ANNUAL REPORTSON THEPROGRESS OF CHEMUTRYGENERAL AND PHYSICAL CHEMISTRY1. INTRODUCTIONTHIS year's General and Physical Chemistry Section is a collection of reportson separate and limited topics rather than one of general reports on broadfields such as reaction kinetics. Consequently the coverage this year is morespecialised and therefore, in some directions, incomplete. However, it isintended that, over two or three years, all important and interesting physico-chemical subjects will be dealt with in Annual Reports.This year publications on ion association and acid-base equilibria inionic solutions have been surveyed as well as work on electrode processes,particular attention being given to adsorption problems. In the kineticsfield there are sections devoted to transformations occurring in organicmolecules and radicals. Here the Report on ion-molecule reactions willbe of interest to radiation chemists. Related to these is the Report onthe many observations made recently on intermolecular energy transfers.This deals with both liquid and gaseous systems.There is also a recordof the observations that have been made on polymerisations induced byradicals. In the field of molecular structure there is a Report on both theobservations and the theory of the intensities of infrared absorption bands.This deals first with gases and then with the more complicated problem ofliquids and solutions. In addition an account is given of the work that hasbeen done to determine precise shapes and force fields of relatively simplemolecules.J.W. L.2. ACID-BASE EQUILIBRIATHIS Report deals with proton-transfer equilibria in aqueous and non-aqueous solvents. The recently published tables of stability constants ofmetal-ion complexes include values for the proton complexes and so alsoconstitute a valuable collection of acidity constants. Papers of generalinterest report a differential potentiometric titration method in whichhydrogen electrodes are used for comparing the purity of acids to a fewparts in 100,000, new standards for pH measurements3 from 60 to 05",J.,,Bjerrum, G. Schwarzenbach, and L. G. Silldn, " Stability Constants.R. G. Bates and E. Wickers, J . Res. Nat. Bur. Stand., 1957, 59, 9.V. E. Bowers and R. G. Bates, ibid., p. 261.Parts Iand 11, Chem.SOC. Special Publ., 1957, No. 6 ; 1958, No. 78 GENERAL AND PHYSICAL CHEMISTRY.H* + H, __t H, + Ha Hammond gives a qualitative discussion ofappropriate models for the transition complex. The transition-state theoryhas come under fresh fire.93 10111Papers upon the theory of chain reactions have discussed the principleand conditions of applicability of the Semenov-Bodenstein method of quasi-stationary states l2 and an estimate of the accuracy of the method,13 con-secutive reactions and chain reactions,l* catalysis and inhibition of chainreactions,15 and the action of inhibitors upon branched-chain reactions.16In the analysis of experimental results, Wideqvist l7 has emphasised theusefulness of substitutions of the form 8 = f(c)dt, f(c) being a suitablearbitrary function of the coficentration and 8 being obtained graphically.Tobin l8 has indicated methods of treating second-order reactions which areautocatalytic or reversible.The applications of least-square deviations tothe evaluation of rate constants have been discu~sed.1~~ 2O Janz and Wait 21have justified the use of space-time yield as measures of velocities of reaction,provided certain experimental conditions are fulfilled. Other short paperson intramolecular energy transfer,22 methods of calculating collision dia-meters,= revised values of diffusion coefficients of certain hydrocarbons,24rates near eq~ilibrium,,~ kinetics in non-isothermal systems,26 kinetics andthermodynamics of irreversible systems,27 and the concept of rate ofreaction 28 have appeared.Some fresh complexities have been suggested in the kinetics of somereactions previously thought simple.Benson and Srinivasan 29 have arguedthat the high temperature coefficients of the forward and backward velocityconstants in the gaseous reaction H, + I, e- 2HI indicate that the reactionproceeds by concurrent bimolecular and chain processes, but their sugges-tions cannot properly be tested because of the scatter of the available dataon the two velocity constants a t different temperatures. In this connectionPheloux 3O suggests a differential method of analysing Bodenstein's data onthe decomposition reaction which gives more consistent results for thevelocity constant. The oxidation of nitric oxide by oxygen has been studiedG. S.Hammond, J . Amer. Chem. SOL, 1955, 77, 334.N. I. Kobozev, Zhur. $2. Khim., 1954, 28, 2067.lo V. A. Pal'm, ibid., 1955, 29, 1116.l1 V. A. Roiter, Ukrain. khim. Zhur., 1955, 21, 296.12 Yu. S. Sayasov and A. B. Vasil'yeva, Zhur. $2. Khirn., 1956, 29, 802.l3 I. F. Bakhareva, Doklady Akad. Nauk S.S.S.R., 1955, 102, 1151.l4 E. Abel, Osterr. Chem.-Ztg., 1955, 56, 305.l6 2. G. Szabo, P. Huhn, and A. Bergh, Magyar Kem. Folyoimt, 1955, 61, 137,l6 D. G. Knorre, Zhur.$z. Khim., 1955, 29, 1285.17 S. Wideqvist, Arkiv Kemi, 1955, 8, 325.18 M. C. Tobin, J . Phys. Chem., 1955, 59, 799.la S. Huyberechts, A. HalIeux, and P. Kruys, Bull. SOC. chim. belges, 1955, 84, 203.2O D. F. DeTar, J . Amer. Chem. SOL, 1955, "7, 2013.21 G.J. Janz and S. C. Wait, jun., J . Chem. Phys., 1955, 25, 1650.22 H. 0. Pritchard, Rec. Trav. chim., 1955, 74, 779.Zs E. Bauer, J . Chem. Phys., 1955, 23, 1087.24 G. A. McD. Cummings and A. R. Ubbelohde, J., 1955, 2524.25 A. PBneloux, Comfit. vend., 1955, 240, 758.26 H. Gaensslen and H. A. E. Mackenzie, J . Appl. Chem., 1955, 5, 552.27 A. PBneloux, Compt. rend., 1954, 239, 1379.28 J . E. Verschaffelt, Bull. CLasse Sci., Acad. roy. Be&., 1956, 4l, 316.29 S. W. Benson and R. Srinivasan, J . Chem. Phys., 1955, 23, 200.30 A. Peneloux, Compt. rend., 1955, 240, 2142.English summary, 145PRUE : ACID-BASE EQUILIBRIA. 9strength, it is said to have been obtained by " extrapolation to infinitedilution ". This phrase is misleading, for it implies that the pK, valueobtained is necessarily independent of assumptions about the activitycoefficients of the ions, which is only true when measurements can be madein very dilute solutions; small changes in the value assumed for a' canoften be compensated by a change in cp alone because mathematicallyI"(1 + Ba'D) N I* - Ba'I.* The failure of plots of pKa' against I fordifferent choices of a' to converge to a common value of pKa is most seriousfor rather strong acids and bases.loU In these cases, dissociation is only in-complete at high ionic concentrations, and the buffer ratio cannot be setequal to its stoicheiometric value; to calculate the ratio a knowledge of theconcentration of hydrogen or hydroxyl ions is required which in turn necessi-tates assuming a value for fHfcl.Hamerll has drawn attention to thissituation for the bisulphate ion. New measurements on this acid arereported by Nair and Nancollas,12 who, following C. W. Davies, set-logl,fi = xi2A{(I*/(l + 14) - 0.201) throughout. The acidity constantsobtained a t 25", 35", and 45" agree with those obtained by an indicatormethod13 within the outer limit of error (6%) suggested for the latterresults, but there are differences of 15 and 20% a t 15" and 5' respectively.Bates and Schwarzenbach l4 show how in cell measurements the bufferratio can in suitable cases be advantageously measured spectrophoto-metrically. Acidity constants and thermodynamic parameters are reportedfor the second acid dissociation of glycerol l-phosphate l5 and the ion l6H2P0,-, the hydrogen I calomel cell being used for the latter study.Nashand Monk l7 have investigated the effect of up to 0.6 mole 1.-l of carboxylicacids on the E" values of the hydrogen I silver-silver chloride cell, and theextent of acid dimerization. The acidity and basicity constants of $-amino-benzoic acid a t 25" have been measured,l* the glass electrode used beingcarefully calibrated against a hydrogen electrode. The acidity constants ofthe isomeric ephedrinium ions [C,H,*CH(OH)*CHMe-NH,Me] have beenmeasured l9 at 0-60" with hydrogen-electrode concentration cells in whichthe effects of junction potentials due to a potassium chloride salt bridge areeliminated by extrapolation. The thermodynamic parameters are evaluatedand discussed.Purlee and Grunwald 20 have made precision measurements on hydro-loaE.J. King and G. W. King, J . Amer. Chem. SOL, 1952, 74, 1212.l1 W. J. Hamer, Abs. Symp., Structure of Electrolytic Solutions, Washington, 1957,l2 V. S. K. Nair and G. H. Nancollas, J . , 1958, 4144.l3 C. R. Singleterry and I. M. Klotz, Theses, Chicago, 1940; R. A. Robinson andR. H. Stokes, '' Electrolyte Solutions," Butterworths, London, 1955, p. 374.l4 R. G. Bates and G. Schwarzenbach, Helv. Chim. Acta, 1954, 37, 1069.l5 S. P. Datta and A. K. Grzybowski, Biachem. J., 1958, 69, 218.l6 A. K. Grzybowski, J. Phys. Chem., 1958, 63, 550, 555.l7 G. R. Nash and C. B. Monk, J., 1957, 4274.l8 M. L. Deviney, R. C. Anderson, and W. A. Felsing, J . Amer. Chem.Sac., 1957,l9 D. H. Everett and J. B. Hyne, J., 1958, 1636.2O E. L. Purlee and E. Grunwald, J . Amer. Chem. Sac., 1957, 79, 1366, 1372.* Similar comments are relevant concerning the determination of any equilibrium+p. 47.79, 2371.constant in which ions are involved10 GENERAL AND PHYSICAL CHEMISTRY.chloric and carboxylic acids in dioxan-water mixtures with a cell incor-porating glass and silver-silver chloride electrodes; the latter have the silverin mirror form and are reported to reach equilibrium very quickly even invery dilute solutions. The same technique 21 has been used to studycarboxylic acids and anilinium ions in methanol-water mixtures, and theacidity constants for acetic acid over the entire range of composition O-%yOmethanol agree 22 with values found from conductance measurements 23(mean deviation 0.017 in pKa).Measurements with conventionalhydrogen I silver-silver chloride cells of the dissociation of hydrochloric acidare reported in ethanol,= acet0ne,~5 ketone-water mixtures,26 and dioxan-water 27 mixtures. The last paper also reports acidity constants for formic,acetic, and propionic acids in the same solvent. Dunsmore and Speakman 28have measured the dissociation constant of benzoic acid in water and inwater-dioxan by e.m.f. and conductance methods.(b) Spectrophotometric methods. Robinson 29 and his collaborators havedeveloped a spectrophotometric method for determining acidity constantsin which the degree of dissociation of the acid is spectrophotometricallydetermined in a buffer of known pH; it has been applied to a wide rangeof weak organic acids.Kok-Peng Ang30 has tested with isophthalic acida new method for spectrophotometrically determining overlapping acidityconstants of dibasic acids. Other spectrophotometric determinations ofacidity constants are for phenol, cresols, and xylenol~,~~ the hydrogensulphate ion in aqueous methanol,32 2,4-dinitrophenol and chloroacetic andpropionic acids in aqueous ethanol,= hydroxycoumarins,34 and NN-di-methylaniline in water and and ~ater-dioxan.~~(c) Conductance methods. Feates and Ives36 report a determination ofthe acidity constants of cyanoacetic acid at 5" intervals from 5 to 45",accurate to 0.005% in In K. The thermodynamic parameters are discussedin relation to the solvent structure.Shedlovsky reports 37 acidity constantsa t 25" for acetic acid in methanol-water covering the entire range of com-position O - l O O ~ o of methanol. Kortiim and Buck 37a have made measure-ments at 25" on 2,6-dinitrophenol in methanol-water and ethanol-water.21 A. L. Bacarella, E. Grunwald, and G. P. Marshall, J . Org. Chew., 1955, 20, 747.22 A. L. Bacarella, E. Grunwald, G. P. Marshall, and E. L. Purlee, J . Phys. Chew.,23 T. Shedlovsky and R. L. Kay, ibid., 1956, 60, 151.24 H. Taniguchi and G. J. Janz, ibid., 1957, 61, 688.25 D. H. Everett and S. E. Rasmussen, J., 1954, 2812.26 D. Feakins and C . M. French, J., 1957, 2284, 3168.27 S. S. Danyluk, H. Taniguchi, and G. J. Janz, J . Phys. Chenz., 1957, 61, 1679.28 H.S. Dunsmore and J. C. Speakman, Trans. Faraduy Soc., 1954, 50, 236.2s R. A. Robinson, Abs. Symp., Structure of Electrolytic Solutions, Washington,30 Kok-Peng Ang, J . Phys. Chew., 1958, 62, 1109.32 J. I. Evans and C . B. Monk, ibid., 1953, 49, 415.33 W. D. Bale and C. 73. Monk, ibid., 1957, 53, 450.34 B. N. Mattoo, ibid., 1958, 54, 19.35 A. V. Willi, Helv. Claim. A d a , 1957, 40, 2019.313 F. S. Feates and D. J. G. Ives, J . , 1956, 2798.a7 T. Shedlovsky, Abs. Symp., Structure of Electrolytic Solutions, Washington,a7' G. Kortum and M. Buck, 2. Elektrochem., 1958, 62, 1083.1958, 62, 856.1957, p. 90.E. F. G. Herington and W. Kynaston, Trans. Furaday Soc., 1957, 53, 138.1957, p. 94PRUE ACID-BASE EQUILIBRIA. 11Conductometrically-determined acidity constants are reported 38 for sub-stituted benzoic acids and for nitrophenols in water.The Hydrolysis of Cations.-Published data for the acidity constants ofhydrated cations in water have been collected and discussed.39 The simplepicture of aquo-cations as Bronsted acids has been considerably modifiedrecently by the realisation that, even in dilute solutions, polymerization ofthe basic species MOHn+ to form polynuclear species often occurs throughformation of dihydroxyl (or oxygen) bridges.An impressive series of papershas come from Sillen’s school in Stockholm. The equilibria involved areoften complicated, and measurements by e.m.f. cells of hydrogen-ion and,when possible, free metal-ion concentrations have been made in constantionic media (NaC104-HC104) ; the effectiveness of this device in maintainingconstant activity coefficients and eliminating the effects of junction poten-tials has been critically examined.40 The 21st paper in the series,4l whichdeals with the hydrolysis of the stannous ion in 3~-perchlorate medium at25”, illustrates well the methods used in obtaining and analysing the expen-mental results.Stringent precautions were necessary to prevent the form-ation of the stannic ion, which is a stronger acid than the stannous ion. Atstannous concentrations 0~0025-0~040~, the principal hydrolytic equili-brium was 3Sn2+ + 4H20 Sn3(OH)42+ + 4H+, but SnOH+ andSn2(OH)22+ were also formed. Complexes of the general formula M[(OH),M],are formed on hydrolysis of FeIII, CuII, ScIII, InIII, VOII, and U0;I.Thecriterion for the existence of the various species is the constancy of law-of-mass-action expressions involving these species, and when several equilibriaare involved small experimental errors can be seriously misleading. Thus,earlier conclusions about the species present in bismuth(m) solutions arefound to have been vitiated by neglect of the effect that the basicity ofbenzoquinone can exert in sufficiently acid solutions on the behaviour of thequinhydrone electrode. Some recent measurements 42 with glass and bis-muth amalgam electrodes a t bismuth concentrations from 0.0001 to 0.050~show that the main hydrolysis product is Bi6(OH)126+ with some BiOH2+.This conclusion agrees with that of Holmberg, Kraus, and Johnson,43 who,continuing studies of the hydrolysis products of metal ions by ultracentrifugemeasurements, concluded that bismuth( 111) forms a complex containing5 or 6 bismuth atoms.report the main product ofberyllium-ion hydrolysis at concentrations from 0-001 to 0 . 1 0 ~ to beBe3(OH),3+ with some Be20H3+ and Be(OH),. It remains to be examinedto what extent change of the anion of the constant-ionic medium, which inthe Stockholm work is universally perchlorate, changes the nature anddistribution of multiply-charged hydrolysis products.The formation of dimeric Fe2(OH)24+ on hydrolysis of ferric ions has38 J. F. J. Dippy, S. R. C . Hughes, and J. W. Laxton, J., 1956, 2995.39 F. Basolo and R. G. Pearson, “ Mechanisms of Inorganic Reactions,” John Wiley,40 G.Biedermann and L. G. Sillen, A r k i v Kemi, 1953, 5, 425.41 R. S. Tobias, Acta Chem. Scand., 1958, 12, 198.42 A. Olin, ibid., 1957, 11, 1445.43 R. W. Holmberg, K. A. Kraus, and J. S. Johnson, J . Amer. Chem. SOL, 1956,44 H. Kakihana and L. G. Sill& Acta Chem. Scand., 1956, 10, 985.Kakihana and SillenInc., New York, 1958, p. 387.78, 550612 GENERAL AND PHYSICAL CHEMISTRY.recently been studied spectrophotometrically by M i l b ~ r n , ~ ~ who has obtainedthermodynamic quantities for the equilibria. Spectrophotometry of cobalticperchlorate solutions, and kinetic observations of the rate of oxidation ofwater by cobaltic ions, are consistent 46 with the predominance of a dimerichydrolysis product CO,(OH)~~+.Polynuclear complexes are not formed onhydrolysis of mercuric ions ; supersaturated solutions 47 of mercuric hydr-oxide have been prepared and it is found that Hg(OH), is about 25 timesweaker as a base than HgOH+, which means that hydrolysed solutions con-tain very little of the latter ion. Other studies of the hydrolysis of cationshave been recently reported for thorium(~v),~~ plutonium(~v),~~ zir-c o n i u m ( ~ ~ ) , ~ ~ and the uranyl ion; 51 polynuclear complexes are also some-times formed on hydrolysis of chelate c ~ m p l e x e s . ~ ~ ~ ~ ~Oxyacids in Aqueous Solution.-(a) Weak acids. A flow apparatus inwhich the pH of a solution can be measured 10" sec. after mixing potassiumhydrogen carbonate and hydrochloric acid enabled Meier and Schwarzen-bach 54 to measure the acidity constant of H2C0 ( K = 3.58 at 20°, I = 0.1mole 1.-l) ; the value agrees with one rep~rtid!~ earlier from high-fieldconductance measurements.It seems likely that the flow apparatus willbe useful for the study of the initial dissociation of acids whose correspondingbases then polymerize; information has already been obtained about theacid dissociation of molybdic and tungstic acids.56 The infrared absorptionspectra of aqueous solutions of carbon and sulphur dioxides confirm thatthey are present mostly as CO, and SO, re~pectively.~~ A similar conclusionis reached by Falk and G i g ~ & e , ~ ~ who estimate that any H,S03 content iscertainly less than 1/30th of that of SO,, and probably much less.Solutionsof silicates undoubtedly contain polymers, but an estimate of the acidity con-stant of the unstable monomeric silicic acid, prepared by hydrolysis of themethyl ester in situ, has been reported.59 Bunton and Stedman 6o concludefrom ultraviolet spectrophotometry that molecular nitrous acid in aqueousperchloric acid is protonated and dehydrated as the acidity of the mediumincreases. Acidity-constant measurements are also reported for the follow-ing acids : arsenious,61 phosphoric,62 the hydrogen chromate germanic45 R. M. Milburn, J . Auuter. Chem. SOC., 1957, 79, 537.46 J. H. Baxendale and C. F. Wells, 'Trans. Faraday SOC., 1957, 53, 800.47 G. Anderegg, G. Schwarzenbach, M. Padmoyo, and 0. F. Borg, HeZv. Chim. A d a ,48 J.Lefebvre, J . Chim. phys., 1955, 55, 227.49 S. W. Rabideau, J . Amer. Chem. SOC., 1957, 79, 3675.A. J. Zielen and R. E. Connick, ibid., 1956, 78, 5785.51 J. A. Hearne and A. G. White, J., 1957, 2168.52 R. F. Bogucki and A. E. Martell, J . Amer. Chem. SOC., 1958, 80, 4170.53 H. Jonassen and G. J. Strickland, ibid., p. 312.54 J. Meier and G. Schwarzenbach, Helv. Chim. Acta, 1954, 40, 907.55 D. Berg and A. Patterson, J . Amer. Chem. SOC., 1953, 75, 5197, 5731.56 J. Meier and G. Schwarzenbach, J . Inorg. Nuclear Chem., 1958, 8, 302.57 L. H. Jones and E. McLaren, J . Chem. Phys., 1958, 28, 995.58 M. Falk and P. A. Gigdre, Canad. J . Chem.. 1958, 36, 1121.59 R. Schwarz and W. D. Muller, 2. anorg. Chem., 1958, 296, 273.8o C. A. Bunton and G. Stedman, J., 1958, 2440.G.Jander and H. Hofmann, 2. anorg. Chem., 1958, 296, 134.62 J. S. Elliot, R. F. Sharp, and L. Lewis, J . Phys. Chew., 1958, 62, 686.63 J. R. Howard, V. S. K. Nair, and G. H. Nancollas, Trans. Faraday SOC., 1958,1958, 41, 988.54, 1034PRUE : ACID-BASE EQUILIBRIA. 13and t e l l ~ r i c , ~ ~ hypochlor~us,~~ lauric and myristic,66 i s o c i t r i ~ , ~ ~ and a-acetyl-succinic.68 Polymerization to form complex anions has been studied in thecase of borates 69 and vanadium(v); 70 in the last paper the Rossottis haveapplied potentiometry and spectrophotometry to unravelling a complex situ-ation. Heats of neutralization have been measured directly for carboxylicacids by a microcalorimetric method,71 and for ethylenediaminetetra-aceticacid.72 Conclusions about the detailed structures of the various speciesderived from ethylenediaminetetra-acetic acid have been drawn from anexamination of the thermodynamic parameters.In concentrated solutions of the '' strong " acids,e.g., sulphuric, nitric, and perchloric, characteristic Raman lines occur foreach molecular species ; with photoelectric recording instruments, theintegrated intensity of a line can now be accurately determined and seemsto be rather exactly proportional to the concentrations of the species towhich it relates and independent of environmental influences (the height ofthe line is Estimates by Raman studies of the amounts of thevarious species present agree well with those determined from nuclearmagnetic resonance shifts,74 which appear to be influenced only by changesin the immediate environment of the nucleus concerned.In solutions ofsulphuric, perchloric, hydrochloric, and hydrobromic acids, Bascombe andBell 75 conclude from the concentration dependence of Hammett acidityfunctions that the oxonium ion is trihydrated, ie., OH,+(OHJ3, presumablyas a result of the formation of strong hydrogen bonds. The infrared spectraof the ions H,O+ and D30+ have been studied in aqueous solution.76Equilibria in Non-aqueous Solvents-(a) Aprotic solvents. In aproticsolvents proton transfers between uncharged molecules produce ion-pairs.Pearson and Vogelsong 77 have made spectrophotometric measurements ofthe reactions between aliphatic amines and 2,4-dinitrophenol in chloroform,chlorobenzene, ethylene dibromide, n-heptane, benzene, dioxan, and ethylacetate.The solvent has a marked effect on the relative basic strengths ofthe amines; tertiary bases are strongest in the first three solvents, secondarybases in the next three, and primary bases in ethyl acetate. The molecularinterpretation of the results is discussed. Bayles and Chetwyn 78 report athorough study of the equilibria between mono-, di-, and tri-n-butylaminewith 2,4-dinitrophenol in chlorobenzene froin 20 to 60". Continuing earlier(b) Strong acids.72 GENERAL AND PHYSICAL CHEMISTRY.those of silver iodide.72 In the case of silver sulphide this also applies tothe variation of the capacity of the inner region with surface charge(cf. Grahame73) and the structures of the double layers must be closelysimilar.Neutral molecules.Many neutral molecules are strongly adsorbed onmercury a t potentials in the vicinity of the electrocapillary maximum.74The rate of adsorption on a clean mercury surface may be limited by one ormore of the following processes: (a) transport (usually diffusion) to the(b) a preceding chemical reaction in solution, (c) rate of adsorption,(d) adsorption-desorption equilibrium, (e) a succeeding chemical reaction onthe electrode surface. Each of the processes (a), (c), and (d) has beenshown 76 to be rate-controlling in suitable circumstances. Adsorption pro-cesses are usually studied by measuring changes in the differential double-layer capacity77-80y86 and it is assumed that these are related to 8 (thefraction of mercury surface covered at equilibrium).By measuring 0 as afunction of c~ncentration,'~ values of Ci (the bulk concentration needed togive 8 = 8) have been determined for 30 organic compounds; values rangefrom Ci = 6 x 1 0 - 6 ~ for Leucomethylene Blue to C6 = 8 x 1 0 - 2 ~ forpyridine. Processes (a) and (d) were rate-controlling ; equilibration followeda Langmuir isotherm and was complete [for acetophenone pinacol (2,3-di-phenylbutane-2,3-diol)] within 6 seconds only if 0 20.75. The last value isto be compared with 8 0-85 *l obtainable from theoretical data. Similarresults have been obtained with series of lower fatty acids 79 and alcohols,80but with increasing chain length breaks occur in the Langmuir isotherm,which are interpretable in terms of an (e) process, probably a two-dimensionalassociation akin to that found at solution-air interfacess2 Theoreticalstudies of adsorption rates have been made for different transport processes,various rate-controlling steps, and several electrode geometrie~.7~*7~.~*84Information concerning the'relative rates of processes (a), (c), and (e) can beobtained from the effect of frequency v a r i a t i ~ n .~ ~ ~ ~ ~The effect of the distribution ofpotential in the double layer and of the adsorption of anions on the rate ofAdsorPtion and electrode veactions.72 E. L. Mackor, Rec. Trav. chim., 1951, 70, 763.73 D. C. Grahame, J . Amer. Chem. SOC., 1954, 76, 4819.74 A. N. Frumkin, 2. Physik, 1926, 35, 792; 1.A. V. Butler, Proc. Roy. SOL. 1929.A , 122, 399.75 A. N. Frumkin and V. I. Melik-Gaikazyan, Doklady Akad. Nazik S.S.S.R.. 1951.77, 855.76 R. W. Schmid and C. N. Reilley, J . Amer. Chem. Soc., 1958, SO, 2087.77 H. A. Laitinen and B. Mosier, ibid., 1958, 80, 2363.78 R. S. Hansen, R. E. Minturn, and D. A. Hickson, J . Phys. Chem., 1956, 60, 1185;79 W. Lorenz, ibid., 1958, 61, 192.80 Idem, 2. Phys. Chem. (Frankfurt), 1958, 18, 1.81 This inequality is derived from Fig. 3 of Delahay and Fike (ref. 84) which isdependent on a specific value of an unknown parameter. Thus agreement with theexperimental value is within likely errors.8% A. N. Frumkin, 2. phys. Chem., 1925,116,466; D. C. Grahame, Chem. Rev., 1947,4, 441.88 V. I.Melik-Gaikazyan, Zhur.fiz. Khim., 1952.26, 560; T. Berzins and P. Delahay,J . Phys. Chem., 1955, 59, 906; P. Delahay and I. Trachtenberg, J . Amev. Chern. SOC.,1957, 79, 2355.84 P. Delahay and C. T. Fike, ibid., 1958, 80, 2628.1957, 61, 953; W. Lorenz and F. Mockel, 2. Elektrochem., 1956, 60, 507FLEISCHMANN AND OLDHAM : ELECTROCHEMISTRY. 73electrochemical reactions has been frequently considered, particularly forhydrogen evolution. A recent paper 85 contains a bibliography and shows acorrelation between the rates of reduction of the iodate ion and nitromethaneand the potential of the outer and inner Helmholtz planes.67The presence of uncharged surface-active substances may affect theelectroreduction of other substances by one or more of the followingmechanisms: (f) chemical reaction in solution; this will alter both thekinetic parameters of the electron transfer (k and a) and the transportparameters (usually 0) ; (g) the adsorbed substance may physically blockpart of the electrode surface; and (h) the adsorbed material (by changing thedouble-layer structure) may affect the kinetic parameters even on theuncovered fraction of the surface.Three groups of workers in Americahave considered this problem: one 76 discounts (g) and explains its resultsin terms of (f) and ( 1 2 ) ; the second 86 expresses its results in terms of (h) ;while the thirds7 considers (g) and (k) only. The last workers, using a.c.methods to measure k and 8 simultaneously during the occurrence of theTiIV-TiTII exchange reaction at a dropping mercury electrode, found thateffect (h) did not exist for cyclohexanol, but was important for thym01.~~The part played by adsorption of the reacting species itself in the electrodeprocess has been the subject of much theoretical speculation, especially inthe case of hydrogen evolution,88 and recently more direct methods ofdetermining the r61e of adsorption have been u t i l i ~ e d .~ ~ Electrode processesmay be affected both by (i) the adsorption of the reactant and by ( j ) theadsorption of the reaction product. The quantity of adsorbed material canbe determined galvan~statically,~~ by a technique which has been most oftenused in the investigation of oxide 1a~er.s.~~ Where the amount of adsorptionis large compared with the amount of material which can diffuse from thesolution, the transition time will be inversely proportional to the current.The adsorption on mercury of Methylene Blue and eosin has been investigatedin this In the latter case, the reduction product is not adsorbed andconsequently the oxidation rate is small. With Leucomethylene Blue,however, processes (i) and ( j ) are both involved and electron transfer is rapidin either direction.Similarly a comparison of cathodic and anodic transitiontimes in the reaction I, + 2e + 21- shows that I, is rapidly adsorbed.92bThe frequency-dependence of impedance measurements at solid electrodeshas also yielded information concerning the adsorption of reactants in redoxreactions.g& Adsorption of the reactants would also be expected to becharacterised by fractional stoicheiometries a t constant ionic strength, andthis is observed in the growth of PbO, deposits.94$5 M.Breiter, M. Kleinerman, and P. Delahay, J . Anzw. ClLenz. Soc., 1958, 80, 5111.86 H. A. Laitinen and W. J. Subcasky, ibid., p. 2623.87 P. Delahay and I. Trachtenberg, ibid., p. 2094.88 J. O’M. Bockris, “ Modern Aspects of Electrochemistry,” Buttenvorths, London,89 H. Gerischer and W. Mehl, 2. Elektrochem., 1955, 59, 1049.90 W. Lorenz, 2. Elektrochem., 1955, 59, 736.91 K. J. Vetter and D. Berndt, ibid., 1958, 62, 378.92 (a) W. Lorenz and E. 0. Schmalz, ibid., p. 301; (b) W. Lorenz and H. Muhlberg,93 J. Llopis, C.I.T.C.E. Meeting (see ref. 3) ; Andes Fds. Quim., in the press.P4 M.Fleischmann and M . Liler, Trans. Furuday Soc., 1958, 54, 1370.1954.2. phys. Chem. (Frankfurt), 1958, 17, 12974 GENERAL AND PHYSICAL CHEMISTRE’.Hydrogen evolution. The diffusion of hydrogen from one polarised side ofa membrane to the other side, which may also be polarised, has been used toobtain direct evidence on the effect of changes in the surface concentration ofhydrogen atoms on the electrode kinetic^.^^,^^ The change in concentrationproduces a change in potential which is determined by the mechanism of thereaction. For an electrochemical desorption step succeeding a rate-determining discharge,97 a decrease is predicted and observed for a numberof metals. The conclusions are similar to those obtained from current-timetransients at constant potential 89 which are also determined by changes inthe concentration of adsorbed hydrogen. The variation of the concentrationof absorbed hydrogen due to a variation of the surface concentration hasalso been examined by measuring the ionisation of hydrogen.98The variation of the exchange current with the heat of adsorption hasbeen r e - e ~ a r n i n e d .~ ~ - ~ ~ ~ A rough prediction is that the rate of the dischargestep will be increased while the rates of electrochemical desorption and of re-combination will be decreased by an increase in heat of adsorption, the effectbeing greatest with the slow recombination step. For a number of metals thelatter behaviour is observed,lW and an electrochemical desorption step issuggested.An analysis, allowing for a change in the degree of coverage withheat of adsorption lol and for this factor, together with non-ideal behaviourin the adsorbed layer,lo2 shows, however, that for all mechanisms theexchange current will vary in a similar manner, passing through a maximumwith increasing heat of adsorption. Many data fit in with this scheme.The form of the Tafel plots has also been discussed Io2 in relation to themechanisms. The changes in slope observed have received a number ofinterpretation^.^^*^^^*^^^ It is of interest to discuss some of the recentobservations on platinum. The ionisation of hydrogen, a useful cri-terion,10*,105 has been measured and on electrodes of low activity is of thefirst order with respect to H,.lO4 It is therefore suggested that the desorptionof H, must be included in the reaction scheme.On electrodes of higheractivity the reaction is of zero order lo5 and this suggests slow surface diffusionor slow ionisation. These experiments have shown a correlation betweenthe “ poisoning’’ for the ionisation and the adsorption of anions.69 Atlower stirring rates the reaction is diffusion-controlled.lo6 A re-examin-ation 106 of the a.c. impedance lo7 of active platinum electrodes suggests afast discharge and a large contribution to the overpotential by diffusion of95 A. N. Frumkin, 2. phys. Chem. (Leipzig), 1957, 207,321; I. Bagozkaya, DokladyAkad. Nauk S.S.S.R., 1956,107, 843; 1956, 110, 397.96 S. Schuldiner and J. P. Hoare, J . Electrochem. Soc., 1957, 104, 564; 1958, 105,278.97 A.N. Frumkin, Zhur.fiz. Khim., 1957, 31, 1875.98 M. Fleischmann, J. Sowerby, and H. R. Thirsk, Trans. Faraday SOC., 1957,53, 91.99 P. Riietschi and P. Delahay, J . Chem. Phys., 1955, 23, 195.100 B. E. Conway and J. O’M. Bockris, ibid., 1957, 26, 532.101 H. Gerischer, Bull. SOC. chim. belges, 1958, 67, 506.102 R. Parsons, Trans. Faraday SOC., 1958, 54, 1053.103 J. O’M. Bockris, I. A. Ammar, and A. K. M. S. Huq, J . Phys. Chem, 1957, 61,104 K. J. Vetter and D. Otto, 2. EZektrochem., 1956, 60, 1072.105 A. N. Frumkin and E. Aikazyan, Doklady Akad. Nauk S.S.S.R., 1955, 100, 315.106 M. Breiter, H. Kammermaier, and C . A. Knorr, 2. Elektrochem., 1956, 60, 37.107 p. Dolin and B. V. Ershler, Acla Physicochim. U.R.S.S., 1940, 13, 747.879FLEISCHMANN AND OLDHAM ELECTROCHEMISTRY. 75hydrogen through the solution.In common with other metalslo8 someauthors conclude lo3 that the electrochemical desorption step is rate-determining in acid solutions. The exact nature of the metal surface isclearly important.There has been a general treatment of the stoicheiometric number,lm thenumber of times the rate-determining step takes place in unit reaction. Theelectrochemical desorption step has been considered in detail.llO*lll It hasbeen shown 110 that, with increasing overpotential, on electrodes with lowcoverages the discharge must become rate-determining even if electro-chemical desorption is slow at the reversible potential. As the exchangecurrent used in the calculation is obtained by extrapolation from highoverpotentials the stoicheiometric number will only be unity provided thedischarge step is slow in the reaction sequence at all overpotentials.Theconclusion that this is generally true ll2s1O8 is unjustified. This treatmenthas been generalised for constant surface coverage.lll If both stages havecomparable rates the stoicheiometric number is 2.1113109In recent years many examples 113-12*have been reported of the occurrence of minima in cathodic current-voltagecurves in regions of potential where a diffusion plateau would be expected.32These minima are not related in any way to polarographic m a ~ i m a . l l ~ ~ ~ ~ Most attention has been devoted to those minima found on the electro-reduction of the large multivalent anions s2082-, Fe(CN)63-, and PtC142- onmercury at negative potentials: the current within such minima iskinetically controlled l 1 5 p 1 1 6 and is often very sensitive to foreign ions.Thus5 x 10-3~-KC1 11’ or 10-2~-Na2S04 is sufficient to eliminate the minimumof K,Fe(CN), completely and it has been suggested 117 that trace quantitiesof cations of high valency may have prevented Kivalo and Laitinen 118,115Minima in current-voltage cwves.108 N. Pentland, J. O’M. Bockris, and E. Sheldon, J . Electrochem. SOC., 1957, 104,109 A. C. Makrides, ibid., p. 677.110 K. J. Vetter, 2. Elektrochem., 1955, 59, 435.111 A. N. Frumkin, Doklady Akad. Nauk S.S.S.R., 1958, 119, 318.112 J. O’M. Bockris and E. C. Potter, J . Res. Inst. Catalysis, 1956, 4, 50; 1956, 4, 256.113 A.N. Frumkin and G. M. Florianovich, Doklady Akad. Nauk S.S.S.R., 1951, 80,114 N. V. Nikolajeva, N. S. Shapiro, and A. N. Frumkin, ibid., 1952, 86, 681.115 P. Kivalo and H. A. Laitinen, J . Amer. Chem. Soc., 1955, 77, 5205.116 G. M. Florianovich and A. N. Frumkin, Zhur. fiz. Khim., 1955, 29, 1827.117 A. N. Frumkin, Birmingham Meeting (see ref. 6).118 P. Kivalo, J . Phys. Chem., 1957, 61, 1126.118 T. A. Kryukova, Doklady Akad. Nauk S.S.S.R., 1949, 65, 517.120 H. A. Laitinen and E. I. Onstott, J . Amer. Chem. SOL, 1950, ‘92, 4565.122 P. Kivalo, Suomen Kern., 1957, B, 30, 208.123 A. N. Frumkin, 2. Elektrochem., 1955, 59, 807.124 Idem, ‘‘ Va Prosy khimicheskoi kinetiki, kataliza i reaktsionnoi sposobnosti,”Akad, Nauk S.S.S.R., Moscow, 1955, p.402.125 N. V. Nikolajeva-Fedorovich, L. A. Fokina, and 0. A. Petry, Doklady Akad. NaztkS.S.S.R., 1958, 122, 639.126 T. V. Kalish and A. N. Frumkin, Zhur. fiz. Khim.. 1954, 28, 473.127 A. N. Frumkin and N. V. Nikolajeva-Fedorovich, Vestnik Moscow Univ. Chem.Ser., 1957, 169; A. N. Frumkin, B. Damaskin, and N. V. Nikolajeva-Fedorovich,Doklady Akad. Nauk S.S.S.R., 1957, 115, 751.12* A. N. Frumkin, N. V. Nikolajeva-Fedorovich, and R. Ivanova, Paper 16a,Toronto Symposium (see ref. 1).182.907.A. N. Frumkin and N. V. Nikolajeva, J . Chem. Phys., 1957, 26, 155276 GENERAL AND PHYSICAL CHEMISTRY.from reproducing the curves obtained by other workers 1133116 with ferri-cyanide solutions. Two early theories 119*120 have been superseded by twonewer ones: the first of these 113*1263129~130 seeks to explain minima in termsof electrostatic principles, while the second ll5s1l8 is based on kinetic effects.In their present forms, neither theory is entirely satisfactory.121J22The effect of added salts in suppressing minima (increasing the rate ofelectroreduction) has been studied most thoroughly for the reduction ofK2S20, at a dropping mercury electrode.The efficiencies of salts insuppressing the persulphate minimum follow the sequences Th(SO,), >BaCl, > KC1,lI6 La,(SO,), > Na,-$O, = NaBr = NaOH, 1 1 3 9 1 1 9 and CsCl >RbCl > KCl > NaCl > LiC1,123 demonstrating the importance of the chargeand size of the cation in determining the efficacy of the suppressor. Frumkinoriginally12, explained this effect in terms of the electrostatic theory, thecations affecting the potential distribution in the double layer, but he now 121shares with Schmid and Reilley131 the opinion that the cation exerts itsinfluence by forming a bridge between the reducible anion and the mercurysurface.The tetrabutylammonium ion is effective in suppressing minimaonly at potentials more positive than the desorption potential of thei0n,117J~~ showing that the adsorbed Bu,N+ cation is the effective suppress-ing agent. It is therefore somewhat surprising to find126 that the I- ion(which is adsorbed on Hg even at negative potentials32) is also capable ofsuppressing the persulphate minimum. However, the nature of the addedcation is also important 12’ and the order of efficacy for certain alkali-metalhalides is 128 CsI > CsCl > KI > KBr > KC1 > NaCl = NaF = NaI.Itis suggested128 that adsorption of iodide ion depends on the formation ofcationic bridges and that the bridging capacity of a large cation is greaterthan that of a smaller ion such as Na+. The localisation of cations on theelectrode surface may then serve to accelerate the electroreduction of theS20,2- anion. The formation of a trinsition complex involving both thepersulphate and the iodide ion at the electrode surface does not appear tohave been considered, though the homogeneous reaction between thesetwo anions is well known.132Electyocry stallisation. The formation of a layer of adsorbed molecules oratoms has been frequently postulated to be an intermediate stage in thegrowthof crystals.It is suggested that the lattice is built up from these adatoms atsteps on the crystal faces such as those formed by screw dislocations.133The growth of deposits on electrodes has been examined in a number ofways. As these are frequently fast reactions some workers have used a.c.impedance measurement^.^^,^^^ The separation of the faradaic componentdue to the electrode process is more difficult than in the case of mercury136as “ perfectly ” polarised solid surfaces always show a resistive component129 J. Koryta, 2. Elektrochem., 1957, 61, 423.130 A brief account of the principles is given by Delahay et al. (see ref. 85).131 R.W. Schmid and C. N. Reilley, J . Amer. Chem. SOC., 1958, 80, 2101.132 T. S. Price, 2. phys. Chem., 1898, 27, 474.133 W. K. Burton, N. Cabrera, and F. C. Frank, Phil. Trans., 1951, A , 243, 299.134 W. Lorenz, 2. phys. Chem. (Frunkfuvt), 1958, 17, 136; 2. Naturforsch., 1954,186 J. O’M. Bockris and B. E. Conway, J. Cheun. Phys., 1958, 28, 707.136 J. E. B. Randles, Discuss. Furaduy Soc., 1947, 1, 11.9a, 716FLEISCHMANN AND OLDHAM ELECTROCHEMISTRY. 77as well as the double-layer capacity. Bockris and Conway, in examiningthe growth of copper, assume that the frequency-dependent values areindependent of potential and subtract (vectorially) the impedance ap-propriate to that frequency.135 Lorenz has examined the deposition ofsilver from a complex so that a value of the non-faradaic component in theabsence of the depositing ion could be obtained a t the deposition potential.The electrode impedance consists of a frequency-dependent resistance andcapacitance in paralle1.lM From the limiting values at low and highfrequencies and from the dispersion frequency the following quantities canbe obtained in the event of slow surface diffusion: the exchange current forthe formation of adatoms and the lifetime of adatoms; the ratio of the meandiffusion path-length and the mean separation of the step lines; the densityof the adatoms. Some of these quantities are naturally not independent.In the case of copper,135 the deduced faradaic impedance has been found tovary in the same way with frequency as that observed for discharge atarnalgams,l36 so that deposition is evidently a normal transfer step with nosubsequent slow stages. The slope of the plot of faradaic resistance againstI/& is greater than that corresponding to unit surface and it is suggestedthat deposition only takes place on part of the surface.Thc concentration polarisation a t an electrode is equal to the over-potential a t which no current would flow a t the concentration established inthe steady state.This principle has been used137 to measure the totalconcentration overpotential by changing the potential to the correct valuewith a potentiostat. The total concentration polarisation is larger than thatcalculated for the solution and it is concluded that this is due to the adatoms.A measure of the concentration of adatoms on silver a t the reversiblepotential has been obtained by measuring the initial rate of change ofpotential a t constant current and equating the anomalously high capacityto the concentration of a d a t ~ m s .l ~ * ? ~ ~ ~ The interpretation also leads to ameasure of the rate of crystal growth. It is found that this is much smallerthan the exchange current for adatoms and this is consistent with anappreciable activation polarisation for lattice formation. An interestingcomparison has been made of the rate of growth of solid and liquid mercury 42near the melting point. As there is very little difference in the kinetics, theprocesses must be similar. This may well be related to the formation ofatomically rough surfaces near the melting point.140A feature of these investigations is that they are restricted to the initialperiod of deposition and it could be argued that they are not related to thecrystal growth process.In the limit, adatoms could be deposited butgrowth take place by direct deposition on step lines or kinks from thesolution, as was originally suggested.l= The steady rate of growth of silverchloride 141 and of lead dioxide 94 has been examined at constant potential157 H. Gerischer and R. P. Tischer, 2. EZeRtrochern., 1957, 61, 1159.138 H. Gerischer, ibid., 1958, 62, 256.139 W. Mehl and J. O’M. Bockris, J . Chem. Phys., 1957, 27, 818; J. O’M. Bockris140 W. I<. Burton and N. Cabrera, Discuss. Faraday Soc., 1948, 5, 33.141 ni.FIeischmann and H. R. Thirsk, C.I.T.C.E. Meeting (see ref. 3) ; EZectrocJLi+nicaand W. Mehl, Paper 8, Toronto Symposium (see ref. 1).L 4 ~ i n , 1959, 178 GENERAL AND PHYSICAL CHEMISTRY.and with use of a sequence of two constant potentials to separate nucleationand growth constants. The growth of a solid such as silver chloride onsilver is a favourable case for observing the effects of lattice formation due tostep lines, owing to the short diffusion path. In this case a transition froma second- to a first-order reaction is observed with increasing potential,which would be characteristic of growth at the steps produced by screwdis10cations.l~~ For such a mechanism an inductive component would, how-ever, be predicted for the electrode impedance whereas a capacitative com-ponent is found.141 The generation of step lines 142 would always beexpected to lead to an inductive component, particularly in the experimentsnear the reversible potential.This will apply even in the event of com-petition for adatoms between adjacent lines (i.e.J in the first order region)and must complicate the interpretation of the impedance and galvanostaticmeasurements. In view of this inductive component it can be stated thathitherto no evidence has been found of the participation of step lines in theoverall growth mechanism. (See however, earlier observations of super-polarisation.143)The formation of oxides, and passivation. The effect of corrosioninhibitors 144 and the pH of the solution 145 in the region where iron dissolvesfreely and the action of passivating inhibitors 146 has recently been consideredin the way first followed by Wagner and Traud. The papers given at acolloquium on passivity have been publi~hed.~The anodic polarisation of several metals 1479148 and alloys 149 in acidsolutions follows a well-defined pattern.If the current-voltage plot isdetermined under controlled-potential conditions 150 it is found that thecurrent first increases owing to dissolution (corrosion) and then reaches alimiting value. On further increase of the potential the current decreasesrapidly to a much lower value. At this " Flade " potential 151 the metalbecomes passive, and when the polarisation is switched off, becomes activeagain. The current remains constant in the passive region and finallyincreases owing to further dissolution and evolution of oxygen.This behaviour is frequently interpreted as being due to the formation ofa film of oxide which dissolves at a slow constant rate in the acid.In thecase of transition metals, ions of the lowest stable valency are formed in theregion of active dissolution and ions of a higher valency in the passive142 D. A. Vermilyea, J . Chem. Phys., 1956, 25, 1254.148 V. A. Roiter, V. A. Juza, and E. S. Polhyan, Acta Physicochim. U.R.S.S., 1939,144 H. Kaesche and N. Hackerman, J . Electrochem. SOL, 1958, 105, 191.145 I. A. Ammar and S. Riad, J . Phys. Chem., 1958, 62, 150.146 M. Stern and A. Geary, J . Electrochem. Soc., 1957, 104, 56; M.Stern, ibid., 1958,147 U. F, Franck, 2. Elektrochem., 1958, 62, 649; Nickel: G. Okamoto, H. Koba-10, 399, 845.105, 638.yashi, M. Nagayama, and N. Sato, ibid., 1958, 62, 775; Chromium: T. Heumann, ibid.,p. 745; Iron: J. H. Bartlett and L. Stephenson, J . Electrochem. Soc., 1952, 99, 504;Iron: U. F. Franck, 2. phys. Chem. (Frankfurt), 1955, 3, 183.148 Chromium: Ya. M. Kolotyrkin, 2. Elektrochem., 1958, 62, 664.149 Iron-Chromium: R. Olivier, Thesis, Leiden, 1955; M. Prazak and V1. Cihal,2. Elektrochem., 1958, 62, 739; Austenitic steel: N. Ya. Bune and Ya. M. Kolotyrkin,Doklady Akad. NUZ& S.S.S.R., 1956, 111; 1050.150 H. J. Bartlett, Tram. Electrochem. SOC., 1945, 87, 521.161 F. Flade, 2. PJqrs. Chem., 1911, 76, 513FLEISCHMANN AND OLDHAM ELECTROCHEMISTRT.79region.l@~ 1529 153 Appreciable quantities of charge are stored and released onincreasing and decreasing the potential 152~1549155 and the potential drop isestablished solely across the oxide layer,lM which grows by high fieldc o n d ~ c t i o n . ~ ~ ~ ~ ~ ~ ~ As the passive electrode responds to redox systems theoxide is electron-c~nducting.~~~~ 154 This electronic conductivity explainsthe onset of passivity due to the oxidation Fe304 ---t y-Fe,O, lS,l5* and alsoother phase changes such as Ag,O + In the absence of a redoxequilibrium in solution there must be a gradient in chemical potential ofelectrons across the layer so as to maintain a constant electrochemicalpotential. This is equivalent to a change of activity of the metal atoms and,at the appropriate potential, a disproportionation or further oxidation setsin.The field strength is simultaneously reduced and prevents the furthergrowth of the lower oxide. Certain aspects of the passivation of metalssuch as the effect of adsorbed carbon monoxide are more easily interpretedby assuming an adsorbed film.160 Electrodes may be passivated for theionisation of hydrogen by the adsorption of anions lo4 and the similarity ofthis process to the curves of anodic dissolution has been emphasised.lM Itis inferred that passivation is due to a similar cause.Othermetals such as zinc 162-164 and cadmium show active and passive regionsin neutral and alkaline solutions which are similar to those observed foriron. The different regions are due to the formation of oxide and hydroxidephases.164 The film in the passive region grows by high field conducti-~ity,~~~and a similar mechanism has been suggested for their inter~onversion.1~However, since the layers on zinc 163~165 and cadmium 166 dissolve in saturatedsolutions, the oxide solution interface cannot be in equilibrium and a dualprocess must operate.The Reporters thank Dr.R. Parsons and their colleagues for helpful dis-cussions and for assistance in translation.The behaviour of iron in alkaline solutions is less certain.161M. F.K. B. 0.152 U. F. Franck and I<. Weil, Z. Elektrochem., 1952, 56, 814.153 N. M. Knasheva and Ya. M. Kolotyrkin, Doklady Akad. Nauk S.S.S.R., 1957,154 K. J. Vetter, 2. phys.Chem. (Leipzig), 1953, 202, 1.15j K. J. Vetter, 2. Elektrochem., 1958, 62, 642.156 Idem, ibid., 1954, 58, 230.157 K. G. Weil, ibid., 1955, 59, 711.15* K. J. Vetter, 2. phys. Chem. (Frankfurt), 1955, 4, 165; H. Gohr and E. Lange,loo For example H. H. Uhlig, 2. Elektrochem., 1958, 62, 626.161 K. G. Weil and K. F. Bonhoeffer, 2. phys. Chem. (Frankfurt), 1955, 4, 175; K.Heussler, K. G. Weil, and K. F. Bonhoeffer, ibid., 1958, 15, 149.lo2 H. Liidering, Thesis, Gottingen, quoted by U. F. Franck, 2. Elektrochem., 1958,62, 652.1G3 I. Sanghi, Thesis, University of Durham, 1955.lo4 K. Huber, Z. Elektrochem., 1958, 62, 675.l o 5 T. P. Dirkse, J . Electrochem. SOC., 1954, 101, 328; 1955, 102, 497.166 P. E. Lake and E. J. Casey, ibid., 1958, 105, 52.114, 1265.hTatztrwiss., 1956, 43, 12; 2.Elektrochem., 1957, 61, 1291.H. Gohr and E. Lange, 2. phys. Chern. (Frankfurt), 1958, 17, 10080 GENERAL AND PHYSICAL CHEMISTRY.8. ENERGY TRANSFER IN LIQUIDS AND GASESA STABLE molecule requires considerably more than its average energy if itsnuclear configuration is to undergo a permanent change. This energy maybe acquired by the nuclei directly in collisional processes, or be communi-cated to the electrons by the absorption of radiation of the appropriatefrequency; in the latter case vibrational activation or change in nuclearconfiguration follows the crossing of two or more potential-energy surfaces.Processes involving one, and more than one such surface, respectivelyclassified as adiabatic and diabatic in the Ehrenfest sense,l form a con-venient subdivision for the report of recent work on energy transfer.Electron transfer processes are not included.Excellent accounts of the various aspects of this subject were presentedat the American Chemical Society’s symposium on “ Intermolecular EnergyTransfer ” held in Atlantic City in September 1956; more recent discussionsinclude those on ‘‘ The Structure and Reactivity of Electronically ExcitedSpecies ” (Ottawa, September 1957 3, and on “ Transfer of the Energy ofLuminescence and Photosensitisation ” (Paris, May 1958 4).Energy Transfer in Adiabatic Processes.-A collision between twomolecules may result in the excitation of translational, rotational, orvibrational energy of one of the colliding partners at the expense of theother.Since the primary process usually involves bond rupture it isevident that thermal reactions proceed by vibrational activation, althoughrotational activation is also important in the dissociation of the simplestmolecules.5 A knowledge of the probability and extent of vibrationalactivation and de-excitation on collision is therefore required for a completeunderstanding of reaction rates. Careri has discussed the various stagesof refinement of the molecular model used to calculate these probabilities,assuming that the energy conditions are met, In a series of importanttheoretical papers Shuler and his collaborators7 have provided a firmtheoretical basis for the treatment of relaxation data under non-equilibriumconditions which obtain in shock waves and chemical reactions.Applicationof their findings for a system of harmonic oscillators to the relaxation ofthe 8th vibrational level of the 0, molecule produced in the flash photolysisof C10,8 leads these authors to the conclusion that the collisional efficiencyof the N, molecules used as a heat bath is too small to account for theobserved rate of depopulation to the 7th vibrational level, and that C10with an estimated efficiency of 1 collision in 200 must be largely responsible1 S. Glasstone, K. J. Laidler, and H. Eyring, “The Theory of Rate Processes,”2 Published in J. Phys. Chenz., 1957, 61, 833-878.a Most of the papers presented have appeared in Canad. J. Chem., 1958, 36, 1-146.4 Published in J .Chim. phys., 1958, 55, 607-712.6 0. K. Rice, J . Chem. Phys., 1953, 21, 749; G. Careri, ibid., p. 749.7 E. W. Montroll and K. E. Shuler. J. Chem. Plzys., 1957, 26, 454; K. E. Shuler,J . Phys. Chem., 1957, 81, 849; N. W. Bazley, E. W. Montroll, R. J. Rubin, and K. E.Shuler, J . Chem. Phys., 1958, 28, 700; 1958, H, 1185; R. Herman and K. E. Shuler,ibid., p. 366; E. W. hlontroll and K. E. Shuler, Adv. Chem. Phys., 1958, 1, 361.8 F. J. Lipscomb, R. G. W. Norrish, and B. A. Thrush, Proc. Roy. SOG., 1956, A , 233,455.McGraw-Hill, New York, 1941. See also ref. 78.G. Careri, Adv. Chem. Phys., 1958, 1, 119STEVENS: ENERGY TRANSFER I N LIQUIDS AND GASES. 81for the effect observed. The consequences of the remarkable stability ofthe vibrationally excited 0, molecule are reported below in connection withthe decomposition of 0,.Some further conclusions of Shuler et al. are:(a) the analysis of relaxation data in terms of half-lives has no significancewhen more than two energy levels are involved; (b) insofar as translational-vibrational transition probabilities are independent of the vibrational levelinvolved, i.e. , for low vibrational levels, the relaxation behaviour of a systemof anharmonic oscillators can be represented by that of a system of harmonicoscillators ; in higher vibrational levels where the vibrational amplitude is nolonger small compared with the interaction range of colliding molecules, someuncertainty attaches to translational-vibrational transit ion probabilities andthe effects of anharmonicity which increase the vibrational excursion maybe pronounced; (c) a system of rigid rotator-harmonic oscillators relaxesas two independent systems of harmonic oscillators and rigid rotators ;rotational relaxation times calculated on the assumption that AJ = &lare some 100 times longer than experimental values, which suggests thatwhere AE < kT, AJ is not so restricted and multiquantum transfers areimportant ; (d) the rate of stepwise activation in a unimolecular dissociationreaction, i.e., A V = 1, calculated on the basis of a harmonic oscillator modelis some l o 5 times smaller than the observed value in the case of I, in thepresence of inert gases, implying that the restriction AV = *l must alsobe relaxed (as for an anharmonic oscillator) when AE( V , ---t Vn+l) < kTat higher vibrational levels.Hornig9 has also pointed out the legalityof multiquantum excitation when the relative kinetic energy of the collidingmolecules is many times the separation of vibrational levels, and states thatthere is no reason why violent collisions should not produce direct dissociationfrom lower vibrational levels. Thus it appears that in addition to allowingdissociation to take place, the anharmonic perturbation of vibrationsaccelerates the rate of activation necessary to produce it, and it is perhapsnot unlikely that this rate is directly related to the anharmonicity constantof the excited vibration.The Lindemann mechanism assumes that collisional deactivation ofvibrationally excited molecules proceeds with unit efficiency.If this is aone-quantum process the assumption is difficult to justify in view of thelarge number of collisions required to deactivate the lowest vibrationallevels.10 Mahan l1 has shown that the efficiency of collisional deactivationis considerably increased if this involves simultaneous excitation of a secondvibration of lower frequency; thus he calculates a collisional probabilityof 10-2 for simultaneous deactivation of v1 (926 cm.-l) and activation ofv3 (830 cm.-l) in the case of F20 whereas deactivation of v1 (V = 1) alonerequires some lo5 collisions. The removal of smaller " difference quanta "from higher vibrational states should be even more efficient and a treatmentof the effect of various gases on nitryl chloride decomposition leads to avalue of 12 cm.-I for the energy removed in the deactivating collision.Since vibrational transfer probabilities vary enormously with the9 D.F. Hornig, J . Phys. Chem., 1957, 61, 856.10 J. C. McCoubrey and W. D. McGrath, Qaart. Rev., 1957, 11, 87,11 B. H. Xlahan, J . Phys. Chem., 1958, 62, 10082 GENERAL AND PHYSICAL CHEMISTRY.vibrational level concerned, recent results will be reported for low, inter-mediate, and high vibrational levels independently along the lines of thevaluable review by McCoubrey and McGrath.lOTranslation-vibration relaxation involvingone or two quanta above the zero-point half-quantum involves smallchanges in translational temperature encountered in sound propagation.The origin of ultrasonic absorption and dispersion in terms of translation-vibration relaxation, together with the results of various workers, and theirsignificance in chemical kinetics has been discussed by Herzfeld andGriffing,lz whilst a review of molecular dispersion in liquids contains a shortaccount of vibrational relaxation in this phase.13 More recently, ultrasonicabsorption data for liquid CO,, SF,, N,O, CH3C1, and cyclopropane in therange 0-50" have been treated in terms of vibrational relaxation, the totalspecific heat relaxing with a single relaxation time, and it is concluded thatvibrational transitions in unassociated liquids occur in binary c0llisions.~4For non-polar liquids the collisional efficiency has a positive temperaturecoefficient whilst for polar ones it is virtually independent of temperatureover the range measured.Bass and Lamb l4 have also observed doubledispersion in liquid SO, which is a feature of this molecule in the gas phase.15The different ratios of the two relaxation times in the liquid (65) and gas (10)are attributed to the effect of environment on the collision frequenciesproducing the transitions. The multiple relaxation of sulphur dioxide gashas been treated theoretically by Dickens and Linnett ,16 their results beingin fairly good agreement with the experimental values; these authorsdiscuss the close resemblance in behaviour of sulphur dioxide and methylenechloride and suggest a number of other molecules in which multiple dispersionmay be expected on the basis of their relaxation mechanism for SO,.As yet, relaxation times cannot be calculated reliably from molecularproperties, although under certain conditions the predicted temperature-dependence is observed.These conditions have been studied by Lambert 17and his school in the past year, who present data for C2H4, CF,, CH,Cl,CH,Br, and cyclopropane over a wide temperature range (290-588') andcorrelate them with data for CH3F and SO, previously obtained.18 Thepredicted T-i dependence of logl, P is observed for non-polar gases overthe whole range studied, and for polar molecules at the higher temperatureswhere they acquire spherically-symmetrical force fields by rotation ; howeverthe exponential temperature coefficients require a much steeper repulsionthan that afforded by the Lennard- Jones and Krieger potentials.A similarstate of affairs exists for a large number of pure and mixed gases and has ledUbbelohde's school to suggest l9 the introduction of a " steric " factor intoLow-Zying vibrational levels.12 K. F. Herzfeld and V. Griffing, J. Phys. Chem., 1957, 61, 844.13 R. 0. Davies and J. Lamb, Quart. Rev., 1957, 11, 134.14 R. Bass and J. Lamb, Proc. Roy. Soc., 1968, A , 247, 168; 1957, A , 243, 94.15 J. D, Lambert and R. Salter, ibid., p. 78.16 P. G. Dickens and J. W. Linnett, ibid., p. 84.17 P. G. Corran, J. D. Lambert, R. Salter, and B. Warburton, ibid., 1968, A, 244, 212.18 P. G. T. Fogg, P. A. Hanks, and J. D. Lambert, ibid., 1953, A , 219, 490; J.Lam-19 J. W. Arnold, J. C . McCoubrey, and A. R. Ubbelohde, Trans. Faraday SOC.,bert and R. Salter, ibid., 1955, A , 232, 537.1957, 53, 738STEVENS: Eh’ERGY THANSFEK I S LIQUIDS AKU GASES. $3the theoretical expressions 2o to allow €or the inefficiency of certain collisionalorientations. At lower temperatures where the dipole interaction energybetween polar molecules is less than kT, the predominance of particularlyefficient oriented collisions leads to a negative temperature coefficient oftransfer probability, and the comparatively small temperature Coefficientof relaxation observed for CH,Br is attributed to the mutual compensationof collisional orientation and factors contributing to normal temperature-dependence. The high catalytic effect of H,O on relaxation in C2H4 andN,O 21 is similarly ascribed to a favourable collisional orientation, compoundformation, as with CO,, being less likely with C2H4 and N,O.Methane andbenzene are also found to be more efficient in heterocollisions than in self-transfer, whilst the catalytic effect of the paraffins on relaxation in C,H,and N,O increases with the number of carbon atoms which may be due torepeated (wrestling) collision involving different parts of the paraffin mole-cule which effectively steepens the repulsion curve, or to vibration-vibrationtransfer.Excitation of low vibrational levels by the absorption of infrared radiationis followed by a slight pressure pulse in the gas as the system relaxes. Jacosand Bauer 22 describe the application of the spectrophone based on thisoptico-acoustical effect to the vibrational relaxation of CO, in whichdifferent vibrations are excited exclusively. The results do not permit thedrawing of quantitative conclusions but it appears that hydrogen selectivelydeactivates the asymmetric CO, stretching frequency. This paper includesa valuable discussion of the problems encountered in this field together witha critical survey of the methods available for the examination of vibrationalrelaxation.One of the major difficulties in theoretical interpretation is thechoice of a satisfactory intermolecular potential to which the calculatedcross-section for excitation of the first vibrational level is extremely sensitiveeven in the collision between two H, molecules.23 has examinedthe feasibility of obtaining vibrational deactivation times from the intensityof radiation emitted by a heated gas; this may be regarded as a quenchingof infrared luminescence which competes with emission, the vibrationaldeactivation time being in principle determined from the half-intensitypressure. In this respect Cashion and Polanyi’s interesting observations 25on the infrared chemiluminescence of HC1 may be mentioned.The reactionbetween atomic H and C1, produces HC1 almost exclusively in the secondvibrational level although the energy of reaction is sufficient to excite 6vibrational quanta; the recombination of H atoms in HC1 alone on theother hand produces emission from the first vibrational level only, indicatingthat further excitation of HC1 is not easily achieved once it is formed.Recombination of 0 atoms produced by a vacuum-ultraviolet flash alsoexcites undissociated 0, molecules to the first vibrational level ; 26 howeLTer,20 E.g., see T.L. Cottrell and N. Ream, Trans. Faraduy SOC., 1955, 51, 150, 1453.21 J . W. Arnold, J . C. McCoubrey, and A. R. Ubbelohde, Proc. Roy. SOC., 1958,22 M. E. Jacox and S. H. Bauer, J. Phys. Chem., 1957, 61, 833.23 M. Salkoff and E. Bauer, J. Chem. Phys., 1958, 29, 26.24 D. A. Dows, ibid., 1957, 27, 1430.25 J . Ii. Cashion and J . C. Polanyi, ibid., 1958, 29, 466.26 J . A. Golden and ‘\. L. RIycrson, zbid., 1968, 28, 978.DowsA , 248, 44584 GENERAL AND PHYSICAL CHEMISTRY.the addition of 7 mm. of argon to the oxygen at 3 mm.pressure produced nosuch excitation, which seems to show either that Ar * is much more effectivethan 0, as third body or that it quenches the excited 0, (V = 1) with greatefficiency.In order to study vibrational relaxationit is desirable to excite a particular vibrational level selectively; althoughthis is not difficult for the lowest levels or for the dissociation region ifstudied from the recombination angle, selection rules forbid the directphotoexcitation of intermediate levels and their collisional population is nolonger selective. However, reactions between atoms and simple moleculescan produce radicals or molecules in more or less well-defined vibrationalstates as in the case of HC1 quoted above. Examples of such chemicalactivation are the production of vibrationally excited oxygen in the flashphotolysis of NO, and ClO, discovered by Norrish and his co-workers,* andthe detection of OH radicals in vibrational levels up to the 9th in the reactionproducts of H atoms with 0, by McKinley, Garvin, and B~udart.,~Collisional efficiencies for the one-quantum deactivation of 0, from the sixthvibrational level are of the order of those found for the lowest levels andrange from one in lo7 for Ar and N, to one in 500 for NO,.The remarkablestability of vibrationally excited 0, has led McGrath and Norrish2* toresuscitate the energy chain theory of 0, decomposition, the propagatingprocesses beingIntermediate vibrational levels.o(3q + o,(~A) --+ o2*(3xO-, v = 12 - 16) + o~(~A,J02* + 0, -+ 20,(3c,-) + o(3qOther excited radicals are formed in the reaction between halogen atomsand ozone 29 thusC1+ 0, ClO(V < 5) + 0,Br + O,+BrO(V< 4) + 0,As Norrish has pointed out in his Liversidge lecture,30 there is a strongtendency for most of the energy of reaction to remain unequilibrated inthe newly formed bond in the exothermic reactionA + BCD-AB + CDThe reader cannot do better than refer to this lecture for an authoritativcand comprehensive account of this work.It is now generally recognised31 that the emitter of the first positivebands in the nitrogen afterglow is the B311, state of N, formed with from7 to 11 vibrational quanta by preassociation of N atoms in the ground (4s)27 J.D. McKinley, jun., D.Garvin, and M. J. Boudart, J. Chem. Phys., 1955, 23,784.28 W. D. McGrath and R. G. W. Norrish, Nature, 1957, 180, 1272; Proc. Roy. SOC.,1957, A, 242, 265.29 Idem, 2. phys. Chem. (Frankfurt), 1958, 15, 245.30 R. G. W. Norrish, Proc. Chem. Soc., 1958, 247.31 K. R. Jennings and J. W. Linnett, Quart. Rev., 1958, 12, 116.* Attention is directed to the recent alteration of the symbol for argon from A to Arby I.U.P.A.C. This change is now adopted for publications of the Chemical Society,but care should be taken to avoid confusion with the standard usage of Ar for aryl.-EDSTEVENS: ENEICGY TRANSFER IN LIQUIDS AND GASES. 85state. By measuring the relative band intensities of this system as a functionof nitrogen pressure, Stanley 32 has obtained the probabilities of collision-induced transition from the 11th vibrational level relative to the spon-taneous radiative transition probability from this level.This ratio for allvibrational transitions is 1.37 x per cm. pressure of nitrogen, for whichone-quantum relaxation is 76% responsible , two- and three-quantarelaxations are 13% and 9% responsible, and single-quantum excitationcontributes 2%. The relative efficiencies of multiquantum relaxation areinteresting but the results are inconveniently expressed for purposes ofcomparison; from Kistiakowsky and Volpi’s 33 NH, quenching data a valueof 1-6 x for the radiative lifetime of N2(B3II,)which, combined with Stanley’s results, provides a collision efficiency of2 x 10” for vibrational transfer from the 11th vibrational level; this orderof magnitude is predicted by Zener’s theoretical e~pression.~~~35 Chartonand Gaydon 36 have attributed the strengthening of OH emission bands withV’ = 2 and 3 observed in hydrogen flames to formation of these vibrationallevels by preassociation of 0 and H, the overall scheme beingsec.can be calculated0 + H __t OH(’C-) + OH(’Z+, V = 2,3) _+ OH(,II) + hvIn electronic transitions AV is not restricted, and intermediate levels ofexcited molecules can be produced selectively by the absorption of mono-chromatic radiation; thus the Hg 5461 A line excites I, to the 26th vibra-tional level of the 3rZ state. Polanyi, and Arnot and McDowell,37 haveseparately investigated vibrational transfer from this level by measuringthe intensity dependence of transfer bands in the emission spectrum atvarious pressures of added gases.Transfer probabilities some 10-15 timesgreater than unity are obtained based on an adopted value of 10-8 secondfor the lifetime of 12(3n); it is indeed remarkable that, in this age ofelectronics, it is necessary to assume a value for the radiative transitionprobability of such a simple and important molecule. From the fluorescenceself-quenching data of these workers Stevens has calculated the muchlonger lifetime of 1.6 x lo* seconds for the excited I, molecule whichreduces the vibrational transfer probabilities to digestible values in therange 10-1-10-2. An interesting feature of the transfer bands in this caseis the comparable intensity of transitions from vibrational levels higher thanthe 26th; for higher levels of lower separation it appears that not only isthe vibrational transfer probability increased but that further excitationis almost as probable as collisional deactivation.High vibrational levels.When the vibrational energy of a molecule is ofthe order of that required for its dissociation, the vibrational separation isoften so small that individual levels are not easily resolved. In simple32 C. R. Stanley, Proc. Roy. SOL. 1957, A , 241, 180.33 G. B. Kistiakowsky and G. G. Volpi, J . Chem. Phys., 1958, 28, 665.34 Calculated from the half-quenching pressure of 0.16 mm. NH,, with the assump-35 C. Zener, Phys. Rev., 1931, 37, 556.36 M. Charton and A.G. Gaydon, Proc. Roy. SOC., 1958, A , 245, 84.37 J. C. Polanyi, Canad. J . Chem., 1958, 36, 121; C. Arnot and C . A. McDowell,38 B. Stevens, ibid., in the press.tion of a quenching collisional efficiency of unity and a quenching diameter of 7.0 A.ibid., pp. 114, 132286 GENERAL AND PHYSICAL CHEMISTRY.molecules this is largely due to vibrational anharmonicity, but in morecomplex systems, additional combination of the various vibrational modesin different levels may be such as to produce a virtual vibrational continuumin this region and the transfer of energy, both internally and externally, ismore amenable to a classical than to a quantum treatment.39 Thus althoughthese levels can be readily excited by collision, recombination, or atom orradical addition and by diabatic processes following electronic excitation,absolute efficiencies of vibrational transitions involving them can only beevaluated insofar as the transitions themselves are defined.Much attention has been given recently to the experimental verificationof one or other of the theories of unimolecular reactions which stand or fallby their ability to account for the pressure variation of the rate constant a tlow pressures.Accurate measurements made in this region by Hinshelwoodand his co-w~rkers~~ have shown that the form of k-p curves is more complexthan was a t first thought. In addition to the inflexion observed whencollisional activation is sufficient to sustain decomposition, other changesof slope are revealed at lower pressures depending on the nature of reactingand foreign gases; indeed the high-pressure rate constant itself shows asimilar dependence.These results, which are of sufficient importance tomerit discussion in the Anniversary Address to the Royal Society by itsPresident,41 require the introduction of additional steps to the Lindemannmechanism such thatNormal - Energised Activatedmoiecu tes - molecules - molecules - Productswith the provisions that any one of the 3 stages may be rate-determining,depending on the total pressure, and that the effect of different gases on eachis specific. That the activated molecule in the case of N20 is in allprobability a triplet has led these authors40 to suggest that a change inmultiplicity may be the rate-determining step for saturated molecules inwhich all electrons are bonding.Gill and Laidler 42 find that with twooscillators contributing to the activation of N,O, the theories of Hinshelwood,Kassel, Rice, and Ramsperger account satisfactorily for the observed de-composition rate in the low-pressure region, whereas the Slater theorypredicts a lower value owing to its more stringent activation requirements.Forst 43 has extended previous work on the unimolecular decompositionof hydrogen peroxide vapour, obtaining frequency factors of 1016 and1013.2 for activation by H20 and He respectively. These require that 5classical oscillators contribute to the activation by peroxide as comparedwith 3 for activation by He; relative efficiencies of the foreign gases in-39 M.J . Boudart and J. T. Dubois, J . Chem. Phys., 1965, 23, 223; B. Stevens,Canad. J . Chem., 1958, 36, 96.40 J . Lindars and Sir C. N. Hinshelwood, PYOC. Roy. SOL, 1957, A , 231, 162, 178;J. Jach and Sir C. N. Hinshelwood, ibid., 1957, A , 229, 143; 1957, A , 231, 145; F. W.Birss, ibid., 1958, A , 247, 281; G. R. Freeman, C. J. Danby, and Sir C. N.HinsheluTood,ibid., 1958, A , 245, 28.4 1 Sir C. N. Hinshelwood, ibid., 1957, A , 243, v.42 E. K. Gill and K. J. Laidler, Canad. J . Chem., 1958, 36, 1570.43 W. Forst, ibid., 1958, 36, 1308; cf. P. A. Gigukre and I. D. Lin, ibid., 1957, 35283; C. N. Satterfield and T. W. Stein, J . Phys. Chem., 1957, 61, 537; D. C. Conway:ibid., p. 1578STEVENS: ENERGY TRANSFER IN LIQUIDS AND GASES.87vestigated are H,O, = 1, H,O = 0.75, 0, = 0.15, He = 0.11. From astudy of the isotope effect on the low-pressure pyrolysis of ethyl bromideand [,H,]ethyl bromide, Blades 44 finds that if the higher activation energyof the deuterated molecule (AE = 2600 cal./mole) is to be explained interms of zero-point energy differences, it is necessary to assume that morethan one vibration is involved in activation. The rate-determining stepin the simple isomerisation of cyclopropane may require some revision inview of the reported geometrical isomerisation of [2H,]cyclopr~pane byRabinovitch and his co-workers ; 45 cis- and trans-isomers undergo reversiblegeometrical isomerisation in addition to a simultaneous structural isomeris-ation, the first-order rate constants beingkgeom = 1016'o exp (-64,20O/RT) sec.-lkseruct = exp (-65,50O/RT) sec.?The pressure variation of kgeom requires that at least 10 oscillatorscontribute, but ring rupture is preferred to the initial hydrogen-migrationmechanism.Cowperthwaite and Warhurst 46 have catalogued the uni-molecular decomposition of phenylmercuric iodide as second-class, with afrequency factor of 1015.7; the activation energy (63 2 kcal./mole)satisfies the criterion that it should be close to the energy sum of the bondsbroken, In this respect an interesting discussion of simultaneous bondrupture in terms of potential-energy surfaces by Szwarc and Herk47 ispertinent; they point out that the primary production of an unstableradical requiring zero activation energy for decomposition can lower theoverall activation energy by an amount equal to its dissociation energy if,and only if, both bonds break simultaneously, i.e., exothermicity of theradical decomposition contributes to the overall activation.An excellentdescription of the application of shock tubes to the study of dissociationrelaxation is provided by Hornig; 48 measurement 49 of the rate of dissoci-ation of Br, in this way shows that rotational energy contributes to activationin the temperature range 1200-2225"~, whilst the dissociation relaxation 50of 0, at higher Mach numbers is consistent with the 0 atom concentrationrequired for a chain mechanism in the N,-0, reaction at 2000-3000"~.As Hoare and Walsh 51 point out, all recombination processes will exhibitthird-order characteristics a t pressures below which the lifetime of theadduct is exceeded by the reciprocal of the collision frequency; this lifetime isshortest for the diatomic case where, since stabilisation requires the removalof small vibrational quanta, all third bodies should behave with perfectefficiency.Collisional stabilisation of larger systems, in which the recom-bination energy is transferred internally to lower levels of greater separation,should be more specific.51 Statistical theories of atom recombination rates44 A. T. Blades, Canad. J . Chem., 1958, 36, 1043.45 B. S. Rabinovitch, E. W. Schlag, and K. B. Wiberg, J . Chem. Phys., 1958, 28, 504.413 M. Cowperthwaite and E. Warhurst, J., 1958, 2429.47 M.Szwarc and L. Herk, J . Chem. Phys., 1958, 29, 438.48 D. F. Hornig, J . Phys. Chem., 1957, 61, 856.49 H. B. Palmer and D. F. Hornig, J . Chem. Phys., 1957, 26, 98.50 H. S. Glick and W. H. Wurster, ibid., 1957, 27, 1224.51 D. E. Hoare and A. D. Walsh, Chem. SOC. Special Publ., 1957, No. 9, 1788 GENERAL AND PHYSICAL CHEMISTRY.have been presented by Keck and by Bunker and David~on,~, and testedon I atom recombination data; Keck's calculated rate constant varies as That lower temperatures and as 1/T above 700"c and is much lower than theobserved value, although the predicted relative efficiencies of third bodiesagree well with less recent data. The latter authors account for the higherobserved rates in terms of a collision complex between the atom and thethird body, the concentration of which is calculated from intermolecularpotentials] and obtain good agreement with experimental relative efficienciesfor heavier non-polar third bodies.Atom recombination produces a steadyincrease in flame temperature above the reaction zone; with sodium atomsas a third-body " thermometer,'] Padley and Sugden 53 obtain rate constantsfor the reactionsH + H + Na--+H, + Na*H+OH+Na-H,O+Na*of the order of molecule-2 cm.6 sec.-l. The chemiluminescence of Nain the presence of H atoms has also been examined by McKinley andPolanyi at lower temperatures, the responsible reactions being eitherNa + Na + H d N a H + Na*with a collision yield of ca. 0.4 x lod3 orNa + H + H+H,(V = 5,J = 3) + Na*with a yield of ca.A convenient method55 of measuring concen-trations of nitrogen atoms in the nitrogen afterglow by titration with nitricoxide led to independent determinations of N atom recombination ratesby Harteck and his co-worker~,~~ who obtaink = 1.72 x molecules-2 cm.6 sec.-lwith argon and nitrogen equally efficient, and by Herron et aZ.,57 who findk = 1-52 x molecules-2 cm.6 sec.-lindependent of temperature in the range 2 7 3 4 5 3 " ~ ~ and with relativethird-body efficiencies, N, = 1, Ar = 0.61, and He = 0.15. Wentink,Sullivan, and Wray58 present a higher value of 3.31 x molecules-2cm.6 sec.-l at room temperature. Kaufman 59 has related the air afterglowintensity to the concentration of oxygen atoms and finds that CO, and N,Oare twice as effective as Ar or N, in the recombination of 0 and NO.Theextremely high efficiency of C1, in oxygen-atom recombination is attributedto a chemical mechanism involving C1 atoms and the C10 radical.52 J. C . Keck, J . Chem. Phys., 1958, 29, 410; P. L. Bunker and N. Davidson, J .53 P. J. Padley and T. M. Sugden, Proc. Roy. SOL, 1958. A , 248, 248.54 J. D. McKinley and J. C . Polanyi, Canad. J . Chem., 1958, 36, 107.55 F. Kaufman and J. R. Kelso, J . Chem. Phys., 1957, 27, 1209; G. B. IGstiakowsky66 P. Harteck, R. R. Reeves, and G. Manella, ibid., 1958, 29, 608.57 J. T. Herron, J. L. Franklin, P. Brandt, and V. H. Dibeler, ibid., p. 230.68 T. Wentink, J. 0. Sullivan, and K. L. Wray, ibid., p. 231.s9 F. Kaufrnan, ibid., 1958, 28, 352; Proc.Roy. Soc., 1958, A , 247, 123,Amer. Chem. Soc., 1958, 80, 5090.and G. G. Volpi, ibid., p. 1141STEVENS: ENERGY TRANSFER I N LIQUIDS AND GASES. 89The longer lifetime of vibrationally excited polyatomic species formedby combination is due to intramolecular energy transfer which may leadto the rupture of a different bond from that initially formed. Possibly thesimplest example is the HO,* radical for which Burgess and Robb 6o havemeasured the rates of both decompositionsH- + 0, + H02* __t He + 0,; k = 2 x lo1, exp (-7100/BT) sec.-l.__)I 0 + *OH; k = 2 x 1013 exp (-21,50O/RT) sec.-l.The beautiful work of Berisford and LeRoy 61 has produced a value of lo*sec. for the lifetime of the methane molecule formed by combination ofCH, + H; although ethane formed in the same way is more complex itcontains a weaker bond and is much less stable.Processes following theaddition of 0 atoms to olefins, and H atoms to alkylamine radicals have beenstudied by the schools of Cvetanovic 62 and Winkler 63 respectively, whilstSteacie and his co-workers suggest that CN abstraction proceeds via a‘‘ cracking mechanism,” and the addition of CH, to but-l-ene results in theformation of propene in similar fashion.65 Vibrational activation of mole-cules by CH, intrusion also affords a means of studying vibrational-energytransfer by analysis of products. This domain is now shared betweenKistiakowsky 66 and Trotman-Dicken~on,~~ who find that the limitingstabilising pressure decreases with increasing complexity of the adduct andthat relative efficiencies for stabilisation of keten formed from CO are:keten = 1, SF6 = 0-8, and N, = 0.1.Frey 68 has suggested that a moreenergetic CH, radical is produced in the photolysis of keten than in thephotolysis of diazomethane. Acetone and methyl iodide have been foundto be some 10 times as efficient as CO, in the third-body combination ofCH,. and 0,,G9 whilst the cyclic structure suggested for the pentylperoxy-radical may form a variety of products depending on the bonds subsequentlybroken.70The removal of vibrational energy from electronically excited fluorescentmolecules has been reviewed recently; 71 the large amounts of energy trans-ferred by more complex molecules suggest a vibration-vibration transfermechanism.Okabe and Steacie 72 have measured the fluorescence stabilis-ation of hexafluoroacetone as a function of inert-gas pressure and find thesame order of efficiency as that obtained from inert-gas effects on the yield60 R. H. Burgess and J. C. Robb, Trans. Faraduy SOC., 1958, 54, 1008.61 R. Berisford and D. J. LeRoy, Canad. J . Chern., 1958, 36, 983.62 R. J. Cvetanovic, ibid., p. 623; S . Sat0 and R. J. Cvetanovic, ibid., p. 970.63 2. M. George, A. N. Wright, and C. A. Winkler, ibid., p. 1171; A. N. Wright,J. W. S. Jamieson, and C. A. Winkler, J . Phys. Chewz., 1958, 62, 657.64 D. E. McElcheran, M. H. J. Wijnen, and E. W. R. Steacie, Canad. J . Chew.,1958, 36. 321.66 W. A. Bryce and P. Kebarle, Trans. Faraday SOL, 1958, 54, 1660.66 T.B. Wilson and G. B. Kistiakowsky, J . Amer. Chem. Soc., 1958, 80, 2934;G. B. Kistiakowsky and K. Sauer, ibid., p. 1066.67 J. H. Knox, A. F. Trotman-Dickenson, and C. H. J. Wells, J., 1958, 2897.68 H. M. Frey, J . Amer. Chem. SOC., 1957, 19, 1259; 1958, 80, 5005.6s M. I. Christie, Proc. Roy. SOL, 1958, A , 244, 411.70 I. R. McGowan and C. F. H. Tipper, ibid., 1958, A , 246, 64.7 1 B. Stevens, Chem. Rev., 1957,57,439; B. Stevens and M. Boudart, Ann. New Yovk72 H. Okabe and E. W. R. Steacie, Canad. J . Chem., 1958, 36, 137.Acad. Sci., 1957, 67, 57090 GENERAL AND PHYSICAL CHEMISTRY.of products of photolysis ; however the collisional reactivation process isomitted from the previous scheme 73 and the doubtful assumption is impliedthat higher vibrational levels of the fluorescent molecule do not emit.Asimilar investigation of the Hg-photosensitised decomposition of cyclo-octatetraene by Yamazaki and Shida 74 shows that this is inhibited by inertgases with the relative efficiencies cyclo-C,H, = 1, He = 0.13, Ar = 0.19,Kr = 0.17. The quantum yield of photolysis of azoethane at 3660 A provesto be pre~sure-dependent,~~ the excited molecule decomposing with anactivation energy of 2.4 kcal./mole. A surprising slow component of thefluorescence of organic vapours is attributed by Williams 76 to the formationof a dimer by excited and unexcited molecules which can be stabilised ordissociated by collision to produce the original fluorescent molecule, thelifetime of which is increased by the duration of the dimer.Rapid removalof excess of vibrational energy of fluorescent molecules by collision withsolvent molecules is admirably demonstrated by the work of Weber andTeale,77 who show that the excitation spectra of 26 compounds coincide withtheir absorption spectra down to 2100 A.Energy Transfer in Diabatic Reactions.-The fundamentals of processesinvolving radiative or radiationless transitions between potential-energysurfaces have recently been reviewed by Eyring, Stewart, and Parlin; 78 thetransmission coefficient is resolved into a diabatic factor based on theLandau-Zener approximation which gives the chance of a transition’soccurring per vibration, and a correcting or recruitment factor which allowsthe equilibrium expressions of absolute rate theory to be applied to the non-equilibrium conditions in chemical reactions.Electronic relaxation maybe a uni- or a bi-molecular process.Radiative transitions will not be reportedexcept insofar as they are involved in the photon theory of energy transfer;the coincidence of excitation and absorption spectra of a large number offluorescent organic molecules in solution over wide frequency ranges 77strongly challenges this theory’s interpretation of the “ cascade ” process bywhich higher electronic states revert to the lowest excited singlet. A strongresemblance between the phosphorescence spectra of naphthyl- and diphenyl-substituted aldehydes and ketones and the spectra of the parent compoundshas led Ermolaev and Terenin 79 to suggest an intramolecular energytransfer between the triplet states of the carbonyl group and of the sub-stituents mentioned.Crosby and Kasha *O have noted the intense emissionby the chelated ytterbium ion a t 9710 A produced by excitation in thelowest X,X* absorption band (3660 A) of the chelating molecule with aquantum yield in the range 0-2-1.0; this extraordinarily efficient transferbetween such widely separated energy states is attributed to vibrationalinteraction. A further interesting case of transfer between the adenine andIlztramoZecuZar processes.7 3 P. B. Ayscough and E. W. R. Steacie, Proc. Roy. Soc., 1956, A, 234, 476.74 H. Yamazaki and S. Shida, J . Chem. Phys., 1956, 24, 1278; 1958, 28, 737.75 H. Cerfontain and K. 0.Kutschke, Canad. J . Chem., 1958, 36, 344.76 R. Williams, J . Chem. Phys., 1958, 28, 577.77 G. Weber and F. W. J. Teale, Trans. Faraday Soc., 1958, 54, 640.78 H. Eyring, G. Stewart, and R. B. Parlin, Canad. J . Chem., 1958, 36, 72.79 V. Ermolaev and A. Terenin, J . Chzm. phys., 1958, 55, 698.80 G. A. Crosby and M. Kasha, Spectrochim. Acta, 1958, 10, 377STEVENS: ENERGY TRANSFER IN LIQUIDS AND GASES. 91nicotinamide groups insulated by a long saturated chain in dihydrodi-phosphopyridine nucleotide is described by Weber ; 81 since no transfer isobserved when the chain is broken, this author suggests a coupled-oscillatormechanism with high (30%) efficiency due to the formation of an intra-molecular complex between the groups concerned.The mechanism of p-bond fission following n,n* excitation in aromaticmolecules has been enterprisingly tackled by Porter 82 in terms of an internalsensitisation of a repulsive state in the side-chain by the In* state of theconjugated system.This problem is of general importance in photo-chemistry where it is becoming increasingly apparent that more than oneprimary dissociation can occur simultaneously; 83 a similar diversity hasbeen suggested to account for the photosensitised decomposition productsof ethyleneimine s4 and the radiation decomposition products of isopropylether.85 The explanation will probably require transitions to differentelectronic states as observed in the case of the simpler N2(5Cg+) system 31which now has three progeny, alll,, B311,, and a new Y state 86 which LeBlancet al.designate 3Au.87 A viscosity dependence of the limiting first-orderrate of naphthalene and anthracene triplet decay in solution seems toindicate a critical nuclear configuration requirement 88 which is suggestedby Bowen and SahuS9 in connection with the internal quenching offluorescence of acridine and acridone in the same phase. Should differentprimary photochemical processes proceed from states of different multi-plicity with possibly different nuclear configurations, these processes mayalso be controlled by the viscosity of the medium and differ from those inthe gas phase.g0An admirable concise review of the circum-stances in which electronic energy is transferred between atoms andmolecules and of the theories put forward to account for these observationshas been given by Livingst~n.~~ Gunning 92 has analysed the products ofHg-photosensitised reactions in which the 202Hg isotope is preferentiallyexcited and finds no enrichment in the case of N20 and 02, which thereforeexcludes primary reaction between these molecules and 202Hg(63.P,) ; fromenergy considerations Gill and Laidler 93 conclude that the sensitised 0,molecule is 3C+u.The pressure-dependence of H, formation in the Hg-photo-sensitised polymerisation of acetylene also suggests the primary formationof an excited C2H2 moleculeg4 which should be in the triplet state; spinIntermolecular pyocesscs.81 G. Weber, Nature, 1957, 180, 1409.82 G. Porter, Chem. SOC. Special Publ., 1957, No.9, 143.8 3 M. H. J. Wijnen, J . Amer. Chem. SOC., 1958, 80, 2394; P. Ausloos, Canad. J .84 C. Luner and H. Gesser, J . Arner. Chem. Soc., 1958, 80, 1148.85 A. S. Newton, J . Phys. Chem., 1957, 61, 1490.86 G. B. Kistiakowsky and P. Warneck, J . Chem. Phys., 1957, 27, 1417.87 F. LeBlanc, Y . Tanaka, and A. Jursa, ibid., 1958, 28, 979.BE G. Porter and M. W. Windsor, PYOG. Roy. Soc., 1958, A , 245, 238.89 E. J. Bowen and J. Sahu, J , , 1958, 3716.90 P. Ausloos, Canad. J . Chem., 1958, 36, 383.91 R. Livingston, J . Phys. Chem., 1957, 61, 860.92 H. E. Gunning, Canad. J . Chem., 1958, 36, 89.93 E. K. Gill and K. J. Laidler, ibid., p. 79.94 S. Shida, 2. Kuri, and T. Furuoya, J . Chem. Phys., 1958, 28, 131.Chem., 1958, 36, 40092 GENERAL AND PHYSICAL CHEMISTRY.conservation also requires that triplet NH, should be a product whenNZ(B3ng) is strongly quenched by this molecule in the nitrogen afterglowalthough Kistiakowsky and Volpi 33 detect no products of its subsequentdecomposition.Birks 95 has challenged Weinreb’s attempt 96 to discriminate betweenradiative and non-radiative transfer of excitation energy in liquid systemson the grounds that use of the technical fluorescence yield of the donor,arbitrarily assigned a value of 33%’ enables the observed transfer to becompletely accounted for by the photon theory.In reply, Weinreb givesfive reasons why secondary donor fluorescence cannot seriously affect hisoriginal interpretation in which photon transfer has a considerable but notexclusive role.Solvent-solute transfer has been treated by Brown, Furst,and Kallmann 97 from the point of view of emission intensities produced by’y- and ultraviolet irradiation; the last two authors 98 find that concentration“ cross-quenching ” between different molecules can take place if thedifference in their energy levels is close to their average vibrational energy.A different approach has been used by Knaqg9 who measures the fluorescencedecay time of anthracene in benzene solution excited directly by ultravioletlight (4 x lo* sec.), and indirectly following transfer from the solventexcited by electrons (9 x sec.) ; the difference in decay time is a measureof the “ transfer time ” which decreases with increasing solute concentrationand thus rules out the photon-transfer theory.Both this theory and theForster dipole interaction theory predict increasing transfer efficiency withincreasing overlap of the donor emission and acceptor absorption spectraand with decreasing separation of the molecules concerned and should nottherefore be considered as mutually exclusive. However from his measuredtransfer efficiencies of carotenoid-sensitised chlorophyll fluorescence in vitrowhich range from 0 to lOOyo for acceptors exhibiting comparable emission-absorption overlap a t the same concentrations, Teale loo concludes thatproximity and overlap are not the only factors controlling transfer. Calvin 101and his coworkers find that a similar sensitisation in ChZoreZZa and spinachchloroplasts is considerably more efficient than in Nostoc, which suggests thata critical orientation is necessary.A valuable account of the roles playedby homogeneous and heterogeneous energy transfer in photosynthesis isgiven by Rabinowitch,lo2 who emphasises the difference in conditionsobtaining in the chloroplast and under experimental conditions in solution ;the delayed onset of sensitised chlorophyll fluorescence by pigments(-15 mp sec.) is that expected from measurements of excitation time andof sensitiser quenching in vitro.100 GENERAL AND PHYSICAL CHEMISTRY.Interesting bridged structures of the electron-deficient compoundsB6H1() and InMe, have been determined57,58 by X-ray studies. Halogenbridges are met in niobium 59a and tungsten 59b derivatives : in the niobiumpentachloride dimer two chlorine atoms link the two NbCl, units, while inthe ion W,Clg3- three chlorine atoms link the two WCl, units; in both theconfiguration about the metal atoms is octahedral. Chlorine atoms also formthe bridge in the molecule 6o (C,H,),TiCl~lEt,, while two carbon monoxidemolecules join the two halves of the dicyclopentadienyldi-iron tetracarbonylmolecule.61A microwave determination 62 of cyclopentadienylnickel nitrosyl showsCsV symmetry with the Ni, N, and 0 atoms lying on the %fold symmetryaxis of the carbon ring.Polyatomic molecules: organic compounds.Most structural determin-ations on simple organic molecules are concerned with increased precisionand small but significant variations. In the microwave field, structuraldeterminations have recently taken second place to measurements ofrotational barriers discussed in the third section of this Report.The organicmolecules considered here are grouped into (a) substituted methanes (in-cluding a number of t-butyl derivatives), (b) substituted acetylenes andolefins, and (c) cyclic compounds.(a) Substituted methanes. Methane itself and [,H&nethane have beenexamined 63 by infrared and Raman spectroscopy, and new rotational con-stants have also been obtained for methyl chloride and for chloroform.65Electron-diffraction measurements have been made on a number offluoro-derivatives: dichlorodifluoromethane,66 trifluoromethyl bromide,67i ~ d i d e , ~ '168 and cyanide:' and trifluoromet hylsulphur pent afluoride .67 Theredetermination 68 of the structure of CF,I by use of complex atomic scatter-ing factors and incorporation of the microwave determination of IB (momentof inertia) leads to C-I = 2.135, C-F = 1.340 A, and LFCF = 108.4", bothbond distances being 0.012 fi longer than Bowen's 69 values.Otherwise,C-F distances fit into the established patterns for CF, groups: the CNdistance 67 of CF,.CN is 1.495 fi, significantly longer than the 1.458 & 0.005of methyl ~yanide.~Another cyanide investigated by electron diffraction is t-butyl cyanide;its isomer t-butyl isocyanide has been investigated '0 by microwave methods :57 F. L. Hirshfeld, K. Eriks, R. E. Dickerson, E. L. Lippert, and W. N. Lipscomb,J . Chem. Phys., 1958, 28, 56.68 E.L. Amma and R. E. Rundle, J . Amer. Chem. Soc., 1958, 80, 4141.69 (a) A. Zalkin and D. E. Sands, Acta Cryst., 1958,11, 615; (b) W. €3. Watson, jun.,and J. Waser, ibid., p . 689.60 G. Natta, P. Corradini, and I. W. Bassi, J . Amer. Chem. SOC., 1958, 80, 755.61 0. S, Mills, Acta Cryst., 1958, 11, 620.63 A. P. Cox, L. F. Thomas, and J. Sheridan, Nature, 1958, 181. 1157.63 D. E. Brown, Diss. Abs., 1958, 18, 2172; G. G. Shepherd and H. L. Welsh, J .64 R. G. Brown and T. H. Edwards, J . Chew. Phys., 1958, 28, 384.65 T. L. Weatherley, Diss. Abs., 1958, 18, 1469.66 J. J. Kristoff, ibid., p. 1997.67 R. E. Andersen, ibid., p. 50.68 C. H. Wong and V. Schomaker, J . Chem. Phys., 1958, 28, 1010.a9 H. J. M. Bowen, Trans. Faraday Soc., 1954, 50, 444.70 B.Bak, L. H. Nygaard, and J. R. Andersen, J . MoZ. Sfiectroscopy, 1958, 2, 54.Mol. Spectroscopy, 1957, 1, 277GRAY : MOLECULAR STRUCTURE AND MOLECULAR VIBRATIONS. 101bond lengths in these molecules are similar to those4 in the methyl com-pounds. Other t-butyl derivatives examined * are isobutane and t-butylfluoride; the C-F distance in the latter, 1.43 rf 0.2 A, is markedly longerthan in methyl fluoride. However, the molecules were studied40 with theaim of determining rotational barriers and this length (and that of the C-Cbond, 1.516 A) depend on assumed dimensions for the methyl groups.Notable determinations of thedimensions of ethylene and allene have been made by fine-structure analysisof vibration-rotation spectra. Allen and Plyler 71 find for ethylenero(C=C) = 1.337, r,(C-H) = 1.086 A, and LHCH = 117" 22'.There areno inconsistencies although four experimental quantities are available todetermine these three parameters : previous electron-diffraction and Ramanwork led to the results 1.334 and 1.3MA respectively for yo. For allene,Stoicheff's Raman work fixes ro(C=C) at 1.309 & 0.001 A and provides arelation between LHCH and r(C-H). Overend and Crawford's 72 newrotational analysis supplies the second relation fixing LHCH at 116" & 0-5"and r,(C-H) at 1.061 & 0.004; this bond length is significantly shorter(0.025 A) than in ethylene. Cyvin 72 has calculated vibration amplitudes forallene and [2H,]allene.Electron-diffraction studies have been made of the isomers cis-l,2-&-chloroethylene and 1, l-dichloroethylene and of the conjugated olefinsbuta-1 J3-diene,7* ~hloroprene,~~ and acryloyl ~hloride.'~ In the two di-chloroethylenes the experimental value of 1-33A for r(C=C) is markedlyshorter than that (1.38 A) assumed hitherto.The LClCCl in vinylidenedichloride, 114.5" &;lo, does not differ significantly from that in tetrachloro-ethylene.Acetylenic molecules are represented by propargyl chloride 77 and di-methyldia~etylene.~~ The single-bond length in propargyl chloride is1.458 A; in butadiene 74 it is 1.483 & 0.01 A, and in chloroprene 76 1.46 A.In dimethyldiacetylene an X-ray study of the solid leads to the bond dis-tances C-c, 1.199 A; CH,-C 1.466 A; and EC-G 1.375 A. A list of carbon-carbon triple bond lengths has been compiled by G~odwin.~~A vibrational analysis of 1,3,5-hexatriene is in accords0 with a planarstructure with the double bonds trans to one another, giving the molecule acentre of symmetry.(c) Cyclic compounds. A complete determination of the structure ofpyridine 81 has been made by microwave spectroscopy, isotopic substitution71 H.C. Allen and E. K. Plyler, J . Amer. Chem. SOC., 1958, 80, 2673.72 J. Overend and B. Crawford, J . Chem. Phys., 1958, 29, 1002; S. C. Cyvin, A d a73 C. C . W. Hoffman, Diss. Abs., 1958, 18, 420.74 A. Almenningen, 0. Bastiansen, and M . Tratteberg, Acta Chem. Scand., 1958, 12,76 P. A. Akishin, L. V. Vilkov, and V. M . Tatevskii, Doklady Akad. Nauk S.S.S.R.,76 T.Ukaji, Bzcll. Chem. SOC. Japan, 1957, 30, 737.77 E. Hirota, T. Oka, and Y . Morino, J . Chem. Phys., 1958, 29, 444.'13 R. C. Himes, Diss. Abs., 1958, 18, 1619.7s T. H. Goodwin, J., 1958, 3893.8o E. R. Lippincott, C. E. White, and J. P. Sibilia, J . Amer. Chem. Soc., 1968,80,2926.B. Bak, L. H. Nygaard, and J. R. Andersen, J. Mol. S@ectroscopy, 1958, 2, 361.(b) Substituted olefins and acetylenes.Chem. Scand., 1958, 12, 233; J . Chem. Phys., 1958, 29, 583.1221.1958, 118, 117102 GENERAL AND PHYSICAL CHEMISTRY.being used for both C and H in every position to derive accurately the tengeometrical parameters of the molecule. The carbon-carbon bond lengthsare identical at 1.3944 or 1.3945 A; the carbon-nitrogen distance is 1.3402 Aand the nitrogen angle 116' 50'.The bond lengths so found had been pre-viously predicted by Cumper 82 on the basis of a correlation between lengthsand angles dependent on hybridization: the errors of the prediction areconcentrated in the region of the nitrogen atom.A new, precise electron-diffraction study 83 of 1,3,5,7-cyclo-octatetraeneconfims Hedberg and Schomaker's results and disagrees with Bastiansen'sprevious work: the D 2 d (tub) form is satisfactory in all respects.84 The bondlengths (A) and angles measured 83 are: C=C, 1.334 & 0.001; C-C,1.462 0.001 ; C-H, 1.090 & 0.005 A; LGC-C, 126.46 & 0.23"; LCzC-H,118.3" & 5.9". An empirical relation 85 between the length of the singlecarbon-carbon bond joining two trigonally hybridized carbon atoms and theinterplanar angle of the linked groups has been suggested.The newestvalues from cyclo-octatetraenes3 and butadiene74 do not appear to fit itperfectly.Bond lengths and angles in cyclopropyl chloride and cyanide have beenderived by Friend and Dailey 86 on the basis of an equilateral triangle withall C-H bonds equal. They find a carbon-chlorine distance (1.7780A)similar to that in unsaturated halides and they ascribe to this bond 4%double-bond and 23% ionic character. Other lengths (A) are: C-C in ring,1*5131A; LHCH, 114'36' in chloride and 115'35' in cyanide; C-CN,1.4679; E N , 1.1574 A.Hexaphenylbenzene has been examined 87 by electron diffraction. Asin 1,3,5-triphenylbenzene the peripheral rings are not coplanar. Theyoscillate to a rather limited extent (&lo") from the orthogonal.(a) Miscellaneous.Bond lengths have been obtained in the course ofdeterminations of rotational barriers in a number of species discussed inthe last section of this Report. Configurations of propene,88 n-propylchloride,sg and of the two substituted ethanes CF,Br.CHFCl andCFCl,CHCl, 91 have also been established. In propyl chloride the greaterstability of the gauche-form (azimuthal angle 59") is in accord with an electro-static attraction between the chlorine atom and the methyl group.Molecular Vibrations and Force Constants.-The arrangement followed issimilar to that of the previous section with the emphasis again on simplesystems. Torsional oscillations are considered in the next section.Allstretching force constants quoted are in lo5 dynes/cm. (millidyneslA) unlessotherwise stated.82 C. W. N. Cumper, Trans. Faraday Soc., 1958, 54, 1261, 1266.8* 0. Bastiansen, L. Hedberg, and K. Hedberg, J . Chem. Phys., 1957, 27, 1311.B4 I. J. Lawrenson and F. A. Rushworth, Nature, 1958, 182, 391.86 J. P. Friend and B. P. Dailey, J . Chem. Phys., 1958, 29, 577.87 A. Almenningen, 0. Bastiansen, and P. N. Skancke, Acta Chem. Scand., 1958,88 D. R. Herschbach and L. C. Krisher, J . Chem. Phys., 1968, 28, 728.88 Y. Morino and K. Kuchitsu, J . Chem. Phys., 1958, 28, 175.n1 R. E. Kagarise, J . Chem. Phys., 1958, 29, 680.D. Cook, J . Chem. Phys., 1958, 28, 1001.12, 1215.J. Lee and L. H. Sutcliffe, Trans. Faraday Soc., 1958, 54, 308GRAY : MOLECULAR STRUCTURE AND MOLECULAR VIBRATIONS.103Pistorius 92993 has carried out normalco-ordinate analyses for a number of species and derived expressions for theforce constants of the valence-force field in terms of the general force con-stants. The species examined are: square-planar X4 (D4h) ; pyramidalXYa (C4J; planar XY4 (Ddh); planar xY6 (&); octahedral xY6 (Oh);and tetrahedral Xq (Td) previously treated by Slater.93 Other species whichhave been treated recently are the square-pyramidal 94 M(XY)S (C,,) ;octahedral 95 M(XY)6 (Oh) ; and pentagonal-bipyramidal 96 M(XY)lo ( D 5 d ) .Apart from their formal value these treatments are of the greatest help incomparing the force fields in different molecules. Basically, two modes ofcomparison commend themselves: one based on general force constants ofthe same symmetry type and the other on, e.g., valence-force field constantsfor a particular bond.The first has the advantage of exactness : the secondthat these are the force constants which are successfully transferred frommolecule to molecule.A second-order sum rule, involving fourth powers of frequencies inisotopic molecules, has been deduced by Bigelei~en.~~ A freqency rule fornon-isotopic species has been applied 98 to CO,, COS, and CS, and to C2F4and C,Cl,; the rule corresponds to transferred general force constants ratherthan valence-force constants which are commonly used (see, e.g., prediction ggof v3 in CTe,).Wilson loo has described a method of determining the order of atoms in alinear molecule and isotopically substituted species from vibration frequenciesonly.Diatomic molecules.The influence of anharmonicity on vibrationalprobability density and mean amplitudes of vibration has been examined byReitan.lol Experimental work has been done on the vibration frequenciesin the Cl,+ ion l6 and in the isoelectronic radicals l7 C10, BrO, and 10. Inall these species, excitation leads to the expected decrease in the firmness ofbinding. Excited states of Cl,, Br,, and I, have also been examined l5 andnew bands of the P, molecule located.18 A comprehensive investigation ofhydrogen, deuterium, and tritium electronic-vibration spectra has beenpublished by Diecke: lo2 all six isotopic pairs have been examined and acatalogue of 100,000 lines compiled and analysed.A number of empirical correlations have been explored.Varshni lo3has made a full investigation of the correlations arising from Sutherland'sNormal co-ordinate analyses.C . W. F. T. Pistorius, 2. phys. Chem. (Frankfurt), 1958,16, 126; ibid., 17, 292;Mol. Phys., 1958, 1, 295; J . MoZ. Spectroscopy, 1958, 2, 287; J . Chem. Phys., 1958,29, 1328.9a N. B. Slater, Trans. Faraday SOC., 1954, 50, 207; C. W. F. T. Pistorius, J. Chem.Phys., 1958, 29, 1421.94 M. F. O'Dwyer, J. Mol. Spectroscopy, 1958, 2, 144.96 H. Murata and K. Kawai, J. Chem. Phys., 1957, 2'7, 605.96 E. R. Lippincott and R. D. Nelson, Spectrochim. Acta, 1958, 10, 307.97 J. Bigeleisen, J. Chem. Phys., 1958, 28, 694.S. Brodersen and A.Langseth, Acta Chem. Scand., 1958, 12, 1111.99 T. Wentinck, J. Chem. Phys., 1958, 29, 188.loo E. B. Wilson, Spectrochim. Acta, 1958, 12, 1.lol A. Reitan, Acta Chem. Scand., 1958, 12, 131.loa G. H. Diecke, J. Mol. Spectroscopy, 1958, 2, 494.lo* Y. P. Varshni, J . Chem. Phys., 1968, 28, 1078104 GENERAL AND PHYSICAL CHEMISTRY.potential formula u = a(r - d)" - b(r - d)* especially of the relationk&, - d), = A , where d and A are constants for each molecular group.A most interesting simple potential function has been suggested by Keyes 104for excited states of diatomic molecules. It requires knowledge only of(I) the Morse function for the ground state and (2) the fraction of valenceelectrons in the excited state occupying bonding orbitals.Agreement withexperimental values of a,' and r,' is very good but estimates of anharmoni-city and dissociation energies are cruder. In certain circumstances thefunction is itself a Morse curve and the relation to the bond order is plain (acorrelation which has been explored lo4 by Stevens).Triatomic molecules. (a) Linear molecules. Zero-order frequencies andthe four general force constants have been derived lo5 for N,O. In valence-force field terms, f" = 17-33, very similar to its value in the similarHN,; fN0 = 12.53; the interaction constant is 0.733 and the bending con-stant 0.66 x erg per radian. For carbon disulphide, Stoicheff'svibrational Raman work 22 leads to accurate zero-order frequencies (there isno Fermi resonance) and anharmonicity corrections.Absolute infraredintensities have been measured lo6 for v3 of CS, in both the gas and the liquidstate: the band in the liquid is twice as intense. In the ion CS2+ themeasured 25 vibration frequencies v1 = 617 or 631 cm.-l and v2 = 409.5 cm.-lare very little changed from the neutral molecule. Fundamental frequenciesin the higher members of the CS, family have been measuredg9 for CSe,,SCSe, and SCTe, and estimates made on the basis of uniform potential-energy functions of the v3 frequency in OCTe, SeCTe, and CTe,.In BeF,, BeCl,, and MgC1, bending and asymmetric stretching forceconstants have been located; lo7 the stretching force constants are close tothose in the corresponding diatomic BeX radicals.The ions NCO- and NCS- have been studied in the solid state.There isFermi resonance between v1 and 2v2 in the cyanate; lo* for the thiocyanate logfundamental frequencies and anharmonicity constants are derived. An in-teresting simplified treatment l1* of the vibrations of the UO, group in uranylcomplexes has been given : the assumption of a free linear group is a good one.Precise work on nitrogen dioxide continues :with a new determination of x , ~ all the zero-order frequencies and an-harmonicity constants of the general force field are determined.lll Invalency-force field terms, fd = 10.927 f J d 2 = 1-125, f & = 2.038, andfdCL/d = 0.390.Among partial vibrational assignments are the identification of two ofthe fundamentals of SiF, 27 and of HNO in its ground and excited 29 states.(b) Angular molecules.The high value of the interaction constant fa is notable.104 R.W. Keyes, J . Chem. Phys., 1958, 29, 523; B. Stevens, Spectrochim. Acta,lo5 G. &I. Begun and W. H. Fletcher, J . Chem. Phys., 1958, 28, 414.Io6 P. N. Schatz, ibid., 1958, 29, 959.lo7 A. Biichler and W. Klemperer, ibid., p. 121.lo* A. Maki and J. C. Decins, ibid., 1958, 28, 1003.Io9 L. H. Jones, ibid., p. 1234.1958, 12, 154.L. H. Jones, Spectrochim. Acta, 1958, 10, 395.E. T. Arakawa and A. H. Nielsen, J. Mol. Spectroscopy, 1958, 2, 413; J. W.Keller and A. H. Nielsen, J . Chem. Phys., 1958, 29, 252; G. R. Bird, A. Danti, andR. C. Lord, Spectrochim. A d a , 1968, 12, 247GRAY: MOLECULAR STRUCTURE AND MOLECULAR VIBRATIONS. 105The Renner effect 112 in the NH, radical has been further discussed.Aspeculative identification of the bending vibration (at 1114 or 1362 cm?)the iong-sought methylene radical has been suggested113 on the basis of a studyof the photolysis of diazomethane at low temperatures in a rigid medium.Vibrational assignments 32 have been made tofour excited states of acetylene: the v5 (nu) vibration of cyanogen has beenmore precisely located 11* at 235.0 cm.-l.Existing data on seven planar AX, (D3h) molecules (BF,, BCl,, BBr,,B033-, C0,2-, NO,-, SO,) have been used115 to evaluate all five forceconstants of the general quadratic force field. All comparisons show thestriking similarities of COZ2- and NO,-; although BO,,- is also isoelectronic,differences are apparent between it and the other two.New measurementsare reported 116 on boron tri-bromide and -iodide. The frequencies of car-bony1 chloride (planar AXY,) have been reassigned 117 and previous third-law entropy discrepancy reduced from 1.6 to 0.36 cal. deg.-l mole-l; forceconstants in nitryl fluoride and chloride have been discussed.llsAmong pyramidal AX, ((4 molecules, ammonia continues to receive 119detailed attention. Further work has also been done120 on the inversionspectrum of ND,. Thefundamental frequencies of the pyramidal trihalides PCl,, AsCl,, SbCl,, PBr,,and SbBr, have been measured122 (they lie in the 85-550 cm.-l range)and used to evaluate four of the general force constants. The expectedregularities are found in the series of chlorides, resistance to both stretchingand bending falling in the order P > As > Sb.A six-constant potentialfunction (valency-force field) has been derived for nitrogen trifluorideby combining experimental distortion constants with the four fundamentalfrequencies. In these terms,fd = 4.36 andfa/d2 = 1.92. The low permanentdipole moment of this interesting molecule owes its origin to opposing factors:these are differently affected123 by different vibrational modes and in fact&/&(D/A) takes the value 1.75 for class A, and 4.5 for class E vibration.The infrared and Raman spectra of chlorine trifluoride and brominetrifluoride have been investigated.124 All six fundamentals of ClF, havebeen assigned on the basis of CBU symmetry. The low-lying lA2 excitedstate of formaldehyde shows 39 sharply changed frequencies (except for C-Hstretching and CH, bending) from the ground state: bonding similar to thatin formic acid has been suggested.Tetratomic molecules.The v2 frequency 121 of PD, has been newly located.J.A. Pople and H. C. Longuet-Higgins, MoZ. Phys., 1958, 1, 372.113 G. C. Pimentel, J . Chem. Phys., 1958, 29, 1405.114 T. Miyazawa, ibid., p. 421.116 C. W. F. T. Pistorius, ibid., p. 1174.116 T. Wentinck and V. H. Tiensun, ibid., 1958, 28, 827.117 E. Catalan0 and K. S. Pitzer, J . Amer. Chem. SOC., 1958, 80, 1054.11s T. A. Hariharan, Proc. Indian Acad. Sci., 1958, 48, 49; L. Burnelle and J.11s W. S. Benedict, E. K. Plyler, and E. D. Tidwell, J . Res. Nut.Bur Stand., 1958,120 G. Hermann, J . Chem. Phys., 1958, 29, 875.121 W. M. Ward, Diss. Abs., 1958, 18, 1823.122 P. TV. Davies and R. A. Oetjen, J . Mol. Spectroscopy, 1958, 2, 253.123 P. N. Schatz, J . Chem. Phys., 1958, 29, 475, 481.lZ4 H. H. Claassen, B. Weinstock, and J. G. Malm, ibid., 1958, 28, 285.Duchesne, Nature, 1958, 182, 653.61, 123; J . Chem. Phys., 1958, 29, 829106 GENERAL AND PHYSICAL CHEMISTRY.Tetrahedral molecules. Methane (as CT, and CHT,) has been investi-gated 125 and the observations combined with existing data for CH, andCD, to calculate all the valence-force constants for the methanes. In thesetermsfd = 5.3985 andfdd = 0.0171. General force constants have also beenobtained 126 for the borohydride ion from a study of its Raman spectrum inliquid ammonia.Interest is added to these measurements by two theoreticalpapers 127 in which hydride vibration frequencies are calculated in speciessuch as NH,+, CH,, and BH,-. For the class E frequency the simple relation~ x ~ v , ~ = 92/6e2/32mrO3 (yo is length of bond) predicts frequencies with about5% error. In the two isoelectronic triads BH,-, CH,, NH,+, and AlH,-,SiH,, PH,+ the force constants of the A , mode have been compared.128There is a steady increase with increasing nuclear charge which is correlatedwith the simultaneous change in bond length.Fundamental frequencies of twenty-two tetrahedral species (mainlyhalides and oxyanions) have been collated 129 and used to derive five of thegeneral valence-force constants.A similar collection of data, together withsome new determination^,^^^ has been made by Woodward 128 and used toinvestigate the systematic variations in the force constant of the A , mode.Among the halides the following six isoelectronic families have been in-vestigated: AlCl,-, SiCl,, PC14+; ZnX,,-, GaX,-, GeX, where X = C1, Br,or I ; CdX,2-, InX,-, and SnX, where X = Br or I. Whether the valence-force constant or the symmetry-force constant of the A , mode is used thesame generalization emerges that there is an increase in force constant withincreasing nuclear charge and a simultaneous shortening in bond length.When the two oxides families: PO:-, SO:-, ClO,-, and WO,2-, ReO,-,OsO, are examined the correlation is not found. In the former triad,phosphate and sulphate are closely similar to one another; perchlorate isless tightly bound. A re-identification 131 of the fundamentals of the chro-mate ion CrO,,- ( T d ) has been made and used to derive two sets of four outof five possible general force constants.Molecules of similar arrangement but lower symmetry which have beenexamined are SiD,I for which a complete assignment 132 has been made,CH,F and CH,Cl (all C,); chromyl fluoride and bromide (C2J for whichall nine fundamentals are assigned; and sulphuryl bromofluoride 135 (CJ.Complete vibrational assignments and force-constant calculations have alsobeen made 138 for CHC1,F and CHF,Cl and their deuterium derivatives (CJ.Pistorius 137 has collected data for fifteen fluorides Octahedral molecuules.125 L.H. Jones and M. Goldblatt, J . M d . Spectroscopy, 1958, 2, 103.126 A. R. Emery and R. C. Taylor, J . Chem. Phys., 1958, 28, 1029.lZ7 H. Hartmann and G. Gliemann, 2. phys. Chem. (Frankjwt), 1958, 15, 108;12s C. W. F. T. Pistorius, J . Chem. Phys., 1958, 28, 514.130 L. A. Woodward and G. H. Singer, J.. 1958, 716.131 H. Stammreich, D. Bassi, and 0. Sala, Spectrochim. Acta, 1958, 12, 403.la2 H. R. Linton and E. R. Nixon, Sfiectrochim. Acta, 1958, 12, 41.133 C. Tanaka, J . Chem. SOC. Japan, 1958, 79, 686.13* W. E. Hobbs, J . Chem. Phys., 1958, 28, 1220.T. I. Crow and R. I. Lagemann, Spectrochim. Acta, 1958, 12, 143.136 H. B. Weissman, A. G. Meister, and P. C. Cleveland, ibid., p. 72.13' C. W. F. T. Pistorius, J .Chem. Phys., 1968, 29, 1328.D. A. Brown, J . Chem. Phys., 1958, 29, 451.L. A. Woodward, Trans. Faraday SOC., 1958, 54, 1217GRAY: MOLECULAR STRUCTURE AND MOLECULAR VIBRATIONS. 107and chlorides of formula MX, (Oh) and calculated six of the seven generalforce constants. In the triad SF, (775), SeF, (710), TeF, (697) the frequen-cies (cm.-l) of the Al, mode show a uniform decrease in force constant;similar trends are present in the data for WF, (770), ReF, (753), OsF, (notgiven), IrF, (696), and for UF, (666), NpF, (648), PuF, (626), though all thechanges are relatively small.The carbonyls and cyanides share thegeneral formula M(AB),: representatives of the classes n = 4, 5, and 6 havebeen investigated this year. Vibrational assignments have been made 138~139for the isoelectronic tetrahedral group Ni(CO),, Ni(CN),4-, and CU(CN)*~-and force constants evaluated.The numerical values13* accord with anormal single nickel-carbon bond in nickel carbonyl.Alternative assignments and force constants, based on square-pyra-midal 94 (C4 or trigonal-bipyramidal95 ( D 4 structures for iron penta-carbonyl, have been suggested : the structure remains 94,95~140 in dispute.Fairly complete Raman spectral investigation has been made 141 of thehexacarbonyls of chromium, molybdenum, and tungsten ; the analogouscyanides of chromium and ruthenium have been studied142 by infraredtechniques, and the force constants of Cr(CN)z- and Cr(CO), compared. Allthese have symmetry Oh.Ferrocene and ruthenocene can be represented as M(AB),, with sym-metry D5d: a detailed account 143 of their spectra has been published.Anexamination of frequencies in thallium and magnesium cyclopen tadien ylshas been interpretedIn the set of tetramethyls [M(AB,),, Td] of carbon, silicon, germanium,tin, and lead 145 the metal-carbon force constants fall regularly from carbonto lead. The nickel derivative, Ni(PF3)4, has a nickel-phosphorus forceconstant consonant with a normal single bond.146Complex molecules lie outside the scope of thisReport but attention is drawn here to some isolated examples, to the fieldsof amide derivatives 14' and silicon compounds148 in which a number ofMetal carbonyls and cyanides.as favouring ionic bonding: Tl+(C,H5-).Polyatomic molecules.la8 L.H. Jones, J. Chem. Phys., 1958, 28, 1215; 1958, 29, 463.la* M. F. El Sayed and R. K. Sheline, J. Amer. Chem. SOC., 1958, 80, 2047.140 W. G. Fateley and E. R. Lippincott, Spectrochim. Acta, 1957, 10, 8 ; F. A.Cotton, A. Danti, J. S. Waugh, and R. W. Fessenden, J. Chem. Phys., 1958, 29, 1427.141 A. Danti and F. A. Cotton, ibid., 1958, 28, 736.142 V. Caglioti, G. Sartori, and M. Scrocco, A t t i Accad. naz. Lincei, 1957, 23, 359;G. B. Borino and G. Fabbri, ibid., p. 191.14a E. R. Lippincott and R. D. Nelson, Spectrochim. A c f a , 1958, 10, 307.144 F. A. Cotton and L. T. Reynolds, J. Amer. Chenz. SOC., 1958, 80, 269.146 D. N. Waters and L. A. Woodward, Proc. Roy. SOC., 1958, A , 246, 119.146 L. A. Woodward and J . R. Hall, Nature, 1958, 181, 831.A.Yamaguchi, T. Miyazawa, T. Shimanouchi, and S. Mizushima, S$ectrochim.Acta, 1957, 10, 170; T. Shimanouchi and S. Mizushima, ibid., 1958, 12, 253; T. Miya-zawa, T. Shimanouchi, and S. Mizushima, J. Chem. Phys., 1958, 29, 611; A. E. Parsons,J. Molec. Spectroscopy, 1958, 2, 566; W. J . 0. Thomas and A. E. Parsons, ibid.. 1958,2, 203; Trans. Faraday SOC., 1958, 54, 460; M. Davies and W. J. Jones, ibid., 1958, 54,1454; J., 1958, 955; M. Davies and N. Jonathan, Trans. Faraday SOC., 1958, 54, 469.14* R. C. Lord, D. W. Mayo, H. E. Opitz, and J . S. Peake, Spectrochim. A d a , 1958,12, 147; H. R. Linton and E. R. Nixon, ibid., 1957, 10, 299; J . Chem. Phys., 1958, 28,990; 1958, 29, 921; R. F. Curl and K. S. Pitzer, J. Amer. Chem. SOC., 1958, 80, 2371;J.Goubeau and J. Reyhling, 2. anorg. Chem., 1958, 294, 92, 96; H. Kriegsmann, ibid.,1958, 294, 113108 GENERAL AND PHYSICAL CHEMISTRY.complete or nearly complete assignments have been made, and to a review 149of valence bonding in nitrogen compounds.Among the most remarkable vibrational assignments are those made byFateley et al. in work 150 on the nitrogen oxides; by condensing the freshlyformed molecules in a matrix on a cold surface they have been able to isolateand identify nitric oxide dimer, nitrous anhydride as ON-NO, and ON-0-NO,dinitrogen tetroxide as 02N*N02 and ON*O*NO,, and covalent dinitrogenpentoxide 02N*O*N02. A tentative identification is made of the D 2 d formof N20,.Vinyl fluoride and its seven deuterated derivatives have been studied 151and eight of the twelve vibrations assigned.Diborane has been investi-gated 152 as 1°B2H6, 11B2H6, "B2D6, and 11B2D6 and as B2H,D and B2D,H.Incompletely deuterated mixtures contain all twenty-one possible forms anddata thus require disentanglement. Assignments 152 on the basis of D2ksymmetry together with non-crossing and product and sum rules are satis-factory .For the isoelectronic molecules BF,*NH, and SO,*NH, (the zwitterionof sulphamic acid) complete vibrational assignments have been made.In SO,*NH,, force constants of the Urey-Bradley potential are 2.2 forsulphur-nitrogen and 7.5 for sulphur-oxygen stretching. The correction lMof an error completes the assignment for the similar molecule c2F6.Potential-energy Barriers to Internal Rotations.-Methods of measuringthe size of the energy barrier to internal rotation have become more diverseand more precise.The original '' entropy deficit " method has been supple-mented by measurements of specific heat, of torsional frequencies by spectro-scopy, of torsional amplitudes by electron diffraction, of nuclear magneticresonance spectra, of the dispersion and absorption of ultrasonics, and ofline splittings and intensities. The cosine form of the potential-energybarrier remains the basis of all estimates of barrier size: so far as the originsof the barriers axe concerned theory has not kept pace with experiment.Some general aspects of the origins of barriers and some values of barriersmeasured by various techniques6 have been recently published.In thisReport barrier heights are given in cal./mole.Lide156 has re-viewed the spectroscopic data for torsional frequencies in ethane: thebarrier which they imply (3030 & 300) is less precise than that from calori-metry which remains the " best " value at 2875 & 125. In propene theRotation of methyl groups abozzt carbon-carbon bonds.149 W. J. 0. Thomas, Chem. Rev., 1957, 51, 1179.150 W. G. Fateley, H. A. Bent, and B. L. Crawford, Symposium on Free Radicals,151 B. Bak and D. Christensen, Spectrochim. Acta, 1958, 12, 355.152 R. C. Taylor and A. R. Emery, ibid., 1958, 10, 419; W. J. Lehmann, J. F.Ditter, and I. Shapiro, J . Chem. Phys., 1958, 29, 1248.153 J. Goubeau and H. Mitschelen, 2. phys. Chem. (Frankfurt), 1958, 14, 61; I.Nakagawa, S. Mizushima, A. J. Sarceno, T. J. Lane, and J. V. Quagliano, Spectrochim.Acta, 1958, 12, 239.154 I. M. Mills, W. B. Person, J. R. Scherer, and B. Crawford, J . Chem. Phys., 1958,28, 851.L. Pauling, PYOC. Nut. Acad. Sci. U.S.A., 1958, 44, 211; H. Eyring, G. H.Stewart, and R. P. Smyth, ibzd., p. 259.San Francisco, 1958.15* D. R. Lide, J . Chem. Phys., 1958, 29, 1426GRAY MOLECULAR STRUCTURE AND MOLECULAR VIBRATIONS. 109barrier is 2000 cal./mole; when, in acetaldehyde,157 the CH, group is re-placed by an 0 atom, the barrier (now determined by three methods) has avalue of 1130 cal./mole.Substitution of halogen atoms on the carbon atom attached to therotating methyl group does not alter the barrier vastly from its value inethane. Thus, in ethyl fluoride values found by three spectroscopicmethods 157~159 are all close to 3300 cal./mole; in ethyl chloride and bromidethey are 3400 and 2800. Even in the triply-substituted molecules160l,l,l-trifluoro- and -trichloro-ethane the barriers remain at 3000 and 2900cal./mole respectively. In isobutane and in t-butyl fluoride the barriers *Oare higher : 3900 and 4300 cal./mole respectively.In theseries CF3*CH,C1, CF,-CHCl,, and CF3*CCl, study 160 of torsional oscillationfrequencies leads to barrier heights of about 6000 cal./mole. In hexa-chloroethane electron diffraction 161 suggests a high barrier, 10,800 cal./mole.These figures are in sharp distinction to those suggested by Lamb andKrebs,lG2 who studied symmetrical tetrabromoethane and reported barrierheights of only 1800 cal./mole above the more stable (gauche) form. In1,2-dibromoethane the torsional frequency has been located at 188 ~ m . - ~ . ~ Rotation of methyl (and substituted methyL) groufis about other bonds. Inthe molecules CH3*SiHF2 and CH,*SiH2F barriers derived 164 from micro-wave measurements are 1255 and 1560 cal./mole; the barrier in methylsilaneitself is 1700 cal./mole, and increasing fluorination clearly lowers the resist-ance to rotation. All these barriers are lower than in the ethanes and thesame is true of the fully chlorinated derivatives. In the series C,Cl,,CCl,SiCl,, Si,C1, barriers are 10,800, 4300, and only 1000 cal./mole re-spectively.161A similar relation exists between trimethylamine 4O with its barrier of4400 (from microwave measurements) or 4270 (from specific heats), similarto that in isobutane40 and trimethylphosphine40 with a barrier of 2600cal./mole. In tri-n-butylamine, ultrasonic measurements 162 lead to abarrier height of 5200 cal./mole. Torsional oscillation frequencies of di-methyl ether have been located 165 at 164 cm.-l (A,) and 265 cm.-l (&);implied barriers are not given.In hydrogen peroxide an assumed potentialZv(0) = vl(l + cos 0) + v,(l + cos 20) has been used to interpret the infra-red absorption spectrum.166 The double-minimum potential corresponds toa barrier 1290 cal./mole above the cis-form and 590 cal./mole above trans.In propylene oxide it is 2560 cal./mole.Rotation of substituted methyl groups about carbon-carbon bonds.Rotation of other groups.15' P. H. Verdier and E. B. Wilson, J . Chem. Phys., 1958, 29, 340.168 D. R. Herschbach and J. D. Swalen, ibid., p. 761.15s E. Catalano and K. S. Pitzer, J. Phys. Chem., 1958, 62, 873.160 E. Catalano and K. S. Pitzer, ibid., p. 838; K. S. Pitzer and J. L. Hollenberg,161 Y. Morino and E. Hirota, J . Chem. Phys., 1958, 28, 185.162 K. Krebs and J. Lamb, Proc. Roy. SOC., 1958, A , 244, 558.I. Ichishima, H. Kamiyama, T. Shimanouchi, and S. Mizushima, J. Chem. Phys.,164 J . D. Swalen and B. P. Stoicheff, ibid., 1958, 28, 671; L. Pierce, ibid., 1958, 29,166 Y. Mashiko and K. S. Pitzer, J. Phys. Chem., 1958, 62, 367.lB6 E. Hirota, J. Chem. PhysJ . Amer. Chem. Soc., 1953, 75, 2219.1958, 29, 1190.383.1958 28, 839110 GENERAL AND PHYSICAL CHEMISTRY.In methyl nitrite, the nitrosyl group rotates about the C-0 bond.Entropy measurements correspond l67 to a barrier height of 7800 cal./molein the gas phase where the cis-form is more stable; in the liquid trans pre-dominates. An interpretation in terms of double-bond character is con-sistent with the absence of a barrier in methyl nitrate.In ethyl formate 168 measurements of sound absorption and dispersionlead to barriers 3380 cal./mole above the higher state.P. G.J. C. BEVINGTON.M. FLEISCHMANN.P. GRAY.J. W. LINNETT.I. M. MILLS.K. R. OLDHAM.J. E. PRUE.B. STEVENS.A. F. TROTMAN-DICKENSON.167 P. Gray and M. W. T. Pratt, J . , 1958, 3403.168 D. Tabuchi, J . Chem. Phys., 1958, 28, 1014