The Significance of the Bond Angle in Sulfur Dioxide Gwdon H. Purser Glendale College, 1500 N. Verdugo Road, Glendale, CA 91208 Sulfur dioxide is an angular molecule with a hond angle of 119.37' and two eoual S - 0 hond lenvths of 0.143 nm ( 1 ) . The nature of the bodding of the sulf& dioxide molecule has been the subied of debate in the literature for manv years (2-20). ~ o m d a u t h o r feel s that there is a major contrib&ion by the sulfur d orhitals in the bondina of sulfur dioxide and that there are double covalent bonds between the sulfur atom and the oxygen atoms. On the molecular orbital representation of sulfur dioxide, Hiller and Saunders suggest (18): The mmt striking feature is the large Ssd,-On,overlap population in the la? MO which is totally non bonding m the absence of sulfur 3d orbitals.
Table 1. Comparison of the treatment ot the Bondlng ot Sulfur Dloxlde In Selected General Chemlstrv Textbooksa
BrW. J.; Holurn. J. (a) Ebbing. 0. (c) Holhclaw, H.. Jr.: Robinson. W. (e) Koh. J.: Fwcell. K. (g) Brescla, F., et al. (I) Masterton, W., et al. (k) Zurndaht. S. (m)
Mortimer. C. (b) Miller. F. (d) McQuarrie,D.; Rock, P. (f) Bailar, J.. Jr., el al. (h) Whitten, K.. et ai. (j) Oxioby. 0.; Nachnieb, N. (I) Brady. J.: Humiston, G. (n)
Other investigators suggest that the sulfur atom uses only 3s and 3p orbitals in bonding t o the oxygen atoms. In The Nature of the Chemical Bond (21), Pauling explains1: In sulfur dioxide the 5-0 distance is ohsewed to be 1.432 & 0.001 .&,whichissomewhat less than that in thesulfateion. The value of the 0-S-0bond angle, 119.549,lies close to that expected for the structure
Gillesple. R., et al. (o)
F'ebuccl. R. (q)
A survey of selected textbooks (see Table 1) shows that the dehate on the nature of the bonding of sulfur dioxide extends into general chemistry. Very few general chemistry textbook authors represent sulfur dioxide with a structure that contains twodouhlecovalent S=O bonds; instead,moat authors report the bonding to be isostructural with ozone. Some of these authors discuss or introduce sections pertaining to resonance using sulfur dioxide ns an exemplary molecule. The fact is. the ozonelike resonance structures of sulfur dioxide prohabiy are unimportant in the description of the bondine of the molecule. proponents of a structure containing double bonds between the central sulfur atom and each of the terminal oxygen atoms suggest that the sulfur atom uses d orbitals as necessarv for the formation of the double bond. The maiority of a&hors who support this bonding picture typically emphasize the short S-0 hond length (2-5). As shown in Table 2, the bondlength of the S-0 bonds insulfur dioxide is similar t o the length of bonds between a sulfur atom and a terminal oxygen atom in other neutral molecules but consistently is shorter than the length of the bonds between a sulfur atom and adicoordinate oxygen atom. Other evidence of double covalent bonds is the small dipole moment of sulfoxides and related com~ounds(2, 6). the hizb heat of formation (2, 7, 8), and the-large S-0 force cons-&nt (3, 9, 10). Critics of the two double bond approach feel that the d ~~
NO Lewk Sbucture oi SO2
Henold, K.; Wairnsley. F. (t)
'
710
Journal of Chemical Education
Brown. T.;
LeMay, E.. Jr. (u)
Table 2. Bond Lengths and Bond Angles in Some Molecules Contalnlna Sulfur Oxvaen Bonds S=O
~
The description of the bonding of sulfur dioxide given by Pauling in me textbook, Chemlshy(22),published subsequent to The Nature of ihe Chemical Bond 1211. . .. involves the two. doublbcovalent bond shucture 01 the molecule.The quore, however, accurately represents the vlew currently held by many chemists.
Dickerson, R.. et al. (r) Boikess, R.; Edelson, E. (6)
Molecule So2
0.143 0.143 OnS(OFeC~rHnNdtb 0.143 OSORh(NOKPCsHrh)* 0.143 [02SSOCo(C2HeN2)2]CI04 0.145
ow%
S--OR (W 0.153 0.151 0.149 0.153
O=S=O RWS--OR angle angle ('1 119.5 114. 116.
113.
(9
ref.
-
(0
108. 101.
-
d
Piscard. R. Compt R M 1955, 240. 2162: Pas&-Billy. C. Acte Cryrf. 1985. 18, 827. 'The S 4 and S--OR bond lengms and angles given for his cmpavnd are typical lor COOminated sullate. Seoltmmas. J. N.; Robinson, P. D.; Fang, J. H. Am Mlnral 1974, 59,582, a M references m r e l n . 'Scheidf, W. R.: Lee. Y. J.; Bamcak. T.; Hatam. K. l n x g Chem 1984,23,2552. 4M00dY. 0 . C.; Ryan. R. R. hag. Chm. 1977, 16.2473. 'Murmsk.A.R.:Tyree,T.;Onwbsin. W.;Kinney.L.;Canerss.M.;Cwper,J.N.:Eldw. R. C. lnorg Chsm. 1985.24.3674,
orbitals are too hieh in enerw and too diffuse to be used for bonding. They constrain theV&lfur atom to using the s and p orbitals onlv and Drooose an ozonelike structure for sulfur dioxide. hey suppori their position by citing the lack of an intense ultraviolet absorption ( l l ) , a low molecular refraction (11-13), and low parachor (11). T o explain the short SO bond length and large negative heat of formation, opponents of the S-0 double .bond picture infer "semipolar"
Predicting a single most likely contributor is difficult. While resonance forms D obey the octet rule, they are destabilized by fewer bonds and the presence of formal charges (although the negative formal charges are located appropriately on the more electronegative oxygen atoms). often in general chemistry a bondingdescription that obeys the octet rule is supposed to he the major contributor to the observed geometry without consideration of the number of honds or formal charees. This is a shortsiphted orediction that mav lead to an erroneous conclusion &ruct&e B ia stabilized b; a greater number of honds and zero formal charge, hut it is destabilized by some fraction of the d orhital promotion enerm. Thus with sulfur dioxide there is no obvious choice of a pr&ipal resonance form based on these arguments, and the answer to the question of the bonding resides in the interpretation of the properties of the molecule. The O-S-0 hond angle in sulfur dioxide provides a clear answer.
Figure 1. Resonance srmctures of the sulfur dioxide molecule.
bonds (bonds with partial ionic character). This partial ionic character is supposed to cause the contraction in bond length observed in Table 2. As early as 1954, the theoretical basis for the formation of d.-p, bonds was established (15). Shortly thereafter, Cruickshank, using predominantly hond lengths, provided honding in XOan- ions (where X = Si, P, S, evidence of d,p, or C1) and related species (24). Recent molecular orbital calculations indicate ;hat, in sulfur dioxide and related molecules, d orbitals play a significant role in the honding between a central sdfu; atom and a terminal oxygen atom (18, 20,24-26). However one need not turn to complex ab initio calculations to answer the ouestiou of whether d orbitals participate in the bonding of sulfur dioxide. Instead, the answer can he found bv scrutinizine the structure of the m~iecule,~ in particular, by examininithe large 04-0 hond angle. Several authors have implied qualitatively that the observed hond angle in sulfur dioxide is consistent with two double S=O binds having steric requirements almost as high as the sulfur lone pair (14,29). Absent from the literature, however, is an attempt to demonstrate explicitly, without the assumptions involved in molecular orhital calculations, how the large O-S-0 hond angle results from the participation of d orbitals in the bonding of sulfur dioxide. Lewls Structures for Sulfur Dloxlde For sulfur dioxide there are nine resonance structures that can he drawn, one of types A, B, and C, and twoeach of types D. E, and F. These are shown in Fieure 1.The circled and -.signs in the figure indicate the formal charges on the atoms. A formal charge indicates a real separation of charge within the molecule although the charges should not he considered to be a full electronic charge as possessed by a monatomic ion. The separation destabilizes the structure relative to one with no separation of formal charge. Many eeneral chemistrv textbooks fail to indicate formal charees " on Lewis structures, a practice that conceals important information about the structure. For this reason the formal charges have been omitted from the structures in the tahle, hut not from the structures in Fieure 1. The structure that is the contributor to the normal state ofsulfur dioxide should he reflected in the propertiesand geometry of the sulfur dioxide molecule. Hased upon observations of other molecular structures, resonance forms and F would be ex~ected to contribute verv of the tvDes C.,E..~ little tdihe normal state of sulfur dioxide since each of the& structures places a positive formal charge on at least one of the electronegative oxygen atoms. The resonance forms of type A and C are unimportant because of the high formal charge associated with the sulfur atom. Consequently, resonance forms B and D might be viewed as the most likely contributors to the observed geometry.
+
-
~~
.
~~
~~~
Discussion Ozone, like sulfur dioxide, is an angular molecule. The 0-0 hond lengths are 0.128 nm, and the hond angle is 116.8' (30). Below are three honding descriptions of ozone and sulfur dioxide; two are based upon the directed valence bond (DVB)model, and one is based upon the valence shell electron pair repulsion (VSEPR) model. In each case, a comparison is made between the observed and predicted bond angles in orone and sulfur dioxide. It is assumed that an accurate bonding description will explain adequately the observed molecular geometries of both sulfur dioxide &d ozone. Directed Valence Bond (DVB)Model
The basic premise of the DVB model is that atomic orhitals on one atom can overlao with the atomic orhitals on another atom to share an eledron pair and form a covalent hond. Whether the orbitals are pure atomic orbitals or hybridized atomic orbitals, they ark directed in space, and the molecular geometry depends upon which orhitals on the ~. central atom are being used. Using hybridized atomic orbitals: In bond formation a linear combinhation of atomic orbitals on a central atom may produce orbitals that have better overlap with atomic orbitals on an adiacent atom than that achieved hv the unhyhridized atomic orbitals. The result is a hybridired set of bonding orhitals. The amount of s, p, d, etc., chaructcr in the resulting hyhrid orhital depends upon the properties of the atom honded to the central atom hy that orhital. The eledronegativity difference between th;two honded atoms is of particular importance to the degree of hybridization of the atomic orhitals (31). Where only s and p orhitals are used, it is observed generally that as a bond becomes more polar, the amount of s character in the hybrid orhital in that bond decreases, and the honding orbital on the central atom becomes more D-like. The essence of this eeneralization is Bent's rule (31,-32). An excellent a~olicationof Bent's rule is the exolanation of the decrease X-GX bond angle in molecuies of the type, OCX2 where X = H, CI, or F. The hybridization of OCXz is expected to he sp2producing X-C-X bond angles of 120'. The electronegativity differences in the C-X hond for the series C-H, C-C1 and C-F are 0.4, 0.6, and 1.4, respectively3. Based on Bent's rule, the amount of p character in the C-X hond should increase in theseries H, Cl, F, resulting in a decrease in hond angle for that series. In agreement with these predictions, the hond angles decrease from 116" for OCH2, to lllDfor OCC12, to 108' for OCF2 (33).
-
While the concept of molecular structure has been questioned recently (28,this paper will work within the context of experimentally measured molecular structure. Pauling electronegativitiesare used throughout this paper. Volume 66 Number 9
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711
Figure 2. A cross &Ion of the ozone molecule (a) wim a bond angle of 9 0 ' . (b) wrm the bmdanglersqulred toellmlnate terminal oxygenatom repulsions. (c) w~mmeob-ed ~ond angle The 0-0 mnd length .SO 128 nm and the van der Waals radius of oxygen is 0.152 nm.
If a similar treatment is given to ozone and sulfur dioxide, a discrepancy between observed and predicted bond angles arises. In the case of ozone. the electroneeativitv difference between the central and terminal atom is small. be electronegativity difference between the oxygen atoms is zero, but the presence of formal charges on the central and terminal atoms can be viewed as introducing a small amount of polarty to the 0-0 bonds (PO, = 0.53 D (34)). In agreement with Bent's rule, the resulting polarity causes the p character of the bonding orbitals to increase, which in turn causes the 0-0-0 bond angle to decrease slightly from the ideal sp2 angle of 120° to the observed angle of 116.8' (30). In sulfur dioxide, the electronegativity difference between the sulfur and oxygen atoms is 0.8 units. Assuming an ozonelike structure (type D), the polarity of the bond isincreased further by the presence of formal charges on the constituent atoms (pso2 = 1.63 D (34)). Based on these considerations, the 0-W bond anele for sulfur dioxide mieht be ex~ectedto be about3' less than the 117'angle observed in ozone, or about 114O. However. the observed hond anale in sulfur dioxide is 119.3O (I), larg&significantly than that of ozone. These data suggest that the bondine- in sulfur dioxide is not similar to that in ozone. Using unhybridized atomic orbitals: In molecules containing a main group central atom with a lone pair of electrons, there is some evidence that the electron lone pair remains in an unhvbridized 2s orbital while the 213 orbitals are used to form thk covalent bonds (35). Since t h e i s orbital is lower in enerev than the 2~ orbital. electron occuoation of tbe 2s orbital s l k l d be maximized. According to thk theory, maximum occupation can be achieved by allowing the 2s orbital to remain unhybridized. Thus the molecule is stabilized by some fraction of the 2s-2p orbital promotion energy. Hall observed the same phenomenon using extended Htickel theory (36). Slater suggested that bonds formed by p orbital overlap tend to be at a 90" angles (37). Angles greater than 90° are explained by steric repulsions and tend to occur when the central atom is small. This model is supported by the decrease in bond angle in the series HzO, HzS, and HzSe' (104". 92.9O. and 91.0°.. res~ectivelv (33)). . . .. ' US& this model, ozone and sulfur dioxide would use two unhvbridized D orbitals to over la^ with atomic D orbitals on the terminal oxygen atoms to form sigma bonds. The re712
Journal of Chemical Education
90". (b) with ms
bond angle required to ellmmate terminal oxygan atom repulsions.(e)wlmmeabserved bcdangls. me S-0 bond length Is 0.143 nm and the van dsr Wasls radii of sulfur and oxygen are 0.180 nm and 0.152 nm. respectively.
maining unhybridized p orbital on the central atom would form a delocalized pi bond. The unhyhridized s orbital would remain occupied fully with the lone pair of electrons. Thus if the bonding in sulfur dioxide and ozone are similar, the 0-X-0 bond angles will be as close to 90" as possible while minimizing oxveen-oxveen renulsions. ~eomethcail;, one & show that using 0.152 nm for the van der Waals radius of oxveen (38)and 90° and 0.128 nm for the bond angle and 0-0 bind length (30),respectively, in a P-bonded ozone molecule there is substantial steric r e ~ u l si& As a result of the repulsion, the bond angle open; to 116.8'. It has been shown that such an opening of the bond angle does not result in poor overlap of the atomic p orbitals (39). As shown in Figure 1, even at the expanded bond angle, some repulsion between the two oxygen atoms remains if the van der Wads radii of the bonding oxygen atoms remain 0.140 nm. Pauline" sueeests that within a few deerees of a covalent bond, there may be a shrinking of the van zer Wads radii of bondine atoms (40). If the van der Waals radii of the bonded oxygen-atoms shrink to about 0.121 nm around the bond axis in ozone, most re~ulsionsbetween the two terminal atoms would be eliminated. If the same treatment is aiven to the sulfur dioxide mole2 and 3), it becomes clear cule as to ozone (shown in'igs. that when using 0.152 nm for the van der Wads radius of oxygen, 0.180 nm for the van der Wads radius of sulfur (38), 90' for the bond angle and 0.143 nm for the S-0 bondlength (1, 41), there should be some repulsion between the two oxygen atoms. Using the above radii and hond length, when the 0-S-0 bond anele becomes 109.4'. renulsion between the oxygen atoms would be eliminated. i f there is any shrinking in the van der Waals radii alone the bondine axis. as appears to be the case in ozone, the angle can aciualli become smaller than 109.4'. The observed bond angle, however, is 119.3': clearly steric effects alone cannot account for such a large angle. Either this model is inadequate, or the bonding in sulfur dioxide is not ozonelike, or both.
--
Valence Shell Electron Pair Re~ulslon(VSEPR) Model The VSEPR model has proven very successful for predictine the aualitative ceometw of molecules and ions. Althoueh &re isdebate as to whetherelectron pair repulsions al&e
(especially repulsions between lone pairs and bond pain of electrons) are responsible for the observed geometry (3642, 43), there is little debate of the success of the model. I t has been noted also that the VSEPR aDDr0ach wmtures the essence of molecular orbital results (&), althougl; it is in no wav as com~licatedor auantitative. Molecules and ions with ge&netriesihat deviatefrom those predicted by the VSEPR model typically have substantial ligand-ligand interactions or involve highly polarizable central atoms. Since neither ozone nor sulfur dioxide fit into one of these categories, it is reasonable to expect the VSEPR approach to predict accurately the geometry of the two molecules. First consider the bonding in sulfur dioxide to be similar to that in ozone, as shown in structure D above. Using the Gilles~ie-Nvholm notation. both ozone and sulfur dioxide E and should have a hent geometry with a are A X ~ mhecules bond anele somewhat less than 120'. The closine of the bond angle of'bzone in the VSEPR model is due to the repulsion between the lone pair of electrons on the central oxygen atom and the two bond pair of electrons. The bond angle of sulfur dioxide, however, should close to an angle smaller than that of ozone since a decrease in the bond angle is expected when the central atom is more electropositivethan the atoms to which it is bonded. This effect is suggestedto be responsible for the bond angle closing from 103O in oxygen difluoride (30) to 98' in sulfur difluoride (45). The irnnlication is that the bond angle in sulfur dioxide' should i o t be neater than about 111'. The observed bond anele in sulfur &oxide of 119.3~indicates that the bonding in sulfur dioxide is not ozonelike. Now consider the structure of sulfur dioxide predicted by VSEPR theory if the bonding involved two S=0 double bonds. It has been demonstrated that there is a directional effect of pi bonds on the molecular geometry of some molecules (46). If the bonding in sulfur dioxide involves two pi bonds instead of only the one that is suggested by the ozonelike structure (type D), then according to the model there should he greater repulsion of the bonds due to greater electron density between the oxygen atoms and the central sulfur atom. The result would be the opening of the bond angle in sulfur dioxide over that observed in ozone. This expectation is in agreement with the observed bond angle.
dioxide as examples of molecules for which resonance is important. Literature Cited
6. 7. 8. 9. 10.
Cumper, C. W . N.; ~ead;~. F.; *%el, A: 1 . j . Chem. Sw. 1965.5323,6MO. Cumper, C. W. N.; Wa1kar.S. Tram. Famdoy Soc. 1956.52,193. Maekle, H. Tetrahedron 1968. 19.1159. Giliospie, R J.; Robinson, E. A. Con. J. Chem. 1963,41,2074. Szmant. H. H.Sulfur in O~goniro d Imrganic Chembtry;Dskksr: Nesv Yo& 1971;
11. 12. 13. 14. 15.
Price, C. C.; Ose, S. SulfurSonding. Ronald: Nea York, l%Z. Vogei. A. J. J. Chem.Sac. 1948,1820.1833. Vogel. A. I.: WwweU, W. T.; Jeffrey, O. H.;Iricester. J. J. Chom. Sw. 1952,514. CarroU.A. C. J. Chem.Edue. 1986.63.28. Craig,D.P.;Maccoll,A.;Nyholm,R.S.;W,LE.;Sutton,LE.J.Chom.Sw. 1954.
.
"3
.>
332.
L h n e q J. W.Direum.FomdoySoe. 1965.95.226. Keton, M.; SaoPI,D. P. Chem.Phys. Lrft. 1970,7,105. Hillier, I. H.: Ssunder8.V. R. Mol. Phya. 1971.22.193. Kwart.H.;King,ll~.d-OartbiffIsiitheChhmbLry'~fSiiiiii,PhoaphhhhndSsflur: Springs Berlin, 1977. 20. Huzaoaga, S.; Yashimine, M. J. Chom.Phyr. 1978,68.4(86. 21. Padin6 L. Tho Notuw of the Chemical B o d , 3rd ed.; CmneU University: lthaea. 16. 17. 18. 19.
Conclusion
The bonding modela above predict that the bond angle for an ozonelike sulfur dioxide molecule will lie between log0 and 114'. The observed bond angle, 119.3', indicates clearly that the bonding in sulfur dioxide cannot be ozonelike and rules out any appreciable contribution to the ground state electronic structure by Lewis structures of type D. As suggested by a small minority of general chemistry textbook authors, the principal resonance contributor to the normal state of sulfur dioxide is the tvoe-B structure containine two, covalent, S=O double bon& The results of this worg agree with those molecular orbital treatments of sulfur dioxide that yield an S-0 bond order of approximately two. Blindly invoking resonance structures where they are not warranted will coitinue to confuse and mislead the general chemistry student. Clearly a concerted effort should be made to (1) use in general chemistry textbooks the twodouble-bond structure for sulfur dioxide instead of the ozonelike structures and (2) use molecules other than sulfur
27 Mprsr. P O . Haa. E C..I.Cbm. Ph>a 19x2,77.8711. 28. Hetntnmr.S J. J. C h e m L d w . 1984.61.939,and 29 Gll, w ~ rR . J. J. Them. Edur. IWO. 47. ih.
rrkrrnr~themm.
Hugh;s.k. H.J.Chem.Phyr. 1956,'24.'131. Huheey, J. E.lnorg. Chem. 1981,20,4033. Bent. H. A J. Chem. Educ 1960.37,616. Gillowie. R. J. Moieevior Geometry; Van Noatrand Reinhold: New Yock. 1972: and ref&neea therein. 34. Ndson, R. D.. Jr.; Lide, D. R.; Manon. A. A Selected Volvea of Electric Dipok Moments of Molomks in the Goa Phare; National Data Referatoe Sari-, National Bureau of Standards-10. 35. Laing, M. J. Chem.Educ. 1)87.64,124. 36. (a) Hd.M.B.lnow. Chem. 1978,17,2261. @) H d , M . B . J.Am.Chem.Sw. 1978,IW.
30. 31. 32. 33.
c,,,
1960; p 263. 41. Clark,A.H.:BeagLsy,B. l h n r . F o m d ~ ~ S o1971,67,2216. c. 42. Palke, W. E.: Kirtmsn, B. J. Am. Chem. Sw. 1978, IW, 5717. 43. Thompson. H. 6 . ; Wells. M.; Weaver. J. E. J.Am. Chem. Sac. 1978. IW. 7213. a.Albright.T.A.;B"de't, J.K.; Whaagb,M.OrbilolhfcroetianrinCh~mbtgl; wi1ey: New York. 1985: p 274. 45. Johnson. D. R: Powell. F. XSeiomo 1%9. 164.954. 46. Kriste, K. 0.;O b e r h m e r , H. Inorg. Chem. 1)81,20,296.
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