3733
J. Phys. Chem. 1981, 85, 3733-3734
densities calculated from the ammonium bisulfate molarities, [NH4HS04],agree well with the theoretical predictions from the data of Young et a1.6 and the data of Tang23and Beattie et al.9 Recent communication from Irish24included a polynomial fit to the NH4HS04density data used in Irish and Chen2 d = 0.99671 0.604706 X 10-l[NH4HS04] - 0.108981 X 10-2[NH4HS04]2+ 0.106394 X 10-4[NH4HS04]3(15)
+
Equation 15 agrees with the data of Tang23and Beattie et a1.: in support with our observation that the water molarities in Table I of Irish and Chen2must have been calculated incorrectly. The NH4HS04solution densities predicted from eq 15 agree with the theoretical predictions based on dissociation and molar volume data within 0.40% for Irish and Chen2 and 0.65% for Young et ala6 In addition to isolating the error source in the paper of Irish and Chen,2we have illustrated a technique by which the densities of ammoniated sulfate solutions can be calculated from dissociation data or vice versa. Specifically, this work discussed ammonium bisulfate solutions but eq 12 can be applied to any aqueous ammonium sulfatesulfuric acid solution. (24) Irish, D. E., University of Waterloo, personal communication.
A. W. Stelson J. H. Selnfeld”
Department of Chemical Engineering California Institute of Technology Pasadena, California 9 1 125
Recelved: April 14, 1981; In Flnal Form: July 15, 1981
Intermediates in the Gas-Phase Disproportionation of HO, Radicalst
Sir: I t is now well established from recent kinetics studi e ~ l that - ~ the gas-phase reaction HO2 + HO2 H202 + 02 (1) is more complex than a simple hydrogen atom transfer as first The observed pressure and temperature dependence of the rate constant has prompted Cox and Burrows2to suggest that the reaction proceeds through an intermediate, the H204 molecule, previously identified in the frozen products from electrically dissociated water vapor.g Of the two possible pathways for the decomposition of that intermediate, I or 11, the former is now ruled +
H
H
I
I1
out following the l80 isotope studies of Pu’iki et al.1° (1) E. J. Hamilton and R. R. Lii, Int. J. Chem. Kinet., 9,875 (1978). (2) R. A. Cox and J. P. Burrows, J. Phys. Chem., 83, 2560 (1979). (3) B. A. Thrush and J. P. T. Wilkinson, Chem. Phys. Lett., 66, 441 (1979). (4) R. R. Lii, R. A. Gorse, Jr., M. C. Sauer, Jr., and S. Gordon, J.Phys. Chem., 83, 1803 (1979). (5) S. N. Foner and R. L. Hudson, J. Chem. Phys., 36, 2681 (1962). (6) T. T. Paukert and H. S. Johnston, J.Chem. Phys., 56,2824 (1972). (7) C. J. Hochanadel, J. A. Ghormley, and P. J. Ogren, J.Chem. Phys., 56. 4426 ~ ~ (1972). - --,(8) A. C. Lloyd, Int. J. Chem. Kinet., 6, 169 (1974). (9) P. A. Gigugre and K. Herman, Can. J. Chem., 48, 3473 (1970). (10) H. Niki, P. D. Maker, C. M. Savage, and L. P. Breitentach, Chem. Phys. Lett., 73, 43 (1980).
--.
\--
However, as noted by these authors, their results cannot distinguish between transition state I1 and a hydrogenbonded cyclic dimer (HO,),. Pending further experimental data a survey of the indirect evidence based on thermodynamics, kinetics, and structure shows that the cyclic dimer is by far a more likely intermediate than the covalent H204molecule, as regards both formation and decomposition. On thermodynamic grounds the formation of a cyclic (HO,), dimer resembles that of double molecules in the vapor of formic and acetic acid,ll with an enthalpy of dimerization of some 15 kcal mol-l. This value agrees nicely with the estimate from the kinetics of the HOz self-reaction.I2 I t also fits almost exactly twice the hydrogen bond energy calculated by Hamilton for the H20HOBc0mp1ex.l~ In contrast, the covalent H2O4 molecule is expected to be unstable with respect to dissociation into two H02, as shown by Benson14from bond energy considerations. Similarly, calculations of the thermodynamic functions of the H2O4 molecule1s lead to an estimate of 6.5 kcal mol-l for its free energy of formation from H 0 2 radicals, as compared with -4 kcal mol-l for the dimer, again by analogy with the double molecules of carboxylic acids.“ As for the decomposition process, the (HO,), complex is clearly favored by a rather low bond-dissociation energy, D(H-02) = 47 kcal mol-’, due to the favorable reorganization energy of the fragment^.^ In contrast, for the tetroxide D(H-O,H) must have nearly double that value again by analogy with hydrogen peroxide16for which D(H-02H) = 90 kcal mol-’. From the viewpoint of kinetics, the formation of a cyclic (H02)2dimer in the gas phase may be seen as a “sticky collision” following suitable 0-H-0 approach and dipole orientation. On the contrary, the covalent H2O4 molecule can only be formed in the condensed phase, thanks to intermolecular forces; that is by the “cage effect” at the surface of a glassy matrix, following the trapping at very low temperature (below 80 K) of a pair of adjacent H 0 2 radicals stabilized by hydrogen bonding.” This explains why it decomposes so readily at the slightest change of environment,for instance, upon devitrification of the glassy deposit at 160 K. In the gas phase, decomposition of the cyclic (HO,), complex is a three-center process, hence more likely than the four-center process for transition state 11. Yet another transition state, 111, yielding H 2 0 and 03,
,-8”-y ‘0-0
11I
considered by Niki et al.,l0was effectively negated by their experimental results. Although thermodynamically possible, it appears still less likely with the (H02)2complex than with the H2O4 molecule which already contains the chain of three covalently bonded oxygen atoms. Lastly, from the structural standpoint the geometry of the hydroperoxyl radicalla is particularly suited to the formation of a strong dimer (IV)because of nearly colinear (11) G. C. Pimentel and A. L. McCellan, “The Hydrogen B o n d , W. A. Freeman, San Francisco, 1960, p 210. (12) B. A. Thrush, Acc. Chem. Res., 14, 116 (1981). (13) E. J. Hamilton, J. Chem. Phys., 63, 3682 (1975). (14) S. W. Benson, J. Chem. Phys., 33, 306 (1960). (15) P. A. GiguBre, Trans. N.Y. Acad. Sei., Ser. II, 34, 334 (1972). (16) P. A. Gigugre, “Peroxyde d’hydroggne e t polyoxydes d’hydroggne”, Val. 4 of “ComplBments au nouveau trait6 de chimie minerale de P. Pascal”. Masson, Paris, 1975, pp 67, 78, and 164. (17) J. L. Arnau and P. A Gigugre, Can. J. Chem., 53, 2490 (1975). (18) J. F. Ogilvie, J. Mol. Struct., 31, 407 (1976).
0022-3654/81/2085-3733$01.25/0 0 1981 American Chemical Society
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The Journal of Physical Chemistry, Voi. 85, No. 24, 198 1
I
la*
IV
hydrogen bonds, as in the cyclic dimers of H202postulated from the matrix isolation spectra.lg Further stabilization of the (H02), complex must also accrue from resonance between various electronic structures featuring single, double, and three-electron bonds between the oxygen atoms, a condition obviously lacking in the a-bonded H204 molecule. As for the disproportionation reaction, that of the (HO,), intermediate requires a shift of a mere 0.7 A of one hydrogen atom compared to that, at least three times larger, in the most favorable configuration of the H2O4 species. Incidentally, one should also consider the formation of open hydrogen-bonded dimers, H02-H02, although their lower binding energy (ca. 5 kcal mol-') may (19)P.A.Gigugre and T.K. K. Srinivasan, Chem. Phys. Lett., 33,479 (1975).
Additions and Corrections
not be sufficient to lead to disproportionation. In that connection, since some of the kinetics studies were carried out by UV absorption spectrometry, it is appropriate to recall here that the electronic spectrum of the H 0 2radical in the dimers will be somewhat perturbed by hydrogen bonding. For instance, the maximum observed a t 2100 A in the gas phase6 was found to be shifted to 2300 A in the radiolysis of aqueous solution^.^ Finally, concerning another important reaction of the hydroperoxyl radical HOz + HO -* H2O + 02 (2) the possibility of its pressure dependence has been mentioned, and the formation of the covalent species H2O39,l6 as an intermediate has been suggested.20 However, the latest measurements12 of that reaction at low pressure indicate that it is 100 times faster than reaction 1. It is unlikely, therefore, that such a fast reaction would be pressure dependent. (20)C. J. Hochanadel, T.J. Sworski, and P.J. Orgen, J.Phys. Chem., 84, 3277 (1980). Presented at the 15th International Symposium on Free Radicals, Ingonish Beach, Nova Scotia, Canada, June 2-7, 1981.
Dgparlement de Chimie Unlversitci Lava1 Quebec, Canada G1K 7P4
Received: August 19, 1981: I n Final Form: October 9, 198 1
ADDITIONS AND CORRECTIONS 1981, Volume 85 Janis L. Dote, Daniel Kivelson,* and Robert N. Schwartz: A Molecular Quasi-Hydrodynamic Free-Space Model for Molecular Rotational Relaxation in Liquids. Page 2180. The sentence in column 1 above eq A1 should read the angular velocity w1 is expressed as. Equation A5 should read
....
2 [ l + 2m(V,/Vp)'/31-4
m=l
aGW=
2 [ l + 2m(v,/vp)'/31-4
m=O
Paul A. GlguQre
