 3 to 8 mm Hg/sec over the range of 150 to 130 mm Hg; the rate will fall off at lower pressures, being
roughly proportional to p,-1.5, the exact exponent depending on the particular capillary used to control the withdrawal rate.
FIG. 2. Variation of second limit with temperature in fresh and aged boric-acid-coated vessels, with the use of rapid withdrawal rates. Mole fraction H~ = 0.28. E), Fresh coating; X, aged vessel.
108
CHEMICAL KINETICS
the limit expression: [M] 1/2 = (2~'2/~'4)';2 + ('no Z'~//~'4~'~[O21)1/~. Because /c5 is diameter dependent, the initiation process no nmst be a surface process to account for the limit being effectively independent of diameter. Although it is possible to interpret the variation of M with mixture composition at 500°C by assuming arbitrary values of p and q in the expression no oc[ It2]~[02] g, the mechanism has a number of unsatisfactory features which have been fully discussed elsewhere.I6 Ileplaeement of (5a) by (10) now requires a gas phase initiation and no reaction satisfying the experimental results can be found. To examine further the role of H202 at the
5 0 0 °C.
second limit in aged boric-acid-coated vessels, tests were carried out in which the manipulation time was deliberately varied. Figure 3 shows the results of tests over the range of 440-500°C in which the evacuation with rapid withdrawal rates was interrupted for various times at a pressure about 20 mm Hg above the limit obtained with no interruption. At 500°C, the limit decreases as the time of interruption is increased. This can be attributed to water formation, and, as would be expected, the effect increases with increasing mole fraction of 0.2 • At 480°C, however, there is an initial rise in the limit, which then falls as the interruption time is further increased. The rise in the limit increases as the mole fraction of 02 decreases, whereas the subsequent fall
75-
480°C"
,oo I
L
,
0o f
0
, 3
, 8
~ -,~251 9 0 TIME IN
t
12
24
36
MINUTES.
FIG. 3. Effect of interrupted withdrawal on second limit. Mole fraction H2 = 0.28. Mole fraction of O2: )<, 0.72; Q, 0.28; A, 0.10; V, 0.025.
109
ROLE OF HYDROGEN PEROXIDE
increases as the mole fraction of 02 increases. The rise in the limit becomes more marked as the temperature decreases to 460 and 440°C, whereas the time to obtain the maximum limit increases. Further tests showed that somewhat higher limits than those indicated in Figure 3 could be obtained at 480 and 460°C either by using moderate withdrawal rates and interrupting the evacuation for the optimum period, or by using extremely slow withdrawal rates without interruption. The latter method could be used only with mixtures of low oxygen content, since with mixture of high oxygen content, complete suppression of explosion resulted from the use of slow withdrawal rates. At 440°C, the maximum limit at low mote fractions of 02 could be obtained only by the use of the slowest withdrawal rates together with interruption periods of at least 15 minutes. All these observations are described in detail elsewhere. ~ The rise in limit with increased manipulation time can be attributed only to the build-up of some relative unreactive intermediate and H.~02 is the only possibility. Since the rise in the limit is most marked at low mole fractions of O : , it is clearly associated with the third term in (iii). Convincing evidence of the role played by H202 is thus provided. Even with rapid manipulation and fast withdrawal rates, the limit rises slightly as the mole fraction of 0.~ decreases, even at 440°C in aged boric-acid-coated vessels. Since the third body coefficient in reaction (4) is less for O2 than for N~, this can be attributed only to some contribution from quadratic branching. The slow build-up of peroxide indicated by Figure 3 suggests that initiation by H20.~ might be negligible when very rapid manipulation is used at 440°C. It is possible, therefore, that this residual quadratic branching is due to a surface initiation which at higher temperatures becomes relatively unimportant compared to initiation by H~O2. Figure 2 shows that higher limits are obtained in freshly coated vessels than in aged vessels, particularly at the low temperatures. This can be explained by assuming that the surface initiation is faster in fresh boric-acid-coated vessels. This would also explain why at 500°C, the limits in fresh vessels are higher than in aged vessels, and increase as the vessel diameter decreases.
Acknowledgments We wish to thank the Preston Education Committee for a grant to L. M. and the Depart-
ment of Scientific and Industrial Research for a grant to P. D. Grants from the Royal Society, Imperial Chemical Industries, Ltd., and Shell Research, Ltd., are gratefully acknowledged. Part of this work was sponsored by the United States Air Research and Development Command under Contract No. A F 61(052)-62. REFERENCES 1. MARSHALL, A. L.: J. Physic. Chem., 30, 34, 1078 (1926). 2. BATES, J. R., AND SALLEY, D. J.: J. Am. Chem. Soc., 55, 110 (1933). 3. PEASE, R. N.: J. Am. Chem. Soc., 52, 5106 (1930). 4. HOLT R. B. AND OLDENBERG, O.: J. Chem.
Phys., 17, 1091 (1949). 5. HINSHELSVOOD, C. N., AND WILLBOURN, A. H.:
Proc. Roy. Soc. (London), A185, 369 (1946). 6. LEWIS, B., AND VON ELBE, G.: Third Symposium on Combustion, Flame, and Explosion Phenomena, p. 484. The Williams & Wilkins Company, Baltimore, 1949. 7. LEWIS, B., AND VON ELBE, G.: J. Chem. Phys., 10, 366 (1942). 8. BALDWIN, R. R., AND BRATTAN, D.: Eighth Symposium (International) on Combustion, p. 110. The Williams & Wilkins Company, Baltimore, 1962. 9. GIG[TERE, P. A., AND LIU, J. D. : Can. J. Chem., 35, 283 (1957). 10. FORST, W.: Can. J. Chem., 36, 1308 (1958). 11. HOARE, D. E., PROTHERO, J. B. AND WALSH, A. D.: Trans. Faraday Soc., 55, 548 (1959). 12. ]-~INSHELWOOD, C. N. AND WILLBOURN, A. H. :
Proc. Roy. (1946).
Soc.
(London),
A185,
353
13. BALDWIN, R. R., AND MAYOR, L.: Seventh
14. 15. 16. 17.
Symposium (International) on Combustion. Butterworth & Company, Ltd., London, 1958. BALDWIN, R. R., AND MAYOR, L.: Trans. Faraday Soc., 56, 80, 102 (1960). BALDWIN, R. R.: Trans. Faraday Soc., 52, 1344 (1956). BALDWIN,R. R., DORAN, P., AND MAYOR, L.: Trans. Faraday Soc., 56, 93 (1960). STEFANJ.: Wien. Sitzber., 63, 63 (1871); 65, 323 (1872).
18. MAXWELL, J. C. : Collected scientific papers I,
p. 393; II, p. 57, 345. 19. WALSH, A. D.: Seventh Symposium (International) on Combustion. Butterworth & Company, Ltd., London, 1958. 20. EGERTON, A., AND WARREN, D. R.: Proc. Roy. Soc. (London), A204, 465 (1951). 21. BALDWIN, R. R., AND DORAN, P.: Accepted
for publication, Trans. Faraday Soc., 1961.