Edited by GEORGE WIGER
textbook forum
California State University Carson, CA 90747
Molecular Association and Structure of Hydrogen Peroxide Paul A. Giguere Universite Laval Quebec, Canada G1K 7P4
than water. The criteria most often quoted in thatconnection are its higher hoiling point and its greater heat of vaporization. But this is ignoring a major factor, i.e., the nearly double molecular mass of H202. Consider, for instance, the case of CH4 versus C2H6 with normal hoiling point -161.5" and -88.3"C, and heat of vaporization 2.2 and 3.8 kcal mol-1, respectively, a situation where molecular association is of little import. To he sure, hydrogen peroxide is a strongly associated substance in contrast with its sulfur analoeue. H9S9 . .(Fie. ,. 1and 2t.I F8~r~, ~ > sociated l i q d s , is approximat& cons&, 21 e.u: (Trouton's rule). For hvdroaen ~eroxidea definitelv hieher value is expected, comparable to that of water, 26.i e.; As a matter of fact the two turn out to he eaual within the accuracv of the experimental data. Indeed, thk accepted value for thenormal boiling point of pure hydrogen peroxide (Tahle 1)was derived by extrapolation of the vapor pressure measurements on very concentrated solutions up to 105°C (4). Differentiation of the vapor pressure equation yielded a value of 11.26 kcal mol-' for the normal heat of vaporization, and therefore, 26.6 e.u. for the entropy ( 5 ) .A slightly lower, and probably more accurate value of the latter, 25.9 e.u., is arrived at from the calorimetric measurements at 25°C corrected for the heat capacity of the vapor (Table 1). Clearly, this does not support the claim of a stronger association f i r hydrogen perox& Another thermodynamics quantity also mentioned in that respect is the heat of fusion of the H202 crystal, which is more than douhle that of ice. However, that property is well known to depend not only on intermolecular forces hut also on the so-called packing conditions, such as symmetry and configuration of the molecules. For instance. ammonia has exactlv the same heat of fusion as ice, yet it is much less strongly associated. Conversely, it would be equally wrong to argue that hydrogen peroxide and water are associated to the same degree because they have the same melting point to within 0.4T (6). Considering their many differences, this near coincidence is remarkable, indeed. Now, the relatively high meltinp point of ordinary ice is a consequence of the great strengti bf its hydrogen-bonded lattice, of the tetrahedrally-coordinated, or tridymite type. With covalent solids this kind of lattice yields some of the most infusible substances, such as diamond, silicon, quartz, etc. In comparison, the lattice of the hydrogen peroxide crystal is not so well balanced. Although each HsOst1101t.,111t, T u r n 1 r c u r hydro.(xidtt'd. the thin i n \v.nrr, ?et l ~ t ~IIII~~:I~~P..:III.FI~II~II?. diiti.n.nw nltiar rhr v.111 der \Vdals t;wcsof iixluctitm . ~ --- --- ~- ~ - re51 ~ with ~ ~ ~ (Debye) and dispersion (London). Exact numerical values of these quantities cannot be calculated for polyatomic molecules, hut for our purpose some meaningful values, relative to those of water. are obtained bv substituting in the amropriate equations(12) the polariiability and dipole moment of the HsOs - - molecule (Table 1).This -gives a ratio of about 2.3, the same, incidentally, as that of the force constants of interaction between the "free" Hz02 molecules and CC4 in very dilute solutions (13).Using Pauling's first estimate of 3.2 kcal ~~
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Figure 4. Approximate shape of the potential curve for the internal rotation of the H202molecule.
mol-' for water, that of hydrogen peroxide is 7.4 kcalmol-', and therefrom. -4 kcal mol-' for each hvdrogen bond in agreement with the above conclusion. ~ r o m theiow value of the heat of fusion of ice Pauling has concluded that "on melting only about 16 percent of the hydrogen bonds are broken." On the same basis the fraction would be double that versus donor sites. The fact that the heat (and hence the entropy) of fusion of the Hz02 crystal is double that of ice must be due to the greater flexibility and lower symmetry of the molecule, as explained hereafter Molecular Structure of H 2 0 2 The hydrogen peroxide molecule is of special interest from the structural viewpoint because it is the s~mplestcase of internal rotation. or torsion. about a single bond. Indeed, the skew-chain configuration(Fig. 3) was shown, first by the auantum mechanical calculations of Pennev and Sutherland I 1 1 1 , 111 he the 111,).1 st:1111e?111~m< mrit 11. 11t4hilitit>.'1'111s u,n; later umtirlw.d hy inrrnrcd s 1 1 1 . 1 r c ~ r w1.51..\n.~t111.r important peculiarityhf that molecule is that the rotation of the two OH groups about the 0 - 0 bond is only weakly restricted by a low potential barrier (1kcal mol-') in the trans confieuration (Fia. 4). the cis barrier being much higher. (Cf. (5) f& a review of the question.) As a result the molecule is quite flexible, and therefore, easily distorted by molecular ~~
~
interactions. For instance, the dihedral angle 'Z' between the planes of the OH groups can vary within the extremes of 90" and 180' in various crystals (Table 2). This may account for the diversity in the values of the structural parameters one finds in chemistry textbooks. An often repeated set, ro.0 = 1.49 A, r o . ~ = 0.97 .&,8 0 0 ~ = 96O 52' and 93" 51', comes from the first single-crystal study by X-ray (7). However, a later neutron-diffraction investigation (8) has shown the 0 - 0 distance to he appreciably shorter than the above. As for the two angles, the &ed figures are definitely of unwarranted precision. (In fact the authors had rounded them off to 97' and 94' in their abstract.) Furthermore, these angles refer, not to the Hz02 molecule itself, hut rather t o the 0 - 0 . ..O planes between adjacent molecules because X-ray diffraction cannot locate H atoms accurately. There was no guarantee that the hydrogen bonds were colinear, which they are not, in fact. As for the liquid, there is unfortunately little information available on its molecular organization. An early X-ray study (16) has indicated only a compact packing of OH groups, probably of the cubic, face-centered type. Contraryto water, the packing is not as close as in the crystal, as shown by the relativelv . laree volume increase (15%) on meltine. From the scanty spectroscopic data the 0-0 bond length seems to be exactly the same as in the cr stal, but the average 0 . . .O distance is a little longer (2.83 ?). The dihedral angle 'Z' must fluctuate with the local environment and temperature-a nice problem of statistical mechanics. Lastly, the structural parameters of the free H201molecule are now known with good accuracy. The 0 - 0 bond length is 1.467 .& according to an electron diffraction study of the vapor (17). From that basis the other three parameters can be derived through correlation of the rotational constants from infrared (18) and microwave measurements (19). The rounded-off values shown in Figure 3 refer to what spectroscopists call the vibrational ground state of the molecule. Strictly speaking this is slightly different from the equilibrium configuration which, however, is mainly of theoretical interest
since i t cannot be realized because of the residual zero-point energy. In the present case it cannot be calculated accuratelv due insuffiiient spectroscopic data. However, by analog; with many related cases (20) one may predict a shortening of ahout 0.004 .&for the equdibrium 0 0 distance, and twice as much for O-H. The one parameter which should be aooreciably different from theground-state value is the dihkdral angle. Because of the very anharmonic shape of the potential well about the minimum (Fig. 4) 'Z', must be smaller than a, = 120'. From their analysis of the rotation-vibration spectra, Redington et a1 (18) found 'Z', = 109.5"C, which seems reasonable considering that the first torsional level is about halfway up the trans barrier. Literature Cited i l l i>ig~Bre,P. A . ? i n n 8 Roy Snr. Con., 3rd Seriea, 35, I (19dl). (21 Paneth, F., "Rvdio~Ele~nentr as Indicators,.' McGraw~HdlBook Co., New Yurk. 192%
0 ) Pauling,L.. "The N8tu.e 0 f t h e C h e m d Bond:Curnell Universityl'rrai, Ithaca. NY; iai Let Ed., 1999, (b) 3rd Ed.. ,960. (4) Scatchard, C., Kuvanagh, G. M. and 'Ticknor. I.. B.. J. Amvi Chem. Soc.. 71, 3715
1
(101 Pimentel. G. C. and McClellan, A. L.."The Hydrogen
Bond."Freeman, Sen Francisco,
llli". ~~
~
L.. Gig~1Pre.P.A.,Abe, M.. sndTsylur,R. C., S u ~ d i n c h ~ rActo. n 30A. 777 11974). (12) Ketelaar, J. A. A , "Chemical Canrtitution: Elsevier I'uhiirhir~g Co., Amsterdam. (111 Amsu,d.
1958.
Bain, 0. andGixuPre,P. A . Con d. Chsin .43, 527 (19551. Pennty, W. C. and Sutherland, G. B. R. M., Tinnr. irorodoy Soc ,30,898 (1934. and AChem. Phys.. 2.442 (1934). GiguBie, P. A.. J . Chvm. Phyi., 18.88 (1960). Randall, ,I. T., Prnt Roy. Soi. ILondunJ, LS9A,8:3 119371. GigaBra,P. A. andSch,,mnker, V.. J Amei Chem S n . , 66, 20'28 Li94:3). Redingtun. R. L.,Olxm W. B., and Cmsr. P. C..J Chem. Phyi., 36 1311 (1962). Oelfke. W. C. and Cordy, W . J Chrm. Phyl.. 12, 5S36 119fi91. Cottrel1.T. L.. "The Strengths of Chemical Bonds," 2nd Ed. Rutferworths, London,
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Volume 60
Number 5
May 1983
401
