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INDUSTRIAL AND ENGINEERING CHEMISTRY
in Figure 4 and listed in Table I. The alkanes have the lowest flame velocities and arecomparablewith the large ringcompounds. The alkenes have higher flame velocities, falling slightly below the small ring compounds. The probable position of cyclobutane has been indicated. The isolated and conjugated dienes are next with the cumulated dienes and alkynes having the highest flame velocities. I n general, branchingor the introduction of side chains
Vol. 43, No. 12
on rings reduces the flame velocity. The extent of the, reduction depends on the parent chain and the number and position of the substituents. LITERATURE CITED
(1) Gelstein, M., Levine, O., and Wong, E. L., J . Am. Citem. SOL, 73, 418 (1951). R~~~~~ED h l a y 16,1951
I Acetylene end Dideuteroacetykne with Air RAYMOND FRIEDMAN AND EDWARD BURKE Pa,
Westinghouse Research ~ a b o r a t o r i e s ,f a s t Pittsburgh,
Little is known of the nature of chain reactions occnrring in gas flames, but it has been suggested that diffusion of free radicals is of critical importance in determining burning velocity. The object of this research was to provide data for comparison with flame theories. Flame speeds of CzHz-air, GDz-air, and mixtures containing both isotopes were determined from flame photographs. From flame area measurements it was concluded that the speed was proportional to burning velocity, independent of isotopic substitutions. The ratio of the burning velocity of CzHz-air to that of CzDz-air was found to vary between 1.16 and 1.22. After calculating the ratio of equilibrium atomic protium concentration to that of the corresponding atomic deu terinm concentration, as well as diffusion-coefficient ratio, the Tanford-Pease theory predicted the ratio of reaction-rate constant for CnHpair to that of CzDz-air as 0.92. A reaction mechanism has been postulated which accounts for the greater rate constant of the heavier isotopic form. When a mixture containing both isotopes was studied, the dependence of burning velocity on the proportion of the heavy isotope in the mixture was found to differ slightly from that predicted by the theory of Tanford and Pease.
ITTLE is known of the nature of chain reactions occurring in gas flames; however, the proposal has been made that diffusion of free radicals, particularly atomic hydrogen, is of critical importance in determining t,he burning velocity. &lathema,tical difficulties prevent obtaining rigorous solutions in closed form of the equat,ions relating burning velocity, diffusion coefficients, and rate constants of the chain reactions. Tanford and Pease (16) have derived an equat,ion based on several approximations; this, however, cannot readily be tested against experimental data. See also Hoare and Linnett (7). An object of this research was to provide data for comparison with flame theories. The plan of investigation wm to replace the hydrogen (protium) in a fuel by deuterium and to determine the resulting change in burning velocity. The simplest such fuel is deut,erium gas, but the thermal conductivity of a deuterium-air mixture is grossly different from that of a hydrogen-air mixture, whereas acetyleneair and dideuteroacetylene-air have essentially the same conductivity. Thus, use of the latter two fuels precludes such ambiguity in interpretation of the results as might be caused by differences in conductivity. Data are reported herein for the rat.io of burning velocities of the t r o types of acetylene with air, over a range of mixt'uree. A second series of measurement,s showed the dependence of burning
L
velocity on the fraction of protium which had been ieplaccd I ) \ deuterium. The rrsults are considered in terms of the TanfoldPease theory, which also involves the equilibrium atomic protiumdeuterium ratio, the diffusion-coefficient ratio, and the rractionrate constant ratio. These quantities, except the last, ma? IF calculated independently, 90 that the isotopic ieaction-rate constant ratio may be determined from the Tanford-Pease theory The result is shown to be rpasonable; however, the desirabilit! of independent measurement of this reaction rate 18 pointed out. EXPERIMENTAL PROCEDURE
The tube technique for measuiing burning velocitj was choit 11 because it is relatively simple, requires onlv a small volume of ga\, and hap already been employed for acetylene-air mixtures bj hIason and Wheeler (11) A photographic technique similai t o that of Coward and HartITell (4)ma4 used for observation of thr flame speed, which is much larger than the true burning veloc it \ However, as long as the flame-fiont area is constant, the ratio of the burning velocity of an acetylene-air mixture to that of the corresponding dideuteroacetylene-air mixture is equal to thr ratio of the flame speeds of the two mixtures. The constant\ of the flame-front area is demonstrated from the photograph. Apparatus. Flame speeds werc determined by the burning of various mixtures in a heavy-n-alled borosilicate glass tube, 1.26 em. inside diameter and 150 cm. long. Successive photographs were taken of the flame as it progressed from thc rpc'n to the closed end of the tube, and the distances betwecii t8heconsecutive 1magc.s on the resulting photographic plates were mwmmd. Only t'hat portion of the flame travel from 10 to 40 cm. fi,om the open ignition end was studied, on the basis of the findings of Mason and Wheeler (11). The flame images were recorded on 4 X 3 inch Eastman Tri-X Panchromatic Type R glass plates which were exposed in a Speed-Graphic camera at f/4.5. 9 rotating disk, having two diametrically opposed slits, \%-asplaced before the camera lens so as to cut off all light to the plate except when a slit passed in front of the lens. The disk was 24 inches in diameter and rotated at 3460 r.p.m.; the width of each of the two slits corresponded to an angle of 6.5". Thus, the effective exposure time was about 300 microseconds. The disk speed was measured with a stroboscope and controlled by varying the motor voltage. Before each run the open end of the tube mas closed off with a steel strip held in place by a spring; the tube together with the rest of the system was evacuated to about 0.2 mm. and was maintained at this pressure for at! least' 6 minutes. The gas mixture was then allowed to enter the tube and was brought to atmoppheric pressure by means of a Toepler pump. The tube was theii closed off. A gas burner, designed to produce a thin flat flame perpendicular to the tube axis, wa8 placed close to the outer surface of the steel strip. This burner was shielded from the air flow set up by the rotating disk. After the burner was lighted, the strip n-as immediately moved downward, causing the flamc to ignite t,he mixture in the tube. From three to five runs were made of each mixture in rapid ~uccession.
December 1951
Figure 1 is a typical flame photograph. The. working portion of the tube was provided with two scales, above and below the tube, for locating the flame images. Previous to the passage of the flame, these scales were photographed, the tube being covered by a mask. Gas Generation. Gas was generated by the reaction of calcium carbide and watereither HzO or D20. Prior to generation, the carbide was extracted with carbon tetrachloride and was subsequently heated under vacuum in a reactor at 300’ C. for 18 hours. Then water vapor waa admitted to the reactor, and the acetylene together with some unreacted water passed into a liquid nitrogen trap, where both were condensed. After this, the liquid nitrogen waa replaced by an alcohol-dry ice bath to permit the acetylene to vaporize into the collection bottle while the water remained frozen. The gas was then mixed with dry air to obtain the desired air-fuel ratio. The composition of each. mixture n7aa determined by Orsat analysis, the absorbent being Burrell’s “Lusorbent.” Measurements with a mass spectrometer indicated that the dideuteroacetylene was about 98.4% deuterated. RESULTS
c
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INDUSTRIAL AND ENGINEERING CHEMISTRY
Two curvea are plotted in Figure 2, showing the flame speed of dry acetylene-air and dideuteroacetylene-air (98.4% deuterated on an atomic basis) as a function of composition, a t 25” C. The acetylene-air curve is based on 42 points, each of which represents an average value of h m e speed as determined from a single plate. This average was obtained from measurements of the interval between each pair of consecutive images. No systematic increase or decrease in flame epeed was observed on any plate, although in some cases an oscillation was present. The mean deviation of the data is 1.3y0, The dideuteroacetylene-air curve is based on 39 points, with a mean deviation of 0.5%. Although Wheatley (18) has reported occasional “anomalous” flame speeds, associated with highly
300
28 0
260
240
W V
m
\22c
B
awm 20c 0 W 0
W
I a
:18C 16C
14C
12(
GAS
I
1
1
6
8
10
COMPOSITION(V0LUME
I
I
12 14 PERCENT FUEL IN A I R )
16
Figure 2. Flame Speed vs. Composition for Acetylene-Air and Dideuteroacetylene-Air Mixtures at 14.3 Lb./Sq. Inch, Corrected to 25” C.
tilted flames, no such effects were encountered in this investigation; no observations were discarded. The data, obtained a t temperatures between 22’ and 29” C., were corrected to 25 O C. taking the flame speed to be proportional to the 0.84 power of absolute temperature, a8 determined in a preliminary study. Certain of the plates revealed oscillations with the natural frequency of the tube superimposed upon the uniform motion. The amplitude was about 5% of the flame speed for peak and rich mixtures and was considerably smaller for lean mixtures. This low-amplitude vibration apparently did not influence the flame speed, as the amplitude often varied appreciably within a series of plates of the same gas mixture without any corresponding changes in the flame speed. The normal burning velocity, uo,rather than the flame speed, t’, is of fundamental importance. Conard and Hartwell ( 4 )propose the relationship uo = vAt/A,, where At and A , are the tube crossscctional area and the flame-front area, respectively. The quantity A//At is plotted in Figure 3 as a function of composition for both acetylene and dideuteroacetylene flames. Flame front areas were determined from the plates, the flame surface being approximated by that portion of a prolate spheroid cut off by a plane normal to and bisecting the semimajor axis. Eachpoint in Figure 3 is the average of a number of images on a given plate. This graph shows that the ratio AjIAt is unaffected by replacement of acetylene by dideuteroacetylene. The peak burning velocity of acetylene-air, as computed from the flame speed and area measurements, is 154 em. per second; Smith and Pickering (14) obtained a value of 145 cm. per second by the Bunsen met hod. It is therefore evident that reliable burning velocity ratios may
2774
INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY
be obt,ainedfrom these flame speed measurements. Such a ratio is plotted in Figure 4 as a function of composition; it' varies between 1.16 and 1.22. The ratio appears t'o increase for leanmixtures and decrease for rich mixtures; in addition, it passes through a local minimum a t 9% acetylene as well as a local maximum a t 10.5%. (The stoichiometric composit,ioncont'ains 7.75% acetylene.) Since these variations are only slight,ly larger than the experimental error, no att,empt,was made t o at>tachsignificance to them.
Vol. 43, No. 12
the burned gases. Assuming the critical species t o be atomic hydrogen, the Tanford-Pease formula may be written
vhere uois normal burning velocity, k is the rate constant for the reaction between atomic hydrogen and the fuel, C is the concentration of combustible, Q is the mole fraction of potential combustion product in the unburned gas, p is the mole fraction of atomic hydrogen in the burned gas, D is the diffusion coefficient of atomic hydrogen in the gas mixture, and B is a factor, usually close to unity, which corrects for the loss of atomic hydrogen due t o chemical processes; it is assumed that R is unchanged by isotopic substitution. An expression may now be written for the burning velocity ratio of two mixtures of identical composition except for an isotopic substitution
Here, the primed symbols denote the heavier isotopic modification. Equation 2, then, should give an approximation to the isotopic effect on burning velocity, as long as diffusion of atomic hydrogen is controlling.
5
2
7 8 9. IO II 12 GAS COMPOSITION (VOLUME PERCENT FUEL IN A I R )
L
13
Figure 3. Ratio, Ar/At, as Function of Gas Composition for Acetylene-Air and Dideuteroacetylene-Air Flames
Figure 5 gives the results oI)taiiicd in an addit,ional series of measurements, made with peak mixturm containing both acetylene and dideuteroacetylene in varying p1,oportions; the end points are taken from the curves of Figure 2. The dotted curve is a plot of Equation 11, the nearlj- linear rcwdt predicted by the modified equation of Tanford and Peascl. Since this approach gives only the form of the dependence, the curve iTas fitted t o the end point,s obtained experimentally in this investigation. Excellent agreement betxeen t'heory and clxperiment occurs from 0 to 44% dideuteroacetylene; hoTvever, the theory appears t o give values between 1 and 2% too high from 59 t o 90% of the heavier isotopic form. The linearity of the right-hand portion of the curve permits a reliable extrapolation from 98.4 t o 100% dideut,eroacetylene. This extrapolation furnishes a correction factor of 1.002 by which to niult,iply the ordinate of Figure 4 t o obtain the burning-velocity ratio of thc pure isotopic forms. FLAME PROPAGATION MECHANISM
Thermodynamic calculations reveal that appreciable concentrations of atomic hydrogen exist a t equilibrium in the comlsustion products of acetylene flames; calculations, such as those of Tanford (16),indicate that atomic hydrogen readily diffuses upstream. The experiments of Badin ( I ) demonstrate that atomic hydrogen can initiate combustion of hydrocarbons even a t room temperature. Therefore, the square root law of burning velocity proposed by Tanford and Pease may be a useful approximation. Relation between Burning Velocity and Reaction Rate. Tanford and Pease (15),by making several approximations, obtained a simple relation between burning velocity, reaction rate constants, diffusion coefficients, and mole fractions of certain active species. Their treatment is based on the concept that the reaction rate is first-order ivith respect t o various active species, the concentrations of rrhich are governed by upstream diffusion from
i
i
l
1
l ~
7 GAS
0 9 10 II 12 COMPOSITION (VOLUME PERCENT FUEL IN AIR)
13
Figure 4. Acetylene-Air/Dideuteroacetylene-Air Burning Velocity Ratio as Function of Composition
Isotopic Effect on Flame Temperature. Rossini, Knowlton, and Johnston ( l a )have shown bv calorimetric measurement that the heat of formation of heavy water is 3.07% greater than that of water hcmuse of differences in zero-point energy of viater, heavy water, hydrogen, and deuterium. Therefore it is pertinent to inquiw whether such effects are important in the combustion of acetylene and dideuteroaeetylene. If the usual assuniption IS made that the internuclear forces are independent of isotopic substitution, it follon-s that the heat of combustion of riideutwoacetylene is greater than that of acetylene by (ZHs0
-
ZDz0)
-
(ZCgH8
-
ZCsDp)
(3)
7vhrre the Z's are zero-point energies. ApproximatP values of the zero-point energies may be obtained from (4) 2
In this equation, which neglects the interaction between vibration and rotation, h is Planck's constant, c is the velocity of light, and the W ( are the 3n - 5 or 3%- 6 fundamental vibrational frequencies of the molecule in question. The w Z values for the mol+ cules of interest are all tabulated by Herzberg (6); computation yields ( Z H ~ O Z D , ~=) 3.38 kcal. per mole and ( Z C ~HZC,D,) ~ = 3.34 kcal. per mole. The net difference of 0.04 lrcal. per mol? is
December 1951
INDUSTRIAL A N D ENGINEERING CHEMISTRY
negligible when compared with the heat. of combustion of 300.1 kcal. per mole. The flame temperature depends not only on the heat of combustion but also on the specific heats of the combustion products and on the dissociations. For stoichiometric acetylene-air, the combustion products contain about 7% water, the other gases being almost entirely nitrogen, carbon dioxide, carbon monoxide, and oxygen. Justi and Luder's (9) calculation gives the mean molal specific heat of heavy water between 0' and 2300 " C. to be 6.4% greater than that of water; computation shows that the mean molal specific heat of the deuterated combustion products is
Figure 5.
2775
where At2 is a number between zero and 0.132, depending on the law of force and the composition, and S is the effective cross section. I n so far as internuclear forces are independent of isotopic substitution, XI' and S are unaffected by the isotopic change, and it follows that
Effect of Isotopic Substitution on Reaction Rate. Bigeleisen (2) has developed a method for computing the rate-constant
Flame Speed of Peak Acetylene-Air Mixtures (9.6% Acetylene) vs. Ratio (CZD2)/[(CzHz) (CZD~)],at 14.3 Lb./Sq. Inch, Corrected to 25" C.
+
0.54% greater than that of the normal products. Hence the flame temperature of acetylene-air would be 12"higher than that of dideuteroacetglene-air, if both the extent of. dissociation and the 'dissociation energies were the same, However, this is not quite the case, because of differences in zero-point energy as well as in flame temperature. Calculations taking these effects into account show that the temperature of the stoichiometric acetylene-air flame is 9' higher than that of the dideuteroacetylene. Isotopic Effect on Equilibrium Atomic Hydrogen Concentration in Burned Gases. The equilibrium constant for dissociation of hydrogen is given as a function of temperature by Rossini et al. (IS). The ratio of this constant to that for dissociation of deuterium may be calculated by the method of Bigeleisen and Mayer (3). The flame temperature of the stoichiometric acetylene-air flame is about 2500" K. The ratio (H)(Dz)'/' of the equilibrium constants a t 2500" K., expressed as
ratio, k / k ' , for a pair of reactions differing isotopically; a knowledge only of the vibrational energy levels of the reactants and the activated complexes is necessary. He derives the equation
where K is the transmission coefficient, m* is the effective mass of the complex along the coordinate of decomposition, and each f is given by
(7) The i's are the fundamental modes of vibration of the molecule in question, which may be either A , B , or Cs, for the reaction
A
(HZ)'/~(D)
is found t o be 1.064. Further, the flame temperature of the dideuteroacetylene-air flame is 9" lower, and d In K / d T = 0.0044a t 2500"K., so that A K / K = 0.040 for AT = 9". Since these effects are both in the same direction, the ratio of equilibrium constants for the two flames is 1.064 X 1.040 = 1.107. Thus the ratio of atomic protium in the acetylene flame to that of atomic deuterium in the dideuteroacetylene flame is 1.107, to a first approximation. Protium-Deuterium Dzusion-Coeflicient Ratio. According to Kennard (IO), the coefficient of diffiusion in a mixture of two gases (atomic hydrogen and a gas of molecular weight about 29, In this case) may be written
+ B + Ct:
+
products
The primed symbols represent the heavier isotopic modification, and u; = hcwi/kT, where the w,'s are the wave numbers of the various modes; s and s' are symmetry numbers, Equation 6 is rigorous except that the tunnel effect has been neglected; fortunately, this effect tends t o vanish a t high temperatures. Equation 6 cannot be applied rigorously t o the acetylene-air flame for two reasons: (1) the reaction mechanism has not yet been established, and (2) the transmission-coefficient ratio may not be precisely equal to unity. The Tanford-Pease model is based on chain initiation by reaction between atomic hydrogen and some other species. Although 0 2 -+ OH 0 is critical in the oxyhydrogen the reaction H flame, it is probably not significant in this case since the reaction is endothermic by 17 kcal., and the activation energy must be a t
+
+
Vol. 43, No. 12
INDUSTRIAL AND ENGINEERING CHEMISTRY
2176
least this great. On the other hand, Tollefson and LeRoy ( 1 7 ) found that atomic hydrogen readily takes part in a n exchange reaction with acetylene, with only 4 kcal. of activation energy. Therefore, it is assumed that the chain-initiating step is
Table I is based on a postulated mechanism and, therefore, serves primarily to show the approximate range of values of kjk’; quantitative conclusions are not warranted. If the flame propagation is controlled by a thermal rather than a diffusional mechanism, then according to Damkohler’s equation (6) UO/U;
To apply Bigeleisen’s equation, vibrational frequencies must be assigned. There are none for atomic hydrogen and deuterium (so thatfH = l), and Herzberg (6) has tabulated the frequencies for acetylene and dideuteroacetylene. It is difficult to make assignments for the activated complex. If it is assumed that the complex does not stabilize to give a vinyl radical a t this high temperature level, but splits to give C2H and H2, it is then possible to estimate the frequencies for (CZH3)’ and (C2D3)x as follows: The force constants for bonds three and five are considered to be very small, so that the bond-stretching frequencies will be essentially those of a triatomic molecule, CtH, and a diatomic molecule, Hz. The two frequencies for C2H are readily computed, using 5.95 X 106 dynes per em. for the bond-one force constant and 15.85 X l o 5 dynes per em. for the bond-tro force constant (6, p. 180). The frequencies for C2H are 3349 and 2051 cm. -1, and those for CZD,2895 and 1907 cm. -1 The hydrogen and deuterium frequencies are assumed to be the same as in normal hydrogen, 4405.3 and 3117.0 cm.-’, as found by Teal and MacWood (16). The remaining five bending frequencies contribute only slightly to ~C,H,Z since the w i are small. This may be seen in the calculation of fc,HI, where each bending mode contributes only about 0.6% at 1500” K., 1.5% a t 1000° K., and 2.7% at 750” K. Therefore it is assumed that the average contribution to f ~ from ~ each ~ bending ~ x mode is the same as the average contribution of the bending modes to ~ c $ H % at the same temperature. Then, m* and na’* are computed by the formula
It is difficult to know the exact value form,. The use of the lower limit of 12 for mmgives (m’*/m*)1/2= 1.363, ivhereas the upper limit of 26 (and 28) gives (m‘*/m*)1/2 = 1.392. The value 1.37 is used. Table I shows the results of the calculation. The factor K / K ’ rrhich appears in the results is often nearly unity, according to Bigeleisen (2). Hulbert and Hirschfelder ( 8 ) , however, made a theoretical investigation which indicates that the transmission coefficient ratio may differ somewhat from unity. The tabular values indicate that, for the model chosen, kjk’ is of the magnitude of unity and increases with temperature at a rate corresponding to a “collision theory” activation energy difference of 0.74 kcal. per mole. Table 1.
+
Solution of Equations 6 and 7 for CzHz H Reaction at Various Temperatures T, O K. fCiHz fCzHsr KIK’ 750 1000 1250 1500 2000
3.199 2.080 1.649 1.425 1.236
4.802 2.746 2.018 1.665 1.357
0.913 1.038 1.119 1,173 1.248
Comparison of Results with Theory. Equation 2 may be solved for the reaction-rate ratio, k/k‘, using the following values: U O / U : = 1.19 (experimental), p / p ‘ = 1.107 (calculated), DID’ = 1.391 (calculated). Then, k/k‘ = 0.920. This is consistent with the reaction model discussed in the previous section if the effective temperature is 765” K. and the transmission-coefficient ratio, KIK’, is taken as unity, as shown in Table I.
=
(k/k’)’/’
(9)
Equation 9 is based on the assumptions that the thermal properties, the ignition temperature, and Damkohler’s dimensionless factor, f, are unaffected by the isotopic substitution. According to Equation 9, when u,/,; = 1.19, k/k‘ equals 1.42. Clearly, it would be desirable to have a direct measurement of k/k’, inasmuch as Tanford and Pease’s diffusion theory requires it to be 0.92, whereas a thermal theory predicts a value of 1.42. (In connection with the thermal theory, the 9’ temperature difference between the two isotopic flames would account for only 0.8% differencein kif the activation energy is 10 kcal., at 2500’ K., and 1.6% difference if the activation energy is 20 kcal.) It is also of interest to consider the variation of burning velocity nith the proportion of protium which has been replaced by deuterium, as shown in Figure 5. Tanford and Pease’s equation, when extended to this case, yields
where the subscript, p , refers to protium. and m refer8 to an isotopic mixture. Equation 10 is equivalent t o
+
where Y = (C2D2)/[(CpH,) ( C 2 D a ) l illcld , the subscript, d , denotes deuterium. Equation 11, which IS plotted in Figure 5, is nearly linear; this curve was based on the Experimentally determined end points, since Equation 11 givee only the form of the dependence. Thus, the extended equR+ion of Tanford and Pease, although not a rigorous solution of the problem, differs only slightly from the experimental results. LITERATURE CITED
(1) Badin, E. J., J . A m . Chem,. Soc., 72, 1550 (1950). (2) Bigeleisen, J., J . Chem. Phys., 17, 678 (1949).
(3) Bigeleisen, J., and hfayer, 11.G., I b i d . , 15, 261 (1947). (4) Coward, H. F., and Hartwell, F. J,,J . Ckem. SOC.Trans., 135, 1996, 2676 (1932). (5) Damkohler, G., 2. Electrochem., 46, 601 (1940). (6) Herzberg, G., “Infrared and Raman Spectra of Polgatomic Molecules,” New York, D. Van Sostrafid Go., 1945. (7) Hoare, M. F., and Linnett,,J.W., J . Clzelrz. Phus., 16, 747 (1948). (8) Hulbert, H. M., and Hirschfelder, J. (9) Justi, E., and Liider, H., Forsch. (1935). (10) Kennard, E. H., “Kinetic Theory oi Gases,” New York, McGraw-Hill Book Co., 1938. (11) Mason, W., and Wheeler, R. V., J . Ch?vi.Soc. Trans., 115, 578 (1919). (12) Rossini, F. D., Knowlton, 3. W.,and Johnston, € L., I.J . Research Natl. Bur. Standards, 24, 369 j1940). (13) Rossini, F. D., et al., “Selected Values of Chemical Thermodynamic Properties,” Washington, D. C., Natl. Bur. Standards, 1947. (14) Smith, F. A,, and Pickering, S.F., Ibid.. 17,7 (1936). (15) Tanford, C., and Pease, R. N., J . CIzerrL. Phus., 15, 431, 433, 861 (1947). (16) Teal, G. K., and RlacWood, G. E., Ibid.. 3,760 (1935). (17) Tollefson, E. L., and LeRoy, D. J., Ibid., 16,1057 (1948). (18) TTheatley, P. J., Fuel, 29, 80 (1950). RECEIVED Xoveinber 15, ScientificPaper 1548.
19.50. Westingho
Research Laboratories
