ILVDLTSTRIALA,ITDESGINEERIATG CHEMISTRY
1018
sulfur in hydrogen sulfide can be oxidized, as follows, from S-- + S o + SI: + S :, indicates that the following reactions can express the conditions that give rise to flame speeds with proportions of hydrogen sulfide in air within its limits of inflammation:
+ 502 + 5 X 3.76N2 = 2H20 + 2SOz f 202 + + 402 + 4 X 3.76N2 = 2H20 + 2SO2 + 02 + -+ 302 + 3 X 3.76Nz = 2H20 + 2S02 + 3 X + 202 + 2 X 3.76N2 = 2H20 + SO2 + S + 2 + 02 + 1 X 3.76N2 = 2H20 + 2s + 1 X 3.76N2
2H2S (7.75%) 5 X 3.76N2 2HzS (9.51%) 4 X 3.76No 2H2S (12.29%) 3.76N2 2H’S (17.35%) X 3.76ih’z 2HzS(29.60%)
From actual analyses of the gases in the flame tube resulting from the combustion, the plots of the amounts of SS,SO*, and SO3, corresponding with the same abscissas as in Figure 3, show that the hydrogen is to a great extent selectively oxidized. This fact was also noted in that gas mixtures that contained percentages of hydrogen sulfide above 12.3 per cent, showed poorer images on the film due to the increasing amount of hydrogen burned and the formation of greater amounts of sulfur. I t is well known that the flame speed of
VOl. 20, s o . 10
hydrogen cannot be determined in the time allowable by photographic method due to the fact that the light rays that are given off are in the ultra-violet and do not affect the photographic film rapidly. Between the points A and B, if no sulfur had been deposited and only sulfur dioxide formed, the curve would no doubt have conformed to its proper shape as shown by the dotted line and the flame speed not abruptly retarded by the formation of suspended sulfur. I t is interesting to note that the slowest maximum flame bpeed heretofore measured was that of carbon monoxide in air in a 2.5-cm. tube and found to be 60.0 cm. per second. I t is now evident that hydrogen sulfide a t its maximum flame speed of about 50.0 em. per second moves much slower than carbon monoxide and thus will affect the burning of combustible gases containing hydrogen sulfide. I n these experiments the sulfur trioxide content of the gases of combustion was a t a maximum on igniting a 7.0 per cent mixture of hydrogen sulfide in air. A continuous method for the production of sulfur trioxide by burning hydrogen sulfide in an internal-combustion engine warrants further study.
The Gaseous Explosive Reaction at Constant Pressure’ F. W. Stevens BUREAUOF STANDARDS, WASHIBCTON. D. C.
The course of the gaseous explosive reaction at constant pressure is described and then followed experimentally by means of photographic time-volume records obtained by a simple device that is found to function as a transparent bomb of constant pressure. It is found that at constant pressure the uniform rate of propagation, s, of the zone of explosive reaction, when measured relative to the active gases, is proportional to the product of their concentrations (partial pressures) : s = k, [AIn1 [B]”2[CIn3... . . . In the light of this relationship studies have been made of the effect of inert gases and of composite fuels on the rate of the gaseous explosive transformation.
N
’EARLY all the investigations that have been made of the gaseous explosive reaction have been carried out under conditions of constant volume. This has seemed necessary from the very nature of gases. Of all these investigations, those that show some connection with the line of substantial development taken by our knowledge of gaseous transformations, and that have sought the direction for further advance indicated by well-established general principles and laws, have been devoted to thermodynamic studies of the reaction and have concerned themselves principally with gaseous equilibria. The significant advance that has resulted from such studies must be attributed in large measure to the fact that they took advantage of the leadership and direction provided by the theoretical consequences involved in the principles and laws of thermodynamics as applied to chemical equilibria. These deductions were early (1876) set forth in the far-reaching theoretical investigations of Gibbs. As a result of his -cork “chemical science has been able to use these results of theoretical physics with immense benefit t o itself and to deal quantitatively with the most complex equilibria without any knowledge of the intimate ‘mechanisms’ underlying physical and chemical phenomena.”* 1 Published
b y permission of t h e Director, S a t i o n a l Bureau of Stand-
ards.
On the other hand, kinetic studies of the gaseous explosive reaction made under conditions similar to those imposed for thermodynamic investigations have not shown a corresponding advance. As compared with thermodynamic studies, the number devoted to the kinetics of the reaction and based in any way upon or directed by the probable consequences of a kinetic theory of gases are few; yet for the kinetic phase of the reaction the opportunity has long been a t hand to adapt experimental devices and methods to the principles of statistical mechanics. Even with a primitive kinetic theory, early attempts in this direction met with significant success: “The first attempt a t a quantitative kinetic expression is met 15ith in the equation pv = RT.”3 Very early also (1864) “the assumed correspondence between the order and mechanism (of a reaction) which finds its rational explanation on the basis of a kinetic theory of molecular motions, was, of course, the original hypothesis of Guldberg and Waage in the formulation of the law of mass action. * * * The rational procedure seems to be to regard the order of any simple reaction as prima facie evidence of its m e ~ h a n s i m . ” ~ The advance in physics of late years has been somewhat diverted from the physics of large aggregates to the physics of individuals, thus depending for a prediction of the behavior of the mass on the behavior of an isolated individual. The direction taken by this more recent development is said “to hold out the hope that the time will come, perhaps in no very distant future, when the structure and activity of the material world will be understood in terms of a theory based on the potentialities and activities of electrons, protons and radiation, or possibly of radiation alone. Although such a theory already exists, it is not sufficiently developed to suffice for the needs of the chemist,”2 whose problems are for the most part concerned with systems, often of great complexity. “Among the immediate developments to be wished for statistical mechanics will be its increasing applicatioris to Ehrenfest, P a n d T., Encyklop. math. Wissen , 4, 4, 11 (1924). Tolman, “Statistical Mechanics with Applications to Physics and Chemistry,” p 239, T h e Chemical Catalog Co , I n c , 1927. 3
4
Donnan, Chem Weekblad, 23, 422 11926)
1019
October. 1928 systems. * * * Tlie problem of reaction velocity is probably nearer the heart of most chemists t,han anything else in their whole range of activity. Rates of reaction are the factors that determine yields and costs, and possibilities and t'lieir theory must eventually succumb to scientific treatment."5 In the present paper are offered some results obtained in a study of gaseous explosive reactions at constant pressure. Since these reactions are confined to the gaseous state, they can never be freed entirely from hydrodynamic disturbances set u p in the gaseous fluid by the explosive reaction itself. These disturbances. afiecting the concentrations of the active gases and their maps niovenient, are much more profouild when the reaction takes place untler conditions of constant volume than they are under conditions of constant pressure. Under t,he latter conditions the gross mechanism of the explosive reaction-the spatial propagation of a sharply defined reaction zone within the gases-may assume a form of nearly perfect ~ y ~ n i i i e t ant1 r y R uniform rate of propagation. This simplification. secured by constant-pressure methods, is essential to kinetic studies of the reaction and advantageous also to thermodynamic investigations. The relation between the thermodynamic results obtained a t constant pressure and those resulting from conditions of constant' volume is espre.setl by thc equation of state,
pi' = TZRT
(1)
The direction taken by the studies here offered has been influenced largely by the known order of the reactions studied. The kinetic principles applied to them are primitive and simple. Characteristics of Gaseous Explosive Reaction
A iiioyt iiiiImrtaiit characteristic of the gaseous explosive reactiun vas early established by the investigations of Bunsen.' of Gouy,; and of hIichelson.8 It was t o the effect t1i:it tlie mo\-ement of the zone of explosive reaction within R homogeneous mixture of explosive gases is constant untlcr conditions of constant pressure, and independent' ( ~ ftlie mass movement of the active gases in which it is I)rop:qiatecl, This result has for years found extensive practical application in those numerous cases where a homogeneuus mixture of explosive gases is fed through a tube a t a constant time-volume rate and ignited. The zone of continuous explosive reaction automatically adjusts itself under these conditions so that' its linear rate of advance measured relative to the active gases is a constant', s, a t any point of the flame surface. If this were not the case, the many indust rial devices based on the gaseous explosive reaction as controllecl by some forin of burner lvould not be practical. This c*harncteristic as expressed by the investigators mentioned may be written
nhew c,, i j the volume a t constant pressure passing unit element of the flame surface, a, in time t. When this principle is applied to ideal conditions where the homogeneous mixture of explosive gases mag be conceived as existing at rest and unconfined in space, and the explosive reaction started at some point within the mixture, then, s being constant. it should be found that the zone of explosive reaction originating a t the point of ignition should propagate itself in all directions from this point a t uniforni rate a t constant pressure. The reaction zone should thus assume the form of a spherical shell of flame expanding a t a uniform linear rate, s', in space. This rate in space, s', is the linear rate s at which the reaction zone is entering the explosive 5
9 7
'
Tolman, O p . c i L , p. 323. Ann. physik. Chem., 17, 2 0 i (1867). Ann. chim. p h y s . , 5, 18 (1879). A n n . p h y s i k . Chem.. 37, 1 (1889).
gases, plus the constant rate a t which the gases are being moved outm-ard against the static pressure of the surroundings, po. The constant pressure. pl. then, a t which the reaction takes place under these conditions. is not po, but pp plus the preswre necessary to produce the obserred rate of movemerit, S I , in space. That is,
where p is the density of the gases. Since the rate of pressure distribution in the gaseous system is limited to the rate a t which sound is propagated in the gases, it mill be seen that as long as the value of s' does not approach too near the velocity of sound in the gases, t'he value of the last term in equation (3) is small and may be negligible. But for values of s' above that of sound in the gases, it becomes the more important factor, since under these circumstances, as Hugoniotg has shown, the law of static adiabatics no longer applies; the pressure in the t'hin impact wave a t the seat of reaction increases for velocities above that of sound much more rapidly than t'he square of s'. It is, therefore, the pressure a t the seat of reaction, and not that indicated a t some point more or less remote, that should be considered in det,ermining the pressure condit'ions of the reaction and its effect upon reaction rate. Applying the law of Hugoniot instead of the simple impact expression giren in equation (3), Chapman,lo Jouguet," Crussard,lz and Becker13 have made extended analyses of tlie impact pressure conditions accompanying the flame when its velocity of propagation exceeds that of sound in the gases, and when, in consequence, the course of the reaction becomes independent of a container. These constant-pressure conditions apply to the high rates of flame propagation met in the Rerthelot explosive wave,14 sometimes called detonation, where the reaction runs its course under conditions of a constant pressure of many atmospheres. The flame velocit,y under these conditions of constant' impact, pressure is found: as in the case of much lower constant pressures dealt with iii this paper. to be strictly constant. Tlie conditions that determine uniform flame movement in a gaseous explosive reaction, whether for the slower reaction rates or for the more rapid rates of the explosive wave, are a homogeneous mixture of the explosive gases and a const'ant pressure during their transformation; for under these conditions only it is possible for the mass movement of t'he active gases and for their concentrations to remain constant during the reaction process. These ideal conditions, under which the gaseous explosive reaction might run its course at a constant' pressure, unconfined in space, may be closely realized in practice by ericlosing temporarily the homogeneous mixture of explosive gases in a soap film and firing tlie mixture from the center. Figure 1 is a photographic reproducticiii of a tinie-volume record of four gaseous explosive reactioiis of tlie same initial composition obtained by such a cle\-ice.'j This simple arrangement is found to function as a bomb of constant pressure. I t thus forms the complement t o the bomb of constant roluine. The diagram in Figure 2 may assist in pointing out this relationship: A silhouette of the bubble giving its horizontal diameter, 2r. through the spark' gap is secured while the photographic film is a t rest. Since the photographs are made to scale, this figure gives the actual diameter of the J . &cole polyieck., 57, 58 (1887). Phil. M a g . , 47, 90 (1899). 11 J . M a t h . , 1, 347 (190.5); 2, 5 (1906). 12 Bull. SOC. i n d . niinCrale St. Etienne, 4, 6, 1 (1907). 1 3 2 . P h y s i k , 8, 321 (1923). 14 Berthelot and Vieille, Bull. SOC. chim., 40, 2 (1883). 15 For a detailed description of the experimental set-up f o r securing these records see J . A m . Chem. Soc., 48, 1896 (1926). 9
10
Vol 20, Nu 10
1020
mation of tlie explosive gaseous system, and Iience witti tkle rate of energy liberation, i t is obvious that its rate should be determined relative t o the gases it is transforming and not relative to space. It is also clear that unless the method employed makes it possible to follow the coneentrations (partial pressures) of the active gmes the zone of explosive reaction is entering, a kinetic reiation connecting the movement of the reaction zone with the composition and concentrations of the explosive gases could hardly result. Suclr a relationship, however, is suggested by a number of considerations. Haher’s has pointed out that in the propess of a gaseous explosion the gaseous system automatically falls into three well-defined zones. These three zones, in the case of a constant-pressure bomb, maintain a symmetrical position about the point of ignition throughout the reaction process. He designates these zones as (11, the region occupied by the esplosive gases, (2) the zone of explosive reaction marked hy flame, (3) the region occupied by the equilibrium products behind the flame. This latter region, he states, “is not from a thermodynamic standpoint free from oxygen, but from an analytical standpoint it is; in this region no further burning t.akes place.” It is a region of chemical equilibrium depending on temperature and pressure and defined by the equilibrium constant,
The kinetic relation leading to the above equilibrium expression is written for the rate of molecular transformation, V = k [Aim jB]*i IC]*,. . . . . -k‘ [A‘!n‘* jB’l*’x [C‘*‘*. . (7) The experimental application of t.he aboveformulat,ed p r i n c i p l e s -C Figure 1 (one-lmtli u c f d rizej may he best illustrated by a pxrtieular case to which they have been sphere of active components w.hose t,raiisformat,iotr is to b~! applied-vis., t o t,he gaseous rem.... ,,’ \. followed. The pliotogrsphic film is then set in rapid motion tion and an ignition spark passed. An image, a, of the spark is 2co O*”2C02 (8) ;’ o b t a i n d on the moving film near the time record, tt, from a of Since a reaction t,he equilibrium for a given condition tempera- b l b7 calibrated fork. The point a marks tlie center of the espanding spheriral zone of reaction. Only its horizontal ture and pressure is independent - Ii motion outward from this point: and perpendicular to tlie of the way by which it is at,tained, direction of motion of the p1iotograpbic film, is recorded. it. may be assumed that the course .._ .__._--.‘ The Aame trace 011 the film is thus the resultaiit of tlie verti- of this trimolecular transformation cal known rate of motion of t,lie pliotographic film and t.lie wit,liin the zone of explosive reachorizontal motion of the zone of reaction. That iis motion. tion is described by the relation under the constant-pressure eonditiom afforded by a s o a p film bomb of constant pressure. is const,airt,is iiidicated by thp 5’ = k [COlz [GI - k‘ lCO~12(9) a -right line, ah, made hp its trace. The slant of this lirie gives and that the equilibriuin condition t the rate of motion of tht? reaetioii zone in space. As the of t.he nrocess is exnrcssed by ,,..- .... figures show, this rate in space, s‘: may he determined ai. any K- = iCO21* (10) inst.ant during the reaction. It, is equal to tile radius of the ICOl? I0,j I , i reaction zone at any instant, r,, divided by the time interval; Should the reaction proceed almost .,. zr ; @ t, between ignition and the sttniiimcnt of Ti: wholly in one direction, as is .’...._.__. ., usually the case in explosive reacFigure 2 tions of eases. the last term in But this rate in space is not t h e rate at which the reactioii equation 19) may be neglected” and the kinetic expression zone is entering the active gases and effecting their trans- for the molecular rate of transformation written formation independent of their mass movement. The V = k [COj’ IO21 (11) velocit.y, 8, of the reaction zone, measured relative to the If, now, by some means the successive concentrations of active gases it is entering is given for the case where tire carbon monoxide aiid oxygen during the period of transzone is &I expanding spherical shell of flame, by formation from tlieir initial to tlieir final condition could be IJ maintained constant by the int,roduction iuto the reaction (5) la r’3 zone of new initial components at {.he same rate that the r e where T and T’ represent the init,ial and final volumes of tlie action products are removed from the reaction zone t o t.he reacting gases considered. 2. 9hgsik. Chrm., 68. 726 (1909). If the rate of movement of t h e reacttion zone is to be 3: Nemst, “Theoretical Cheinirtry,” p 785, Macmillan. 1823: LeChaconnected in any way with tlie rate of molecular transfor- telirr, Z.Dhsiik. C i r m . , a, 728 (1888).
\;, __----
+
’.
_
I
”..’.,
s
=
%
?
=
,
,
L
October, 1928
INDUSTRIAL AND ENGINEERING CHEMISTRY
equilibrium zone, then the zone of explosive reaction would represent a constant reaction gradient across it, and the relative rate of motion, s, between the reaction zone and the initial gaseous components would remain constant and s would express the gross rate a t which equilibrium was being established in the gaseous system. But this imagined Drocess of supplying initial active components to a reaction zone al the same rate that the equilibrium products are removed -an analytical device first made use of by van’t Hoff 18is automatically carried out wherever a gaseous explosive reaction is so conditioned that it may run its course in a homogeneous mixture of explosive gases a t a constant pressure. Observation shows that under these condi2 4 6 8 10 12 ld /6 r x ,02 tions the rate of propagation, s, of the zone of explosive reFigure 3 action, measured relative t o the initial active gases, remains constant during the reaction. Since the rate of molecular transformation a t any instant between the initial and end conditions of the reaction process remains proportional to the product of the concentrations of the active gases, it was assumed that s, analogous to V , would sustain a like relation to the composition of the explosive gases, the initial concentrations of which may be U
L
1021
time by thermodynamic calculation.* * * A specially high value must be attached to explosion methods since, by suitable variations of the experimental conditions, it enables both the specific heats and the equilibrium to be determined.f’20 Table I-Rate
RECORD 9-7-27
Iio.
1t o 3 4 to 7 8 to 11 12 to 15 16 t o 19 20 to 23 24 to 27 28 to 31 32 to 35 36 to 39 40 to 43 44 to 47 48 to 51 52 to 55 56 to 59 60 to 63 64 to 67 68 t o 71 72 to 75 76 to 79 80 to 83
of F l a m e Pro agation i n ZCO
’ARTIAL
Alm. 0.224 0.260 0.279 0.310 0.325 0 359 0.388 0.416 0 460 0.491 0.523 0.574 0 622 0.688 0.726 0.775
Alm. 0.776 0.740 0.721
0.848
Explosive Reaction
~
LO21
0.883 0.903
0 2
PRESSURE
IC01
0.810 0.840
+
at Ebnstant Pressure
0.690
0.675 0.641
0.612 0.584 0.540 0.509 0.477 0 426
0.378
0.332 0.274 0.225 0.190 0.160 0.152 0.117
0.097
0.0389 0.0500 0.0561 0,0663 0.0713 0.0826 0,0921 0.1011 0.1140 0,1227 0.1305 0.1404 0.1463 0.1480 0,1444 0.1351 0.1247 0.1129 O.lP93 0.0912 0.0791
I
C m . / s e c . lCm./sec. 27.6 191 34.7 226 37.5 279 45.3 335 50.3 365 55 5 434 63.3 487 71.1 561 80.3 632 84 3 660 88.4 715 99.8 794 100 6 858 102.8 870 101.9 849 92.2 814 86.4 733 79.2 632 614 77.7 63.9 463 320
50.1
I
709 694 668 683 705 672 687 703 703 687 678 711 688 694 706 682 693 701 711 700 633
It was of interest to examine the effect of inert gases on the rate of propagation of the zone of reaction in the light of the statistical relation expressed in (12); and, by a method suggested by that employed by the investigators, mentioned above, in determining the e€fect of inert gases upon the thermodynamic equilibrium (6) and the degree of dissociation h0Wn: of combustion products. s = k [CO]’ [ 0 2 ] (12) Since the sum of the partial pressures of the gaseous comIncluding equation (5) ponents present in the reaction a t pressure p must equal p , r3 equation (12) may be written for atmospheric pressure, s = S’ - =: k [CO]’ [Oz] (13) 7‘3 s = k [CO]’ [l - CO] (15) and since the method employed determines s directly, without designating the composition of the factor [l - C O ] r3 further than to indicate that the sum of the partial pressures k = (14) r t 2t [C0l2 [ 0 2 ] of its components remains the same as the partial pressure of In Table I are set down the experimental results obtained t h e f a c t o r [O,] in from the photographic records of the explosive reaction 2CO equation (12); and I“ O2 +. These results cover the range of mixture ratios that under the same /w of [CO] and [O,] that will support a zone of explosive reaction. conditions both ex- f Figure 3 illustrates graphically the relation between the rate p r e s s i o n s , [CO]?of propagation, s, of the reaction zone and impact probability, [ 0 2 ] a n d [COIL- ,~ I’ = [ C o l a [O,], for this (order of reaction. Figure 4 illus- [l - C O ] .repreqent r, trates the more familiar relationship betrreen rate of propa- the same impact gation, s, and the partial pressures of the active gases. Solid p r o b a b i l i t y . I?, $ 5 0 r3 circles represent observed values, s = s’ F ~the ; open circles though not the same $, proportion of favorand continuous line represent calculated values, s = k [C0l2- able impacts nor the [Ozl. same potential energy. I n case the ’0 Effect of Inert Gases component [I -CO] 90 eo 70 ca so lo 20 m o [ qi The effect of inert gases on the thermodynamic equilibrium is made up of the of gaseous explosive reactions has received extensive con- fraction a of the acFigure 4 sideration both from experimental and theoretical standpoints. tive gas O2 and the in which a spherical bomb of fraction 1--a of an inert gas, the partial pressure of this comThis series of investigati~ns,~g constant volume with central ignition was used, formed a ponent may be expressed as part of the most extensive investigation of gaseous reactions [l - COI = [ l - c o l a [l - CO] (1 - a ) (16) involving the equilibrium products of combustion, carbon active inert dioxide and water vapor, that has yet been carried out. Equation (15) may then be written “NO other chemical equilibrium has so far been investigated S = ki [CO]’ [l - C o l a f ki [CO]’ [l - CO](1 - U ) (17) by so many methods which can also be controlled a t the same Should all of the impacts involving the inert gas be futile “Etudes de mechanique chimique,” Amsterdam, 1884. and the possible effect of its various physical properties, aa 3’ Langen, Mitt. Fovscharbetten, 8, 1 (1903); Pier, Z . Elektrochem , 15, molecular heat, heat conductivity, etc., on the course of the 536 909) Bierrum, Z Phrstk C h e n . , 79, 513 (1912), Siegel, I b d , 87,
+
F:
1.’
‘
-v)
+
641 $14);
18
Nernst, 00.cit., p. 783.
1022
IXD CSTRIAL An‘D ENGINEERIiVG CIIE.VISTRY
IO
90
20 80
30 70
44
50
60
So
60 40
70 30
80 20
90 /0
Vol. 20, No. 10
iW [CO;
0 [!-CO]
Portio1 Pressures
Figure 6
Figure 5
reaction be disregarded, then the last term in equation ( I T ) niay be neglected and the effect on reaction probability of replacing the fraction (I -a) of an active gas by a n inactil-e one be written s = k [CO]’ [l - C O ] U (18) This expression takes into account the effect of the remaining active components only, and this is the major effect to be expected; but while the inert gas introduced niay take no part in the molecular transformation, its presence in the zoiie of esplosive reaction and in the active gases adjacent to it would naturally affect the heat distribution in that region. The effect of different inert gases upon the thermodynamic equilibrium is not the same; a quantitative estimate of their different effects permits their specific heats to be determined under the conditions resulting from the explosive reaction of the known active gases. It might therefore be expected that the presence of inert gases in the zone of reaction would likewise have different effects upon the propagation of the reaction zone due to their indilidual characteristics. I n carrying out the observations on the effect of inert gases, the experiments were so arranged that the explosive trail+ formation of the same partial prebsures of the active gake-. carbon monoxide and oxygen. could be observed on the w i i e partial pressure of each of the inert gases used, and this over the entire range of mixture ratios of the gases that would ignite. The inert gases made use of xere helium, argoii. nitrogen. and carbon dioxide. Table I1 gives some of t l x physical properties of the gases involved in the transformitions studied. Table 11-Molecular
Heats and Heat Conductivities of Gases Studied
GAS Helium Argon Xitrogen Oxygen Carbon monoxide Carbon dioxide
MOLECULAR HEAT HEAT^ COKDLXTIVITY 1’ 5.c7
5.07 6.90 6 90 6.90 9.00
336.0 39.0 56.6 57.0 54.2 33.7
Partington a n d Schilling, “Specific Heats,pf Gases ” Vol I, p 92.
b Taylor, “Treatise on Physical Chemistry,
Figure 5 shows graphically the experimental values of r3 s = s’ rwhen 10 per cent of the component [l - CO] con‘3 sisted of an inert gas. The values for helium are indicated on the figure by the solid triangle; those for nitrogen by (x) ; those for carbon dioxide by the solid square; and those for A by (v). The same system of marks will be used for these gases in the other figures to be given. The upper continuous curve in this figure indicates values of s for the CO-02 reaction when no inert gas is present. It is the curve given in Figure 4 and is reproduced here as a convenient reference. The lower continuous curve corresponds to
Figure 7
equation (18). .c = 691 [CO]?[ l - C O ] 0.9. I t is t h e tlieoretical locus of s values on the assumption that the inert gases have no effect whatever on the reaction. In this case the observed values with all the inert gases agree fairly well with this theoretical curve. Figure 6 shows experimental results obtained when 20 per cent of the component [l - CO] corisisted of a n inert gas. The upper continuous curve in this figure again represents the locus of s values when no inert gas is present. The lower continuous curve corresponds to equation 118) for this case: s = 691 [COl2 [l - C O ] 0.8. In Figure i are shown the experimeiital results obtained when 40 per cent of the component [I-CO] consisted of an inert gas. The upper continuous curve corresponds to equation (12) when no inert gas is present. s = 691 [C0l2[O2]. The Ion-er continuous curve corresponds to equatioii (18) for this case: s = 691 [CO]’ [l-CO] 0.6. To illustrate how all of the results are tabulated, the results with helium are given in Table 111. From these results and from the coordinate figures given it may be seen that n-hen small amounts (partial pressures) of different inert gases are present in the explosive mixture. there is not niuch difference in their individual effects; their different physical properties do not mask t,he effect of t’he active gases, but. as the relative amounts (partial pressures) of the inert gases become greater and the partial pressures of the active gases less, a difference in their effect on the same CO-02 reaction becomes apparent. (Figure 7) The observed s values not only diverge more widely from values indicated by equation (18). but they also differ characteristically from each other. It is further to be noticed that this divergence in each case is the greater the greater the amount (partial pressure) of inert gas in t,he mixture. In column 4, Table III! is given the partial pressure of H e in each mixture ratio of [PO] and [I-CO]. In column 8 of this table are given the corresponding values of kl = 5. r The values of X.1 i n this colnmn, according to equation (IS), should be a fair constant and equal to 415 if the inert gas was without effect. The values of klare seen to be far from constant in this ease and only approach the theoretical value as the partial pressure of helium in the mixture decreases. The highest value of X.1 is seen to correspond to the greatest amount of helium in the explosive mixture! and vice versa. Having in mind the method by which the effect of inert gases on the thermodynamic equilibrium was determined, it was conceived that the relationship shown in the table b e tween the values of kl and [He] could be due to characteristic physical properties, whatever they might be, of the inert gas present in the mixture, and that the magnitude of their different effects upon the CO-O? reaction might be directly pro-
October, 1928
1023
portional to the partial pressure of the inert gas in the mixture. That is, s =
S'
13 = r'3
ki
[CO]? [l - COIU
+ a[Gs]
(19)
[G,) is the partial pressure of the inert gas and 3 a proportionality factor. The observed results were examined for this relationship. The last column of Table I11 gives the estimated value of 3 for each niixture ratio of [CO] and [ l CO] that n-ould support a zone of reaction
-
u [CO]* [l -
CO]) 1-30) Me1 When the average value of 3 so found, 109. is substituted in
P =
s
(k1
equation (19), the curve represented by open circles and a continuous line, marked H e in Figure 7 is determiiied. 111 a similar way it n as found that the d u e of p for each of the other inert gases used n-as also a fair coiistarit. Its value for 40 per cent nitrogeii in this reaction is 41, for carbon dioxide. -41.8, aiid f o r a r g o n . 112. Hrlium and argon are both monatomic gxsec: a n d h e n c e have the same mol e c u l a r heat iiidependent of teinperature. But their heat coiiriuctiviti+ vary greatly. 130th gases have practically the same effect oil the s d u e s of the CO-Oe exulosive reaction. It is of interest to compare the relations shown by the coordinate figures with the table giving some of the physical properties of the gases involved in the different reactions. Some Observations on a Study of a Composite Fuel
I n the practical application of the gaseous explosive reaction as a source of power in the gas engine. the fuels employed are composite, with characteristics that are likely to be due to the characteristics of their components and hence may be somewhat complex. The simplest problem that could be proposed in an investigation either of the thermodynamics or kinetics of the gaseous explosive reaction of a composite fuel would seein t o be a separate study of the reaction characteristics of each component of the fuel and then a study Table 111-Results RECORD 2-6-27
5' to 8'
4 to 8 to 12 to 16 to
7 11
15 19 20 to 23 24 to 27 28 t o 31 32 to 35 36 to 39 40 t o 43 44 t o 47 48 to 51
S = SI-
Y3 r'd
=
K , [F]", [O:!]"!!
(21)
Within the reaction zone the explosive gases proceed to an equilibrium condition of reaction products, however complex, I
