3359
COMMUNICATIONS TO THE EDITOR molecule. The limiting dielectric permittivities at low and high frequencies are eo and em respectively; p0 is the permanent dipole moment of the free molecule; and d is the liquid density measured a t temperature T . The correlation factor g is a measure, through statistical mechanics, of the short-range effects which hinder orientation between a molecule and its surrounding neighbors. For systems in which specific intermolecular forces orient neighboring dipole vectors in a parallel fashion, g is greater than unity; for an antiparallel configuration of dipoles, q is less t’han unity. For systems in which specific intermolecular forces are absent, g equals unity and Kirkwood’s equation reduces to the Onsager expression for a normal polar l i q ~ i d . ~ Hence a calculation of g from available dielectric data should provide a measure of the association present in a polar liquid. Three possible association complexes have been proposed to explain the properties of liquid The suggested complexes would arise from the formation of 0-H, S-H, or S-0 intermolecular bridges. It has been convincingly pointed out by Allerhand and t3chleyer5that hydrogen bonding will not involve C(sp3)-H as a proton donor unless at least two adjacent electron-withdrawing groups are present on the carbon. This would appear to eliminate the possibility of an 0-H bridge occurring in DMSO. Sulfur being less electronegative than oxygen, an S-H bridge seems to be even less likely to occur in I n all three cases, one can show that the existence of such association complexes would give rise to a correlation factor greater than unity. The proposal that 0-H and 5-H bridges are formed in liquid DR4SO leads one to a predominately three-dimensional liquid structure. That such a structure would arise follows from both the nonlinearity of the molecule and the multiple proton sites for hydrogen bonding. Kirkwood has shown that structures of this type, if predominant, will produce a correlation factor greater than unity. For example, calculations based on a similar model for water yielded a g value of 2.81, in good agreement with the experimentally determined value.3a An S-0 intermolecular bridge would generate a linear n-mer. It has been shown that such a parallel arrangement of neighboring dipoles leads also to a correlation factor greater than unity and equa,l to the average number of monomer units in the chain.0a A good example of this is liquid cyanoacetylene, in which g is 2.08 at 281°K.eb From the dielectric data of Schlafer and Schaffernicht,‘ the correlation factor of liquid DXSO has been calculated and plotted in Figure 1 as a function of temperature. Also included are literature values for K,K-dhethylformamide8 and nitrobenzene, two nonassociated liquicls.10 It is evident that within experimental error the g values for all these liquids are near unity and have a temperature dependence which is consistent with normal polar-liquid behavior. Hence we conclude that
310
350
330 T‘, K
Figure 1. Plot of Kirkwood correlation factor, g as a function of temperature: 0 , DMF; A, DMSO; nitrobenzene.
.,
the physical properties of DMSO cited as evidence for association in the liquid (boiling point, entropy of vaporization, etc.)2 are due primarily to its large molecular dipole moment (4.3 D) and to the presence in the liquid of strong but nonspecific dipole-dipole forces. Acknowledgment. Several helpful djscussions with Robert Chang are gratefully acknowledged. (4) R.H.Cole in “Progress in Dielectrics,” Vol. 3, J. B. Birks, Ed., Heywood & Co. Ltd., London, 1961, p 70. (5) A. Allerhand and P. Schleyer, J. Amer. Chem. Soc., 85, 1716 (1963). (6) (a) R.H. Cole, ibid., 77, 2012 (1955);(b) W. Dannhauser and A. F. Flueckinger, J. Chem. Phys., 38, 69 (1963). (7) H.L. Schlafer and Sohaffernicht, Angew. Chem., 72,618 (1960). (8) R.M.Meighan and R. H. Cole, J.Phys. Chem., 68, 509 (1964). (9) J. Timmermans, “Physico-Chemical Constants of Pure Organic Compounds,” Vol. 1, Elsevier Publishing Co., New York, N. Y., 1950,pp 591-593. (10) For comparison purposes, em was represented in each case by the usual approximation, ,e = 1.1~~2, where n is the refractive index measured a t optical frequencies. Larger assumed values for e, will result in somewhat reduced g values.
DEPARTMENT OF CHEMISTRY OCCIDENTAL COLLEGE LOS ANOELES,C.4LIFORNI.4 90041 RECEIVED JUNE 17, 1968
RALPHL. AMEY
On Radical Recombination Rates in
SOz-Doped Flames
Sir: I n recent work on the ternary kinetics of radical recombination in S02-doped Hz--air flames, Fenimore and Jones‘ and also Kallend2 have attributed the accelerated recombination rates to a catalytic mechanism H
+ SO2 + M +HSOz + M
(1)
followed by regeneration of SO2by either of the reactions
+ H +Hz + SO2 HSOz + OH +HZO + SO2 HSOz
(2)
(3)
(1) C. P. Fenimore and G. W. Jones, J . Phys. Chem., 69, 3593 (1965). (2) A.S.Kallend, Trans. Faraday SOC.,63,2442 (1967).
Volume 78, Number 9 September 1968
COMMUNICATIONS TO THE EDITOR
3360 Reaction 1 is favored because of the work of Webster and Walsh3 who studied the inhibiting influence of SO2 on the second explosion limit of H2-02 mixtures as measured in KC1-coated vessels. The lowering of the second pressure limit a t 784°K is consistent with step 1 occurring with a ternary constant kl = 4 X cm6 molecule-2 sec-I (where XI is Hz). Fenimore and Jones reported a higher value, kl = 19 X cm6 molecule-2 sec-’, measured in low-pressure flames at 1550”K, while Kallend found the value 3.5 X < kl < 4.4 X (where M is the total flame gases) in atmospheric flames at temperatures ranging from 1620 to 1720°K. The purpose of this communication is to draw attention to three points regarding this work. First, in flames it is doubtful that reaction 1is the only catalytic reaction of SO2 as a scavenger of radical excesses. The hydroxyl addition OH
+ SO2 + R!t
+HOSO2
+M
(4)
seems just as likely and in fact would be indistinguishable from reaction 1, owing to the quasi-equilibrium maintained between [OH] and [HI by (5)
About 10 years ago McAndrew and Wheeler4made measurements of the effects of various additives on recombination rates in propane-air flames. Their SO2 results were reported later in terms of a ternary rate constant for an over-all combination of reactions 1-4, ie., k1+2+3+4 = 1.1 x cm6molecule-2 sec-l (where M is SO2). If we now recalculate these measurements assuming a slow step of either reaction 1 or 4, we find that k1+4 = 11.0 X cm6 molecule-2 sec-I at 2080°K (where M is the total flame gases). This compares favorably with the later results in H2-air flames. Second, it is important to note that the propaneflame value was obtained in direct comparison with other additives to the same flame. There is no doubt of the superiority of SO2as a scavenger. If a similar catalytic scheme exists for C02,then McAndrew and Wheeler’s work shows that the corresponding ternary constant at 2080°K is k1t+4, = 1.3 X (where M is the total flame gases). Finally, the structure of the intermediate radicals is of interest. HOS02 would be quite probably pyramidal about an apex of the atom s. The S-0 bond strength is likely in excess of 100 kcal/mol and for this
The Journal o j Physical Chemistry
reason reaction 4 should be considered in any flame system. Webster and Walsh suggested that the HS02 radical contains direct S-H bonding because the most weakly held electrons in SO2 are constrained to an orbital on the S atom. Nevertheless, a structural case can be made for a thionyl form, HOSO, treating OH as a pseudofluorine atom. Also it is known that S-H bonding in most compounds is noticeably weaker (D(S-H) 85 kcal/mol) than S-0 bonding in comparable compounds (D(S-0) 115 kcal/mol). As an additive C02is a good yardstick for comparison with SO2, because the C and S electronegativities are nearly identical and yet the geometries are decidedly different. The propane-flame work suggests that corresponding COz intermediates just do not form, or if they do there is no regeneration via reactions 2’ and 3’ and the COZ is lost. Unless some ionization process follows reactions 1’ and 4’ in preference to regeneration of C02 by reactions 2’ and 3’ (and this is difficult to believe), the assumption must be that very little HCOz or HOC02 is formed in these flames. Using any of the empirical methods for estimating bond energies, it is apparent that the C-H or C-OH bond would be stronger than the corresponding S-H and S-OH bonds. Structurally, both HC02 and HOC02 would be probably planar or nearly SO. However, in order to form at all, a considerable decrease in bond angle from the stable 180” in COZis necessary. Perhaps this requirement is just too great making for high activation energies in reactions 2’ and 4’. Because SO2 is already in a triangular configuration, rearrangement to form any of the pyramidal intermediates is much less severe with corresponding lower activation energies in reactions 1 and 4. It might be easier to make a case for a linear HOC0 radical as opposed to a triangular HC02, but the lack of efficiency of C02 as a scavenger suggests that HOC0 is not an important species in flames. The inference here then is that the catalytic effect on recombination is through reaction of the additive with OH (reactions 4 and 4’) rather than with H (reactions 1 and 1’).
-
-
(3) P. Webster and A. D. Walsh, Symp. Combust., loth, Cambridge, Cambridge, Engl., 1064,463 (1965). (4) T. McAndrew and R. Wheeler, J . Phys. Chem., 66,229 (1962). OF CHEMISTRY DEPARTMENT QUEEN’SUNIVERSITY KINGSTON, ONTARIO, CANADA
RECEIVED JTJLY 10, 1968
ROBERTWHEELER
