Dec., 1960
1891
KINETICSOF COMBUSTION OF CYANOGEN
runs with excess C6C&do not produce even a transient formation of the blackish copper-containing precipitate, again arguing that reaction 1 must be a rapid equilibration which ties up an appreciable portion of the Cu(1). But if reaction 4 were ratedetermining, two other problems would appear. The over-all rate would be proportional to the square of the concentration of the less abundant reactant, which is contrary to the experimental data. Furthermore, the observed pre-exponential factor is very large for the formation of an oriented transition state involving two complex molecules. On the other hand, the Ea of 13.7 kcal. and the large pre-exponential factor seem appropriate to the monomolecular decomposition of the C6Clg CuCl complex (reaction 2). For this mechanism, with rapid complex equilibration and K1 of moderate size (say, between 1 and 25 1. mole-’), the overall observed dependency would be essentially first order (with respect to the less abundant reactant) at reactant concentrations of about 1M and greater, and essentially second order (first order with
respect to each reactant) a t reactant concentrations of the order of 0.1 M and less. This latter case conforms to our observations, both of the kinetics and of the unusual stoichiometry of the reaction. Finally, the reacting system of C6Ch and CuCl rapidly decolorizes diphenylpicrylhydrazyl, while in the absence of either reactant the color is comparatively stable (it is slowly discharged by CuCl alone). This is strong evidence for radical intermediation. In view of this, the failure of the reacting system to initiate styrene polymerization may be ascribed to the extremely high stability, due to resonance and symmetry, of the C6C16-radical. This radical is too inert to initiate vinyl polymerization; its stability limits it to reactions with other radicals (e.g., other C5C16. radicals and diphenylpicrylhydrazyl) . Acknowledgment.-The authors are indebted to Drs. T. Alfrey, Jr., and R. H. Allen for helpful discussions, and to the Referees for their excellent criticism of the original manuscript.
KINETICS OF COMBUSTION OF CYANOGEN AND THE BURNING VELOCITIES OF CYAXOGEN-OXYGEN-NITROGEN MIXTURES BY EMILERUTNER,KARLSCHELLER AND WILLIAM H. MCLAIN,JR. Chemistry Research Laboratory, Aeronautical Research Laboratories, Wright-Patterson A i r Force Base, Ohio Received M a y 31, 1980
Burning velocities of cyanogen-air, and cyanogen-oxygen-nitrogen mixtures (Oz/N* = 30.8/69.2) were measured by the tube and balloon methods. The maximum burning velocity of dry CINrair mixtures was found to be approximately 10 cm./sec. Enrichment of the air mixtures with 0 2 , increased the burning velocity, as did the addition of HZand Df. The results of these measurements were correlated with the Semenov-Zeldowitch-Frank-Kemmenetsky thermal theory of flame propagation, and alfio with the Tanford-Pease theory. In the application of the thermal theory it was found necessary to use a value of E = 39.9 kcal. for the tube data, and 35.0 kcal. for the balloon data. The observed variation of E can be related to the increase in the rate of reaction with an increase in O2 concentration, and the subsequent closer correspondence of the actual flame temperature to the calculated one. In using the Tanford-Pease theory to correlate the data involving Hz and Dz it was found necessary to postulate that the effective reaction is: CO OH COS H. The OH producing reaction was assumed to be: 0 2 H + OH H ; while the inhibiting reactions which could account for a decrease in the effect of HZ and DZ with an increase in CZNZconcentration were assumed to be: H CzHz -+ HCN CN, and H HCN + HI CN.
+
+
+
+
+
Introduction Previous investigation of the slow oxidation of C2N2-02systems by Hadow and Hinshelwood’ and investigations of the burning velocities of lean C2N2-02-A systems by means of the bunsen burner technique2 indicate that the acceleration of the reaction between C2N2and O2 in the presence of H 2 0 is consistent with the idea that the effect may be due to the influence of HzO on the CO-O2 reaction. A study of the burning velocities of wet and dry, lean and rich CzN2-air mixtures, and the burning velocities of other CzNz-02-N2systems was undertaken to elucidate the effect of the variation of O2 and Hz on the burning velocities of CzN2-Oz systems. These studies were carried out utilizing the tube method of Gerstein, Levine and (1) H. J. Hadow and C. N. Hhshelwood, Proc. Rev. SOC.(London), AlS4, 376 (1931). (2) R. N. Pesse and R. 9. Brokaw. J . Am. Clem. Soc.. 76, 1454 (1953).
-+
+
+
+
Wong,a and the rubber balloon method of Price and Potter. Experimental Preparation of Mixtures .-Cyanogen was prepared b,y the thermal decomposition of AgCN under vacuum at 400 , the evolved C2N2 was condensed at liquid air temperature, and fractionated into breakseals. A mass spectrographic analysis of a gaseous sample indicated that it contained traces of 0 2 and NZbut no detectable amounts of HzOor HCN, and was 99+% C2Nz. Mixture of CzNZ-OrNz were prepared by subliming desired amounts of CzNz into an evacuated vessel and adding appropriate amounts of air and 0 2 . The gases were dried by passing them through magnesium perchlorate and Ascarite. Besides air(I), another mixture of NZ and Oz (30.8% 0 ~ , 6 9 . 2 %Nz)(II), was used. Tube Method.-Burning velocities were measured by the tube method3 and rubber balloon methods.‘ In the use (3) M. Gerstein, 0.Levine and E. L.Wong. tbid., 75,418 (1951). (4) W. T.Prioe and J. H. Potter, “Fourth Symposium on Combuation,” The Williams Q Wilkina Co.. Baltimore, Md., 1953, pp. 363-
368.
E. RUTNER, K. SCHELLER AND W. H. MCLAIN,JR.
T'ol. 64
into glass tubing connected to the vacuum system. The balloon was attached to a sleeve 10 mm. long which wm friction-fitted to the electrode. The whole assembly was 40 inclosed in a jar, constructed from two desiccator tops of 12.7 cm. diameter. The procedure followed when making a determination was to flush the balloon several times with the combustible \ mixture and blow i t up to a diameter of 40 to 50 mm. 30 .ilfter this operation, the balloon was centered on the electrode and the mixture sparked by discharging a 0.Ol-Mfd. 0 EXPERIMENTAL I condenser. The energy of the spark was controlled by limiting the output (5,000 to 10,000 volt) of the Hivolt Power Supply used to charge the condenser. The balloon was fired 0.45 sec. after the camera (Wollensak Fastax 16 d mm.) was started, the delay time being controlled by using an Industrial Timer Corporation automatic control. Durf2& ing the delay time, several still shots of the balloon and desiccator top were obtained by illuminating them with a stroboscopic light. Timings were obtained from the millisecond timing marks which were imprinted on the side of the film. Eight to ten runs were made for each mixture, since the balloon had a tendency to develop asymmetrically, and such shots could not be used for data. The data required to determine the fundamental flame 10 velocity Ur is given by the relation Ur = (drr/dt) (ro3/~i3) (2) where TO is the initial radius of the balloon, rl is the final radius of the balloon and flame, and (drrldt) is the rate of growth of the radius of the flame. All the above quantities were obtained from measurements on the film, the standard length being the diameter of the desiccator top. 0 5 10 15 20 25 30 I n general, it can be said that in the use of both methods non-uniform propagation was observed for some ranges of C2N2 (%I. Fig. 1.-Flame velocities of C2Ng-I(air) and C~NZ-11- composition. I n the use of the balloon method, for example, it was found that CzNz-air mixtures could not be (69.2% Nz; 30.8% 0 2 ) mixtures. Exp. curves were measwhile mixtures of CtNroxygen-nitrogen (11) ured values; Calcd. curves were obtained from equation 3 ignited; containing less than 12.0% C2N2 did not propagate symwith E = 39.9 kcal., for I, and E = 35.0 kcal. for 11. metrically because of the high spark energies required to of the tube method a tube 27.0 mm. inside diameter and ignite them. Except in the case of 30% CzNz mixtures, no 122 cm. long was utilized which had four marks, 17.60 reproducible value of Ur could be obtained for rich mixtures because of the blurring of the image of the wall of the balloon & 0.01 cm. apart etched on its outside surface, the first mark being 15 cm. from the firing end. The combustion by brightness of the flame. Although the tube technique mixture was ignited with a hot wire, and the motion of flame was used for a wider range of compositions, it could not be as i t proceeded down the tube was photographed with a used for mixtures in which the ratio (Oz/Nz), was greater Fairchild Oscillo-record camera. Millisecond timing marks than in mixture 11, since flames of such mixtures had a were imprinted on the side of the film, and the spatial tendency to accelerate. A comparison between the tube and velocity U. was determined from the number of timing the balloon methods was obtained for a mixture containing marks between consecutive intersections of the trace of the 0.236 C2N2,0.236 Oz, 0.528 Nz, the tube method giving a flame front with the images of the marks on the tube. A value of Uf 0.36.9 Z!Z 1.2 cm./sec. in contrast to 37.5 f.2.4 Bell-Howell Foton camera was mounted on the oscillo- cm./sec. for the balloon method. graphic camera so that images of the flame front could be Discussion obtained simultaneously with the trace. Enlargements of the 35 mm. images were then used to determine the flame The observed burning velocities of dry C2N2-air area Ar. and oxygen enriched dry CzN2-air mixtures are The flame areas, whose shapes were incomplete semiellipsoid, were calculated by a suitable modification of the depicted in Fig. 1, as a function of the cyanogen method described by Gerstein, et u Z . , ~ and Coward and content of the mixtures. It is seen that, despite Hartwell.6 their relatively high calculated flame temperatures The burning velocity Ur is obtained from the spatial Tf , the maximum burning velocity of cyanogen-air flame velocity U , and the calculated flame area Ar in accordmixtures (I)is small compared with that of ordinary ance with the relation hydrocarbon flames, which are of the order of 40 Cf = ( G s Ug)(At/Ai) (1) ~m./sec.~.The low velocity may in part be atwhere At is the cross-sectional area of the tube and Ug tributed to the fact that the actual flame temperais the stream velocity of the unburned mixture. It was found that U, could be neglected in this work, since its tures were lower than Tfbecause of the incomplete value was small in comparison with the spatial flame combustion of the cyanogen. Some evidence for velocity. incomplete combustion of cyanogen-air mixtures is The root-mean-square deviations for the experimentally presented by Berl and Barth,B who observed that measured quantities in equation 1 were 9% for At and 370
i
---
/It/
--.
'\ >'
~~
-
for
Us.
Balloon Method.-The ballon method used was that of Price and Potter' modified so that samples could be run without exposure to moisture. This was done by using an electrode system consisting of a single steel tube 3.2 rnm. outside diameter with an insulated iron wire 0.38 mm. diameter running down the center which protruded about 1 mm. above the tube and terminated in a sphere 0.76 mm. diameter. The tube was sealed with black wax ( 5 ) H. Coward, F. Hartwell and E. Georgeson, J . Chem. Sac., 1482
(1937).
no COz was formed in moderately lean mixtures, and the observations in the present work that no carbon formed in rich, dry mixtures. Furthermore, evidence for the lack of complete combustion in oxygen enriched mixtures is given by observations of Scheller and McKnight7 that the expansion
(6) E. Berl and K. Barth, Z. physik. Chem., Bodenstein-Festband, 211 (1931). (7) K. Soheller and W. E. McKnight. "Seventh Symposium on Combustion," Butterworth Sci. Pub]., London, 1959, p. 369.
Dec., 1960
KINETICS O F C O M B U S T I O N O F CY.4NOGEN
ratios in measurements on the flame velocities of (C2N2,CO, 02,N2)mixtures by the balloon method were in most cases less than that expected on the basis of the calculated flame temperatures. The characteristics of these flames (Le., high Tf and low burning velocity) suggested that it might be interesting to compare the experimental data with the predictions of the Semenov-ZeldovitchFrank-Kamenetskys thermal theory of flame propagation. Their expression for the burning velocity, specialized to the case of cyanogen flames, may be written as
1893
Equilibrium flame temperatures required for the calculation of the burning velocity were determined upon the assumption that the following equilibria were obeyed on the lean side
co +
co
1/202
N2
x2 + 02 0 2
(5)
2n‘
2x0
20
(7) (81
On the rich side only the cyanogen decomposition equilibrium CzN2
2CN
(9)
was considered, since there was no experimental evidence of carbon formation in these flames. Necessary thermodynamic data for the calculations L-f burning velocity, cm./sec. were obtained from the tabulations of Lewis and A* thermal conductivity of product gases von Elbe” save those for C2N2 and CN which were z kinetic collision number L heat of combustion per gram of com- taken from the data of Rutner, McLain, Scheller’2 bustible mixture including diluents and Johnston, et aZ.13 The calculated flame temR ideal gas constant peratures for both mixtures are given in Table I. Ti adiabatic flame temperature E mtivation energy for reaction between Values of other molecular properties of both oxygen and fuel product and cold-gas mixtures were estimated from [021eff effective concn. of oxygen, L e . , concn. in their composition while the value E = 39.9 kcal. reaction zone of flame [C~r\i2]0, [C2N2Ierf iconcn. of cyanogen in unburned gas and was used for the activation for the tube data and 35 kcal. for the balloon data because these gave the in reaction zone, resp. best fit for the experimental curves. The effective concentrations of fuel and oxygen Figure 1 shows the relation between Vf and appearing in equation 3 are determined from the composition for dry C2X2-air (I) and CzK2-oxygenstoichiometry of the reaction between cyanogen nitrogen (11) mixtures, and corresponding curves and oxygen, corrected for the change in temperature obtained from the Semenov equation. The Semebetween the burned gas and the fresh gas and for nov equation gives a reasonable fit with the data the back diffusion of products from the burned obtained from mixtures I, using a value of E = gases. For the case of rich mixtures, for example 39.9 kcal., while the data from mixtures I1 required a value of 35 kcal. to obtain an approximate [CzNzIeff= [([Cd210- [021~)(To/Tr)(no/nr)(A/B)fI [Ozl e f f fit. The variation in the value of E required to iO?leri = [Oplo(Ta/Tf)(RTf2/E)(no/nf)(B/B)~(1/To - Tr)l fit the two sets of data can be related to the observations6 that the actual flame temperatures (4) may be low. For example, if the real flame temwhere perature is lower than Tf,the use of Tfin equation 3 concn. of oxygen in unburned mixture io210 will give a high value of E , and the closer the actual initial temp. of combustible mixture To the lower the observed value ratio of no. of moles in fresh gas to that in product temperature is to Tf, ndnf of E would be. This explanation requires that the gas actual flame temperature approach Tf as the con(-4IB)f = X/pDC,, determined a t flame temp. density of mixture P centration of 0 2 increases. The evidence that this thermal conductivity x requirement is fulfilled is given by the observaD diffusion coefficient t i o n ~ noted ~ ~ ’ above, and also by the following facts: specific heat a t constant pressure of mixture c, increase in O2 concentration for a given C2N2 Values for the thermal conductivity and dif- An concentration increases the flame velocity, and fusion coefficients were obtained from gas kinet’ic theoretical temperatures have been observed in theory considerations9 pure C2N2-O2mixtures.14 D 1.336 ( A l p ) In contrast to the values of E observed for these X 1/4 (97’ - 5)sCv flame reactions, the observation of James and Lafe coefficient of viscosity fitteIs on the variation of the induction period with specific heat ratio temperatures for the explosion of C2K2-air mixtures C, specific heat a t constant volume In the rate expression used above the steric factor (10) John B. Fenn a n d H. F. Calcote “Fourth Symposium on was allowed to be unity, since the uncertainty in Combustion,” The Williams & Wilkins Co., Baltimore, hld., 1953 p. the steric factor is overshadowed by the uncer- 231.(11) B. Leais and G. von Elbe, “Combustion, Flames a n d Explctainty in the temperature dependence of the trans- sion of Gases,” Academic Press, Inc. XCMYork, N. Y., 1951. port and thermad properties of the gas a t the flame (12) E. Rutner, W. H. McLain, J r , and Karl Scheller, J . Chem. Phys., 24 173 (1956). temperature. lo (3)
in which
+
’
(8) N. N. Semenov, Prog. Phys. Sci. (U.S.S.R.), 24, no. 4, 433 (1940). (NACA TM 1026, 1942). (9) J. H. Jeans, “1)ynamical Theory of Gases,” 4th Ed., Dover Publications.
(13) H.L. Johnston, Jack Belzer and Lydia Savedoff, T R 316-7 Cryogenic Lab., Ohio State Univ., 1953. (14) N. Thomas, A. G. Gaydon and L Brewer, J . Chem. Phys., 2 0 , 369 (1952). (15) H.James and P. Laffitte, Compt. rend., 236, 1038 (1953).
E. RTJTNER,K. SCHELLER AND W. H. MCLAIN,JR.
1894
TABLB I FLAMETEMPERATURES AND EQUILIBRIUM CONCENTRATIONS OF SPECIES IN FUMESCONTAINING H*
1600
CsNi"
Equilibrium ooncn., atm. X
Ti,
OK,
10
0.20 0.80 1.50 2.40 3.20
1200 "*
c
3
12.5 14.3 16.7
800
18.0 20.0
1
I
I 2
I
I
3
HZor D2 (%I. Fig. 2.-Relation between U f zand HZor Dn for various CzNz-air mixtures. See table I, note (a) for definition of (CANz). Concentration of H porDp is given as % of total gas mixture.
gave a value of E = 66 kcal. The observations' on the oxidation of C2N2a t 700" indicated that the C2N2was oxidized to CO before an explosion took place; thus one is led to the conclusion that the value of E for the induction time observed by James and Laffitte was that for the oxidation of CzNzto CO; and, therefore, a t least for this reason, it may vary somewhat from the value of E obtained from flame velocities, since scme C02may be formed in the flames. Other contributions to divergences between the values of E obtained from the two methods arise from differences in the course of the flame reaction and the slow oxidation, and the fact that the value of E obtained from flame data depends on the nature of the temperature variations which are assumed for other parameters in equation 3. The squares of the measured burning velocities of cyanogen-air mixtures admixed with small quantities of hydrogen or deuterium are recorded in Fig. 2. It may be observed that the effect of these additives decreases in the richer mixtures, becoming negligible at a cyanogen concentration of 30%. I n the lean mixtures, the effect is similar to that observed by Brokaw and Pease2 on their cyanogen-oxygen-argon mixtures. The squares of the burning velocities are plotted against the equilibrium concentrations of HzO, D20, OH and OD in Fig. 3. In agreement with Brokaw and Pease, a correlation was found to exist between Uf2 and the equilibrium concentrations of OH and OD. Furthermore, a correlation was also present between Uf2and the equilibrium H20 and D20 concentrations. The equilibrium concentrations required for the graphs iii Fig. 3 are recorded in Tables I and 11.
..
... ...
... ... ...
0.23 0.80 1.58 2.44
1.19 2.17 2.24 2.76
13.8 28.5 49.6 56.3
..
2550 2400
... ... ...... ... ...
..
.. ..
... ... *..
.
0.84 1.60
3033 3100 3160
..
..
... ...
...
C~Nz-30.8%0, 16.7 20.0 23.0 30.0
... ... ... ...
*..
... ...
..
2280 2200 2100 2020
...
H¶
....
.... 0.95 51.6 10.8 18.6 28.0
.... .... ....
.... ....
....
3.41 8.92 12.3 40.9 20.7 91.7 32.6 149.0
....
....
.... ....
.
...
... ... ... ...
... ... ...
..
..
.
I
.
....
....
....
....
.... ....
.... .... .... .... ....
....
.... ....
....
+ 69.2% N, (11)mixtures
..
lo4
HtO
3.96 11.2 9.34 56.5 13.4 114.0 17.7 187.0 21.0 252.0
...
.
1.80 2.0 22.5 25.0 27.5 29.5
...
9.9 21.5 29.7 37.4 41.0
..
2720 2710 2625
400
I
H
...
..
2620
O /
I
OH
fbb
CnNg-air mixtures
/
-5i3
Vol. 64
....
.... .... ....
.... ....
.... ....
100 x (atm. of C2Nd or the E ( ' ~ ~ 2 ) = (atm. of c ~ N ~ ) (atm. of air) ratio: (CzN2)/(02)was constant for the series. (H2) = 100 X (atrn. of Hs) (atm. of Hz) (atm. of C2N2) (atm. of air)'
+
+
*
+
They were calculated upon the assumption that the following equilibria were satisfied in addition to those postulated for reactions 5 to 8 CO
+ HzO
COz
H2
2H
HzO _IH
+ HI
+ OH
(10) (11)
TABLE I1 BURNINGVELOCITIES AND EQUILIBRIUM CONCENTRATIONS OF SPECIESFOR FLAMES CONTAINING D, Ur em./ (CZNI)~ sec. 1
Dab
Equilibrium ooncn., atm. X IO4 D DaO Dt
OD
2.24 5.90 28.0 0.43 16.6 14.7 1.97 34.8 15.1 151.0 23.3 2.90 41.4 19.1 228.0 4.99 20.7 1.09 19.9 16.7 0.42 13.0 41.0 2.02 28.0 .80 25.7 113.0 2.39 46.6 1.90 37.1 186.0 2.72 59.6 2.95 100 X (atm. of CZNZ) or the (CzNz) = (atm. of C2N2) (atm. of air) ratio: (C2N2)/(O1)was constant for the series. (H2) = 100 X (atm. of Hz) (atrn. of H2) (atm. of C2N2) (atm. of air)' 10
15.1 27.3 32.9 15.4 12.8 21.1 21.2
+
+
+
KINETICS OF COMRUSTION O F CYANOGEN
1895
7--__I_.
500
LOO
I soa
.a1
I
P'
/ -
.at
I
.0 3 ,
I i
.04
J
9-
I I
I
2.0 3.0 4.0 Atm. x 10-2 between UP and equilibrium concentrations of OH, OD, H20 and D20, in the flame front of CrN2-air mixtures. Definition of (CZNZ) given in Table I note (a).
1.0
Fig. 3.--Kelation
It was assumed, also, that the addition of H2 (or D2) t o these mixtures in the quantities used in these experiments did not change their flame temperature significantly from that of the dry mixtures. This assumption was checked for a 10% cyanogen-air mixture t o which 3% of hydrogen had been added. The calculated flame temperature differed by less than 0.5yo from that of undiluted mixture. For the case of deuterium-bearing mixtures, the appropriate equilibrium constants [reactions 10 to 121 were corrected for the isotopic effect of substitution of deuterium for hydrogen. The data presented for rich mixtures, Table I, show that the effect of €I2 and D2 additions on their burning velocity is negligible, indicating that these substances have little influence on the oxidation of cyanogen to carbon monoxide. Furthermore, it was found that C02may be formed in very rich mixtures which do not contain enough oxygen to oxidize all of the cyanogen present to CO. This fact was demonstrated by igniting a sample consisting of 9.7% GN2, 8.1% 0 2 , 79.2% N2 and 301, H2 in a closed vessel and analyzing the product gases in a mass spectrograph. The burned gases contained 1.4% COz and 1.9% HCN, indicating that in the presence of H2, the oxidation of CO t o COz and C2N2to CO occurred simultaneously and competed with one another for the available oxygen. The little effect of O2 on the rate of C2Nz Hz reaction even a t 600°17makes it apparent that the products observed were the result of the flame reaction rather than any subsequent low-temperature reaction.'B
+
Thus, it appears that the influence of H2 and D2 on the burning velocity of stoichiometric and slightly rich as well as lean cyanogen mixtures may be attributed to their accelerating effect upon the oxidation of CO. These conclusions are in contrast to those of Brokaw and Pease2 who assumed that the addition of H, and Dz to mixtures of C2K2-02-argon mixtures did not affect the combustion of the CO which was formed, although, as noted above, their results follow the TanfordPeasel' theory. The accelerating influence of H2O on the burning velocity of CO-OP is well e~tablished,*J*~~~ and it has been postulated that the reaction*O CO
+ OH +COZ + H
(13)
is the predominant step in this process, for both C2N2-02and CO-O2 flames containing H2 or H20. This last postulate can be tested if the flame velocity should be proportional to the square of the OH radical concentration in the flame front2O; this relation has been found to hold for lean C2N2air flames containing H2 or DZ(Fig. 3). The decrease in the effect of Hz on the flame of rich C2N2-air mixtures can be attributed to the (16) N. C. Robertson and R. N. Pease, J. Am. Chem. Soc., 64, 1880 (1942). (17) C. Tanford and R. N. Pease, Jr.. J . Chem. Phys., 15, 861 (1947). (18) E. Fiock and C. F. Marvin, Jr., Chem. Reus., 21, 307 (1937). (19) G. A. Barskii and Ya. B. Zeldovitch, Zhur. Pis. Chem., Z6, 523 (1951). (20) K. Scheller, "Sixth Symposium on Combustion," Reinhold Publ. Corp., New York. N. Y.,1956,p. 280.
M. ANBARA N D S. GUTTMANN
1896
decrease in the concentration of H atoms in the flame front by the reactions (a) CzNz
Yol. 64
and
+ H -+ HCN + CN, (b) H + CN +HCN
which are similar to the effect found in halogenhydrogen reactions.21 The decrease in H atom concentration results in a decrease in the OH concentration, and subsequently in the decrease of the rate of reaction 13 and the flame velocity. The effect of halogens2*in reducing the flame velocity of wet CO-02 mixtures has already been observed. If the reaction between the OH radical and CO controls the flame propagation in moist CO-Oz mixtures, a difference in effect between hydrogen and deuterium additions may be expected in view of the difference in reactivity between the OH and OD radicals. The ratio of the reaction rate constants for OH and OD may be calculated from an expression derived by Biegelei~en~~ for the effect of isotope substitution on the rate of reaction. His theoretical relation for the ratio of the reaction rates i.
in which the indices 1 and 2 refer to the hydrogen and deuterium isotopes, respectively, to the reactants, and * t o the activated complex. K1*/Kzc 1 the ratio of the transmission coefficients effective mass of the activated complex along ,1.I the reaction coordinate (21) G . Hadman, H. K. Thompson and C. N. Hinshelwood, Proc. Roy. SOC.(London), 8137, 98 (1932). (22) E. Sterling and R. Arthur, “Third Symposium on Combustion, Flame, Explosion Phenomena,” The Williams & Wilkins Co., Baltimore, Md., 1949, p. 476. (23) J. Bigeleieen, Til18 JOURNAL, 66, 823 (1952).
In expression 1.5, S1/Szis the ratio of the symmetry numbers, and Ui = h c w i / k T , wi being the vibration frequency in cm. -l of the appropriate normal mode. The activated complex in the reaction between CO and OH was assumed to have the form [CO-0-HI. Values for the vibration frequency for OH and OD in the activated complex were taken as those of the corresponding groups in formic acid (3570 and 2666 cm.-l for OH and OD, respectivelyz4),yielding a value for f * of 1.07. The ratio of the partition functions of the OH and OD radicals was calculated to be 1.02 for vibration frequencies equal to 3735.21 and 2720.9 cm.-l for the respective species.25 The ratios of the symmetry numbers and the partition function for GO were both assumed to be unity. The introduction of these quantities into equation 14 gave a value for ~ O & O D = 1.33. In accordance with the square-root relation rate and burning velocity the ratio of the flame speeds of hydrogen to deuterium-containing mixtures may be expected t o equal 1.15. This ratio was observed for a mixture of 10% C2Nzplus 3% H2 or D Pand air. Acknowledgment.-The authors wish to express their appreciation to Dr. L. A. Wood for his helpful criticisms of this paper and to Dr. P. C. Colodnj7 for aid with the calculations. (24) G . Herzberg, “Infrared and Raman Spectra of Poly-atomic Molecules,” D. Van Nostrand Co., New York, K Y . , 1945, p . 321. (25) G . Hersberg, “Spectra of Diatomic Molecules,” D. Van Nostrand Co., New York, N. y., 1950, p. 560.
THE ISOTOPIC EXCHBNGE OF FLUOROBORIC ACID WITH HYDROFLUORIC ACID BY M. ANBARAND S. GUTTMAXN Isotope Department, WeizmannInstitute of Science, Rehoooth, Israel Received May S I , 1960
The rate of isotopic exchange of fluorine between fluoroboric and hydrofluoric acids has been investigated. The rate of exchange R = 4.5 X 104 e--24.7WlRT [BFI-) [Hf]. 1. mole-’ set.-'. The exchange was found to proceed oia HBF4 Ft H F HBF,OH followed by rapid isotopic equilibration between BF30H- and HF. The mechanism of exBF,, BF3 H,O change was found identical with the mechanism of hydrolysis in acid medium. The non-acid hydrolysis of BF4- proceedP by a S N 1 mechanism with a rate constant k = 8 X lo6 e-15J001RTsec.-l.
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The chemistry of fluoroboric acid HBF4 has been extensively studied by Ryss, et aL,l and by WamserZJ who have determined the equilibrium constants for the formation of HBF4, HBF30H, HBF2(OH)zas well as the rates of formation and hydrolysis of HBF4 at room temperature. Wamser has pointed out that the rate of HBF, formation is affected by acidity though he did not present a rate law including hydrogen ion concentration. The purpose of this study was to investigate the rate of (1) I. ( 2 . Ryss, M. M. Slutskaya and S D Palevskaya. Dokl. S.S.S.R., 62, 417 (1946); 67, 689 (1947); Zhur. Obshchei KhLm., 19, 1827, 1838 (1949); 26, 19 (1955). 12) C . A. Wamser, J. Ana. Chem. Sac., 70, 1209 (1948). (3) C . A, Wamser. ibid., 73,409 (1951).
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isotopic exchange of fluorine between fluoroboric and hydrofluoric acids over a range of hydrogen ion concentration and to compare it with the rates of formation and hydrolysis of fluoroboric acid over a similar range of acidity. Quantitative data on the rates of exchange and hydrolysis of fluoroborates are of importance in applying KBF418as a tracer in biological systems.4 Experimental A. Materials.-Potassium fluoroborate commercially available was three times recrystallized from water. Technical sodium fluorohorate was first purified from insoluble (4) M. Anbar, 9. Guttmann and Z. Lewitus. Endocrinolopy. 66, 888 (1960),
