T H E
J O U R N A L
OF
PHYSICAL CHEMISTRY Registered i n U. S. Patent Office 0 Copyright, 1977, by t h e American Chemical Society
VOLUME 81, NUMBER 9 MAY 5, 1977
Shock Tube Decomposition of Dilute Mixtures of Nitrosyl Cyanide in Argon Ernest A. Dorko,*+ Paul H. Flynn,t U. Grlmm,t K. Scheller,t and Gerhard W. Mueller9Wright-Patterson Air Force Base, Ohio 45433 (Received May 20, 1976; Revised Manuscript Received February 14, 1977) Publication costs assisted by the Air Force Institute of Technology
The decomposition of 0.4% NCNO in argon was studied in a reflected shock wave. The temperature range of the study was 1400-1700 K and the total pressure range was 0.98-2.12 atm. Under these conditions the total gas concentration range was 0.83-1.7 x 10” mol/cm3. Kinetic measurements were made by following the decay of emission of the v1 mode of NCNO at 4.59 pm. The unimolecular rate constants of the Lindemann mechanism were obtained from the emission decay data and were converted to second-order rate constants. The Arrhenius parameters calculated by a least-squaresanalysis of the second-order rate constants are given as k = 101’.36exp(-18700/RT) cm3/mols. Calculated rate constants obtained by the use of the RRKM integral were in good agreement with experimentalresults. The evidence strongly suggests that the reaction is occurring at or near its low pressure limit.
Introduction A study to determine the rate of breakage of the center C-N bond of nitrosyl cyanide (NCNO) has been undertaken. The reaction is postulated to occur as NCNO + Ar -+ .CN + .NO+ Ar (1) The decomposition was induced by means of a shock wave traveling through a very dilute mixture of NCNO in argon. The shock tube used in the study was equipped with windows through which the infrared emission could be observed. From the observance of the decay of intensity of the emission, the kinetics of the decomposition were determined. This technique has been used successfully in the past to study similar decompositions.lp2 Previous work with NCNO has been concerned mainly with the elucidation of p h ~ s i c aand l ~ ~chemical6properties. A report has also dealt with its formation as a transient species during flash phot~lysis.~ However, no work has been done to elucidate the kinetics of decomposition of the ‘Department of Aero-MechanicalEngineering, Air Force Institute of Technology. 1: Chemistry Research Laboratory,Aerospace Research Laboratories. # Universal Energy Systems.
compound. The present report describes the analysis of decomposition under the assumption of a unimolecular decomposition according to the Lindemann’ mechanism. Experimental Section The stainless steel shock tube employed has been described previously? The NCNO was prepared and purified as described elsewhere.’ The sample used for the study was 95% pure. Major impurities were NO and NOCl. The test gas mixtures used in the shock tube were made up of 0.4% NCNO in argon (99.999% purity). During the c o m e of the experiments a number of explosions occurred during the purification process. In addition, it was discovered that metals catalyze the decomposition of NCNO. Therefore, using great caution, the test gas mixtures were made up in glass containers. The diluted test samples were reacted immediately after introduction into the shock tube. The use of this procedure allowed a certain number of trials to be concluded successfully so that the kinetic analysis could be performed. Of the 30 experiments performed it was found that 14 were utilizable for the kinetic analysis. The remaining analyses were not utilizable for various reasons; Le., too high or too low a temperature, inadequate detector sensitivity, etc.
Dako et al.
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5
6
7
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Flgure 1. Typical oscilloscope trace of the IR emission at 4.59 pm. The vmical scale is 10 mvlcm and the haizcntal scale is 100 p s l m (time increases from left to right.) The reflected shock temperatwe was 1482 K and the total gas concankatbn was 1.53 X md/cm3.
Kinetic measurements were made for the reaction occurring behind the reflected shock by means of infrared emission measurements? For this purpose CaF2windows were placed in the flat wall of the shock tube 12 m m from the end flange of the driven section. Shock parameters were calculated for the specific gas mixtures from the initial shock velocity assuming frozen chemistry. Heat capacities for NCNO were obtained from the literature? The total gas concentration behind the reflected shock ranged from 8.3 X 10 ' to 1.7 X mol/cm'. The temperature range was 1403-1700 K and the total preasure range was 0.98-2.12 atm. The lense and detector systems used to detect the IFt emission from the shock tube were similar to systems described previou~ly.~.~ The band corresponding to the C-N stretch of NCNO at 4.59pm was used for the kinetic studies. An interference filter transmitting a t 4.770 pm (half-bandpass width of 0.4 pm) was placed in the beam to eliminate emissions from other species present during the reaction. The output signal from the IR detector was fed through an impedance matched preamplifier into an oscilloscope which was triggered by the heat gauge a t the last velocity station. A typical oscilloscope trace is shown in Figure 1. The trace exhibited a short induction period (up to a maximum of l(t20 ps a t the lower temperatures) followed by an exponential decay portion. The induction period in shock tube studies has been noted previouslFR,'O and the exponential decay is expected for simple, unimolecular reactions. It was not possible, using this p r e cedure, to eliminate the emission at 4.65 pm corresponding to the 9mode of cyanogen" and 80 the decomposition was followed to an equilibrium emission line on each trace. The oscillograms were reduced according to the procedure described previously.' The rate constants calculated by this procedure are designated k,.;. Total and NCNO gas concentrations were calculated at reflected shock conditions for ideal gases. The decomposition of NCNO is postulated to occur by means of an initial rupture of the central CN bond. The Lindemann mechanism for the system is
-
NCNO + M 2 NCNO* NCNO' NC. + .NO
+M
(2)
(3)
A subsequent reaction which can be reasonably postulated is" 2NC. + M C,N, + M (4) +
In addition a bimolecular mechanism 2NCNO
-
C,N,
+ 2NO
(5)
may be operational. The rate expression for the unimoleeular decomposition pathway, eq 2 and 3, is
T h s J a m a l o l R y s * r a l ~ Vd. . 81. No. 9. 1977
IO' I T'K
FW.2. A p b t o f k g ~ wl/T(K). . Theupperhrepesentsb best s h a m line fil of data taken at a total gas carmatian of 1.56 x 10.~ mol/cm3(f5%). 0 . he lower line represents the best m of data taken at 0.86 X loJ d / m 3(&5%). 0.The separaban between lines is 0.232 b g mb. Ms separatbn conespondr to an a r m power dependence of 0.90. The units of b a r e s-'.
where k., kd. and k. are the rate constants for activation, deactivation, and decomposition, respectively, and [MI and [NCNO] represent total and nitrosyl cyanide concentrations, respectively, in mol/cm'. The straight lines obtained by the reduction of oscillograms (vide supra) provided evidence' that at a given constant [MI there is a first-order dependence of the rate on [NCNO]. Due to the instability of NCNO its concentration had to be kept quite low in the test gas mixtures so that the concentration range could not be varied enough to completely establish the zero order dependence of k,i on [NCNO]. However, a t the low percentage of NCNO (0.4%) in the test gas mixtures and based on prior 'experiencez9it is felt that there is no interference from the bimolecular decomposition mechanism in the present case. Calculations of the rate of the formation of cyanogen according to eq 5 based on the rate constant reported by Tsang. Bauer, and Cowperthwaite" indicate that for the first 25% of the unimolecular reaction the concentration of cyanogen is not appreciable. However, at the end of the reaction period this is not the case and the cyanogen emission prevents the emission curve from returning to the base line. (See Figure 1.) The concentration dependence of kh on [MI can be Been by a comparison of the data shown in Figure 2. In the figure (an Arrhenius plot of k,J are shown the best straight line fits of data sets obtained under conditions of constant [MI. The ratio of total gas concentrations for the data sets is 1.81. The separation between the two lines correspondsto a factor of 1.71. From a comparison of these two numbers the decomposition rate is shown to have power dependence on [MI of 0.90. From these results, then, it is concluded that kWi is independent of [NCNO] and has an approximate first-order dependence on [MI. Under the assumption of the Lindemann mechanism the near first-order power dependence on [MI indicates that the molecule is decomposing near its second-order limit. The rate constants were converted into second-order constants (kw dr) by dividing each by [MI. The reaulting
Shock Tube Decomposition of Nitrosyl Cyanide In Argon
813
TABLE 11: Length of the C-N Bond in Compounds Containing the Cyano Group Bonded to Nitrogen
TABLE I: Experimental Rate Constants Temp, K 1417 1423 1453 1465 1468 1482 1555 1561 1562 1583 1601 1616 1630 1731
ku,,i,
I
k2nd order
t3-l
6.31 x 1.83 x 9.83 x 4.82 x 3.34 x 6-72 x 4.28 x 7.10 x 8.34 x 8.18 x 5.56 x 6.81 x 4.96 x 15.51 X
lo4
104 10" I
Compd N,-CN OCN-CN ON-CN F,N-CN
4.22 x 109 2.19 x 109 6.75 x 109 3.30 x 109 2.11 x 109 4.39 x 109 2.57 x 109 4.50 x 109 5.39 x 109 5.36 x 109 6.46 x 109 7.87 x 109 5.52 x 109 16.99 x lo9
104 104 104 104 104 104 104 104 104 104 104
I
E,-Eo=
I
10.0
%
U
9.8
U c N
X
cn
0
9.6
J
9.4
""\
9.2
I
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5.0
6.0
7.0
8.0
IO' /T°K
Figure 3. Arrhenius plot of kZndorder for the pressure range 1-2 The units of the rate constant are cm3/mols.
atm.
rate constants are presented in Table I and displayed in Figure 3. The Arrhenius parameters were obtained by means of a least-squares analysis of the rate constants as - 1012.36hO.54
k2nd order -
e-18700+40OO/RTc m 3 / m o l s
Ref 17 18 4 19
kcal/mol. This value is reported as an upper limit for the bond strength since it is based on an electron impact method. If this value is taken as a reasonable estimate of the activation energy in the high pressure limit then eq 6 can be used in order to estimate a reasonable value for the activation energy in the low pressure limit.
10.2
b
C-N bond length, A 1.389 1.283 1.401 1.39
(7)
Since significant scatter is evident in the data, and since only one data point could be obtained at the high temperature end of the analysis, an extensive error analysis was performed in order to set confidence limits on the Arrhenius parameters reported. The standard deviation in the rate constants is 1.5 X 10'. Combining this error with an estimate of the uncertainty in temperature measurements in the shock tube of 25 K the total error in the activation energy is estimated by the method of Benson and O'Neal13 to be f 4 kcal/mol. The error in log A is f0.54 log units. The correlation coefficient14for the Arrhenius plot was calculated to be -0.659. This correlation is considered substantial or marked. Also, it is negative due to the inverse correlation between log k2nd order and ? / T * The activation energy for the reaction is quite low. It is instructive, at this point, to make a comparison of this value with the central C-N bond strength value reported previously6 especially in light of the large scatter in the data points. Gowenlock et al.6 report a value of 28.8 f 2.5
( s - 1)RT
(8)
Equation 8 is obtained from the simple HinshelwoodLindemann theory.15 If s taken to be 4 (2/3 of the total number of normal modes) then E, - Eo = 9 kcal/mol for the temperature range included in this report. Then Eo = 20 kcal/mol. This value agrees with the experimentally determined low pressure activation energy. It is reasonable to assume that under the present experimental conditions (1-2 atm) the deviation from the low pressure regime i s slight. Since the present kinetic analysis supports the value for the bond strength of the C-nitroso bond in NCNO of about 29 kcal/mol, it is instructive to compare NCNO with C-nitroso compounds in general in order to better understand the structural behavior of NCNO. The central C-N bond energy of NCNO is the lowest measured energy for any organic C-nitroso compound.6 At the same time the length of the central C-N bond is one of the shortest for C-nitroso compounds. These facts imply that the behavior of NCNO is in direct conflict to the general principle that, as a chemical bond decreases in length, the energy needed for bond dissociation increases. Gowenlock's explanation for the low bond energy is that the governing factor for this value in NCNO is the reorganization energy of the liberated nitric oxide.6 Indeed it is known that the N=O bond length in NCNO (1.228 A)4 is uite long compared to the bond length in free NO (1.15 .16 If the transition state for the reaction is taken to be one in which the central C-N bond is already weakened, then the N=O bond is expected to start shortening. However, there are other considerations which must also be taken into account. Actually, the NCNO molecule is not quite like other C-nitroso compounds in that the carbon atom in this case is part of a cyano group. Therefore, it is instructive to consider the compound as a member of a group in which the cyano group is bonded to a nitrogen atom. Table I1 gives a list of representative compounds. A glance at the table shows that in comparison to other, similar compounds the central C-N bond in NCNO is somewhat lengthened. This lengthening indicates bond weakening. In addition, a recent normal coordinate analysis5 also indicates that the central C-N bond in NCNO is slightly weaker than the C-N bond found in similar molecules. Thus, it is concluded that the experimentally determined bond strength is consistent with the qualitative assessment of the character of the central C-N bond of NCNO.
8,
Numerical Analysis In order to further test the reasonableness of the values obtained under the assumption of a unimolecular decomposition, and to extend the useable range of the data, calculations of the rate constants were performed by use The Journal of Physical Chemistry, Vol. 81, No. 9 , 1977
814
of the RRKM integral with the method developed by B ~ n k e r . ~The , ~ collisional ~ ’ ~ ~ frequency, to, was calculated as a product of the collision number, 2 (obtained by the kinetic gas theory with no repulsive potential), and the total gas concentration, [MI. The collisions were assumed between NCNO and Ar. The cross-sectional radius for collision was taken to be 3.23 A. The final expression for Z was Z = 5.957 x 10’2T’’2cm3/mol s (9) The expression used to calculate kE,the rate constant for decomposition, was obtained in the following way. Because the rotational levels were assumed not to change during the activation process, the ratio of the partition functions, Q;/Qr, became the ratio of the square roots of the products of the moments of inertia.15 The molecular dimensions for the ground state molecule were obtained from the literat~re.~ In the transition state, it was assumed that the reacting C-N bond length had increased to 1.601 A and that the angle measured clockwise between the C-N and N=O bonds had decreased to 90”. All other molecular parameters (including the N=O bond distance) were assumed to remain constant during reaction. Based on these assumptions, the ratio of the rotational partition functions was calculated to be 1.203. In order to determine the ratio of vibrational fundamentals, the data of Dorko and Buelow‘ for NCNO were used for the ground state. For the transition state the following assumptions were made. The vibration due to the C-N stretch became the reaction coordinate. The N=O stretch vibration was increased by 315 cm-’ and the NEC-N and C-N=O angle bend vibrations were decreased by 50 and 20 cm-l, respectively. The C=N stretch and out of plane vibrations were left unchanged. Based on these assumptions the ratio of vibrational fundamentals is 2.751 X 1013s-’. The EZ and Ez+,zero point energies of the ground state and transition state, respectively, were calculated to be 7467.6 and 6645.8 cal/mol. E,, the lower energy limit, was taken to be the experimental bond strength value, 28800 cal/mol.6 When the ratios for rotational and vibrational partition functions were multiplied together, the value was designated D. The value obtained for D was 3.31 X 1013 s-’. The classical expression developed by RRK for the energy probability term, P(E) dE, was ~ s e d . ~ ’ ~ ~ Initially, the value of [MI was calculated as P/RT. An additional factor was included in the calculation in order to take into account the fact that less than 1% of the gas collisions actually involved NCNO. A value of 0.0013 for this factor eventually gave the best fit between the computed values and the experimental data. The final nondimensionalized integral expression used to calculate kunihas been given elsewhere.’ Solutions for the values of kuniwere obtained by means of a numerical integration using program KUNI’~written for a CDC 6600 computer. A parametric approach was utilized during solution in order to produce the best fit of the calculated curves to the data, The value of s was varied from 6 (the value required by the RRKM approach) to 2. The closest fit occurred when s was taken as 4. Representative plots of log kuni vs. log P at various temperatures based on the results of these calculations are shown in Figure 4. For comparison, experimental data points are also shown in the figure. It is evident that the calculated rate constanta
The Journal of Physlcal Chemlstry, Vol. 8 1 , No. 9 , 1977
Dorko et al.
4
0
0.25
030
0.75
1.00
Log P (ATM)
Figure 4. Plot of log k, vs. log P(atm). The lines represent the values calculated by use of the RRKM integral at 1470 (A), 1560 (B), and 1615 K (C). The data points are the experimentally determined values at or near (kl.O%) 1470 (A),1560 (0), and 1615 K (0).
are of the right order of magnitude and give a reasonable estimate of the experimental rate constants. It is concluded that the RRKM integral developed in the present case is a good one for extending the range of the experimental results up to about 10 atm.
Acknowledgment. One of us (G.W.M.) wishes to acknowledge sponsorship of this research by the Aeropropulsion Laboratory, Air Force Systems Command, United States Air Force under Contract No. F33615-74-C-4006. References and Notes E. A. Dorko, U. Grlmm, K. Scheller, and 0. W. Mueller, J. phys. Chem.,
79, 1625 (1975). E. A. Dorko, U. Grimm, K. Scheller, and G. W. Mueller, J. Chem. Phys., 63,3596 (1975). P. Horsewood and G. W. Kirby, Chem. Commun., 1139 (1971). R. Dickinson, G. W. Kirby, J. G. Sweeny, and J. K. Tyler, Chem. Commun., 241 (1973). E. A. Dorko and L, Buelow. J . Chem. Phw.. 62. 1869 (1975). B. G.Gowenlock, C. A. F. Johnson, C. M. Keary, and J. Pfab, J.‘Chem. Soc., Perkin Trans. 2, 351 (1975). N. Basco and R. G. W. Norrish, Proc. R. SOC.London, Ser. A , 283,
291 (1965). F. A. Lindemann, Trans. Faraday Soc., 17,598 (1922). E. A. Dorko, R. W. Crossley, U. Grimm, G. W. Mueller, and K. Scheller J . Phys. Chem., 77, 143 (1973). J. P. Appleton, M. Steinberg, and D. J. Liguarnik, J. Chem. Phys.,
52, 2205 (1970).
G.Herzberg, “Molecular Spectra and Molecular Structure”, Vol. 2, Van Nostrand-Reinhold, New York, N.Y., 1945,p 294. W. Tsang, S.H. Bauer, and M. Cowperthwaite, J. Chem. Phys., 37,
1768 (1962).
S.W. Benson and H. E. O‘Neal, Natl. Stand. Ref. Data Ser., Natl. Bur. Stand., No. 21 (1970). I.G. Sokolnikoff and R. M. Redheffer, “Mathematlcs of Physics and Modern Engineering”, McGraw-Hill. New York, N.Y., 1958,p 666. R. E. Weston, Jr., and H. A. Schwarz in “Chemical Kinetics”, Prentlce Hall, Englewood Cliffs, N.J., 1972, Chapter 5. L. Pauling, “The Nature of the Chemical Bond”, Wiley, New York, N.Y., 1965. H. F. Shurvell and D. W. Hyslop, J . Chem. Phys., 52,881 (1970). W. H. Hocking and M. C. L. Gerry, J. Chem. Soc., Chem. Commun.,
47 (1973).
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P. L. Lee, K. Cahn, and R. H. Schwendetnan, Inorg. Chem. 11, 1920
11972). \
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D. L. Bunker in “Theory of Elementary Gas Reaction Rates”, Pergamon Press, Oxford, 1966,Chapter 3. G. W. Mueller and E. A. Dorko, Program KWI, QCPE No. 282,Quantum Chemistry Program Exchange, Chemistry Department, Indlana University, Bloomington, Ind.
