KINETICS OF
August, 1955
THE
HYDROGEN-OXYGEN-METHANE SYSTEM
TABLE I TABLE OF EQUILIBRIUM CONSTANTS Resin sample
Exchange
TABLE I11 SELECTIVITY SCALEFOR DOWEX50 RESINS
Equilibrium constant
1.71 1.82 TI-H 4.00 8% DVB Rb-H 2.29 CS-H 2.31 TI-H 7.67 16% DVB Rb-H 2.89 CS-H 2.86 TI-H 15.3 Cs-Li 4.16 i 2% Cs-Li 4.15" a Calculated from ratio of cesium-hydrogen and hydrogen-lithium exchanges.
4% DVB
72 1
Rb-H CS-H
4%DVB
8%DVB
16%DVB
1 .oo 1.30 1.49 1.75 2.09 2.22 2.37 4.00 5.20
1.oo 1.26 1.88 2.22 2.63 2.89 2.91 7.36 9.60
1 .oo 1.45 2.23 3.07 4.15 4.19 4.15 19.4 22.2
Li + H+
Na + NH4+ K+ Rb + CB' Ag +
T1+
The tabular and graphical data indicate that thallous ion is similar in behavior to silver ion, although its selectivity coefficient is appreciably higher and the characteristic water uptake lower. The equilibrium quotients for thallous-hydrogen TABLE I1 MAXIMUM WATERUPTAKEOF DOWEX 50 RESINSI N VARI- exchanges, like those of the silver-hydrogen exchanges, are relatively independent of resin comOUS IONIC FORMS (G./EQUIV.) position between 10 and 90% thallous resinate for 4% DVB 8%DVB 16%DVB the lower cross-linked resins. In this respect silver Li + 418 21 I 130 and thallous ion differ greatly from the alkali metal H+ 431 200 136 and ammonium ion in exchange reactions with Na 372 183 113 hydrogen ion. It appears that the contribution NH4 360 172 106 of the activity coefficients of the resinates to the K+ 341 163 106 selectivity coefficient is much greater than that Rb 342 159 106 of the pressure-volume term for these exchanges. cs+ 342 159 102 The positions of these "heavy metal" ions in the Ag + 289 163 102 selectivity scale is that which one would predict T1+ 229 113 85 from comparisons of a.ctivity coefficients of aquenation is probably necessary t'o account for rever- ous solutions of silver, thallous and the alkali metal sals of selectivity. salts. +
+
+
KINETICS OF THE HYDROGEN-OXYGEN-METHANE SYSTEN!. I. INHIBITION OF THE SECOND EXPLOSION LIMIT' BY ARTHURLEVY Batlelle Memorial Institute, Columbus, Ohia Receiued February 18, 1966
Hydrocarbons commonly interfere with the combustion of hydrogen and oxygen. The purpose of this investigation waR to determine the manner by which this inhibition occurs. Methane a t low concentrations reduces the pressure a t the second explosion limit in hydrogen-oxygen mixtures by an amount directly proportional to the mole fraction of methane added, At a certain concentration, referred to as the critical methane concentration, there is a sharp break in the explosion pressuremethane concentration curve and the explosion reaction is completely inhibited. This effect has been studied in the temperature range 490-550' for mixtures with Hz:Ol ratios of 4, 2, 1 and 0.5; KC1-coated Pyrex and clean Vycor reaction vessels have shown similar results. Analysis of the results indicates that the reduction in explosion pressure is related to a methane-hydrogen atom reaction step, and that total inhibition is probably relat,ed to a formaldehyde chain-termination step.
Studies of the combustion of mixed fuels have revealed that, when two or more fuels are burned together, each fuel promotes the combustion process no more than to the extent to which it adds its own heat of combustion to the reaction. It is usually observed, furthermore, that two or more fuels burning together in rich mixtures inhibit the over-all combustion process. Therefore the LeChatelier principle, by which the upper or lower limit of in(1) This study has been sponsored by the Aeronautical Research Laboratory of the Wright Air Development Center, Wright-Patterson Air Force Base, Ohio, Contract No. AF 331038)-12650, E.O. No. 46035 S.R.43. Presented in part at the 122nd National Meeting of the American Cheniical Society, Atlantic City, New Jersey, September 1952.
flammability of many mixtures of gaseous fuels may be calculated, cannot be applied to rich mixtures.2 Interactions in the oxidation processes of mixed fuels have also been observed in the studies of Foord and Norrish.3 In studying the kinetics of the hydrogen-oxygen reaction catalyzed by nitrogen dioxide, they observed that an exceedingly small concentration of methane, as low as one part in a thousand, was sufficient to suppress ignition in H2-02-N02 mixtures, indicating that the hydro(2) H. F. Coward, C. W. Carpenter and W. Payman, J . Chew&. Soc., llS, 27 (1919).
(3) S. G. Foord and A l I P , 196 (1935).
R. G . W. Norrish, Proc.
R o y . Soc. ( L o u d o n ) ,
722
ARTHURLEVY
carbon was exerting a strong influence on the normal chain-branching and chain-breaking’ processes in the hydrogen-oxygen reaction. To understand these phenomena more fully, studies have been made on the combustion of mixed fuels for the purpose of determining the extent and nature of the interactions between fuels in burning. This paper describes a part of this research program covering studies of the reduction and inhibition of the second explosion limit of hydrogen and oxygen by methane. Theory of the Hydrogen-Oxygen Reaction.Hydrogen and oxygen react by a chain mechanism involving the atoms and radical, H, 0 and OH. When the rate of formation of these active particles exceeds their rate of destruction, an explosion occurs. In the temperature range of 400 to 560” there are three explosion limits, which are dependent mostly on the pressure of the reacting system. The first explosion limit occurs a t very low pressures of less than 4 mm. The second explosion limit for stoichiometric hydrogen-oxygen mixtures in KC1coated Pyrex vessels is in the pressure range of 4 to 300 mm. Between the first and second pressure limits the hydrogen-oxygen mixture will explode. At the higher pressures, between the second and third explosion limits, no explosion will occur. A chain reaction theory of the mechanism for the explosion reaction of hydrogen and oxygen a t the second explosion limit has been worked out in detail by Lewis and voii Elbe.4 This theory fits experimental observations well and is the one studied here. I t is proposed by this theory that the rate of chain branching is equal to the rate of chain breaking a t the explosion limit. A chain propagating reaction and two chain branching reactions are illustrated below. OH + H1 +H2O + H (chain propagation) (I)
VOl. 59
intermediates, H, 0, OH and HOZ,is constant, so that just prior to explosion, the rate of the chain breaking reaction is equal to the combined rates of chain branching reactions, that is r4
= r2
+ r3
(1)
Furthermore, since the concentration of oxygen atoms must be constant a t any instant under these steady-state conditions, and since oxygen atoms are generated by reaction I1 and destroyed by reaction 111, then rz = r3
(2)
For any constant Hz/Oz ratio, equation 1 may then be rewritten as 2k2(H)(02) = k.#o(Oz)(H)
(3)
where the concentrations of the reactants are expressed by enclosing their symbols in parentheses, kz and le4 are specific rate constants for the reactions indicated by their subscripts, and Po is the total pressure, which is proportional to (M) in reaction
IV. By rearranging equation 3, the explosion pressure, Po,may be expressed as Po = 2kg/k4
(4)
With methane present other chain-breaking steps besides reaction 4 are also made possible. Methane may react with any of the active centers produced in the reaction in the manner
+ + +
+ H2 + H2O + He0
CHa H = CH3 CHI 0 = CHz OH = CHZ CH4
The methyl and methylene radicals may rapidly terminate the chains by forming formaldehyde, in reactions such as CHI
+
0 2
+HCHO
+ OH +CHO + HzO
The chain terminating reactions are generalized as CHd
+ X = CHa + HX
( VI1)
where X represents any one of the atoms or radical. Any reactivity of the HOz radical has been negThe chain breaking reactions, by which the radi- lected in this simplified development because of its cal and atoms produced in reactions I, I1 and 111 short lifetime. Its possible importance in these reare consumed, occur both in the gas phase and a t actions is discussed later in the section devoted to the wall. Some of these reactions are given below, the water vapor effect.. Applying steady-state theory again to these reacH + 0 2 + M +HO2 + M (chain breaking, gas phase) tions, an explosion equation can be developed
,x,o
(IV)
1I
f
’‘ 1
Hz’J 02,
\
(5)
I
(chain breaking wall)
Since reactions in the region of the second explosion limit are primarily homogeneous, gas phase reactions, reactions V and VI at the wall surface are disregarded and reaction I V is assumed irreversible for the purposes of this study. M denotes any third molecule that stabilizes the combination of H and 02. Applying these assumptions, a simplified rate equation for the pressure, P , a t the second explosion limit can be derived. Let r2, r 3 and r4 be rates of reactions 11, 111 and IV, respectively. Then under steady state conditions the concentration of (4) B. Lewis and G.von Elbe, “Combustion, Flames and Explosions of Gases,” Academic Press, Inc., New York, N . Y., 1951, Chapter 2.
where Po is the uninhibited explosion pressure for methane-free hydrogen-oxygen mixtures and PCH( is the explosion pressure for the hydrogen-oxygen mixture containing methane. For the case where X refers to hydrogen atoms as the active species in the interaction, equation 5 reduces to
where x represents mole fraction. Equation 5a is in general agreement with a similar development by B a l d ~ i n . ~Baldwin has inferred however that the linear decrease of explosion pressure should only come about from interactions with hydrogen atoms. ( 5 ) R . R . Baldwin, Fuel, 31, 312 (1953).
August, 1955
KINETICS O F THE HYDROGEN-OXYGEN-METHdNE
SYSTEM
723
times with distilled water, washed again with a soap solution, rinsed with distilled water many times, and finally rinsed with a saturated, aqueous solution of KC1. After gentle drying with a water aspirator, the vessel was placed on the vacuum line and pumped dry a t 400". This procedure gave a uniform, translucent, KCl coating, Operation.-To determine the explosion pressures, the reaction vessel was evacuated first t o less than mm. pressure, flushed with hydrogen, and re-evacuated. Next, the reaction vessel was refilled with hydrogen to a pressure near or above the second explosion limit. Then the oxygen was transferred rapidly into the hydrogen-filled reaction vessel until the desired total pressure was reached. I n approaching the explosion limit, the pressure was reduced rapidly to about 5 mm. above the explosion pressure, and then more slowly a t a rate of about 1 mm. in 3 seconds, until When this expression is substituted into equation 5 explosion occurred. The explosion was characterized by a it is then apparent that low concentrations of meth- sharp pressure decrease, a flash, and an audible click when working a t higher pressures. I n any series of tests of the ane may still cause a reduction of the explosion effect of methane concentration on the explosion limit, the pressure that is approximately linear with respect Hz:0 2 ratio was held constant while the methane concentrato methane mole fraction. The case for interac- tion was increased. Observation of the Limit.-Although the second explosion tions with oxygen atoms is similar. limit is determined essentially by gas-phase reactions, and The development of the reduced-explosion equa- for this reason is relatively independent of the nature of the tion, as performed here or in Baldwin's s t ~ d yis, ~ reaction vessel, it has been shown477 that different coatings of necessity a rather simplified one. Besides being may cause variations in the explosion data. Two identical based on only a minimum number of interactions, Pyrex reaction vessels were made for these studies and both were coated using the same procedure. Some difference it also has been assumed that the addition of the was found, nevertheless, in the results from the two vessels, third reactant into the hydrogen-oxygen reaction especially for the oxygen-rich mixtures. For example, with has only a negligible effect on the role of M in re- mixtures having Hz: 0 2 ratio of 1:2, a t temperatures of 490, action IV. As pointed out by Walsh6 the efficiency 510, and 530°, the reactions in vessel 2 required about 1% methane for inhibition than th: reactions in vessel 1, of the third body in reaction IV increases with the less and about 3% less methane a t 550 . The results checked frequency of collisions and with the ability of the reasonably well for explosion in the range where the Hz:02 colliding molecules to take up the vibrational energy ratios varied from 4:1 to 1:1. It is important in these studies to condition the reaction from HOZ. It is probably safe to assume that the to avoid obtaining false (low) methane-inhibition coiicentration of methane is sufficiently low that its vessel values. It was necessary to run off several preliminary effect on the collision frequencies is not significantly explosions before determining the critical methane concenlarge. The ability of methane to take u p the vibra- tration that caused complete inhibition of explosion. Othertional energy of HO; is difficult to approximate wise a slight error was noticeable to the extent of 0.4% however. It has been assumed therefore that the methane in a mixture requiring 12.8% methane.
Although subsequent arguments in this paper support the importance of the methane-hydrogen atom reaction, it is the opinion of the author that interactions with the hydroxyl radical and oxygen atom must also be considered. Approximately linear equations similar to Equation 5a are also obtained when small concentrations of hydrocarbon are considered in the interactions with OH and 0. The steady state concentration of OH radicals from reactions I, 11, 111, IV, and VI1 is
total effect of methane in reaction IV, although not readily calculable, is sufficiently low that the general conclusions are not seriously in error. Experimental Apparatus.-These studies were performed in a conventional high-vacuum system. Apieaon grease, Type N, was used on all the joints except those in the vicinity of the furnace, where Apieaon, Type T, was used at the joint between the reaction vessel and the feed line; aluminum stearate was added to the Apieaon T t o form a heavier grease which would not channel at temperatures of 80". The furnace was made from a 15-inch length of brass tubing, 41/4 inches in diameter, and was wound with No. 20 Chrome1 A wire, using one large central winding and two smaller end windings. Temperatures were recorded by means of a Chromel-Alumel thermocouple, located at the junction of the capillary inlet tube and the reaction vessel, and connected t o a Leeds and Northrup potentiometer, Model 8657-C. The temperature was held constant t o f l Dby means of two fine-control, external rheostats in series with two Variacs. All data reported are for reactions in spherical, 200-cc., KCl-coated Pyrex vessels, or uncoated Vycor vessels, 7.4 cm. in diameter. Materials.-The methane was 99% pure, Matheson, C.P. grade. It was charged into the gas reservoir after drying over CaCL and PzOS, and passing through a D r y Ice trap. The hydrogen was Matheson electrolytic grade, 99.8% pure. It was purified further by passing over CaC12, platinized-asbestos a t 250°, and Pz05,and finally through a Dry Ice trap. The oxygen was prepared by warming K M n 0 4 gently and passing the gas over CaClz and P z O ~ . Procedure. KC1 Surface Coating.-The vessels were cleaned in hot dichromate cleaning solution, rinsed several (6) A. D. Walsli, Fuel., 33, 247 (1954).
Experimental Results The results of the studies performed in the two KCI-coated Pyrex vessels were essentially the same, except for the variations reported above. Figure 1 presents graphically the results observed in vessel 1. A similar set of results for the reactions in vessel 2, have been recorded in Table I.8 Table I also includes results on ?. :2 H z : 0 2mixtures, not shown in Fig. 1. I n general, the sensitivity of the methane additions was such that a further increase in methane mole fraction of 0.001 was sufficient to inhibit explosion completely. A comparison of the data obtained from vessels 1 and 2 shows good reproducibility for the hydrogenrich and the stoichiometric mixtures. Since Warren was able to show such pronounced effects of some surface coatings on the second explosion limit,' a brief investigation of the methane interactions in clean Vycor vessels was also made. Table I1 shows these results and compares them 'with the previous results obtained in KCI-coated Pyrex vessels. The data refer to stoichiometric Hz-02 mixtures, to which methane was added R o y . Soe. (London), 8304, (1951); 8 2 1 1 , (7) D. R. Warren, PTOC. 86, 96 (1952). (8) Table I has been deposited a8 Document number 4533 with the AD1 Auxiliary Publications Project, Photoduplication Service, Library of Congress, Washington 25, D. C. A copy inay be secured b y citing the Document number and h y remitting $1.25 for photoprints, or $1.25 for 3 5 min. microfilm in advance payment by check or money order payable to: Chief, PI~otoduylicationService, Library of Congress.
ARTHURLEVY
724
VOl. 59 tor which is probably produced in the pre-explosion reaction CH3
+ 02 = HCHO + OH
CHO
+ HzO
This reaction probably does not become predominant until the methane reaches a concentration capable of forming that concentration of formaldehyde necessary to suppress further chain branching. Methane is the only hydrocarbon that exhibits the abrupt break in the explosion pressure curve. Propane, for example, causes an almost linear and continuous decrease in the second explosion limit.g Why then is the abrupt break observed for Mole Fraction, CH,. Mole Fraction, CH,. Fig. 1.-The inhibition of the H2-Oz ex losion by methane in a KC1-coated Pyrex methane additions, attributed to formaldehyde - formation, when vessel ?vessel 1). . . higher hydrocarbons produce until explosion was completely inhibited. PO formaldehyde a t an even greater rate a t these tem, ~ rate of derepresents the methane-free H2-Oz explosion limit peratures? As shown by B a l d ~ i n the pressure and X Z H ~represents the critical methane crease of the explosion pressure with hydrocarbon mole fraction required for total inhibition of explo- concentration increases with hydrocarbon chain length; and propane is approximately thirty times sion a t each temperature. more effective than methane in completely inhibiting TABLE I1 explosion.9 As a result the explosion pressure is reEXPLOSION PRESSURESFOR STOICHIOMETRIC HTOZ MIX- duced so readily by the combination of water vapor TURBS AND CRITICAL METHANE CONCENTRATIONS FOR TOTAL and formaldehyde produced in the preexplosion reINHIBITION OF EXPLOSION actions, that there is no opportunity to build up a KC1-coated Pyrex Uncoated Vycor critical concentration of formaldehyde, as can be Tyw, Po * Pa, * done in the methane system. C. mln. XCH4 mm. XCH4 Reduction of the Explosion Limit by Water 470 ... ... 27.0 0.026 Vapor.-Whereas the role of formaldehyde has been 490 35.0 0.043 38.2 ,045 postulated by the author, Baldwin,6 and others, on 510 55.5 ,056 60.6 ,057 the basis of most probable reaction steps, the effect 530 76.0 .076 83.2 .070 of water vapor on the second explosion limit has 550 117.5 .095 127 .078 been well-established experimentally. The simiDiscussion of Results larity in the effects of water vapor and of methane has been reported earlier.1° Figure 2, reproduced Reduction of the Explosion Limit by Methane.Figure 1 has shown that the pressure a t the second from the previous study, illustrates this similarity. explosion limit decreases linearly for all Hz/Oz Until the point of discontinuity is reached, both ratios with increasing mole fraction of added methane and water vapor show identical effects on methane. The simplified analysis of the primary the chain breaking and chain branching pressures inhibition reactions of methane presented earlier causing explosion in hydrogen-oxygen mixtures. predicts that the reduction of the explosion limit This similarity in the effects of the two additives should be linear, but equation 5a also indicates also extends to slow reaction processes. Consideration of these similarities has led to that the pressure of the limits should fall continuously to zero pressure. The complex nature of the following proposed mechanisms for these jnterthe methane interaction thus becomes apparent, actions because all the curves drop abruptly to zero presCH, HOz = CH3 HzOz HCHO OH = CHO HzO sure (no explosion) a t a so-called critical methane CH3 0 2 concentration. Above the critical methane con- The first of these steps is analogous to the step procentration, capture of active radicals by the reac-, posed by Voevodskii for the accelerating effect of tion water vapor on the combination of hydrogen and CHI X = CH3 + HX (VI11 oxygen. Since the stability of the HOz radical is questioncannot be the sole inhibiting reaction of methane. Two strong inhibitors in the explosion reactions able a t the temperatures of these studies the reacare water vapor and formaldehyde. As will be tivity of the HOz radical was neglected in the de(9) A. Levy, Fifth Symposium (International) on Combustion, shown in the following section, water vapor causes a No. 17. reduction but does not completely inhibit explosion, Paper ( l o ) A. Levy, J . Chem.P h g s . , 21, 2132 (1953). at least up to concentrations of 40 mole per cent. (11) A. Levy a n d J. F. Foster, THISJOURNAL, 69, 727 (1955). water vapor. Formaldehyde is the chain-termina(12) V. V. Voevodskii, J . P h y s . Chem. ( U B S R ) , 22, 457 (1948). 1
+
+
+
+
+
+
August, 1955
KINETICSOF
r &
725
HYDROGEN-OXYGEN-METHANE SYSTEM I
1
-----
14.
I
THE
,
o
o
0
Additive Water vopor Methone I
I
Y
SO8
0.16 0.20 0.24 0.28 0.32 0.36 0.40 Mole Fraction of Additive, Pig. 2.- -The inhibition of the second explosion limit of stoichiometric H2:OZmixtures by methane and water vapor; Vycor vessel, T = 560".
0.00
0.04
0.12
velopment of the reduced-explosion equation. Alternatively, the H02-reaction step may be included in the manner proposed by Prettre,13 that is, as a rapid succession of two reactions
+ + M = H0.z + M
H CH?
0 2
+ HOz = CHa + H2On
These equations may then be combined and written as CHa
+ H + 02 = CHI 3. H202
This reaction step, as written, represents the observed dependence of the reduction of the second explosion limit on the hydrogen atom concentration, without the necessity of assuming direct dependence on the elusive HOz radical. Difficulties Inherent in Interpretation of Variations of the Critical Methane Concentration.-An analytical interpretation of the experimental results is difficult for two reasons. First, it has already been shown that the simplified development of the explosion pressure equation predicts a continuously decreasing explosion pressure as the hydrocarbon concentration is increased. This is found in all hydrogen-oxygen-hydrocarbon mixtures except methane. Thus, the analytical basis for interpreting the results is incomplete. Second, surface effects appear to cause major problems in attaining complete reproducibility of the data €or oxygen-rich mixtures. This is illustrated in Fig. 3 where the oxygen mole fraction is correlated with the critical methane mole fraction for studies in two KC1-coated Pyrex vessels. Although the critical methane mole fractions are in close agreement for the two vessels up to xo2% 0.45, they do not agree as well above xo, = 0.45, and also above this point there is a sharp change in the relationship of the two variables. The poor reproducibility of the experimental data in the oxygen-rich mixtures, xOe5 0.45, is probably related to increased pre-explosion reactivity of these mixtures, and a resulting enhanced effect of the withdrawal rate on the observed pressure a t the explosion limit. Lewis and Von Elbe have shown that the shift from slow reaction t o explosion js a continuous p r o ~ e s s .Therefore, ~ although the water formed initially may suppress explosion, the water is also responsible for a n increased rate of combina(13) M. Prettre, J . chim. phvs., 33, 189 (1936).
tion of the hydrogen and oxygen in the slow reaction." As a result the rate at which the gases are withdrawn from the explosion vessel becomes critical if the experimental error is to be minimized. Egerton and Warren1*have observed, in an investigation of the effect of the withdrawal rate on the second explosion limits, that the effect was negligible with rich mixtures and quite noticeable with lean mixtures.
07
206 . I
05
c
0 04 + 0
P
03
-01
02
3
01
LL
O 0 001
003
005
007
009
011
013
Mole Fraction, CH,. Fig. 3.-The
dependence of the critical methane concentration on the oxygen concentration.
Two mechanisms that may affect the explosion pressure have been described. Baldwin and Precious's have suggested that quadratic branching reactions such as H HOz = 20H are responsible. Egerton and Warren disagree with this explanation and suggest instead that the net branching factor is reduced to zero by the products formed during the initial stages of explosion. Although neither mechanism can be proved to complete satisfaction, the present studies lend support to Egerton and Warren's suggested mechanism.
+
(14)A. C. E g e r t o n a n d D. R. Warren, Nuture, 170, 420 (1952). (15) R. R. Baldwin and R. M. Precious, zbid., 169, 290 (1952).
ARTHURLEVY
726
Temperature Dependence of the Explosion Reactions.-The temperature dependence of the explosion reactions also indicates sharp differences bet.ween the reactions of rich and lean mixtures. Grant, and HinshelwoodlB describe the second explosion limit of hydrogen and oxygen by the expression P H z f apOa = k' (7) where K is a constant which is proportional to the branching probability of the active radicals in the reaction. As such, K depends upon the frequency and energy of the collisions between particles, and varies with temperature according to the Arrhenius equation. The coefficient a, on the other hand, which reflects chain breaking via three-body collisions in the gas phase, increases gradually with temperature. This suggested to these authors that the chains are being broken in the gas phase by three-body reactions of the type X
+ 02 + M +products
where X is a chain carrier and M is any molecule, including the excess oxygen and water vapor. Figure 4 is a plot of the hydrogen pressure against the oxygen pressure a t the second explosion limit. The solid lines represent hydrogen-oxygen mixtures with no methane present, and the dashed lines represent mixtures containing methane at the critical concentration just prior to complete inhibition of explosion. The methane-free data (solid lines) show that equation 7 is satisfied a t 530 and 550". At 490 and 510°, there is some curvature, signifying that the three-body gas phase collision is less predominant at these lower temperatures and that the importance of wall destruction is increasing.
Vol. 59
The extreme curvature of the dashed lines in Fig.
4 signifies that methane is not acting solely as a third body upon which the chains may be broken, but is participating in some other way. The locus of maximum curvature occurs in the portion of the graph bounded by the 3 :2 and 1:1 Hz:O2 constant ratio lines. This is the same observation as was shown in Fig. 3 where the proportionality between xo2and X ~ ends H ~ a t xOn= 0.45. A standard method for calculating the activation energy of the hydrogen-oxygen explosion reaction is from a consideration of the temperature dependence of the branching probability term, K. Table 111 lists the values of a and K for equation 7 obtained from the experimental data for methanefree mixtures. The values of a, the coefficient for three-body, gas-phase collisions, are shown to increase fairly uniformly with temperature, but at a much slower rate than K. The activation energy, Eo, obtained from these data for the methane-free explosion is 22,600 cal. per mole. This agrees well with values between 20 and 26 kcal. obtained by others. l6-lS TABLEI11 EXPERIMENTAL VALUES OF a A N D K Temp., C. 490 510 530 a 0.30 0.34 0.40 K 30.8 44.9 62.0
550 0.45 97.6
Since one cannot justify such a plot for the hydrogen-oxygen-methane mixtures, apparent activation energies were determined from the temperature dependence of the slopes in Fig. 1. These results are shown in Table IV. TABLEIV THETEMPERATURE DEPENDENCE O F THE SECOND EXPLOSION LIMITIN HzOrCH4 MIXTURES Hz: 02 ratio 4:l 2:l 1:l 1:2 Apparent activn. 15.7 15.6 9.4 fideterenergy, kcal./mole minate
Fig. 4.-The
P a r t i a l Pressure, 0 2 , rnm.Hg. relationship between the hydrogen and oxygen pressures a t the second explosion limit.
(16) G. H . G r a n t and C. N. Hinslielwood, Proc. Roy. Xoc. (London). A141, 29 (1933).
Whereas the activation energy of the reaction in methane-free mixtures is independent of stoichiometry, activation energy in the ternary mixtures appears t o be especially sensitive to excess oxygen. The fuel-rich mixtures, Hz: 0 2 4: 1 and 2: I, gire essentially the same value. The 1: 1 Ha:O2 murtures on the other hand appear to have a much lower apparent activation energy, and in the case of the 1:2 Hz:02 mixture the reciprocal temperature plot of the explosion pressure slopes was too nonlinear for even an approximation of an apparent activation energy. Summary and Conclusions An equation has been developed, based on the principal chain-branching and chain-breaking steps of the hydrogen-oxygen mechanism, which describes the linear reduction of the second explosion limit by methane. The linearity in the pressureconcentration curve, and the similarity of methane and water vapor in this regard, suggest that the (17) H. P. Broida a n d 0. Oldenberg, J. Chem. Phys., 19, 196
(1951). (18) A. A. Frost a n d H. N. Alyea, J. A m . Chem. Sac., 6 5 , 3227 (1933).
August, 1955
SLOW
REACTION IN
THE HYDROGEN-OXYGEN-METH.4NE
principal methane termination step involves interaction with the hydrogen atom. The break in the pressure-concentration curve, which is not predieted by this mechanism, is probably related to the formation of formaldehyde. For fuel-rich mixtures, the critical methane concentration correlates
SYSTEM
727
linearly with the oxygen mole fraction, a i d the apparent activation energies are constant. Excess oxygen however destroys both of these correlations, suggesting that under such conditions the oxidation of methane is also occurring tjo an appreciable extent.
KINETICS OF THE HYDROGEN-OXYGEN-METHANE 11. THE SLOW REACTION1
SYSTEM.
BY ARTHURLEVYAND JOHN F. FOSTER Raltelle Memorial Institute, Cohmbiis, Ohio Received February 18, 1966
The slow reaction of hydrogen-oxygen-methane mixtures has been studied to explain more fully some of the anomalous results that are obtained in the region of the second explosion limit. Studies a t 560" and 360-480 mm. pressure show that methane increases the initial rate of combination of hydrogen-oxygen mixtures. The maximum rate of reaction, however, may be either increased or decreased by the addition of methane, depending upon the oxygen concentration of the mixture. A similar dependence on oxygen concentration is also found in determinations of the orders of reaction. The composition of the reaction products indicates that the two mixed fuels are oxidized simultaneously a t approximately equivalent rates. The general conclusion from these rate studies and from previous studies of the explosion reaction is that water vapor produced in the early stages of reaction serves as a homogeneous catalyst.
In a preceding paper the effect of methane on the explosion reaction of hydrogen and oxygen has been related t o probable reactions with the active centers.2 I n the present study the slow reaction in Hz-02-CH4 systems is investigated t o determine which pre-explosion reactions may influence the interaction of methane on the second explosion limit of hydrogen and oxygen. Complex chain reactions of this type are not readily measured in terms of the rate functions of classical kinetics, so that other, less direct, analyses must be applied. Two different reaction rates are considered here, namely, the initial rate and the maximum rate of reaction. Each is determined from the time rate of decrease of total pressure in the system. Experimental
The initial reaction rate is reported either as the time required to reach 10% reaction, t l o % , or as the time required to reach maximum rate, The maximum rate is reported as the rate of pressure decrease in the system in mm. per minute. Proper conditioning of the reaction vessel to attain acceptable reproducibility is a difficult experimental problem in slow reaction studies. Fairly good success was obtained by producing one or two preliminary explosions in the reaction vessel and by following these with two preliminary slow-reaction runs, before preceding to the actual series of experiments scheduled for that day. Although the procedure works quite well, a definite trend toward a more active vessel surface ( L e . , faster reaction rates) was ohserved over a period of time.
Apparatus.-The apparatus and materials are the same as those described in the previous article, except that the oxygen used in these studies was Matheson Extra-Dry grade. It was found that this substitution was unimportant because there was no difference in results from those which were obtained using oxygen prepared by the KMnOc method. A one-liter sampling bulb and a Toepler pump have been added to the line for the purpose of withdrawing the partialreaction products a t various times during an experiment. Procedure.-The rate studies are performed in the following manner. Hydrogen and methane are first introduced into the reaction vessel, and then oxygen is added ns rapidly as possible until the desired total pressure is reached. Reaction time is measured from the beginning of the addition of the oxygen, which requires about 10 seconds, although most of the oxygen is added within five seconds. Except for the extremely rapid reactions, however, the timing error is much less than other experimental errors. The course of the reaction is followed by measuring on a Hg manomet.er the rate of decrease in pressure as water vapor is formed. To prevent any condensation of water vapor in the line connecting the reaction vessel t o the manometer, the line is kept at 70' by a wire-wound resistance heat,er.
Experimental Results of Slow Reaction Studies A compilation of the results of the slow reaction studies performed in a KC1-coated Pyrex vessel, has been recorded in Table I.3 Table I lists the maximum and initial rates a t T = 560" of G8 mixtures a t total pressures of 360,390,420,450 and 480 mm. The experimental run numbers, which were assigned in chronological sequence are also shown, to give some indications of the reproducibility of the data. As pointed out above, it is important to eliminate any surface conditioning effects, and thus to make certain that a change in reaction rate is the result of gas phase reaction and not of surface reaction. An example of surface conditioning is shown by comparing the identical runs 84 and 134 at 390 mm. pressure in Table I. These runs were made with stojchiometric hydrogen-oxygen mixtures, containing no methane. The maximum rates for runs 84 and 134 were 7.5 and 9.0 mm. per minute, respectively, and the initial rates were 11.5 and 8.5 minutes to reach maximum rate, respectively. A period of three weeks separated these runs and the rates showed a decided increase at the end of the
(1) This s t u d y has been sponsored b y the Aeronautical Research Laboratory of the Wright Air Development Center, Wright-Patterson Air Force Base, Ohio. Contract No. AF 33(038)-12656, E.O. No. 460-35 S.R.4. Presented in part at t h e 125th meeting of the American Chemical Society, Kansas City, Missouri, March, 1054. (2) A. Levy, THISJOURNAL, 59, 721 (1955).
(3) Table I has been deposited as Docunient number 4532 with the AD1 Auxiliary Publications Project, Photoduplication Service, Library of Congress, Washington 25, D. C. A copy may be secured b y citing the Docunient number and b y remitting $1.25 for photoprinta, or $1.25 for 35 mm. microfilm in advance by check or money order payable to: Chief, Photoduplication Service, Library of Congress.
