ANNUAL REPORTSON THEPROGRESS OF CHEMISTRY.GENERAL AND PHYSICAL CHEMISTRY.1. MOLECULAR SPECTRA.SOME sections of this survey provide a continuation of subjects reported in1952.lMolecular Dimensions.-Much effort has been directed to the more precisedetermination of molecular dimensions. Pure rotational spectra in themicro-wave region and the far infra-red, and the Raman effect have been used,together with detailed analyses of the rotational fine structure of vibrationalbands in the near and photographic infra-red and in Raman spectra.Methane has been studied as such by Raman spectroscopy,2 as methane3and deuteromethane by absorption in the 3-p region, and as mono- andtri-deuteromethane 6 in the first overtone 7 and photographic infra-red. Theresults for monodeuteromethane give ro = 1-0936 A, and for trideutero-methane yo = 1.0919 fi.A difference in this sense is to be expected becauseof zero-point energy. However, for methane ro is found unexpectedly to be1.0931, which is between the value for monodeuteromethane and that fortrideuteromethane. The Q-branch of a band of 13CH4 has also been studied.Nitrous oxide provides a comparison between the results of micro-waveand infra-red spectroscopy. Values obtained for B, for the lowest vibrationstate (in Mc./sec.) are : Micro-wave J , 0-1 transition, 12561.64; J , 1-2transition, 12561.55 5 0-025; J , 3 - 4 and 4-5 transitions, 12561.65 -&0.025; lo vibration bands near 1 p, 12564.5; l1 vibration band near 4-5 p,12565-3 & 4-5.12 The results demonstrate the accuracy obtainable.Ifvalues of B are measured for enough excited vibrational states, correctionscan be made and the equilibrium configuration determined. Values of B forexcited states can be obtained from fundamental and overtone bands in theJ. W. Linnett, Ann. Reports, 1952, 49, 7.B. P. Stoicheff, C. Cumming, G. E. St, John,and H. L. Welsh, J . Chem. Phys., 1952,20, 498.A. H. Nielsen and H. H. Nielsen, Phys. Review, 1935, 48, 864; D. R. J. Boyd,H. W. Thompson, and R. L. Williams, PVOG. Roy. Soc., 1952, A , 213, 42.D. R. J . Boyd and H. W. Thompson, ibid., 1953, A , 216, 143.W. H. J. Childs and H. A. Jahn, ibid.. 1939, A , 169, 428.L. F. H. Bovey, J . Chem. Phys., 1953, 21, 830.T. A. Wiggins, E. R. Shull, J. M. Bennett, and D.H. Rank, ibid., p. 1940.D. K. Coles, E. S. Elyash, and J. G. Gorman, Phys. Review, 1947, 72, 973.S. J . Tetenbaum, ibid., 1952, 88, 772.lo C. M. Johnson, R. Trambarulo, and W. Gordy, ibid., 1951, 84, 1178.l1 G. Herzberg and L. Herzberg, J . Chern. Phys., 1950, 18, 551.l2 H. W. Thompson and R. L. Williams, Proc. Roy. Soc., 1951, A , 208, 32610 GENERAL AND PHYSICAL CHEMISTRY.infra-red. If rotational transitions can be observed for molecules in excitedvibrational states, it is also possible to determine them by using the micro-wave spectrum. This can be done only when the vibrational quanta aresmall, and has been achieved in part for carbonyl sulphide and cyanogenbromide. l3 When a molecule possesses larger vibration frequencies infra-red spectra must be used to obtain Be, the rotational constant for the equili-brium configuration.Ivash and Dennison l4 have made calculations on methyl alcohol by usingmicro-wave data.15 The dimensions for the lowest vibrational state are :CH, OH, and CO bond-lengths 1-093,0.937, and 1.434, and CCH and HcHangles 105" 56' and 109" 30' (cf.0.958 and 104" 31' in H20 Is). The oxygenatom does not lie on the symmetry axis of the methyl group but 0.079 fromit. The barrier height, a sinusoidal potential being assumed, was 374.8 cm.-l(1071 cals.). .The micro-wave spectra of SiD3C1,17 SiD,F,18 HSiC13,19 CH3SiCl3,19(CH3)3SiCI,19 HGeC1,,20 CH2C1F,2l (CH3),CF,22 and CF&1 2, have beenAexamined. In HGeCI, the ClGeC1 angle is 108" 17' & 12'.This shows that,when C1-Cl repulsion is minimised, chlorine can, like fluorine (cf. HCF, 24 andHGeF, 25), lead to a reduction in the inter-bond angle below the tetrahedralvalue. In CH2ClF 21 the Cl?F angle (110" 1') is greater than 109" 28', but itis surprising that the opposite HCH angle (111" 56') is also greater than thetetrahedral. In CH,ClF, the C-C1 bond length is 1-759 A, which is less thanthat in CH,C1 (1.779),26 but about the same as that in carbon tetrachloride(1.755) ; 26 while in CF,Cl it is 1-74 A, which is less than in carbon tetra-chloride. The effect in CF,C1 has been explained by resonance but it might,equally, be due to the high electronegativity of fluorine.Several diatomic molecules have been examined by micro-wave andinfra-red spectroscopy.Thompson and his co-workers have analysed thefundamental bands of hydrogen chloride,27 deuterium chloride,28 13C160 and12C180.29 The results for carbon monoxide are consistent with the data ofPlyler et aZ.,O and with micro-wave 31 and ultra-violet results.32 Hansler13 S. J. Tetenbaum, Phys. Review, 1952, 86, 440.I4 E. V. Ivash and D. M. Dennison, J . Chem. Phys., 1953, 21, 1804.l5 W. D. Hershberger and J. Turkevich, Phys. Review, 1947, 71, 554; 13. P. Dailey,ibid., 1947, 72, 84; D. K. Coles, ibid., 1948, 74, 1194; R. H. Hughes, Mr. E. Good, andD. K. Coles, ibid., 1951, 84, 418.l6 B. T. Darling and D. M. Dennison, ibid., 1940, 57, 128.l7 €3. Bak, J. Bruhn, and J. Rastrup-Andersen, .{. Chem. Plzys., 1953, 21, 753.l8 Idem, ibid., p.752.23 P. Venkateswarlu, R. C. Mockler, and W. Gordy, ibid., p. 1713.21 N. Muller, J . Amer. Chem. SOC., 1963, 75, 860.22 F. Andersen, J. Rastrup-Andersen, B, Bak, 0. Bastiansen, E. Risberg, and23 J. Sheridan and W. Gordy, ibid., 1952, 20, 591.24 S. N. Ghosh, R. Trambarulo, and W. Gordy, ibid., p. 605.25 W. E. Andersen, J. Sheridan, and W. Gordy, Phys. Review, 1951, 81, 819.26 P. W. Allen and L. E. Sutton, Acta Cryst., 1950, 3, 48.2 7 I. M. Mills, H. W. Thompson, and R. L. Williams, Proc. Roy. soc., 1953, A , 218. 29.2 8 J . Pickworth and H. W. Thompson, ibid., p. 37.*S I. M. Mills and H. W. Thompson, Tra?zs. Faraday s o s . , 1953, 49, 224.39 E. K. Plyler, W. S. Benedict, and S. Silverman, J . Clzem. Phys., 1952, 20, 175.31 0.R. Gdliam, C . M. Johnson, and ?V. Gordy, Phys. Review, 1956, 78, 140.32 I<. E. McCulloh and G. Glockler, ibid., 1953, 89, 145.AID R. C. Mockler, J. H. Bailey, and W. Gordy, ibid., p. 1710.L. Smedvik, J . Chem. Phys., 1953, 21, 373LINNETT : MOLECULAR SPECTRA. 11and Oetjen have studied the pure infra-red rotational spectra of hydrogenchloride, deuterium chloride, hydrogen bromide, and ammonia with agrating spectrometer ; 33 the results for the diatomic molecules agree with thedata compiled by Herzberg34 who gives 1.27460 and 1.274, A for re forhydrogen chloride and deuterium chloride. Thompson et al. give for these1.274, 27 and 1.2746 28 A. The micro-wave spectra of l6ol60 and l6oi70have been measured,35 and the effect of added gases on the line breadth hasbeen used to determine molecular collision diameters.36The micro-wave spectrum of the hydroxyl radical has been observed bystreaming water vapour through a discharge tube and then into the absorptioncell.,' The authors conclude that the proportion of hydroxyl radical is a fewtenths of l%, and that it should be possible to study " hydroxyl radicalsproduced by a variety of chemical reactions, and that other free radicals mayprove accessible to micro-wave techniques." This may mark the beginningof an important application of micro-wave spectroscopy.The micro-wave spectrum of ozone has been studied by Hughes 38 and byTrambarulo et aL39 The former gives the bond length as 1.276-1.279 andthe angle as 116~-117°, 10" less than the value obtained by electrondiffraction.The latter authors give 1.278 & 0.003 A and 116" 49' zt 30'.Another interesting molecule studied by micro-wave spectroscopy is chlorinetrifluoride.40 It is T-shaped with one bond length of 1-598 and two of1.698 A ; the interbond angle is 87" 29' (X-ray diffraction results 41 oncrystalline chlorine trifluoride confirm the shape, giving for the dimensions1.621, 1.716, and 86" 59'). This molecule appears to be based on a trigonalbipyramid in which two equatorial positions are occupied by lone pairs ofelectrons. The tendency of fluorine to cause a decrease in FXF bond anglesis also in evidence here.,2There has been some work during the year 011 ammonia3, and relatedmolecules.43 The pure rotation spectrum of ND, from 60 to 200 cni.-l hasbeen examined ; 44 the value determined for the centrifugal distortioncoefficient agrees with that to be expected. The micro-wave spectrum ofND, has been measured,45 and also the fine structure of an NH, band appear-ing in the Raman spectrum.46 Coriolis coefficients of these molecules havebeen discussed.47The molecular dimensions of benzene have been determined from therotational Raman spectrum of the vapour ; 48 B, = 0.18955 5 0.00005, andDo = 1.2 x cm.-l If the C-H length is between 1.06 and 1-09 A, the33 R.L. Hansler and R. A. Oetjen, J . Chern. Phys., 1953, 21, 1340.34 G. Herzberg, " Spectra of Diatomic Molecules," Van Nostrand, New York, 1950,3G R. S. Andersen, W. V. Smith, and W. Gordy, ibid., 1952, 87, 561.37 T.M. Saunders, A. L. Schawlow, G. C. Doumanis, and C. H. Townes, ibid., 1953,R. Trambarulo, S. N. Ghosh, C. A. Burrus, and W. Gordy, J . Chem. Phys., 1953,/\p. 534.89, 1159.21, 851.35 S. L. Miller and C. H. Townes, Phys. Review, 1953, 00, 537.38 R. H. Hughes, ibid., 1952, 85, 717.I 0 D. G. Smith, ibid., p. 609.41 R. D. Burbank and F. N. Bensey, ibid., p. 602.42 C. E. Mellish and J. W. Linnett, to be published.43 V. M. McConaghie and H. H. Nielsen, J . Chem. Phys., 1953, 21, 1836; W. H.4r'R. E. Stroup, R. A. Oetjen, and E. E. Bell, ibid., p. 2072.4 5 R. G. Nuckolls, L. J. Ruiger, and H. Lyons, Phys. Review, 1953, 89, 1101.d6 C. Cumming and H. L. Welsh, J . Chewz. Phys., 1953, 21, 1119.4 7 H. H. Nielsen, ibid., p. 142.Haynie and H.H. Nielsen, ibid., p. 1839.48 B. Stoicheff, ibid., p. 141012 GENERAL AND PHYSICAL CHEMISTRY.C-C length is between 1.396 and 1.401 A. The spectra of hydrogen cyanideand deuterium cyanide between 0.5 and 2-5 p give 1.0657 and 1.1530 for theequilibrium C-H and C-N bond lengths.49 The pure rotational spectra ofhydrogen cyanide and deuterium cyanide have also been studied, givingbond lengths for the ground vibrational states.”Other molecules that have been examined are SOF,,51 S02Cl,,52 COCl,,53CH,I, e t ~ . , ~ ~ D20,55 HD0,56 HCNS,57 C5H,N,5* C,H,NH,59 NaCl and CsC1,G0C8H13C1 and C8Hl,Br,61 PH2D and PD,H,62 C2N2,63 C,H2,63 CH3*C--CH,63DI,64 and H,S.65Molecular Vibrations-The vibrational spectra of simple polyatornicmolecules continue to be investigated extensively.A number of fluorine-substituted ethanes 66 and aromatic compounds 67 have been studied;Cleveland, Meister, and their co-workers have continued their examinationof substituted methanes 68 and other simple molecules ; 69 and several siliconcompounds have been in~estigated.~O More work has been carried out onrotational isomerism. 7149 A. E. Douglas and D. Sharma, J . Chem. Phys., 1953, 21, 448.50 A. H. Nethercot, J. A. Klein, and C. H. Townes, Phys. Review, 1952, 86, 798;J. W. Simmons, R. S. Andersen, and W. Gordy, ibid., p. 1055; T . L. Weatherly and D.Williams, ibid., 1952, 87, 517. 61 R. C. FergusonandE. B. Wilson, ibid., 1953, 90, 338.52 R. M. Fristrom, ibid., 1952, 85, 717.53 G. W. Robinson, J . Chem.Phys., 1953, 21, 1741.64 T. A. Wiggins, E. R. Shull, and D. H. Rank, ibid., p. 1368.55 W. S. Benedict, N. Gailar, and E. K. Plyler, ibid., p. 1301.66 Idem, ibid., p. 1302; D. W. Posener and M. W. P. Strandberg, ibid., p. 1401.5 7 G. C. Dournanis, T. M. Sanders, C. H. Townes, and H. J. Zeiger, ibid., p. 1416.5 8 B. Bak and J. Rastrup-Andersen, ibid., p. 1306.59 W. S. Wilcox, K. C. Brannock, W. DeMore, and J. H. Goldstein, ibid., p. 563;6J M. L. Stitch, A. Honig, and C. H. Townes, Phys. Review, 1952, 86, 813.61 A. H. Nethercot and A. Javan, J . Chem. Phys., 1953, 21, 363.62 R. E. Stroup and R. A. Oetjen, ibid., p. 2092; M. H. Sirvetz and R. E. Weston,ibid., p. 898.63 D. R. J. Boyd and H. W. Thompson, Trans. Farnday Soc., 1953, 49, 141; G. D.Craine and H.W. Thompson, ibid., p. 1273.64 J. A. Klein and A. H. Nethercot, Phys. Review, 1953, 91, 1018.6 5 C. A. Burrus and W. Gordy, ibid., 1953, 92, 274; W. Gordy and W. C. King,ibid., 1953, 90, 319.6 6 J. R. Nielsen, C. Y. Liang, R. M. Smith, D. C. Smith, M. Alpert, and C. W. Gul-likson, J . Chem. Phys., 1953, 21, 383, 1060, 1070, 1416. See also D. E. Mannand E. K.Plyler, ibid., p. 1116.6 7 J. R. Nielsen, E. E. Ferguson, R. L. Hudson, D. C. Smith, R. L. Collins, and L.Mikkelsen, ibid., p. 1457, 1464, 1470, 1475, 1727, 1731, 1736.6 8 F. F. Cleveland, A. G. Meister, F. L. Voelz, C. E. Decker, R. B. Bernstein, S. I.Miller, A. Weber, J. P. Zietlow, and J. E. Lamport, ibid., p. 155, 189, 242, 930, 1778,1781, 1903. See also P. H. Lindenmeyer and P.A$. Harris, ibid., p. 408; H. D. Rix,ibid., p. 1077; S . R. Polo and M. K. Wilson, ibid., p. 1129; W. F. Edge11 and C. May,ibid., p. 1901.69 F. F. Cleveland, A. G. Meister, S. M. Ferigle, A. Weber, and C. E. Decker, ibid.,p. 90, 722, 1613. See also F. A. Miller and R. B. Hannan, ibid., p. 110; B. D. Saksena,R. E. Kagarise, and D. H. Rank, ibid., p. 1613 ; D. E. Mann, N. Acquista, and E. K.Plyler, ibid., p. 1949.7O H. Murata, ibid., p. 181 ; J. A. Hawkins and M. K. Wilson, ibid., p. 360; H.Murata and M. Kumada, ibid., p. 945; J. A. Hawkins, S. R. Polo, and M. K. Wilson,ibid., p. 1122; A. L. Smith, ibid., p. 1997; A. Monfils, Compt. rend., 1953, 236, 795.S. I. Mizushima, T. Shimanouchi, I. Nakagawa, A. Miyake, T. Miyazawa, I.Tchishima, and K.Kuratani, J , Chem. Phys., 1953, 21, 215, 815, 1411; B. Bak, L.Hansen, and J. Rastrup-Andersen, ibid., p. 1612; G. D. Buckley, J., 1953, 1325; L. A.Duncanson, J., 1952, 1753; G. J. Szasz and N. Sheppard, Trans. Fwaday Soc., 1953,49, 358; J. K. Brown and N. Sheppard, ibid., 1952, 48, 128.R. D. Johnson, R. J. Myers, and W. D. Gwinn, ibid., p. 1425LINNETT : MOLECULAR SPECTRA. 13The Raman spectrum of thionyl chloride 72 shows four displacements forwhich the scattered radiation is polarised. If the molecule were planar onlythree fundamentals should lead to polarised Raman lines, so the results showit to be non-planar. A similar approach has been made for selenium tetra-fluoride.73 It appears that the symmetry is C2u, and that the structure isderived from a trigonal bipyramid with one lone pair in an equatorial position.The Raman and infra-red spectra of ferrocene and ruthenocene have beenexamined 74 to obtain information about their structure.75 The smallnumber of lines and bands indicates that the molecules are highly symmetricaland that the interaction between the two rings is small.The Raman spectrum of gaseous ethylene has shown 76 that the partiallysymmetric Raman active C-H bond stretching vibration has a frequency of3108 cm.-l (cf.Plyler 77) and not 3272.78 Crawford et aE. have measured thethe infra-red spectrum of 1 : l-dideuteroethylene and have deduced all thegeneral valency force field-potential constants of ethylene. 79 As withethane 8o the bond-angle constants seem to be larger than all other interactionconstants.A thorough study has been made of the fundamental, overtone, and com-bination infra-red bands of hydrogen cyanide and deuterium cyanide.49The first-order anharmonic constants have been obtained and certain errorsin previous work corrected.No simple formula can reproduce accuratelyall the excited vibration levels as perturbations lead to irregularities whichhave been clearly observed.Bethel1 and Sheppard 81 have been able to identify certain infra-redbands in the spectra of the hydrates of nitric and perchloric acids as beingdue to H,O+. Another study of inorganic compounds has been that of theions UO,++, NpO,++, PuO,++, AmO,++, NpO,+, and Am02+.82 The singlycharged ions have a smaller antisymmetric valency vibration frequency thanthe doubly charged ions, indicating that the additional electron is antibond-ing.This vibration frequency is greater for PuO,++ than for the otherdoubly charged ions. Another inorganic application is the investigation ofthe Raman spectra of mixtures of the chlorides and iodides of silicon, tin, andgermanium, showing that mixed chloroiodides of these elements exist in themixtures.83 The infra-red spectra of the hexafluorides of sulphur, selenium,tellurium, tungsten, molybdenum, and uraniumJS4 and their Raman spectra,are consistent with these molecules’ being regular octahedra.Crawford and Dagg 85 have shown that, in an intense electric field, linesin the Q-branch for the fundamental vibrational transition of molecularhydrogen can be observed by infra-red absorption. Comparison with Raman72 C.A. McDowell, Trans. Faraday SOC., 1953, 49, 371.73 J. A. Rolfe, L. A. Woodward, and D. A. Long, ibid., p. 1388.74 E. R. Lippincott and R. D. Nelson, J . Chenz. Phys., 1953, 21, 1307.J. D. Dunitz and L. E. Orgel, Nature, 1953, 171, 121.75 H. H. Jaffe, J. Chem. Phys., 1953, 21, 156.7 6 B. P. Stoicheff, ibid., p. 755.7 8 D. H. Rank, E. R. Shull, and W. E. Axford, ibid., 1950, 18, 116.79 B. L. Crawford, J. E. Lancaster, and R. G. Inskeep, ibid., 1953, 21, 678.81 D. E. Bethel1 and N. Sheppard, ibid., 1953, 21, 1421.8 2 L. H. Jones and R. A. Penneman, ibid., p. 542.83 M. L. Delwaulle, M. B. Busset, and M. Delhaye, J . Amev. Chem. SOC., 1952, 74,5768.84 J.Gaunt, Trans. Faraday SOC., 1953, 49, 1122.8 5 M. F. Crawford and I. R. Dagg, Phys. Review, 1953, 91. 1569.See also7 7 E. K. Plyler, ibid., 1951, 19, 658.G. E. Hansen and D. M. Dennison, ibid., 1952, 20, 31314 GENERAL AND PHYSICAL CHEMISTRY.data suggests that there is a real discrepancy between the infra-red and Ramandata which increases with increasing rotational quantum number. Chisholmet aZ.86 have obtained infra-red absorption corresponding to the fundamentalvibration transition of hydrogen when other gases or hydrogen itself areadded at very high pressures (up to 1500 atmos.). Under these conditionsthe Q-branch is split.0 ther simple molecules that have been examined by infra-red and Ramanspectra are S2F10,87 Pb(CH,),, etc.,88 C(CD,),,89 and N,S,.90 Theoreticaltreatments and force-constant calculations have been made by Cra~ford,~lH i g g ~ , ~ ~ T~rkington?~ Thomas,94 Pitzer and G e l l e ~ , ~ ~ Heslop and Linnett ,96and othersg7Structure Determination.-A few examples of the application of vibra-tional spectra to the determination of structure will be presented.Flett 98 has examined thioamides containing the grouping *NH*CS* forevidence of the existence of the form *N:C(SH)-. He found a sharp band at3430 cm.-l and a broad one at 3000 cm.-l, which, because of its strength andby analogy with other molecules, was ascribed to the hydrogen bond:NH - * SC:.There were no bands near 2500 cm.-l indicating that S-Hbonds were not present. Goulden 99 has examined the quaternary methio-dides of NN-disubstituted thioamides, and from the decrease in the C-Nvibration frequency from 1611 in MeS*CPh:NPh to 1562 cm:l in(MeS*CPh:NPhMe) + concludes that there is a small contribution from thestructure MeSXPh-NPhMe. There is no frequency decrease when thesulphur atom is absent.Various studies have been made of organic phos-phorus compounds.lW Haszeldine lo1 has made a most interesting study ofaliphatic nitro-compounds, and the effect, on the cyano- and two nitro-groupstretching frequencies, of substituents on the carbon atom adjacent to thenitro-group. For example, he finds that halogen atoms and additionalnitro-groups lead to a rise in the antisymmetric and a fall in the symmetricnitro-group stretching frequencies.This implies a greater interaction be-tween the N-0 bonds. He has also examined the infra-red spectra of somefluorinated alcohols.lo2 Duncanson lo3 has shown that, in some cases, theketo-forms of some tetronic acids predominate in solution; and the effect ofstructure on the characteristic carbonyl frequency in about 130 quinonoidcompounds has been measured.104 Davison and Bates Io5 examined vinyl+86 D. A. Chisholm, J. C. F. Macdonaid, M. F. Crawford, and H. L. Welsh, Phys.8 7 D. Edelson, J . Awzer. Chem. SOC., 1952, 74, 262.88 E. R. Lippincott and M. C. Tobin, ibid., 1953, 75, 2436.89 E. R. Shull, T. S. Oakwood, and D. H. Rank, J . Chem. Phys., 1953, 21, 2024.99 E. R. Lippincott and M. C . Tobin, ibid., p. 1559.0 1 B. L. Crawford, ibid., p.1108.92 P. W. Higgs, ibid., p. 1131.94 W. J. 0. Thomas, Trans. Faraday SOC., 1953, 49, 855.g 5 K. S. Pitzer and E. Gelles, J . Chem. Phys., 1953, 21, 855.O 6 W. R. Heslop and J. W. Linnett, Trans. Favaday SOC., 1953, 49, 1262.9 7 J. S. Ziomek and C. €3. Mast, J . Chem. Phys., 1953, 21, 862; E. Ferguson, ibid..p. 886; J. C. Decius, ibid., p. 1121 ; C . Y . Pan and J. R. Nielsen, i b i d . , p. 1427.g8 R.I. St. C. Flett, J., 1953, 347.l o o M. Halman and S. Pinchas, J., 1953, 626; L. J . Bellamy and L. Beecher, J . ,1953, 728.lo2 Idem, e'bid., p. 1757.lo4 M. L. Josien, N. Fuson, J. M. Lebas, and T. M. Gregory, J . Chem. Phys., 1953,Review, 1952, 88, 957.O3 P. Torkington, ibid., p. 83.gg J. D. S. Goulden, J., 1953, 997.lo1 R. N. Haszeldine, J., 1953, 2525.lo3 L.A. Duncanson, J., 1953, 1207.lo5 W. H. T. Davison and G. R. Bates, J., 1953, 2607. 21, 331LINNETT : MOLECULAR SPECTRA. 15and isopropenyl compounds containing polar groups, considering shifts inthe characteristic C X bands. The characteristic frequencies of the azo- andisocyanate-groupings have been disccssed by Le Fcvre et d 1 0 6 and byDavison lo7 and Thomas.lO8N-substituted amides show a characteristic frequency at 1560 cm.-lwhich has been ascribed to C-N valency lo9 and also to N-H deformationvibrations.l1° Letaw and Gropp ll1 conclude from their examination of anumber of such compounds that the former assignment is correct, and suggestreasons for the absence of this band in NN-disubstituted amides. Kesslerand Sutherland have discussed the out-of-plane N-H deformation frequencyin the peptide link 112 (cf.Davies and Evans l13).The infra-red and Raman spectra of hydrocarbons have been discussed intwo valuable reviews by Sheppard and Simpson 114 (see also Stein andSutherland 115).Far Infra-red Spectroscopy.-Measurements have been extended furtherinto the infra-red by using new prism materials, grating instruments,l16 or byemploying residual rays.l17 These have been used to determine purerotational spectra and also low vibration frequencies. For example,O’Loane 117 observed vibration bands of C,O, at 192 crn.-l, PCl, at 190, andCH,*CHO at 120 and 245 cm:l Hansler and Oetjen33 observed purerotation spectra between 70 and 250 cm.-l Pitzer and Hollenberg 11*examined the spectrum of CH3*CC1, from 130 to 430 cm.-l, observing bands at239 and 344 together with a sequence of absorption peaks at 135,154, and 172which seemed to be related to another series at 565, 548, and 533 cm.-lThey ascribed the last six bands to transitions involving various levels of thetorsional vibration combined with the 0 + 1 transition of a fundamental offrequency 351 cm.-l and concluded that the successive levels of the torsionalvibration lay at 214, 412, and 591 cm.-l (transitions suggested were:351 - 214= 137;351 + 214 = 565;351 + 214- 412 = 153;351 + 412 - 214 = 549;351 + 412 - 591 = 172;351 + 591 - 412 = 530).The successive levels of the torsional vibration were interpreted in terms of apotential functionV(+) = 4V3(l - cos 34) + $V6(l - cos 64).The levels observed lead to V3 = 1017 cm.-l (2910 cals./mole) and v6 = 19.9cm.-l (57 cals./mole).So the height of the barrier is 2967 cals. and theminimum narrower and the maximum broader than for a function withv6 = 0.loti R. J. W. Le Fbvre, M. F. O’Dwyer, and R. L. Werner, Chenz. a;zd I n d . , 1953,378.lo’ W. H. T. Davison, J., 1953. 3712.lo8 W. J. 0. Thomas, Chem. and Ind., 1953, 567.log H. Lenormant, Ann. Chim., 1950, 5, 459.110 R. E. Richards and H. W. Thompson, J . , 1947, 1248.ll1 H. Letaw and A. H. Gropp, J . Chem. Phys., 1953, 21, 1621.112 H. K. Kessler and G. B. B. M. Sutherland, ibid., p. 570.llS M. Davies and J. C. Evans, J., 1953, 480.114 N. Sheppard and D. M. Simpson, Quart.Reviews, 1952, 6, 1 ; 1953, 7, 19.115 R. S. Stein and G. B. B. M. Sutherland, J . Chem. Phys.. 1953, 21, 370.116 C. R. Bohn, N. K. Freeman, W. D. Gwinn, J. L. Hollenberg, and K. S. Pitzer,ibid., p. 719; R. A. Oetjen, W. H. Haynie, W. M. Ward, R. L. Hansler, H. E. Schwau-wecker, and E. E. Bell, J . Opt. SOC. Amer., 1952, 42, 559.117 J. K. O’Loane, J . Chem. Phys., 1953, 21, 669.11* K. S. Pitzer and J. L. Hollenberg, J . Amer. Chem. SOC., 1953, 75, 221916 GENERAL AND PHYSICAL CHEMISTRY.There is no doubt that a study of the region 7 0 4 0 0 cm? would be mostvaluable.Intensities of Infra-red Bands.-The present paragraphs supplement lastyear’s section, under the same title.Penner and Weber 119 have measured the intensities of the fundamentaland first overtone bands of nitric oxide, hydrogen chloride, and hydrogenbromide, the pressure-broadening technique being used.120 Their measuredintensity for the fundamental of nitric oxide is about half that observed byother workers. The value for the first overtone agrees with that given byCrawford and Dinsmore 121 however. With hydrogen chloride there is muchbetter agreement for the fundamental,122 though Penner and Weber do notagree with Dunham’s value for the 0 ~ e r t o n e . l ~ ~ These results show somedisagreement even for the measured relative intensities (cf. results for car-bony1 sulphide 12*).From the intensities of fundamental and overtone, Penner and Weber 119find for hydrogen chloride :(where represents the electric moment), demonstrating that when theresults for two bands are combined, there are alternative sets of results whichsatisfy the data, because the intensity of a band is dependent only on themagnitude and not on the sign of the moment change.It is often impossibleto choose between these alternative sets.Schatz and Hornig l 2 5 have determined the intensities of the two infra-redbands each of carbon tetrafluoride, silicon tetrafluoride, and sulphur hexa-fluoride. Graphs presented show that the deduced values for the bondmoment, p’, and its derivative with respect to bond length, dp’/dr (cf. ref. l),are very dependent on the particular potential-energy function selected. Innone of these molecules can a unique force field be derived from the fre-quencies. So there is uncertainty in the deduced bond-moment data becauseof uncertainty in our knowledge of the potential constants.This demon-strates a difficulty often encountered in making reliable use of intensity data.Schatz and Hornig list sets of most likely p’ and dp’/dr for these threemolecules. For example they give for carbon tetrafluoride p‘ = 1-12 D,and dp’/dr = 4.88 D/L% (a less likely set is 2.36 D and 3.35 D/A). They com-pare their value for dp‘ldr with that of 4.70 for the C-F bond in methylfluoride.By examining band intensities in hydrogen cyanide and deuteriumcyanide, Hyde and Hornig 127 obtained values for the C-H and C-N bondmoments, assuming these to remain constant and directed from atom to atomduring the bending vibration. The vector sum of these bond moments11° S.S. Penner and D. Weber, J . Chem. Phys., 1953, 21, 649.lZo E. B. Wilson and A. J. Wells, ibid., 1946, 14, 578.121 B. L. Crawford and H. L. Dinsmore, ibid., 1950, 18, 983, 1682.122 D. G. Bourgin, Phys. Review, 1927, 29, 794; 1928, 32, 237; R. Rollefson and A.Rollefson, ibid., 1935, 48, 779. la3 J. L. Dunham, ibid., 1929, 34, 438; 1930, 35, 1347.12* D. 2. Robinson, J . Chem. Phys., 1951, 19, 881; H. J. Callomon, D. C. McKean,and H. W. Thompson, Proc. Roy. Sic., 1951, A , 208, 341.lz5 P. N. Schatz and D. F. Hornig, J . Chem. Phys., 1953, 21, 1516.lZ6 G. M. Barrow and D. C. McKean, Proc. Roy. Soc., 1952, A , 213, 27.12’ G. E. Hyde and D. F. Hornig, J . Chem. Phys., 1952, 20, 977LINNETT MOLECULAR SPECTRA.17agreed quite well with the observed moment of hydrogen cyanide. However,in other molecules (e.g., the methyl halides) the agreement is not good.128This, along with other results, makes it doubtful whether the approximationof additive bond moments is a goodThe above examples demonstrate some of the difficulties arising in thedetailed interpretation of band intensities in simple molecules. Consequentlysome workers have felt that more progress could be made by examiningintensity variations in series of molecules. Richards and Burton 130 studiedthe bands due to N-H and C=O vibrations. They found that the intensityof the characteristic C=O band near 1700 cm.-l increased in the series:aldehyde, ketone, acid chloride, ester, and amide. The intensity of thecarbonyl bond in a series of molecules in the vapour state and in solutionhas since been studied by Barrow.131 He ascribes increased intensities overthose in simple aldehydes and ketones to the effects of conjugation (cf.Fraserand Price 132) and obtains a quantitative correlation of increase in intensitywith the resonance energy. Liddel, Wulf, and Hendriks 133 studied N-H andO-H bands, Fox and Martin 134 C-H, and Francis135 C-H bands (cf.Mecke 136).There seems little doubt that both types of approach are valuable.A valuable application of intensity measurements has been made to thedetermination of structure in steroids.137 had given a numberof relationships which enabled changes in the carbonyl characteristic fre-quency to be used in assigning structures in these molecules ; but ambiguitiesarose when frequencies of two groupings were very nearly the same.In suchcases changes in integrated band intensity, the determination of which hasbeen considered by Ram~ay,13~ can sometimes be used to differentiate be-tween different side-chain carbonyl groupings. The intensity may vary by afactor of four, and systematic changes occur when the carbonyl group isconjugated. For ring carbonyls the intensity varies only slightly withposition so, for these, integrated band intensities may be used to determinethe number of them.Whiffen 140 examined the effect of solvent on the intensity of the 760ern? band of chloroform. The integrated area is approximately indepen-dent of the solvent ( * l O ~ o ) , but the peak height and width at half-heightvary much more (3 40%).This is important for the use of such measure-ments for structural determinations.Herman and S h ~ l e r , l ~ ~ and Heaps and Herzberg 142 have obtained ex-12* I am grateful to A. V. Golton for discussions of these topics.120 A. M. Thorndike, J . Chem. Phys., 1947, 15, 868.130 R. E. Richards and W. R. Burton, Trans. Faraday SOC., 1949, 45, 874.131 G. M. Barrow, J . Chem. Phys., 1953, 21, 2008.132 R. D. B. Fraser and W. C. Price, Nature, 1952, 170, 490.133 U. Liddel, 0. R. Wulf, and S. B. Hendriks, J . Autzer. Chem. SOC., 1933, 55, 3574;134 J . J. Fox and A. E. Martin, Proc. Roy. SOC., 1937, A, 162, 417.136 S. A. Francis, J . Chem. Phys., 1950, 18, 861.136 R.Mecke, ibid.. 1952, 20, 1935.13' R. N. Jones, I). A. Ramsay, D. S. Keir, and K. Dobriner, J . Awzer. Chenz. SOC.,lS8 R. N. Jones, P. Humphries, and K. Dobriner, ibid., 1950, 72, 956.130 D. A. Ramsay, ibid., 1952, 74, 72.140 D. H. Whiffen, Trans. Faraday SOC., 1953, 49, 878.142 H. S. Heaps and G. Herzberg, 2. Physik, 1052, 133, 48.Jones et1953, 57, 1464; 1936, 58, 2287.1952, 74, 80.R. C . Herman and K. E. Shuler, J . Chern. Phys., 1053, 21, 37318 GENERAL AND PHYSICAL CHEMISTRY.pressions for transition probabilities, continuing the work of Dunham,l23R ~ s e n t h a l , ~ ~ ~ and Crawford and Dinsmore.121Intensities of Raman Lines.-The study of intensities in the vibrationalRaman effect is more difficult, both experimentally and theoretically, thanthat of infra-red intensities. Theoretically this is because polarisability is atensor and six quantities are required, in the absence of symmetry, to specifyfully its change during a vibration.In general the dipole moment, being avector, can be specified by three quantities, though again symmetry mayreduce this number. A consequence of this greater complexity is thatassumptions regarding the cause of polarisability changes have to be intro-duced at an earlier stage in the theory of Raman intensities than in that ofinfra-red intensities.Long,144 in a paper on intensities in Raman spectra, discusses a bond-polarisability theory according to which the polarisability associated witheach bond can be specified by four quantities : the equilibrium longitudinaland transverse polarisabilities, and the changes in these with length.I t isalso assumed that the bond polarisabilities can be added vectorially.Wolkenstein 145 applied this successfully to a number of halogen derivativesof methane, supposing that the bond properties could be transferred fromone molecule to another. An alternative hypothesis was suggested byCabannes and Rousset 146 who regarded the atoms as centres of constantpolarisability and ascribed changes that occurred during vibrations tochanging interactions between them. Bhagavantam 14’ treated hydrogen,nitrogen, oxygen, and chlorine according to this model ; success was greatestfor chlorine, in which most of the electrons are in lone pairs, and least inhydrogen where all electrons are bonding.Rao 148 treated carbon tetra-chloride similarly [k., as C4’ (Cl-)4]. Assuming the polarisability of C4+ tobe zero, he obtained a derived polarisability for the symmetric vibration closeto the experimental value. Woodward and Long 149 showed that similarcalculations for silicon tetrachloride, stannic chloride, carbon tetrabromide,silicon tetrabromide, and stannic bromide were unsuccessful. Matossi 150employed a similar approach but found it necessary to suppose that theatomic polarisabilities themselves vary during the distortions. A similarapproach has been made by Heslop and L i ~ ~ n e t t , ~ ~ who treat boron tri-fluoride as B3+(F-),, it being supposed that the polarisability resides solelyin the fluoride ions.They are able to account for the observed relativeintensities, a constant polarisability for the fluoride ion being used, but thededuced depolarisation factor is much greater than that to be expectedexperimentally by analogy with boron trichloride. So it appears that theCabannes and Rousset approach is only partially successful but, nevertheless,that it is worth further study. On the other hand the most successful treat-143 J. E. Rosenthal, Proc. Nat. Acad. Sci., 1935, 21, 281.144 D. A. Long, Proc. Roy. Soc., 1935, A , 217, 203.145 M. Wolkenstein, Acta Physicochenz. U.R.S.S., 1945, 20, 161, 174, 525, 544, 835,883; J . Exp. Theor. Phys. U.S.S.R.. 1948, 18, 138; Conzpt. rend. Acad. Sci. U.R.S.S.,1941, 32, 185; J . Phys. U.S.S.R., 1945, 9, 101, 326.146 J.Cabannes and A. Rousset, J . Phys. Radium, 1940, 1, [viii], 138, 155.14’ S. Bhagavantam, “ Scattering of Light and the Raman Effect,” Chem. Publ.Co. Inc., New York, 1942, p. 103.lo8 B. P. Rao, Proc. Indian Acad. Sci., 1940, 11. 1.149 L. A. Woodward and D. A. Long, see ref. 144.lS3 F. Matossi, J. Chem. Pliys., 1951, 19, 1007LINNETT MOLECULAR SPECTRA. 19ment of a wide range of molecules is that of the halogenomethanes byW ~ l k e n s t e i n , ~ ~ ~ who used a bond-polarisability theory. 151Further experimental results are needed in this most interesting field.It may then be possible to choose between the different hypotheses.Quadrupole-coupling Coefficients.-The quadrupole-coupling coeficients,obtained by micro-wave spectroscopy, allow the determination of the electricfield gradient at a nucleus having a known quadrupole moment.This fieldgradient is caused by the asymmetry of the electron cloud, and so thesemeasurements provide information about the electron distribution. Thishas often been interpreted in terms of hybridised orbitals. References topapers describing such measurements were given in 1952.1 During 1953further results have been published. Klein and Nethercot 64 have concludedthat in deuterium iodide, in which the electronegativities indicate that thereis 5% ionic character, there is also 15-20% s-hybridisation in the bondingorbital of the iodine atom. Sheridan and Gordy 23 have concluded that therewas 6.6% double-bond character in the C-C1 bond of chlorotrifluoromethane.From the micro-wave spectrum of arsenic trifluoride Kisliuk and Geschtvind 152obtain one moment of inertia and a quadrupole-coupling coefficient.Bycombining these, interpreting the latter in terms of sfi-hybridisation, anddrawing analogies with arsenic trichloride they deduce an approximate valuefor the FAsF angle. Robinson 53 has studied carbonyl chloride whichcontains two chlorine nuclei, and in C035C137C1 two different chlorine nuclei.The theory of this has been examined by Robinson and Corn~e11.l~~ Theresults indicate that the electron distribution is not cylindrically symmetricabout the C-C1 bond, but that it extends to a greater degree out of the planeof the molecule. This might be due to (a) some x bonding in the C-C1 bond;(b) a distortion of the closed shells of the chlorine atom; or (c) a distortionof the charge distribution in the C-C1 bond by mutual repulsion.It is notpossible to differentiate between these, but Robinson concludes that perhapsthe first is the most important (cf. vinyl chloride). Burrus and Gordy 65have studied H:% and state that 3% s-character is necessary to account forthe angle of 92", but that this would not account for the observed splitting.They suggest that the two results could be simultaneously explained bysupposing that the bonding orbitals are sfid-hybrids (15% 2s and 15% 3 4 ,while one non-bonding orbital is pure p and the other is 30% p . From themicro-wave absorption spectrum of oxygen, Miller et aZ.154 conclude thatthe unpaired electrons are in orbitals that are primarily fix, but haveapproximately 2.5% s-character.It seems that we should be cautious for the present in interpreting themeasured quadrupole-coupling coefficients in the above simple terms ofhybridisation changes.The field gradient at the nucleus must be affectedconsiderably by a small degree of asymmetry in the electron cloud near thenucleus. It is impossible to be sure that such asymmetry does not outweigheffects farther out on which, say, bond angles are dependent. Also thesymmetry of bonding and lone-pair orbitals may be affected by inter-electron repulsion and exclusion effects. The justification for linking bondA151 K. G. Denbigh, Trans. Faraduy SOL, 1940, 36, 936.lS2 P. Kisliuk and S.Geschwind, J . Chem. Phys., 1953, 21, 828.153 G. W. Robinson and C. D. Cornwell, ibid., p. 2436.154 S. L. Miller, C. H. Townes, and M. Kotani, Phys. Review, 1953, 90, 54220 GENERAL AND PHYSICAL CHEMISTRY.angles with quadrupole-coupling coefficients in deducing extents of hybrid-isation is, therefore, uncertain.Excited States of Polyatomic Molecules.-Ingold et a,?. 155 studied in detailan ultra-violet band system of benzene and obtained information about theupper electronic state of benzene. The forces in this upper state were com-pared with those previously known for the lower. Ingold and King 156 havenow made a detailed study of a band system of acetylene (both acetyleneand dideuteroacetylene were used). Their most important conclusion isthat the molecule is not linear in the upper state but has a centrally sym-metric trans-configuration. The evidence for this lies in both the rotationaland the vibrational structure of the system.For example, the ground-state progression appearing strongly is that associated with the centrallysymmetric bending vibration which is Raman-active. This, on the abovehypothesis, has the same symmetry as the molecule in its upper state andwould therefore be expected to appear strongly. Likewise the frequenciesobserved for the upper state can be reasonably ascribed to the symmetricvibrations of such a bent molecule. Since symmetric vibrations are expectedto appear on excitation this again supports the bent form. The rotationalstructure yields moments of inertia for the upper state, one being the sumof the other two, showing that the molecule is planar.The most likelydimensions consistent with these two independent moments of inertia seemto be r a = 1.383, ~ C H = 1.08 A, and the CCH angle 120.2". Ingold andKing point to the similarity between these figures and those for benzene,and suggest a three-electron C-C bond. The vibration frequencies forthe symmetric vibration of the excited state of acetylene are 1049, 1380,and ca. 3000 cmrl, and of dideuteroacetylene 844, 1310, and 2215 cm.-l.From these values it is deduced that the C-C force constant is 7.2 x lo5,close to that found for benzene, and between that of the single (4.5 x lo5) 15'and that of the double bond (9.8 x 105).158 Hence Ingold and King favouran electronic structure for the excited state involving a doubly-occupiedG and a singly-occupied x bonding orbital.It is noteworthy that the excitedstate has a larger bending frequency than the ground state.159Duchesne and Burnelle l60 have discussed the molecular vibrations of theground and excited states of Clo,, c10,-, SO,, CF,, and C6H6. In sulphurdioxide they find that the bond force constant falls from about 10 x lo5 inthe ground state to about 4-3 x 105 in the excited state. This suggeststhat a bond whose strength corresponds to a double bond is, on excitation,replaced by one whose character corresponds more to that of a single one.Delsemme and Duchesne have also considered difluorobenzene, andDuchesne thiocarbonyl chloride.16, Duchesne, and also Duchesne andBurnelle, make certain tentative conclusions about the cross-term potentialconstants in the excited states.A155 F.M. Garforth, C. K. Ingold, and H. G. Poole, J., 1948, 406 417, 427, 433, 440,156 C. K. Ingold and G. W. King, J., 1953, 2702, 2704, 2708, 2725, 2745.15' F. Stitt, J . Chew. Phys., 1939, 7, 1115.158 J. W. Linnett, Quart. Reviews. 1947, 1, 73.159 J. W. Linnett, D. F. Heath, and P. J. Wheatley, Trans. Furuduy S ~ C . , 1949, 45,161 A. Delsemme and J. Duchesne, Compt. rend., 1952, 234, 612.162 J. Duchesne, J . Chem. Phys., 1953, 21, 548.445, 456, 461, 475, 483, 491, 508.833. 160 J. Duchesne and L. Burnelle, J . Chew. Phys., 1953, 21, 2005LINNETT : MOLECULAR SPECTRA. 21Walsh,163 in an interesting series of ten papers under the general title,'' The Electronic Orbitals, Shapes, and Spectra of Polyatomic Molecules,''has considered the electronic orbitals occurring in various molecular systems(e.g., AH, AB,, BAC, HAB, HAAH, AH,, H,AB, and the specific moleculesacetaldehyde, methyl iodide, ethylene, and benzene), also the way in whichthese orbitals may be expected to be affected by molecular shape, andthe possible transitions between the various orbitals.For example, for AH,a correlation graph plots the energies of the various orbitals against the inter-bond angle from 90" to 180". It is concluded that orbitals of lower energyare more stable in the linear form, while the higher ones have a lower energywhen the molecular angle is 90'.Consequently molecules like berylliumhydride, BeH,, with few valency electrons, would be expected, in the groundstate, to be linear; while those with more electrons, such as NH, and OH,,with electrons in the orbitals of higher energy, which favour an inter-bondangle closer to go", should be non-linear. From the changes in the occu-pation of the orbitals that occur on excitation, and the correlation diagram,Walsh draws certain conclusions regarding changes of shape that occur onelectronic excitation. For example, he concludes that the longest wave-length system of NH, should involve an excited state with an inter-bondangle greater than, but a bond length about equal to, that in the groundstate, Walsh draws attention to the decrease in angle in AB, molecules asthe number of valency electrons increases from 16 to 20.For example,carbon dioxide with 16 is linear ; nitrogen dioxide with 17 has an interbondangle of 130"; ozone with 18, 116"; chlorine dioxide with 19, 1164"; andfluorine oxide with 20, 101". These changes are explained by the correlationdiagram for AB,. The trihalide ions, with 22 valency electrons, are againlinear because in AB, molecules the highest molecular orbitals favour alinear structure. Walsh has discussed the electron transitions observed orexpected for the various molecular types. For example, with hydrogencyanide two band systems are observed near 1900 and 1450 A. The structureof the former suggests an excited-state vibration frequency of 450 cm.-l.This is probably a bending vibration frequency and indicates that the trans-ition is to a bent upper state.The excited-state frequency appearing in the1450 A system is about 900 cm.-l, which Walsh concludes is due to a weakenedC-N bond in a linear upper state. In the series the spectra of HCO, HO,,C,H,, H,CO, H,O, etc. are discussed.Sutcliffe and Walsh 164 have obtained the absorption spectrum of allenein the vacuum ultra-violet. This extends the work of Price, Teegan, andWalsh 165 on keten.Diatomic Molecules.-The dissociation energy of fluorine now seems tobe definitely fixed a little below 40 kcals./mole. Doescher,166 from PVTmeasurements on the gas, obtained the value of 37.4; while Wise,167 byan effusion method, obtained 39-9.Gilles and Margrave,168 using a methodsimilar to Doescher's, conclude that the best value is 36 3. Barrow andCaunt ,169 from extensive measurements of the ultra-violet spectra and163 A. D. Walsh, J., 1953, 2260, 2266, 2288, 2296, 2301, 2306, 2318, 2321, 2325, 2330.16d L. H. Sutcliffe and A. D. Walsh, J., 1952, 899.165 W. C. Price, J . P. Teegan, and A. D. Walsh, J., 1951, 920.166 R. N. Doescher, J. Chern. Phys., 1951, 19, 1070; 1952, 20, 330.16' H. Wise, ibid., p. 927.lB9 R. F. Barrow and A. D. Caunt, Proc. Roy. Soc., 1953, A , 219, 120. 368 P. W. Gilles and J. L. Margrave, ibid., 1953,21,38122 GENERAL AND PHYSICAL CHEMISTRY.dissociation energies of the alkali-metal halides, conclude that the best valueis 37.6 5 1.6. This is in the middle of the range suggested by Evans etObservations have been made on the ultra-violet spectra of AlF,171GaF, and InF.17, The ground-state dissociation energies of the last twocan be deduced easily, but the case of AlF is difficult.Rowlinson and Barrowhave studied the A l I I - XIZ+ emission system. A short extrapolation ofthe vibrational levels of the lll upper state leads to a ground-state dissoci-ation energy (Do") of 7.2 & 0.3 ev. Levels are observed in this lrI state upto such an energy that Do'' must be greater than 6-51 ev. However, thermo-dynamic data lead to a value of 6.3, (147 kcals.) for the dissociation energy.There seems to be little doubt, therefore, that in A1F there is a maximum inthe potential-energy curve. In the case of Sn0,173 however, the spectro-scopic and thermodynamic values for the dissociation energy agree.Otherdiatomic molecules whose ultra-violet spectra have been examined recentlyinclude I3Cl6O 32 , N 2, 174 CSe,175 NO,176 HBr+,177 C12+,17'3 and SnS.179Attempts have been made by Pillow I8O and by Wu lS1 to account forthe relative intensities of the various bands in an ultra-violet system. Pillowused a method which involves displacing and altering the scale of the simpleharmonic oscillator wave functions, which are available. Wu has given anapproximate method for employing the Morse function. Both have beenapplied to the second negative system of 0,+(A2111, - X 2 n g ) . Both treat-ments agree, in the general pattern, with the observed intensities,ls2 butthere are differences in detail. Pillow 183 also calculated the band intensitiesin the Herzberg system of oxygen, observed by Broida and Gaydon in anoxygen after-glow.The agreement between theory and experiment wasquite good. She has also treated the CN violet system observed in acarbon arc.lS4 One set of results leads to a vibrational temperature in theexcited-state molecules of 8000" 500" K, while another set leads to 6200" K.In this case the intensity of all the observed bands did not fit accuratelyinto the theoretical pattern.Flash Photo1ysis.-More investigations have used the technique of flashp h o t o l y s i ~ . ~ ~ ~ For example, the absorption spectra of the free radicalsproduced during combustion of acetylene have been photographed.ls6 Inaddition to the usual systems, the Mulliken bands arising from the lC-stateof C, have been observed, and also a line at 4051 A.which may be identicalwith that observed in emission by Swings et aZ.lS7 and by Herzberg,lss andl70 M. G. Evans, E. Warhurst, and E. Whittle, J . , 1950, 1524.171 H. C. Rowlinson and R. F. Barrow, Proc. Phys. soc., 1953, A , 66, 437, 771.172 D. Welti and R. F. Barrow, ibid., 1952, A , 65, 629.173 G. Drummond and R. F. Barrow, ibid., p. 148.174 R. E. Worley, Phys. Review. 1953, 89, 863.175 R. K. Laird and R. F. Barrow, Proc. Phys. soc., 1953, A , 66, 836.176 L. H. Sutcliffe and A. D. Walsh, ibid., p. 217.177 R. F. Barrow and A. D. Caunt, ibid., p. 617. 178 H. G. Howell, ibid., p. 759.170 R. F. Barrow, G.Drummond, and H. C. Rowlinson, ibid., p. 885.180 M. Pillow, ibid., 1949, A , 62, 237; 1950, A , 63, 940; 1951, A , 64, 772; 1952,181 T.-Y. Wu, ibid., 1952, A , 65, 859.lS2 M. Feast, ibid., 1950, A , 63, 557. lS3 M. Pillow, ibid., 1953, A , 66, 733, 1064.lS4 M. Pillow, ibid., p. 737.lS5 R. G. W. Norrish and G. Porter, Proc. Roy. Soc., 1952, A , 210, 439; G. Porter,ibid., 1950, A , 200, 284; R. G. W. Norrish, G. Porter, and B. A. Thrush, Nature, 1952,i89,5a2 ; i953,172,71. 188 I d e m , Proc. Roy. SOC., 1953, A , 216, 165.A , 65, 859.187 P. Swings, C . T. Elvey, and H. W. Babcock, Astrophys. J . , 1941, 94, 320.G. Herzberg, ibid., 1942, 96, 314LINNETT : MOLECULAR SPECTRA. 23ascribed to C,.1B9 The photochemical reaction between chlorine and oxygenhas been studied and the growth and decay of the C10 radical followedspectroscopically.l e O By the flash photolysis of several aldehydes Ramsayobtained bands which he has ascribed to CHO.lgl The band structuresuggests that the transition may be from a bent ground state to a linearexcited state. The dimensions given for the ground state are YCH = 1-08 -&0.02 A, rco = 1.19 0.01, and the HCO angle" 120" & 4". Continuousillumination 192 with a multiple-reflection cell,lg3 and flash p h o t o l y ~ i s , ~ ~ have been used to photograph the absorption bands of NH, and ND,.Flash photolysis has also been used to show the presence, after intenseillumination, of triplet states in molecules, such as anthracene, in solutionand to study their decay.lg5Flame Spectra.-Much work has been carried out recently on the emissionfrom flames.lg6 There has been great interest in, and discussion of, thespectroscopic measurement of rotational temperatures in flames, and in theabnormally high values sometimes obtained.Papers on this topic havebeen published by Gaydon and Wolfhard,lg7 by Penner,lg8 by Broida andhis co-workers,lg9 and by Shuler.200 Experiments have been carried out onatomic flames,201 on flames supported by fluorine,202 on diffusionon low-pressure and on flames at atmospheric pressure.205 Measure-ments have also been made on flames by a fast scanning infra-red spectro-meter.206AJ. W. L.lS9 A. E. Douglas, Astrophys. J . , 1951, 114, 466.leO G. Porter and F. J. Wright, Discuss.Fnvaday Soc., 1953, 14, 23.lS1 D. A. Ramsay, J . Chzm. Phys., 1953, 21, 960.lQ2 Idem, ibid., p. 165.lo3 J. U. White, J . Opt. SOC. Awzer., 1942, 32, 285; H. J. Bernstein and G. Herzberg,J . Chem. Phys., 1948, 16, 30.lS4 G. Herzberg and D. A. Ramsay, Discuss. Faraday SOC., 1953, 14, 11.Ig5 G. Porter and M. W. Windsor, J . Chem. Phys., 1953, 21, 2088.lg6 A. G. Gaydon, Quart. Revieus, 1950, 4, 1 ; A. G. Gaydon and H. G. Wolfhard," Flames, their Structure, Radiation and Temperature," Chapman and Hall, London,1953.lS7 A. G. Gaydon and H. G. Wolfhard, Proc. Roy. Soc., 1949, A , 199, 89; 1948, A ,194, 169; 1950, A , 210, 561, 570; 1951, A , 200, 118.lQ8 S. S. Penner, J . Chenz. Phys., 1951, 19, 272; 1952, 20, 507, 1175, 1341; 1953, 21,31, 686.lg9 H.P. Broida, ibid., 1951, 19, 1383; 1953, 21, 340; H. P. Broida and G. T. Lalos,ibid., 1952, 20, 1466; H. P. Broida and W. R. Kane, ibid., 1953, 21, 347; idem, Phys.Review, 1953, 89, 1053.2Ju I<. E. Shuler, J . C h e w Phys., 1950, 18, 1221; J . Phys. Chem., 1953, 57, 396.831 A. G. Gaydon and H. G. Wolfhard, Proc. Roy. SOC., 1953, A , 213, 366; H. P.Broida and A. G. Gaydon, ibid., 1953, A , 218, 60.2 J 2 R. A. Durie, Proc. Phys. SOC., 1950, A , 63, 1292; Proc. Roy. SOC., 1952, A , 211,110.203 H. G. Wolfhard and W. G. Parker, Proc. Phys. SOC., 1949, A , 62, 722; ibid., 1952,A , 65, 2.2d4 A. G. Gaydon and H. G. Wolfhard, Third Symposium on Combustion Flame andExplosion Phenomena, Williams and Wilkins, Baltimore, 1949, 504.205 P. Ausloos and A.van Tiggelen, Bull. SOC. chim. Belg., 1952, 61, 569; 1953, 62,223.276 P. J. Wheatley, E. R. Vincent, D. Rotenberg, and G. R. Cowan, J . Opt. SOC. Amer.,1951. 41, 665; G. R. Cowan, E. R. Vincent, and B. L. Crawford, ibid., 1953, 43, 710;H. F. White, G. R. Cowan, D. Rotenberg, and B. L. Crawford, J . Chem. Phys., 1953, 21,139924 GENERAL AND PHYSICAL CHEMISTRY.2. THERMOCHEMISTRY.Thermochemistry may be formally defined as that branch of chemicalthermodynamics which deals with changes in internal energy or heat contentassociated with chemical reactions. I t may lead to a knowledge of theheats of formation of compounds from their elements and, if the subsidiarydata are available, to heats of formation from gaseous atoms. The topiccan then be widened to include mean bond energies and bond dissociationenergies and the methods, thermochemical and otherwise, of measuring them.The main emphasis of the Report is on work published during 1953, butthe Reporter has tried to make one year stand for several by linking past andpresent work through the references.Bond Dissociation Energies and Mean Bond Energies.-The first expressionrefers to the energy required to break a particular bond in a molecule, asdistinct from a mean bond energy, which is the mean contribution from eachbond of a given type to the total heat of formation of the compound fromits constituent at0ms.l The dissociation energy of a bond can be obtaineddirectly from the energy involved in either the formation or the rupture ofthe bond in question, but apart from some work on hydrogen 2 and oxygen,3the direct determination of bond dissociation energies has been confined tobond-breaking reactions.The energy required to break the bond can besupplied in different forms, and the dissociation and ionization of moleculesby the impact of an electron beam of controlled energy have been studied byStevenson,4 who has extended his earlier work on hydrocarbons to includethe normal alkanes from C, to C,. It is assumed that in the case of the alkaneR-R’, if the ionization potential of R, I(R), is less than that of R’, then theappearance potential of the alkyl ion Ri, A(R+), corresponds to the processR-R’ + e- ---t R+ + R’ + 2e-. If R+ is formed through the excitation ofthe molecule to the dissociation limit of the lowest stable state of R-R’+, sothat the appearance potential contains neither excitation- nor kinetic-energy terms, then the appearance potential is related to the dissociationenergy of the bond joining R and R’ by the expressionA(R+) = I(R) + D(R-R’).There is evidence that this is a valid assumption.The expression can beextended to include C-H dissociation energies if the heat of the reaction,AH, of R’H + RR” = R”H + RR‘ is known. ThenThe following values have been obtained :D(PrLH) = 4.3 & 0-04 ev;I(Bus) + D(BuS-H) = 11.1, 5 0.1 ev;I(AmS) + D(AmS-H) = 10.8, 5 0.1 ev.Aal<,(R’+) - ARn*,(R+) D(R’-H) - D(R”-H) - AHD(BuLH) = 4.3, & 0.1 ev;1 H. A. Skinner and H. D. Springall, Nature, 1948, 162, 343; M.G. Evans and M.Szwarc, J . Chein. Phys., 1950, 18, 618.F. R. Bichowsky and L. C . Copeland, J . Anzer. Chenz. SOC., 1928, 50, 1315.W. H. Rodebush and S. M. Troxel, ibid., 1930, 52, 3467.D. P. Stevenson, J . Chew. Plzys., 1942, 10, 291; D. P. Stevenson and J. A. Hipple,J . Amer. Chern. SOC., 1942, 64, 1588, 2766; D. P. Stevenson, Discuss. Faraday SOL.,1951, 10, 35.4 D. P. Stevenson, Tffans. Faraday SOC., 1953, 49, 867CARSON : THERMOCHEMISTRY. 25A table of the best electron-impact values of D(R-H), where R changesfrom Me to But is also given, and the values I(Prn) = 7-9 & 0.1 ev andD(HS-H) = 4.0 & 0.1 ev are obtained by combining the above quantitieswith known data on chlorides and thiols. Branson and Smith have studiedthe molecules methane and methyl chloride, bromide, and iodide underelectron impact.They conclude that positively charged carbon ions appearin the process CH,X + e- ----t C+ + 3H + X + 2e- so that the appearancepotential can be expressed as A(C+) > D(C-3H-X) + I(C). The equalitysign is not used alone since the products may contain excess of energy.The second term in the expression allows the latent heat of vaporization ofcarbon to be evaluated, if the heat of formation of the undissociated com-pound is known ; this point is discussed later in the report. CH+ appears inthe process CH,X + e- _t CH+ + 2H + X + 2e- so that A(CH+) >D(CH-2H-X) + I(CH). The dissociation energy of the CH molecule,D(C-H), can then be expressed in terms of the two appearance potentialsA(C+) and A(CH+).The mean value for the substances considered isD(C-H) < 3.5 & 0-7 ev, which is in good agreement with the vahe obtainedspectros~opically.~ In determination of the dissociation energy D(Me-X),except in the case of methane, two processes were considered :(1) MeX +e- ----t Me+ + X + 2e- ;(2) MeX + e- ---t Me + X+ + 2e-A(Me+) = D(Me-X) + I(Me) and A(X+) = D(Me-X) + I(X).D(Me-H) < 4.2 & 0.2 ev;D(Me-Br) < 3.1 5 0.4 ev;which are in fair agreement with the figures quoted by Roberts and Skinner,*S ~ w a r c , ~ and McDowell and Cox.lOThe dissociation energies D(C-3H) > 11.2 ev and D(C-2H) < 7.4 evare also obtained and the four values involved in the stepwise dissociationof methane can be calculated.These values may be compared with theelectron-impact results of McDowell and Warren l1 and the theoreticalcalculations by Voge.12The ionization and dissociation of methylsiloxanes by electron impacthave been examined by Dibeler, Mohler, and Reese.13The energy required to break the bond may also be supplied in the formof heat, and the two methods that have been widely developed, the equili-brium method and the kinetic method, have been reviewed by S ~ w a r c . ~The kinetic method depends on the determination of the activation energyof the simple unimolecular dissociation which yields two atoms or radicalsthrough the breaking of a bond. If the reaction in the reverse direction has’ G. Herzberg, “ Molecular Spectra.I. Spectra of Diatomic Molecules.” 2nda J. S. Roberts and H. A. Skinner, Trans. Faraday Soc., 1949, 45, 339.givingThese two appearance potentials yield the following mean values :D(Me-I) < 2.3 3 0.2 ev ;D(Me-C1) < 3.4 & 0-5 ev,H. Branson and C. Smith, J . Amer. Chein. SOC., 1953, 75, 4133.Edn. Van Nostrand, New York, 1950.M. Szwarc, Chern. Reviews, 1950, 47, 75.lo C. A. McDowell and B. G. Cox, J . Chew,. Phys., 1952, 20, 1496.l1 C. A. McDowell and J. W. Warren, Discuss. Faraday SOC., 1951, 10, 53.l2 H. H. Voge, J . Chem. Phys., 1936, 4, 581 ; 1948, 16, 984.l3 V. H. Dibeler, F. L. Mohler, and R. M. Reese, J . Chem. Phys., 1953, 21, 18026 GENERAL AND PHYSICAL CHEMISTRY.no activation energy, then the activation energy for the dissociation processwill be equal to the bond dissociation energy.It seems very probable thatthe activation energy for the recombination of atoms or radicals is negligible,especially when steric hindrance cannot occur, and bond dissociation energiescalculated on this basis are in good agreement with values found by othermethods.Szwarc and his co-workers have started a study of the variations in bonddissociation energies of aromatic compounds. In the first paper l4 thepyrolysis of a series of aryl bromides is described. By use of the toluenecarrier-gas technique the primary, rate-determining step is shown to beAr-Br + Ar + Br, and the following dissociation energies are found :D(pheny1-Br) = 70.9 ; D(p-naphthyl-Br) = 70-0 ; D(a-naphthyl-Br) = 70.9 ;D(9-phenanthryl-Br) = 67.7 ; and D(9-anthryl-Br) = 65.6 kcal./mole.A11are subject to an uncertainty of A2 kcal./mole.Szwarc concludes that the C-Br dissociation energy does not seem tobe affected by the increase of the rI-electron system. On the other hand itdoes seem to be influenced by the fusion of a benzene ring in the ortho-position, and on the whole the C-Br bond dissociation energies in thearomatic compounds appear to be higher than in methyl bromide.The second paper l5 investigates the effect of substituents on the C-Brdissociation energy in a series of substituted bromobenzenes. The sub-stituents are F, C1, Br, CH,, C6H5, CN, and OH ; and the study was extendedto include broinopyridine and bromothiophen. The frequency factor wasassumed to be constant for the series of decompositions, and the difference indissociation energy D(Ph-Br) - D(Ph,,b.--Br) was obtained for 20 compounds.Only in the bromopyridines was there an increase in the C-Br dissociationenergy.The most marked decrease was due to the hydroxy-substituent andthe effect was much the same for ortho-, meia-, and para-compounds. Replace-ment of hydrogen by halogen, methyl, phenyl, or nitrile groups has only aslight effect, which is enhanced if the substitution is in the ortho-position,the increase depending on the bulkiness of the group.Chilton and Gowenlock 16 have examined the pyrolysis of diisopropyl-mercury in a flow system with nitrogen or a mixture of nitrogen and nitricoxide as carrier gas.The reaction is predominantly homogeneous andunimolecular. In view of the high value of the frequency factor the meanactivation energy of 39.8 kcal./mole is considered to be the energy neces-sary to break both Hg-C bonds, and this agrees excellently with the valuequoted by Mortimer, Pritchard, and Skinner.17The heats of formation of dimethyl- and diethyl-mercury have beenredetermined in recent years 1 8 7 l9 and although the data can be used toevaluate the sum of the two Hg-C bond dissociation energies it cannot giveany information about the individual bond-breaking energies. From adetailed pyrolytic study of dimethyl- and diethyl-mercury Warhurst 2o and hisco-workers have now obtained this information. The rate-determining stepl4 M. Ladacki and M. Szwarc, Proc.Roy. Soc., 1953, A , 219, 341.15 M. Szwarc and D. Williams, ibid., p. 353.16 H. T. J. Chilton and B. G. Gowenlock, Trans. Faraday Soc., 1953, 49, 1451.17 C. T. Mortimer, H. 0. Pritchard, and H. A. Skinner, ibid., 1952, 48, 22C.18 K. Hartley, H. 0. Pritchard, and H. A. Skinner, ibid., 1950, 46, 1019 ; 1951,47,254.19 A. S. Carcon, E. M. Carson, and B. R. Wilmshurst, Nature, 1952, 170, 320.?O €3. G. Gowenlock, J. C. Polanyi, and E. Wsrhurst, Proc. Roy. Soc., 1953, A , 218,269CARSON : THERMOCHEMISTRY. 27was the breaking of the first Hg-C bond, and the activation energy wasassumed to be the dissociation energy of this bond, i.e., D(MeHg-Me) =51.5 & 2 kcal./mole. The data on the temperature coefficient of the diethyl-mercury pyrolysis were not complete but the dissociation energy was esti-mated to be D(EtHg-Et) = 41.5 kcal./mole.When combined with theheats of formation 189 l9 these figures confirm the belief that in the dissoci-ation of these mercury compounds into Hg + ZR, most of the energy isrequired to break the first Hg-C bond.The heats of formation of ethyl chloride and bromide and the C-halogenbond dissociation energies in these compounds have been determined by Lane,Linnett, and Oswin,21 using an equilibrium flow technique. The heat of thereaction C2H4 + HX = C,H,X, where X = C1 or Br, was calculated atvarious temperatures by combining the equilibrium constant a t that temp-erature with the calculated entropy change. The value of 3.7 kcal./moleobtained by Gordon and Giauque 22 for the barrier which restricts rotationin ethyl chloride was used, and with ethyl bromide the barrier height wasassumed to be about 4 kcal./mole. The heats of reaction corrected to 298" Klead to the following results: AHfO(EtC1, g) = - 26.7; AHfO(EtBr, g) =-15.3; D(Et-Cl) = 80.9; and D(Et-Br) = 67.2 kcal./mole, i f a value of97.5 kcal./mole is assumed for the dissociation energy of the first C-H bond 23in ethane.These values are in good agreement with those quoted in refs. 8,9,and 19. The authors also discuss the differences in the R-X dissociationenergies in a series of RX compounds where R is Me, Et, Prn, Pri, Bun, and But.For many years the dissociation energy of fluorine was thought to be63 kcal./mole but in a critical review Evans, Warhurst, and Whittle 23decided that a value in the region of 37 kcal./mole was probably correct, andthis figure has received support from subsequent work by Doescher 24 andWise.25 Wicke and Friz 26 have obtained the value D(F,) = 37.0. & 2 kcal./mole by exploding mixtures of hydrogen and fluorine in a steel sphere, themaximum pressure being corrected for impurities and for pressure oscillationsfollowing the explosion.ANfO(C1F) = 11.7 & 0.5 kcaI./mole was also found,and the method was checked by using mixtures of hydrogen and chlorine.Their value agrees excellently with that obtained by Barrow and Gaunt,,'who examined the fluctuation bands in the ultra-violet absorption spectrumand deduced the upper limits of the dissociation energies of the twelvepotassium, rubidium, and czsium halides.The dissociation energy of thegaseous halide is related to the dissociation energy of the halogen and onthis basis the mean value D(F,) = 37.6 5 1.6 kcal./mole was obtained. Alower value, D(F2) = 31.5 -+ 0.9 kcal./mole, was, however, found by Gillesand Margrave from a study of the pressure exerted by fluorine in a closedcopper system over the range 300-860" K.Farber and Darnel1 29 have used the Langmuir hot-wire technique todissociate hydrogen and nitrogen. The power necessary to heat the tungsten21 M. R. Lane, J. W. Linnett, and H. G. Oswin, Proc. Roy. SOC., 1935, A , 216, 361.22 J. Gordon and W. F. Giauque, J . Anzer. Chem. Soc., 1948, 70, 1506, 4277.24 R.N. Doescher, J . Chem. Phys., 1952, 20, 330; 1951, 19, 1070.25 H. Wise, zbzd., 1952,20,927.27 R. F. Barrow and A. D. Caunt, Proc. Roy. Soc., 1953, A , 219, 120.28 P. W. Gilles and J. L. Margrave, J . Chern. Phys., 1953, 21, 381.19 M. Farber and A. J. Darnell, ibid., p. 172.M. G. Evans, E. Warhurst, and E. Whittle, J., 1950, 1524.26 E. Wickeand H. Friz, 2. Elektrochem., 1953, 57, 928 GENERAL AND PHYSICAL CHEMISTRY.filament both in vacuo and in the gas is measured ; the total power differenceis divided between gas conduction and dissociation. The accommodationcoefficient is assumed to remain constant during the dissociation. Thedissociation energies so determined are D(H,) = 101 3 kcal./mole,D(N,) > 225 kcal./mole. The value for nitrogen is important since con-siderable controversy has surrounded 309 31 this dissociation energy, andvalues ranging from 170 to 250 kcal./mole have been quoted.Taylor andWijnen 32 claim to have eliminated the lower value in view of their failureto achieve the xenon-sensitized photosynthesis of ammonia by irradiatingmixtures of nitrogen and hydrogen with a xenon-resonance lamp which hadan energy equivalent of 194-5 kcal., the indication being that this energywas insufficient to break the N-N bond.Van Artsdalen and his collaborators, whose previous work33 in thekinetics of gas-phase bromination yielded much valuable data on bonddissociation energies, have now described 34 the thermal and photochemicalbromination of toluene. Substitution occurred in the side-chain, and theactivation energy of the overall reaction was assigned to the rate-determiningstep, Br + RH = R + HBr.The photochemical reaction was stronglyretarded by hydrogen bromide in the range 82-132" c, and this enabledthe activation energy of the back-reaction to be estimated. Using theknown value for D(H-Br), they obtain D(PhCH,-H) = 89.5 5 1.4 kcal./moleat 25" C, a figure which differs considerably from the value (77.5 kcal./mole)measured by S~warc.~5Skinner and his co-workers have described a series of reactions of phos-phorus, arsenic, and boron compounds. The heats of formation of phos-phorus trichloride, tribromide, oxychloride, and oxybromide were foundfrom their heats of hydr0lysis,3~ and the mean bond energies in phosphorustrichloride.and tribromide, D(P-Cl) = 77-9 kcal./mole, D(P-Br) = 63.4kcal./mole, and the P=O dissociation energy in phosphorus oxychlorideand oxybromide, D(Cl,P=O) = 121.8 kcal./mole, D(Br3P=O) = 119.3kcal./mole, can be deduced. These energies tend to confirm the view thatthe P-0 bonds resemble double rather than single bonds. There is as yetno reliable evaluation of the single P-0 link but a value has been reported 37for the heat of formation of P406, which leads to E(P-0) = 98-8 kcal./mole.D(F,P=O) is also known from work 38 on the direct oxidation of phosphorustrifluoride, and it is seen that there is a decrease in D(X,P=O) as X changesfrom F to C1 to Br. A simple steric explanation for this seems inadequatein view of the constancy of the P=O bond length in phosphorus oxychlorideand oxyfl~oride.~~The heats of formation 40 of trimethyl, triethyl and tripropyl arsenite30 A. G.Gaydon, " Dissociation Energies," Chapman and Hall, London, 1953.31 G. Gloclrler, J . Chenz. Phys., 1951, 19, 124.32 H. A. Taylor and N. H. J. Wijnen, ibid., 1953, 21, 233.33 E. R. van Artsdalen, ibid., 1942, 10, 653 ; C. B. Kistiakowsky and E. R. van Arts-dalen, ibid., 1944, 12, 469; H. C. Andersen and E. R. van Artsdalen, ibid., p. 479; E.I. Hormats and E. R. van Artsdalen, ibid., 1951,19, 778.34 H. R. Anderson, jun., H. A. Scheraga, and E. R. van Artsdalen, ibid., 1953,21, 1258.3 5 M. Szwarc, ibid., 1948, 16, 128. 36 H. A. Skinner and T. Charnley, J., 1953,450.a7 W. E. Koerner and F. Daniels, J .Chew. Phys., 1952, 20, 113.38 Fr. Ebel and E. Bretscher, Helv. Chim. A d a , 1929, 12, 450.39 W, Gordy, Q. Williams, and J. Sheridan, J. Chern. Phys., 1952, 20, 164.4O T. Charnley, C. T. Mortimer, and H. A. Skinner, J., 1953, 1181CARSON : THERMOCHEMISTRY. 29have been found from their heats of hydrolysis in 4~-sodium hydroxide, andthe following mean bond energies have been calculated, B(As-OMe) =62.64 2.3, n(As-OEt) = 64.45 & 1.4, and D(As-OPr) = 66.44 & 2.7kcal./mole. The calculations involve the heat of fonnation of the -ORradicals, and an account is given of the estimation of these quantities. TheD(As-OR) values are smaller than the D(As-0) value in As,O, and thedifference may lie in the hyperconjugation stabilization of the -OR radicals.The heat of the reaction between phenylarsine and iodine has beenmeasured 41 in carbon tetrachloride solution at 25" c, and the result enablesthe difference between the As-H and As-I mean bond energies in the com-pounds phenylarsine and phenyldi-iodoarsine to be expressed, AD -{:IF} =17.0 & 2-3 kcal./mole.This difference is in close agreement with thatbetween B(As-H) = 56.6 kcal./mole in arsine and AS-I) = 42.6 kcal./molein arsenic tri-iodide,,, and on the basis of this and earlier l8 results it issuggested that in mixed compounds of the general type R,MX,, where Mis the (m + n)-valent central atom, the values are transferable from theparent compounds when R = Ph and X = H or I, but that enhancementoccurs in one or more of theSkinner and Smith43 have found the heat of formation of liquid borontrichloride, AHfo(BC1,) = -103.0 -+ 1 kcal./mole, and Skinner and Tees44have studied calorimetrically a series of reactions involving tri-n-butyl-boron and the di-n-butylboron halides.By assuming that the mean B-CIbond energy in boron trichloride is the same as the dissociation energyD(Bu,B-Cl), the following dissociation energies can be calculated :D(Bu,B-OH) = 118.3 kcal./mole ; D(Bu,B-C1) = 93-9 kcal./mole ;values, when R = alkyl and X = halogen.D(Bu,B-Br) = 74-7 kcal./mole ; and D(Bu,B-I) = 56.2 kcal./mole.The absolute magnitude of these quantities may be in doubt, but thedifferences between them should be correct; also, since the value for thelatent heat of sublimation of boron is uncertain, the D and Dvalues quotedmay have to be increased by 14.6 kcal./mole.Thompson 45 has burnt the first four members of the linear poly(dimethy1-siloxane) series Me*[SiMe,*O];SiMe, in a combustion bomb and from theirheats of formation has calculated the mean bond energies B(Si-C) = 64kcal./mole and b(Si-0) = 117 kcal./mole.Drummond and Barrow 45a have estimated the dissociation energy ofgaseous beryllium oxide, basing their calculations on vapour-pressure,thermochemical, and spectroscopic data.The value obtained, 127 & 5kcal./mole, is lower than would be expected from a comparison between thedissociation energy and force constant of this molecule and those of theother oxides in this sub-group.Heats of Reaction.-When a compound is burnt in oxygen the productsof the combustion are usually simple molecules with well-known heats of41 C.T. Mortimer and H. A. Skinner, J . , 1953, 3189.43 H. A. Skinner and N. B. Smith, Trans. Faraday SOL, 1953, 49, 601.44 H. A. Skinner and T. F. S. Tees, J., 1953, 3378.45 R. Thompson, J . , 1953, 1908.450G. Drummond and R. F. Barrow, Trans. Famday SOC., 1953, 49, 599.42 Idem, J., 1952, 433130 GENERAL AND PHYSICAL CHEMISTRY.formation, and consequently this highly precise method is much used in findingheats of formation. The heats of formation of the following compounds havebeen found in this way, tetramethyltin and tetrameth~l-lead,~~ berylliumoxide,47 diazoaminobenzene, benzotriazole and 2-azidoethan01,~~ stannous andstannic hafnium oxide and nitride,50 and cerium Since 1934,in the University of Lund over 130 organic chloro- and 19 iodo-compoundshave been examined by combustion, the quartz-fibre technique being used ;128 of these values have now been corrected and published.51 Sunner 52has made a detailed study of the combustion of organo-sulphur compoundsin a rotating bomb.In his most recent paper 53 he suggests the useof thianthren as a secondary standard in bomb calorimetry for sulphurcompounds. Coops 54 and his co-workers have studied the heats of com-bustion of some 0- and P-tolylethylenes and phenylbutadienes, the veryprecise combustion calorimeter previously described 55 being used.A wide range of reactions, other than combustions, have been studiedduring the year.Koch and Cunningham 56 have continued their work onthe vapour-phase hydrolysis of the lanthanon halides and have obtainedheat and free-energy data for the hydrolysis of samarium and gadoliniumtrichlorides. The thermochemistry of the alkali and alkaline-earth metalsand halides in liquid ammonia has been examined by C o ~ l t e r . ~ ~ Jenkinsand Style 58 have obtained the heat of formation of bishydroxymethylperoxide by measuring its heat of reaction with sodium hydroxide; itsh2at of solution and latent heat of sublimation have also been measured.The heat of formation of thorium sesquisulphide 59 has been found from itsheat of solution, and the heats of solution of the cobaltous chloride hydratesin water and a number of oxygenated organic solvents have been measured.60Latimer and Jolly have determined calorimetrically at 25" c the heats ofthe six successive reactions between F- and A13+ to form AlF63-, and withHepler 62 they have calculated the heat of ionization of hydrogen fluorideby measuring the heat of solution of sodium fluoride in water and in aqueousperchloric acid. Mel, Jolly, and Latimer e3 have determined the heat offormation of the bromate ion by finding the heat of solution of potassiumbromate and the heats of reduction of potassium bromate with Br- and I-.4 6 E.R. Lippincott and M. C. Tobin, J . Amer. Chem. Soc., 1953, '95, 4141.4 7 L. A. Cosgrove and P. E. Snyder, ibid., p. 3102.49 G. L. Humphrey and C. J . O'Brien, ibid., p. 2805.5O G. L. Humphrey, ibid., p.2806.500 E. J. Huber and and C. E. Holley, jun., ibid., p. 5645.51 L. Smith, L. Bjellerup, S. Krook, and H. Westermark, Acta Chem. Scand., 1953,53 S. Sunner and B. Lundin, Actn Chew. Scand., 1953, 7, 1112.54 J . Coops, G. J. Hoijtink, Miss Th. J. E. Kramer, and hlise A. C. Faber, Rec. Trav.5 5 J. Coops, K. Van Nes, A. Kentie, J. W. Dienske, D. Mulder, and J. Smittenburg,5 6 C. W. Koch and B. B. Cunningham, J . Amer. Chem. Soc., 1953, 75, 796.5 7 L. V. Coulter, J . Phys. Chem., 1953, 57, 553.5 8 A. D. Jenkins and D. W. G. Style, J . , 1953, 2337.59 L. Eyring and E. F. Westrum, jun., J . Amer. Chem. Soc., 1953, 75, 4802.6O L. I. Katzin and J. R. Ferraro, ibid., p. 3821.61 W. M. Latimer and W. L. Jolly, ibid., p. 1548.62 L. G.Hepler, W. L. Jolly, and W. M. Latimer, ibid., p. 2809.63 H. C. Mel, W. L. Jolly, and W. M. Latimer, ibid., p. 3827.T. F. Fagley, E. Klein, and J . F. Albrecht, jun., ibid., p. 3104.7, 65.chim., 1953, 72, 765.ibid., 1947, 66, 113-176.5 2 S. Sunner, Thesis, Lund, 1949CARSON : THERMOCHEMISTRY. 31Andrianov and Pavlov 64 have investigated the heats of hydrolysis of com-pounds of the type RSiC1, and R,SiCl, where R = Me, Et, or Ph. Thesecompounds will form polymeric substances on hydrolysis with limited amountsof water, but hydrolyse to R,Si(OH), or RSi(OH), if a large excess of wateris used. Setton 65 has measured directly the heat liberated in the reactionnCs + nCO = (CsCO),, and Kroger 66 has calculated the heats of formationof ternary sodium calcium silicates from the oxides.Latent Heats.-It is unfortunate, in view of its importance in thermo-chemical calculations, that as yet there is no value for the latent heat ofsublimation of carbon, L(C), that will reconcile the conflicting data.Spring-all 67 and Gaydon 30 have reviewed the problem, and it is fair to say that inthe last few years the balance has definitely altered in favour of the " high "value (170 kcal./g.-atom).The direct methods for finding L(C) have been criticized on three countsthat (a) the accommodation coefficient is not unity, (b) the major part of thespecies evaporated is C, and (c) the carbon atoms may have to evaporateover a potential barrier. The last two criticisms have been answered byChupka and Inghram,68 who have used a mass spectrometer to identifythe products evaporated from a carbon filament.The relative amounts ofthe various products were measured and a retarding potential showed thatthe C+ ions produced by electron impact had only thermal energies. TheC atoms are produced in their ground state; the authors find thatL(C) = 178 -& 10 kcal./g.-atom. They hope later to investigate the questionof the accommodation coefficient. Margrave and Wieland 69 find that whencarbon tetrafluoride is thermally decomposed under equilibrium conditionsin a graphite furnace, CF, absorption bands are present at 1900" K and CFbands a t 2400" K. These results are in approximate agreement with thethermodynamic functions calculated by Potocki and Mann,'O if L(C) isassumed to be 170 kcal./g.-atom and f, which is related to the transitionprobability for the transition observed, is assumed to be for both CFand CF,.find that L(C) = 136 kcal./g.-atom, basingtheir calculation on the appearance potential of the C+ ion. It appears,however, that CH,+ is formed in the following way; CH,X + e- __tCH,+ + HX + 2e- and this at once casts doubt on the schemes envisagedfor the production of C+ and CH+. If H, or HX occurs as fragments inthese processes the values based on A(C+) and A(CH+) will have to be raised,but by how much is uncertain since the products may contain excitationalor excess of kinetic energy. The Knudsen method has been used to find thelatent heats of sublimation of tin,71 copper,', and gallium.73 A fluorescencemethod has been used by Stevens 74 to obtain vapour-pressure data andhence the heat of sublimation of anthracene and 9 : 10-diphenylanthracene.The heat of vaporization of hydrogen fluoride has been determined by JarryK. A.Andrianov and S. A. Pavlov, Doklady Akad. Naztk S.S.S.R., 1953, 88, 811.65 R. Setton, Compt. rend., 1953, 236, 1959.C. Kroger, Glastech. Ber., 1953, 2'7, 171.13' H. D. Springall, Research, 19.50, 3, 260.13* W. A. Chupka and M. G. Inghram, J . Chem. Phys., 1953, 21, 371.6Q T. L. Margrave and K. Weland, ibid., p. 1552.70 R. Potocki and D. Mann, Nut. Bur. Stand. Rpt., 1952, 1439.L. Brewer and R. F. Porter, J. Chem. Phys., 1953, 21, 2012.72 H. N. Hersh, J . Amer. Chem. Soc., 1953, 75, 1529.i3 R. Speiser and H.L. Johnston, ibid., p. 1469.Branson and Smith74 B. Stevens, J., 1953, 297332 GENERAL AND PHYSICAL CHEMISTRY.and Davis 75 from vapour-pressure data in the range 0-105" c. I t has beenpointed out 76 that both liquid and gaseous hydrogen fluoride may consistof polymers, (HF),, and it is not correct to assume that the liquid and thevapour consist of the same species and in the same proportions ; consequentlythe heat of vaporization has a meaning only when expressed on a weightbasis. Other work 77 on the fusion and vaporization of hydrogen fluoridehas been carried out by H u , White, and Johnston. Gottschal and Korvezee,'Susing their general vapour-pressure equation, have calculated a vapour-pressure curve for benzene, and obtained its heat of vaporization.Skinnerand Tees44 have quoted values for the heats of vaporization of tributyl-boron and butylboron halides.Thermodynamic Properties.-The compounds grouped together here havehad a wider range of thermodynamic properties determined. Diborane,between 13" K and its boiling point,79 and above its boiling point,*O 3-methylthiophen in the range 0-1000" K , ~ ~ thiacycZobutane,s2 2-methyl-propane-Z-thi01,~~ molybdenum trioxide at high temperature^,^^ andmercury. 85Theoretical.-In dimethylmercury the energy required to break the firstHg-C bond is much greater than that required to break the second20 andWarhurst et aZ.86 in considering this point suggest that the Hg-C bond inthe MeHg radical is predominantly a " polarization '' bond and that thechange from the bivalent to the zerovalent state of mercury occurs duringthe first dissociation. To bring the bond to the required strength someresonance with a bivalent covalent state of mercury is also envisaged.The relationship between mean bond energies and bond distances in thehydrocarbons has been discussed by G l ~ c k l e r , ~ ~ who assumes that it isparabolic between the C-C bond energies, B(CC), and distances, R(CC), andlinear between B ( C H ) and R ( C H ) .These assumptions when applied toacetylene, ethylene, ethane, methane, and diamond lead to the relation-ships : B(CC) = 1450.762 - 16440151 R(CC) + 491.936 R(CC)2, and B ( C H ) =Enough data are now known to give a reliable relationship betweenR(CC) and R ( C H ) , viz., R ( C H ) = 1.396 - 0.594 R(CC) + 0-261 R(CC)2,so that B ( C H ) = 98.104 - 0-075 B(CC) + [3.196 B(CC) - 246.04814.Theserelations are based on L ( C ) = 169.75 kcal./g.-atom, and similar expressionsbased on L ( C ) = 124.3 or 135.8 kcal./g.-atom are derived. The equationsare used in several cases to find how the atomic heat of formation is dis-tributed over the various bonds in the molecule. The following values in252.956 - 141.721 R ( C H ) .7 5 R. L. Jarry and W. Davis, jun., J . P h y s . Chem., 1953, 57, 600.7 6 J. H. Simons and A. S. Russell, ibid., 1939, 43, 901.7 7 J-H. Hu, D. White, and H. L. Johnston, J . Amer. Chern. Soc., 1953, 75, 1232.7 8 A. J. Gotfschal and Miss A. E. Korvezee, Rec. Tmv. chim., 1953, 72, 473.79 J.T. Clarke, E. B. Rifkin, and H. L. Johnston, J . A m e r . Chem. Soc., 1953, '75, 781.81 J. P. McCullough, S. Sunner, H. L. Finke, W. N. Hubbard, M. E. Gross, R. E.82 D. W. Scott, H. L. Finke, W. N. Hubbard, J. P. McCullough, C. Katz, M. E.83 I d e m , ibzd., p. 1818.85 R. H. Busey and W. F. Giauque, ibid., p. 806.8 6 B. G. Gowenlock, J . C. Polanyi, and E. Warhurst, Proc. Roy. SOC., 1953, A , 219,270-8 7 G. Glockler, J . Chem. Phys., 1953, 21, 1242 (see also ibid., 1951, 19, 124, andE. C. Herr, E. B. Rifbin, and H. L. Johnston, i t i d . , p. 785.Pennington, J. F. Messerly, W. D. Good, and G. Waddington, ibid., p. 5075.Gross, J. F. Messerly, R. E. Pennington, and G. Waddington, ibid., p. 2795.84 L. H. Cosgrove and P. E. Snyder, ibid., p.1227.Discuss. Faraday Soc., 1951, 10, 26)CARSON : THERMOCHEMISTRY. 33kcal./mole, B(CC, C2H,) = 62-194, B(CH, C2H6) = 85.440, B(CC, C2H,) =81.599, and B(CH, C2H4) = 89.749, are then used to calculate the resonanceenergy of benzene, which at 74.86 kcal./mole is about twice the conventionalvalue.88 This figure refers to an ethane-ethylene-like Kekuld structure andGlockler points out that the resonance energy will be very different if anothertype of Kekulk reference structure is used. This work is linked with thatof Mulliken and Parr,sg and a “ vertical ” resonance energy of 111.5 kcal./mole is obtained, the increase being due to the change C,H, (Kekulg, 1.54,1.35) ---t C6H6 (Kekuld, 1-39), which is necessary to bring the Kekulestructure into the correct configuration for resonance to occur.The“ hydrogenation ’ ’ resonance energy of benzene and the resonance energyof butadiene are also considered.The heats of formation of cycloalkanes up to C, are known, and if theheat of formation of the diradical produced by breaking a C-C bond is alsoknown, the dissociation energy of the bond can be found. SeuboldgO hascalculated the heat of formation of the diradical by combining thermochemicaldata with the energy required to transfer the corresponding alkane from astaggered to a coiled configuration. The D(C-C) values in the series C,-Cgare 50, 58, 82, 85, 83, 83, and 84 kcal./mole, with an uncertainty of &Z.Hugginsgl has pointed out that departures from the strict additivityof radii in normal valency compounds can be related to variations in the bondenergy. By using an expression of the type Y A ~ : = YA’ + YB’ - 4 log D A B ,interatomic distances can be calculated and are usually within 0.02 ofthe best experimental values.Huggins 92 has also applied new electro-negativity data to Pauling’s hypothe~is,~~ which regards a covalent bond asbeing the sum of polar and non-polar parts, in order to calculate meanbond energies which agree well with the experimental values.Both the molecular-orbital and valence-bond methods have been usedby Franklin and Fieldg4 to calculate the I1-electron resonance energies ofvarious organic free radicals and ions. The values are then used to obtainbond dissociation energies in compounds containing the radicals.Franklinhas also calculated the heats of formation of gaseous free radicals and ions 94aIto 95 has expressed intramolecular potential as the sum of interatomicbonding energies and inter-non-bonding atomic potential energies and heconcludes that irregularities in the heats of formation and the origin of thepotential barriers hindering rotation in hydrocarbons are due mainly tointeractions between non-bonding atoms in the molecule.Reviews.-Stout 96 has reviewed the whole field of thermochemistry andthe thermodynamic properties of substances. Baughan 97 has discussedthe thermochemistry of the elements of Groups IV B and IV and Long 98 theheats of iormation of simple inorganic compounds.A. S. C.G. Glockler, J . Chem. Phys., 1953, 21, 1249.F.H. Seubold, jun., ibid., 1953, 21, 1616.89 R. S. Mulliken and R. G. Parr, ibid., 1951, 19, 1271.91 M. L. Huggins, J . Amer. Chem. SOC., 1953, 75, 4126.93 I d e m , ibid., p. 4123.94 J. L. Frank’in and F. H. Field, ibid , 1953, ‘75, 2819.94a 1. L. Franklin, J . Chem. Phys., 1953, 21, 2029.95 K. Ito, ibid., p. 2430.9 7 E. C. Baughan, Quart. Reviews, 1953, 7, 103.g3 L. Pauling, ibid., 1032, 54, 3570.96 J. W. Stout, Ann. Review Phys. Chem., 1953, 4.O8 L. H. Long, ibid., p. 134.REP.-VOL. L 34 GENERAL AND PHYSICAL CHEMISTRY.3. CHEMICAL CHANGE IN HOMOGENEOUS SYSTEMS.It is hoped that, by slight variation of emphasis from year to year, thecontributions to this section of the report over any short period will togethercomprise a balanced and comprehensive account of the major contemporarydevelopments in this very large field of enquiry.The order of presentationis substantially the same as that adopted last year, but where it has seemedjustified the classification has not been rigidly adhered to.General and Theoretical.-It has long been realised that the study of veryrapid reactions is likely to yield results of high intrinsic interest, and im-portant developments have taken place in the application of four experi-mental methods. Bryce Crawford, jun., and his co-workers have describedthe adaptation for kinetic studies of a fast scanning infra-red spectrometerpreviously constructed in his laboratories2 If it is necessary to followsimultaneous changes in the concentration of two or more molecular speciesinvolved in the reaction then repetitive scanning is necessary and it is notpossible to follow reactions of half life <1 sec. If it is required to measurethe concentration changes of a single component, scanning is unnecessary,the instrument can be preset at a selected wave-length, and it becomespossible to study reactions of half life down to 0.01 sec. The mass spectro-meter, which has hitherto been used mainly for product analysis, can alsobe adapted to permit cathode-ray oscillographic presentation of mass-analyses repeated every few milli~econds.~ Flow methods are frequentlyused for studying very rapid reactions occurring in liquid media but theirapplicability is limited to reactions whose half lives exceed sec.,below which diffusion becomes rate controlling.Useful kinetic data can,in principle, be obtained for more rapid reactions than these by investigatingthe excess of acoustic absorption over a range of frequencies for a system inwhich a chemical reaction is slightly displaced from equilibrium by the soundenergy which it absorbs. The general theory of this method has been givenby Manes,5 and a less comprehensive theory by Freedman.6 The latterauthor has applied his theory to calculate from existing data the energiesof activation and the frequency factors of the dissociation of the dimers ofacetic acid and propionic acid. A weak shock wave can be used to increasethe translational and rotational temperature of a gas by a definite amountin a time of the order of few collision times.By selecting a suitable methodfor following the subsequent chemical reaction the kinetics of a rapidreaction may be determined. This method has been successfully applied byCarrington and Davidson to the dissociation of dinitrogen tetroxide in alarge excess of nitrogen or carbon dioxide at pressures between 0.5 and7 atm. and in the range -20" to 28" c.There have been several interesting developments in the theory of1 G. R. Cowan, E. Vincent, and Bryce Crawford, jun., J . Opt. Soc. Amer., 1953,43, 710.2 P. J. Wheatley, E. Vincent, D. Rotenberg, and G. R. Cowan, ibiiZ., 1951, 41, 665.3 F. P. Lossing, K. U. Ingold, and A. W. Tickner, Discuss. Faraday Soc., 1953, 14,34; K. U. Ingold and F. P. Lossing, Canad.J . Chem., 1953, 31, 30.4 E. G. Lkger and C. Ouellet, J. Chem. Phys., 1953, 21, 1310.5 M. Manes, ibid., p. 1791.7 J. Lamb and J. M. M. Pinkerton, Proc. Roy. Soc., 1949, A , 199, 114; J. Lamb and* T. Carrington and N. Davidson, J . Phys. Chent., 1953, 57, 418.E. Freedman, ibid., p. 1784.J. Huddart, Trans. Faraday SOC., 1950, 46, 540COLLINSON, DAINTON, AND IVIN : HOMOGENEOUS SYSTEMS. 35chemical kinetics. Slater has extended his earlier theory lo to cover thevariation with pressure of the first-order rate constant of a gaseous uni-molecular process. Assuming a classically vibrating molecule which disso-ciates when a particular internal dimension reaches a critical value, Slaterdeduces an expression for the ratio of the rate constant to its limiting valueat infinite pressure ; and values of this ratio at a given pressure are calculatedfor molecules with effective numbers of normal vibrations (n) varying from1 to 13.The pressure at which the rate declines from its first-order valueis shown to decrease as n is increased. Slater’s calculation leads to a pressuredependence of the rate similar to that predicted by Kassel’s theory 11 pro-vided the number of loosely coupled oscillators in the latter is set equal to(n + 1)/2. In a later paper l2 Slater applies his theory to the isomerisationof cydopropane, assuming this reaction to occur when one of the hydrogenatoms approaches within a certain distance of a neighbouring methylenegroup. His calculation leads to a frequency factor for the high-pressurerate of 4 x 1014 sec.-l and a decline of the rate constant with pressure whichis in good agreement with 0bser~ation.l~ It would be particularly valuableto extend Slater’s theory to the decomposition of dinitrogen pentoxide andnitrous oxide, for which conflicting claims as to the applicability of Kassel’sexpression have been made.l49 l5 Benson and Axworthy l6 have consideredthe kinetic consequences of distinguishing between two species, one relatedto the reactants and one to the products, both possessing the critical energyincrement, freely convertible into one another, and subject to deactivation.I t appears that in unimolecular Jissioiz processes only the activated complexcorresponding to the reactant is ever of importance whereas in bimolecularassociation reactions the complex corresponding to the products dominatesthe reaction.Almost all theories of unimolecular dissociation processeslead to the conclusion that the frequency factor will be of the same orderas the vibration frequency of a strong bond seccl). Recent worksuggests that when dissociation occurs into two large polyatomic fragmentsthe frequency factor may be several powers of ten larger than this value.An obvious explanation in terms of the transition-state theory is that whenthe reaction is the detachment of a single atom only, the formation of theactivated complex is not associated with any appreciable gain of entropy,whereas when two large fragments are formed any freedom of rotationwhich they may separately possess in the activated complex will cause anappreciable increase of entr0py.l’ This problem has been further consideredby Luft.lsAttempts to deduce a friori explicit expressions for the rate constantsof particular chemical reactions now seem to be largely abandoned in favourof seeking general relations connecting the frequency factor and energy ofactivation with one another or with other parameters.Thus Smith and9 N. B. Slater, Phil. Trans., 1953, A , 246, 57.10 Idem, PYOC. Roz. Soc., 1948, A , 194, 112.11 L. S. Kassel,New York, 1932, p. 93.l3 See ref. 44.1 5 L. S. Kassel, ibid., 1953, 21, 1093.1 6 S. W. Benson and A. E. Axworthy, ibid., p. 428.17 See also M. Szwarc, Discuss. Faraday SOC., 1953, 14, 125.18 N.W. Luft, J . Chem. Plzys., 1953, 21, 754.Kinetics of Homogeneous Gas Reactions,” Chem. Catalog. Co.,l2 N. B. Slater, Proc. Roy. SOL, 1953, A , 218, 224.14 H. L. Johnston, J . Chein. Phys., 1952, 20, 110336 GENERAL AND PHYSICAL CHEMISTRY.Eyring l9 have pointed out that in reactions involving the detachment ofa hydrogen atom from a CH group by a given reagent, e.g. , RH + C1 __tR= + HCI, the factor determining the trend of activation energies withstructure of R is the same factor which determines the bond dissociationenergy R-H and the ionisation potential of the radical R. All these pro-cesses involve the removal of charge from the carbon atom and there mustbe a flow of charge to fill this charge " hole." This flow occurs by induction,the ease of which increases in the series R = Me, Et, Prn, Pri, But, andhence the energy of activation of the hydrogen atom abstraction from RHshould (and does) decrease in that order.An alternative approach to theproblem of calculation of energies of activation of bond dissociation reactionsis to calculate the resonance energies of the resultant radical or ionic species.For this purpose x-bond resonance energies have been evaluated 2O by both" valence-bond " and the '' molecular-orbital " method for a variety oforganic radicals and ions. The dissociation of a hydrogen molecule wasconsidered in 1941 by 0. K. Rice 21 who assumed that only thermal collisionsof extremely high vibrationally excited molecules are responsible for disso-ciation. Careri22 has attempted to allow for the influence of excitedrotational states which Rice admits having overlooked.However, thereremain several unsatisfactory features in Careri's treatment.In triatomic metatheses of the type A + BC-AB + C it is usuallyassumed that there is a progressive increase in potential energy of the systemas A approaches B owing to the repulsion between atoms A and B. Bauerand WuZ3 have adopted the different view that A-B interactions can beneglected during this approach and that reaction consists of the suddenconversion of kinetic into vibrational energy when ABC has the transition-state configuration. By using values of AEI previously calculated on theEyring theory for the reaction H, + Br __t HBr + H the P factor isevaluated.The value obtained is in accord with the well-knowndifficulty of transferring energy between translational and vibrationalmodes. This method has been criticised by S. Golden 24 (and the criticismshave in turn been rebutted 25) who has presented an alternative calculationnot involving the concept of an activated complex.In transition state theory the predicted effect of pressure (fi) on the rateconstant ( k ) of a reaction is given by the equation (a In k / a f ) T = - A V ,where AVJ is the increase in volume which occurs when the activated complexis formed from the reactants, and the extensive and precise measurementsof the Imperial Chemical Industries Limited group 26 seem at first sight toprovide qualitative confirmation. Thus, they observed (1) that bimolecularassociation reactions such as the Menschutkin reaction, which are presumablyaccompanied by contraction , are greatly accelerated by increased pressure,(2) that so-called '' normal " bimolecular reactions (usually metatheses),for which A V is probably small, are only slightly influenced by pressure,19 R.P. Smith and H. Eyring, J . Amer. Chem. SOL, 1953, 75, 5183.2o J. L. Franklin and F. H. Field, ibid., p. 2819.21 0. K. Rice, J . Chetn. Phys., 1941, 9, 258.22 G. Careri, ibid., 1953, 21, 749; 0. K. Rice, ibid., p. 750.23 E. Bauer and Ta-You Wu, ibid., p. 726.24 S. Golden, ibid., p. 2071.26 See M. W. Perrin, Trans. Faraday SOG., 1938, 34, 144, and earlier papers cited in25 E. Bauer and Ta-You Wu, ibid., p. 2072.that referenceCOLLINSON, DAIKTON, AND IVIN : HOMOGENEOUS SYSTEMS.37and (3) that a reverse Menschutkin reaction, regarded as a unimoleculardissociation process and having AVt positive, decreases in rate as fl is in-creased. However, Buchanan and Hamann2' have pointed out that allthe reactions investigated involve ionic species as reactants or products orboth and that for reactions in ionising solvents the volume changes areprincipally determined by the relative degrees of solvation of the activatedcomplex and the reactants, higher solvation being accompanied by con-traction. These authors therefore measured the effect of pressure on theS N 1 type of solvolysis of tert.-butyl chloride and benzotrichloride in 80%ethanol. On Perrin's interpretation the unimolecular heterolysis which isthe rate-determining step should have AVI positive, and the reaction shouldbe retarded, If the authors' contention is correct the polarity of the transi-tion state is much greater than that of the undissociated halide and there-fore the solvation will increase, AV$ will be negative, and the reaction shouldbe accelerated.Many reactions of practical importance, eg., those leading to the produc-tion of macromolecules or involving biological substrates, are highly co-ordinated systems of simpler reactions.The mathematical treatment ofcertain of these combinations has been developed by several authors.28Bimolecular Gas Reactions.-The velocity constants of a number ofsimple bimolecular reactions have been determined, either by direct measure-ment or by measurement of the rate of the back reaction and the equilibriumconstant. The dimerisation of perfluoroethylene to perfluorocyclobutane 29and of borine to form diborane 30 have the low frequency factors expected onthe transition-state theory.An acceleration was in fact observed for both halides.It has been shown31 that the oxidationnitrosyl chloride by ozone is not a simple oxygen-atom transfer, butcatalysed by dinitrogen pentoxide, the mechanism being :123NO2 O,-NO3 + 0 24NXO, @ NO, + NO3NO, + NOCl+ NO, + NOZCIAt 40" c the rate constant k, = 0.7 x lo6 1.mole-l sec.-l. The mechanismofisofthe pyrolysis of nitric oxide- is still not settled, owing to disagreements overexperimental findings.32.30Termolecular Gas Reactions.-All the known third-order gas reactionsfall into two classes : (a) those involving two " odd-electron " molecules,e.g., nitric oxide, and (b) atom or ion recombination processes requiring athird body. Measurements have been reported on examples from eachcategory. Fairlie, Carberry, and Treacy33 have shown that the formation27 J. Buchanan and S. D. Hamann, Trans. Favaday SOC., 1953, 49, 1425.28 (Sir) Cyril Hinshelwood, J., 1953, 1947; C. A. Stewart, Biochenz. J , , 1953, 54,117; H. G. Higgins and E. J. Williams, Austral. J . Chem., 1953, 6, 195; (Mme.) M.Lautout, G. Wyllie, and M. Magat, J . Chim. Phys., 1953, 50, 199.29 B. Atkinson and A. B. Trenwith, J . , 1953, 2082.30 S. H. Bauer, A. Shepp, and R.E. McCoy, J . Amer. Chem. SOC., 1953, 75, 1003.31 H. S. Johnston and F. Leighton, ibid., p. 3612.32 F. Kaufman and J. R. Kelso, J . Chew. Phys., 1953, 21, 751; H. Wise and M. F.33 A.M. Fairlie, J. J. Carberry, and J. C . Treacy, J . Amer. Chem. SOC., 1953, '95, 3786.Frech, ibid., p. 75238 GENERAL AND PHYSICAL CHEMISTRY.of alkyl nitrites by the reaction of nitrogen dioxide on alcohols is of secondorder with respect to the dioxide and of first order with respect to the alcohol.I t is interesting to note that the rather meagre data on the methyl alcoholreaction indicate that the rate increases with decreasing temperature, andit is possible that the reaction is not termolecular but proceeds throughdinitrogen tetroxide as an intermediate according to the equations :2N0, __I, N,O, and N,O, + ROH __+c RO-NO + HO-NO,The technique of flash photolysis has been applied to the determination ofthe rate constants of the three-body recombination of iodine atoms. Thedata of all three groups of investigators agree reasonably well.Davidsonand Marshall have extended their measurements 34 to solutions in n-heptaneand carbon tetra~hloride,~~ and have shown that the rates of recombinationare respectively 130 and 40 times faster in these solvents than in argon at1 atm. pressure. Norrish and his co-workers35 have shown that thethird-order rate constant increases with atomic weight when the inert gasesare used as third bodies. Russell and Simons 36 have studied the effect ofstructure on third-body efficiency, and point out that with a large number ofcompounds investigated the only valid correlation of this efficiency appearedto be with the strength of the general van der Waals field of the third bodyas judged by the value of its boiling point.They also showed that with sixdifferent compounds used as third bodies the reaction rate fell by the sameamount (-60%) when the reaction temperature was raised from 20 to 127" c.First-order and Unimolecular Gas Reactions.-A very large number ofinvestigations of first-order gas reactions have been reported. The objectsof the researches are generally one or more of the following : (a) mechanistic,i.e., the identification of the precise chemical nature of the unimolecularstep, (b) where this is known, to evaluate the Arrhenius parameters, and(c) to discover the effect of pressure on the first-order rate constant for com-parison with theoretical predictions. Attainment of objective ( a ) is mademore difficult because many first-order decompositions occur by two con-current mechanisms, a chain reaction, the first step of which is often aunimolecular fission of a bond, and a single-stage unimolecular dissociationinto the products.Both of these unimolecular processes have intrinsictheoretical interest, and a method of distinguishing between them whichhas been frequently used is to suppress the chain reaction by the additionof an inhibitor such as nitric oxide or an olefin. This method must beapplied with care since inhibition by nitric oxide may not indicate a radicalmechanism.37 The retarding power of unsaturated compounds in dehydro-halogenation reactions appears to depend on the weakness of the C-H bondsin the retarder.38 Since an olefin is one of the products of these reactionsthe overall reaction may show aut~retardation.~~ The single-stage dehydro-halogenation reactions all have frequency factors in the range 1 0 1 2 v 5 to1014.5 sec:l which show no correlation with the activation energies. iso-34 R.Marshall and N. Davidson, J. Chem. Phys., 1953, 21, 659, 2086.35 M. I. Christie, R. G. W. Norrish, and G. Porter, Proc. Roy. Soc., 1953, A , 216, 152.36 K. E. Russell and J . Simons, ibid., 1953, A , 217, 271.37 F. H. Pollard, H. G. B. Marshall, and A. E. Pedler, Nature, 1952, 171, 1154.35 K.E. Howlett, J., 1953, 945.39 R. J . Williams, J., 1953, 113; J . H. S. Green, G. D. Harden, A. Maccoll, andP. T. Thomas, J. Chem. Phys., 1953, 21, 178COLLINSON, DAINTON, AND IVIN HOMOGENEOUS SYSTEMS. 39Propyl vinyl ether decomposes into propylene and acetaldehyde at a rategiven by kuni. = 3.8 x 1012exp( -43,56O/RT) sec.-l and with only minor free-radical side-reacti~ns.~~ Unimolecular bond-fission processes have beeninvestigated by the flow pyrolysis method,41 largely for the purpose ofdetermining bond dissociation energies (see Section 2 of this Report). Someof the frequency factors so found seem suspiciously large.42 The explanationof large frequency factors given on p. 35 may apply here and receivedsupport from a most thorough investigation of the decomposition in toluenesolution of a series of, structurally related azodinitriles of general formula([CH,],>C(CN)*N:), where x = 3, 4, 5, 6, 7, and 9.43 Very high frequencyfactors (-lo1' sec.-l) are found although E varies from 25.9 to 35.4 kcal.mole-1 owing to variations in the strain energy of the cycloparaffin rings.Trotman-Dickenson44 and others have made a careful study of theisomerisation of cyclopropane to propylene at 490" c and find their resultsagree with those of Chambers and Kistiakowsky 46 in the overlapping pressurerange and that the rate constant declines with pressure in a manner pre-dicted by Slater 12 over the range 84 to 0.07 mm.Hg. The efficiency relativeto the reactant of various added gases in collisional activation has also beendetermined for both this reaction 44 and the dissociation of cycZob~tane.4~Further studies have been made of the decomposition of n-butane4' andethane,48 both of which are somewhat complex.Isotopic-exchange reactions between dinitrogen pentoxide and l 8 0 , 4 9or 15N02 50 have been investigated and not only afford evidence of theexistence of nitrogen trioxide, which on Ogg's mechanism is considered to bean intermediate in decomposition of dinitrogen pentoxide, but also indicatethat the value of the rate constant for the unimolecular dissociationN,O, _+ NO, + NO, is 6.0 x 1012exp(-19,000/RT) sec.-l.In the pre-sence of nitric oxide every nitrogen trioxide molecule produced in theabove reaction reacts with nitric oxide according to NO, + NO --+ 2NO,,and the rate of the primary dissociation can therefore be determined. H.S.Johnston 51 has applied this principle to the determination of the activatingefficiencies of various non-reacting gases relative to dinitrogen pentoxide.The mechanism of the dinitrogen pentoxide-nitric oxide reaction has re-cently been confirmed by using the technique of fast-scanning infra-redspectroscopy to follow (a) the reaction itself and (b) the nitrogen exchangereaction between nitrogen dioxide and dinitrogen pentoxide. 52 The pyrolysis40 A. T. Blades, Canad. J . Chem., 1953, 31, 418.41 M. Ladacki and M. Szwarc, Proc. Roy. SOC., 1953, A , 219, 341, 353 ; B. G. Gowen-42 M. Szwarc and J. W. Taylor, J . Chem. Phys., 1953, 21, 1746.43 C.G. Overberger, H. Biletch, A. B. Finestone, J. Lilker, and J. Herbert, J . Amer.44 H. 0. Pritchard, R. G. Sowden, and A. F. Trotman-Dickenson, Proc. Roy. SOC.,415 T . S. Chambers and G. B. Kistiakowsky, J . Amer. Chem. SOC., 1934, 56, 399.4 7 V. A. Crawford and E. W. R. Steacie, Canad. J . Chem., 1953, 31, 937.48 B. C. Spall, F. J. Stubbs, and (Sir) Cyril Hinshelwood, Proc. Roy. SOC., 1953, A ,218, 439; C. J. Danby, B. C. Spall, F. J. Stubbs, and (Sir) Cyril Hinshelwood, ibid.,p. 450; A. D. Stepukhovich and A. G. Finkel, Zhur. Fiz. Khim., 1952, 26, 1413, 1419.C9 R. A. Ogg, J . Chem. Phys., 1953, 21, 3079.6o A. R. Amell and F. Daniels, J . Amer. Chem. Soc., 1952, 74, 6209.61 H. S. Johnston, ibid., 1953, 75, 1567.62 G. R.Cowan, D. Rotenberg, A. Downie, Bryce Crawford, jun., and R. A. Ogg,lock, J. C. Polanyi, and E. Warhurst, ibid., 1053, A , 218, 269.Chem. SOC., 1953, 75, 2078.1953, A , 217, 563. 45 Idem, ibid., 1953, A , 218, 416.J . Chew. Phys., 1953, 21, 139740 GENERAL AND PHYSICAL CHEMISTRY.of nitric acid vapour has been shown to involve the primary dissociationHNO, + HO + NO, for which the velocity constant at 400" c is 0-12sec.-l.= A decision has been made in favour of the unimolecular mechanismfor the decomposition of nitrous oxide according to the scheme :by L. Friedman and J. Bigeleisen 55 who have shown that 15N14N0 does notexchange with nitrous or nitric oxide as would be required by Pease'schain rnechani~m.~~N,O+N, + 0 ; 0 + N20+N2 + 0, or 2NO; 0 + 0(+ M)+O,N,O-N+NO; N+N,O+Ng+NONO + NO,---wN, + 0, + N ; N + NO+ N20Atomic and Free-radical Processes.-Processes involving Alkyl Radicalsand Hydrogen Atoms.-Such reactions may be conveniently classified interms of four equilibria :1Hydrocarbon + H Radical + H, ; Olefin + H ==d= Radical2Paraffin Radical + Radical ;Hydrocarbon + Radical Radical + HydrocarbonRelations of the type El - E, = AH may be used to check the experimentalenergies of activation, El and E,, or to predict one when the other is known.This is made possible by the calculation of AH froin known dissociationenergies. Complementary relations of the type R In A,/A, = AS" may beused to check the experimental frequency factors A, and A , or to predictone when the other is knowfi.This requires a knowledge of the standardentropy change AS" of the forward reaction (the standard state must bespecified when A,/A, is not dimensionless), which, in turn, requires a know-ledge of the entropy of the appropriate radicals. By assuming that theentropy of a radical R is equal to that of the hydrocarbon RH, with a cor-rection for electron degeneracy, Trotman-Dickenson 563 57 has estimatedentropy changes for the four types of process listed above, and for others.In this way a useful correlation of many experimental frequency factors canbe made.Two reviews of the kinetics of the gas-phase reactions of methyl radicalshave been The rate of combination of two methyl radicalshas been studied at high temperature by the methods of mass spectro-rnetry,61* 62 and at 165" by the rotating-sector meth0d.6~ The collisionefficiency is of the order of unity at 165" but appears to fall off at hightemperature.A pressure dependence of the bimolecular velocity constanthas been observed at 165" and low pressure, both for the combination oftwo methyl and of two trideuteromethyl radi~als.6~ The form of thedependence accords with the idea that the initially formed ethane moleculemust be stabilised by a favourable collision.5953 H. S. Johnston, L. Foering, and R. J. Thompson, J. Phys. Chem., 1953, 5'4, 390.54 R. N. Pease, ibid., 1939, 7, 749.55 L. Friedman and J . Bigeleisen, J . Amer. Chem. Soc., 1953, '75, 2215.5 6 A. F. Trotman-Dickenson, J. Chem. Phys., 1953, 21, 211.5 7 I d e m , Discuss.Faraday SOC., 1953, 14, 124.58 I d e m , Quart. Reviews, 1953, 7,198. 5s J . W. Smith, Sci. Progress, 1953, 41, 648.61 K. U. Ingold and F. P. Lasing, J. Chem. Phys., 1953, 21, 368, 1135.62 K. U. Ingold. F. P. Lossing, and A. W. Tickner, Discuss. Faraday Soc., 1953,14, 34.63 G. B. Kistiakowsky and E. K. Roberts, J. Chem. Phys., 1953, 21, 1637COLLINSON, DAINTON, AND IVIN : HOMOGENEOUS SYSTEMS. 41Relative rates of combination to disproportionation have been given forpairs of the following radicals : ethyl, approx. 8 : 1 'at 370" 64; isopropyl,2 : 1 at room temperature,65 and approx. 2 : 1 at 200-300".66The reactions of the radicals methyl and trideuteromethyl with hydrogen,deuterium, and hydrogen deuteride have been studied at 1 3 0 4 2 0 " ~ bySteacie and his co-workers 673 68 and it has been concluded 69 that all pub-lished data can be reconciled with the values 10.0 & 0.5 and 11.7 * 0-5kcal./mole, respectively, for the energies of activation of the two processes,CH, + H, CH, + H and CH, + D, CH,D + D.At a giventemperature the interaction of methyl and hydrogen deuteride to givemethane is rather faster than that to give deuteromethane. For all theseprocesses the P-factors are of the order lo-,. The thermodynamic relationslead to E = 7.0 & 1.5 kcal./mole and P -lo-, for the process CH, + HH,. These values are not compatible with the data from earlier work orwith the preliminary results of more recent work.7o It has been shownthat the exchange of deuterium atoms with methane at 350" proceeds viathe hydrogen-abstraction process CH4 + D _t CH, + HD, followed byexchange processes of the type CH, + D + CH,D + H.Tetradeutero-methane is a major product.71For the process H + C2H6 - H, + C,H5, the values E = 6.8 kcal.,P = 4.8 x have been obtained by Berlie and Le Roy,72 who used adischarge tube to generate the hydrogen atoms, and measured the rate ofconsumption of both hydrogen atoms and ethane. These values are inreasonable accord with those for the reverse process. However, Danventand Roberts,73 using the photolysis of dideuterium sulphide as source ofdeuterium atoms, find E = 9.0 kcal./mole, P = 0.6 for the analogousprocess D + C2H6 __t HD + C2H5. This energy of activation is based onthe experimental value of E = 5 kcal./mole for the process D + D,S _.+D, + DS.Other hydrocarbons give values of E which are parallel to thosefor the abstraction of hydrogen atoms by methyl radicals. Data have alsobeen obtained for the addition of hydrogen and deuterium atoms to olefins,which are in essential agreement with those of Melville and Robb. Thelatter have extended their molybdenum oxide method and have obtainedcollision efficiencies of the order 10-5-10-4 for the addition of hydrogenatoms to certain aromatic hydrocarbon^.^^Steacie and his co-workers have studied reactions of the type CH, +RH --+ CH, + R, using the photolysis of dimethylmercury 75 and ofazomethane 76 as sources of methyl radicals. The values of E and P so64 B. G. Gowenlock, J.C. Polanyi, and E. Warhurst, Proc. Roy. SOC., 1953, A,218, 269.6 5 R. W. Durham and E. W. R. Steacie. Canad. J . Chern., 1953, 31, 377.6 6 H. T. J . Chilton and €3. G. Gowenlock, Trans. Faruday SOL, 1953, 49, 1451.6 7 T. G. Majury and E. W. R. Steacie, Discuss. Faraday SOC., 1953, 14, 45.6 8 E. Whittle and E. W. R. Steacie, J . Chern. Phys., 1953, 21, 993.69 M. H. J . Wijnen and E. W. R. Steacie, Discuss. Faraduy SOC., 1953, 14, 118.70 D. J . Le Roy, ibid., p. 120.71 D. W. Coillet and G. M. Harris, J . Amer. Chem. SOC., 1953, '95, 1486.72 M. R. Berlie and D. J . Le Roy, Discuss. Faraday SOL, 1953, 14, 50.73 B. de B. Darwent and R. Roberts, ibid., p. 55.74 H. W. Melville and J . C. Robb, ibid., p. 122; P. E. M. Allen, H. W. Melville, and75 R.E. Rebbert and E. W. R. Steacie, J . Chern. Phys., 1953, 21, 1723.76 M. H. Jones and E. W. R. Steacie, Canad. J . Chenz., 1953, 31, 505.J. C. Robb, Proc. Roy. SOL, 1953, A , 218, 31142 GENERAL AND PXYSICAL CHEMISTRY.obtained are in good agreement with those from earlier work in which thephotolysis of acetone'was used as the source of methyl radicals. Energiesof activation and frequency factors have also been obtained for the attackof the alkyl radical on the parent molecule in the photolyses of dimethyl-mercury,77 a~omethane,~~ azoisopropane,65 hexadeuteroacetone,6* anddia~etyl.'~ It has been shown that at 100" methyl radicals abstract thea-hydrogen atom in isobutyryl chloride 12.4 times as fast as a p-hydrogenatom and 1.2 $: 0.2 times as fast as an a-deuterium atom.80 The processCH, + HC1- CH, + C1 has been found to occur very readily,81 withE = 2.1 5 1 kcal./mole and P -7 x Traces of hydrogen chloride areformed on photolysis of mixtures of the vapours of acetone and carbon tetra-chloride; the bearing of this on the reactions of methyl radicals with thepartially chlorinated methanes has been discussed 82 and it is concliidedthat the previously reported trend of decreasing energy of activation withprogressive substitution by chlorine atoms is still qualitatively correct.Experiments on the photolysis of methyl iodide have provided moreevidence that methane is formed only by interaction of " hot " methylradicals with methyl ** In the presence of sufficient inert gas nomethane is formed.83The possibility of the reaction CH, + CO - CH,*CO has been investig-ated at 150" by using di-tert.-butyl peroxide as radical source, andradioactive carbon monoxide.85 No reaction was detected, from which itwas concluded that k < 3 x lo6 1.mole-l sec.-l. The reverse reaction isreported to have E = 13.5 -+ 2 kcal./mole, while for Me&O --+ Me +Me2C0, E = 11.2It is well known that nitric oxide inhibits or retards reactions involvingalkyl radicals, and the occurrence of the interaction of the radicals and nitricoxide has generally been postulated. However, the nature of the primaryproducts has remained somewhat obscure. In the case of the isopropylradical it has now been shown by a flow method that the primary productsare 2-nitrosopropane Me,CH*NO, and acetone oxime Me,C:N=OH.87 In thecase of the 2-cyanoisopropyl radical also there is evidence of the formation ofan intermediate nitroso-compound.88Other RadicaZ Processes.-Information has been obtained on the rate ofaddition of trichloromethyl radicals to a variety of aromatic compoundsrelative t o that to hexadecene or styrene.89 In this way a scale of reactivitieshas been obtained which is in good agreement with theory. Melville and hisco-workers 90 have described a method by which absolute rate constants forsuch reactions of trichloromethyl radicals may be determined. Data have7 7 R. E. Rebbert and E. W. R. Steacie, Canad. J . Chern., 1953, 31, 631.7 8 M. H. Jones and E. W. R. Steacie, J . Chern. Phys., 1953, 21, 1018.79 F.E. Blacet and W. E. Bell, Discuss. Faraduy Soc., 1953, 14, 70.80 C. C. Price and H. Morita, J . Amer. Chern. Soc., 1953, 75, 3686.81 R. J. Cvetanovic and E. W. R. Steacie, Cunud. J . Chena., 1953, 31, 158.82 R. J. Cvetanovic, F. A. Raal, and E. W. R. Steacie, ibid., p. 171.83 F. P. Hudson, R. R. Williams, and W. H. Hamill, J . Chem. Phys., 1953, 21, 1894.84 R. H. Schuler and C. T. Chmiel, J . Amer. Chem. SOC., 1953, 75, 3792.85 G. B. Porter and S. W. Benson, ibid., p. 2773.8 6 D. H. Volman and W. M. Graven, ibid., p. 3111.8 7 H. T. J. Chilton and B. G. Gowenlock, I., 1953, 3232.8 8 B. Gingras and W. A. Waters, Chem. and Ind., 1953, 615.89 E. C . Kooyman and E. Farenhorst, Trans. Faraday Soc., 1953, 49, 58.90 H. W. Melville, J.C . Robb, and R. C. Tutton, Discuss. Faraduy SOG., 1953, 14, 150.2 kcal./mole.8COLLINSON, DAINTON, AND IVIN : HOMOGENEOUS SYSTEMS. 43been obtained for the addition of these radicals to cyclohexene and vinylacetate. This work provides further evidence that pairs of dissimilarradicals interact more easily than pairs of similar radicals. The ability oftrichloromethyl radicals to abstract hydrogen atoms from polyalkylbenzenesand other hydrocarbons has also been quantitatively studied.g1A neat general method, based on that of Semenov, has been given for thederivation of the rate expression of a non-branching chain reaction withalternating centres ; 92 the method is applied to the reaction between hydrogenand chlorine in the presence of nitrosyl chloride.Experimental results onthis system in the region of 300°, are in accordance with a non-branchingmechanism in which the main initiation step is NO + C1, --+ NOCl + Cl.g3The velocity constant of the process C1 + H, - HCl + H is derived andshown to fit other data, giving E = 5.5 & 0.2 kcal./mole and A - 1011 1.mole-1 sec.-l. The decomposition of nitrosyl chloride proceeds by a chainmechanism at 300' in contrast to the bimolecular mechanism at lower tem-peratures.94 Published data have been used to calculate A = 4 x 109 1.mole-1 sec.-l, E = 20.3 kcal./mole for the process NO + C1, _t NOCl +Cl.95 I t has been shown that nitrogen trichloride undergoes explosivedecomposition below a certain pressure and will induce explosive combinationof hydrogen and chlorine at low pressure in the dark.96The exchange of iodine atoms between organic iodides and elementaryiodine usually proceeds via iodine atomsg7 Two mechanisms have beendistinguished : type 1, RI + I* __t RI* + I, is shown by allylic and aryliodides; type 2, RI + I __t R + I,, R + I, -+ RI + I, is shown byalkyl iodides.Ally1 iodide is exceptional in exchanging mainly by a non-atomic mechanism.98 The photochemically induced exchange of ally1iodide proceeds rapidly by an atomic mechanism.99Photochemistry.-Actinometry.-The photolysis of potassium ferrioxalatein aqueous solution results in the formation of ferrous iron which may beestimated colorimetrically in very small amounts by means of the complexformed with o-phenanthroline. This photolysis provides a chemicalactinometer which is 100 times more sensitive than the uranyl oxalateactinometer, and approximate quantum yields have been determined a ttwelve wave-lengths between 4900-2537 A.Absorption Spectra of Intermediates.-The absorption spectra of a numberof intermediates of photochemical reactions have been observed by themethod of flash photolysis. In this way the spectra of ClO,105 CHO,101NH and NH, lo2 have been observed.By using a multiple-reflectionsystem providing an effective path length of 20 m., Ramsay lo3 has alsobeen able to observe the NH, bands in continuously photolysed ammonia.The intensity of the bands was comparable with that of the bands obtainedby flash photolysis. It is interesting to note that a similar multiple-reflectionDl E.C. Kooyman and A. Strang, Rec. Trav. chim., 1953, 72, 329, 342.92 P. G. Ashmore, Trans. Faraday SOC., 1953, 49, 251.D3 P. G. Ashmore and J. Chanmugam, ibid., p. 254.94 Idem. ibid., p. 265.96 P. G. Ashmore, Nature, 1953, 172, 449.D7 R. M. Noyes and D. J. Sibbett, J . Amer. Chem. Soc., 1953, 75, 767.Ds Idem, ibid., p. 761.D5 Idem, ibid., p. 270.O9 Idem, ibid., p. 763.loo C. A. Parker, Pvoc. Roy. Soc., 1953, A , 219, 104.lol D. A. Ramsay, J . Chem. Phys., 1953, 21, 960.102 Idem, J . Phys. Chem., 1953,57,415. lo3 Idem, J . Chem. Phys., 1953,21,16544 GENERAL AND PHYSICAL CHEMISTRY.method has enabled the absorption spectra of the radicals OH, SH, CS, CN,and NH, to be observed on passing an electric discharge through appropriatecompounds.lo4The absorption bands of C10 have been observed after flash irradiationof a mixture of chlorine and oxygen.lo5 The radicals disappear by a bi-molecular process which has no energy of activation and a collision efficiencyof the order Since the direct process 2C10 ---;tCl, + 0, would beexpected to have a considerable energy of activation it is postulated thatC1,0, is formed as an intermediate. The chlorine-photosensitised exchangebetween the isotopes of oxygen probably involves the intermediate formationof C10 radicals.lo6Photolysis of Aldehydes and Ketones.-The photolysis of glyoxal vapourby light of wave-length 3130 A results in the formation of carbon monoxide($GO = 1-2), hydrogen (+H~ = 0-13), and f0rma1dehyde.l~~ The quantumyields are relatively insensitive to changes of temperature and pressure or toaddition of inert gas, so that the photolysis may be represented completelyin terms of the two primary processes :(15%) 2CO 3.H, f-- (CHO),* __t CH,O + CO (85%)An explanation of certain discrepancies arising in the high-temperaturephotolysis of acetaldehyde has been suggested. lo8 The photolyses ofacetaldehyde, acetone, and diacetyl have been studied at very high in-tensity. 109 Under these conditions radical-radical reactions predominate,and the reactions of radicals with the parent molecules are unimportant.Particularly striking is the fact that ethane is formed in the photolysis ofacetaldehyde, even in the presence of an excess of carbon dioxide (whichminimises the temperature rise).Ethane has hitherto been undetected inthe normal photolysis at room temperature, owing to the rapidity of theprocess, CH, + CH,*CHO __t CH, + CH,*CO. The ratio of the quantumyields for the primary processes (1) and (2) is found to be +1/+2 < 1-1.CH, and CH, remain undetected by absorption spectra.104(2) CH, + CHO f-- CH,CHO* + CH, + CO (1)that diacetyl formation in the photolysis ofacetone cannot account for the apparent change in the energy of activationof CH, + CH,*CO*CH, __t CH, + CH,CO*CH, at about 120". Thefluorescence of acetone and diacetyl 112 vapour has been studied. Inboth cases fluorescence occurs from two excited states, one of which isquenched by oxygen. The photolysis of diacetyl vapour has been investig-ated at 2654A between 28-200°, and a mechanism proposed to accountfor the experimental quantum yields.l13 An investigation of the photolysisof acetone vapour in the presence of carbon tetrachloride has shown thatthe latter does not act simply as a diluent but is involved in some processIt has been concluded104 P.J. Dyne, Canad. J . Phys., 1953, 31, 453.105 G. Porter and F. J. Wright, Discuss. Faraduy SOL, 1953, 14, 23.106 R. A. Ogg, J . Chem. Phys., 1953, 21, 2078.107 J. G. Calvert and G. S. Layne, J . Amer. Chem. Soc., 1953, 75, 856.1 0 8 H. 0. Pritchard, G. 0. Pritchard, and A. F. Trotman-Dickenson, J . Chem. Phys.,109 M. A. Khan, R. G. W. Norrish, and G. Porter, Proc. Roy. SOL, 1953, A , 210, 312.110 H.J. Groh, E. D. Becker, and W. A. Noyes, Discuss. Faraduy Soc., 1953, 14, 128.111 H. J. Groh, G. W. Luckey, and W. A. Noyes, J . Amer. Chew SOL, 1953, 21, 115.112 H. J. Groh, J . Chem. Phys., 1953, 21, 674.113 F. E. Blacet and W. E. Bell, Discuss. Faraday Soc., 1953, 14, 70, 131.1953, 21, 748COLLINSON, DAINTON, AND IVIN HOMOGENEOUS SYSTEMS. 45leading to the formation of hydrogen chloride.*l It appears that carbontetrachloride undergoes an acetone-photosensitised decomposition to giveCCl, + C1. The hydrogen chloride subsequently formed has a markedeffect on the relative amounts of the photolysis products of acetone (seep. 42).Reactions Involving Halogen Atoms.-The photochemical formation ofcarbonyl chloride has been further studied and the mechanism extended toinclude wall-termination a t low pressure.114 The photolysis of methyliodide has been shown to involve " hot " methyl radical^.^^^^^ The photolysisof trifluoromethyl iodide results in the formation of perfluoroethane andiodine. 115 The gas-phase bromination of toluene has been studied, bothphotochemically (82-132') and thermally ( 166').l16 The combined resultslead to a value of E = 7.2 kcal./mole for the process Br + Ph-CH, -+Ph*CH,* + HBr. A study of the kinetics of the inhibition by hydrogenbromide gives a value of E = 5.0 kcal./mole for the reverse process (cf.p. 28). The photochlorination of methyl chloroformate has been studiedin the gas phase and the results compared with those obtained for thereaction in carbon tetrachloride solution.117Other Direct Photochemical Reactions.--A detailed investigation has beenmade of the photochemical and thermal decomposition of hydrogen sulphidein the range 27-650"/8--550 mm. and at wave-lengths 2288 A and 2550 A,11sthe decomposition of hydrogen bromide being used as actinometer at 2288 A.The quantum yield +Ez at room temperature is found to increase slightly withpressure to a limiting value of 1-26. At high pressures it is assumed thatall the hydrogen atoms produced in the primary process (1) disappear byprocess (2) so that the mechanism simplifies to :hv(1) H,S+H + HS(2) H + H,S--+H, + HS(3) 2HS+Hz + '32(4) 2HS ---P 33,s + sand the limiting quantum yield is accounted for by supposing that k,/k, -6.7.The photolyses of the vapours of dirnethylmerc~ry,~~ azomethane,78 andazoisopropane 65 have been investigated as potential sources of alkyl radicals(see p.42). In the case of azomethane it was shown that +N$ = 1 and isindependent of temperature in the range 24-190".The photolysis of ethyl nitrate vapour has been studied at a number oftemperatures, and the products analysed. 119 The evidence indicates thatthe ethoxy-radical formed in the primary process can undergo two modesof decomposition :(1) C,H,.O __)_ CH, + CH,.O; (2) C,H,.O + H + CH,*CHOThe final products of photolysis of anthracene (A) in carbon tetrachloridecan be explained by assuming the intermediate formation of AC1 and CCI,radicals.120 The effects of temperature, solvent, and a second aromatic114 L.Fowler and J. J. Beaver, J . Amer. Chem. SOL, 1953, 75, 4186.115 J. R. Dacey, Discuss. Furuduy Soc., 1953, 14, 84.116 H. R. Anderson, H. A. Scheraga, and E. R. van Artsdalen, J. Chem. Phys., 1953,117 J. H. Brandy and D. J. Le Roy, ibid., p . 1049.11* B. de B. Darwent and R. Roberts, Proc. Roy. Soc., 1953, A, 216, 344.119 J. A. Gray and D. W. G. Style, Trans. Furaday SOC., 1953, 49, 52.E. J. Bowen and K. K . Rohatki, Discuss. Furuduy SOC., 1953, 14, 146.21, 125846 GENERAL AND PHYSICAL CHEMISTRY.hydrocarbon on the fluorescence of substituted anthracenes have beeninvestigated, and it is concluded that transfer of energy can occur overdistances of many molecular diameters.1211122Photosensitised. Reactions.-An unsuccessful attempt has been made tosynthesise ammonia from nitrogen and hydrogen by xenon-photosensitisation(1470 This lack of success is taken as evidence against the valueD(N,) = 171 -3 kcal./mole.The mercury-photosensitised reaction of cyclo-butane results in the formation of hydrogen, n-butylcyclobutane and asaturated compound, CSH14, which is apparently ~yclobutylcyclobutane.~~~Quantum yields were measured at 30". The proposed mechanism involvesthe primary process, cycZo-C4H,* __t cyclo-C,H, + H, followed by dimeris-ation of the cyclobutyl radicals to form n-butyl- and cyclobutyl-cyclobutane.The mercury-photosensitised decomposition of ethylene has been re-investig-ated, very monochromatic light of wave-length 2537 A being used.125Reactions Involving Oxygen.-The mechanism of quenching of mercury6(3P1) atoms by oxygen has been discussed in relation to ozone formation,126exchange of 0, and 1802,12' and the photosensitised oxidation of paraffins.12,The exchange reaction occurs by a chain mechanism and must involve theprocess 0 + 0, - 0, + 0.The same process must occur in the ozone-catalysed exchange between oxygen molecules.129 The mercury-sensitisedphoto-oxidation of propane to give isopropyl hydroperoxide has beenstudied.130 The photo-oxidation of solutions of various substituted anthra-cenes by dissolved oxygen has been followed by measuring the rate of uptakeof 0xygen.1~1 The quantum yield is independent of the oxygen concentrationbut is a function of the anthracene concentration.The reaction is interpretedin terms of a reactive intermediate for which anthracene and solvent moleculescontaining C-H bonds compete.A detailed mechanism has been proposed for the anthraquinone-sensitisedphoto-oxidation of alcoh01s.l~~ In the case of ethyl alcohol it has beenshown that the products are acetaldehyde, acetic acid, and hydrogen per-oxide. Acetic acid is a primary product and is not formed by secondaryoxidation of the aldehyde. The quantum yield 40, =1 1, and is independentof temperature. The sensitiser (A) acts by breaking a C-H bond of thealcohol, A + CH3*CH2*OH - AH + CH,CH*OH, but is regenerated bythe process, AH + 0, - A + HO,. The relative proportions of theproducts depend on the relative concentrations of the intermediate peroxy-radicals, which in turn depend on the concentrations of sensitiser andpressure of oxygen, but which are independent of light intensity and alcoholconcentration.The kinetics of photo-oxidation of benzaldehyde in n-decane at 5-20'121 E.J. Bowen and R. J. Cook, J . , 1953, 3059.122 E. J. Bowen and €3. Brocklehurst, Trans. Favaday Soc., 1953, 49, 1131.123 M. H. J. Wijnen and H. A. Taylor, J. Chem. Phys., 1953, 21, 233.124 D. L. Kantro and H. E. Gunning, ibid., p. 1797.125 ,4. G. Mitchell and D. J. Le Roy, ibid., p. 2075.126 D. H. Volman, ibid., p. 2086.1 2 7 W. H. Johnston and C. J. O'Shea, ibid., p. 2080.128 J. A. Gray, ibid., p. 1300.129 R. A. Ogg and W. T. Sutphen, ibid., p. 2078.130 N. V. Fok and A. B. Nalbandyan, Chem.Abs., 1953, 47, 3124.131 E. J. Bowen, Discuss. Faraday Soc., 1953, 14, 143.132 J. L. Bolland and H. R. Cooper, Nature, 1953, 1'92, 413COLLINSON, DAINTON, AND IVIN HOMOGENEOUS SYSTEMS. 47are in accord with the following chain mechanism at high concentrations ofoxygen, when (4) is the main termination process : 133hv(1) PhCHO PhCO + H(2) PhCO + 0, + PhCO.00(3) Ph.CO.00 + Ph-CHO + PhCO*OOH + PhCO(4) 2Ph.CO.00 __t terminationBy the use of the retarder and rotating-sector techniques the followingvalues have been obtained : E, = 1-8 0.5, E, - 1 kcal./mole ; A , = 5 xlo4, A , = 8 x lo9 1. mole-l sec.-l. The mechanism is analogous to that ofa simple vinyl polymerisation reaction. Further, it has been shown thatthe kinetics of the simultaneous photo-oxidation of benzaldehyde anda-decanal are analogous to those of a copolymerisation r e a ~ t i 0 n .l ~ ~ Bothaldehydes are involved in a single kinetic chain and by the application ofstandard copolymerisation methods the rate constants of the four propagationsteps, as well as the cross-termination coefficient, have been evaluated. Thephoto-oxidation of pure liquid acetaldehyde between -90" and -40" showskinetics which are identical in every respect with those for benzaldehyde andn-decanal in s01ution.l~~Some exploratory investigations have been made of the photo-oxidationsof acetone 1369 13'9 138 and diethyl ketone 139 below 200". The reactionsproceed via the initial formation and subsequent oxidation of alkyl radicals.A comparison has been made with the photo-oxidations of dimethylmercuryand methyl iodide,140 the conclusion being that both carbon monoxide anddioxide ultimately result from the oxidation of the methyl radical. In thecase of diethyl ketone, tracer experiments using Et,l*CO indicate that at30" most of the carbon dioxide formed is 14C0,, whereas at 102" a largeproportion comes from the oxidation of the ethyl radical.The kinetics of the chemiluminescent reaction between zinc tetraphenyl-porphin and tetralin hydroperoxide have been investigated as part of a studyof the mechanism of dye-sensitised photo-oxidation reactions.141Fluorescence.-A method of determining fluorescence life-times with anaccuracy of 1% at 2 x 10-8 sec. has been described.142 The fluorescence isexcited by light modulated at high frequency, and the life-time estimatedfrom the phase difference between the exciting light and the resulting fluor-escence.Measurements on the fluorescence of acetone,lll diacetyl,l12and substituted anthracenes already have been referredReactions in Solution.-Electron-transfer Processes between Ions containingthe Same MetaL-In an earlier theory of electron-exchange reactions amechanism based on the tunnelling of a potential barrier was advanced; 143133 T. A. Ingles and H. W. Melville, Proc. Roy. Soc., 1953, A , 218, 175.13* Idem, ibid., p. 163.135 P. Fillet, M. Niclause, and M. Letort, Compt. rend., 1953, 236, 1489.136 P. E. Frankenburg and W. A. Noyes, J . Amer. Chew Soc., 1953, 75, 2847.13' D.E. Hoare, Trans. Faraday SOC., 1953, 49, 1292.13* R. R. Heutz, J . Anzer. Chem. Soc., 1953, 75, 5810.139 A. Finkelstein and W. A. Noyes, Discuss. Faraday SOC., 1953, 14, 76, 81.140 R. B. Martin and W. A. Noyes, J . Anzer. Chem. SOC., 1953, 75, 4183.141 H. Linschitz and E. W. Abrahamson, Nature, 1953, 172, 909.142 E. A. Bailey and G. K. Rollefson, J . Chem. Phys., 1953, 21, 1315.143 R. J. Marcus, B. J. Zwolinski, H. Eyring, and J. D. Spikes, US. Atomic En.Commiss. Report, AECU-227148 GENERAL AND PHYSICAL CHEMISTRY.a more quantitative extension of this theory has now been made.144 Asjudged by the experimental results so far available, there are apparently twotypes of electron-exchange reactions : (i) those with low activation energyand negative entropy of activation and (ii) those with high activation energyand positive entropy of activation.The theory developed, which agreeswith that by Libby 145 inasmuch as it depends on the applicability of theFranck-Condon principle, provides an explanation for these two possibilities.The expression derived for the specific rate constant of electron exchangecontains a negative entropy of activation term in the form of an electronictransmission coefficient, and a positive entropy of activation term as partof the free energy of rearrangement, the sign of the actual entropy of activ-ation depending on which is predominant. The expression implies that theremay not in fact be two clear cut groups of reactions. On the basis of theelectron tunnelling theory it is claimed that the current " catalytic,"" bridge," and " group exchange '' theories can be reconciled.In reactions of this type it has generally been found that only systemsinvolving positive ions react at measurable rates.However Sheppard andWahl 146 have been able to investigate the rate of electron transfer betweenmanganate and permanganate ions in sodium hydroxide solution. Theexchange follows a second-order law with a half life of 12 sec. at a concen-tration of 9 x 1 0 - 5 ~ . The fact that the rate of exchange is small com-pared with the collision frequency indicates that in aqueous solution theprobability of electron transfer from the MnO,= ion to a contiguous Mn0,-ion is small.In any given case it is not yet known whether electron transfer involvesthe jump of a free electron or whether a group such as OH or H accompaniesit.Another effect not fully understood is the catalysing action of anioniccomplex-forming agents in many of the exchange reactions between simplecations. It has been pointed out that the reason for the lack of informationin these directions lies in the general lability of changes in the co-ordinationBy oxidising Cr(I1) in the presence of chloride ions, chlorine wasfound to be attached to the resulting Cr(m), indicating that Cr-Cl bondswere formed in the activated complex. By using a complex oxidising ion,slow with respect to substitution, viz., Co(NH,),C12+, the electron transferin this case was shown directly to involve chlorine-atom transfer. Hydrogen-atom transfer has been suggested as the mechanism of electron transferbetween the ions Fe2+ and FeF2+, FeF2+, or FeF3,148 since the effect of theaddition of fluorine ion is to bring about very little change in either the ratesof exchange or the entropies of activation.Earlier work on the disproportionation of PU(IV) in perchloric acidsolutions has been corrected for the influence of M particles, and the mechan-ism found to be consistent with that previously deduced from the dis-proportionation of P U ( V ) .~ ~ ~ These results have also been confirmed byother workers,150 the most probable rate-determining step being PuOH3+ +P u ( O H ) ~ ~ +144 R. J. Marcus, B. J. Zwolinski, and H. Eyring, U.S. Atomic En. Commiss. Report,AECU-2620.145 W. F. Libby, J . Phys. Chem., 1952, 56, 863.1 4 6 J. C. Sheppard and A. C. Wahl, J . Amer. Clzem. Soc., 1953, 75, 5133.147 H. Taube, H. Myers, and R. L. Rich, ibid., p. 4118.1 4 8 J. Hudis and A. C. Wahl, ibid., p. 4153.149 R. E. Connickand W. H. McVey, ibid., p. 474.Pu3+ + PuO,' + H20 + H+.I5O S. W. Rabideau, ibid., p. 474COLLINSON, DAINTON, AND IVIN HOMOGENEOUS SYSTEMS. 49Atom and Group Transfer.-Apart from reactions involving Cr(rr),exchanges of chromium between different Cr(m) species have generallybeen found to be slow. It has now been shown that there is negligibleexchange between the chromic ion and the chromate ion in aqueous solu-tion.151 The exchange of lead between the plumbite and the plumbate ion in7~-potassium hydroxide solution occurs at approximately 80".152 In agree-ment with the non-existence of exchange between Pb(r1) and Pb(1v) inacetic acid,153 it was found that a heterogeneous exchange of lead betweensolid Pb,O, and a solution of Pb(r1) involved only the bivalent lead in theoxide.Several investigations involving the exchange of sulphur have beenmade. Exchange of sulphur between sulphurous acid and dithionous acidwas complete within 20 sec. for solutions on the acid side of pH 7.15, InN-sodium hydroxide no exchange occurred in 90 sec. A study of the exchangeof 35S between the diethyl polysulphides indicated that exchange occurredonly with sulphur atoms not attached to carbon and that the sulphur atomswere not equivalent. On the other hand all the sulphur atoms in the sodiumpolysulphides appeared to be equivalent The exchange of sulphurbetween solutes and liquid sulphur dioxide l56 or liquid hydrogen sulphide 15'has been investigated.Unlike the exchange of iodine between molecular iodine and alkyl iodides,which proceeds by a free-radical mechanism, 158 the corresponding exchangewith ally1 iodide does not involve radicals.159 In this respect its behaviouris claimed to be unique among organic halides.The mechanism is bi-molecular and its high negative entropy of activation suggests the formationC H ~ ~ C H - C H ~ of an activated complex of the type shown inset. ThereI-----I-----I iodine monochloride and benzyl halides or isopropyl iodidein carbon tetrachloride.160 The mechanism is obscure, but a complex[RX-ICl] is probably formed with the isopropyl iodide.A complex of thetype [Br*-EtBrJ has been shown to be formed during the exchange of brominebetween ethyl bromide and sodium bromide in ethyl alcohol.161The exchanges of X between K,PtX, and NH,X* in aqueous solution(where X* = 38Cl, 8oBr and s2Br, lzaT or C15N) proceed at very differentrates.162 Paradoxically the exchange is faster the greater the stability ofthe complex, this being understandable if the exchange is regarded from theviewpoint of the ease of penetration of the added anions into the inner co-ordination sphere. The exchange of oxygen between water and hydrated151 A. H. W. Aten, H. Steinberg, D. Heymann, and A. Fontijn, Rec. Trav. cltim., 1953,72, 94.153 E.A. Evans, J. L. Huston, and T. H. Norris, J . Amer. Chem. Soc., 1952, 74, 4985.15* H. B. van der Heijde, Rec. Trav. chzm., 1953, 72, 95.155 E. N. Gur'yanova, Y . K. Syrkin, and L. S. Kuzina, Doklady A k a d . Nauk S.S.S.R.,I 1 may be a different mechanism for exchange of iodine between152 A. Fava, J . Chim. Phys., 1953, 50, 403.1952. 86. 107.156 R. H. Herber, T. H. Norris, and J. L. Huston, U.S. Atomic En. Commiss. Report,1 5 7 T. H. Norris and R. C. Smith, ibid.. AECU-2657.AECU-2606.15* R. G. Badger, C. T. Chmiel, and R. H. Shuler, J . Anzcr. Chem. Soc., 1953, 75,180 R. M. Keefer and L. J. Andrews, ibid., p. 543.161 M. B. Neiman, G. V. Makstmova, and Y . M. Shapovalov, Doklady Akad. NaGk2498. 15n D. J. Sibbett and R. M. Noyes, ibid., p.761.S.S.S.R., 1952, 85, 1289.A. A. Grinberg and L. E. Nikol'skaya, Zhur. Priklad. Khim., 1951, 24, 89350 GENERAL AND PHYSICAL CHEMISTRY.chromic chloride 163 has been examined in non-acid solutions. In contrastto the results for solutioiis containing mineral acid 164 there is no specificeffect of anions, and the activation energy for the exchange in non-acidsolutions is significantly higher. An anion-exchange mechanism equivalentto isomerisation is suggested. In non-acid solutions direct exchange ofthe hydroxyl ion is assumed to predominate, whilst in acid solutions exchangeis brought about mainly by other anions.The exchange of oxygen between gaseous oxygen and liquid water hasbeen found to occur in the presence of hydrogen peroxide or of catalysts fordecomposition of the latter.165 Since catalase comes into this category, carewill be needed in the interpretation of tracer experiments in photosynthesis.At low concentrations of nitric acid the exchange of oxygen betweennitric acid and water occurs only in the presence of lower oxides of nitrogen(“ nitrous acid ”), but at higher acid concentrations these are not necessary.166The kinetics suggest a two-stage mechanism involving exchanges betweenwater and nitrous acid and between nitrous acid and nitric acid.Some interesting experiments have been reported on exchanges betweengaseous hydrogen and various solutions.The exchange between hydrogengas and aqueous potassium hydroxide, studied with both deuterium andpara-hydrogen, was found to be homogeneous and of first order in hydrogenand hydroxyl-ion concentration.167 No exchange occurred in acid solutions,and arguments are advanced for considering the mechanism to beD, + OH- _+ D- + DOH, followed by H,O + D- ---+ OH- + HD. Asimilar, but experimentally less well founded, mechanism has beensuggested for the corresponding exchange between hydrogen and potass-amide in liquid ammonia.16s Exchanges involving hydrogen gas can alsobe brought about by the use of solutions of cuprous acetate in quin-0line,1~~ 170 a system which can be used for homogeneous catalytic reduction.The rate of exchange is found to be proportional to the first power of thehydrogen concentration and to the square of the cuprous acetate concen-tration, which may indicate that the mechanism involves a dimeric coppercomplex and that the rate-determining step is (CuI), + H, + (Cu1),*2H,the hydrogen being in a dissociated state.169 I t has also been suggestedthat the mechanism involves addition of hydrogen to the double bond in thequinoline ring, giving an unstable c0rnp1ex.l~~ The fact that other solventscan be used, provided they are nitrogen bases,169 seems to be against thishypothesis.Electron-transfer Reactions Involving the Formgtion of New Species.-Anew method has been proposed for utilising the oxidation of hydrazine inclassifying oxidising agents as l-electron or 2-electron transfer agents.171On this basis the previous classification of hydrogen peroxide as a “ di-delectronator,” and of halogens as “ monodelectronators,” is disputed.163 H.A. E. Mackenzie and A. M. Milner, Trans. Faraday SOC., 1963, 49, 1437.f G 5 H. A. E. Mackenzie and A. M. Milner, J , S. African Chem. I m t . , 1931, 4, 79.166 C. A. Bunton, E. A. Halevi, and D. R. Llewellyn, J . , 1952,4913,4197; 1953, 2653.16’ W. K. Wilmarth, J. C . Dayton, and J . M. Floumoy, J . Amer. Chem. Soc., 1953,lB9 S. Weller and G. A. Mills, ibid., p. 769.170 W. K. Wilmarth and M. K. Barsh, ibid., p. 2237.171 W. C. E. Higginson, D. Sutton, and P. Wright, J . , 1953, 1380.R. A. Plane and H. Taube, J . Chem. Phys., 1952, 56, 33.75, 4549. 16* W. K. Wilmarth and J. C. Dayton, ibid., p. 4553.R. E. Kirk and A. W. Browne, J . Anzer. Chem. SOC., 1928, 50, 337COLLINSON, DAINTON, AND WIN : HOMBGENEOUS SYSTEMS.51The mechanisms proposed for the l-electron and %electron transfer reactionsof hydrazine have been confirmed by using 15N as a tra~er.l7~ Anothercriterion 174 for distinguishing l-electron and %electron transfers has beenapplied to the reduction of aa-dimethylbenzyl hydroperoxide by the iodideion. A single stage 2-electron transfer process was indicated but successivel-electron transfers were not eliminated.175Participation of radical ions of the type X,- (where X = C1, Br, I, orCN) has frequently been postulated for processes involving electron transfer.The (SCN),- ion has now been added to the list, having been found to occuras an intermediate in the spontaneous bleaching of acid aqueous solutions offerric thi0~yanate.l'~ This reaction occurs via the FeSCN2+ and Fe(SCN), +ions, and also involves (SCN), as an intermediate.The I,- ion is apparentlythe only possible intermediate which can act as a catalyst for the reductionof oxygen in the pervanadyl-iodide rea~ti0n.l~' The complete mechanisminvolves a tennolecular process, I,- + 0, + H+ - I, + O,H, which,owing to the low concentration of I,-, seems rather unlikely. Consequentlyit is suggested that the ion HO,+ may have independent existence.The kinetics of the Ce(Iv)-Cl- reaction in perchlorate have been studied.178The formation of higher oxidation states of chlorine at low chlorine concen-trations was prevented by adding thallous perchlorate, Tl(r) not being oxidiseddirectly by Ce(1v) when chloride ion is present. The most probable firstproduct is the radical ion C1,- formed in the process CeCP+ + Cl- -+Ce3+ + C1,-.The mechanism of the Ce(1v)-Br- reaction in sulphuric acidappears to involve activated complexes of two different compositions, viz.,Ce(SO,),Br," and Ce(S0,),Br-.179 The radical ion Br,- probably cccursas an intermediate. The Ce(1v)-I- reaction in sulphate media at pH 3appears to involve the existence of colloidal Ce(Iv), which is responsible fora slow reaction.lT9 Heterogeneous effects have also been observed in thephoto-reduction of Ce(w),lS0 and a surface-catalysed mechanism involvingadsorbed hydroxyl radicals has been suggested for the thermal oxidation ofwater by cerium perchlorate.lslTwo authors have reconsidered the mechanism of the autoxidation offerrous ions in aqueous solution.ls29 lS3 Both agree that the exothermicinitial step, Fe2+ + 0, =$z Fe3+ + 02-, cannot be correct.For solutionshaving a high concentration of hydrochloric acid, in which the autoxidationis rapid, Posner considers the initial step to be HFe,+Cl + 0, _t HO, +Fe3+ + C1-. There is some independent support for the existence of thecomplex HFe2+C1. Weiss suggests that the primary step should be writtenFe2+ + 0, + (Fe3+0,-). The overall accelerating effect of some anionsis then interpreted as due to stabilisation of the above complex in additionto the subsequent complex formation with ferric ions. The kinetics of the1'3 W. C . E. Higginson and D. Sutton, J., 1953, 1402.174 H. Taube, J .Amer. Chem. SOC., 1942, 64, 161.175 H. Boardman and G. E. Hulse, ibid., 1953, 75, 4272.176 R. H. Betts and F. S. Dainton, ibid., p. 5721.177 M. H. Boyer and J. B. Ramsey, ibid., p. 3802.17s F. R. Duke and C. E. Borchers, ibid., p. 5286.179 E. L. King and M. L. Pandow, ibid., P. 3063.1 8 0 B. Y . Dain and A. A. Kachan, Doklady Akad. Nauk S.S.S.R., 1949, 67, 85.181 F. R. Duke and J. A. Anderegg, Iowa State Coll. J . Sci., 1953, 427, 491.182 J. Weiss, Experientia, 1953, 9, 61.183 A. M. Posner, Traits. Faraday SOC., 1953, 49, 38252 GENERAL AND PHYSICAL CHEMISTRY.autoxidation in the presence and absence of fluoride ion suggest that in thelatter case the complex is stabilised to some extent by ferrous ions, e.g.,(Fe3+*02-) + Fe2+ ( Fe3+.0,-.Fe2+) e-(Fe2+.0,*-.Fea+) --+ 2Fe3+ + H0,- + H+The kinetics of the Fe(n)-Tl(IrI) reaction in perchloric acid have againbeen examined; 184 they are consistent with the mechanism :Though it is known that the reaction can take two paths involving twotransition complexes, it is still uncertain just what ion species take part.In the initiation or catalysis by metal ions of certain types of reactioninvolving organic compounds, iron salts continue to be of major interest.Thus Bates and Uri 185 have examined the oxidation, induced by photo-excited electron transfer in iron complexes, of various aromatic compounds.The initial step in the reduction of aa-dimethylbenzyl hydroperoxide by thef errocyanide ion 186 or the reaction between aa-dimethylbenzyl hydro-peroxide and ferrous salts The reaction be-tween organic hydroperoxides and iodide is catalysed by the presence offerrous salts which act by the alternate oxidation and reduction ofiron.ls8 Ferrous salts also catalyse the reactions between aa-dimethylbenzylhydroperoxide and polyethylene polyamines 189 and between the nitrosyl-disulphonate and the hydroxylaminemonosulphonate ions.lS0 Fenton’sreaction comes into this category and aspects of it have been discussed intwo papers.19l~ 192 Baxendale and Magee have gone far towards elucidat-ing the mechanism of the oxidation of benzene.The products are phenoland diphenyl only. The phenyl radical does not react with hydrogenperoxide but may be reduced by ferrous ions to benzene and oxidised byferric ions to phenol.Thus care is needed in comparing the action ofFenton’s reagent on a substrate with that of other sources of hydroxylradicals. The above type of behaviour is considered to be general, andWaters 19% 193 has suggested that chain reactions arise when the organicradicals concerned have reduction potentials less negative (on the U.S.scale) than that for the process Fe3+ & Fe2+ + e. This is the startingpoint of a revised theory of enzyme oxidations lS2 in which no free radicalsare generated.The catalyses of the chain autoxidations of aldehydes and unsaturatedhydrocarbons by the cobaltic ion are initiated by electron transfers of thetype,lS4 C O ~ + , ~ . + RH R + CO’+~~. + Hfaq..Reactions of Hydrogen Peroxide.-The rate constant for the initial step ofthe H202--Fe2+ reaction in dilute sulphuric acid has been redetermined.lg5 Theresults can be expressed as k , = 3.9 x 109exp(-11,000/RT) 1.mole.-l sec.-l.T~(III) + Fe(I1) Tl(11) + Fe(m) ; T~(II) -J- Fe(1r) + T~(I) + Fe(II1).is a single-electron transfer.184 K. G. Ashurst and W. C. E. Higginson, J., 1953, 3044.195 H. G. C. Bates and N. Uri, J. Amer. Chem. Soc., 1953, 75, 2754,186 H. Boardman, ibid., p. 2648.1 8 7 W. S. Wise and G. H. Twigg, J., 1953, 2172.lag R. J . Orr and H. L. Williams, Discuss. Faraday Soc., 1953, 14, 170.lgo W. J . Ramsey and D. M. Yost, J. Chem. Phys., 1953, 21, 957.191 J . H. Baxendale and J . Magee, Discuss. Faraday SOC., 1953, 14, 160.lg2 D. J . Mackinnon and W. A. Waters, J., 1953, 323.193 W.A. Waters, Discuss. Faraday SOC., 1953, 14, 233.194 C. E. H. Bawn, ibid., p. 181.195 W. Taylor and J. Weiss, J. Chern. Phys., 1953, 21, 1419.Idem, ibid., p. 2168COLLINSON, DAINTON, AND IVIN : HOMOGENEOUS SYSTEMS. 53The mechanism of the H202-Ce(1v) reaction in sulphate media is claimedto be : 196It is concluded that the system is a source of HO, radicals only, though noindependent checks on the absence of hydroxyl radicals appear to have beenmade.The rate of decomposition of hydrogen peroxide catalysed by the copper-ammonia complex is a maximum at a ratio NH, : Cu = 4 - 5 : 1. Thecatalysis may be due to co-ordinated hydroxyl groups in the complex.197Reactions of Oxygenated Anions.-The mechanism of oxidation by per-manganate proves to be of perennial interest.A very useful analysis hasbeen presented by Drummond and Waters,lQ8 who have attempted toelucidate the stages in the overall change, MnO,- + 8H+ + 5e --+ Mn2+ +4H20, by determining the effect of isolated valency changes on differentorganic groups. In alkaline solution all organic compounds except ethers,saturated carboxylic acids, and tertiary monohydric alcohols are oxidised atthe MnO,- _t MnO," stage. Some of the compounds oxidised cannot beoxidised by hydroxyl radicals and it is concluded, contrary to the views ofother investigator~,l9~9 200 that the hydroxyl radical plays no part a t thisstage. The oxidising action of alkaline permanganate is considered to bedue to a strong tendency of the MnO,- ion to abstract an electron froma substrate.The Mn(m) __t Mn(I1) stage is not capable of oxidisingolefins, formic acid, or alcohols other than 1 : 2-glycols. The mechanism ofoxidation at this stage involves a single-electron transfer of the typeRH + Mn3+ _t R* + Mn2+ + H+, resulting in the production of anactive free-radical R-, which is capable of initiating polymerisation or ofreducing mercuric chloride.2o1 The oxidation of pinacol in this manner hasbeen elucidated inPersulphate oxidations have been the subject of a number of studies.A heterolytic cleavage S,O,' +, SO, + SO,= is suggested as the first stepin the uncatalysed reaction, and the mechanism is capable of giving a fullinterpretation of the oxidation of thiols.2*3 The behaviour of the sulphateradical with water is assumed to be SO, + H20 __t HO+ + H+ + SO,=,followed by HO+ + H20 _t H30+ + 0.A similar suggestion has beenmade to explain the kinetics of the oxidation of formate and formic acid.204I n this case the initial step postulated is S,O,= + H,O _+ SO,= + HSO,- +OH+. The nature of the catalytic oxidation processes with persulphate andmetal ions (especially silver ions) is still not fully understood. The Ag3+ ion,the OH radical, the SO,- ion, and indeed the SO, radical and OH+ ion mayall play a part. Two classes of reaction have been found to exist, viz.,(i) oxidative coupling and (ii) oxygenation, and it is suggested that type (ii)may well occur via hydroxylati~n.~~~H,O, + Ce4+ __t HO, + H+ + Ce3+; HO, + Ce4+ .- 0, + H+ + Ce3+lS6 S.Baerand G. Stein, J., 1953,3176.Is* A. Y. Drummond and W. A. Waters, J., 1953, 435.19s M. C. R. Symons, Research, 1953, 6, 55.zoo F. R. Duke, J . Amey. Chem. SOC., 1948, 70, 3975.2ol A. Y. Drummond and W. A. Waters, J., 1953, 2836.202 Idem, ibid., p. 3119.204 S. P. Srivastava and S. Ghosh, 2. fihysikal. Chem., 1953, 802, 191, 198.,05 R. G. R. Bacon, R. W. Bott, J. R. Doggant, R. Graime, and D. J. Munro, Chem.and Ind., 1953, 897; R. G. R. Bacon and R. W. Bott, ibid., p. 1285.lS7 B. Kirson, Bull. SOC. chim., 1952, 957.203 L. S. Levitt, Canad. J. Chem., 1953, 31, 91554 GENERAL AND PHYSICAL CHEMISTRY.Neptune and King206 have shown that the reaction between the iodideion and selenious acid involves the formation of two activated complexes buta single reaction path.Reactions of Complex Ions.-Basolo 207 has published a review of thestereochemistry and reaction mechanisms of sexicovalent inorganic com-plexes.The factors controlling the steric course of substitutions at octa-hedrally co-ordinated centres are as yet unknown. In a full analysis of theproblem and its difficulties 208 Ingold and his co-workers conclude thatmany of the present structural assignments are suspect because of possiblestereo-changes involved in the conversions forming the basis of the assign-ment. A survey of the literature suggests the possible co-existence ofbimolecular and unimolecular mechanisms ( S N 2 and &1), with perhapsintermediate or quite different mechanisms also. The nucleophilic substitu-tion of chlorine from the cis-dichlorobisethylenediaminecobalt (111) ion hasbeen studied in methyl alcohol as a solvent.209 Four weakly nucleophilicanionic substances reacted by an S N 1 mechanism, whilst three other, morestrongly nucleophilic, substances reacted by an S~2-type mechanism.Theresults are considered to justify an extension of the dual mechanism, so wellestablished for substitutions at the carbon atom, to substitutions on cobaltand to octahedral substitutions generally. I t has further been shown 210that the optically inactive quinquecovalent ion formed in the first stage cantake up the substituting ion at comparable rates in all positions. A tri-angular bipyramidal structure is favoured for this ion. Pearson, Boston,and Basolo 211 have continued their investigation of the kinetics of aquationof cobalt complexes with different bidentate groups.In every case theyfound an S N 1 mechanism. However as the solvent was always water thereis some doubt as to the correctness of this interpretation.208 A tetragonalbipyramidal intermediate has been suggested in the substitution reactionsinvolving chloronitrobisethylenediaminecobalt (111) ion in aqueous solu-tion.212 Tracer studies with I 8 0 have shown that there is a gradual changeof the position of bond fission in hydrolyses of compounds of the type[R-CO2*Co(NH,),]2+ as the group R changes.213 For R = Me the Co-0 bondis broken; whilst for R = CF, the C-0 bond is broken. Aquation of theion never leads to breakage of the C-0 bond.Davis and Dwyer 214 conclude from their experiments on the racemisationof the optically active tris-1 : 10-phenanthrolinonickel salts in water thatthe first step in the unimolecular reaction does not involve bond breakagebut merely a distortion of octahedral configuration.Their reasons forreaching this conclusion have been disputed215 and it has been suggestedthat both for this ion and for the tris-2 : 2’-dipyridyl-Ni2+ ion the first stepin racemisation is dissociation. Davis and Dwyer have also studied theA species of Se(I1) acts as an intermediate.Io6 J. A. Neptune and E. L. King, Chem. and Ind., 1953, 3069.207 F. Basolo, Chem. Reviews, 1953, 52, 459.zo8 D. D. Brown, C. K. Ingold, and R. S. Nyholm, J., 1953, 2674.209 D.D. Brown and C. K. Ingold, J . , 1953, 2680.211 R. G. Pearson, C. R. Boston, and F. Basolo, J . Amer. Chem. Soc., 1953, 75, 3089.112 G. Basolo, B. D. Stone, J. G. Bergmann, and R. G. Pearson, U.S. Atomic En.213 C . A. Bunton and D. R. Llewellyn, J . , 1953, 1692.*14 N. R. Davis and F. P. Dwyer, Trans. Faraday SOL, 1952, 48, 244.215 F. Basolo, J. C. Hayes, and H. M. Neumann, J . Amer. Chem. S t . , 1953, 15, 5102.D. D. Brown and R. S. Nyholm, J., 1953, 2696,Commiss. Report, 1953, AECU-2476COLLINSON, DAIXTON, AND W I N : HOMOGENEOUS SYSTEMS. 55rates of racemisation of optically active complexes of both iron and nickel.216The values of the temperature independent factor in the expressions forthe rate constants are of the expected order for unimolecular reactions inwhich the entropies of the initial and activated states are comparable.Thereaction rates of the first transition series metal ions with 1 : 10-phen-anthroline have been classified, and deviations from recent theoreticalapproaches discussed.217Other Reactions in Solution.-Most of the many studies of the kinetics oforganic reactions in solution have followed conventional lines. A fullre-examination of Hammett’s equation has been made,2f8 and it has beenextended to include many other types of system not previously con-sidered.218* 219 Theoretical treatments of the constants p 220 and a 221 havebeen advanced.The activation energies of two Diels-Alder syntheses involving butadienehave been found to be larger than those of similar reactions with cyclo-pentadiene.222 The suggested explanation for this is that the double bondsof the open-chain and the cyclic diene are respectively trans and cis.An investigation of the rate of iodination of acetone 223 showed that thereactive enol form was probably produced by a ternary mechanism.After astudy of the general consequences of such a mechanism in the light of experi-mental evidence, these authors conclude that, contrary to Swain’s ideas,224ternary mechanisms are not of major importance in reactions catalysed byacids and bases.The acid-catalysed hydrolysis of NN-benzylideneaniline in methane-water solution (50/50) is exceptional in that Hammett’s equation cannot beapplied to the behaviour of its para-substituents, and the dependence of therate on the hydrogen-ion concentration is The experimentalmethod was checked with diazoacetic ester, which showed typicalbehaviour.226The theory of ion-dipole reaction mechanisms has been confirmed forthe hydrolysis of ethyl acetate 227 and of methyl propionate,228 both of whichproceed by such a mechanism.Evidence for quantum-mechanical leakage in proton-transfer reactions atlow temperature has been sought by studying the reactions of the ethoxideion with trinitrotoluene 229 and tris-~-nitrophenylmethane.230 In neithercase did the expected deviation from the Arrhenius relation arise.Bell and Pearson have shown that proton transfers to or from oxygenand nitrogen will normally be too fast for direct observation.2312 l 6 N.R. Davis and F. P. Dwyer, Trans. Faraday SOL, 1953, 49, 180.217 D. W. Margerum and C. V. Banks, U.S. Atomic En. Commiss. Report, 1-853,228 H. H. Jaffe, Chem. Reviews, 1953, 53, 191.219 Idem, Science, 1953, 118, 246. 220 Idem, J . Chem. Phys., 1953, 21, 415.221 F. L. J. Sixrna, Rec. Trav. chim., 1953, 72, 673.222 B. Eisler and A. Wassermann, J., 1953, 979.Z23 R. P. Bell and P. Jones, J., 1953, 58.224 C. G. Swain, J . Amer. Chevn. SOC., 1950, 72, 4578.225 A. V. Willi and R. E. Robertson, Canad. J. Chem., 1953, 31, 361.226 Idem, ibid., p. 493.227 P. M. Nair and S. V. Anantakrishnan, Proc. Indian Acad. Sci., 1952, 32, A , 330.228 J. L. Hockersmith and E. S. Amis, Analyt. Chim. A G ~ u , 1953, 9, 101.29s E. F. Caldin, G. Long, and F. W.Trowse, Nature, 1953, 171, 1124.230 E. F. Caldin and J. C . Trickett, Trans. Faraday SOG., 1953, 49, 772,esl R. P. Bell and R. G. Pearson, 1.. 1953, 3443.ISC-36656 GENERAL AND PHYSICAL CHEMISTRY.Isotope Effects.-Ropp 232 has reviewed investigations made between1948 and 1952 of the effect of isotopic substitution on organic reaction rates.In an earlier calculation of the relative velocities of reactions involvingisotopic molecules, Bigeleisen considered only simple bond rupture or form-ation pro~esses.23~ An expression has now been derived for simultaneousbond rupture and formation in reactions involving carbon isotopes.234Investigations which have recently been found to give results in agree-ment with theoretical predictions include the ozonisation of [a-14C]stilbene,235the non-enzymic hydrolysis of urea 236 (in contrast to the enzymic hydrolysis),and the reaction of formaldehyde with dimed~ne.~~' In addition, Bigeleisenand Wolfsberg 238 claim that Ropp and Raaen's results on decarboxylationare consistent with a 14C-isotopic effect which, as predicted by theory, istwice that of 13C.On the other hand several investigations have produced results which donot agree with theoretical predictions. Thus Yankwich and Stivers 239find that although the magnitude of the intramolecular 13C-isotope effect inthe decarboxylation of malonic and bromomalonic acids conforms to theory,the 14C effect is markedly greater than expected. A ratio of the two effectsas high as 4.8 -& 0.9 has been found for the bromo-acid.Ropp, Raaen, andWeinberger 240 find an unexpectedly high isotope effect in the decompositionof mercurous [14C]formate, and a complete lack of effect, for which there isno obvious explanation, in certain addition reactions. In both the ethan-olysis of [~-~~C]benzoic anhydride and its reaction with #-toluidine 241 theintramolecular isotope effects agree with theory inasmuch as they show nochange with change of temperature. The actual values are, however, verydifferent from theoretical expectations. Pitzer and Gelles 242 have suggestedthat anomalous results with carbon isotopes may be due in part to themagnetic properties of 13C.Bigeleisen's theory has been so successful in explaining isotope effects indecarboxylation reactions that when exceptions are found in such cases thetendency is to use this information as a guide to peculiarities of mechanism.The magnitude of the intermolecular 13C-isotope effect in the decarboxylationof malonic acid in 80% sulphuric acid was found to be in accord with theory,but the temperature dependence was not.243 For the same decarboxylationin quinoline neither the magnitude nor the temperature variation was thatexpected.244 A combination of isotopic data with kinetic data indicates thatthe mechanism comprises a solvation equilibrium followed by a bimoleculardecomposition of the complex.Isotopic fractionation has also been usedas a method of studying the mechanism of the decarboxylation of barium233 G. A. Ropp, Nucleonics, 1952, 10, (lo), 22.233 J. Bigeleisen, J .Chem. Phys., 1949, 17, 675; J. Phys. Chem., 1952, 56, 823.234 J. Bigeleisen and M. Wolfsberg, J . Chem. Phys., 1953, 21, 1972.235 A. Bonner and C. J. Collins, J . Amer. Chem. Soc., 1953, 75, 3693.236 J. A. Schmitt and F. Daniels, ibid., p. 3564.237 A. M. Domes, Austral. J. Sci. Res., 1952, 5, A, 521.238 J. Bigeleisen and M. Wolfsberg, U.S. Atomic En. Commiss. Report, 1953,240 G. A. Ropp, V. F. Raaen, and A. J. Weinberger, J . Amer. Chem. Soc., 1953, 75,242 K. S. Pitzer and T. E. Gelles, J . Amer. Chem. Soc., 1953, 75, 5132.243 P. E. Yankwich, R. L. Belford, and G. Fraenkel, ibid., p. 832.244 P. E. Yankwich and R. L. Belford, ibid., p. 4178.BNL- 1487.3694.23D P. E. Yankwich and E. C. Stivers, J .Chem. Phys., 1953, 21, 61.241 V. F. Raaen and G. A. Ropp, J . Chem. Phys., 1953, 21, 1902COLLINSON, DAINTON, AND IVIN : HOMOGENEOUS SYSTEMS. 57a d i ~ a t e , ~ * ~ and it has been suggested that applied to hydrogen isotopes themethod may be used to detect hyperconjugation in the transition ~ t a t e . 2 ~ ~Fractionation of the oxygen isotopes indicated that the hydroxyl radical isnot the sole primary product in the photolysis of hydrogen per0xide.~*7Condensation Polymerisation.-Papers have been published on the kin-etics of polycondensation of 1 l-aminoundecanoic acid 248 and of adipicacid with pentane-1 : 5-diol in diphenyl ether.249 With the former case thereaction order is two, but in the latter the order is only approximately twoand is not constant.This variable order is discussed in terms of an initialtermolecular activation step. A theory of stepwise polymerisation underpressure has been put forward and applied to the condensation of acetone at3000 atm.250Radical Polymerisation and Depo1ymerisation.-Initiators and InitiationRates.-In this section have been included the kinetics of decomposition ofa number of azo- and peroxy-compounds which have not been used speci-fically as polymerisation initiators but are grouped here for convenience.The rate of decomposition of diacetyl peroxide has been measured ina number of solvents and found to be roughly parallel to the rate of decom-position of dibenzoyl peroxide in these solvents.251 The mechanism of itsdecomposition has also been studied by using [14C]acetic acid as solvent.252The work of Volman and Graven 253 on the photochemical decomposition ofdi-tert.-butyl peroxide vapour between 30-120" is in substantial agreementwith earlier results.The effect of phenols on the rate of decomposition ofdibenzoyl peroxide solutions has been shown to be complex.254 The effectof substituents on the rate of decomposition of substituted dibenzoyl per-oxides in styrene and on the rate of the induced polymerisation have beenfurther investigated.255Cooper256 has examined 11 hydroperoxides as initiators for the poly-merisation of styrene at 70". Apart from more rapid initiation due to arylgroups, changes of structure have only small effects on the rate of poly-merisation. The thermal decomposition of cyclohexenyl hydroperoxide hasbeen investigated in a number of hydrocarbon s0lvents.2~7.258 In olefins,at concentrations > 0.03 M, decomposition takes place by a chain mechanisminvolving the solvent, the initiation process being of second order withrespect to the peroxide. In benzene the chain process is suppressed almostcompletely and the decomposition approximates to a one-stage second-orderreaction. At very low concentrations ( < 0.02 M) , the hydroperoxide decom-poses mainly by a first-order process. Decalin hydroperoxide also decom-poses by a first-order chain-reaction in this concentration region, and the245 J. Bigeleisen, A. A. Bothner-By, and L. Friedman, J . Amer. Chem. Soc., 1953,246 E. S. Lewis and C.E. Boozer, ibid., 1952, 74, 6306.247 J. P. Hunt and H. Taube. zbid., p. 5999.248 R. Vergoz, Ann. Chim., 1953, 8, 101.249 M. Davies and D. R. J. Hill, Trans. Faraday SOL, 1953, 40, 395.251 W. M. Thomas and M. T. O'Shaughnessy, J . Polymer Sci., 1953, 11, 455.252 A. Fry, B. M. Tolbert, and M. Calvin, Trans. Faraday Soc., 1953, 49, 1444.z53 D. H. Volman and W. M. Graven, J . Amer. Chem. SOG., 1953, 75. 3111.254 J. J. Batten and M. F. R. Mulcahy, Nature, 1953, 172, 72.255 M. Takebayashi and T. Shingaki, Bull. Chem. Soc., Japan, 1953, 26, 137.256 W. Cooper, J . , 1953, 1267. 257 L. Bateman and H . Hughes, J., 1952, 4594.258 L. Bateman, H. Hughes, and A. L. Morris, Discuss. Faraday SOL, 1953, 14, 190.75, 2908.M. G. Gonikberg, Chem. Abs., 1953, 47, 38958 GENEKAL AND PHYSICAL CHEMISTRY,energy of activation has been determined in several ~olvents.2~9 The photo-chemical decomposition of tert.-butyl hydroperoxide in carbon tetrachlorideand in n-hexane proceeds by a short chain mechanism yielding tert.-butylalcohol, oxygen, and small amounts of other compounds.260 In dioxan thechains are not able to propagate owing to the reactivity of the solvent, anda quantum yield of I is found.260The kinetics of the first-order decompositions of azo-compounds of thetype fi-X*C,H4*N2*CPh, have been investigated, and the results compared withthose on the decomposition of similarly substituted peroxy-compounds.261N-Nitrosoacetanilide has been shown to initiate radical polymerisation.262Tobolsky and Baysal 263 have correlated much of the published data on thecatalysed bulk polymerisation of methyl methacrylat e and styrene, respec-tively.If the rate of decomposition of the catalyst (C) is given by 2Ki[C]and the rate of initiation of polymer chains is given by Ri, then the catalystefficiency f may be defined as f = &/Zki[C], lOOyo efficiency correspondingto two polymer chains initiated per catalyst molecule decomposed. It isreadily shown that, for a system in which transfer to catalyst and thermalinitiation are negligible, f = K1K2/ki(l + x), where K , and K2 are thetemperature-dependent constants in the experimental relationshipsl/Fn = I< + K1Rp/[M]2 and lip = K2[M][C]iand R, is the rate of polymerisation for monomer concentration [MI, Fpt isthe mean degree of polymerisation of the polymer formed, and x = Ktd/(ktd +&).KM and Kt, are the velocity constants for termination by dispropor-tionation and combination, respectively. In spite of the work by Arnett,264the value of x for methyl methacrylate cannot be said to be settled. Arnettconcluded that x = 0 andf = 0.5, but this does not fit in withf = 0-94/(l +x ) , derived from the equation above,263 or with new polymer-degradationevidence 265 which indicates a value of x close to 1 (see below).Further light has been thrown on the question of diradical polymerisationby a study of the inhibition of the thermal polymerisation of styrene by2 : 2-diphenylpicrylhydrazyl and benzoquinone.266 It now appears probablethat in the absence of inhibitors, a growing diradical will cyclise very readily,SO that only those diradicals which are converted into monoradicals beforecyclisation can occur, will, in fact, give rise to high polymers.The validity of current methods of determining Ri from retarder experi-ments has been examined by detailed kinetic analysis.267Polymerisation of Single Monomers.-The polymerisation of butadiene inthe gas phase, initiated by radicals from the photolysis of di-tert.-butylperoxide and acetone, has beenIn the polymerisation of styrene, chain-transfer constants have beendetermined for 12 solvents268 and a number of organic compounds.269259 C .F. H. Tipper, J., 1953, 1675.260 J . T. Martin and R. G. W. Norrish, PYOC. Roy. SOC., 1953, A, 220, 322.261 S.G. Cohen and C. H. Wang, J. Amer. Chem. SOC., 1953, 75, 5504.262 D. F. Detar and C. S. Savat, ibid., p. 5716.263 A. V. Tobolsky and B. Baysal, J . Polymer Sci., 1953, 11, 471.264 See An%. Repovts, 1952, 49, 58.265 N. Grassie and E. Vance, Trans. Faraday SOC., 1953, 49, 184.266 K. E. Russell and A. V. Tobolsky, J . Amer. Chem. SOC., 1953, 75, 5052.2 6 7 G. M. Burnett and P. R. E. J. Cowley, Trans. Faraday SOC., 1953, 49, 1490.268 S. I,. Kapur, J. PoZymer. sci., 1953, 11, 399.269 R. A. Gregg and F. R. Mayo, J . Amer. Chem. SOC., 1953, 75, 3530COLLINSON, DAINTON, AND WIN HOMOGENEOUS SYSTEMS. 59That chain transfer with disulphides occurs by a process of the type :P, + RSSR’--t P;SR + R’S, has been confirmed by the fact thatcyclic disulphides become copolymerised with both styrene 270 and vinylacetate.271The order with respect to monomer has been determined for the catalysedpolymerisations of methyl methacrylate, vinyl acetate, and vinyl chloridein various solvents.272 For methyl methacrylate in benzene the normalorder of one is found; for other systems observed orders of 1-5 and variableorders are interpreted in terms of complex formation between monomer andcatalyst.Polymethyl methacrylate has been shown to initiate polymeris-ation of its monomer ; but addition of the same polymer to other monomersor of other polymers to methyl methacrylate does not induce polymeris-ation.273Further information concerning the termination step in methyl meth-acrylate polymerisation has been obtained by two methods.274, 275 Both setsof results support disproportionation, as opposed to combination, of twopolymer radicals as the termination step.However the first method, inwhich rate and molecular-weight measurements of the retarded and un-retarded reactions are compared, is admitted by the authors to be somewhatambigu0us.~~4 The second method depends upon a comparison of the ratesof degradation of polymers made by bulk polymerisation and by polymeris-ation of the monomer in benzene.275 The results are interpreted on theassumption that initiation of degradation occurs most easily at the double-bond end structure, formed when two polymer radicals terminate by dis-proportionation. There will be fewer such end structures in the polymerprepared in solution owing to the occurrence of chain transfer with thebenzene, and accordingly, lower rates of degradation are observed.How-ever, it should be noted that when vinyl acetate is polymerised in labelledbenzene, a small amount of solvent becomes incorporated into the polymerby copolymerisation rather than through the transfer pr0cess.2~~ Thepossible effect of traces of copolymerised benzene on the rate of degradationis thus an uncertain factor in the work described above.The equilibrium pressure of monomer over polymethyl met hacrylate hasbeen measured at various temperatures; 277 the results lead to values for theheat and entropy of polymerisation in reasonable agreement with calorimetricand kinetic data. Magnetic studies have thrown some light on the modeof action of retarders in the catalysed polymerisation of methyl meth-a ~ r y l a t e .~ ~ * The velocity constants for the bulk polymerisation of n-butyland n-propyl methaccylate have been compared with those for the poly-merisation of the methyl ester.279Evidence for a monomer-termination process has been obtained in theNo satisfactory explanation of this phenomenon has been found.270 A. V. Tobolsky and B. Baysal, J . Amer. Chem. SOC., 1953, 75, 1757.271 W. H. Stockmayer, R. 0. Howard, and J. T. Clarke, ibid., p. 1756.272 A. Conix and G. Smets, J . Polymer. Sci., 1953, 10, 525.273 H. W. Melville and W. F. Watson, ibid., p. 299.274 E. P. Bonsall, L. Valentine, and H. W. Melville, Trans. Faraday SOC., 1953, 40, 686.275 N.Grassie and E. Vance, ibid., p. 184.278 W. H. Stockmayer and L. H. Peebles, J . Amer. Chem. SOC., 1953, 75, 2278.277 P. A. Small, Trans. Faraday Soc., 1953, 49, 441.278 J. L. Ihrig and H. N. Alyea, J . Amer. Chem. SOC., 1953, 75, 2917.27s G. M. Burnett, P. Evans, and H. W. Melville, Trans. Faraday SOC., 1953, 49,1096, 110560 GENERAL AND PHYSICAL CHEMISTRY.catalysed polymerisations of ethyl acrylate,280 vinyl benzoate,281 and ally1[2HJacetate.282 Mutual termination is indicated in the case of vinyl pro-pionate.28lThe methacrylate ion has been shown to polymerise in aqueous solutionat a rate much smaller than that of the undissociated The kineticsof the polymerisation of aqueous methyl acrylate and acrylonitrile have beeninvestigated, initiation being effected by P-nitrobenzenediazo-radicals.284Three kinetic investigations have been made on bulk polymerisations inwhich the polymer is insoluble in the 286, In common withvinyl chloride, vinylidene chloride 285 and acrylonitrile exhibit a steadilyincreasing polymerisation rate, due to catalysis by the precipitated polymer.Bamford and Jenkins suggest that growing radicals become occluded inpolymer aggregates during polymerisation, so reducing kb and, under severeconditions, k, also.It is interesting to note that polyvinylidene chlorideloses its catalytic activity on exposure to air, and that polyacrylonitrileprepared at room temperature is able to initiate the polymerisation ofseveral monomers at higher temperatures.An exploratory investigationof the kinetics of polymerisation of chlorotrifluoroethylene both in bulk andin solution has revealed no such complexities.251CopoZymerisatiout.-Relative reactivity ratios have been determinedfrom monomer-polymer composition relations for a number of monomerpairs,251127g~287-291 and in some cases Q and e values have been de-287-289 The copolymerisation behaviour of methacrylic acid bothwith diethylaminoethyl methacrylate and with acrylonitrile dependsmarkedly on the pH of the polymerising system.289 This is attributed toa distinctive copolymerisation behaviour of the methacrylate ion. Thecompositions of copolymers made from mixtures of three monomers havebeen found to be in fair agreement with predictions based on the relativereactivity ratios of the two component systems.290 It has been shownthat the variation with pressure in the composition of the copolymer formedfrom ethylene and carbon monoxide at high pressure can be explained byassuming that a 1 : 1 complex is one of the effective mon0mers.2~4Bengough and Norrish 291 have measured the rate of copolymerisation ofvinyl chloride with vinylidene chloride, catalysed by dibenzoyl peroxide.They were able to measure the rate of consumption of each monomer bymeans of an ingenious device for following continuously the change of vapourpressure of the monomer mixture.The overall rate passes through aminimum as the composition is varied and increases with time at all com-positions. In the system styrene-maleic anhydride-solvent there is a rangeof composition over which the polymer remains in solution but outside which280 H.Sumitomo and Y . Hachihama, Chem. Abs., 1953, 47, 10318.281 G. M. Burnett and W. W. Wright, Trans. FaradQy SOL, 1953, 49, 1108.282 P. D. Bartlett and F. A. Tate, J . Amer. Chem. SOC., 1953, 75, 91.283 G. Blauer, J . Polymer Sci., 1953, 11, 189.284 W. Cooper, Chem. and Ind., 1953, 407.285 W. I. Bengough and R. G. W. Norrish, PYOC. Roy. SOC., 1953, A , 218, 149.286 C. H. Bamford and A. D. Jenkins, ibid., 1953, A, 216, 515.287 S. H. Pinner, J . Polymer S C ~ . , 1953, 10, 379.288 C. C. Price and H. Morita, J . Amer. Chem. Soc.. 1953, 75, 4747.280 T. Alfrey, C. G. Overberger, and S. H. Pinner, ibid., p. 4221.200 S.L. Aggarwal and F. A. Long, J . Polymer Sci., 1953, 11, 127.291 W. I. Bengough and R. G. W. Norrish, PYOC. Roy. SOC., 1953, A , 218, 155COLLINSON, DAINTON, AND IVIN : HOMOGENEOUS SYSTEMS. 61it is precipitated. Bamford and Barb292 have studied the kinetics in thetwo regions and find in the homogeneous region a steady rate and catalystexponent of 0-5, whereas in the heterogeneous region there is an increasein rate with time and a catalyst exponent greater than 0-5. It is concludedthat the stationary state treatment is inapplicable to such heterogeneoussystems. Barbzg3 has concluded that certain abnormalities in the com-positional relationship of styrene-maleic anhydride copolymers indicate thatnon-terminal monomeric units in a polymer radical can detectably influencethe radical reactivity.Kinetic studies have been made on the copolymerisation of methylmethacrylate with ethylidene dimetha~rylate.~~~ The degree of branchingof the polymer can be expressed as a function of the extent of reaction.Barb z97 has deduced the values E d = 12-15 kcal./mole, A d = 4 x l0-lo-3 x 10-l2 sec.-l for the depropagation process in the copolymerisation ofstyrene with sulphur dioxide.DepoZymerisation.-In the past, rates of degradation have generally beenmeasured by determining either the rate of evolution of volatile products orthe rate of loss in weight when the polymer is heated in vacuo, and suchmethods continue to be e r n p l ~ y e d .~ ~ ~ ~ 298 However, the results can only beof real value when the overall stoicheiornetry is known.Past and presentmeasurements have shown that only in a few cases does a polymer degradecleanly to monomer, and the formation of other products must be taken intoaccount in any detailed mechanism. The application of direct mass-spectrographic methods of analysis of the volatile products promises toclarify the interpretation of experimental data.300 Thus from a series ofmeasurements on polystyrene between 260" and 330", in which less than 1%of the sample was degraded in each experiment, energies of activation of65, 57, and 56 kcal./mole have been found for the rate of production ofstyrene, benzene, and toluene, r e s p e c t i ~ e l y . ~ ~ Dimers, trimers, tetramers,and pentamers are also produced.301 Velocity constants have been deter-mined for the initiation and propagation processes in the molecular chainelimination of acetic acid from polyvinyl acetate.302 The kinetics andproducts of thermal degradation of polyethylene terephthalate have beenexamined over a range of temperature; the results are consistent with aninitial random chain scission.303Grassie304 has reviewed the work on the degradation of polymethylmethacrylate.An extension of this work has been referred to earlierSimha 305 has applied his general treatment of degradation chain mechan-isms to the particular case of terminal initiation and absence of transfer.(Pa 59).Z s 2 C. H. Bamford and W. G. Barb, Discuss. Faraday SOC., 1953, 14, 208.Zs3 W. G. Barb, J . Polymer Sci., 1953, 11, 117.204 W.G. Barb, J . Amer. Chem. SOC., 1953, 75, 224.296 G. Smets and J. Schmets, Bull. SOC. chim. Belg., 1953, 62, 358.z97 W. G. Barb, J . Polymer Sci., 1953, 10, 49.Z s 8 S. L. Madorsky, ibid., 1953, 11, 491.299 H. H. G. Jellinek and K. J. Turner, ibid., p. 353.30° P. D. Zemany, Nature, 1953, 171, 391.301 P. Bradt, V. H. Dibeler, and F. L. Mohler, J . Res. Nut. Bur. Stand., 1963, 50, 201,302 N. Grassie, Trans. Faraday SOC., 1953, 49, 835.3OS I. Marshalland A. Todd, ibid., p. 67. 304 N. Grassie, Chem. undInd., 1953, 022.30s R. Simha, J . Polymer Sci., 1953, 10, 49962 GENERAL AND PHYSICAL CHEMISTRY.Jellinek 306 has considered random initiation and has calculated for variousdegradation mechanisms the initial rates of formation of monomer as afunction of the total weight of polymer, initial molecular weight, etc.Thebreakdown of large free radicals has been discussed in terms of the accom-panying changes of enthalpy and entropy.307 Some preliminary resultshave been given on the effect of olefin structure on the ceiling temperaturesobserved in olefin-sulphur dioxide copolymerisation. In the case of the cis-and the trans-but-2-ene system it has been shown that cis-trans isomerisationaccompanies polymerisation in the region of the ceiling temperature, thusproviding added evidence that the ceiling-temperature phenomenon is causedby the occurrence of depropagation processes.30sMolecular-weight Distribution.-The form of the molecular-weightdistribution curve of a polymer provides a means of checking or determiningthe termination process in a given polymerisation reaction, but its experi-mental determination is not easy and the number of theoretical papers onthe subject continues to exceed the number of experimental papers.Newmethods have been given for the calculation of distribution functions,3099 310and these and other methods 311 have been applied to mechanisms involvingvarious types of termination process. In two experimental papers on themolecular-weight distribution of polymethyl methacrylate prepared by redoxpolymerisation in aqueous solution, it has been shown that at high concen-trations of emulsifying agent, termination occurs mainly by combination,though somewhat different molecular-weight distributions are given bydifferent experimental methods312Ionic Polymerisation.-The proceedings of an informal conference held atStoke in March, 1952, on " Cationic Polymerisation and Related Complexes "have been published.313 No attempt will be made here to review theseproceedings since most of the papers contained therein have been published.Attention will therefore be confined to those papers which have appearedthis year in the normal way.system " may be defined as monomer-catalyst-co-catalyst-solvent.A number of systems are known to requirethe presence of traces of water as co-catalyst in order that polymerisationshall occur, and to these have been added the following: (1) a-methyl-styrene-stannic chloride-water-ethyl chloride ; 314 (2) cis- or traws-stilbene-boron trifluoride- or -titanium tetrachloride-water-carbon tetrachloride orno solvent ; 315 (3) styrene-titanium tetrachloride-water-hexane or toluene ; 316(4) isoprene-stannic chloride-water-no solvent (at - 80" c) .317 However,in the systems : (5) styrene-titanium tetrachloride-X-dichloroethane ordibromoethane ; 316 (6) isoprene-stannic chloride-X-ethyl chloride andsystem (4) at 0" c, 317 it is claimed that a co-catalyst of the normal type ( e g .,In cationic polymerisation a306 H. H. G. Jellinek, J . Polymer Sci., 1953, 10, 457.307 F. S. Dainton and K. J. Ivin, Discuss. Furaday Soc., 1953, 14, 199.308 G. M. Bristow and F. S. Dainton, Nature, 1953, 173, 804.309 W. F. Watson, Trans. Faraduy SOC., 1953, 49, 842, 1369.310 C.H. Bamford and H. Tompa, J . Polymer Sci., 1953, 10, 345.311 D. Tabuchi, Chem. Abs., 1953, 47, 7818, 11798.312 A. F. V. Eriksson, Acta Chem. Scand., 1953, 7, 377, 623.313 Ed. P. €3. Plesch, Publ. W. Heffer and Sons Ltd., Cambridge, 1953.314 F. S. Dainton and R. H. Tomlinson, J., 1953, 151.315 D. S. Brackman and P. H. Plesch, J., 1953,1289.3 1 7 A. R. Gantmakher and S. S. Medvedev, Chena. Abs., 1953, 47, 4713, 4714.s16 P. H. PIesch, J . , 1953,1693COLLINSON, DAINTON, AND IVIN : HOMOGENEOUS SYSTEMS. 63water or trichloroacetic acid) is not required although addition of water doesgreatly increase the rate in system (5). Infra-red absorption of the polymersformed in the system (7) styrene-titanium tetrachloride-trichloroacetk acid-toluene318 shows that a large fraction of the polymer molecules containtolyl end groups but that groups derived from trichloroacetic acid are notincorporated in the polymer.However, in system (5) and similar systemswith alkyl halide solvents the polymer contains initial and end groups derivedfrom the solvent. This is taken to indicate that the co-catalyst X in system( 5 ) , and presumably also in system (6), is in fact the solvent. A solvent maythus act in three ways in ionic polymerisation : by its dielectric effect on theelectrostatic forces, as the co-catalyst, and as a transfer agent.319In system(1) the rate is independent of the co-catalyst-catalyst ratio when this isgreater than 3. The rate is then proportional to [SnCl,][M,]y where yincreases with [M,] from 1-2 to 2.The proposed mechanism involves theusual initiation and propagation processes, with termination by spontaneousproton release, which may be accompanied by cyclisation. With dideuter-ium oxide as co-catalyst, the polymer formed contains C-D bonds. Theinitial rate is lower than with water, but increases until it has the valuecharacteristic of the latter. This effect is ascribed to the gradual conver-sion of the dideuterium oxide into water as reaction proceeds. In system (5)the rate is proportional to [TiCl,][M,]2. In system (2) the polymers formedare mixtures of dimers and trimers. No isomerisation is observed in thesesystems and distinct complexes are formed with titanium tetrachloride alone.The red complex formed during the sodium catalysed polymerisation ofstyrene has been shown to be paramagnetic and the stable radical ion(C,H,*CH=CH,)- has been postulated.320Radiation Chemistry.-Primary Processes.-Lindholm 321 has carried outan interesting investigation of the ionisation of hydrogen sulphide by bom-bardment with electrons and a variety of atomic ions.The relative pro-portions of the ions H,S+ : HS+ : Si from electron bombardment were100 : 43 : 46. For the other bombarding ions the proportions of the differentspecies varied, and in many cases the mass spectrum was simpler than forelectron bombardment. Of particular interest are the results of the bom-bardment by rare-gas ions, where the ions HS+ and S+ invariably occur ingreater amounts than does H,S+.The energy of the ions (500 ev) was ofcourse low compared with energies used in typical radiation chemical studies,but the differences between the electron results and the results for heavyions arouse a long standing suspicion that some of the differences found for,say, or-particle irradiations and electron irradiations in water may be due todifferences of primary product as well as to the much discussed ion-densityeffect.Radiation Sources and Actinometry.-The reliability of radioactive iso-topic sources and their increasing availability are factors causing this typeof source to replace machines for experiments with photon radiations. Forsuch sources a disc shape offers the greatest general effi~iency,~~2 but hollowDetailed kinetics have been obtained for systems (1) and (5).318 P.H. Plesch, J., 1953, 1659.320 D. Lipkin, D. E. Paul, J. Townsend, and S. I. Weissmann, Science, 1953, 117, 534.321 E. Lindholm, Proc. Phys. SOC., 1953, 66, A, 1068.322 M. Brucer, W. G. Pollard, H. Leiter, and H. Scarf, Xucleonics, 1963, 11 (2), 38.319 Idem, ibid., p. 166264 GENERAL AND PHYSICAL CHEMISTRY.cylinders have also been 324 The 60cobalt isotope is at presentthe most popular for y-irradiations, but several others have been proposed.Freundlich and Haybittle 325 have used an 192iridium teletherapy unit.Manowitz 324 describes a source of 182tantalum, and other practicable y-sourcesare 152-154e~r~pi~m, 137caesium, and 144cerium.326The energy yield for the ferrous sulphate-0-8~-sulphuric acid system usedin actinometry remains uncertain.As the uncertainty appears to arise fromthe physical rather than from the chemical side, it is reasonable to assumethat all other chemical actinometers are virtually in the same position. Ayear ago a value of G(Fe2+),,,kd = 20 seemed to be favoured, but since thenthere has been an ever increasing indication that the value of G = 15.5 ismore nearly correct. Much of the relevant work has yet to be published.In all, four methods have been employed for measurement of the energyabsorbed to produce a given change. These are ionisation measurements,calorimetry, charge measurements with electron beams, and absolute count-ing methods with radioactive isotopes. Miller,327 using an ionisation methodto measure the energy absorbed, has carried out experiments with X-radi-ation, of energy between 1-5 and 2-25 Mv, and has found a constant yield,G = 20.3 & 1.0, for dose rates up to 100,000 r/min. Ebert and Boag328obtained the same result in similar experiments, and Magat and Chapiro 328have also found a similar value.Hummel and S p i n k ~ , ~ ~ ~ using less rigorousmethods of relating ionisation measured to energy absorbed, found G = 16.8for radium y-rays, and G = 15-8 for betatron X-rays of energy 24.5 Mvp.For 60Co y-radiation a value of G = 17.4 was found.330Two results based on calorimetric measurements have appeared : Davisonet aZ.331 found G = 20, whilst Hochanadel and Ghormley332 found G =15-6 & 0.3, both for 6oCo radiation. Hochanadel and Ghormley also usedan ionisation method and obtained G = 16.7, but in the geometry of theirexperiments the Bragg-Gray conditions were not fulfilled.By measure-ment of the charge-input for 1.33-Mev Van de Graaff electrons they obtainedG = 16.8 & 0.3, the difference from their calorimetric result being due toundetermined back-scatter. Amphlett 333 found G = 17 by the samemethod. A more rigorous measurement of this type has recently been madeby Saldick and Allen 334 who found G = 15.6 5 0-5. Minder 335 has studiedthe effect of a mixed source of s6Rb and 35S in solution; the energy absorp-tion was calculated from known constants and the geometry of the system,and the result obtained was G = 14.6 I;t 0.3. By using 6oCo, and againcalculating the absorbed energy, he obtained G = 14.4 & 0.2. Taken as awhole the results for ferrous sulphate actinometry seem to indicate that a323 D.F. Saunders, F. F. Morehead, and F. Daniels, J . Amer. Chem. Soc,, 1953, 75,325 H. F. Freundlich and J. L. Haybittle, Acla Radzologica, 1953, 39, 231.326 T. Leucutia, Amer. J . Roentgenol., 1953, 69, 108.327 N. Miller, Nature, 1953, 171, 688.328 R. W. Hummel and J. W. T. Spinks, Canad. J . Chem., 1953, 31, 250.330 G. R. Freeman, A. B. van Cleave, and J. W. T. Spinks (see ref. 329).331 S. Davison, S. A. Goldblith, B. E. Proctor, M. Karel, B. Kan, and C . J . Bates,332 C. J. Hochanadel and J. A. Ghormley, J . Chem. Phys., 1953, 21, 880.333 C. B. Amphlett, Discuss. Faraday SOC., 1952, 12, 272.334 J.Saldick and A. 0. Allen, to be published.335 W. Minder, Helv. Phys. .A&, 1953, 26, 407.3096. 324 B. Manowitz, Nucleonics, 1953, 11 (3), 18.328 See ref. 327.Nucleonics, 1953, 11 (7), 22COLLINSON, DAINTON, AND W I N : HOMOGENEOUS SYSTEMS. 65value of G = 20 is obtained by rigorous ionisation-measurement methods,whilst a value of G = 15.5 is obtained by rigorous calorimetric or charge-counting methods. Although flaws have been sought in all aspects ofthese techniques, they have not been found in sufficient magnitude toexplain the difference of 30y0.336A new method of measuring the conversion of ferrous into ferric ion forthe ferrous sulphate actinometer has been proposed; 337 this consists of theuse of 59Fe as a tracer and the measurement of the radioactivity of theFe(rr1) formed.I t is claimed that doses in the range 0-100 r can be measuredwith an accuracy of &2 r.Non-aqueous Vapcur and Liquid Systenzs.-Despite the evident complexityof such work, an appreciable number of investigations of the chemical effectproduced in electric discharges have appeared. Yields of product withrespect to electrical energy input have generally been determined undervarying conditions and in some cases mechanisms have been proposed. Theuse of deuterium in the study of the decomposition of methane has proveduseful in this respect .338 Other investigations include the decomposition ofcarbon dioxide,339 met hane,340 a m m ~ n i a , ~ ~ l l 344 and hydrogen peroxide,342 theproduction of ozone,343 reactions of toluene and ben~ene,3~4 and the oxidationof ethanol 345 and benzene.346The decomposition of carbon dioxide by ionising radiations is a t leastpartly heterogeneo~s.~4' The exchange reaction between tritium andhydrogen gas brought about by the p-radiation of tritium itself has beenfound to be a chain reaction, the rate of which is proportional to the squareroot of the intensity of theSchuler and his co-workers have investigated the radiolyses of liquidalkyl halides.349 Comparison of the results for methyl iodide with those forthe photolysis indicates that processes peculiar to radiation chemistry cccur,the importance of ionic processes being apparent.The effect of 60Co y-radiation on the liquid chloroform-oxygen systemhas been examined.350 Analysis of the products was made for differentvalues of temperature, oxygen concentration, and time of irradiation.Though the reaction undoubtedly proceeds by a chain mechanism it has notyet been possible to elucidate this completely.The radiolysis of chloroformhas also been studied with diphenylpicrylhydrazy! as solute.351 This solute336 T. J. Hardwick, Canad. J . Chenz., 1953, 31, 512.337 G. Rodstam and T. Svedberg, Natztre, 1953, 171, 648.338 H. Weiner and M. Burton, J . Anzer. Chem. SOC., 1953, 75, 5815.359 K. A. Wilde, B. J. Zwolinski, and R. B. Parlin, U.S. Atomic En. Commiss. Report,341 K. Ouchi and T. Takamatsu, J , EZectvochem. SOL. Japan, 1953, 21, 75, 132.342 J. S. Batzold, C. Luver, and C. A. Winkler, Canad. J .Chew&., 1953, 31, 2G2.343 E . Brmer, V. Spreter, and B. Kovaliv, Bull. SOC. china. Belge, 1953, 62, 55.344 H. Schiiler and V. Degenhart, 2. Naturforsch., 1952, 'Sa, 763.345 R. H. Sahasrabudhey, S. M. Deshpande, and R. V. G. Rao, Proc. Iizdian Acad.346 J. C. Chu, H. C. Ai, and D. F. Othmer, Ind. Eng. Ckenz., 1953, 45, 1266.347 S. Dondes and A. J. Hogan, U.S. Atomic En. Commiss. Report, 1953, SO-3251.348 L. M. Dorfman and 13. C. Mattraw, J . Phys. Chem., 1953, 57, 723.349 R. H. Schuler and W. H. Hamill, ibid., 1952, 74, 6171; R. C. Petry and R. H.360 J. W. Schulte, J. F. Suttle, and R. Wilhelm, J . Anzer. Chenz. SOC., 1953, 75, 2222.361 A. Chapiro, J. W. Boag, M. Ebert, and L. H. Gray, J . Chinz. $hys., 1953, 50, 468.1953, AECU-2582. 340 R.Miquel, B.ul1. SOL. chim., 1053, 970.Sci., 1952, 36, A , 258.Schuler, ibid., 1953, 75, 3796.REP.-VOL. L 66 GENERAL AND PHYSICAL CHEMISTRY.acts as an acceptor of the radicals formed from the solvent, and theresults can be explained on the basis of a mechanism advanced by Daintonand Miller.35Z A very interesting feature of the work, which is developedfurther in another paper,353 is that the effect of dose-rate variation can onlybe explained on the basis of an increasing non-uniformity of radical distri-bution with decreasing dose rate, in the manner already pcstulated foraqueous solutions.354 In agreement with the results for aqueous solutionsthe degree of non-uniformity was found to be independent of the radiatioEquality. Experiments with chloroform and with methyl acetate indicateduniformity of radical distribution for dose rates greater than 250 and1000 r/min., respectively.353Copolymerisations of styrene-methyl methacrylate mixtures have beeninduced by p-irradiati~n.~~~ Subsequent analyses of the copolymers showedthem to contain about equal molecular proportions of each monomer, therebyestablishing that this polymerisation proceeds by a free radical rather thanby an ionic mechanism.If the reaction is homogeneous, only a lowpercentage of the absorbed energy is effective in producing polymerisation.In the y-ray polymerisation of pure acrylonitrile the polymerisation rate isproportional to Rz (where R = dose rate and fr < x < l).356 It is suggestedthat the mechanism involves two termination steps, a bimolecular and aunimolecular step, and it is claimed that the results are explained on thisbasis.However, the experimental results indicate a constant value of ?G,whilst the deduced expression gives a value of x which increases as Rdiminishes.Solids.-Though most of the studies of the action of ionising radiations onsolids are primarily physical, some of chemical interest have appeared. Manyof these concern investigations of the irradiation of polymers. The effectsproduced by the irradiation of a variety of polymers with pile radiation andelectrons are very dependent on the presence or absence of oxygen and onthe dose rate.357 The most stable types of polymer are those which canform close-packed crystallites, e.g., linear polymers without side-chains,and two quite clear-cut classes exist, viz., those which are predominantlydegraded and those which are predominantly cro~s-linked.~~~ Polyethyleneis in the latter class.359 y- or Neutron-irradiation causes C-H bond fracture,with the liberation of hydrogen gas and the production of cross-linking.Fracture of C-C bonds does not occur.Polystyrene, poly(ethy1ene tere-phthalate), nylon, and unvulcanised rubber also fall into this butpolytetrafluoroethylene 361 and polymethyl methacrylate 362 are degraded,C-C bonds being preferentially fractured. All these results are in keepingwith observations on depolymerisations by non-radiation methods. An352 F. S. Dainton and N. Miller, Proc. Int. Congress of Pure and Applied Chemistry,1947, 1, 77.354 E.Collinson and F. S. Dainton, Discuss. Faraday SOC., 1952, 12, 251.355 W. H. Seitzer, R. H. Goeckerman, and A. V. Tobolsky, J . Anaer. Chew. SOC., 1053,75, 755.S56 I. A. Berstein, E. C. Farmer, TV. G. Rothschild, and F. F. Spalding, J . Chem.PAYS., 1953, 21, 1303. 357 K. Little. Nature, 1952, 170, 1075.358 E. J. Lawton, A. M. Bueche, and J. S. Balwit, Nature, 1953, 172, ?6.359 A. Charlesby, Proc. Roy. SOC., 1952, A., 215, 187.360 Idem, Nature, 1953, 171, 167.381 Idem, Atomic En. Research Establishment Report, 1952, A.E.R.E.-M/R-978.363 A . Charlesby and M. Ross, Natzire, 1953, 171, 1153.353 A. Chapiro, Conapt. rend., 1953, 237, 247COLLINSON, DAINTON, AND IVIN: HOMOGENEOUS SYSTEMS. GTinvestigation of the effect of pile irradiation on several polymers, by meansof subsequent viscosity measurements of the polymer solutions, supports theabove results,363 and it is suggested that pre-determined amounts of cross-linking might be produced by introducing suitable groups into the polymer.There was some indication of the existence of free immobilised radicals inthe solid polymers after irradiation.During the irradiation of nitrate crystals in the atomic pile, oxygengas and nitrite ions were formed in equivalent amounts.The effects weremainly produced by electronic ionisation and excitation rather than by elasticcollisions with particles.364 The primary products of the decomposition ofpotassium perchlorate by 50 kvp X-rays are potassium chlorate, potassiumchloride, and oxygen.365 The reaction is of first order and has a yield,G, of 5.3.Water and Aqueous Solutions.-" In spite of the large amount of carefulexperimental work which has gone into the subject, we are still a good wayfrom providing firm experimental groanding for any theory of the radiationchemistry of water," states a leading worker in this field.366 However, thisdoes not prevent new theories from being advanced. Samuel and Magee,3G7in developing a theory in which hydrogen atoms and hydroxyl radicals areconsidered to be the only active radicals produced, have concluded, contraryto earlier theories,36s that the radicals are most likely to be formed in pairs,approximately at the sites of ionisations.Calculations based on the diffusionand recombination of radicals lead to the view that with the exception of theforward ( F ) and the radical (I?) reaction,* effects of geometrical distributionof reactive species can be ignored for all cases of the reaction of a solute inaqueous solution.In the past it has been assumed thatthe yields of hydrogen and hydroxyl radicals, denoted by GR, were equal,and that the " molecular " yields of hydrogen and hydrogen peroxide,denoted by Gp, were also equal.Direct evidence has shown that thisassumption is incorrect and that the yields of hydrogen peroxide and hydro-gen radicals are respectively greater than those of hydrogen molecules andhydroxyl radicals.369 This result necessitates the introducticn of threeequations to represent the primary effect of ioiiising radiations on water.Dainton and Sutton write these as 2H,O -++ 20H + 2H ; 2H20 --+ H +20H ; and 2H20 -+ H202 + 2H. Allen 366 allows for the new effect byadding the last of these processes [called by him reaction ( E ) ] to his earlierequations (3') and (R), and summarises other indirect evidence for and againstreaction ( E ) .On the assumption of the existence of this reaction he hassurveyed and re-evaluated the existing experimental data on rzdical and(i) The molecular and radical yield.363 L. A. Wall and M. Magat, J . Chiiiz. phys., 1953, 50, 305.364 G. Hening, R. Lees, and M. Matheson, J . Chem Phys., 1953, 21, 664.365 H. G. Heal, Canad. J . Chem., 1953, 31, 91.366 A. 0. Allen, U.S. Atomic En. Commiss.Report, 1953, BNL-1498.367 A. H. Samueland J. L. Magee, J . Chem. Phys., 1953, 21, 1080.36* D. E. Lea, " Actions of Radiations on Living Cells," 1947, Cambridge University36* F. S. Dainton and H. C. Sutton, Trans. Faraday SOL, 1953, 49, 1011. * These reactions arePress; J. Read, Brit. J . Radiol., 1951, 24, 345.H,O ---+ I3 + OH ( R )H,O ---+ +H, + +H,O, (I;) (See Ann. Reports, 1952, 49, 7 2 . 68 GENERAL AND PHYSICAL CHEMISTRY.molecular yields.one in his paper.y-rays.]Radiationy ..................... x ..................... x ..................... x ..................... x ..................... x .....................Tritium 6 .........u (Po) ...............The following table is an extract from a more complete[The yields are based on the value G(Fe2+),,,.= 15-5 forInitialelectronenergyW ) GH2 GHpOz GOHSolvent : 0~8N-sulphuric acid500 0.48 0.87 2.8627 0.5 0.97 2.5823 0.55 1.01 2.5620 0-6 1.05 2.4320 0.6 1.08 2.3811 0.7 1.17 2-235.7 0.9 1.59 1.35- 1-57 1.87 0.2GH3-643.523-503.333.343.172.730.84.604.624.604.534-544.574-533.94Solvent : watery ..................... 500 0.6 1.05 1.7 2-6 3.8A' ..................... 30 0-56 1.43 0.9 2.64 3-76o! (Rn) ............... - 1.8 1.9 0.1 0-3 3.9The molecular yields are seen to increase, and the radical yields to de-crease, as the ion-density increases. It is found, however, that the imtnn,-taneozls yields (like the overall yields, GHZO) remain constant down to thelowest energies used, and it is suggested that the changes in the observedradical and molecular yields are due to the higher proportion of track-ending concomitant with electrons of lower initial energy.The constancyof GR,O suggests that the radicals are initially separated rather than sideby side, a conclusion which is at variance with the theory mentioned earlier.367The difference in behaviour of water and aqueous sulphuric acid is interest-ing. Allen suggests that there may be complex-formation between hydroxylradicals and sulphuric acid or its ions, and that there is a more ready neutral-isation of positive and negative ions in the acid. In water a greater mole-cular yield may arise from a process of the type 2H,O+ __+t H,02 + 2H+.It should be remembered that complete and consistent as the data lookthey have all been obtained from a limited number of systems. The highvalue of G B (12.6 & 1.8) obtained from the radiolysjs of hydrogen peroxide,linked with the fact that no hydrogen production was detected in theseexperiments,370 evokes the suspicion that the measured yields, and alsothe ratios between Gn, Gp, and GE may be very dependent on the soluteused as well as on the type of radiation.Dewhurst 372 has studied the effect ofmany variables on the kinetics of the 50 kvp X - and 6oCo-y-ray oxidations offerrous sulphate solutions; the results indicate that there is no difference inthe effects of the two types of radiation.The mechanism proposed by Rigg,Stein, and Weiss 371 is not adequate to explain some of the results, especiallya t low acid concentrations, and no other homogeneous stationary-statetreatment could be found to explain all the facts.It is suggested that thesystem may involve non-stationary-state kinetics. Dainton and Sutton 369also found indications of the reaction's occurring in localised zones alongelectron tracks. Both Dewhurst and Dainton and Sutton found the exist-(ii) The ferrous-ferric system.370 F. s. Dainton and J. Rowbottom, Tyans. Faraday SOC., 1953, 49, 1160.371 T. Rigg, G. Stein, and J. Weiss, Proc. Roy. SOC., 1952, A , 211, 375.372 H. A. Dewhurst, Traits. Faraday SOC., 1053, 49, 1174COLLINSON, DAINTON, AND IVIN HOMOGENEOUS SYSTEMS. 69ence of a post-irradiation oxidation of ferrous ions in dilute aerated solutions.This was shown to be due to the slow reaction between hydrogen peroxideand ferrous ions.The latter authors also found a post-irradiation effect inde-aerated solutions a t concentrations lower than those used by Dewhurst.This was attributed to the molecular production of hydrogen peroxide.Amphlett 373 has confirmed that the reduction of aerated ferric-ion solutionsby y-rays occurs with high yield in solutions of high pH. At pH 2.46,G = -16. A steady state, in which the ratio of Fe3+ : Fe2+ depends on thetotal iron concentration, is soon attained. The steady state does not havethe same value if reached by the oxidation of ferrous ions, indicating thatthe system is not thermodynamically reversible with respect to hydrogenatoms and hydroxyl radicals.I t is suggested that at high pH there is com-petition between the processes FeOH2+,,. + Haq. -+ and H + 0, --+HO,. Dewhurst 372 was unable to detect the formation of stationary statesof this type. The temperature coefficient for the oxidation by y-rays hasbeen r e m e a s ~ r e d . ~ ~ ~The oxidation of ferrous ions in aerated 0.8~-sulphuric acid by the x-raysof polonium (dissolved in the solution) gives a yield, G, = 6, which does notvary with the intensity of the irradiati0n.37~ Employing a method of cal-culation which depends on the additivity of the effects of a-, (3-, and y-radiation on the ferrous-0-8~-sulphuric acid system, Lefort 376 deducesthat for aerated solutions G, = 6.2, and for de-aerated solutions G, = 3.7.The reduction of aerated ferric tris-o-phenanthroline by y-irradiation iscomplicated by an after-effect lasting for several The effect isless marked in more acid solutions, less important at low dose rates, andabsent in de-aerated solutions.Yields in aerated solution are G = 12 atpH = 0 and G = 14 at pH = 4 (the after-effect being allowed to go tocompletion); in de-aerated solution G = 3.5 at pH = 0 and G = 4.5 atpH = 4.A large number of inorganic and organicsystems have been examined, and in this section only those aspects of thegreatest general interest will be covered.An apparent dose-rate effect has been found in the reduction of cericions by polonium a - r a y ~ , ~ ~ ~ the yield decreasing with increasing dose rate.A dependence on the cube root of the dose rate for the yield of the destruc-tion of tartrazine by electrons 378 has been conceived as due to greater com-petition by the reaction H + OH --+- H,O at higher dose rate^.^'^ Thisdoes not seem to be a likely explanation for the above a-ray results.A dose-rate effect has also been found in the formation of hydrogen peroxide by thel-Mev-proton irradiation of water,380 the yield decreasing as the dose rateincreases. The results suggest that there may be a maximum efficiency ofhydrogen peroxide production at a particular dose rate for each type ofradiation.For a-irradiations G, = 0.95.376(iii) Other aqueous systems.373 C. B. Amphlett, Nature, 1953, 171, 690.374 T. J. Hardwick, Canad. J . Chem., 1953, 31, 881.3 7 5 M.Haissinsky and (MIle.) C. Anta, Compt. rend., 1953, 236, 1161.376 M. Lefort, ibid., 237, 159.377 M. J. Pucheault and M. Lefort, J . Chim. phys., 1953, 50, 196.378 A. Brasch, W. Huber, and A. Waly, Arch. Biochern. Biophys., 1952, 39, 245.379 W. Dittride, 2. Naturforsch., 1953, 68, 10.350 R. J. Shalek and T. W. Bonner, Nature, 1953, 172, 25970 GENERAL AND PHYSICAL CHEMISTRY.The actions of various ionising radiations on solutions of phosphites pro-vide further evidence that more complex entities than hydrogen atoms andhydroxyl radicals must be formed from the ~olvent.~8lThe reduction of ceric ions by y-radiation appears to take place via theaction of hydrogen peroxide and not via OH or HO, radicals as was earliersuggested.382 This contrasts with the suggestion that the Ce4+-H,O,reaction takes place via HO, radi~a1s.l~~The hydroperoxide radical is considered to be the effective entity in thedegradation of poly(methacry1ic acid), and this has been suggested as amethod of testing the biological protective action of chemical compounds.383Of bearing on this work is that of Wall and Magat 363 who studied degradationof polymers in non-aqueous solutions.In carbon tetrachloride the activedegrading agent clearly cannot be HO,, but oxygen is still necessary fordegradation. They suggest that polymer chains are here broken by directaction of the radiation and that the effect of oxygen is to prevent recom-bination of the broken chains. A protecting agent is then envisaged as achain-transfer agent which stabilises the radicals before oxygen can inter-vene.In support of this, the action of cystine on the polymerisation ofacrylonitrile indicates that it behaves as a transfer agent.384 It has alsobeen suggested that the effective entity in the oxidation of indigo carmineby y-rays is the HO,E. C.F. S. D.K. J. I.4. REACTIONS AT SOLID INTERFACES.This Report has been restricted by limitations of space to decompositionsproceeding at solid interfaces; no Report 1 on this topic has previouslyappeared although there are recent reviews on solid-solid interface reactionsand on reactions of gases at the surfaces of solids3 The latest surveys onsolid decompositions were published in 1938 ; 43 5 consequently althoughemphasis is given to current developments, the progress over the past 15years is summarized.Nucleus Formation and Growth.-The original concept that the overallrate of decomposition can be expressed in terms of the rates of nucleusformation and growth is still retained.In general terms, the nucleus maybe regarded as a localized array of product in the reactant matrix; reactionnormally proceeds preferentially at the interface because, on account ofreactant-product co-operation, the activation energy is here a minimum.Two types of nuclei may be distinguished : the growth nucleus which has381 M. Cottin and M. Haissinsky, J. Chirn. phys., 1953, 50, 195.382 T. J. Sworski, J. Chem. Phys., 1953, 21, 375.383 P. Alexander, Brit. J . Radiol., 1953, 26, 413.334 (Mme.) A.Prdvot-Bernas, J. Chim. phys., 1953, 50, 445.385 L. Mongini and E. L. Zinimer, ibid., p. 491.Cf., however, H. W. Melville, Ann. Reports, 1938, 35, 81.,,J. A. Hedvall, " Einfuhrung in die Festkorperchemie, 1952 ; InternationalJ . S. Anderson, Tilden Lecture, 1953.W. E. Garner, Sci. Progress, 1935, 33, No. 130.Faraday Society Discuss., 1938, 34, especially pp. 821-1010.Symposium on the Reactivity of Solids, Gothenburg, 1952TOMPKINS AND YOUNG REACTIONS AT SOLID INTERFACES. 71a predominant tendency to grow, and the germ nucleus which has dimen-sions less than the critical requirement and tends to decrease in size andultimately disappear.treatment, who applied the formalism of the Volmer-Becker theory tonucleation in solids; in this context, the nucleation rate reflects, in part, themobility of atoms (ions) in the crystalline lattice as a function of the activ-ation energy for diffusion (or ion conductance) and contains an exponentialterm related to the entropy decrease attending nucleus formation.Turnbulland Fisher have recently introduced derivations using the method of theabsolute reaction theory and further developments using this approach aregiven in two later papers.9~ 10 For simplicity, nuclei are assumed to bespherical, although, both from experimental observations and theoreticalconsiderations, disc- or needle-shaped clusters with definite preferred orient-ations with respect to the parent lattice should be considered.ll Similarly,any rigorous theory should consider the strain energy arising from latticedeformations.Such energy forms part of the free energy of formation ofthe germ nucleus since specific volume changes, occasioned by the produc-tion of ions of different size and number, invariably occur ; and these changes,which become greater with increasing size of the nucleus, can only be accom-modated by strains in both the reactant and product. However, althoughthe strain energy is a minimum for disc-shaped nuclei, the anisotropy l3 ofthe interfacial energy of reactant and product often controls the shape ofthe nucleus, since there will be a definite crystallographic relation such thatplanes having greatest similarity in atomic packing will tend to be parallel.Theoretically the problem may be treated by considering the interface as amisfitting monolayer.l4 In addition, from X-ray evidence, it now seemsclear that there are present nuclei of varying composition and stability, allof which have some tendency to grow into stable growth n~c1ei.l~It is now, how-ever, accepted that real crystals contain non-equilibrated imperfections(e.g. , Frank-Read sources 16) that generate dislocations thereby permittingplastic flow under small stress.Growth of nuclei will consequently bepreferred in those crystal elements having dislocations in their vicinity,since large stress cannot be supported there ; and, moreover, because stressesmay be relieved more readily at interfaces, nucleation will be easier at grainboundaries and free surfaces, as has been experimentally demonstrated byHedges and Mitchell l7 for the photodissociation of silver bromide.In general, diffusion rates in solids are small and the time to attain asteady-state production of nuclei becomes comparable with that required to13.Becker, Ann. Physik, 1938, 32, 128.R. Becker and W. Doring, ibid., 1935, 24 ( 5 ) , 719; M. Volmer, “ Kinetik derPhasenbildung,” Steinkopf, Dresden, 1939.D. Turnbull and J. C. Fisher, J . Chem. Phys., 1949, 17, 71.D. Turnbull, zbid., 1950, 18, 198.lo I d e m , ibid., 1952, 20, 411.l1 See, for example, A. Guinier, PI^. Phys. Soc., 1945, 5’7, 310; C. S. Barrett andA. H. Geisler, J . Appl. Phys., 1940, 11, 733.l2 D. Turnbull and B. Vonnegut, I n d . Bng. Clienz., 1952, 44, 1292.l3 Cf. ref. 4 and J.N. Hobstetter, Metals Tech., 1948, 15, t.p. 2447.l4 F. R. N. Nabarro, Pmc. Phys. Scc., 1940, 52, 90; Proc. Roy. Soc., 1941, -4, 175, 519.l 5 Ci. Borelius’s theory; G. Borclius, A m . Physik, 1938, 33, 517.l6 F. C. Frank and W. T. Read, Phys. Review, 1950, 79, 722.l 7 J. M. Hedges and J. W. Mitchell, Phil. Mag., 1953, 44, 357.Theoretical developments have followed Becker’sAs yet, the assumption has been that the solid is ideal72 GENERAL AND PHYSICAL CHEMISTRY.complete the reaction; consequently the nucleation rate is a function oftime. In such circumstances, Frenkel’s method,18 in which the size ofthe germ nucleus is treated as a continuous variable, has greater validity;this treatment has been recently rigorously developed by Turnb~1l.l~ Anattempt has also been made to take account of the influence of the growingnucleus on the probability of nucleation in its proximity.20 The ingestionof preferred nucleation sites by the growing nucleus and the elimination ofsmall nuclei by overlap with large ones has been considered by Avrami,21by Turnbull,22 who considers the effect of the presence of initial transients,and by others23Most of the theoretical treatments have been concerned with homo-geneous, structure-insensitive nucleation in the interior of the reactant ;the interest for interface reactions is, however, centred on the structure-sensitive nucleation at the interface.It is, therefore, important to notethat analogous expressions can be derived for this latter case.24 Neverthe-less, it is normally implicit in all derivations that the properties of germ andsmall growth nuclei containing only 10-30 units can be described in termsof macroscopic thermodynamic properties.Some doubt, however, hasbeen expressed about the validity of this extrapolation and modified expres-sions have beenFrom the viewpoint of thermal decompositions the tendency recentlyhas been to favour this concept of discrete nuclei in interpreting the resultsof kinetic studies, and the theory of diffuse nuclei has not been developed.The most general mathematical treatment applied directly to decom-positions has been given by Mampel; z8 it includes the combined effects ofrandom formation and growth together with corrections for the overlappingof nuclei and the ingestion of nucleation sites.His final equation is formallythe same as that of Avrami and of E r ~ f e e v , ~ ~ viz., cc = 1 - exp(- W ) ,where a is fractional decomposition, k a velocity constant, and n a constantwhich includes the power dependence of formation and growth on time.Mampel has also investigated the effect of particle size on the form of thedecomposition curve and derived various equations depending on therelative magnitude of the velocity constant of growth and the particleradius.Although the original linear branching chain mechanism 31 has lostMacdonald’s two-dimensional analogue 33 applied to silver oxalat eJ. Frenltel, “ Kinetic Theory of Liquids,” Clarendon Press, 1946; J. Zeldovich,Acta Physzcochinz. U.S.S.R., 1943, 18, 1.l9 D.Turnbull, Metals Tech., 1948, t.p. 2265.2o W. G. Burgers, Nature, 1946, 157, 76.21 M. Avrami, J . Chem. Phys., 1939, 7, 1103; 1940, 8, 212; 1941, 9, 177.22 D. Turnbull, Amer. Inst. AJiuz. Met. Eng., t.p. 2365, Metals Tech., 1948.23 A. Kantrowitz, J . Chem. Phys., 1951, 19, 1097; R. F. Probstein, ibid., p. 689.24 D. Turnbull, in “ Phase Transformations in Solids,” 1951, p. 180.25 13. Reiss, J . Chem. Phys., 1952, 20, 1216; R. C. Tolman, ibid., 1949, 17, 333.26 J. G. Kirkwood and F. P. Buff, ibid., 1949, 17, 338; 1950, 18, 991.2 7 F. P. Buff, zbzd., 1961, 19, 1591.K. L. Mampel, 2. physikal. Chenz., A , 1940, 187, 43.29 B. V. Erofeev, Doklady Akad. Nauk, S.S.S.R., 1946, 52, 511.30 K. L. Mampel, 2. physikal. Chem., A , 1940, 187, 235.n1 W.E. Garner and H. R. Hailes, Proc. Roy. Soc., 1933, A , 139, 576.‘? J. Y . Macdonald, Trans. Faraday Soc., 1938, 34, 977.33 Idem, J . , 1936, 832, 839TOMPKINS AND YOUNG: REACTIONS AT SOLID INTERFACES. 73has been generalized 3* in crystallographic terms to include interference ofchains, and the Prout-Tompkins equation in the form log {$/(P, -p)> =kt + constant, where fif is the final pressure corresponding to completedecomposition, has been applied to the kinetics of decomposition of variouscompounds, e.g., permanganates, oxalates, fulminates, etc. The mechanismhas recently been reformulated in terms of dislocation theory.35Decompositions of Specific Compounds.-Hydrates.-Recent investigationshave been confined almost entirely to the alums.Cooper and Garner,36 ina re-examination of the dehydration nuclei on single crystals of chrome alumi n uac~to now distinguish two types: (I) pink, formed above 20" c withE(growth) = 31 kcal./mole, and (11) white, formed below 20°, with E(growth)of 28-5 kcal./mole and converted into (I) on coalescence with (I) nuclei. Theentropy, or B-factor, of (I) is 10l2 times greater than that calculated theoretic-ally from the Polanyi-Wigner equation. Anous, Bradley, and C~lvin,~'using a specially designed microbalance, however, find a normal B-factorwith E(growth) = 23 kcal./mole between 15" and 35", and E(growth) = 30kcal./mole and a B-factor 1O1O greater than the theoretical value between-1-7" and -12". No completely satisfactory explanation has beenadvanced for the abnormally high B-factor; in part, it is attributed to thedecrease in thickness of the amorphous-product transition-layer withincreasing temperature 36 or, alternatively, to a rapid reaction through thecrystal mosaic blocks with delays between blocks due to the requirement offresh n~cleation.~' The initial slow-growth rate of small nuclei on chromealum, previously attributed to the variation of interfacial tension withcurvature of the nucleus,38 has received two alternative explanations ;Bradley 39 shows theoretically that the presence of the dehydrated phaseincreases the activation energy for the escape of water molecules from theinterface as the curvature of the interface increases.Ma~donald,~~ how-ever, from more general considerations of the difference of lattice energiesof reactants and products and the surface migration of vacancies, concludesthat the increase of activation energy for water molecules to pass acrossthe interface with decreasing size of the nucleus is the determining factor.A new phenomenon with chrome alum is reported by Garner and Jennings ; 41the original spherical nuclei formed in vacua are accompanied by a largenumber of smaller nuclei which become visible only when the crystal isexposed to a critical water-vapour pressure; the effect is not found withpotash alum.The authors account for the occurrence of these satellitenuclei in terms of the irreversible production of a zeolitic zone; furtherevidence of the irreversibility of the dehydration process is given in a studyof the rehydration of dehydrated potash alum by Tompkins and Bielanski,&dwho find that the rate of uptake of water, after an initial monolayer adsorp-tion, is diffusion-controlled.The first attempt to formulate a detailed mechanism of nucleus formation34 E.G. Prout and F. C. Tompkins, Trans. Faraduy Soc., 1944, 40, 488.35 A. Finch, P. W. M. Jacobs, and F. C. Tompkins, J . , 1954, in the press.36 J . A. Cooper and W. E. Garner, Proc. Roy. Soc., 1940, A , 174, 487.3 7 M. M. T. Anous, R. S. Bradley, and J. Colvin, J., 1951, 3348.38 J. A. Cooper and ?V. E. Garner, Trans. Faraday SOC., 1936, 32, 1730.39 R. S. Bradley, ibid., 1951, 47, 630.42 A. Bielanski and F. C. Tompkins, Trans. Faraday Soc., 1950, 46, 1072.40 J .Y . Macdonald, e'bid., p. 860.W. E. Garner and Jennings, personal communication74 GENERAL AND PHYSICAL CHEMISTRY.has been made by Acock, Garner, Milsted, and Willa~oys.~~ The initialstage is thought to be the aggregation of lattice vacancies at the crystalsurface; these are produced by surface evaporation of water molecules andby migration of defects from the interior to the surface. Nucleus formationceases when the rate of surface evaporation is too small to maintain the rateof formation of the small aggregates. In addition, the paper gives a largenumber of experimental data on the shape and appearance of nuclei andon the magnitude of the B-factors and ,!?(growth) for a series of mixedalums.Additional data, mainly concerning equilibrium water-vapour pressuresand heats of dissociation, are given by Hepburn and Phillips,44, 45 whoattribute the primary dissociation to the reactionM+(6Hz0)R13+(H,0),(SO~)~ M+M3+(H,0),(S0,), + 6H,Oi.e., to loss of water molecules cc-ordinated to the univalent cation.Theyconclude that the stability of alums to dehydration decreases with decreasingsize of the M+ ion and increasing size of the M3+ ion, and suggest that ondehydration, a residual skeleton lattice film held to the reactant latticeby valency forces is first formed; only the outer layers are metastable andundergo rearrangement. This theory differs from Garner's concept of aninitially-formed zeolitic structure which later collapses and recrystallizes.The effect of an ambient water-vapour pressure on the rate of decom-position of finely divided samples of copper sulphate pentahydrate has beeninvestigated by Frost and Campbell,46 following the suggestion by Frost,Moon, and Tompkins 47 that similar behaviour to that found with manganeseoxalate dihydrate should be observed.Discontinuities in the rate curves forthe dehydration of nickel sulphate heptahydrate and in the rehydration ofthe products have been recorded4* and ascribed to the formation of inter-mediate hydrates. Roginskij has reported on some electron-microscopicobservations made during the dehydration of hydrates.49Oxides and Carbonates.-The autocatalytic nature of the decompositionof silver oxide in an oxygen atmosphere, first investigated by Lewis,50 hasbeen confirmed by Hood and Murphy,51 but Pavlyuchenko and Gurevich 52obtained complex fi-t plots and a very low activation energy of doubtfulvalidity.However, many of the previous divergent results have now beenresolved by Garner 2nd Reeves 53 who used an oxide prepared similarly toLewis's but annealed in oxygen at 200-340" for 8-10 days. They obtainedsimple kinetics for its decomposition i p 2 vacuo that were consistent with thethree-dimensional growth of a constant number of nuclei ; with un-anneaIedoxide the normal interface reaction is obtained. If the decomposition takesplace in presence of oxygen the growth of small silver nuclei is inhibited.43 G. P. Acock, W. E. Garner, J. Milsted, and H. J. Wiliavoys, PYOC. Roy. SOC., 194.7,4 5 R.F. Phillips, J., 1952, 2578.46 G. €3. Frost and R. A. Campbell, Canad. J . Clam., 1053, 31, 107.4 7 G. €3. Frost, K. A. Moon, and E. H. Tompkins, ibz'd., 1951, 29, 601.48 B. Ghosh, J. Indian Chem. Soc., 1941, 18, 472.49 S . 2. Roginskij et al., Doklady Akad. Nauk S.S.S.R., 1940, 68, 879.50 G. N. Lewis, 2. physikal. Chem., A , 1906, 52, 310.51 G. C. Hood and G. W. Murphy, J . Chew. Educ., 1049, 26, 169.52 M. M. Pavlyuchenko and E. Gurevich, Zhur. Obshchei Khim., lMP, 21, 467.83 W. E. Garner and L. W. Reeves, Trans. Faraday SOC., 195% 88, in the press,189, 309. 44 J. R. I. Hepburn and R. F. Phillips, J., 1952, 2569TOMPKINS AND YOUNG : REACTIONS AT SOLID INTERFACES. 75The semi-conductivity of the oxide was also measured but there seemed nolink between this property and the mechanism of decomposition.Dolomite, because of its industrial importance, has been the most exten-sively studied of the carbonate^.^^ The products depend on whether thedecomposition takes place in vacuo or in an atmosphere of carbon dioxide :in vacuo : MgCa(CO,), -P CaO + MgO + 2C0, .. * ( 1 )in carbon dioxide : CaCO, + MgO + CO, . . - (2)The initial product in (1) is said to be (Ca,Mg)O, having a pseudo-dolomitestructure which later breaks down into separate crystallites of calcium oxideand magnesium oxide,55 the size of which increases regularly with increasingtemperature of decomposition.60 There is little agreement as to the mechan-ism of formation of the " half-burned " dolomite [reaction ( Z ) ] ; the followinghave been suggested : (i) an initial dissociation 56 into the constituentcarbonates, involving cation-site interchange, followed by independentdissociation of these; (ii) a direct decomposition 57 into calcium oxide andmagnesium oxide and re-formation of calcium carbonate with the escapingcarbon dioxide; (iii) the initial production 58 of some magnesium oxide anda solid solution of calcium carbonate and " magnesium carbonate deficientin MgO " ; and (iv) partial dissociation 59 into calcium oxide and magnesiumoxide followed by the reaction, CaO + CaMg(CO,), --+ 2CaC0, + MgO,since it is found that admixture with dry calcium oxide reduces the tem-perature of decomposition in an atmosphere of carbon dioxide.X-Rayanalysis 6o shows that there is a minimum in the particle size of the productsat 685", the larger calcite crystallites being aligned parallel to the originaldolomite lattice whereas the magnesium oxide is irregularly oriented.Atthis temperature the Mg2r ions are mobile in a highly defective lattice anddiffuse across the plane of the interface, whereas the Ca2+ ions are practicallyimmobile. The function of added dry calcium oxide is, therefore, to providea larger interface (by reaction with carbon dioxide) and thus to facilitatedecomposition. No satisfactory explanation has been given of the retentionof half the content of carbon dioxide and the lowering of the activationenergy to half the normal value when the decomposition is effected in ahydrogen atmosphere.61With the simple carbonates, it is confirmed that calcite and magnesite 62decompose in vacua by an interface mechanism, although there are departuresfrom the rate equation expected for the penetration of a completely nucleatedsurface. These are attributed to the slow rate of nucleation, self-cooling,and impedance to the escape of carbon dioxide.Cremer,63 however, con-54 TV. 24011, Angeu. Clzenz., 1950, 62, 567; R. A. W. Haul and J . Marlrus, J . A$pl.Chein., 1952, 2, 298.5 5 13. T. S. Britton, S. J. Gregg, and G. W. Winsor. Trans. Faraday SOC., 1952, 48, 70.5 6 C. W. Potapenko, Zhuv. Priklad. Khim., 1932, 5, 693; M. Faqueret, Bull. SOC.frang. Miiz., 1940, 63, 88; 1'. Schwob, @omn$t. r e d . , 1947, 224, 47.5 7 H. Flood, K g l . Norske Vidensk.Selsk. Fsrh., 1930, 22, 188.5 8 P. V. Gel'd and 0. A. Esin, Zhztr. Priklad. Khinz., 1949, 22, 240; 0. A. Esin,P. V. Gel'd, and S. I. Popel, ibid., p. 354.59 J. A. Hedvall, 2. anorg. Chew., 1953, 272, 22.Go R. A. W. Haul and F. R. L. Schoning, Z. anorg. Chem., 1952, 269, 120; R. A. W.Haul and H. Wilsdorf, Actn Cryst., 1952, 5 , 250; R. Meldau and R. H. S. Robertson,Nature, 1953, 172, 998.6z H. T. S. Britton, S. J. Gregg, and G. W. Winsor, Trans. Faraday SOC., 1952, 48, 63.63 E. Cremer, Z. apzorg. Chem., 1949, 258, 123.61 F. Bischoff, Z. anorg. Chew., 1950, 262, 28876 GENERAL AND PHYSICAL CHEMISTRY.cludes that for the first 10-50% decomposition the rate for magnesitevaries as tf and suggests a rate-controlling diffusion process.As is fairlygeneral, values of the activation energies of these dissociations are aboutthe same as the heats of reaction. Zinc carbonate 64 is an exception to thisrule, the heat of activation being much the larger owing to lack of reversibilityof the dissociation. The decomposition of sodium and potassium hydrogencarbonates obeys complex kinetics-decomposition of the former 65 is at firstunimolecular, then of zero order, but finally a fractional order less thanunity is obtained. Formation and decomposition of intermediates arepostulated 66 in the decomposition of potassium hydrogen carbonate.Formates and 0xaZates.-Both nickel and cobalt formate decomposeaccording to the scheme :M(H*COO), M + H, + 2C0, . * (i)M + H,O + CO + CO, . . (ii)Zelinskaya and D ~ b y t s h i n , ~ ~ however, reported that (i) predominates forthe nickel salt and gives a simple dependence of the pressure increase on thethird power of time.Erofeev,68 using cobalt formate, also consideredreaction (i) only and found Mampel’s equation valid up to 50% decom-position. Bircumshaw and Edwards 69 produce analytical data for theexistence of both reactions with nickel formate and, despite their findingthat grinding did not accelerate the rate, showed that the Prout-Tompkinsequation was applicable. It seems more probable that these decompositionsare similar to that of silver oxalate but that the kinetics are complicated notonly by the retardation effect of one product (water) and an accelerationby another (the but also by the different contributions of (i) and (ii)to the pressure increase as the reaction proceeds.70Further attention has been given to silver oxalate since it decomposessmoothly and stoicheiometrically to metal and carbon dioxide.Earlierlack of reproducibility has been rectified 71 and the kinetics are shown todepend on the age of the sample as well as on the conditions of prepar-ation.71’ 72 A well-aged stoicheiometrically-prepared sample gave resultsconsistent with three-dimensional growth subsequent to nucleus formationat a limited number of sites according to a first-order decay, whereas asimilar, but freshly prepared, specimen gave results corresponding to thebranching of two-dimensional plates,723 73 as might be expected from thelayer-lattice structure deduced by Griffith 74 from X-ray measurements onthe original and the decomposed salt.These different theories have beenbrought together by postulating nucleation and branching at di~locations~7~64 J. Zawadzki and W. Szamborska, Bull. Acad. polonaise, A , 1948, 27. For a reviewin English of Zawadzki’s work on carbonates see “ Festskrift tillagnad J . A. Hedvall,”Goteborg, 1948.G 5 R. Tsuchiga, J . Chern. SOC. Japan, 1953, 74, 16. 6 6 Idem, ibid., p. 97.6 7 N. D. Zelinskaya and D. B. Dobytshin, quoted by S. 2. Roginskij, Trans.6 8 B. V. Erofeev, Zhur. Fiz. Khim., 1940, 14, 1217; 0. M. Todes, ibid., p. 1224.69 L. L. Bircumshaw and J. Edwards, J., 1950, 1800.70 A. A. Balandin, E. S. Gsegorian, and Z. S. Janischeva, Zhur.Obshchei Khim.,71 F. C . Tompkins, Trans. Faradq SOC., 1948, 44, 206.72 A. Finch, P. W. M. Jacobs, and F. C. Tompkins, J . , 1954, in the press.73 J. Y . Macdonald, J . , 1936, 832, 839.74 R. L. Grifith, J . Chem. Phys., 1946, 14, 408.Faruday SOC., 1938, 34, 959.1940, 10, 1031TOMPKINS AND YOUNG : REACTIONS AT SOLID INTERFACES. 77i e . , that the determining factors are the crystallographic characteristics of thesalt. Measurements of ionic conductance 729 75 confirm that the decom-position is an interface reaction ; the lack of photoconductance under irradi-ation and the similarity of the kinetics of prolonged photolysis 72 to thosefound with azides are explained in a theory involving exciton production.Other oxalates, in particular those of lead and mercuric mercury, decom-pose to the metal, its oxide, carbon monoxide, and carbon dioxide.TheProut-Tompkins equation 34 holds for the decomposition of the lead salt.76The kinetics for mercuric oxalate 77 are similar to those found with the silversalt although complications arise from the production of mercurous oxalateas an intermediary. An initial accelerating rate due to an expanding surfacereaction is followed by a constant rate of penetration of the interface, butafter ultra-violet irradiation a rapid first-order decay proceeds initiallybefore the constant rate is attained. Both 72 oxalates react similarly tothe silver salt under prolonged photolysis. The study of the complexdecomposition of hydrated thorium oxalate has yielded little of kineticvalue.78Permanganates.-The products of decomposition are oxides of manganeseand the cation (together with compounds of these) and oxygen. Exceptwhen the kinetics are determined predominantly by crystallographic ratherthan chemical properties, simple p-t plots are not obtained. With thepotassium salt,79 a branching mechanism dependent on lattice strains, setup by the difference of lattice parameters of products and reactant, is foundto be applicable, but the theory is not valid for the silver salt unless thebranching coefficient is assumed to vary with the fractional decomposition.Erofeev and Smirnova 81, 82 have applied the Mampel equation to the break-down of potassium permanganate but give different values for the exponentin two separate investigations.The decomposition of ammonium per-manganate 83 is most complex; not only is the ammonium ion oxidisedduring the decomposition but one of the products (ammonium nitrate) isthermally unstable and its breakdown is catalysed by one of the otherproducts, manganese dioxide.A new technique of examining the physical nature of the product layerformed on the surface of the barium salt has been devised by Roginskijet al.; 84 this layer, which is amorphous with a high surface area (6 m.2/g.from gas-adsorption measurements), is found to be an exact replica of thesurface of the original crystal. The particles of product penetrate into thereactant but only attain a linear dimension of low5 mm.; these findings arenot inconsistent with the Prout-Tompkins theory.The effect of the nature of the cation on the ease of decomposition of aseries of permanganates has been studied.By arbitrarily defining the75 W. E. Garner and L. W. Reeves, private communication.7 6 L. L. Bircumshaw and I. Harris, J., 1939, 1637; 1948, 1898.7 7 E. G. Prout and F. C. Tompkins, Trans. Faraday Soc., 1947, 43, 148.7 8 R. Beckett and M. E. Winfield, Austral. J . Sci. Res., 1951, 4, 644.7Q E. G. Prout and F. C. Tompkins, Trans. Faraday Soc., 1944, 40, 488.82 Idem, ibid., 1952, 26, 1233.83 L. L. Bircumshaw and F. M. Tayler, J., 1950, 3674.84 S. 2. Roginskij, E. I. Shmuk, and M. Kushnever, Izuesti Akad. Nauk S.S.S.R.,Idem, ibid., 1946, 42, 468.B. V. Erofeev and I. I . Smirnova, Zhur. Fiz.Khirn., 1953, 25, 1098.1950, 57378 GENERAL AND PHYSICAL CHEMISTRY.decomposition temperature as that at which the maximum rate is attainedin 120 min., Roginskij et aZ.85 show that the electrostatic-potential term Ze/r,where r is the cation radius, 2 its valency, and e the electronic charge, is thepredominant factor. Cations with unfilled inner shells, however, have amarked specific effect in further lowering the decomposition temperature.Similar regularities are found with azides, formates, and oxalates.Chlorates and PerchZorntes.-Both Glasner and Sinichen,s6 and Bircum-shaw and Phillips 87 find two maxima in the rate of decomposition of potass-ium chlorate if chloride is present. With a small amount of chloride (eitheradded, or as a product), surface melting of the chlorate occurs and thedecomposition rate is accelerated.As the chloride content increases,resolidification with a consequent decrease in rate takes place. Glasnerdevelops an equation to account for his results based on the assumed mobilityof oxygen atoms in the lattice ; his expression includes terms characterizinga surface, and a simdtaneous bulk autocatalytic, process. Preliminarystudies of the breakdown of guanidine perchlorate 88 and of the Li, Na, K,Ca. Mn, and Fe salts have also been made.89hides.-Interest in this class of compound has been stimulated byMott’s applicationg0 of solid-state physics to the results of Wischin9l andof Garner and Maggsg2 on the thermal decomposition of barium azide;the theoretical treatment is similar to that postulated for the photodecom-position of silver bromide.W i s ~ h i n , ~ ~ using a photographic technique, hadshown that the rate of both nucleus formation and of three-dimensionalgrowth varied as the square of the time. The stable nucleus could, there-fore, be formed by the trapping of two electrons at an interstitial Ba2+ ion;similarly growth proceeds by further alternate trapping of eIectron pairsand mobile interstitial cations. However, the calculations based on measure-ment of the ionic conductance 93 of the salt and Wischin’s experimentallyobserved rates of growth do not support a theory of growth by internalelectrolysis, and reaction at the metal-salt interface is suggested. Detailedstudies of the kinetics of the photo- and thermal decornpo~ition,~~~ 95 coupledwith measurements of the photoconductance of the salt under irradiation,also show that few free electrons are produced, and a modified theoryinvolving “ uncharged ” mobile excitons, or excited azide ions, was proposed.Nucleus formation, following Mitchell,96 was conceived 97 as the aggregationof F-centres rendered mobile by the presence of anion vacancies, the stablenucleus being a double F-centre associated with a lattice Ba2+ ion.Pre-irradiation by ultra-violet light caused acceleration of the thermal processby producing anion vacancies, thereby increasing the mobility of F-centresand the rate of nucleus formation. The exciton theory was further de-85 S. Elovich, S. 2. Roginskij, and E.I. Shmuk, ibid., p. 469.8 6 A. Glasner and A. E. Simchen. Bull. SOC. chim., 1950, 18, 233.L. L. Bircumshaw and T. R. Phillips, J., 1963, 703.A. Glasner and L. Weidenfeld, J . Amer. Chenz. SOC., 1952, 74, 464.s9 G. G. Marvin and L. B. Woolaver, I n d . Eng. Chem. Anal., 1945, 17, 474.N. I;. Mott, Proc. Roy. SOC., 1939, A , 172, 325.91 A. Wischin, ibid., p. 314.92 W. E. Garner and J. Maggs, ibid., 1939, 172, 299.93 J. G. N. Thomas and F. C. Tompkins, J . Chem. Phys., 1952, 20, 662.O4 Idem, Proc. Roy. SOC., 1951, A , 209, 550.D6 J. W. Mitchell, Phil. Mag., 1949, 40, 249, 667.s7 F. C. Tompkins, I n d . Eng. Chem., 1952, 44, 1336.95 Idem, ibid., 1951, 210, 111TOMPKINS AND YOUNG: REACTIONS AT SOLID INTERFACES. 79veloped 98, 99 by the introduction of the concept of a coloration complex,100an entity resulting from the trapping of the excitation energy at an anionvacancy with a consequent quantum-mechanical tunnelling of the excitedelectron to the vacancy thereby forming a F-centre coupled to a positivehole. Pre-irradiation of the potassium salt, however, effected no thermalacceleration ; lol this was attributed to the production and evaporation ofpotassium atoms ; the catalytic effect of an atmosphere of potassium vapourduring decomposition is consistent with the lowering of the activationenergy 99 for the removal of the valency electron from the azide ion.Freeelectrons and positive holes can be produced, however, by using higherincident energies, e.g., by electron bombardment,lo2 and the kinetics displaynew features, such as a decrease of rate with time of bombardment and asubsequent slow recovery of the original rate.The critical decompositionenergy in electron bombardment is given as 11.65 ev.lo3 The ultra-violetemission taking place during thermal decomposition of alkali-metal andalkaline-earth azides, first noted by Audubert lo* by using photoelectriccounters, has been re-investigat ed. The activation energies derived fromthe tFmperature coefficient of emission agree with those obtained from thep-! curves of the thermal decomposition of sodium azide Io5 and silverazide lo6 at various temperatures. The emission is probably associated withthe bimolecular exothermic reaction of azide radicals producing activatednitrogen molecudes.Thus Haycock lo7 finds that nitrogen peroxide isproduced when silver azide is decomposed in an atmosphere of oxygen.Bowden and Singh l o 8 have found that neutron irradiation accelerates thethermal decomposition of lithium azide and lead azide, and Yoffe lo9 hasdiscussed the thermal decomposition, leading to explosion, of calcium andbarium azides.Misce2Zaneous.-The decomposition and explosive characteristics ofmercury fulminate l1O* ll1 and some nitrobenzenediazo-oxides 112 have beenstudied by Vaughan and Phillips. Although the Prout-Tompkins equationwas well obeyed, suggesting a branching mechanism for the fulminate, thep-t plots after an induction period are also consistent with the three-dimensional growth of a fixed number of nuclei.ll3Information concerning the initial stages of nucleation has been obtainedin the decomposition of lithium aluminium hydride 113 to lithium hydride,aluminium, and hydrogen.There is an initial surface reaction penetrating20-30 layers followed by an acceleration obeying a cube law. The hydrideis shown to be a semi-conductor ; on being heated, its conductance increases9 8 P. W. M. Jacobs and F. C. Tompkins, Pvoc. Roy. Soc., 1952, A , 215, 454.gs Ideni, ibid., p. 265.loo F. E. Schneider in “ Photographic Sensitivity,” Ed. J. W. Mitchell, Butter-worths Sci. Publ., 1951, p. 18. Iol ’CV. E. Garner and D. J . €3. Marke, J., 1936, 657.lo2 J . M. Groocock and F. C . Tompkins, Proc. Roy. Soc., 1934, A , in the press.lo3 R. H. Muller and G.C. Brous, J. Chew. Phys., 1933, 1, 482.lo4 R. Audubert, Trans. Faraday Soc., 1939, 35, 433.lo5 R. Audubert and J. Roberts, J. Chim. phys., 1946, 43, 127.lo6 R. Audubert, ibid., 1952, 49, 575.lo’ E. W. Haycock, private communication from W. E. Garner, Dec. 1953.lo8 F. P. Bowden and K. Singh, Nature, 1953. 172, 378.lo9 A. D. Yoffe, Proc. Roy. Soc., 1951, A, 208, 188.I1O J. Vaughan and L. Phillips, J., 1949, 2741.113 \V, E. Garner and E. W. Haycock, Proc. Roy. Soc., 1952, A , 211, 335.Idem, J.. 1949, 2736. 112 Idem, J . , 1947, 156080 GENERAL AND PHYSICAL CHEMISTRY.as F-centres diffuse into the lattice and then decreases near the end of theinduction period owing to the association of these centres which later formthe growth nucleus.The decomposition of mercurous formate,l14 magnesium hydroxide,l15ammoniacal and pyridine complexes of mercury ha1ides,ll6 and the chromatesof ammonium 117 has also been studied.F.C. T.D. A. Y.5. THE THEORY OF LIQUIDS AND LIQUID MIXTURES.Recent work has tended towards the elaboration of existing theoriesrather than the development of new concepts, but it is not yet possible toassess with any finality the merits of the different theoretical approaches. Ageneral survey of the literature dealing with the statistical mechanics andthermodynamics of the liquid state is likely, therefore, to be more usefulthan an exhaustive exposition of one or two particular topics. We haveomitted reference to papers dealing with transport phenomena, viscosity,surface tension, spectroscopic properties, and X-ray scattering because,although theoretical prediction of some of these properties is possible, theydo not form the most suitable criteria for assessing the validity of the theories.Furthermore, transport processes and viscosity have both been reviewedelsewhere recently.1sTheories of Pure Liquids.-Free-valztme, Lattice, or Cell Theory.-Theoriginal theory of Lennard-Jones and Devonshire has been modified byseveral authors to allow for the interchange of molecules between cells,for the non-occupation of cells, and for interaction between molecules whichare not nearest neighbours. These modifications have been reviewed andgeneralised in excellent papers by Rowlinson and Curtiss and by de Boer,5where references to earlier work will be found.The equilibrium concentra-tion of unoccupied cells (or “ holes ”) is evaluated by the quasi-chemicalmethod (cf. Guggenheim 6). This, together with a knowledge of the volumeof the cell, gives the effective free volume per molecule. Rowlinson andCurtiss chose values for the cell volume to fit the experimental data, whilede Boer obtained a theoretical value by minimising the free energy. A moreelegant treatment by Kirkwood allows the deduction of the free-volumetheory from the Gibbs configuration integral, subject to well-defined approx-imations, and leads to an integral equation for the probability density ($)within each cell of a reference lattice. t,b is related to the free volume. Inthis work no attempt is made to evaluate the “ communal entropy.’’ Afirst approximation to a solution of this equation yields a partition function1 1 4 G.A. Miller and G. W. Murphy, J . Amer. Chenz. Soc., 1951, ‘73, 1871.115 S. J . Gregg and R. I. Razouk, J . , 1949, S 36.116 D. R. Glasson and S. J. Gregg, J . , 1953, 1493.117 K. Fischbeck and H. Spingler. 2. anoi’g. Chem., 1939, 241, 209.1 R. Eisenschitz, PYOG. Roy. Soc., 1952, A , 215, 29.2 E. N. da C. Andrade, ibid., p. 36.3 J. E. Lennard-Jones and A. F. Devonshire, ibid., 1937, A , 163,63; 1938, A , 1 6 4 , l ;1939, A , 169,317. J. S. Rowlinson and C. F. Curtiss, J . Chem. Phys., 1951,19, 1519.J. de Boer, PYOC. Roy. Soc., 1952, A , 215, 4.E. A. Guggenheim, “ Mixtures,” Oxford, 1952, pp. 38 ff.J.G. Kirkwood, J . Chem. Phys., 1950, 18, 380CRUICKSHANK AND EVERETT: THE THEORY OF LIQUIDS. 81identical with that of the original treatment.3 havedeveloped Kirkwood’s approach by assuming the position of a moleculewithin its cell to be governed by a Gaussian distribution function and byallowing for the non-occupation of cells. Careri has shown that this approx-imation is good up to the critical point, while Wood lo has given an exactsolution for rigid spheres, and obtained an equation of state similar to thatobtained by Buehler et aZ.ll on the basis of the Lennard-Jones and Devon-shire theory. Lund l2 has suggested that Wood’s solution may apply totypes of molecular packing of rigid spheres other than the face-centred cubic.In general the cell theory gives an entropy for the liquid state which istoo low, but the precise way in which this extra entropy can be introducedinto the model is uncertain.5 On the other hand the cell theory is still themost convenient on which to base a theory of solutions.Molecular Distribution Function Approach.-The thermodynamic func-tions of liquids are related by the Gibbs theory of the canonical ensembleto the molecular distribution functionsnh(rl, .. . r h ) = ___- .Mayer and CareriN ! Je--m/kT drh+l. . . dr, b-@lkT dr, . . . drN( N - h ) !(cf. de Boer 13), where nh(rl, . . . rh) is the probability density of findingan arbitrarily selected set of h molecules in the configuration rl, . . . rh ; ri isthe vector defining the position of the ith molecule relative to a chosenorigin, and @ is the potential energy of the whole system.When <D can berepresented as the sum of potential energies between pairs, a knowledge ofthe pair distribution functions (closely related to the radial distributionfunctions obtained from X-ray scattering) as a function of density enablesthe thermodynamic functions to be calculated. In the theories of Kirk-wood and Boggs,14 Born and Green,15 Yvon,lG and Mayer,l79 l8 systems ofintegro-differential equations for the radial distribution function, formulatedin several equivalent forms, are solved approximately by means of the so-called superposition approximation. This work, together with the conse-quences of the superposition approximation, has been reviewed by de Boer(cf.also refs. 19, 20). Salsburg, Zwanzig, and Kirkwood21 have derivedexact expressions for the molecular distribution functions in a one-dimen-sional fluid, the molecules interacting with a nearest-neighbour pair potential ;the superposition approximation is exact in this case. McLellan 22 hasexpanded Born and Green’s equation for the radial distribution function asa power series in density. For a fluid of rigid spherical molecules the resultsJ. E. Mayer and G. Careri, J . Chenz. Phys., 1952, 20, 1001.G. Careri, ibid., p. 1114. lo W. W. Wood, ibid., p. 1334.l3 J. de Boer, Rep. Prog. Phys., 1949,12,305.l1 R. J. Buehler, R. H. Wentorf, J. 0. Hirschfelder, and C. F. Curtiss, ibid., 1951,19, 61.l2 L. H. Lund, ibid., 1952,20, 1977.l* J.G. Kirkwood and E. M. Boggs, J . Chem. Phys., 1942, 10, 394.l5 M. Born and H. S. Green, Proc. Roy. Soc., 1946, A , 188, 10.l6 J. Yvon, “ Actualit& Scientifiques et Industrielles,” Herman et Cie., Paris, 1935,l7 J. E. Mayer and E. Montroll, J . Chenz. Phys., 1941, 9, 2.l9 B. R. A. Nijboer and L. van Hove, Proc. K. hTed. Ahad. Wet., B, 1951, 54, 256;21 Z. W. Salsburg, R. W. Zwanzig, and J. G. Kirkwood, J . Chew Phys., 1963, 21,pp. 203 ff.Phys. Review, 1952, 85, 777.1098.J. E. Mayer, ibid., 1947, 15, 187.G. S. Rushbrooke and H. I. Scoins, Phil. Mag., 1051, 42, 582.22 A. G. McLellan, Proc. Roy. Soc., 1952, A , 210, 50982 GENERAL AND PXYSICAL CHEMISTRY.are in good agreement with those of Kirkwood, Maun, and Alder,23 obtainedby numerical integration, and with those of Rushbrooke and Scoin~.~*Kirkwood, Lewinson, and Alder 25 have evaluated the radial distributionfunction in Kirkwood’s and in Born and Green’s approximations for Lennard-Jones and Devonshire’s (6 : 12) interaction.The thermodynamic functionsderived therefrom are compared with experimental results for liquid argon.Because the thermodynamic functions are very sensitive to small changesin the distribution function the agreement is not entirely satisfactory.Zwanzig, Kirkwood, Stripp, and Oppenheim 26 give a method of modifyingthe theoretical distribution function so that one thermodynamic quantity(e.g., the pressure) agrees with its experimental value. They suggest that,in the absence of exact theoretical distribution functions, these empiricallyadjusted functions should be used for correlating thermodynamic data andfor calculating transport properties.Rushbrcoke and Scoins 27 have shown that the second approximationto the direct correlation function of scattering theory may be used to im-prove Born and Green’s approximation to the radial distribution function,and that this leads to a critical point at which PV/h7kT = 6.Kirkwoodand Salsburg 2* have developed a new system of integral equations for themolecular distribution functions based on partial cluster expansions of theMayer type.l7> 29-31 The new cluster expansions are of finite degree andthus converge for all densities. Earlier, Katsura and Fujita 32 had suggestedthat the unsatisfactory nature of Mayer’s cluster integral treatment forliquids (cf.ref. 17) is a result of ignoring the volume dependence of the clusterintegrals, and this dependence is discussed.The main shortcoming of the radial distribution function approach is thatnumerical results for comparison with experiment can be obtained only by veryextensive computations or by making simplifying assumptions whose effectson the validity of the theory are difficult to estimate. Experimental verifica-tion may be facilitated by an equation due to Zimm 33 connecting the chemicalpotential, the compressibility, andone of the pair distribution functionintegrals.CrystaZZite Theory.-Several years ago O ~ k a w a , ~ ~ following Frenkel,35developed a semi-empirical theory in which a liquid at low temperatures isconceived as a mosaic of crystallites in contact along interfaces with whichare associated a boundary energy.An attempt was made to interpret theheat capacity of liquids, of which there is no satisfactory theory, and todiscuss the solid-liquid transition and the viscosity. Ookawa now claims 36that identification of the boundary energy with a free energy improves theagreement with experiment.23 J. G. Kirkwood, E. K. Maun, and B. J. Aider, J . Chenz. Phys., 1950, 18, 1040.24 G. S. Rushbrooke and H. I. Scoins, Nature, 1951, 167, 366.25 J. G. Kirkwood, V. A. Lewinson, and B. J. Alder, J . Chein. Phys., 1952, 20, 929.26 R. \V. Zwanzig, J. G. Kirkwood, K. F. Stripp, and I. Oppenheim, ibid., 1953, 21,28 J. G. Kirkwood and 2.W. Salsburg, Discuss. Faraday Soc., 1953, 15, 28.29 J. E. Mayer and S. F. Harrison, J . Chewa. Phys., 1938, 6, 87.3O J. E. Mayer, ibid., 1942, 10, (329;31 J. E. Mayer and M. G. Mayer,33 B. H. Zimm, ibid., 1953, 21, 934.34 A. Ookawa, .J. Phys. SOC. Japan, 1947, 2, 108; 1948, 3, 295; 1949, 4, 14.35 J . Frenliel, “ Kinetic Theory of Liquids,” Oxford, 1946.s 6 A. Oolrawa, J . Plays. SOC. Japan, 1952, 7, 543.1268. 2 7 G. S. Rushbrooke and H. I. Scoins, Pvoc. Roy. Soc., 1953, A , 216, 203.Statistical Mechanics,” Wiiey, New York, 1940,Ch. 13. 32 S. Katsura and H. Fujita, J . Chem. Phys., 1951, 19, 795CRUICKSHANK AND EVERETT: THE THEORY OF LIQUIDS. 83Associated Liquids.-Intermolecular potential energies which are func-tions of the relative orientations of the molecules have been reduced by Cookand Rowlinson 37 to a form similar to that for simple spherical moleculesby taking a statistical average over all configurations.On the other hand,Stockmayer38 and Rowlinson39 have evaluated the free energy of polarliquids as a sum of the free energy for the liquid, neglecting dipole inter-action, plus a dipole-interaction term. Pople 40 has used Kirkwood'smethod 7 for the first term, and a model of freely-rotating dipoles fixed onlattice sites for the second. Dipole interaction alone is found to be insuffi-cient to account for the difference between polar liquids and similar non-polar liquids. The theory has been extended 41 to the case of simultaneousdipole and quadrupole interactions, and some general conclusions are drawnapplicable to all types of directional forces.Liquid Mixtures-Regular SoZ~tions.-Guggenheim (ref.6, Ch. I11 andIV) has defined a strictly regular solution as one in which the molecules ofthe different species pack in the same manner as in the pure components,and in which the interaction between the species may be assumed not toalter the internal partition fuiictions or the acoustic factor in the translationalpartition functions (cf. Guggenheim 42), These restrictions reduce the cal-culation of the excess thermodynamic functions" of the solution to theevaluation of the configurational partition function. This was first doneon the basis of a fixed lattice model using the quasi-chemical approx-imation, which is equivalent to assuming the non-interference between pairsof occupied sites.Guggenheim et aL6 have shown that higher approx-imations, obtained by considering non-interference of larger local groupsof sites, do not differ greatly from the pairs approximation, but apparentlyconverge slowly. However has proved formally that they doconverge ultimately and has suggested an alternative generalisation of thequasi-chemical treatment which gives results identical with those of KikuchL44For two-dimensional lattices, for which exact results are known, Barker'smethod is an improvement on the quasi-chemical approximation, and itmay be presumed to be so in other cases also. The method used by Guggen-heim et aL6 to normalise the combinatory factor in regular assemblies hasbeen modified by Prigogine, Mathot-Sarolea , and van Hove.45 Onsager'smethod 46 is used to calculate the exact combinatory factor for square andtriangular plane lattices, and an extra parameter is introduced into theGuggenheim normalising factor to make it exact for the perfectly orderedstates, leading to a good estimation of the critical tem~erature.~737 D.Cook and J. S. Rowlinson, Proc. Roy. Soc., 1953, A , 219, 405.38 W. H. Stockmayer, J . Ckem. Phys., 1941, 9, 398.39 J. S. Rowlinson, Tyans. Faraday Soc., 1949, 45, 984.4o J. A. Pople, Proc. Roy. Soc., 1952, A , 215, 67.41 J. A. Yople, Discuss. Faraday Soc., 1953, 15, 35.42 E. A. Guggenheim, ibid., p. 24. 43 J. A. Barker, Proc. Roy. SOC., 1953, A , 216,45.44 R.Kikuchi, Phys. Review, 1951, 81, 988.45 I. Prigogine, L. Mathot-Sarolea, and L. van Hove, Trans. Faraday Soc., 1953,48, 485.4 7 L. Mathot-Sarolea, " Changements de phases," Compt. rend. 2e Reunion deChimie physique, SOC. Chim phys. (Paris 1952) [referred to later as " Changements dephases "I, p. 197. * The excess thermodynamic function is defined as the amount by which the valueof the corresponding function in a real solution exceeds that which i t would have if thecomponents formed a perfect solution.4 6 L. Onsager, Plays. Review, 1944, 65, 14084 GENERAL AND PHYSICAL CHEMISTRY.The quasi-lattice theory takes no account of the volume change of mixingand consequently is not satisfactory for evaluating thermodynamic functionsin systems where volume changes occur (cf.Longuet-Higgins *9. A steptowards overcoming this limitation has been taken by applying the celltheory of Lennard- Jones and Devonshire to regular solutions. Prigogineand Garikian 49 suppose each molecule to vibrate as a harmonic oscillatorwithin a cell, while Prigogiiie and Mathot 50 have used a square-well poten-tial, which they claim best fits the experimental data. Assuming randomdistribution of the various types of pairs, they have evaluated the volumeof mixing and its effect upon the heat of mixing and excess entropy ofregular solutions. Reasonable agreement with experiment has been ob-tained.51 The effect of non-random mixing has been studied by Sarolea,52but is considered not to affect the conclusions of the previousNasielski 53 has calculated the partial molar quantities corresponding to thismodel.Pople 54 has employed a 6 : 12 interaction in the cell theory ofregular solutions and has taken account of non-random mixing. Thetheory is claimed to be an improvement on that of Prigogine and M a t h ~ t , ~ obut is unable to account quantitatively for the experimental values ofthe excess entropy in some simple systems in which it is suggested thatmutual orientation effects are significant. R o ~ l i n s o n , ~ ~ in a more generaltreatment, expresses the free volume in terms of the cell dimensions for thepure components, the interaction energy, and the composition. The quasi-chemical approximation is again used. Four approximate solutions to theproblem are discussed.The first, by the assumption that the free volumesare independent of the mixing process, leads to the strictly regular solutiontheory, the second to Ono’s results,56 and the third to those of Prigogine andGa~-ikian.~~ The fourth, probably the most accurate, gives results for thevolume change on mixing in agreement with the conformal solution theory,57the latter being essentially a first-order perturbation from the ideal solution(cf. also Prigogine 58). Salsburg and Kirkwood 59 have extended theprevious work to multi-component mixtures, expanding the Gibbs configur-ation integral by the method of moments. Retention of the first moment(corresponding to random mixing) and use of an approximate smoothedpotential is said to yield the results of Prigogine and Garikian.49 An altern-ative approximation for the first moment, but with a 6 : 12 interaction, isderived.It is pointed out that until the restriction of equal molecular sizecan be overcome, and the problem of “ communal entropy ” solved, furtherelaboration of the theory is of minor practical importance. Rowlinson 60has attempted to assess the relative merits of the various cell theories byusing them to evaluate equations of state for a pure liquid. He concludes48 H. C. Longuet-Higgins, Ann. Reports, 1951, 48, 73.49 I. Prigogine and G. Garikian, Physica, 1950, 16, 239.6o I. Prigogine and V. Mathot, J . Chem. Phys.. 1952, 20, 49.51 V. Mathot and A. Desmyter, ibid., 1953, 21, 782.52 L. Sarolea, J . Chem. Phys., 1953, 21, 182; see also ref.9.53 J. Nasielski, ibid., p. 184.6 5 J. S. Rowlinson, Proc. Roy. SOL, 1952, A , 214, 192.S. Ono, Mem. Fac. Eng. Kyushu, 1950, 12, 201.5 7 H. C. Longuet-Higgins, Proc. Roy. SOC., 1951, A , 205, 247.5 8 I. Prigogine, “ Changements de phases,” p, 97.59 Z. W. Salsburg and J. G. Kirkwood, J . Chem. Phys., 1952, 20, 1538.6o J. S. Rowlinson, Discuss. Faraday SOG., 1963, 15, 52.54 J. A. Pople, Trans. Fwaduy SOC., 1953, 49, 591CRUICKSHANK AND EVERETT: THE THEORY OF LIQUIDS. 85that only the 6 : 12 interaction applied over all neighbours of a given mole-cule is likely to give satisfactory agreement with experiment. The restric-tion of equal molecular size (cf. ref. 59) has been relaxed in a new treat-rnent.61, 62 It is shown that the sign of the volume of mixing is dependenton the ratio of the molecular sizes and the nature of the intermolecularforces.Some anomalies in the earlier theory 49-51 are thereby removed.Rushbrooke63 has shown that Born and Green’s equations for binarymixtures are related to certain approximations to the integrals in Mayer andMontroll’s l 7 expansions of the radial distribution functions in powers ofdensity and composition. Ono 64 has used a method previously developed 65to derive the generalised Born and Green equations for solutions of electrolytesand non-electrolytes, using the superposition approximation. The resultingequations may be used to compute the deviation from ideal-solution be-haviour if the potentials of the mean force at infinite dilution are known.Adifferent approach has been developed by Kurata 66 who has derived on akinetic basis equations for the vapour pressure of a regular solution whichagree with those derived by statistical methods.Co-operatine Orientation Efects.-Miinster 6 7 has evolved a statisticaltheory of binary mixtures in which one component is subject to co-operativeorientation ; this has been applied to the system ben~ene-cyclohexane,~~ (c)and, with a semi-empirical correction to the theory of polymer solutions, tothe system benzene-rubber.68 In both cases there is good agreement withthe experimental excess free energy, the values of the molecular orient-ation energy of benzene which give the best fit being identical, and in fairagreement with that calculated quantum-mechanically .6g Tompa 70 hasapplied essentially the same concept to regular solutions, using the simplercombinatory method (ref.6, Ch. IV) instead of the local grand partitionfunction method.67 Barker 71 has used the conformal solution method 56to obtain the excess free energy of mixing of a binary system in which onecomponent displays weak dipole interaction, in terms of the properties ofthe pure dipolar component. In an approximate treatment of solutions ofalcohols, Barker 72 has applied a method of direct enumeration of configur-ational probabilities, similar to that used by Guggenheim (ref. 6, p. 193), toa formalised model of spherical molecules with tetrahedrally disposed inter-actions and arranged on a three-dimensional lattice.I t is concluded thata more general treatment of the three-dimensional array might providea satisfactory basis for the complete description of the experimental facts.The quasi-chemical treatment has been applied in a manner similar tothat of Munster 679 68 to this model, the approximations being checked againstthe conformal solution method.71 Reasonable agreement with the experi-mental data is found. A qualitative interpretation of both upper and lowerconsolute temperatures is also given. The accuracy of this quasi-chemicalI. Prigogine and A. Bellemans, J . Chem. Phys., 1953, 21, 561.62 I d e m , Discuss. Faraday Soc., 1953, 15, 80.63 G. S. Rushbrooke, Phil. Mag., 1952, 43, 1276.64 S. Ono, Prcg. Theor. Phys. Japan, 1951, 6, 447.6 5 I d e m , ibid., 1950, 5, 822.6 6 M. Kurata, Bull. Soc. Chem. Japan, 1952, 25, 363.67 A. Miinster, ( a ) Trans. Faraday Soc., 1950, 48. 165; ( b ) 2. Electrochem., 1950, 54,68 Idena, Trans. Favaday SOC., 1953, 49, 1.69 J. de Boer, ibid., 1936, 32, 10. ‘O H. Tornpa, J . Chenz. Phys., 1963, 21, 250.71 J. A. Barker, ibid., 1951, 19, 1430.71 I d e m , ibid., 1952, 20, 794. 73 Idem, ibid., p. 1526.443; ( c ) 2. Physikal. Chem., 1950, 196, 10686 GENERAL AND PHYSICAL CHEMISTRY.approximation has been examined 74 and higher approximations are derivedby the methods quoted in ref. 43. The quasi-chemical approximation forpairs is satisfactory for lattices other than close-packed. Barker 75 hasalso calculated the electrostatic energy of a system of molecules with per-manent and induced dipoles as a power series in the polarisabilities, thefirst and second moments of the electrostatic energy being evaluated to thefirst order in polarisability. These are used to give approximate expressionsfor the contribution of the electrostatic forces to the free energy of polarliquids and solutions. Pople 41 has extended his theory 40 of associated liquidsto include mixtures, while Sarolea-Mathot, 76 developing earlier work,77 hasdiscussed the thermodynamic properties of associated solutions in terms of thechange in the number of orientations on formation of a molecular complex.Mixtures of Single and Mu.tiple Molecules. Polymer Solutions.-The majordifficulty in calculating the thermodynamic properties of these mixturesremains that of deriving an adequate expression for the free energy of aso-called athermal solution, in which all configurations have the same internalenergy. From this it is possible,6 by using the quasi-chemical approxim-ation in pairs, to calculate the thermodynamic properties of interactingassemblies. Rushbrooke, Scoins, and Wakefield 78 have expanded therestricted grand partition function for an assembly of N , monomers andN, r-mers occupying ( N , + rN,) sites by Mayer’s cluster integralExpressions are derived for the partial vapour pressures of the two com-ponents as a power series in the volume concentration 0 of the larger species.The coefficients of successive powers of 8 are shown to be analogues of thefunctions P k of Mayer’s theory. The simplest approximation to P k leads toFlory’s vapour pressure equations, and the next most simple to those ofMiller and Guggenheim (cf. ref. 6, pp. 205 ff., pp. 193 ff.). An accurateexpression for p k is given, and for a monomer-dimer solution a sufficient numberof p’s have been calculated to give close estimates of the best solution withinthe limitations of the model. The theory gives good agreement with theexperimental values of the activity coefficient of benzene in mixtures ofbenzene and di~henyl.7~ Guggenheim 80 has pointed out (cf. McMillan andMayer 81) that in the evaluation of the cluster integrals Zimm 82 and Hug-gins 83 treat the solvent effectively as a continuum. This is justified onlyif the solute molecules are very much larger than those of the solvent. Ifthis is not so it is necessary to use a lattice model to obtain tractable mathe-matical relations. The cell theory has been extended to mixtures of r-mersand monomers 843 85 by assuming a quasi-crystalline lattice with the elementsof the r-mer as interacting point centres. The first paper assumes a square-well cell potential, and the second a potential of the harmonic-oscillatortype. In both cases the thermal factor is introduced through the quasi-74 J. A. Barker, J . Chenz. Phys., 1953, 21, 1391.7 5 Idem, Proc. Roy. SOL, 1953, A , 219, 367.76 L. Sarolea-Mathot, Trans. Faraduy SOL, 1953, 49, 8.7 7 I. Prigogine, V. Mathot, and A. Desmyter, Bull. SOC. chim., Belg., 1949, 58, 647.78 G. S. Rushbrooke, H. I. Scoins, and A. J. Wakefield, Discuss. Furaduy SO^.,O 9 D. H. Everett, ibid., p. 114.s1 W. G. McMillan and J. E. Mayer, J . Chem. Phys., 1945, 13, 276.8 2 B. H. Zimm, ibid., 1946,14,164.84 V. Mathot, “ Changements de phases,” p. 115.6 5 I. Prigogine, N. Trappaniers, and V. Mathot, Discuss. Faraday SOC., 1953, 15, 93.1953, 15, 57.E. A. Guggenheim, ibid., p. 68.83 M. L. Huggins, J . Phys. Chern., 1948, 52,248CRUICKSHANK AND EVERETT: THE THEORY OF LIQUIDS. 87chemical method (cf. ref. 6, Ch. XI). This treatment makes it possible tostudy the excess thermodynamic functions which result from the changesin the mean field caused by mixing. It is shown 84 that the contribution tothe excess properties caused by the variation of mean field with concen-tration can be quite large in the case of r-mer-monomer mixtures. Analternative approach which avoids the concept of the potential of the meanforce has been given by Tchimura.86Longuet-Higgins 87 has introduced an ingenious approximation basedon the assumption that the probability distribution function for a pair ofends belonging to different molecules depends only on temperature anddensity and not on the lengths of the molecules. He obtains an expressionfor the Gibbs free energy of mixing in a binary mixture of different types ofchain molecules which is independent of the restrictive assxmptions implicitin the quasi-lattice theory, provided that the two types of molecules aresufficiently long. I t also provides a theoretical interpretation of Brransted'sprinciple of congruent mixtures.88Critical Phenomena.-There are two opposing views of the nature of thecritical region, and the situation has been rather obscured by some ambiguityin the experimental findings. In a comprehensive review 89 Mayer hasre-affirmed his opinion that the liquid-vapour co-existence curve in the P-Vdiagram is flat-topped and that isotherms have a horizontal portion for arange of temperature above that at which the meniscus disappears. Asimilar behaviour is predicted for the co-existence curve of two liquid phasesat an upper critical solution temperature.have investigated the co-existence curve of very pure xenon in both long andshort tubes mounted vertically and conclude that in the limiting case of atube of zero height there would be a unique critical point. Further work 91with a long thin tube mounted alternately in vertical and horizontalpositions confirms the large influence of gravitation on the form of the co-existence curve. Murray and Mason ga have studied the gravitationaleffect in ethane by light-scattering methods, and Schneider 91 that in xenonby using radio-xenon as a tracer. MacCormack and Schneider 93 found noevidence for the anomalous second-order transition in sulphur hexafluorideabove the temperature at which the meniscus disappears. Co-existencecurves of binary liquid mixtures do not seein to have been studied withsufficient precision to allow any final conclusions to be reached.94 Theultrasonic absorption of xenon,95 sulphur he~afluoride,~~ and some binarysystems 97 has been studied. A maximum in the attenuation at the criticalWeinberger and Schneider8 6 H. Ichimura, J . PJzys. SOC. Japan, 1952, 7, 152.8 7 H. C. Longuet-Higgins, Discuss. Faraday Soc., 1953, 15, 73.89 J . E. Mayer, " Changements de phases," p. 35.91 W. G. Schneider, " Changements de phases," p. 69.92 F. E. Murray and S. G. Mason, Canad. J . Clzem., 1962, 30, 550.s3 K. E. MacCormack and W. G. Schneider, ibid., 1951, 29, 699.94 R. W. Rowden and 0. K. Rice, " Changements de phases,s5 A. G. Chynoweth and W. G. Schneider, J . Chein. Phys., 1952, 20, 1777.96 W. G. Schneider, ibid., 1950, 18, 1300; Canad. J. C h e w , 1951, 29, 243.9 7 A. G. Chynoweth and W. G. Schneider, J . Chcm. Phys., 1951, 19, 1566;20, 760; G. F. Alfrey and W. G. Schncider, Discziss. Faraday SOC., 1053, 15, 218.J. N. Brernsted and J. Koefoed, KzZ. Danske Viaem. Selsk., 1946, 26, no. 17.M. A. Weinberger and W. G. Schneider, Canad. J . Chem., 1952, 30, 422.p. 78; D. Atach and0. K. Rice, Discuss. Faraday Soc., 1953, 15, 210; B. H. Zimm, J . Chew. ,rhys., 1952,20, 538. pp. 66, 91. See also general discussion of papers in " Changements de phases,195288 GENERAL AND PHYSICAL CHEMISTRY.point is ascribed to configurational relaxation processes. Michels andStrijland 98 have shown that near the critical point the molar heat capacitya t constant volume of carbon dioxide can have abnormally large values. Theresults are explained in terms of clusters in the gas and holes in the liquid.Calorimetric determinations of the molar heat capacity a t constant pressurenear the critical point of binary solutions have also been reportedJg9 andsimilar phenomena are observed. The viscosity of binary liquid systemsalso shows a maximum near the critical temperature.100There have not been any recent purely theoretical developments con-cerning the existence of an anomalous region near the critical point althoughRocard lol has claimed that by an empirical modification of the law ofattraction between hard spheres it is possible to account for Schneider’sexperimental results. The experimental evidence seems to indicate, how-ever, that the anomalous region, if it exists, occupies an exceedingly smalland possibly undetectable area of the P-V diagram. In a series of briefpapers van Dranen lo2 has investigated the hypothesis that at the criticalpoint the kinetic energy of the molecules is equal to their negative potentialenergy so that the total internal energy, relative to the molecules at rest atinfinite separation, is zero. Calculations based on models of the liquid andthe gas state support this idea, but it is too early to assess its validity. Notheoretical basis for it has been advanced.Further developments have been made in the theory of critical-solutiontemperatures in binary liquids especially with reference to lower consolutepoints. A discussion of the cell model lo3 shows that molecules withspherically-symmetrical force fields cannot show a lower critical temperatureand that this phenomenon is associated with the existence of orientationeffects. Barker and Fock l o 4 have made a more detailed study of thisproblem in relation to several specific models. The thermodynamic char-acteristics of systems exhibiting critical solution phenomena have also beendiscussed. lo5A. J. B. C.D. H. E.A. S. CARSON.E. COLLINSON.A. J. B. CRUIKSHANK.F. S. DAINTON.D. H. EVERETT.K. J. IVIN.J. W. LINNETT.F. C. TOMPKINS.D. A. YOUNG.gs A. Michels and J. Strijland, “ Changements de phases,” p. 87.O9 V. K. Semenchenko and E. L. Zorina, Doklady Akad. Nauk S.S.S.R., 1950, 73,2 ; V. K. Semenchenko and V. P. Skripov, Zhur. Fiz. Kkim., 1951, 25, 362; G. Jura,D. Fraga, G. Maki, and J. H. Hildebrand, PVOC. Nut. Acad. Sci., 1953, 89, 19.loo V. K. Semenchenko and E. L. Zorina, ?;kZady ARad. Nauk S.S.S.R., 1951,80,903.l01 Y. Rocard, “ Changements de phases,lo2 J. van Dranen, J . Chem. Phys., 1952, 20, 1175; 1953, 21, 567, 1404.lo3 I. Prigogine, ‘‘ Changements de phases,” p. 95; A. Bellemans. J. Chem. Phys.,lo* J. A. Barker and W. Fock, D~SCUSS. Faraduy SOC., 1953, 15, 188.Io5 J. L. Copp and D. H. Everett, ibid., p. 174.p. 45.1953, 21, 369