1622
J. Phys. Chem. 1981, 85, 1622-1624
to a relatively unstable Fe(C0)4 (high AHf) only if the reverse recombinationreaction has no significant activation energy, Le., if there is no large steric and electronic reorganization energy. Relaxation of the Fe(C0)4fragment during the bond break may contribute little energy, since calculations5 indicate the CZugeometry of singlet Fe(C0)4 and the C3"geometry likely in the Fe(C0)6 dissociation transition state lie very close in energy. Matrix experimen@ report that the ground state of Fe(C0I4is high spin (triplet), but the bond cleavage should produce a singlet. Irradiation at 1880 cm-l, and particularly at 9000-13000 cm-l, isomerizes triplet Fe(C0)4and promotes the recombination reaction,l' suggesting a reorganization energy less
than 29 kcal and possibly less than 5 kcal. The possibility of a significant electronic reorganization energy limits any thermodynamic conclusions to AHf(Fe(CO)J I -99 kcal/mol, although the important kinetic value for the first bond cleavage of 48 kcal/mol is not affected.
Acknowledgment. This work was supported, in part, by the National Science Foundation, Grant CHE-7923569. (11)Davies, B.; McNeish, A.; Poliakoff, M.; Turner, J. J. J. Am. Chem. SOC.1977,99, 7573. Barton, J. J.; Grinton, R.; Thomson, A. J.; Davies, B.: Poliakoff. M. J. Chem. SOC..Chem. Commun. 1977. 841. Davies. B.: McNeish, A.; Poliakoff, M.; Tranquille, M.; Turner, J. J. Chem. Phys: Lett. 1978, 52, 477.
Direct Observation of the Equilibrium between Allyl Radicals, O p , and Allylperoxy Radicals Rennie P. Ruiz, Kyle D. Bayes," Department of Chemistry, University of California, Los Angeles, California 90024
Martyn T. Macpherson, and Michael J. Pllling Physical Chemistry Laboratory, Oxford University, Oxford OX 1 302,United Kingdom (Received: March 17, 198 1; In Final Form: April 29, 1981)
Allyl radicals have been formed in low concentrations in the gas phase and detected with a photoionization mass spectrometer. With 0 2 also present, the form of the allyl decay suggests that an equilibrium is established between C3H5and C3H50p The relative amplitudes of the signals of free allyl and total allyl, as obtained from an analysis of the decay data, are used to calculate the equilibrium constant. Measurements on the rate of approach to equilibrium give both the forward and reverse rate constants and the ratio k l / k l gives an equilibrium constant in good agreement with that determined from amplitude measurements. Use of the equilibrium constant together with an estimated ASo for the reaction yields a C3H5-02bond energy of 17.2 f 1.0 kcal/mol. Reactions of hydrocarbon radicals with O2 are very common in combustion and air pollution chemistry.lI2 At 300 K the reaction of radical R with O2 is thought to form the peroxy radical, R02. Since the carbon-oxygen bond in R02 is weak, the ROz molecule becomes unstable toward decomposition at high temperatures. This transition from stable to unstable R 0 2 has been involked as the cause of the changeover from cool flame combustion to high-temperature cracking comb~stion.~Benson has estimated these bond energies, but they have never been measured dire~tly.~ We have been able to follow the reaction of the allyl radical with 02, reaction 1, and to observe the equilibrium
between R and ROz in the gas phase. The allyl radicals were formed by flash photolyzing 1,5-hexadiene4at 193 nm using an ArF eximer laser. The radical concentration was followed as a function of time by using a photoionization mass spectrometer, as described previ~usly.~ When using the xenon resonance line at 147 nm (8.4 eV) only the allyl (1) M. F. R. Mulcahy, "Gas Kinetics", Wiley, New York, 1973. (2) K. L. Demerjian, J. A. Kerr, and J. G. Calvert, Adu. Enuiron. Sci. Technol., 4, 1 (19j4). (3) S. W. Benson, J. Am. Chem. SOC.,87, 972 (1965). (4) C. L. Currie and D. A. Ramsay, J. Chem. Phys., 45, 488 (1966). ( 5 ) E. A. Ogryzlo, R. Paltenghi, and K. D. Bayes, Znt.J. Chem. Kinet., in press. 0022-3654/81/2085-1622$01.25/0
radical contributed to the signal at m l e 41; at room temperature and with O2 present the m / e 41 signal decayed completely to the background count rate, indicating no contribution from the allylperoxy radical or from the parent 1,Bhexadiene. The allyl radical concentrations were kept low, typically l o l l ~ m - in ~ order , to simplify the kinetics by avoiding radical-radical reactions. In the absence of 02,the allyl radical signal decayed slowly with a rate equal to the rate of pumpout of the cell, approximately 10 s-l. This pumpout rate is obtained by dividing the flow rate of the gas in cms s-l at the pressure and temperature in the reaction vessel by the cell volume (52 cm3). Since the observed decay rate is equal to that calculated from the flow rate, other radical loss processes, such as reaction on the cell walls or radical-radical reactions, are not significant. In the presence of oxygen the behavior is more complex. Figure 1 shows signal decays for three different temperatures. At room temperature and with 11.5 mtorr of O2 present (Figure la), the allyl signal decays exponentially, as expected for pseudo-first-order kinetics. The rate of this exponential decay at room temperature can be increased or decreased by increasing or decreasing the O2 concentration. At 94 "C (Figure lb), the signal shows a rapid initial decay followed by a slower decay at the pumpout rate. At a temperature of 119 "C (Figure IC),the decay reverts to first order and the decay constant now corresponds to the pumpout rate, i.e., oxygen has little effect on the decay of the allyl radical. This behavior is 0 1981 American Chemical Society
The Journal of
Letters
TABLE I: Parameters Resulting from Fitting the Data to Eq VI' [O,]/mtorr T/"C A,/s-' A2/s-' B/s-' 14.64 21.96 24.90 4.10 9.70 19.46 27.44 9.08 5.70 6.43
74.2 74.5 75.1 75.2 74.7 75.5 75.6 76.4 76.2 75.3
139 i 17 138 f 1 5 184 i. 1 8 103 * 11 72.9 t. 5.2 52.7 f 6.0 1 2 1 + 14 85 i. 1 9 73.7 t 5.6 28.1 2 4.4
55.7 f 7.5 41.2 f 2.6 4 4 . 2 f 2.8 144 f 11 41.9 f 3.3 23.0 f 1.8 28.4 i. 2.5 47.9 f 9.5 52.6 t 4 . 1 24.8 i 2.9
28 24 7 11 21 14 22 26 42 14
Physical Chemistry, Vol. 85, No. 12, 1981 1623
k/s-' 86 -t 146 f 139 i 53 f 90 f 96 f 180i 65i 58i 85t
k,/s-'
18 20 16 10 12 19 25 22 9 24
&,/lo3
10.4 f 3.0 10.0 f 2.0 6.7 i. 1.9 9.8 t 1 . 2 11.5 f 1.7 8.1 f 2.9 13.5 f 2.3 11.1 f 3.1 8.5 f 1.9 12.9 * 2.1
atm"
129 f 27 116 f 1 8 127 i. 1 9 133 f 22 136 f 20 9Of 1 5 1 1 8 f 21 149 f 47 1 8 7 i 28 134 f 29
a All runs were at a total pressure of 2.8 torr with He as the carrier gas. The l,&hexadiene concentration was 2.8 cm-j and the laser intensity was approximately 1 mJ per pulse. The error limits represent one standard deviation.
X
interpreted as follows. Initially, the laser flash prepares only allyl radicals. At room temperature the equilibrium for (1) is well to the right, so that allyl reacts irreversibly with O2 to form the allylperoxy radical, which is not detected by the mass spectrometer, and so the signal decays monotonically. At 94 " C , as allyl reacts with O2 the allylperoxy radical concentration increases until its rate of decomposition back to allyl + O2just balances the forward rate. Thereafter the equilibrium mixture is slowly pumped out of the cell; since the O2concentration remains constant during this pumpout (the incoming gas contains O2but no allyl radicals), the ratio of allyl peroxy:allyl remains constant and the loss of signal just follows the cell pumpout rate. At high temperatures, kl>> k1[02]and very little net reaction with O2 occurs. The rate law for the allyl radicals can be written as follows, where R represents the allyl radical and R 0 2 the allylperoxy radical: (1) d[Rl/dt = -k1[Rl[021 + k-1[ROz1 - kp[Rl The last term represents the rate of cell pumpout. Radical-radical reactions have been neglected. A similar equation can be written for R02: d[ROJ/dt = ki[R][02] - k-l[ROzl - kp[R021 (11) If eq I and I1 are added together d([Rl + [ROzl)/dt = -kp([Rl
TIME + [ROzl)
Equation I11 has the simple solution: [R] + [RO,] = Ro exp(-k,t)
(111) (IV)
where Ro is the total initial allyl radical concentration formed by the laser flash. Substituting eq IV back into eq I and solving gives
The observed signal at m l e 41 is the sum of two terms, one proportional to the allyl radical concentration and the other a background count rate represented by B: signal = Al exp(-kt) A2 exp(-k,t) B (VI)
+
+
where
+ k-1 + k,
(VII)
= ~l[OZl/~-l
(VIII)
k = k,[0,] -%/A2
The experimental data have been fit to eq VI by using the c w r r least-squares program6to find values for Al, A2,B, k, and k,. The least-squares parameters for a variety of (6) P. R. Bevington, "Data Reduction and Error Analysis for the Physical Sciences", McGraw-Hill, New York, 1969.
(MSEC)
Flgure 1. Allyl radical signals as a function of time for three different conditions: (a) 23 OC with 11.5 mtorr of O2present; (b) 94 O C with 47.3 mtorr of O2present; (c) 119 O C with 164 mtorr of O2present. All runs used approximately 10 mtorr of 1,5-hexadiene and enough helium to give a total pressure of 2.8 torr. A xenon resonance lamp was used to photoionize the allyl radicals.
runs at 75 f 1 " C are listed in Table I. There are two different ways of determining the equilibrium constant for reaction 1 using the equations and data given above. Once values for Al and A2 are determined, the equilibrium constant can be calculated from relation VIII: K e g = Al/(AZ[OZI) (IX) Thus each experiment in which a double exponential is required to fit the data yields a value for the equilibrium constant. Values for Kw calculated according to eq IX are given in the last column in Table I along with their estimated standard deviations, determined from the standard deviations of Al and Az and the estimated uncertainty in O2 concentration, which was approximately 10%. As can be seen, the resulting Keqvalues are reasonably constant. The weighted average of the values in the last column of Table I is K,, = (132 f 14) X lo3 atm-l, where the error limits represent 90% confidence limits for the average using the Student's t method. The rate of approach to the equilibrium state can also be used to calculate the equilibrium constant. According
J. Phys. Chem. 1981, 85,1624-1626
1624
2oc
7 100 s.
0 0
10.0
[02]
20.0
30.0
(mtorr)
Flgure 2. Observed values of kas a function of the O2partial pressure. These values are for 75 f 1 O C , as reported in Table I.
to eq VII, if k is plotted against the O2 concentration, a straight line should result with slope kl and intercept k-l k,. The values of k in Table I have been plotted in this manner in Figure 2. Although there is considerable scatter in the data, the points are consistent with a linear relationship. A weighted linear least-squares treatment gives kl = (4.38 f 0.88) mt0rr-ls-l and k-l = (26.0 f 9.6) s-l, where error limits are again 90% confidence limits. The ratio of these two values gives another value for the equilibrium constant, K,, = kl/k-, = (128 f 54) X lo3
+
atm-l, which agrees well with the average of values determined by using eq IX. The more precise value, (132 f 14) X lo3 atm-’, will be used as the best estimate of the equilibrium constant at an average temperature of 348.4 K. This equilibrium constant for reaction 1 can be used to estimate the bond energy for the allyl peroxy radical. The AGO for reaction 1is calculated to be -8160 f 130 cal/mol. Reasonable estimates for the entropies of R and ROz have been taken from B e n ~ o n ; by ~ J correcting for the temperature change from 300 to 348 K, the for reaction 1is estimated to be -26.4 eu. From these two values one can calculate AHo= = -17.4 kcal/mol, with an uncertainty of approximately f l . O kcal/mol due mainly to the uncertainty in the estimated ASo. Using Benson’s estimated C, values to correct to 300 K gives AH0300= -17.2 kcal/ mol. This calculated bond energy for the allylperoxy radical is only sightly larger than the estimate of 15 kcal/mol made by B e n ~ o n . ~ By measuring the equilibrium constant for reaction 1 over a range of temperatures, it should be possible to calculate ASo and AHo directly, thus reducing the uncertainty in the bond energy. Such experiments are currently in progress. Acknowledgment. Support for this work was provided by the National Science Foundation under Grant CHE7823867 and by a NATO Research Grant, No. 1849. (7) S. W. Benson, “Thermochemical Kinetics”, 2nd ed, Wiley, New York, 1976.
Proton Affinity of the Gaseous Azide Ion. The N-H Bond Dissociation Energy in HN3 Mark J. Pellerite, Robert L. Jackson,+ and John I. Brauman” Department of Chemistry, Stanford University, Stanford, California 94305 (Received: March 27, 198 1)
Three different sources of azide ion have been used in conjunction with ion cyclotron resonance spectrometry to measure the gas-phase proton affinity of azide ion, PA(N3-). The result, PA(N3-) = 344 f 2 kcal/mol, is in significant disagreement with that calculated by use of literature data obtained via indirect methods. Reliability of our value is confirmed by the consistency of results obtained from the different azide sources. Our experiments also allow other thermochemical parameters to be determined: iVI,0(N3-(g))= 48 f 2 kcal/mol, AHfo(N3(g)) = 112 f 5 kcal/mol, and Do(H-N3) = 92 f 5 kcal/mol.
Introduction Organic and inorganic azides have been the subject of extensive investigation for many years from the standpoint of both chemical reactivity and thermodynamic properhas also ties.l The simplest azide, hydrazoic acid (”,), been well studied and characterized.2 However, owing to the thermal instability of HN3, direct study of its gas-phase thermochemistry is difficult. In the past, indirect metho d ~such ~ ~as ,Born-Haber ~ cycles have been used in determinations of such quantities as AHfo(N3-(g)) and Do(H-N3). The value of AHHfO(N3-(g))is currently the subject of some c o n t r o v e r ~ yand , ~ ~widely ~ different values of Do(H-N3) can be found in the literature.lG5 We present here results of some experiments which allow direct determination of these quantities, and thus more accurate and complete characterization of the thermochemical t Corporate Research Center, Allied Chemical Corporation, Morristown, N J 07960.
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properties of gaseous HN,. Our initial work in this area6 was a measurement of the electron affinity of the azide radical, EA(NJ. Here we report the proton affinity of (1)(a) Patai, S., Ed. “The Chemistry of the Azido Group”; Interscience: London, 1971. (b) Fair, H. D.; Walker, R. F., Ed. “Energetic Materials”; Plenum: New York, 1977; Vol I. (c) Evans, B. L.; Yoffe, A. D.; Gray, P. Chem. Reu. 1959,59,515. (d) Gray, P. Q.Rev. Chem. SOC. 1963, 17, 441. (2) (a) Mason, K. G. In “Mellor’s Comprehensive Treatise on Inorganic and Theoretical Chemistry”; Wiley: New York, 1967; Vol. 8, Suppl. 11, pp 1-15. (b) Jones, K. In “Comprehensive Inorganic Chemistry”; Bailar, J., et al., Ed.; Pergamon Press: Oxford, 1973; Vol. 2, pp 276-293. (3) (a) Gray, P.; Waddington, T. C. Proc. R. SOC.London, Ser. A 1956, 235, 106. (b) Gray, P.; Waddington, T. C. Ibid. 1956, 235, 481. (c) Jenkins, H. D.; Pratt, K. F. J. Phys. Chem. Solids 1977,38, 573. (4) Franklin, J. L.; Dibeler, V. H.; Reese, R. M.; Krauss, M. J. Am. Chem. SOC. 1958,80, 298. (5) (a) Clark, T. C.; Clyne, M. A. A. Trans. Faraday SOC.1970,66,877. (b) Okabe, H. “Photochemistry of Small Molecules:” Wiley-Interscience: New York, 1978; p 287. (6) Jackson, R. L.; Pellerite, M. J.; Brauman, J. I. J. Am. Chem. SOC. 1981,103,1802.
0 1981 American Chemical Society
