NOTES
1429
for such oxidation and, also frequently, isotopically labeled acetic acid or acetate is the isolate under study. Earlier investigations3v4 have demonstrated that there is an appreciable kinetic isotope effect associated with the wet oxidation of acetic acid (as acetate) labeled with C14; the results, however, are discrepant. Evans and Huston3 do not indicate the degree or increment of decomposition involved in their experiments (in which specific activity measurements were made on “two consecutive fractions of roughly the same weight”), but Eyring and Cagle5 estimated their results to be equivalent to a 5% isotope effect in the oxidation of the carboxyl-labeled acetate. In the later experiment^,^ an effect of 1.7 f 0.5% was observed in the oxidation of carboxyl-labeled acetate, but a 4.0 f 0.6% effect in that of the methyl-labeled compound was observed. Because of the intrinsically more accurate measurements possible of CI3 isotope effects compared with those of CI4,it was of interest to attempt to resolve the discrepancy described above by investigations of the oxidation of acetate containing CI3 a t the natural abundance level.
From the three experiments we obtain k l / k z = 1.0098 f 0.0030. Combination with the assumed value for (k3/kZ) yields k l / k 3 = 1.0221 f 0.005. Though the value of kl/kr is not independent of the earlier CI4 results, it is, nevertheless, of interest to compare these isotopic rate constant ratios for the C’3 effects with those calculated directly from the CI4 data. We have ( k l / k 2 ) e a l c d = 1.0087 (compare with 1.0098) and ( k l / k 3 ) c a l c d = 1.021 (compare with 1.0221). The present results are thus consistent with the earlier findings of Zlotowski and Zielinski for the wet oxidation of acetic acid.
Experimental
(1) Department of Nuclear Poland.
AcknowZedgment. The author expresses his thanks to Professor Robert N. Clayton for making possible his stay at the Enrico Fermi Institute and for assistance in the preparation of this note. Also, the author expresses appreciation to Professor Peter E. Yankwich, the referee of this note, for introducing substantial changes which made the whole note clearer and more systematic. The research was supported in part by a grant from the National Science Foundation (NSF-GP-2019). Chemistry, University of Warsaw,
Samples of acetate mixed with excess solid sodium (2) D. D. Van Slyke and J. Folch, J . Biol. Chem., 136, 509 (1940). hydroxide were pyrolyzed quantitatively in copper (3) E.A. Evans and J. L. Huston, J . Chem. Phya., 19, 1214 (1951). vessels to methane and carbonate-the former being (4) I. Zlotowski and M. Zielinski, Nukleonika, 4, 5 (1959). (5) H. Eyring and F. W. Cagle, J. Phys. Chem., 56, 889 (1952). oxidized to carbon dioxide over copper oxide, the latter being converted to carbon dioxide with phosphoric acid. Isotope ratio measurements on these samples permitted evaluation of the ratio (C13HaC1zOOH/C12H2C1300H) Magnetic Resonance of the Triplet State of = Q. Qowas found to be 1.0074for the acetate used, and the average of the methane-carbon and carboxyl-carOriented Pyrene Moleculesla bon isotope ratios was identical with that obtained for carbon dioxide resulting from complete combustion by 0. Hayes Griffithlb (over copper oxide) of the original acetate, Ro. The partial oxidation experiments were carried out Gates and Crellin Laboratories of Chemistry, lo California Institute of Technology, Paaadena, California (Received November 2, 1964) using the Van Slyke-Folch procedure. Values of Qf and R , (the ratio indicated above and the ratio Cl3O2/ CI2O2at time 1 or degree of reaction f) were obtained Bree and Vilkos2 have recently completed an optical in each of three runs. polarization study of the lower singlet states of pyrene Where kl is the specific rate constant for the oxidain a fluorene matrix a t 77°K. The crystal structure of tion of C12H3C1200H,k2 that for C12HaC1300H,and fluorene is orthorhombic, the space group is Pnam, k3 that for Cl3H3ClZ00H,it can be shown that and there are four molecules per unit cell.3 This crystal is a convenient matrix because the long axes of the fluorene molecules are all parallel to the crystalline c axis. We report here the observation of electron Use of this formula with the present data requires a value for k3/k2; this we take from the CI4 results of Zlotowski and Zielinski to be 0.9879 f 0.004, assuming that the C14 kinetic isotope effect would be twice the C13 effect.
(1) (a) Supported by the National Science Foundation under Grant No. GP-930; (b) National Sbience Foundation Predoctoral Fellow; (c) Contribution No. 3181. (2) A. Bree and V . V. B. Vilkos, J . Chem. Phys., 40, 3125 (1964). (3) D.M.Burns and J. Iball, Proc. Roy. SOC.(London), A227, 200 (1955).
Volume 69,Number 4
April 1065
NOTES
1430
spin resonance of the lowest triplet state of pyrene in a fluorene matrix. The fluorene (C1lHlo), kindly supplied by D. E. Wood, was prepared from comniercial reagent grade fluorenone. The fluorenone was purified by column chroniatography (column : alumina ; wash : spectral quality cyclohexane) and was reduced with hydrazene h ~ d r a t e . ~ The resulting fluorene was then chroniatographed as mentioned previously and sublimed.5 The pyrene (Cl6Hl0)was prepared by zone refining (30-50 zones) commercial reagent grade pyrene. The crystals of pyrene-doped fluorene were grown from a melt initially containing 1.0 mole % of pyrene, but the actual concentrations of pyrene in the crystals were not determined.6 These crystals were found to cleave in the (001) plane, and the positions of the a, b , and c axes were determined by X-ray crystallographic techniques. The actual crystal fragments used in the e.s.r. experiments were initially oriented with a polarizing microscope and were not subjected to X-irradiation until after the e.s.r. experiments were complete. The crystals were illuminated in situ with a General Electric BH-6 Hg arc lamp, and the temperature of the sample was maintained at 100°K. throughout the experiments with a conventional nitrogen gas flow system. A Varian X-band spectrometer was used to obtain the spectra. Magnetic fields corresponding to the extrema (or near extrema) splittings were measured with :t rotating coil gaussmeter, and the remainder of the fields were measured with a Hall-eff ect probe. The e.s.r. spectra were recorded with the magnetic field, H, in the ac, bc, and ab planes of the pyrene-doped fluorene crystals. Two e.s.r. lines displaced synimetrically about g = 2.0030 were observed with H in the ac or bc planes, and the maximum splitting between these two lines occurred when H was perpendicular to the cleavage plane. In general, four lines were observed with H in the crystallographic ab plane. All of the e.s.r. lines decayed rapidly upon removal of the light source (lifetime < 1-2 sec.). Using- the method of Hutchison and R/Iangurn,'J' the g values and zero field splitting parameters of the = bH ' g ' f Dxz2 + - 'g2) were found to be gZz = 2.0033, guy = 2.0026, gLZ = 2.0033, D(Xy)/hC = *0.0806 cm.-l, D ( z ) / h c = *O.O8lo cni.-1, and E/hc = j~0.0182cni.-l. The estiinated D , and E are in the 9 *o'oo12, and f 0.0009, respectively. The h i t s of error are uncomfortably large because the e.s.r. signals were very weak, frequently being only a factor of 1.5 to 8 above the noise level. Employing these values of the parameters in the above spin-Haniiltonian arid allowing for the syliinietry properties Of the fluorene lattice, the P s i The Journal of Physical Chemistrg
tions of all observed lines can be predicted within experimental error. Therefore, it is clear that the e.s.r. signals result from one type of molecule, and this molecule occupies a substitutional site in the fluorene lattice. It remains to show that this molecule is pyrene. Single crystals of fluorene exhibited a faint blue-green phosphorescence at boiling nitrogen temperatures, and corresponding weak lines were present in the phosphorescence emission spectra of these crystals. However, under the same experimental conditions that the em-. spectra were obtained from the pyrenedoped fluorene crystals, no e.s.r. signals were observed from single crystals of fluorene, and therefore it is highly unlikely that the above e m . spectra are due to either fluorene or an impurity in fluorene. The zonerefined pyrene undoubtedly contains impurities, the most troublesonie of which is probably naphthaceneg (C,HI2). A single crystal of naphthacene-doped fluorene wafi grown from a melt containing 0.01 mole % of naphthacene, and no e.s.r. signals were observed at 100°K. in these crystals. The pyrene-doped fluorene crystals exhibited a reddish phosphorescence at low temperatures similar to the phosphorescence of pyrene in a hydrocarbon glass. The maximum of the only line observed in the 77OK. phosphorescence spectra of the pyrene-doped fluorene crystals occurred a t 16,750 60 cm.-1, which is in good agreement with the phosphorescence maximum reported for pyrene in glasses at 77OK.lo The emission lines observed in the fluorene
*
(4) J. H . Weissberger and P. H. Grantham, J . Org. Chem., 21, 1160 (1956). (5) Fluorene prepared by this procedure exhibited far lower phosphorescence intensity a t 77'K. than did zone-refined commercial reagent grade fluorene. According t o D. E. Wood (private communication), some samples of fluorene prepared by this technique (with additional zone refining in some cases) produced a negligible phosphorescence. (6) Cold traps were used during the crystal preparations to prevent possible contamination from stopcock grease, and the chemicals were melted only under reduced pressures of prepurified nitrogen gas to minimize oxidation and decomposition. (7) C. A. Hutchison, Jr., and B. W. Mangum, J . Chem. Phys., 34, 908 (1961). (8) D ( w ) is the value of D obtained along with E from the (extrema) splittings corresponding t o the molecular z and y directions, and D ( z ) is the value of D obtained using E and the (extremum) splitting corresponding to the molecular z direction. The agreement of these two values of D constitutes a partial verification of the proper choice of molecular axes. Using these values of D and E , (0' 3 E 2 ) ' / 2 = 0.0868 f 0.002. This value is in only fair agreement with the value 0.0929 cm.-1 obtained by Smaller [B. Smaller, J . Chem. Phys., 37, 393 (1963)l (and confirmed b, us) from the Am = f 2 transition of randomly oriented pyrene molecules (9) However, the zone-refined, crystalline pyrelle appeared white rather than the yellow color characteristic of small concentrations of naphthacene, ( i o ) McClure reports [D. S. McClure, J . Chem. Phys., 17,910 (1949)] that for pyrene in a rigid glass a t 77'K. the phosphorescence maximum occurs a t 16,800 cm.-l, the ratio of phosphorescence yield to fluorescence yield is 0.001, and the mean lifetime is about 0.2 sec.
+
NOTES
1431
crystal were apparently quenched in the pyrene-doped fluorene crystal. All of the above evidence supports the conclusion that the e.s.r. spectra observed in the pyrene-doped fluorene crystals arise from the (lowest) triplet state of pyrene. Further splitting of the fine-structure e.s.r lines into hyperfine lines was not observed in any of the spectra recorded,11 and, therefore, it is not possible to determine uniquely the orientations of the pyrene molecules in the fluorene lattice. However, one of the principal magnetic axes of pyrene lies approximately along the crystalline c axis (the long axis of fluorene), and the other two magnetic axes correspond to the short axis and a normal to the molecular plane of fluorene. It appears, therefore, that the molecular plane and long axis of the pyrene molecule are oriented with respect to the fluorene lattice in the same manner as the displaced fluorene molecule. If we assume this to be the case, then the molecular z, y, and x axes of pyrene would be parallel to the long axis, the short axis, and the normal to the molecular plane of the pyrene molecule, respectively. l 2
Ackno wbdgments. We are indebted to Professor Harden M. McConnell for the generous use of his laboratory facilities. We are also indebted to Dr. Richard E. Marsh for help concerning the X-ray photography, to Professor Melvin W. Hanna for helpful discussions, and to Xrs. Lelia M.Coyne for obtaining the optical spectra. (11) The lack of resolution is presumably due to the large number of protons interacting with the electron and to crystal disorder. Laue photographs disclosed that the first crystals obtained were badly disordered. The crystals used for the e.s.r. study were of much better quality but could have been sufficiently disordered to reduce resolution of the hyperfine structure. D and E for pyrene were arbitrarily chosen (12) By to have opposite signs. If D and E were chosen to have the same sign then the 2 and g axes would be interchanged. This indeterminancy affects only the relative signs of D and E and not their magnitudes. We are indebted to Dr. J. H. van der Waals for a discussion on this point.
Complexions' A n Exact High Speed Method Of
"'*
by E. W. Schlag, R. A. Sandsmark, and W. G. Valance ~
Department of Chemistry, A~orthwestern UnheTsity, Evanston. Illinois (Receitied Nonember 6 , 196.4)
There has been a substantial increase in interest in obtainirlg information about kinetic rate processes on a
molecular level. For such experiments it is necessary that one is able to define initial states as closely as possible in order to be able to discriminate between various possible theoretical models on the basis of the experimental results. One such approach has been to study the reactions of monoenergetically excited species.' One then wishes to compute a set of theoretical transition probabilities for reaction or energy transfer and then use this set to generate the appropriately predicted laboratory observable.2 If the set of transition probabilities involves any statistical factors, then one needs to know the number of states that all have a total energy between E and E dE, known simply as the density of states p(E) a t E . For example, in the RRKM version of unimolecular rate theory, the transition probability for reaction at E is just proportional to a simple ratio3 of two such numbers, that for an activated complex (at a reduced E ) to that for excited molecules at E. Similar considerations may arise for some theories of energy transfer.2 Hence, ideally, one would like to generate a set p(E) for all E of interest, for all relevant species. The primary information for such a computation would just be the frequency spectrum of each of the species. In detail, the generation of such a complete set of p(E) just amounts to a computation which takes the molecule to be a collection of nonconimensurate and perhaps anharmonic oscillators. The approximation that considers all oscillators to be identical leads to serious inaccuracies.* One can, however, simplify - the probleni by neglecting anharnionicity effects, which may often be a justifyable approximation,j There has been Some question as to the formula to be employed in the computation of this density at E. ~i~~ and Marcus3 presented a modification Of the for use a t higher energies. (At lower energies they suggested a count Of possible complexions') Rabinovitch and Diesens Dointed to inadeauacies in this expression for typical high energies of kinetic
+
(1) For examples, see: (a) B. S. Rabinovitch and 31. C. Flowers. Quart. Rev. (London), 18, 122 (1964); (b) G. B. Porter and B. T. Connelly, J . Chem. Phys., 33, 81 (1960); (c) A. N.Btrachan, R. K. Boyd, and K. 0. Kutschke, Can. J . Chem., 42, 1345 (1964). (2) For a discussion of the various methods of calculating laboratory observables from transition probabilities and their difficulties, see R. V. Serauskas and E. W. Schlag, J . Chem. Phys., in press, and references cited therein. (3) R. A. Marcus and 0. K. Rice, J . Phus. Colloid Chem., 5 5 , 894 (1951). (4) This can be seen from the expression developed by L. S. Kassel for nonidentical harmonic oscillators, ibid., 32, 1065 (1928). ( 5 ) See E. W. Schlag, R. A. Sandsmark, and W. G. Valance, J. Chem. Phys., 40, 1461 (1964), for a typical evaluation of the anharmonic contributions to the density of states. (6) B. S. Rabinovitch and R. W. Diesen, ihid., 30, 735 (1959). See also G. 2. Whitten and B. 9. Rabinovitch, ibld., 3 8 , 2466 (1963).
Volume 69, .\Tumber 4
April 1965
