484 T H I R D SYMPOSIUM ON COMBUSTION, FLAME AND E X P L O S I O N P H E N O M E N A

experimental observations that H atoms are pro- duced in O H - - O H reactions, both by regrouping reactions and by chemical reaction with tungsten oxide.

Acknowledgment. The experiments described in this paper have been carried out under the sponsorship of the Air Materiel Command, United States Air Force.

60

THE MECHANISM OF CHAIN INITIATION IN THE THERMAL REACTION BETWEEN HYDROGEN AND OXYGEN

By BERNARD LEWIS I AND GUENTHER VON ELBE z

INTRODUCTION

In a previous paper (1) the authors have de- velopeII a mechanism of the reaction between hy- drogen and oxygen which permits the quantita- tive description of the explosion limits and the reaction rate between the second and third limits. Recently Hinshelwood and coworkers (2) and Ashmore and Dainton (3) have questioned the mechanism of chain initiation proposed by the authors an([ have argued in favor of chain initia- tion by the thermal dissociation of hydrogen in bimolecular collisions in the gas phase. The reasons advanced are (a) that this reaction is consistent with the observed dependence of the rate of water formation on mixture comt)osition and pressure, and (b) that its activation energy is found to he larger than 100 Kcah I t will be shown that these reasons are invalid because the rate of dissociation of hydrogen is far too small to account for the rate of water formation.

17NTEXTABILITY OF CHAIN INITIATION 13Y H2

DISSOCIATION

It is convenient to summarize briefly the work of Hinshelwood and coworkers. The mechanism which they write for the chain reaction in a mix- ture of hydrogen and oxygen is:

it H.., + M = 2H + ell

I OH + He = H2() + H

II H +()._, = ()H + ()

III () + t{2 = OH + H

Physical Chemist, Chief, Explosives Branch, Cenlrat l':xperiment Station, Bureau of Mines, Pitts- burgh. Pa.

2 Supervising Chemist, Physical Chemistry and Physics Section, Explosives Branch, Central I:]xperi- ment Station, Bureau of Mines. Pittsburgh, Pa.

IV H + O 2 + ell = HO,, + M

wall , V HO2-- - -+ (~) H._,()

VI HO2 + He = H_4) + OH.

The authors (4) had proposed this mechanism earlier but subsequently modified it in the light of their later experimental results (1).

The rate of water formation in the steady state according to the above scheme is

1.5kv + 2 k v , ( H : ) ]

d(H,,O) (~//~ = f l k v " q - k v ~ : ) l (1) l - 2 k , / v ~k , v (M )

- - k,,, (H~) / (kv + kv, (H2))

kiv(~II) = kiv,H2 (H2) + kzv,o2 (02) + kzv,x (X),

where X is any other gas molecule. The factor t l is equal to k,(H2)(M). The equation for the explosion limits is obtained by equating the de- nominator to zero. At the second explosion limit the third term is small compared to the second term; at the third explosion limit the reverse is the case. Data on these limits permit evaluation of the ratios 2klt/~,klv and kvr(H2)/kv. Equation 1 is now separated into f l and a factor R* and the latter may be calculated for any set of conditions. At a temperature of 570~ Willbourn and Hinshelwood obtained the rate expression

r ' = (H2) (M)R*/(33.4 • 104), (2)

where r ' is the rate of pressure decrease in mm. Hg/min. 3 The corresponding rate of water formation is 2 / . Hence

k~ = 2/(33.4 X 10 4) m m . Hg - t min. -1.

a In their paper, Hinshelwood and Willbourn use the symbol fi somewhat inconsistently to denote both

- k,(H._,)(M) and (Ho.)(M).

KINETICS AND MECHANISM OF COMBUSTION REACTIONS 4 8 5

To express k~ in uni ts of cm. a sec_ x it mus t be divided by the factor 60(2.7 X 10 ~9) (273/843) / 760 cm. --a mm. Hg -1 sec. m i n _ 1, so t ha t

k~ = 9 X 10 -24 cm. a s e c t 1.

Similarly, from Ashmore and Da in ton ' s two ex- perimental series, k~ a t 570~ is found to be 1.3 X 10 -:24 and 8 X 10 -24 cm. a s e c t I, respectively, in good agreement with Willbourn and Hinshe]- wood. From theoretical considerations one may admi t a value of k~ no larger than the product of the collision frequency factor and the Arrhenius probabi l i ty factor, namely,, k~ <~ Ze -~/~r For bimolecular collisions

Z = 2r 2 (2rrRT m!m~m2 +- rn''~'-''/

For a mixture of hydrogen and oxygen an average a o f 3 X 10 - s cm. and an average mass factor of 0.8 are taken. E cannot be smaller than the heat of dissociation of hydrogen, 103.5 Kcal. Hence,

k,, ~< 4 • 10 a7 cm.a sec.-l.

This is smaller than the experimental rate coef- ficient of reaction a by a factor of I0 Ia. For this reason, which has not previously been s tated, dis- sociation of hydrogen in the gas phase is ruled out as the chain init iat ing reaction.

IMPROBABILITX OF CHAIN INITIATION AT THE

SURFACE

The question may be raised whether chain init iation, either hydrogen dissociation or some other reaction, takes place at the wall. An answer is furnished by examining the experimental facts in the l ight of the diffusion theory of chain carriers. The t r ea tmen t of the case of chain in- i t iat ion and chain breaking a t the wall in a spheri- cal vessel where E, the chain breaking efficiency of the wall, is large compared to the rat io of mean free pa th to vessel diameter , 4 leads, with close approximation, to the equat ion (5)

= 3(too~r) (2X/~r) (3)

9.86D/F" - a

where 1) is the average chain carrier concentra t ion in the s teady si~ate, mo is the . ra te of format ion of chain carriers per uni t area, X is the mean free path , ~ is the chain breaking efficiency of the sur- face defined as the ratio of destruct ive collisions to all surface collisions of chain carriers, D is the

4 This magnitude of ~ corresponds to experiments in salt-coated ves~ls.

diffusion coefficient, ~ is the chain branching coefficient and r is the radius of the vessel. The numera tor is evidently the ra te of chain ini t ia t ion per unit volume. Two considerat ions will now be advanced t ha t make chain ini t iat ion at the wall improbable: (a) The rate at which chain carriers are formed a t the surface divided by the volume of the vessel is 3 too~r, which is considerably larger than 3 mo/r • 2x/er. This signifies t ha t many chain carriers re turn to the surface wi thout in- i t iating a chain and compara t ive ly few chain carriers escape permanent ly into the gas phase. I t is fair to assume tha t for each one or two chain carriers formed a molecule of water is also formed. Thus, water is formed at the surface at a rate of approximately 3 m,,/r and in the gas phase by the chain reaction at a rate (3 mo/r) (2X/cry R*. Since, over a wide range of experimental con- ditions. R* is not large, being of the order of 10, and 2 x/er is very small, one should observe a substantial heterogeneous reaction which should t)redominate over the chain reaction. This is certainly not the case except in a lower tempera- Iure and pressure range where the chain reaction practically vanishes and the rate is very smal l - -of the order of 0.01 ram. Hg/min . Here the rate is found to be inversely as the d iameter of the vessel (1) as predicted by' the theory. (by The factor X in the expression for the rate of chain ini t iat ion per unit volume decreases with increasing pressure. Fur thermore, it is difficult to imagine t ha t mo can increase with more than the first power of the part ial pressure of hydrogen. Thus, the rate of chain ini t iat ion can hardly be of more than zero order with respect to pressure. However, the experimental facts demand tha t the order of the ini t iat ing reaction shouhl be abou t two.

DEVELOPMENT OF THE PROBABLE MECHANISM

Inasmuch as the foregoing considerations demonst ra te t ha t chains arc ini t iated in the gas phase and t ha t the init iat ion reaction cannot be H2 dissociation because of the large dissociation energy, ~ it becomes necessary to find a chain init iat ion mechanism which is kinetically similar bu t which involves a conq)ound of low dissociation energy. The authors have been unable to find an

5 The earlier arguments ruling out any initiating re- action involving 02 or He + 02 still retain their validity. Over a wide range of experimental conditions the addi- tion of oxygen has no greater effect on the reaction rate than a corresponding addition of nitrogen. Cf. B. Lewis and G. yon Elbe, Combustion, Flames and Explosion of Gases, p. 39; also A. H. Willbourn and C. N. Hinshelwood, work cited (2).

486 T H IR D SYMPOSIUM ON COMBUSTION, FLAME AND EXPLOSION PHENOMENA

alternative to the mechanism which they proposed previously (1). This is embodied in the following complete reaction mechanism:

i H202 + M = 2 O H o r H _ ~ O + O

1 OH + H . 2 = H 2 0 + H

2 H + O 2 = O H + O

3 O + H 2 = O H + H

6 H + O 2 + M = H 0 2 + M

wall 12 2 HO2 ---)I-[~O2 + 02

11 HO2 + H2 = H20.o + H

5 H + 02 + H202 = H20 + 0`-, + OH

7 HO2 + H202 = H~O + O2 + OH

13 H2Oe~'-al-~t H.,O + (~)(1.,

wall 14 It2 + 02 ---oti,2(12

The dissociating compound is H202 which may dissociate into H2() + O (34 Kcal.) or 2OH (52 Kcal.). ~ The stead.v state concentration of H202 is controlled by several reactions. Under conditions where reactions 7 and 11 are largely involved the steady state concentration of H202 is approximately equal to kn(He)/kr and the rate of chain initiation becomes approximately equal to klkn(H.,_)(M)/k;, that is, its dependence on pressure and mixture composition becomes simi- lar to that of the He dissociation. Experimental support is provided by the work of Pease (6), He found that on passing a mixture of H2 and 0`-, at 1 atmosphere pressure through a clean pyrex tube at temperatures from 531) to 550~ H-~(12 attained a fairly reproducible steady state con- centration which was independent of the rate of water formation 7 and al)l)roximately proportional to the H._, concentration. In a salt-coated (KC1) tube the H202 concentration was generally lower suggesting substantial heterogeneous decompo- sition of H~.O., on the salt surface. The experi- mental conditions--flow experiments and narrow

From 2 OH = H._,O + (I/210~ + 76.7 • 1.3 Kcal. at 0 ~ K. (R, J. Dwyer and O, Oldenberg, J. Chem. Phys. 12, 351, 19441; H.20.,.~) = H._,O._, liq, -1-- 11.61 Kcal at 300~ (O. Maas and P. G. Hiebert, J. Am. Chem. Soc. 46, 2693, 19241; H202 llq. = n.oo liq. -1- (1/2)O~ + 23.45 Kcal. at 300 ~ K. (G. L. Matheson and O. Maas, ibid. 51, 674, 19291; H._,O(g) = H20 liq. + 10.50 Kcal. at 300 ~ K.

The rate of water formation is erratic under these conditions because on clean pyrex or quartz surfaces

<< 2 X/r and is variable.

tubes--no doubt accentuated this reaction, but it must also occur in experiments with quiescent mixtures in wide reaction vessels. I t is repre- sented by reaction 13 in the above scheme.

Reactions i, 1, 2, 3, 6, 7, 11, 12, and 13 form a se!f-contained reaction mechanism which operates after the H202 concentration has reached its steady state value. This will be the case after an induction period which is triggered by some mimae reaction forming /t202 o r chaiJ~ carriers Whose exact specification is not essential to the scheme. Reaction 14, for example, could serve this purpose but it has been introduced primarily for other reasons. I t is found that toward lower temperatures and pressures, that is, in a range where reaction 13 becomes increasingly the con- trolling reaction, the scheme, in the absence of reaction 14, predicts a zero reaction rate when actually some small heterogeneous reaction is found to persist. The exact surface mechanism of reaction 14 need not be specified. I t could, for example, involve the intermediate surface forma- tion of H atoms. Reaction 5 is introduced in order to account for a small but definite increase of the second explosion limit with increasing vessel diameter which cannot be explained by surface destruction of H, O, or OH, nor by chain continua- tion by reaction 11. The effect of diameter on the second limit requires a special mechanism con- sisting of a reaction which interferes with HO= reaching the surface (i'eaction 7 already serves this purpose in addition to its function of regulating the steady state H._,O2 concentration), and a coun- teracting reaction. Reaction 5 has been chosen for the latter because it gives the closest approxi- mation to the experimental facts. In this reaction H202 is destroyed and hence it is com- petitive with reaction 7.

I t is observed (1) that in vitreous spherical ves- sels coated with the salts, KCI, BaCk,, Na2WO4, K~B407 and K2B20, + KOH the reaction rates in the region of predominant chain reaction (large rates) are approximately identical and in the region of predominant surface reaction (small rates) are variable. According to the diffusion theory of chain carriers 8 the rate of destruction of a species at a surface is not significantly affected by' changes in the destructive efficiency of the sur- face unless the latter is small compared to 2X/r. The observed behavior of the various surfaces means therefore that ~, the chain breaking ef- ficiency of the surface for HO~ (reaction 121, is

s B. Lewis and G. yon Elbe, work cited (5), p. 13 et seq.

K I N E T I C S A N D M E C H A N I S M O F C O M B U S T I O N R E A C T I O N S 487

always >> 2X/r even though it may be variable; and that e', the efficiency of the surface for the destruction of H..,O2 (reaction 13), is << 2x/r .

As a consequence of the smallness of e' in the region of predominant chain reaction, reaction 13 is obscured by the more powerful H20,.,--destroy- ing reaction 7 in the gas phase.

It has been shown (1) that by means of the above complete mechanism, reaction rates and explosion limits are very well represented over a wide range of temperatures, pressures, mixture compositions and vessel factors. Rate coefficients of various elementary reactions were evaluated which are consistent with the products of collision frequency and Arrhenius probability factors. The energy of activation of reaction i was found to be 45.5 Kcal., which is larger than the dissociation energy of H202 to H20 + 0 and also is not in- consistent with the energy of dissociation of H202 to 2 OH considering the allowable variations of the several constants in these calculations.

N U M E R I C A L CALCULATIONS AND COMPARISON W I T H

DATA OF CULLIS AND HINSH.ELWOOD

Since these calculations have hitherto been made only with data obtained by the present authors it is of interest to extend the calculations to the experimental conditions of other authors. For this purpose the method of computation (I) is briefly reviewed. Coefficients of surface reac- tions are denoted by K, all others by k. Let

2k~/ks(M) = a ki(M)K12/k~ = I

kn(H2)/K12 = b �9 K la / k i (M) = u

k s K 1 2 / k T k 2 = c k~K14/ki(M)KI2 = s

These quantities are dimensionless except I, which has the dimension of a rate. They are functions of the absolute temperature, T, the pressure p ifi mm. Hg, the diameter d in cm. of the reaction vessel (assumed to be a sphere), and tool frac- tions f of the components of the mixture as follows :

0.0556 a ~-

f , , + 0.35fo~ + 0.43fN, + 14.3f.~Q

__,)] p L803R

(pd)~ b = 0.0232 -~- f ~ (fH~ -t-6.88fo2 + 7.84fN:)

r 000 X e x p - L80'3R .-=-_ - 1

C = 6.03 T

fH2 + 6.88fo~ + 7-84fN2 pJ'- r ,o00(? O]

X exp + L 803-R -

fn2 + 0.414fo._, + 0.454fy 2

fH~ + 6.8Sfo: + 7.84f~

ral ~176 s~ ) ] - ' X exp -- L 803R - - - 1 mm. Hg ram.

T 1 u* =3.12 pdfH: + 0.414fo., + 0.454f.~

s* = 4.26 X 10 .3 d f ~ + 6.88fo_~ + 7.84fN, f~ + 0.414fo~ + 0.454/N,

* These expressions for u and s apply to a KCI- eoated surface.

R is the gas constant. The functions are written for mixtures of hydrogen, oxygen and nitrogen. Function a also contains a term for water vapor, the significance of which will be clarified later.

Let kT(H20.a)/K12 = x. The equations for the steady state concentrations are derived from the reaction mechanism and are combined to give the equation

0.5~ + b + s [ 1 - a(1 + x + b ) ] / 2 x

= x + 0.5 cxa (1 + x + b)

+ 0.5 [1 - a (1 + x + b)](1 + u) (4)

denotes the fraction of H202 formed at the sur- face in reaction 12 that escapes into the gas phase. On surfaces such as KC1, ~, may be taken as sub- stantially equal to 1. Equation (4) is solved for x by trial and error after values of the functions a, b, c, u, and s have been calculated for a given set of conditions. The reaction rate expressed as decrease in pressure (oxygen consumption) in ram. Hg per minute is found to be

dp _ I x r l + o .5u + dt L

(s) a ( l + x + b ) ( l + c x ) + 2 x ]

1 - - a ( 1 - ~ x + b ) .]"

I = 6.36 X 10 -4 T3'': d 2

4 8 8 T I I 1 R D S Y M P O S I U M O N C O M B U S T I O N ~ : F L A M E A N D E X P L O S I O N P H E N O M E N A

Cullis and Hinshelwood (2) used a cylindrical KCl-coated silica reaction vessel 9 cm. long and 6.9 cm. in diameter. This is not too far from a spherical shape and the calculations can be made with reasonable approximation for a spherical vessel of the same surface to volume ratio, namely, a vessel of 7.8 cm. diameter. The effect of vessel size may be gauged from corresponding calcula- tions for a 7.4 cm. vessel. The results are given

TABLE 1

p:t2 = 300 mm. Hg; p~ = 100 mm. Hg.

T ( ~

a

b 6

I, mm.Hg/ min.

S

X

-- dp/dt , ram. Hg/min.

d = 7.8 cm. d = 7.4 cm.

560 I 570

0.206 0.233 1.032 1.18 0.0411 0.034 0.177 0.228

0.450 0.355 0.053 0.042 1.29 i 1.57 2.7 12.0

0.24710.20610.233 I 1.29 10.93011.06 r 0.031/0.046/0.0381 0. 257 0. 191 0.25,

0.31510.47~ 0.37, 0.03810.05 0.04 1.76 1.16 1.41

2.3 7.3

575

0.247 1.16 0.034 0.285

0.332 0.04 1.59

25.9

TABLE 2

po2 = 100 mm.; T = 560~ d = 7.8 cm.

prlo, mm. Hg. t/

b 6

I, ram. Hg./min.

S

x

- -dp/dt , ram. Hg./min.

250 0. 243 0.818 0.046 0.160 0.528 0.059 1.08 1.9

300 0.206 1.032 0.041 0.177 0.450 0.053 1.29 2.7

350 0. 180 1.28 0.040 0.194 0.394 0.048 1.55 4.1

in tables 1 and 2 and are plotted in figures 1 and 2, together with the experimental data of Curtis and Hinshelwood. The agreement is quite satis- factory.

I N H I B I T I O N B Y I - ~ 2 0 A N D T t t E R M A L A C C E L E R A T I O N

NEAR THIRD EXPLOSION LIMIT

The calculations forcefully illustrate the ex- treme difficulty of obtaining reliable rate measure- ments in the neighborhood of the third explosion limit. This point which is of considerable im- portance in any discussion of the reaction mecha- nism has been stressed in our previous publication (1) and will again be discussed with special refer- ence to the new data reported by Cullis and Hin-

shelwood. The difficulty arises from the very large value of the rate coefficient k6 when H20 is the third body. This value has been determined (1) accurately at the second explosion limit and is found to be forty times larger than K6 when 02

I I I I

/ J / /

v--0i.--r78cm. / / Y /

/

I I ' 56O 570 , .~4 / 580

TEMPERATURE, ~ i , FiG. 1. Reaction rate in KCl-coated vessels as

function of temperature. Pa2, 300 mm. Hg, Po2, 100 mm. Hg.

IOO 9 0 r i i I

LEGEND 7~ Calculated curves for 60 spherical vessels

50 Data of Cu}lis and Hinshelwood for a

40 0 vessel of 6,9 cm. diameter and

30 9 cm length

w

~20

iO u~9

6

m

31

I I /

/

5

r162

~3

~2

0 2OO

LEGEND Calculated curves for

spherical vessel of J f 7,8 cm. diameter /

Data of CuIlis and Hinshelwood for a j vessel of 6.9 cm. /

diameter and / 9 cm lenffth /

I 250 300 350

PH2 , MM Hg P~2/

FIG. 2. Reaction rates in KCl-coated vessel as func- tion of pressure and mixture composition. Tempera- ture, 560 ~ C.; Po2, 100 mm. Hg.

is the third body. The remarkable efficiency of H20 in causing combination of H and 02 to HO2 and thus depressing the second e~plosion limit is illustrated in figure 3. The effect of other gases is also shown. The curves are calculated from the foregoing equations by means of the relation

1 - a(1 + x + b ) = 0 . (6)

The points are experimental.

K I N E T I C S A N D M E C H A N I S M O ~ ' C O 3 ~ B U S T I O N R E A C T I O N S 489

The rate calculations shown in figure 1 were made under the assumption that the mixtures were water-free. For a vessel diameter of 7.8 cm. the condition of equation 6 corresponding to the third explosion limit is reached at a tempera- ture of 575~ However, in an actual experiment, a finite reaction rate instead of an explosion will be observed because already in the process of admitt ing the gases to the reaction vessel, that is, before the theoretical conditions for explosion can be established, some water is formed. A very small amount suffices to greatly reduce the reac- tion rate and render the reaction nonexplosive. For example, the formation of only 1.4 mm. Hg of H20 corresponding to a pressure decrease of 0.7 mm. Hg will cause the rate to drop from in- finity to the experimental rate of 26.9 mm. H g / min. reported by Cullis and Hinshelwood. This effect is the larger the more nearly equation 6 is fulfilled, that is, under conditions of high reaction rates near the limits, and thus it is not surprising that a break is found in the experimental rates above about 8 mm. Hg/min. (see fig. 1). The present authors (1) have made a detailed study of self-inhibition due to water vapor in the vicinity of the second and third explosion limits. Hy- drogen was first admitted to the vessel and the rates were taken at different times counted from the moment oxygen began to enter. Typical re- sults are shown in figure 4. From observations of this type it would seem possible to obtain true reaction rates for the water-free system by extra- polating to zero observation time. However, such a procedure does not seem to be feasible for reaction rates exceeding about 20 ram. Hg/min . In figure 5 some experimental rates between 13 and 17 mm. Hg/min. are shown which were ob- tained by extrapolation to zero time. They fit very well onto the theoretical curves.

Another serious disturbance at high reaction rates arises from the temperature rise in the reac- tion vessel. The effect of the lat ter is opposite to that of water vapor. As pointed out previously 9 inhibition by water vapor predominates near the junction of the second and third explosion limits, whereas acceleration of the reaction by tempera- ture rise predominates near the third explosion limit at temperatures considerably below the junction. The reason for this is that as the ex-

plosion limit is approached near the junction the increase of the reaction rate is essentially due to

9 G. von Elbe and B. Lewis, work cited (1), pp. 381, 386-7, and figures 7 and l l in this reference.

the decrease of the term t - a(1 + x + b) which, as illustrated above, is sensitive to H..,O. On the

" - o

!ll t I I, 0.2 0.* Oe . 0 O0 o~e o oa o I os o's z

~ P

Fro. 3. Second explosion limit pressures as functions of mixture composition. Temperature, 530~ Sphe- rical vessel, 7.4 cm. diameter; salt-coated Pyrex surface. - - - - - - Calculated curves.

\

Vessel diamete~ 7 4 cm. ~. K28407 coating

2H2+02 I

\ o-.,

Temperature - 550 = C. " Initial pressure* 141.5 ram. Hg

Second limit pressure-126 mm. Hg ~

-

0~ 6

20 ,%

lo=~:

0 I 2 3 4 5

L L l l ~ 3 0 Vessel d~ameter, 7.4 cm.

KCI coating 2 H 2 + 0 2 [ l Temperat ute=570 ~ C. Ioitial pressure=485 ram. Hg Third limit pcessure=540 mm Hg

25

\ Q % 20 \ t ~ " /

/ / 10 f -

/ O

O 04 08 1.2 1.6 2.0 2 . 4 ~IME IINCLUDING ADMIT3"ANCE OF OXYGEN), MINUTES

FIG. 4. Self-inhibition of reaction rates near ex- plosion limits.

other hand, if the third explosion limit is ap- proached at temperatures considerably below the junction the term 1 - a(1 + x + b) is not very small, i.e., the reaction rate is not particularly

4 9 0 T I I I R D S Y M P O S I U M O N C O M B U S T I O N ~ ~ L A M E A N D E X P L O S I O N P H E N O M E N A

sensitive to H20 when the reaction rate is already very large owing to the marked pressure depend- ence of the terms in the numerator of equation 5. This illustrates the inadvisability of attempting to use data of the third limit for the determination of quantitative kinetic relationships as was done by Hinshelwood and coworkers and Ashmore and Dainton.

100 ii

,o \

10

\

t \ 1 td

g ~o .4

.,2

.04

\ \

\ \%1

\

\ xt

\

\ \

\ \

\

\

\

.02 I " ~ N

s,0oc sro 520 o11 l [ I I I tt

1.18 1.20 1.22 1.24 1,26 1.28 _1 X I O 3 T

I FIG. 5. Reaction rate vs. T at constant pressure.

2H2 + 02, 7.4 cm. vessel, salt coated. Calculated curves. Experimental rates: >( KC1 coating; O K2B407 coating; [] K.~B204 + KOtt coating.

B E H A V I O R OF VARIOUS SURFACES TOWARD HO2 AND H'_,O 2

The surface of the vessel serves both as a cat- alyst and an inhibitor. The latter role is generally more important and in the region between the second and third explosion limits consists in the destruction of both HOe and H202. I t is reason- able to assume that ,, the chain breaking ef- ficiency for HO2, is always larger than ~'~ the surface destroying efficiency for HzO2.

In the following discussion comparisons of and Z with 2X/r refer to the usual pressure range

of a few hundred ram. Hg. Three classes of sur- faces may be distinguished:

1. ~ and g << 2X/r. The reaction rate is large and erratic and the nonexplosive region is narrowed. Examples (1, 2) are clean quartz and pyrex, B203, MnC12.

2. ~ >> 2X/r and e' << 2X/r. The reaction rates are much lower than class I, are reproducible, and are identical for the various surfaces. Ex- amples (1, 2, 7) are LiC1, KC1, RbC1, BaC12, Na2WO4, K2B204, porcelain.

3. ~ >;> 2X/r and ~' 2>> 2x/r. Nonexplosive chain reaction is suppressed; explosion limits are displaced to higher temperatures. Example (8) is Ag.

NaCI (2) and K2B407 (t) are found to be in- termediate between classes 1 and 2. KF (2) and CsC12 (2) are intermediate between classes 2 and 3.

Cullis and Hinshelwood (2) who investigated a CsCI surface and found rates smaller than with KC1, etc., conclude, "the condition that the chain breaking efficiency of the walls approximates to unity is therefore more closely satisfied in pres- ence of CsCI." It should be noted that the limit- ing condition for ~ is not unity but >> 2X/r; that is, ~ may be considerably smaller than unity without affecting the reaction rate. On this basis Cullis and Hinshelwood's statement implies that surfaces in class 2 have values of , which are identi- cal and are smaller than 2X/r. Identity of the values is in itself highly improbable and the con- dition e smaller than 2X/r leads to kinetic relation- ships which do not describe the experimental facts. The introduction of g explains the behavior of CsC1 in a logical manner. With increasing d, the H202 concentration is lowered and hence x is smaller. This results in a decreased reaction rate (equation 5) and a widening of the nonexplo- sive region (equation 6). In contrast to KC1, the behavior of the gases on CsC1 was found to be erratic which is to be expected for the case that Z is sufficiently large to affect the reaction but is still smaller than 2x/r. Quantitative description of the data of CuUis and Hinshelwood in a CsC1- coated vessel is not possible because in these ex- periments inhibition by H20 formed during ad- mission of the gases to the vessel is sharply ac- centuated owing to the fact that large rates are attained only when the term 1 - a(1 + x + b) is close to the vanishing point. Thus, minute amounts of H20 suffice to rende~ the rate non- explosive and there is little doubt that the J.ctual rate measurements by these authors were made

K I N E T I C S AND M E C H A N I S M OF COMBUSTION REACTIONS 491

largely in a region where the rate for the anhydrous mixture would have been explosive. One may nevertheless make an estimate of the value of d using the lowest observed reaction rate, viz., 2.7 mm. Hg/min. at 578~ for a mixture 300 ram. H2 and 100 ram. 02. For these conditions, a = 0.261; b = 1.34; c = 0.028; I = 0.273 ram. t tg /min . ; and s is negligible. Using equations 4 and 5, x and u are calculated to be 0.6 and 6.4, respectively. For comparison, it for a KC1 surface is found to be 0.29. From previous cal- culations (1) J on a KC1 surface was found to be 4 X 10 s. I t follows that for CsCl, e' = 6.4/0.29 (4 • 10 - s ) or ,~ 10 -6, which is smaller, though not greatly so, than 2 x/r = 1.4 • 10 -5.

Under the above conditions , ' may increase about 100 times before its effect on the coefficient Kt3 vanishes, that is, with a highly destructive surface the H202 concentration and therefore x drops to about 1/100. of the value in the CsC]- coated vessel. Thus, measurable rates are not encountered until the temperature has been sub- stantially increased. This may be said to apply to a silver vessel. I t does not, however, fully explain the data (8) obtained with this vessel. The chain reaction was found to be replaced by a catalytic surface reaction whose rate is propor- tional to the 02 concentration but is independent of H~ concentration. Up to the highest tempera- tures worked at (700~ no explosion was ob- served. Assuming total destruction of H202 at the surface (x = 0), we calculate that H20- inhibition of the explosion in a mixture of 200 ram. H2 and 100 mm. O2 at 700~ requires the formation of 80 ram. of H20 or 40 mm. Hg pres- sure decrease in the process of admitt ing the gases to the reaction vessel. The initial reaction rate found by Hinshelwood and coworkers (8) was 30 mm. Hg/min. which seems to be far too small to ascribe the inhibition of the explosion to H20 only. On the other hand, it is known that a sub- stantial sputtering or volatilization of silver in the form of metal or oxide occurs in the presence of a mixture of H2 and O2 already at about 600~ (9). Thus, it is highly probable that the suppression of the explosion limits is due to the destruction of chains in the gas phase by silver in some form.

REMARKS ON THE :FIRST AND SECOND EXPLOSION

LIMITS

The reaction scheme presented represents a closely knit system of reactions which cannot be altered by addition or omission of reactions with-

out far-reaching kinetic consequences. Since it quanti tat ively describes the effect of temperature, pressure, mixture composition and vessel factors on the course of the reaction in agreement with the experimental facts and the requirements of kinetic theory, 1~ it is believed that the reaction scheme is basically correct. The question arises why certain plausible reactions have no place in the scheme. The answer may ult imately be found in the theory of rate processes but at present it can only be stated that their inclusion would lead to kinetic relationships which are seriously at variance with experimental facts. This is not to say that the reactions do not occur at all; but rather that they are too infrequent to be of im- portance.

One such reaction is

O + H 2 + M = H 2 0 + M .

In a recent paper (10) Hinshelwood suggests that this reaction, along with reactions 1, 2, 3, and 6, may be operative in the mechanism of the second explosion limit. However the inclusion of this reaction leads to the following expression for this limit:

2k2/'k6 = (M) + k6(M)2k'/ka,

where k ~ is the rate coefficient of the above reac- tion. The experimental facts specifically exclude a quadratic term in M. I t is also noted that without reaction 6 no limit is obtained. Simi- larly, the incompatibility of all other imaginable chain breaking reactions has been demonstrated, u

I t is remarkable that chain breaking in the gas phase by recombination of two HO2's or H and H02 is excluded from the scheme particularly at higher pressures where a considerable number of such collisions occur. The exclusion of such re- actions in favor of surface chain breaking is neces- sitated by the effect of vessel diameter on the reac- tion rate.

The Arrhenius factor of the function 2k2/k6 corresponds to an activation energy of 17,000 cal. This value is found4 from an analysis of the tem- perature dependence of the second limit by means of the complete equation for explosion, 1 - a(1 + x + b) = 0. A value of.26,000 cal. was recently quoted by Hinshelwood (10), which, how- ever, is based on the less accurate limit equation 1 - a = 0 .

to G. yon Elbe and B. Lewis, work cited (1), section 6. 11 G. yon Elbe and B. Lewis, work cited (1), section

3a.

492 THIRD SYMPOSIUM ON COMBUSTION~ FLAME AND EXPLOSION PHENOMENA

The determination of the absolute values of the rate coefficients is a problem of considerable in- terest. Assuming that reaction 6 has no activa- tion energy, 17,000 cal. represents the activation energy of reaction 2. Using a value of K6,H2 at 24~ of 2.26 X 10 -a~ cm. 6 sec- - t (11), k2 at 530~ is found to be 10 -17 cm. a s e c t I. Placing this equal to the product of steric factor, collision frequency factor and Arrhenius probability factor, one obtains a steric factor of 10 -a. This value is subject to revision pending further information on reaction 6. I t appears possible that independent information on k2 can be obtained from studies of the first explosion limit which involves compe- titions between the branching mechanism and destruction of chain carriers H, O, and OH at the wall. Some recent work has been published (12) which merits careful study, consideration of which is outside the scope of this paper.

REFERENCES

1. VON ELBE, G., AND LEWIS, B.: J. Amer. Chem. Soc., 10, 366 (1942).

2. WILLBOURN, A. H., ANn HINSHELWOOO, C. N.: Proc. Roy. Soc. (London), 185A, 353, 369, 376 (1946).

CULLIS, C. F., AND HINSHELWOOD, C. N.: Ibid., 186A, 462,469, 194 (1946).

3. ASHMORE, P. G., AND DAINTON, F. S.: Nature, 158,416 (1946).

4. LEWIS, B., ANn VON ELBE, G.: J. Amer. Chem. Soc., 50, 656 (1937); also, "Combustion, Flames and Explosions of Gases," Cambridge Univ. Press, (1938), pp. 30 et seq.

5. LEwis, B., ANn YON ELBE, G.: "Combustion, Flames and Explosions of Gases," p. 21; also, J. Amer. Chem. Soc., 59, 970 (1937).

6. PEASE, R. N.: J. Amer. Chem. Soc., 52, 5106 (1930).

7. GIBSON, C. H., ANn I-IINSHELWOOD, C. N.: Proc. Roy. Soc. (London), 119A, 591 (1928).

8. HINSHELWOOD, C. N., MOELWYN-HUGHES, E. A., AND ROLFE, A. C.: Proc. Roy. Soc. (London), 139A, 521 (1933).

9. HEIPLE, H. R., AND LEWIS, B.: J. Chem. Phys., 9, 120 (1941).

10. HINSHELWOOD, C. N.: Bakerian Lecture, Proc. Roy. Soc. (London), IgSA, 1 (1946).

I1. VON EImE, G., AND LEWIS, B.: J. Chem. Phys., 7, 710 (1939).

12. VOJEVODSKY, Z.: Acta Physicochim. U.S.S.R., 22, 45 (1947).

DISCUSSION

A. D. WA~SH: There is now much evidence to support the view expressed many years ago by

Rice and Teller that the steps involved in gas phase chain reactions are usually of very simple types. One of the most commonly found of these is hydrogen abstraction from a molecule by a radical. For that reason, remembering that the oxygen molecule has a radical structure, one has a strong expectation of the occurrence of reactions such as

02 + H 2 = HO2 + H (1)

02 + R H = HO2 + R (2)

Both of these represent initiation reactions and there is now increasing evidence 12 for tile import- ance of (2) as one of the main ways in which chain centres come to be formed in paraffin oxidations. There is agreement that the reaction

H + 02 = HO~

is exothermic at least to the extent of 50 Kcal. and there are some indications la that the exo- thermicity is even higher than this. I t is fair to conclude that (1) is unlikely to require an energy of activation of more than ,! , 50 Kcal. This, and its general nature, suggest .that (1) is at least as fast as any other initiation mechanism that can be proposed for the thermal hydrogen-oxygen reac- tion. Has specific consideration been given to the possibility of (1) as an initiating mechanism and, if so, is it possible to summarise briefly the kinetic arguments against its participation? If (1) is not involved as an initiating mechanism, then the important problem of why it should not occur re- quires an answer.

G. VON ELBE: The question of chain initiation by a gas phase reaction between I-[2 and 02 has already been considered by Hinshelwood and his coworkers. Gibson and Hinshelwood (Proc. Roy. Soc., Al19, 591, 1928) have sho~m that addition of oxygen to a hydrogen-oxygen mixture has sub- stantially the same effect on the rate of the chain reaction as the addition of an equal amount of nitrogen. As corroborated by our own experi- ments, the effect corresponds to the inert-gas effect on diffusion, etc., and can similarly be pro- duced with helium and argon. This eliminates the possibility of chain initiation by the reaction 1 of Dr. Walsh. The question of why this reaction

n Kooijman, Dissertation, Delft, 1942, quoted by Minkoff, Faraday Symposium on the LabiLe Molecule, September, 1947; Cullis and Hinshelwood, Faraday Symposium on the Labile Molecule, September, 1947; Chamberlain and Walsh, Symposium held at Paris, April, 1948.

13 Walsh, J. Chem. Soc., 1948, 331.

KINETICS AND MECIIANISM OF COMBUSTION REACTIONS 493

does not significantly enter into the mechanism must remain unanswered at present.

K. J. LAIDLER: An important argument ad- duced bv Lewis and yon Elbe against the chain- initiating mechanism

H,, + M = M + 2H

maintained by Hinshelwood and by l)ainton is that the activation energy must be at least the heat of dissociation of hydrogen, and that the rate would be too low. It may be worth mention- ing that there is a mechanism for the dissociation of hydrogen which would allow it to occur with an activation energy of not much more than one half of the heat of dissociation. This may be formulated as

1M MH ~ --~ }M2 + H, ~H, + ~ 2 ~

MH ~ representing the activated complex for the process: an analogous mechanism for the dissocia- tion of hydrogen on tungsten was proposed in 1940 by Laidler, Glasstone and Eyring to account for the results obtained by Roberts and by Bos- worth. Chain initiation by such a mechanism in the gas phase, in which 312 could be O2, is therefore possible theoretically. I t is true that Lewis and von Elbe have given other reasons for believing that initiation involves the dissociation of H..,O2, but these are not altogether unequivocal; in any case one requiresa mechanism for the formation

of H..,()2, and the process here suggested might play a role in connection with this.

B. LEWIS: I)r. Laidler has suggested that forma- tion of an activated complex at a surface could result in a mechanism for dissociation of hydrogen which would allow it to occur with an activation energy of not much more than one-haft of the heat of dissociation. Without discussing the merits of this proposal here, I should like to restate that the assumption that chains are initiated at the wall leads to results which are at variance with the experimental facts. I find it difficult if not im- possible to visualize a mechanism whereby this process could take place in the gas phase,

Our scheme does not have a clearly identifiable chain initiating reaction such as the dissociation of H,., would be. This is because the H202 concen- tration which determines the rate of reaction i is not an initial parameter of the system as the hydrogen concentration but is determined by a number of peroxide-forming and -destroying reac- tions. Among the peroxide-forming reactions is "reaction" 14 which for lack of information is not specified in detail. It seems that Dr. Laidler's suggestion should be considered only in any at- tempt to specify "reaction" 14 in detail. It does not furnish a basis for replacing the chain initiat-

ing mechanism which consists of reaction i plus a series of reactions which determine the steady- state concentration of H202.

61

THE R E A C T I O N B E T W E E N H Y D R A Z I N E A N D H Y D R O G E N P E R O X I D E IN ] 'HE LIQUID P H A S E 1

By ALVIN S. GORDON 2

The kinetics and mechanism of the uncatalyzed and cobalt-catalyzed reaction between hydrazine and hydrogen peroxide have been investigated. A study of this system was undertaken many years ago by Browne and Shetterly (1) during an investigation of the action of oxidizing agents on hydrazine solutions. They reported hydrazoic acid was formed in acid solution and ammonia in

This research is part of the work being done at the U. S. Bureau of Mines on Project No. NA onr 25-47 supported by the Office of Naval Research and the Army .Mr Forces.

2 Physical Chemist, Physical Chemistry and Physics Section, Explosives Branch, Bureau of Mines, Pitts- burgh, Pa.

alkaline solution. Gilbert (2) investigated the oxidation of hydrazine in alkaline solution by oxygen and found the reaction to be heterogeneous. He reports that one of the products is hydrogen peroxide.

CHEMICALS~ APPARATUS~ AND PROCEDURE

High-purity hydrazine, 98.7 percent, and hy- drogen peroxide, 90.7 percent, were kindly fur- nished by the Western Cartridge Company and the Buffalo Electrochemical Company, respectively. The hydrazine contained 1.3 percent water. The peroxide contained 9.3 percent water and no