GENERAL AND PHYSICAL CHEMISTRY.I. INTRODUCTION.IN the present Report an attempt has been made to review some ofthe subjects which, on account of shortage of space, and for otherreasons, were omitted from the previous Report. The application ofquantum mechanics to the study of molecular structure and relatedproblems has given important results but it has not been previouslydiscussed adequately in the Annual Reports : this is no doubt to beattributed to the inherent difficulty of reviewing a subject of suchcomplexity in the short space available. It may be noted, however,that a valuable survey of the quantum theory of valency has beenmade by J. H. Van Vleck and A. Sherman.1 Spectroscopic methodscontinue to provide valuable information concerning moleculardimensions and valency force constants, and the article on spectro-scopy in the present Report is a continuation of the previous onedealing with polyatomic molecules.The second volume of (Frl.)H. Sponer’s book on Molecular Spectra which was published during1936, deals with a number of topics of special interest to chemists.Mention may also be made of the appearance of a Comprehensivearticle on Raman spectra of organic compounds by J. H. HibbenY3and of a compilation of data of the Raman effect, covering the years1931 to 1934, made by M. Magat.4 Although the method of investi-gating molecular structure and inter-atomic distances by means ofelection diffraction in gases and vapours has been mentioned previ-ously in these Reports, the subject has not been treated fully.Animportant review has appeared during the year by L. 0. BrockwayY5one of the chief workers in the field : this deals more particularly withthe experimental method, and includes a comprehensive tabulationof the results obtained, with complete references, but the implicationsof the results are considered only briefly. In the present Report theemphasis is mainly on the significance of the measurements, althoughthe principles involved in the interpretation of electron-diffractionphotographs are also considered,1 Rev. Nod. Physics, 1935, 7, 167.2 ‘‘ Molekulspektren,” Vol. 11, Springer, Leipzig, 1936.a Chem. Reviews, 1936, 18, 1.4 ‘‘ Annual Tables of Constants and Numerical Data-The Raman Effect,1931-4,” Gauthier-Villms, Paris, 1930.5 Rev.Mod. Physim, 1936, 8,231PENNEY AND KYNCH: QUANTUM MECHANICS OF MOLECULES. 37Fundamental advances still continue to be made in the field ofchemical kinetics, and the importance of the possibility of calculatingthe velocity of a chemical reaction from purely theoretical consider-ations of the molecules involved cannot be over-emphasised. It isinevitable, therefore, that there should again be a report on chemicalkinetics.In the Report for 1935 certain aspects of surface chemistry werediscussed, and in the present Report two further aspects, vix., colloidalelectrolytes and unimolecular surface films, are reviewed. Duringthe year the collected papers of Sir William B. Hardy have beenpublished, and a number of useful short monographs dealing withvarious topics in colloid and surface chemistry have been issued.'A very large number of measurements of dipole moments in solutionhave been described in recent years, and it is of importance to knowhow the values so obtained are related to the true values obtainedirom the temperature variation of the polarisation of the substanceas vapour.Important progress has been made in this connexion anda report on the subject should not be out of place.It will be observed that there is no special report on deuteriumthis year : there are several reasons for this omission, the chief beingthat the main interests of deuterium, namely, in spectroscopy andkinetics, are considered in the reports on these subjects. It is hoped,however, to review in a subsequent Report such properties ofdeuterium and of other isotopes as are not covered in this manner.Finally, it may be recorded that a report on photochemistry, forwhich the time is undoubtedly ripe, is in preparation and it is hopedto publish it next year.S. G.2. THE QUANTUM MECHANICS OF MOLECULES.The interpretation of chemical binding offered by quantummechanics has not been previously discussed in the AnnmE Reports,although J. H. Van Vleck and A. Sherman1 have published acomprehensive review of the subject, including work to June 1935.The present Report is an attempt to combine a very brief surveyof the whole field with an account of the main developments sincethis date.The Report may be conveniently divided into sections, classifiedas follows :(1) Variation methods for accurate calculations.(2) Structural problems by approximate methods.6 Collected Scientific Papers, Cambridge University Press, 1936.7 Actualitks Scientifiqzres, Hermann, Paris.1 Rev.Mod. Physics, 1935, 7, 16738 GENERAL AND PHYSICAL CHEMISTRY.(3) Resonance and related properties.(4) Interaction of atoms with solid surfaces.(5) Miscellaneous.Discussions on lattices and on activation energies and reactionrates are omitted, since the former topic has been dealt with verythoroughly in a recent book by N. F. Mott and HI. JonesY2 and thelatter is dealt with later in this vol~irne.~(1) Accurate Cidczclations by Vuyiational Methods.Although quantum mechanics defines quite clearly a mathe-matical process by which the energy of formation of a moleculefrom atoms may be calculated, computational difficulties haveprevented much progress from being made in all but the simplestcases.Two methods of approximation have been tried. The fistis a generalisation of the Heitler-London theory of the hydrogenmolecule. Molecular wave functions are constructed as the sum ofproducts of atomic orbitals of the separate atoms, and the energyof formation of the molecule is evaluated as a first-order perturb-ation. This type of calculation has given many results of im-portance, but attempts to improve the numerical accuracy have ledto many difficulties. The more obvious corrections, of which thereare many, are relatively enormous, and it seems clear that themethod cannot claim to havc much more than qualitative sig-nificance.In spite of thirj, the application of the theory in itssimplest form to the calculation of activation energie~,~ one reactionbeing calibrated in terms of another, has been remarkably successful.Because of this, the method is usually accepted as “ semi-empirical.”The second possibility €or calculating the energy of formation ofa molecule makes use of the Ritz variation prin~iple.~ A promisingform is selected for the approximate wave function of the groundstate of the molecule, but the exact expression is left arbitrary tothe extent of involving a, number of parameters. The numericalvalues of these parameters are chosen in such a way that a certainintegral, which is an approximation to the energy of the molecule,has its least value.The strength of this method lies in the factthat a first-order variation of the wave function from its truecharacter causes only a second-order increase in the energy. Themethod therehre always gives a lower limit for the energy offormation.2 “ Properties of Metals,” Oxford, 1936.3 P. 56.4 See, e.g., ref. (l), or L. Pa.ulhig and E. B. Wilson, “ Introduction to&nantum Mechanics,” McGraw-IIIill, 1935, Chapter XIIPENNEY AND KYNCH: QUANTUM MECHANICS OF MOLECULES. 39At least half -a-dozen attempts have been made to calculate theenergy of formation of the hydrogen molecule by a variationmethod.* Each succeeding author irisertcd more and more para-meters into the wave function, thereby increasing the accuracy, buta t the same time making the calculations much longer.Even so,the results were very disappointing until H. M. James and A. S.Coolidge made a classical improvement. These authors demon-strated that it is absolutely essential to introduce the inter-electronicdistance rI2 explicitly into the wave function; otherwise, it isimpossible to make proper allowance for the repulsion between theelectrons. They assumed a 13-term expansion for the wave func-tion, and adjusted each of the coefficients to give a minimumenergy of formation. Their final result for the energy of dis-sociation, allowance being made €or the residual energy,6 was4.454 0.013 e.v., the accuracy being about the same as thatobtainable by spectroscopic methods.H. M. James, A. S. Coolidge,and R. D. Present have also considered the energy of the repulsivestate of H, which dissociates into two normal hydrogen atoms.The same authors then investigated the validity of the Franck-Condon principle by calculating the intensity throughout thecontinuous spectrum arising from transitions from an upper stablotriplet level to the repulsive state. d t appears that this principleleads to results incompatible with the experimental data. Whichof the two is in error is not yet clear. has made a13-term expansion of the wave function of the ground state oflithium hydride, and has also considered thc binding of the LiH-ion. Both systems are stable, and in the case of the former thecalculated energy is in fair agreement with experiment.The ionhas so far not been observed experimentally. J. P. Beach 10 hasmade a variation calculation on the ion He€€+, and finds a dis-sociation energy of about 2.0 e.v. The doubly charged ion HeHf+is shown to be unstable. J. Hirschfelder, H. Eyring, and N. Rosen 11have made a variation calculation on the energy of the linear H3molecule. They obtain 27 kg.-cals./mol. for the activation energyof the ortho-para hydrogen conversion, compared with theexperimental value 7 kg.-cals./mol.12J. K. Knipp6 J . Chem. Physics, 1933, 1, 825.6 C. G. Darwin (Nature, 1936, 138, 908) makes the excellent suggestion7 J . Chem. Physics, 1936, 4, 187.8 Ibid., p. 193.Ibid., p. 300.11 Ibid., p.121.12 See, e.g., A. Farbs, “ Ortho-Hydrogen, Para-Hydrogen and Heavythat residual energy should be used instead of xero-pint eneTgy.lo Ibid., p. 353.Hydrogen,” Cambridge University Press, 193640 GBNERAL AND PHYSICAL CHEMISTRY.(2) Structural Problems by Approximate Methods.Suppose that the energy of a molecule for all possible geometricalconfigurations can be calculated, Then the most stable arrange-ment is that where the energy function has its least value. Unfor-tunately, as explained in the previous section, a t present it isimpossible to make accurate calculations of the energy of formationof molecules other than the very simplest. Approximate methodsmust therefore in general be employed, and in practice there are twopossibilities, known as the orbital method and the pair method.Both must be considered as limiting cases, and neither can claimalways to be a better approximation than the other.The orbital method attempts to solve separately the motion ofeach electron in the time-average potential field of the other par-ticles of the system. Since an electron moves freely through thecharge-density distribution representing the other electrons, theorbital method gives a finite probability that any two electrons willbe at the same place at the same time.This is the main weaknessof the orbital method, since, of course, the electrostatic repulsione2/rij between any two electrons i and j effectively prevents theirever simultaneously occupying the same spot.The pair method attributes chemical binding to a number ofbonds, each of which arises from the interaction of a pair of electronson different atoms.Each bond is assumed similar in type to theHeitler-London bond of the hydrogen molecule. From the theoryit appears that a necessary condition for a bond to be formed is thateach electron entering into a bond should be in a singly occupiedorbit of its atom (compare H + H and H + He; in the latter casethere are two electrons in the same orbit, giving rise to anti-bondingor repulsion). The total energy of a molecule is the sum of theenergies of the bonds, together with the sum of the interactions ofelectrons in different bonds. To make the energies of the bonds aslarge as possible, directed wave functions are employed, and it isfrom the mathematical construction of these wave functions thatthe spatial arrangement of the molecule is revealed.The structures of a number of molecules and ions have been con-sidered either by the pair method or by the orbital method. Oftheae we may mention water, methane, ethylene, ethane, hydrogenperoxide, hydrazine, benzene, and related systems, and [Ni( CN),]2-and other complex ions.Details will be found in the review articleof 5. H. Van Vleck and A. Sherman,l where references to the originalpapers are also given. As an illustration, however, we compare theview-points of the two methods on the ion [Fe(CN),]4-.The neutral iron atom has 26 electrons, of which all except two,the 3d electrons, are in closed shells. According to the pair theoryPENNEY AND KYNCH: QUANTUM MECI-TANICS OF MOLECULES.42therefore, iron is at most bivalent. To possess a valency of six, theatom must acquire four more electrons, and these are provided inthe ion. As shown by L. Pauling,13 in order to construct sixequivalent orbits, pointing to the corners of a regular octahedron,the six valency electrons of the central atom must have the aggregateconfiguration d2sp3. Moreover, only d orbitals of the symmetrytype dE (of which there are three), and not orbitals of the symmetrytype dy (of which there are two), must be used. The orbital theoryalso predicts the regular octahedral configuration, and uses onlydc, p , and s orbitals of the central atom. To this extent there isagreement between the two methods, but clearly the pair theoryover-emphasises the capacity of the iron atom for absorbing elec-trons. On the other hand, the conventional structure E’e++(CN-),goes too far in the other direction.Since, in the orbital theory thereis no location of electrons on particular atoms, the “ ionicity ” 14can assume a state intermediate between that of the pair model andthat of the conventional model. For this reason the orbital methodmay be considered to give a better approximation than does thepair method for compounds involving iron-group atoms.There has so far always been agreement between the predictionsof the pair theory and those of the orbital theory for the forms ofvarious specific molecdes. Hitherto, this has been consideredmerely a fortunate circumstance, because it was felt that theapproximations in the two methods were so drastic, and different,that sooner or later an example would be found where the methodsseriously diverged.This rather worrying situation has to someextent been cleared up by J. H. Van Vleck.15 His conclusions areso important that it is worth while suminarising his arguments.Consider a multivalent atom surrounded by a number of univalentatoms. According to the orbital theory, one constructs molecularorbitals of the formwhere #(C) is an atomic orbital of the central atom conforming tothe symmetry of the whole molecule, #a is the atomic orbital of theattached atom i, and ai is a constant yet to be determined. Now,in general, there will be orbitals of the central atom whose symmetrytypes cannot be matched by linear combinations of the atomic13 J .Arner. Chern. SOC., 1931, 53, 1367.l* For want of a better word, w0 use “ ionicity ” ; Mulliken uses “ ionicness ”and Van Vleck *‘ ionic cliaracter.” Distinguish between ionic and polar.Part of the bonding in H, is ionic because the molecule may have the instan-taneous character H 8- + H-, but the molecule is not polar because the ioniccharacter averages out t o zero.+ = +(Q) + &ai+i,l5 J . Chem. Physics, 1935, 3, 80342 GENERAL AND PHYSICAL CIIEMISTRY.orbitals of the surrounding atoms, even though they obey thesymmetry properties of the moleculc. When this is so, the over-lapping of the orbital of the central atom with that of the attachedatoms will not be perfect, and anti-bonding, or a t best weak bonding,results.Thus, in iron-group compounds with six univalent groupsarranged octahedrally, the ds orbitals are bonding and the dy arcnot. Let us now consider the situation according to the pair theory.Here the object is to construct combinations of atomic orbitals ofthe central atom in such a way that each of the resulting wavefunctions is directed tow:irds a particular attached atom. Hencethese central directed wave functions have the same transformationproperties as do those of the orbitals Cpit.ji of the attached atoms inthe orbital theory. As we have already explained, the orbitalmethod requires only those orbitals of the central atom which areof the same symmetry types as linear combinations of orbitals ofattached atoms. Therefore, the same atomic orbitals for the centralatom must be used in the pair theory and in the orbital theory.Fromgroup-theory symmetry arguments he shows that if six atoms areattached either octahedrally or at the corners of a trigonal prism,only s, p , and d orbitals of the central atom are needed.Sincethese are commonly available, an immediate explanation of thefrequent appearance of co-ordination numbers six is obtained. Onthe other hand, if eight atoms are attached to the central atom theirfull bonding power is not used unless f wave functions of the centralatom are included. As a rule f orbits are considerably higher inenergy than d, p , or s orbitls, but this is no longer true for veryheavy elements.Prior to Van Vleck’s paper, J. E. Lennard-Jones l6 had suggested that only very heavy elements could have avalency of eight, and quoted OsO, as an example. The atoms in theneighbourhood OP osmium in the periodic table are the first wherethe outermost electrons can be easily changed from s to f orbits.MuWiken’s Papers.-R. S. Mulliken,l7 in a formidable series ofpapers extending over several years, has made an intensive studyof thc molecular orbitals, ionisation potentials, dipole moments, andelectron affinities of a number of triatomic, tetra-atomic, and evenmore complicated molecules. Pdost of his papers are mainly con-cerned with the spectroscopy of polyatomic molecules and aretherefore hardly appropriate for review here.Paper VIIJ deals with the effect of dipoles in the molecule on theVan Vleck’s paper contains further results of importance.16 J .SOC. Chem. Ind., 1934, 53, 249.17 VIII, J. Chem. Physics, 1935, 3, 514; IX, ibid., p. 51s; X, ibid., p. 564;XI, ibid., p. 579; XII, ibid., p. 586; XIPI, ibid., p. 635; XIV, ibid.,p. 720PENNEY AND KYNCH: QUANTUM MECHANICS OF MOLECULES. 43ionisation potential. W. C . Price l8 has shown experimentally thatan effect of this type is present in methyl iodide.Paper IX enumerates the one-electron molecular orbitals ofmethane, ethane, ethylene, and acetylene. By considering theultra-violet absorption spectra and the ionisation potentials ofthese molecules, fairly precise estimates of the bonding powers ofthe various orbitals are obtained.Similar considerations foraldehydes, ketones, and related molecules are given in Paper X .Papers XI and XI1 consider the molecular orbitals of moleculeswhich are appreciably polar, and supply a rough theoretical justi-fication of L. Pauling’s electronegative scale for atoms.lg FromPauling’s values, the polarity of molecules can be estimated; forexample, Mulliken finds, very roughly, C-072(H018)4 for methaneand C@60( Cl-O’15), for carbon tetrachloride.Theexperimental fact that this compound is diamagnetic at room tem-peratures 2O requires a singlet for the ground state. Previously, itwas thought that a triplet state might be lowest.21I. Lmgmuir 22 intro-duced this term to denote molecules having the same number ofelectrons and the same electronic structure as judged by theirproperties ; e.g., nitrogen and carbon monoxide, nitrous oxide andcarbon dioxide. Mullilren considers 15 isosteres of the lest anddiscusses their molecular orbitals, “ ionicity,” ionisation potentials,and ultra-violet spectra.As a rule, molecules containing the samenumber of electrons, and whose nuclei correspond closely in nuclearcharge, have the same shape and similar physical properties. Thisrule has been verified by W. G. Penney and G. B. B. M. Sutherland 23in the case of a number of triatomic systems.Valemy Xtcctes of Carbon.-A type of calculation where the pairmethod has so far proved more fruitful than the orbital method isin estimating the energy of valency states of atoms. By far themost inkeresting case from a practical point of view is, of course,carbon. The first explicit calculation of the energy of the valencystate of carbon was given by J.H. Van Vleck 24 on the assumptionof an aggregate sp3 configuration. For any particular arrangementof the four bonds, the valency state involves to a varying extentthe various states of the free atom in the sp3 configuration (vix.,Paper XIII deals with the molecular orbitals in diborane.Paper XIV is concerned with “ isosteres.”19 J. Chern. Physics, 1936, 4, 539.XI J. Amer. C‘hem. SOC., 1932, 54, 3570.20 L. Farkas and H. Sachsse, Tram. Paraday SOC., 1934, 30, 331.2 1 R. S. Mulliken, Physical Aev., 1933, 43, 765.29 J . Amer. Chem. SOC., 1919, 41, 868, 1543.23 Proc.Roy. SOC., 1936, A, 156, 654.24 J . Chern. Physics, 1934, 2, 20, 29744 GENERAL AND PHYSICAL CHEMISTRY.5*3X, 3*1.D, 3*1P), and the energy of the valency state is easilyevaluated by the pair method in terms of these states. The resultswere 163 kg.-cals./mol. for the energy in the tetrahedral arrange-ment (e.g., as in methane, ethane, etc.), and 167 kg.-cals./mol. forthe trigonal arrangement (e.g., as in ethylene, benzene, etc.). Thedifference is practically without significance.He assumesthat the valency state is a mixture of sp3 and s2p2, and adjusts the‘( coefficient of mixing ” in such a way that the energy of methaneas calculated by the pair method is a minimum. He concludes thatthe valency configuration is mainly sp3 and that the energy of thevalency state is about 106 kg.-cals./mol., a figure appreciably lowerthan Van Vleck’s estimate.However, the gross bonding energy isalso affected, and the net calculated heat of formation of methaneis increased by only 28 kg.-cals.jmo1.Voge assumes from the experimental evidence that the heat offormation of methane from atoms is 390 kg.-cals./mol. Thisenables him to fix certain parameters which are then used to calculatethe heats of formation of CH, CH,, and CB3. We finds 92, 194,and 278 kg.-cals./mol. respectively. There is no indication thatCH, occupies a favourable position with respect to the others. Themost stable arrangement of CH, is planar, in agreement with earliercalculations.26 No att’empt was made to calculate the energy offormation of CH5.H.H. Voge 26 has improved on the above estimate.(3) Resonunce .The word resonance is being used in many different senses in thetheory of the structure of molecules. We shall follow Pauling andhis collaborators2‘ and say that “resonance” is present in anysystem which cannot be adequately described in terms of s singlebond diagram. The choice of the term is hardly a happy onebecause the connexion between “ resonance ” in the present senseand resonance in the ordinary mechanical sense is rather remote.The word, however, was introduced before the precise nature of theeffect was understood, and the mechanical analogy did at leastoffer a plausible interpretation of the experimental facts. In anycase, the word is now so commonly used that it would be a mistaketo attempt to substitute another.A better word, ‘‘ mesomerism,”has indeed been suggested by C. K. Ingold,28 and this fits in well withz 5 J. Chem. Physics, 1936, 4, 581.z6 J. H. Van Vleck, ibid., 1934, 2, 20; W. G. Penney, Trans. Pa~uday SOC.,97 L. Pauling and G. W. Wheland, J . Chem. Physics, 1933,1,362, and many28 Nature, 1934, 133, 946.1935, 31, 734.subsequent papersPENNEY AND HYNCH: QUANTUM MECHANICS OF MOLECULES. 45all the other “ merisms ” of chemistry. &om the construction ofthe word mesomerism, a situation is implied where the actual con-ditions are intermediate between various extremes.The mathematical calculations of the theory of resonance haveachieved two results of importance.These are best illustrated byreference to benzene. The main result is that all of the bondsbetween neighbouring carbon atoms are similar, and are inter-mediate between single and double bonds. Hence all carbon atomsare equivalent, and the chemical stability (Le., reactions with acids,etc.) is greater than would be expected if the molecule containedthree locslised double bonds. The second result is that the effectof resonance is to increase the mechanical stability (i.e., the energyof formation from atoms) beyond that expected on the hypothesisof a, single bond structure. The increase is not very much com-pared with the energy of formation of the molecule (in benzene, forexample, about 2 e.v. in 60 e.v.), but it is quite enough to be detectedin the ordinary calculations of heats of formation in terms of bondenergies.It is noteworthy that the first of these results cannot be upset byimproving the accuracy of the calculations, but that the secondmay be.This, it seems to us, is an important point not explicitlymentioned before. One of the most surprising features of the longseries of calculations made by Pauling and his collaborators on theincrease of mechanical stability of a molecule due to resonance isthat the results are so remarkably consistent. No doubt it is anexample of a simple theory which concentrates on an essential pointgiving results with an accuracy very difficult to obtain by morecomplicated theories, because in these the second, third, and higherapproximations, although all large, practically b &lance out to zero.Effect of Resomnce on Internuclear Distances.-It is well knownthat internuclear distances in molecules are affected by resonance.For example, the carbon-carbon distance in benzene is 1.39 A.,29intermediate between the single-bond value 1.54 A.30 and the double-bond value 1.33 A.31 L.Pauling, L. 0. Brockway, and J. Y. Beach 32have suggested a method of estimating internuclear distancesaffected by resonance. We may illustrate their suggestion by con-sidering the benzene molecule. Here the resonance is mainlybetween the two Kekulh structures. Since neighbouring carbon29 L. Pauling and L. 0. Brockway, J. C‘hem. Physics, 1934, 2, 867.3O See, e.g., Sidgwick, “ The Electronic Theory of Valency,” Oxford, 1927.31 Pauling, Brockway, and Beach use 1-37 A.As will be shown by oneof the Reporters in an article soon to appear in the Proc. Roy. SOC., the value1.33 is probably the correct one.32 J . Amer. Chem. SOC., 1036, 57, 270646 GENERAL AND PHYSICAL CHEMISTBY.atoms linked by a single bond in one structure are linked by a doublebond in the other, the carbon-carbon linkage may be said to be oforder 3/2. Considerations of a similar sort 33 show the linkage ingraphite to be of order 4/3, while the internuclear distance is knownaccurately to be 1-41 A.34 Thus four simultaneous pairs of valuesof internuclear distance and bond order are known. By plottingorder against distance a smooth cuhe results. This curve may beused to predict distanccs in molecules where it is possible to estimatethe bond order.To find the order of the linkages in any molecule,Pauling, Brockway, and Beach proceed as follows. The resonanceproblem is solved by the pair method, and the wave function of theground state is obtained in the formwhere kj is a numerical constant, and $j is the wave function corre-sponding to the canonical structure j . The order of the linkage pbetween neighbouring carbon at'oms is then defined aswhere g3 is unity if the canonical structurej has a, bond between thetwo atoms, and is zero otherwise.By substituting for naphthalene the values of the coefficients kjas calculated by L. Pauling and J. it is found that thelinkages are not all equivalent.Variations of some 0.06 A. aboutthe mean 1.41 A. are to be expected. J. M. Robertson36 finds amean internuclear distance 1.41 A,, in exact agreement with khis.No attempt has so far been made to measure deviations from themean.Pauling, Brockway, and Beach suggest that the curve relatinginternuclear distance with bond order which they obtain for carboncompounds may be used for molecules containing other elementsprovided a suitable change of scale and end-points is made. Al-ternatively, if an internuclear distance is known from experimentaldata, then, by using Pauling's values of single-, double-, and triple-bond ionic radii,37 the order of the linkage may be calculated. Inthis way, e.g., the carbon-chlorine bond in carbonyl chloride iscalculated 5s 83% single and 17% double bond.Many otherexamples are considered.33 5. E. Lennard-Jones, Trans. Faraday SOC., 1834,30, 58; G. W. Wheland,31 G. I. Finch and H. Wilman, Proc. Roy. Xoc., 1936, A , 155, 345.35 J . Chm. Phpica, 1933, 1, 679; {bid., 1934, 2, 488.36 Proc. Roy. Soc., 1933, A, 142, 674.37 Proc. Nat. Acad. Sci., 1932, 18, 293.J . Chem. Phys$cS, 1934, 2, 474(4) Interaction of Atoms with Solid Xurfaces.Leniiard- Jones and his collaborators 38 have made an extrerriclypromising start a t a detailed theory of Dhe interaction of atoms andmolecules with the surfaces of crystals. The type of system whichthey consider is one where the absorbed atom is held only looselyby the crystal, probably by forces of a van der Waals character.The atom can exist in one of a small number of vibrational levels or,if its energy is great enough, can leave the surface altogether.Questions which are studied are the spacing of the energy levels,transitions between them, and between them and the continuum,caused by the thermal agitation of the surface, the migration of theatom over the surface, and the scattering of a homogeneous beamof the atoms by the crystal.The fundamental approximation of the theory is that the energyof interaction of the absorbed atom and the crystal may be repre-sented by a Morse function.39 Let the x axis be drawn through theabsorbed atom, perpendicular to the surface of the crystal.Write2 for the displacement at a particular instant of the surface atomsof the crystal in the neighbourhood of the absorbed atom from theirmean position 2 = 0, and x for the displacement of the absorbedatom from 2 = 0 a t the same instant.Let b be the equilibriumdistance of the absorbed atom from the surface a t the absolutezero of temperature. Then the interaction energy of the absorbedatom with the crystal is writtenThe first of these terms represents the short-range repulsive field,and the second the long-range attractive field. The constant D isthe energy required to take the atom off the surface a t absolutezero, and K is a parameter controlling the breadth of the potentialtrough holding the atom on the surface.The motion of the surface atoms of the crystal is small comparedwith the range of the potential field V .Hence V may be expandedin a power series in 2, and terms after the second rejected. We thenobtainI V = vo + yl == [ & - 2 K k - - b ) - 2De-/d.~--b)] + 2~-Zl]e-Z/ck-b) - e-di-b)The first term gives the interaction onergy of the atom and crystal38 I, J. E. Lennard-Jones and C. Strachan, Proc. Roy. SOC., 1935, A , 150,44,"; 11, C. Strachan, ibid., p. 456; 111, J. E. Lennard-Jones and A. li'.Devonshire, ibid., 1936, A , 156, 6 ; IV, 'idem, ibid., p. 29; V, A. F. Devon-shire, ibid., p. 37 ; J. E. Lennard-Jones and A. P. Devonshire, A'atuw, 1936,39 See, e.g., L. Pauling and E. B. Wilson, L c Introductian to Quantum137, 1969.Mechanics," McGraw-Hill, 1935, p. 27148 GENERAL AND PHYSICAL CHEMISTRY.at absolute zero, and the second gives the coupling between thevibrations of the attached atom in the field of the stationary surface,and the thermal vibrations of the lattice.The effect of Vl is tocause a surge of energy to and fro between the crystal and theattached atom.An important step has now been made. The perturbing potentialVl and the complete wave functions of the system are all in productform, one factor of each depending only on the lattice, and the otherdepending only on the attached atom. Straightforward perturb-ation technique may be applied, and there results the probabilitythat the lattice loses to the atom just the right amount of energyneeded to cause excitation to a higher vibrational level. Thisprocess may occur in many ways, because of the large number ofdegrees of freedom of the lattice.An averaging process over allthe normal modes present at any temperature must therefore bemade, and a t this point temperature appears explicitly in theformula. The final result of paper I is the life-time of the attachedatom in a vibrational level on the surface. For argon on potassiumchloride a t low temperatures, the atom vibrates many times inthe ground state before being activated to the first excited state,while a t room temperatures thc intcrval is of the same order as thevibration period.Paper I1 extends the above calculations to transitions of theabsorbed atom from a discrete state to the continuum. By inte-grating over the continuum, an expression is obtained for theprobability of evaporation from the surface.The average lengthof time spent by an absorbed atom on a surface may thus beestimated as a function of temperature.Formula? arefound for the probability that an impinging particle will condenseon a solid surface. The constants which occur in Langmuir’sisotherm are thus for the first time explicitly calculated in termsof the physical properties of the solid and its surface field. Evapor-ation processes are also considered. It is found that evaporationmay, even at low temperatures, take place in two or more stages,the atom being first excited to a higher vibrational level and then,while in that excited state, receiving another quantum of energysufficient to cause evaporation. The theory is illustrated by con-sidering the condensation and evaporation of H,, HD, and D, onthe same solid surface.Thistime the potential holding the atom on the surface is dssumed tohave central symmetry about the point of attachment.Paper V gives an interpretation of the experiments of R.FrischPaper I11 extends the calculations of paper 11.Paper IV covers roughly the same ground as paper 111PENNEY AND KYNCH: QUANTUM MECHANICS OF MOLECULES. 49and 0. Stern 40 on the scattering of beams of helium by crystals oflithium fluoride and sodium fluoride. The theory shows that whenthe components of momenta of the incident beam satisfy certainrelations, involving the energy intervals of the vibration spectrumof the atom on the crystal, absorption without loss of energy canoccur, thus accounting for minima in the reflected and refractedbeams.Excellent agreement with experiment is obtained if it isassumed that helium on lithium fluoride can exist in two vibrationallevels, given by - 129 cals./mol. and - 57 cals./mol. severally.Similar values hold for helium on sodium fluoride, but here the exactfigures are somewhat doubtful because the experiments were not socomplete.( 5 ) Miscellaneous.A number of papers have recently appeared dealing with thetheory of various physical properties of molecules and crystals.For want of space, these are grouped together under this heading.Restricted Rotutiolz.-To account for the temperature variation ofthe specific heat of certain crystals (e.g., oxygen, nitrogen, iodine,methane, carbon dioxide, etc.), L.Pauling suggested in a classicalpaper 41 that above a critical temperature, depending on the crystal,the molecules rotate more or less freely, but that at lower tem-peratures rotation is inhibited and only oscillation occurs. Eachmolecule is supposed to be influenced by an inhomogeneous potentialfield due to the surrounding molecules. When the mean thermalenergy, as measured by kT, is small compared with the restrictingpotential, most of the molecules have not enough energy to turnover, and their motion is therefore mainly oscillatory. At hightemperatures, however, the mean thermal energy is more thanenough to overcome the restricting potential, and rotation iscommon throughout the crystal. According to these ideas, thespecific heat of the crystal should show a maximum a t temperatureswhere IcT is about equal in magnitude to the restricting potential.By observing where the maximum occurs, a rough estimate of therestricting potential may be obtained.The above theory is unable to account for a maximum in thespecific heat-temperature curve of anything like the magnitude andsharpness of that observed. R.H. Fowler42 has explained thereason. It is because the restricting potential acting on one moleculedepends on whether the other molecules near it are also rotating.By making the magnitude of the restricting potential a function ofthe amount of rotation already present in the crystal, the specific4O 2. Physik, 1933, 84, 430.41 PhYSiCcGl Rev., 1930, 36, 430.42 Proc.Boy. SOC., 1935, A , 151, 1heat curve can be made to follow the experimental results veryclosely. Similar calculations on the dielectric constants along thethree principal axes of susceptibility of certain crystals also givegood agreement with the somewhat peculiar observed results.43Suppose that the restricting potential on one molecule due to therest of the crystal is expanded in a Taylor's series about the centreof the molecule. Apart from an additive constant which does notaffcct the freedom of rotation, the potential V may be writtenSincc V is a potential in a region due to outside charge distributions,the terms of each order in V must satisfy Laplace's equation.Assume now that the molecules are arranged in the lattice withcubic symmetry.Then the first non-vanishing terms in B are thoseof fourth order, and they may be writtenV = (AX2 + By2 + CX2) + (Dx3 + . . .) + . . . . . (1)V = E(3r4 - 5(x4 + y4 + z~)). . . . (2)A. P. Devonshire 44 has investigated the effect of the potentialfield [equation (a)] on the energy levels of the dumb-bell rotator.The way in which the various rotational levels, characterised by therotational quantum number J , split up under the influence of thefield had already been worked out by H. Bethe 45 from the methodsof group theory. The levels belong to five different symmetrytypes (irreducible representations), and therefore the infinitesecular equation giving the energy levels of the system factorisesinto five equations, each of which is infinite and refers to one of therepresentations.Devonshire confined his attention to the f i s t fewrows and oolumns of each determinant, and obtained the approxi-mate roots with the aid of an electrical calculating machine.46The calculations were straightforward for the levels up to aboutJ = 5 and ]kl not too large. Special considerations were neededfor ]k1 large, and the asymptotic behaviour of the levels was con-sidered. Curves showing the behaviour of the energy levels askcranges from - 60 to + 60 are given in the papeF. The notationused to describe the levels is that suggested by R. S. Mulliken.47Whether there is any molecular crystal to which the theory workedout by Devonshire would apply has not yet been considered. Theinterpretation of the experimental results will in any case be verydifficult, because the crystalline forces will probably break downmost of Che ordinary selection rules, and levels considerably higherthan J = 6 will be present even at low temperatures.43 h.13. Fowler, Proc. Roy. SOC., 1935, A , 149, 1.44 Ibid., 1936, A , 153, 601.46 R. R. M. Mallock, Proc. Roy. Soc., 1932, A , 140, 457.4 7 Pkgsical Rev., 1933, 43, 278.46 Ann. Physik, 1933, 3, 133PENNEY AND KYNCW: QUANTUM MECIEANICS OF MOLECULES. 51Paramagnetic Properties of Crystals.-There is a very close formalconnexion between the calculations of the previous section and thosegiving the paramagnetic properties of crystals of iron-group andrare-earth salts. The paramagnetism arises from the presence inthe metallic ion of electrons in incomplete shells to a large extentunaffected by the crystalline forces. For this reason, the crystallinepotential acting on an ion may be expanded in a Taylor’s seriessimilar to (1).If the atoms surrounding the ion have cubic sym-metry, then once again we have the potential (2). Now very oftenthe atoms surrounding the ion are arranged with cubic symmetry,and therefore the study of the effect of the field ( 2 ) on the energylevels of paramagnetic ions is of real practical importance. Thetheory in the case of hydrated crystals has already been carried tothe point of accurate quantitative agreement with e~perirnent,~~but in the case of certain complex salts, notably ferro- and ferri-cyanides, and cobaltammines, the theory is not so well developed.These salts are diamagnetic if they involve a complex ion containingan even number of electrons, e.g., [2’e(CN>,l4-, and have a suscep-tibility of order of magnitude corresponding to one free spin if thisnumber is odd, e.g., [Fe(CN),I3-.L. PaulingI3 was the first toaccount for this behaviour, but his explanation was not entirelyaatisfactory because it was based on directed wave fmctions andperfect electron pairing. J. H. Van Vleck 49 has now put the matteron a much wider foundation. He shows that the method of crystal-line fields, as obtlined above, the method of electron pairs, and themethod of molecular orbitals all formally predict similar results.The crystalline forces are so strong that the Russell-Saunderscoupling is broken down and the state of lowest energy is one oflowest possible spin for the whole complex ion, rather than one inwhich the central metallic ion has its greatest allowed spin.I nother words, the complex ion must be considered as a unit in whichthe interactions between electrons in orbits of the metallic ion areof subsidiary importance to interactions between these electronsand the electrons of the surrounding co-ordinated systems.has made detailed numerical calculations on theprincipal magnetic susceptibilities of potassium ferricyanide by themethod of crystalline potentials. His results confum the abovetheory of Pauling and Van Vleck.Diamagnetic Anisotropy of Aromatic Molecules.-When thestructure 01 a molecule may be represented by a single bond diagram,48 See, e.g., a review article by R.Schlapp and W. G. Penney, “Reportson Progress in Physics,” 11, 1935, Physical Society, p. 60.49 J . Chem. Phy8iC8, 1935, 3, 807.J. 13. Howard50 Ibid., p. 81352 GENERAL AND PHYSICAL CHEWSTRY.the diamagnetic susceptibility may be calculated by adding togetherthe susceptibilities of the separate atoms of the molecule.51 Thisis because the susceptibility of a free atom is proportional to Z?where ? is the mean square radius of an electron’s orbit, and thesum is over all the electrons of the atom. If resonance occurs in themolecule, however, the situation is different. Consider the benzenemolecule, for example. Here, the electrons concerned in bonds inthe plane of the ring, i.e., those whose atomic orbitals are symmetricalabout the plane of the ring, are regular, and for these the additiveprinciple applies.The resonance electrons have a chttrge dis-tribution which is practically cylindrically symmetrical about theaxis of the molecule, and is large only in two anchor-ring regions,one above and one below the carbon hexagon. When the magneticfield is parallel to the plane of the molecule, the contribution to thesusceptibility is normal, because the mean square distance of theanchor rings above or below the central plane is about the same asr2 for a p orbit of carbon. When the magnetic field is perpendicularto the plane of the molecule, 011 the other hand, the contribution tothe susceptibility is not normal, as it is proportional to R2, where Ris the radius of either anchor-ring region, and is also approximatelythe C-C distance in the ring (since the side of a regular hexagonequals the radius of the circumscribing circle).Now, R2 is severaltimes larger than for a p orbit of carbon, and the susceptibilityof benzene in a direction perpendicular to the plane of the moleculeis therefore much greater than that in a direction parallel to thisplane.L. Pauling 52 has estimated the principal diamagnetic suscep-tibilities of a number of aromatic molecules, using the above ideasas a basis. He finds almost exact agreement with experiment inthe cme of benzene. More complex molecules he calibrates veryingeniously in terms of benzene, and for these, too, obtains excellentagreement with experiment.The method of calibration is to replaceany pair of neighbouring electrons in the resonance problem by aconstant electrical resistance. A conducting network is thenobtained, and the currents induced in this network when a time-varying magnetic field acts in a direction perpendicular to the planeof the network, and hence the magnetic moment of the network,are found in terms of those corresponding to benzene. The contri-butions of the resonance electrons of the molecules to the magneticsusceptibility are linearly proportional to the magnetic momentsof the networks. For naphthalene and anthracene the calculatedand the observed values do not agree so well as do those of other5 1 See, e.g., E. Stoner, “ Magnetism and Matter,” Methuen, 1934, p.469.52 J . Chem. Physics, 1936, 4, 673.SUTHERLAND : SPECTROSCOPY. 53molecules. Pauling therefore considers that the experimentalresults for these molecules are probably in error.Vibrational and Rotational Levels of Polyatomic Molecules.-Thecalculation of the vibrational and rotational levels, and theirstatistical weights, has an important bearing on specific heats.However, the subject is more appropriately dealt with in the theoryof infra-red spectra and will therefore not be considered here. Anadequate review of the subject, treated by the methods of grouptheory, has rcceiitly been given by J. E. Rosenthal and G. M.3Xiirphy.53W. G. P.G. J. K.3. SPECTROSCOPY.In this section of last year’s Reports a general review was givenof the various types of vibration spectra associated with polyatomicmolecules ; the information derivable from them was indicated, andits limitations considered, but little attention was paid to particularinstances.This year it is proposed to exemplify the more importantresults by a small compilation. We shall follow the classificationof molecules given in last year’s Reports, oix., linear molecules,spherical molecules, symmetrical-top molecules, and asymmetrical-top molecules. The examples we have taken in each class are theonly ones for which the moments of inertia have been determinedwith any degree of certainty from the rotational fine structure of thebands. The methods of finding molecular dimensions from vibra-tional frequencies alone cannot yet be regarded as giving precisionvalues : these methods will be discussed later in this Report.It willbe observed that several molecules have been listed containing thedeuterium isotope ; in all of these cases it has been assumed that thedimensions are exactly the same as for the molecule containingthe corresponding hydrogen atom; in fact, this assumption hasoccasionally made it possible to determine the dimensions. Theinaccuracy from this cause cannot be more than about 0.001 A. in aninternuclear distance. The values of the fundamental frequencies ofthe molecules have only been given to within lOcm.-l, since correctionshave not been made for anharmonicity, and accordingly these valuesmay be in error by approximately that amount.The figure inparentheses after certain of the frequencies indicates the degree ofdegeneracy for frequencies which are isotropic in two (2) or in three(3) dimensions. Data which are not connected to a specific referencenumber have been taken from H. Sponer’s compilation.1 Paren-53 Rev. Jlod. Ph7JSiC8, 1936, 8, 317.1 “ Molckulspektrcn,” Springer, 193554 QENXRAL AND PHYSICAL CHEMISTRY.theses placed round a frequency indicate that the value is a cal-culated one, inchded. €or completeness, and probably correct towithin 30 crn.--lMolecule.ocoscsNNOHCNDCNHCiCHHCjCDDCtCDTABLE I.Linear Molecules.Internuclear Moment of inertia, Fundamental fre-distance, A. g.-em. x 1040.quencies, em.-l.CO 1.16 70.6 23601320670 (2)CS 1-52 a 247 1620660400 (2)- 66 22201290590 (2)CH 1.06 18-7 3290CN 1.15 2090CD 1-06 3CN 1-15CH 1.057 cc 1.204CH 1.057CD 1.057CC 1.204CD 1.067CC 1-204712 (2)22.9 2630190023.5 329033701980570 (2)730 (2)610 (2)27.9 2590 4 p33801880680 (2)520 (2)(2410) 4~27001760540 (2)500 (2)I n addition to those in Table I, the followiiig molecules and ionshave been shown to be linear and have had their vibration frequen-cies determined ; their actual dimensions, although not determinedapectroscopically, are known in many cases from studies on X-rayor electron-diffraction (see p. 65) : carboriyl sulphide,l cyanogenchloride,l cyanogen bromide,l cyanogen iodidc,l cyanogen,6 C,lH,,lq-, 7 s CN -.2 J.A. Sanderson, PhysicaZ Rev., 1936, 50, 200.3 P. F. Bartunek and E. F. Barker, ibid., 1935, 48, 516.4 G. Herzberg, F. Patat, and J. VET. T. Spinks, 2. PhpiE, 1934, 92, 87;G. Herzberg, F. Patat, and H. Verleger, ibid., 1936, 102, 1.6 W. F. Colby, Physical Rev., 1935, 4'7, 388 ; G. Glockler and C. E. Morrell,ibid., p. 569.S. C. Woo, T. K. Liu, and T. C. Chu, J . C'hinese Ghem. Soc., 1935, 3, 301.7 'tV. G. Penney and G. B. B. M. Sutherland, Proc. Roy. Xuc., 1936, A, 156,654SUTHERLAND : SPECTROSCOPY. 55In the ease of carbon dioxide the value given for one of the fre-quencies as 1320 cm.-l requires further explanation. Actually,one observes no frequency of this magnitude, but a pair of frequenciesa t 1286 crn.-l and 1388 cm.-l.This arises because the overtone of thefrequency a t 670 cm.-l falls very closo to this fundamental, so causinga " resonance " splitting.8 The value given is therefore an estimateof the unperturbed frequency and is sufficieptly good for most cnl-culations. The frequency at 660 cm.-l for carbon disulphide isprobably slightly erroneous for the same reason.In addition to those in Table 11, the following molecules and ionshave been shown to be spherical; their vibration frequencies m eTABLE 11.Spherical Molecules.CH, CH 1-09 9 5.298 9 FLH 1.78.5 5.47 105.27 11CCl, CCI 1.755 l 7ClCl 2.877.08.92920:H)W ( 3 )1300 ( 3 )2260 ( 3 )990 ( 3 )2110 ( 3 )930 (J)2180 ( 3 )980 ( 2 )$110 ( 3 )y o (!)f20so 13, 14(1070)($)19'30S? (?)21904 ti0760 (3)31CJ ( 3 )220 (?)known and thcir dimensions have been deduced in many cases fromdata on X-ray and electron diffraction (see p.65) : carbon tet'ra-bromide,l silicon tetrLzchloride,l titanic chloride,l stannic chloride,lstannic bromide,l SO,",l* CIO,'ls. It will be noticed that three dries8 Cf. this section in last year's Reports.9 N. Ginsburg and E. P. Barker, J. C'hern. Physics, 1933, 3, 668.10 Physical Rev., 1935, 48, 868.11 W. H. J. Childs, Proc. Roy. Xoc., 1936, A, 153, 555.12 A. H. Nielsen and H. H. Nielsen, Physicul Rev., in the press.13 D. M. Dennison and M. J. Johnston, ibid., 1935, 47, 93.14 G. E. MacWood and H. C. Urey, J . Chem. Physics, 1936, 4, 402.15 A.H. Nielsen and H. H. Nielsen, Physical Rev., 1935, 48, 861.16 W. B. Steward and H. H. Nielson, ibid., 1935, 47, 828; F. B. Stitt and17 Electron-diffraction values. Cf. L. 0. Brockway, Rev. 3f od. Physics,18 J. E. Rosenthal, Physical Rev., 1934, 46, 730.n. M. Yost, J. Ckem. Physics, 1936, 4, 82.1936, 8, 23156 GENERAL AND PTIYSTCAL CHEMISTXY.have been given for the moment of inertia of methane. The firstone is that deduced from the investigation of the deuteromethanemolecule and is presumably the most accurate value. The other.values have been deduced from the CH, bands only, by the method ofM. Johnston and D. M. Dennison,lo and are the ones which shouldbe compared with that given for CD,, the latter having been obtainedby a similar method from observations solely on CD,.In addition to those in Table 111, the following molecules and ionsare known to belong to this class and have had their vibration fre-TABLE 111.Xyrnrnetr ical- t op Molecules.NH 1.016 l9 I* 2.782 loHH 1.64511 0.36 I c 4.497ND 1.016 l g I A 5.397DD 1.645h 0.36 I c 8-985CH 1.093 I A 7.16GHH 1.785 I ( ; 5.298CD 1.093CH 1.09 -CD 1.09DD 1.8CF 1.6 In 38.6CH 1.1HH 1.8 I c 5.61CC1 1.6 I A 50.0CH 1.2HH 2.8 Ic 5.43330 9O(3450)( 2)1630 (2)9502420 2O(2560) (2)1160 (2)7502980221013103030 (2)1480 (2)1160 (2)(2100)(990)(2220)(2)(1290)(2)f 1020)( 2)(2990)2970148010502990 (2)1480 (2)1200 (2)297013507323050 (2)1460 (2)1020 ( 2 )qizencies determined with a reasonable degree of certainty : PH3,20n 21PD3,22 AsH~,~O PF,,l PC13,1 PBr3,23 AsF3,1 AsC13,1 SbCl,,l BiC1,,2319 M.V. Migeotte and E. F. Barker, Physical Rev., 1936, 50, 418.20 5. l3. Howard, J. Chem. Physics, 1935, 3, 207.2 1 L. W. Fung and E. 17. Barker, Physicql Rez:., 1934, 45, 238.22 M. de I-Iemptinne and J. M. Delfossc, Bull. Acad. TOY. Belg., 1935, 21,793; G. B. B. M. Sutherland and G. K. T. Conn, Nature, 1936, 138, 641.33 J. B. Howard and E. B. Wilson, J. Ghem. Physics, 1934, 2, 630SUTHERLAND : SPECTROSCOPY. 57BF3,25 BCI 3, 249 26 BBr3,25 N03',SG C0,",26 CH,Br,l CH31,1 CHCl,,lCHBr,,l POC1,,1 and C2H6.27 A certain amount of knowledge isavailable about their dimensions both from spectroscopic and fromdiffraction sources, but it is not sufi?ciently complete to warrant itsinclusion here without more discussion than space permits.Besides those in Table IV, the following molecules may be said tohave had their fundamental frequencies assigned beyond reasonabledoubt : sulphur d i ~ x i d e , ~ nitrogen d i ~ x i d e , ~ and chlorine dioxide1TABLE IV.As ymmetrical-top Molecules.OH 0-955 I* 1.009a 105" I B 1.901.7c 2.908a 105" -3 3 2 0D,O OD 0.955 -HOD As above -SH 1-36 I* 2.68a 92' I B 3.08As above -332sD2SI c 5.85-HSD As above -CH,O CH 1.04 I* 24.3CQ 1.2 J B 21.4HH 1.88 I c 2.9CH2D, '3 l3 CH 1.09- CD 1.093650 28376016002670 29278011802720 29372014002616265012651900 3019409001910 302620108029702900174014601040920(2 140)( 1420)(2230) 1240(2970) 1040(1320)(3010) 1090The references cited should be consulted for the state of currentknowledge regarding their exact dimensions.In the following casesthere is still a certain doubt about the assignment of one, or at most24 A. B. D. Cassie, Proc. Roy. Soc., 1935, A, 148, 87.25 T. F. Anderson, E. N. Lassettre, and D. M. Yost, J . Chem. PhysiC8,26 A. C . Menzies, Proc. Roy. SOC., 1931, A , 134, 265.37 E. Bartholomi, and H. Sachsse, 2. physikal. Chem., 1935, B, 30, 40.28 D. Bender, Physical Rev., 1935, 47, 252.29 E. F. Barker and W. W. Sleator, J. Chem. Physics, 1935, 3, 660; E.30 C. R. Bailey, J. W. Thompson, and J. B. Hale, J . Chem. Phl~si~.~, 1936,1936, 4, 703.Bartholorn6 and K.Clusius, 2. EZektrochem., 1934, 40, 530.4, 625; A. H. Nielsen and H. H. Nielson, ibid., p. 22958 GENERAL AND PHYSICAL CEEMISTRY.two, of the fundamentals : ozone,? oxygen fluoride,' chlorine mon-oxide," 31 ethylene,32* nitrosyl chloride,l formic oxalic a ~ i d , ~ 5acetic acid.36 Although enormous numbers of complex moleculeshave been investigated, the analysis of their vibration spectrahas only been partial (certain groups being recognised by theircharacteristic frequencies), and here we can only refer to a few of t hmore important contributions to structural problems.Particular XtructuyaZ Problerns.-The molecule which continues toreceive most attention is that of benzene, and the past year isremarkable for the number of important papers concerning it.Themost outstanding come from a group of workers 37 in University Col-lege who have made a very thorough study of the infra-red, Raman,and fluorescence spectra of benzene and hexadeuterobenzene. Theimportance of their work lies in the fact that until this was done thecoincidences between infra-red and Raman frequencies in the spec-trum of benzene made it appear as though the molecule did not possessthat hexagonal symmetry which modern resonance theories demand.They have been able to show that these coincidences are either acci-dental or else are due to a breakdown of the strict selection rules inthe liquid state. They have also been able to identify many of the20 fundninental frequencies. 0. Redlich and TV. Stricks 38 fromobservations on the Raman spectra of mono-, di-, and tetra-deutero-bcnzene have also been able to correlate the frequencies of benzeneand to correct earlier provisional assignments by E.B. Wilson.39C. Maimebaeh48 has made an analysis of the data on the isotopicmolecules to evaluate many of the constants of a very general poten-tial function for the force field in benzene. He has shown that appre-ciable interaction occurs betwcen non-adjacent carbon atoms.The other important development is the use of infra-red andRaman spectra for the detection of hydrogen bonds, particularlyin molecules containing hydroxyl groups. It is manifested eitherby a shift in the position of the frequency characteristic of the31 R. Pohlmann and W. J. Schumacher, Z .Physik, 1936, 102, 678.32 E. Teller and B. Topley, J . , 1935, 885.33 L. G. Bonner, J . Amer. Chem. Soc., 1936, 58, 34.34 G. Herzberg and 11. Verleger, PhysihZ. Z., 1936, 37, 444; J. Gnpta,Indian J . Physics, 1936, 10, 117, 313; C. S. Venkateswaran, Proc. IndinnAcad. Sci., 1936, 2, A , 615; Current Sci., 1936, 4, 736; P. B. Sarkar andB. C. Ray, Nature, 1936, 137, 495.35 J. H. Hibben, J. Chem. Physics, 1935, 3, 676; W. R. Angus and A. H.Leckie, ibid., 1936, 4, 83, 324.96 W. R. Angus, A. H. Leckie, and C. L. Wilson, Nature, 1935, 135, 913.37 W. R. Angus, C. R. Bailey, J. B. Hale, C. K. Ingold, A. H. Leckic,38 Molzatsh., 1936, 68, 374; J . Chem. P?qsics, 1935, 3, 834.39 Physical Rev., 1934, 46, 146.C. G. Raisin, J. W. Thompson, and C.L. Wilson, J., 1936, 912-971SUTHERLAND SP:ECTROSCOPY. 59013 vibration or by its non-appearance. The particular applicationsof this 40 would take t;oo much spacc: to be summarised adequatelyhere, particularly as many of them are still rather controversialsub j ect s .Intramolecular Forces.Next in importance to the dimensional coiistants of a moleculecome those characterising the forces requircd to alter the distancesbetween the constituent atoms, since they presumably bear a fairlydirect relation to the strengths of the corresponding chemical bonds.The magnitudes of the vibration frequencies of a molecule dependsolely on the inasses of the various atoms and on the forces broughtinto play when the latter are displaced from their equilibrium posi-tions.A proper analysis of the vibration spectra of a moleculeshould $heref w e give information coiicerning this interatomic forcefield. The early steps in this direction have already been reviewedin these Report>s,*1 but much progress has been made in the past twoyears. We sh:tll accordingly treat this problem from a more generalstandpoint and endeavour to show how the various methods arerelated to one another.It is well known that in a system executing simple harmonicmotion the potential energy may be expressed as $Ex2, where x is theco-ordinate which varies harmonically, and Ex is the restoring forcecalled into play when the system is displaced from its equilibriumposition in which x is zero. For example, in a diatbmic molecule, xdescribes the variation in the internuclear distance during the vibra-tion, the frequency of which is given by 2;72/lc(ml $- m,)/mp2, ml andm2 being the masses of the atoms.The force constant E may there-€ore be directly determined from the vibration Irequency. In thecase of a polyatomic molecule consisting of n atoms, the matter is notso simple. The 3n - 6 internal degrees of freedom may each be char-acterised by a co-ordinate xT ; the corresponding general expressionfor the potential energy is____--Using the methods of classical medianics, one obtains expressionsfor the 3n - G frstqixencies of the form v = f(kl . . . k13 . . . ml . . .).In other words there are only 3'1~ - G equations from which to deter-mine all the force constants E,, k,, .. . El, . . . etc. Clearly thisis impossible, unless some assumption is made which reduces the40 L. Pauling, J . Amer. Chern. SOC., 1935, 57, 2680; 1936, 58, 94; L.Onsager, ibid., p. 1486; R. H. Gillette and A. Sherman, ibid., p. 1135; R. H.Gillette and F. Daniels, ibid., p. 1139; W. Gordy, J . Ghem. Physics, 1936,4, 750.4 1 Ann. Reports, 1934, 31, 2160 GENERAL AND PHYSICAL CHEMISTRY.number of arbitary constants in (1) to not more than 3n - 6. Alltheories of the intramolecular force field are directed towards sur-mounting this difficulty by making some specific assumption regard-ing the nature of the field which will effect the required reduction.It is, of course, desirable that the number of constants to be deter-mined should be less than 3n - 6, for there must then exist certainrelations be€ween tlie frequencies and hhe atomic masses which areindependent of the force constants.The cxactness with which theserelations are fulfilled forms a test of the validity of the assumptions.We shall consider briefly the types of assumption which have beentricd, and how these are related to the chemical conceptions of thebonds in a molecule.The VaEency Force Field.-The assumption which is based mostdirectly on chemical ideas is that of the valency force field.42 Hereeach chemical bond in the molecule has associated with it a forceconstant, Ic (analagous to that for a diatomic molecule), while theangles between neighbouring bonds each have a characteristicconstant, 0, measuring their resistance to deforniation.This meansthat the vibrations of the molecule are described in terms of thechanges in the lengths of the bonds (a), and of the angles between thebonds ( E ) , the potential energy being writtenV = &(kld: + k,d$ + . . . + 0,c4 + O2E; + . . . 1The number of arbitrary constants is obviously considerably re-duced, since all interaction terms of tlie type 2E1,x1x2 have beenomitted. The valency force field is liherefore essentially an inade-quai;e representation, in that one assumes that the only forces actingon the atoms are those rcsishing simple stretching and deformationof the bonds, and (what is more important) that these stretchingsand deformations are quite independent of one another. Neverthe-less, it has been applied not uiiprofitably to a great number of mole-cules by many different workers over a number of years, and it isonly rccently that its limitations and value have been criticallyexamined.For the symmetrical triatomic molecule XYX, only two constantsare required to describe this field, one giving the force needed toalter the length of the UX bond, the other giving that needed toalter the XYX angle.This means that a relation must exist betweenthe three frequencies of the molecule, the masses of the atoms, andthe angle CI between the YX bonds. W. G. Penney and G. B. B. 3%.Sutherland have tested this relation for the molecules sulphurdioxide, water, deuterium oxide, sulphur dioxide, nitrogen dioxide,42 R. C. Yates, Physical Rev., 1930, 38, 555; R.Meckc, 2. physikal. Chem.,1931, B, 16, 409, 421; 1032, 17, 1SUTHERLAND : SPECTROSCOPY. 61carbon dioxide, carbon disulphide, and the CH, group. They foundthat for all except carbon dioxide and disulphide the discrepancieswere less than 5%. On the other hand, the converse process ofemploying the valency force field to determine the angle a of themolecule cannot be relied on to give a result with an error of less than20’. For pyramidal molecules of the type YX, again only two con-stants are needed to correlate the four frequencies, so the adequacyof the representation may also be tested here. This has been donefor NH,, ND,, PK, and As€€, by Howard20 and for PP,, PCl,, PBr,,Ass,, AsCl,, SbCI,, and BiC1, by Howard and Wilson.23 The resultsindicate that as a first approximation the valency force field is reason-ably satisfactory, but that interaction forces (particularly in the lattergroup of molecules) are by no means negligible.For regular tetra.hedral molecules of the form YX,Rosenthal l8 has made a very carefulinvestigation of CH,, CCl,, SiCl,, TiCI,, SnCl,, CBr,, SnBr,, SO4”,CIO,”, and finds that methane is the only one for which the valencyforce field is a reasonably good approximation. This field has beenwidely applied by K. W. H. Kohlrausch43 to many more complexsystems. His results may be regarded as a useful confirmation of thegeneral correctness of the assignment of fundamental frequencies ;the actual values given for the force constants should not be regardedas more than a first rough approximation to a description of themolecule.Central Force Field-Another simple type of force field whichwas tried out44 but which has not been so successful is basedon the assumption that the only forces which act are directed solelyalong the lines joining the atoms.Thus if r,,, r23 . . . denote thedistances between the centres of the atoms then the potential energyis writtenAlthough this is possibly a better approximation than the valencyforce field for certain tetrahedral molecules such as carbon tetra-chloride and for some symmetrical plane ions such as CO,’ and NO,’,yet it cannot be said to be very suitable either from a chemical or froma physical point of view. Attempts to improve it by bringing inadditional forces have been made by H.C. Urey and C. A. Bradley 45and by A. Eucken and IF’. S a ~ t e r . ~ ~43 Monatah., 1936, 68, 349; 2. physikal. Chem., 1935, B, 30, 298. Theseare only two typical examples from a very large number. They are chosenhero because they are referred to in Table V.44 N. Bjerrum, Verhandl. deut. physikal. Qea., 1914, 16, 737; D. M. &Mi-son, Phil. Mag., 1926, l, 195.45 Physical Rev., 1931, 38, 1969.46 2. physikal. Chem., 1934, B, 26, 46362 GENERAL AND PHYSICAL CHEMISTRY.Hore General Types of Force. Field.-A more general method ofapproaching the problem has been pursued by J. E. F t ~ s e n t h a l ~ ~C. Manneba~h,~~ G. B. €3. M. Sutherlancl and D. &I. Dennison 49 andothers. Assuming that the potential function possesses the samegeometric symmetry as docs the molecule itself, they investigatethe miniinurn num'ncr of arbitrary coixstants required in the generalpotential function (1).Thus for the isosceles triangular moleculeYX, it is 4, for tho regular pryarnidal YX,, 6, for the regula8r tPetm-hedral PX,, 6, for axially symmetrical ZYX3,50 9, for ethylene,sl 15,and for bcan~cne,*~, 34. The corresponding number of fundamentalfrequencies in such molecules being respectively 3,4,4,6, 12, and 20,some further reduction is still nccessary. This has been attempted intwo ways, either by introducing some generalised type of valencyforce field which does take account 01 the more importantinteractions,239 257 33,489 51 or a!Gcriiativelg, by assuming that certaingroups in the molecule are practically indcpeiident of the rest of themolecule.The latter assuniption is suficiently justified by a mass ofempirical data showing that whenever certain groups are prcsentin a molecule certain characteristic frequen cics appear in its vibrationspectra. It was first applied to the CI-I, and the CH, groups in somesimple compounds by Sutherland and Dennison ; 49 its generalisedextension to the series of molectrles methane, methyl chloride,chloroform, and carbon tetrachloiide by €I. H. Voge and J. E.nosentha152 has proved it to be a reliable method of computing thefrequencies of a molecule from a knowledge of the force constants ofits constituent groups. It should Fc emphasised that the values ofthe potential constants in this method may not always be capable of adirect physical interpretation ; yet ccrtain combinations of them canbe shown to be equivalent to the " bond strengths " ( k l , E, .. . ) ofthe valency forco field.There are, however, two i ~ ~ t h o d s (each applicable t o a, limitedclass of molecule) whereby all the constants of the Rosenthal-Mannebach generalised function may be found. The first is from theisotope effect ; if the molecule coiicerned coiitsins one or morc hydro-gen atoms, thcn when thcse am replaced by dcuteriuni the frequen-cies are altered while the potential constants remain Dhe same. Onelias consequently two or more sets of frequencies from which todetermine the same set of constants.This has been done for47 Physic*at Rev., 1934, 45, 835; 46, 730; 1935, 47, 235; 1936, 49, 535.48 A m . SOC. sci. Rruxelles, 1935, B, 55, 5, 129, 237; Van den Boasche andt!. Mannebach, ibid., 1934, 54, 230.4 9 PTOC. ROY. SOC., 1935, A, 148, 250.611 J. E. Rosenthal and H. H. Voge, J . Chem. Phgsics, 1936, 4, 131.5 1 J. M. Delfosse, Ann. SOC. sci. Bruxelles, 1935, 55, 114.J . G%em. Physics, 1036, 4, 137SU'I'HKRLAND : SPEUTBOSCOPY . 63smnxxria 19 and methane and will doubtless soon be extended. Theother nieChod depends on the interpretation of the anomalous spacingof the rotation lines in the degenerate vibrations of symmetrical-topand spherical molecules. This has becn accomplished by Johnstonand Dcnnison,10 who have extended the earlier work of E.Teller 53on this subject, vix., thc interaction between vibration and rotation,and have applied it t o the calculation of the five potential constantsof mcthane.I n all of the above methods no account has been taken of possiblecubic terms in the potential function, i.e., of the anharmonicity of thcvibrations. The frequencies cmp1oyt:d in the calculations shouldtherefore not be the observed ones but the frequencies €or infinitesi-mally small amplitude of vibration. The latter can be deduced fromthe observational data provided a number of the overtone frequenciesare known. The errors introduced from this cause are probablynot more than a few units yo. Anothcr common feature of all of themethods is that cerhain constants or combinations of them (in par-ticular, the bond constants or" the valency force field) differ very litthno matter which approach is employed ; it, is the interaction constantswhich differ very greatly on tihe various theories.Fortunately, thebond constant, i.e., the force required to stretch a definite bond agiven distance, is 01 more chemical interest than the latter at themoment. Accordingly we have gathered together in Table V a,number of the values now available for some of the commoner bonds.I n this connection it is important to note the work of R. M. Badger 54and C. If. D. Clark 55 on the relation between the force constant andthe internuclear distance in a bond. Originally given for diatomicmolecules as an extension o€ Morse's relation r30, = const., it hassince been modified by several workers 5G in attempts to correlate itwith the position of the two atoms in the periodic table and to makeit applicable to polyatomic molecules.The most; convenient form inwhich to state it is possibly that used by Badger himself, viz.,where re is the equilibrium internuclear distance, k, is the bond forceconstant, Qij and dij are constants the values of which depend on thopositions of the constituent atoms in the periodic table. If a forceconstant for a particular bond is evaluated by the methods we have53 '' Hand- und Jahrbuch der Chemischsn Physik," 1934, Band 9/11.54 J . Chew%. Physics, 1934, 2, 128.6 6 1%. M. Badger, ,7. ( ' J i ( m . Phy&s, 1935, 3, 710; C . H. D. Clark, Phil.Jlq., 1935, 19, 470; PlLysicnl Rev., 1935, 47, 338; Trans.Fnraduy Sac.,1935, 31, 1017; Proc. Lee& Phil. Soc., 1936, 3, 218, 221; 13. S. Allen aiidA. K. Longair, Phil. Mag., 1935, 19, 1032; W. Lotmar, Z. Physik, 1935, 93,528; M. L. Huggins, J . Chem. Phys'k8, 1935, 3, 473; 1936, 4, 309.66 Phil. Mag., 1934, 18, 45964 GENERAL AND PHYSICAL CHEMISTRY.been considering, this relation enables the corresponding internucleardistance to be computed. This has been done for several mole-cules,23* 251 331 4*#51 and the results are in surprisingly good agreementwith the distances deduced from X-ray and electron-diffraction data.Regarding the values listed in Table V, it is interesting to noticethat those below 7 x lo5 dynes/cm. are associated with single bonds,TABLE V.Force Constants Characteristic of Bonds in PolyatomicMolecules.Forceconstant,Type of dynes/ Moleculebond.cm. x or group. Ref.c=cC E NN=Nc-cc-0N=OS-0 c=sO-H15.717.916-716.916.717.514.615.022.09.59.88.68.213.414-215.319.09.113-710.07.68.07.0C,H2 - HCNClCNBrCNICNC,N,NNON-N,c2CZI-1439OZH, ocs ococoNO,NNOso2cs, ocsH2O497777677494951534977497777757-Forceconstant,Type of dynes/bond. em. x low6.N-H 6.4S-H 4.0C-H 5.95.85.04.95.04.85-0 c-c 5.04-87.6c--0 4.5C-S 3.0 c-I? 5-8C-C1 3.63-45.2C-Br 2.94-2c-I 2-33.0Ref.2074974952337434964343434940527497497those between 7 and 15 x lo5 dynes/cm.with double bonds (in theconventional sense), and those over 15 x lo5 dynes/cm. with triplebonds. This is important when one remembers that the agreementbetween various methods is within 10% on any particular molecule.One therefore finds pleasing confirmation that the C-0 bond incarbon monoxide and dioxide is nearer triple than single in accord-ance with the theory of resonance (see p. 45). Similarly the C-Cbond in benzene is half-way between a single and a double bond.These examples might be multiplied, but sufficient has been said toindicate the great possibilities of this method of putting a quantitativeestimate to the shades of difference between the many types of bind-ing which we are realising exist in chemistry.G.B. B. M. S.57 J. H. Van Vleck and I?. C. Cross, J . Chem. Physks, 1933, 1, 357GLASSTONE : ELECTRON DIFFRACTION. 654. ELECTRON DIFFBACTION AND m E STRUCTURES OFGASEOUS MOLECULES.Theoretical.-In 1915 P. Debye 1 and P. Ehrenfest 2 independentlydeveloped equations giving the angular distribution of the intensityof X-rays when scattered by non-crystalline substances ; these areparticularly applicable to scattering by a gas or vapour, since themolecules are sufficiently far apart to make intermolecular effectsnegligible in comparison with the total scattered radiation. Theobserved effects then virtually result only from scattering byatoms within the individual molecule, and the random movementsof the latter do not affect the interference of X-rays.Electronwaves, the existence of which can now be regarded as definitelyestablished, behave like X-rays in so far as they are scattered byindividual atoms in a given molecule, and M. Mark and R. W i dfound that the intensity of the coherent (elastic) scattering forhigh-velocity electrons could be represented by an equation similarto that of Debye and Ehrenfest; thus, a t an angle e between theprimary and the scattered electron beam, the intensity -Ic,,. of thelatter is given by(1)where E is a constant, $ is the scattering factor of the particularatom for electrons, andxij = ( 4 x / ~ ) . Zij sin e/a . . . . * ( 2 )the term Zzj being the distance between the atoms designated byi and j.The equivalent wa.ve-length of the electrons, A, is deter-mined by the relationshipx 10-scm. . . 1where V is the potential in volts applied to accelerate the electrons.In this equation, the first term is the equivalent of the de Broglieequation, A = himu, and the second term is the relativitycorrection.In determining the total coherent scattering by means of equation(l), it is necessary to sum the terms for all possible pairs of atoms inthe molecule; the scattering due to individual atoms must beincluded, and this is given for each atom by the corresponding $2,since now i = j and consequently xi.i is zero and (sin xij)/xij is unity.Ann. Physik, 1915, 40, 809.Vera. K . Akad. Amsterdam, 1915, 32, 1132.Natzcrwiss., 1930,18, 205, 778 ; Z.Physik, 1930, 60,741 ; 2. Elektrochem.,REP.-VOL. XXXIII. C1930, 36, 675; R. Wierl, Physikal. Z., 1930, 31, 366, 102866 GENERAL AND PHYSICAL CHEMISTRY.If free rotation is possible within the molecule, then the distance Zijbetween a given pair of atoms may not remain constant, and allow-ance for this variation must be made in the calculations.4Strictly speaking, the factor Q varies with the scattering angle 0,and for the ith atom is given by the formula. . (4).Zi being the atomic number of the atom and Fi its scattering, or" form," factor for X-rays.5 The form factors, which decrease as(sinO/2)/~ increases, have been calculated by Rl. W. James and0. W. Brindley,6 and by L. Pauling and 5. the valuesof the latter authors being, apparently, in better agreement withexperiment.I n addition t o the coherent scattering already considered, allow-ance must be made for incoherent scattering, consisting of electronswhich have undergone change of wave-length.According t oL. Bewilogua,O this is given by the relation( 5 )ill whichf(v,) is a function of tii, andvi = 4~(0.176/Zi2/3)(sin8/~)/~ . . . . (6)The values of j ( v i ) for various values of vi are quoted by Bewiloguu.It appears from his calculations that for electron diffraction theintensity of the incoherent scattering, which is added to the coherentamount so as to give the total scattering, falls off rapidly as(sin ~/Z)/X increases and becomes quite small a t appreciable scatteringangles, especially if the atomic number is large.The coherent scattering may be divided into two parts : first," atomic " scattering due to individual atoms, and secondly," molecular " scattering in which two atoms are concerned.Theformer, as shown above, is given by $2 for each atom and hencefalls off continuously as the scattering angle increases, but theexpression for the latter contains the (sin x)/x terms of equation (l),R. Wierl, Physikal Z . , 1930,31, 266; Ann. Physik, 1933, 13, 453; L. E.Sutton and L. 0. Brockway, J . Amer. Chem. SOC., 1935, 57, 473; see also,S. H. Bauer, J . Ghem. Physics, 1936, 4, 406.H. Bethe, Ann. Physik, 1928, 87, 55; 1930, 5, 325; N. F. Mott, Proc.Roy. SOC., 1930, A , 127, 658.Phil. Mag., 1931, 12, 81, 739 (correction).7 Z. Krist., 1932, 81, 1.See R.W. G. Wyckoff, &id., 1930, 75, 632; cf. V. 33. Cosslett, Trtrtw.Faraday SOC., 1934, 30, 987.Physilcal. Z . , 1931, 32, 740; 1932, 33, 688GLASSTOFIX : ELECTRON DIFFRACTION. 67and hence passes through a series of maxima and minima as 8increases. If a beam of high-velocity electrons after traversing agas in an appropriate manner falls on a photographic plate, and thisis examined photometrically after development, the record showsa steadily decreasing background intensity, due mainly to atomic,and at small scattering angles also to incoherent, scattering, withoccasional inflexions corresponding to the maxima in the coherentscattering. Visual examination of the plate appears to show, how-ever, a central spot, caused by the unscattered electron beam,surrounded by a series of concentric diffraction rings, apparentlyalternately light and dark, suggesting a series of maxima andminima of scattering without a falling background.This is never-theless a purely psychological effect, since photometric investigationgives an intensity curve of the type anticipated from theoreticalconsiderations, the positions of apparent maximum density in thediffra ctioii rings corresponding approximately to the inflexions inthe curve.Experimental Methods and Interpretation of Results.-The experi-mental method in general use is bascd on that devised by €3. JVierl,loalthough important modifications ha've been made.ll A fine boamof electrons, accelerated by a potential of about 50,000 volts, ismade to pass at right angles through a narrow stream of the gas orvapour under investigation, and then falls on a photographic plate.The electrons are produced either by a heated cathode in it high-vacuum type of discharge tube, or by gas-discharge, in either airor hydrogen, using a cold cathode.Although some authors haveused the latter, a t the California Institute of Technology, wherethe most important recent work on electron-diffraction of vapourshas been done, the hot cathode is preferred.12 The electron-accelerating voltage is measured either by an electrostatic (or other)voltmeter, or else by a milliammeter in series wit'h it suitableresistance; the instrument is calibrated with the aid of electron-diffraction photographs obtained through thin gold foil, for whichthe space-lattice dimensions are accurately or by the useof ammonium ch10ride.l~ A method for studying electron diffrac-tion by gases in which a relatively low voltage, vix., 6,400 volts, isemployed has been described recently l5 ; it is not capable, however,of giving such accurate results as the high-voltage method.lo Ann.Physik, 1931, 8, 521.11 V. E. Cosslett, Zoc. cit., ref. (S), p. 981; H. cle Laszlo, Proc. Roy. Xoc.,12 L. 0. Brockway, Zoc. cit., p. 240.l a E. A. Owen and J. Iball, Phil. Nag., 1932, 13, 1020; M. C. Neuborger,1 5 P. G. Ackermann and J. E. Mayer, J . Chem. Physics, 1936, 4, 377.1934, A , 143, 672; L. 0. Brockway, Rev. Mod. Physics, 1936, €?, 231.2. Krist., 1936, 93, 1. lP IT. Boersch, Monatsh., 1936, 65, 33 I 68 GENERAL AND PHYSICAL CHEMISTRY.Since the quantity xij in equation ( 2 ) depends on the correspondinginteratomic distance ZiJ, it is evident that the positions of thediffraction rings, or the discontinuities in the photometric curve,will be related to the various atomic separations within the mole-cule, and it was shown by Mark and Wierl that the electron-diffrac-tion patterns could be used to determine int,eratomic distances ina molecule.The principle of the method is analogous t o thatpreviously used in connexion with the scattering of X-rays bygases : certain definite configurations are assumed for the atomswithin the given molecule, a i d the theoretical scattering curves arecalculated and compared with the experimental results.Theconfiguration for which the best agreement is obtained is regardedas being correct, and from this the interatomic distances aredetermined. When the molecule is relatively complex, the calcul-ations may become laborious, although certain simplifications(see below) can be made without involving serious error.Prom equation (4) it may be seen that it is possible to write + = Z+, wherei$ = (1 - F/Z)/[(sin8/3)/~]2 . . . ' (7)and consequently, as a first approximation, since P, which is alwaysless than 2, decreases as the scattering angle increases (p. 66),equation (1) can be put in the formFor a simple molecule, e.g. , carbon tetrachloride, the configurationof which can be taken with confidence as tetrahedral, thisapproximate equation for the coherent scattering can readily bewritten in terms of one parameter, e.g., xc-cI, and of the atomicnumbers of carbon and chlorine.By taking a series of arbitrarynumerical values of x, the corresponding values of .Ico. can be calcul-ated and the resulting hypothetical scattering curve, showing aseries of maxima and minima, plotted. From the electron-diffrac-tion photograph, or from the photometric curve obtained therefrom,the actual positions of the maxima and minima of scattering aredetermined and expressed in terms of (sine/2)/h, since 8 can becalculated from the corresponding displacement of these positionson the plate and the dimensions of the apparatus, and A from fireaccelerating voltage (equation 3). A comparison of the x valuesfor the calculated maxima and minima with the observed (sin 0 / 2 ) / hvalues gives an approximate relationship between these twoquantities which can be used t o calculate the atom-form correction4 (equation 7) in terms of x.The approximate -Ico. values, forvarious distances x, are now multiplied by the corresponding 4 a GLASSTONE : ELECTRON DIFFRACTION. 69each point to give the correct coherent scattering intensities, whichcan now be plotted against x ; the new values of the latter for themaxima and minima are then compared with the correspondingobserved (sin 0/2)/1 values, and the distance between the atoms,e.g., Zcc-cI, calculated by means of equation (2). If the configurationchosen for the molecule is the correct one, all the maxima andminima should give approximately the same value for the inter-atomic distance ; should this not be the case, however, the configur-ation is probably incorrect and a new one must be sought whichgives more satisfactory constancy.The correctness of any configur-ation can usually be determined by a general comparison of thediffraction rings and the calculated scattering curve for thatconfiguration. A further correction for incoherent scattering shouldbe made before the final comparison of observed and calculatedpositions of maxima and minima, but as this quantity diminishessteadily and has to be added to Ice., the positions of the inflexionsin the curve are not appreciably affected. The main objection tothe inclusion of .linco.is that its rapidly falling value tends to suppressthe maxima in the scattering intensity curves and makes theiridentification difficult : this has been overcome to some extent byplotting the total intensity multiplied by [(sin o/2)/hj2 against x,when definite maxima and minima appear in the curves.16When the configuration of a molecule can only be expressed interms of two parameters, e.g., for compounds of the type Y/- -"Y,then it is convenient t o chose these as the distance lx-y and thevalency angle a. The values of Ipo. are then plotted against x fordifferent probable values of a, and the general shape of the curveis compared either with the actual diffraction pattern or with itsphotometer record ; the value of a giving a calculated curve showingthe best agreement, as far as the positions and intensities ofmaxima and minima are concerned, is assumed t o be the correctone, and from the corresponding curve the distance Zx-y is cal-culated. Frequently it is not possible to be quite certain as towhich curve gives the best agreement, and then the molecular con-figuration is in doubt ;l7 this weakness of the method will certainlybe overcome in time, as the experimental technique is improved.When more than two parameters are required to define thedimensions and configuration of a molecule, e.g., in benzenederivatives, a large number of calculated intensity curves may have16 L.R. Maxwell, S. R. Hendricks, and V. M. Mosley, J . Chem. Physics,1935, 3, 699.17 See, e.g., L.R. Maxwell, V. M. Mosley, and L. S . Deming, ibid., 1934, 2,331.x70 GENERAL AND PHYSICAL CHEMISTRY.to be plotted. If something is known about the molecule, as isgenerally the case, then the calculations are limited to the mostprobable configurations in the fist place. A number of approxi-mations can also be made which do not seriously affect the accuracyof the final results but greatly simplify the calculations; some ofthese simplifications are mentioned below. l8One of the main sources of error in the application of the electron-diffraction method to the determination of interatomic distanceslies in the identification of the points on the photometric recordcorresponding to the maxima and minima of coherent scattering in-tensity.Since the continuously falling background tends to flattenout the photometric maxima and makes their accurate identificationdifficult, it is desirable to compensate for the background intensity ofthe photographic plate. One means of achieving this end is to printthe original plate by allowing the incident light to pass through aspecial revolving sector so designed as to compensate for fhe steepfalling off, from the centre outwards, in background blackening ofthe plate :I9 this method has the disadvantage that the relativeintensities of the various maxima and minima are altered, whereasa knowledge of such intensities is often of importance in determiningthe correct molecular configuration. An alternative method 20is to make a special compensating cell having the same shape asthe photometric background-scattering curve.This cell is filledwith a dark coloured liquid and light is allowed to pass through itand to fall on a photographic plate: the plate will, therefore,hecome fogged and the density of fogging will be almost the exactreverse of the background blackening of the original plate. Thelatter and the compensating plate are then placed together andprinted on to a third plate, giving a series of sharp dark and lightbands ; a photometer record of this shows clear maxima and minimaof coherent scattering. The compensation process described isparticularly valuable for giving accurate measurements of thepositions of the first few maxima, but its use is limited to thisregion; a t greater scattering angles the fall in the background andthe prominence of the maxima above it become so small that it isalmost impossible to construct a compensation cell that will permitof the separation of one from another with any accuracy. It is aremarkable fact, however, that the eye is more sensitive than anymechanical photometer, and it is possible by direct visual examin-For full discussion, see L.Pauling and L. 0. Brockway, J. Chern. Phylsics,lB F. Trendelenburg, Naturwiss., 1933, 21, 173; F. Trendelenburg and*O V. E. Cosslett, bc. cit., ref. (11).1934, 2, 867.E. Franz, W k . Veriff. Siemens-Konz., 1934, 18, 48GLASSTONE : ELECTRON DIFFRACTION. 71ation of the plates to detect ten or more diffraction maxima, afiwell as several minima.Owing to the intenbe blackening of thec*sntral spot, caused by unscattered electrons, however, the positionsof the maxima in the first one or %wo diffraction rings cannotgenerally be estimated correctly : this is mainly due to the St. Johneffect,Z1 a physiological phenomenon which militates against theaccurate estimate of the position of maximum density of a photo-graphic plate when the rate of decline of the background intensityis different on both sides of the maximum. The effect is alsooperative when two diffraction rings are close together ; under theseconditions the photometer and the calculated intensity curves haveSL “ shelf.” 22 Measurements liable t o be in error because of theSt. John effect should not be used in the final calculations, althoughthe approximate positions of the diffraction maxima may be usedfor purposes of qualitative comparison with the positions in thecalculated intensity curves, in order t o determine which of theserepresents the correct molecular configuration.Approximation Methods.-In applying the correction for theatom-form factor (equation 7), it is found that the value of 4approaches a constant as the scattering angle increases, so thatfor the higher orders of maxima and minima # may be replacedby 2, the atomic number, without appreciable error ; consequently,under conditiions such that visual identification of the positions ofmaxima and minima is satisf sctory, the approximate equation (8)can be used with reasonable accuracy.This simplification wasintroduced by and it has been subsequently confirmedthat the use of 2 instead of does not introduce any appreciableerror in the calculation of interatomic distances.Although someauthors use the simple form of the acattering-intensity equation inconjunction with the photometric method of identifying the positionsof inflexions, it has been shown by L. Pauling and L. 0. Brockway,lsin a very comprehensive study of the visual method of observingthe maxims and minima in diffraction photographs, that there isreason for supposing that because of the nature of the backgroundthe eye automatically corrects, a t least approximately, for thedifference between 2 and 4. Quite accurate results should, there-fore, be obtained by supposing the scattering factor of an atom tobe proportional to its atomic number, and finding the positions ofapparent maxima and minima of scattering, other than the firstone or two, by visual examination : under these conditionsincoherent scattering can be neglected in calculating the intensityvalues, The conclusion is borne out by the fact that, using this21 E.C. St. John and L. W. Ware, Astrophya. J . , 1916, 44, 35.22 I,, 0. Brockway and F. T. Wall, J . Anzer. Chem. SOC,, 1934, 56, 237372 GENERAL AND PHYSICAL CHEMISTRY.method, Pauling and Brockway found the C-C1 distance in carbontetrachloride to be *1*76A., whereas the careful work of V. E.Cosslett,l'$ 23 who applied corrections for the atom-form factor andfor incoherent scattering, and also compensated for backgroundscattering in determining the positions of the first few maximaand minima, led to a value of 1.74 -+ 0.02 A.The accuracy ofinteratomic distances obtained by electron-diffraction methods isgenerally stated to be 4 1%.A further approximation made by some workers, in order tosimplify the calculations for molecules containing both light andheavy atoms, is to ignore the scattering due to the lightest atoms,e.g., hydrogen; this is justified by the fact that the scatteringfactor of an atom is approximately proportional t o its atomicnumber. I n halogenobenzenes, for example, the intensity of thescattering caused by halogen-carbon and by halogen-halogen is solarge compared with that due to carbon-carbon, hydrogen-carbon,or hydrogen-hydrogen, that the corresponding scattering terms ofthese latter in the intensity equation (8) may be neglected withoutserious error.Using this simplified procedure and the visualmethod of examining the diffraction photographs, H. de Laszlo 24obtained 2-05 jI 0.01 A. for the C-I distance in p-di-iodobenzene,based on the positions of twelve scattering maxima, whereasS. B. Hendricks and his co-workers,25 who studied the photometricrecords of the plates, applied corrections for atom-form factors,and took into consideration the scattering from all the atoms,gave 2.00 A. (probably, a t least, 3 0.05). It may be concluded,therefore, that until there is a marked improvement in the technique:which permits of more accurate identification than is a t presentpossible of the positions of maxima and minima in the electron-diffraction photographs, the application of the approximationsdescribed can be generally justified.26Analytic Method-An analytical procedure which facilitates theaccurate interpretation of electron-diffraction photographs has beenproposed by S.H. Bauer 27 : the first step involves the differentiationof equation (8) so that the positions of maxima and minima of scat-tering are given by23 See also V. 12. Cosslett and H. de Laszlo, Na,ture, 1934,2 1 PTOC. Roy. SOC., 1934, A , 146, 690.2 5 S. B. Hendricks, L. R. Maxwell, V. L. Mosley, and26 See, however, L. R. Maxwell et nE., Zoc. cit. ref. (16).2' LOC. cit., ref. (4).J . Chem. Physics, 1933, 1, 649.134, 63.M.E. JeffersonGLASSTONE : ELECTRON DIFFRACTION. 73As before, a probable configuration is choscn with definite values ofI,; these are inserted in equation (9) together with a value of( ~ T c / A ) sin el2 representing the position of an observed inaximuinor minimum, and if the parameters chosen are correct, the sum ofthe terms will reduce to zero for every maximum and minimum.As it is improbable that the first model tried will be the right one,the equations will, in general, lead to a set of residuals, and Bauerhas shown how by a process of successive approximation it is possibleto obtain a set of Zij values which satisfy equation (9). These onlyrepresent the true inter-atomic distances, however, if the valueschosen arbitrarily a t the commencement of the calculation are closeto the correct ones, Only the positions of sharp, well-defined ringsmay be used in the calculation, and maxima associated with a“ shelf’’ or a low “trough” should be ignored.Although themethod may be useful in certain cases, the limitations are such as toprevent it from being generally applicable until improvements intechnique permit more complete diffraction patterns to be obtained.Radial Distribution Method.-L. Pauling and L. 0. Brockway 28have described a procedure, known as the “ radial distributionmethod,” for the examination of electron-diffraction rings which isrelated t o that used for the interpretation of X-ray diffractionpatterns obtained with It has the advantage of not re-quiring any assumption or previous knowledge concerning the con-figuration of the molecule or of inter-atomic distances.A distribu-tion function for scattering power is calculated representing, in termsof 1, the product of the scattering powers in volume elements,instead of by atoms, at a distance I apart. Since the electrons arescattered mainly by atomic nuclei, a maximum in the functionrepresents an inter-nuclear distance in the molecule equal to thecorresponding value of I ; thus the inter-atomic distance is deter-mined. The theoretical intensity equation (1) is based on theassumption that discrete atoms act as scatterers, but if the scatteringpower is regarded as spread over the molecule as a whole, thenintegration replaces summation, thusf , ~ o m 12D(1) sin sl dl .. . . I = k -~s4 * slwhere s is used for (4x11) sin 012, so that sl is identical with x. I nthis equation l20(1) represents the product of the scattering powersin all volume elements a t a distance I apart. Equation (10) beingwrittjen in the form&51 = kftLw ID(,!). sin 81. dl . . . . (11)28 J . Amer. Chem. SOC., 1035, 57, 2684.29 P. Zernike and J. A. Prins, 2. Physik, 1927, 41, 18474 GENERAL AND PHYSICAL CHEMISTRY.it mn be inverted, thusmorsind ds . . . . (13)For practical purposes the integral may be replaced very approxi-mately by a sumsin s,l D(Z) = XIn-- . . . . . (14)n 41in which one term appears for every ring in the diffraction pattern ;s, is the s value for the nth ring and In is its intensity.The latterquantity is estimated visually for each diffraction ring, and s iscalculated from its position determined by the visual method : it isthus possible to evaluate D(Z) for a series of I values, generally atintervals of 0.1 A. between 0 and 4 A. The positions of the maximain the curve of D(Z) against I give the distances apart of importantscattering centres in the molecule. The method can only be used,a t present, for the complete analysis of simple molecules in whichthere are few important inter-atomic distances involved, and itfails when two of these distances are close togother, so that the twoseparate maxima ,%re fused into one broad one.Applicatim.-Bond distances. The interest of electron-diffrac-tion measurements of gaseous molecules lies mainly in two directions:first, for the determination of interatomic distances with the objectof testing the Pauhg-Sidgwick rule 30 of the additivity of covalentbond distances and the possibility of throwing light on the type oflinkage in a given molecule; and secondly, for the investigation ofmolecular configuration and the evaluation of valency angles,With simple molecules, for which atomic radii obtained from theirband spectra are available, it is found that the electron-difbactionmethod gives results in good agreement with those expected, asmay be seen from the following data for the interatomic distancesin chlorine,l8 bromine,la iodine,26 and iodine monochloride.18Interatomic distances, A.f Molecule.Electron diffraction.Band spect>a.c1-Cl 2.0 1 1.99Br-Br 2-29 2.281-1 2.64 2-66I-CI 2-30 2.3 1so N. V. Sidgwick and E. J. Bowen, Ann. Reporb, 1931, 28, 385; N. V.Sidgwick, “The Covalent Link in Chemistry,” 1933, p. 64; L. Pauling,Proc. Nat. A c d . Sci., 1932,18,293 ; see also W. H. Rodebush, [I’mnR. FnmdaySoc., 1934, 30, 778; C. H. D. Clark, {bid., 1935, 31, 1017GLASSTONE : ELECTRON DIFFRACTION. 75Tho I-Cl distance calculated from the C1-C1 and the 1-1 value, onthe assumption of additivity, is 2-325A., which differs from theobserved results by no more than the experimental error.Until recently, the C-Cl distance in aliphatic compounds was 25.31accepted as 1.81-1433 A., approximately the same value beingfound in carbon tetrachloride, aa- and ap-dichloroethane, cis- andtrans-dichloroethylene, tri- and tetra-chloroethylene, and in carbonyland acetyl chlorides ; later work 18?20*23,32 has indicated that thebond distance is actually somewhat less, zlix., 1.76 &- 0.02 A., thisvalue having been obtained in all four chlor0methanes.~3 Furtherinvestigation of the six chloroethylenes has shown that in thesesubstances the 6 4 1 distance is less than in the chloromethanesand varies from one compound to another : the following distancesare given by L.0. Brockway, J. Y. Beach, and L. Pauling 34 :vinyl chloride, 1.69 A. ; ax-dichloro-, 1.69 A. ; cis-dichloro-, 1.67A. ; trans-dichloro-, 1-69 A. ; trichloro-, 1.71 A. ; and tetrachloro-ethylene, 1.73 A. These results have been interpreted 35 as im-plying resonance involving two states of the type >C--d-Cl and> & b d l , so that the G-Cl distance tends to approach that for adouble bond; in vinyl chloride the shortening should be greatest,since there is only one chlorine atom to take part, but in tetra-chloroethylene the effect of the double bond is divided amongst fourchlorine atoms and the bond distance should approach the normalsingle bond value.It may be noted that H. de Laszlo,36 in apreliminary communication, has given the C-C1 distance in bothtrans-dichloro- and tetrachloro-ethylene as 1.74 A. ; this authorhas also reported the length of the C-Br bond as 1.93 A. incarbon tetrabromide, 1.91 A. in trans-dibromoethylene and intetrabromoethylene, and 1.84 A. in dibromoacetylene ; beforethis, an almost constant distance of 2-05 -+ 0.05 A.had beenrecorded for the four brornomethanes, tert.-butyl bromide, cis-and t m?zs - dibr omoe t hy lene s , t ri br omoet h y lene , and c arb ony 1 andacetyl bromides.10~37 Similarly, the constant value of 2-283 1 R. Wierl, Zocc. cit., refs. (4) and (10); J. Hengstenberg and L. Brfi,Anal. Pis. Quim., 1932, 30, 341; S. B. Hendricks et al., Zoc. cit., ref. (25);R. W. Dornte, J. dmer. Chern. SOC., 1933, 55, 4126; J . Chem. Pkylsics, 1933,1, 566.32 H. Braune and S. Knoke, 2. physikd. Chem., 1933, B, 21,297 ; C. Degard,J. Pierard, and W. van der Grinten, Nature, 1935, 136, 142; C. Degard,Compt. rend., 1935, 201, 951; Bull. SOC. chim. Belg., 1936, 45, 15.33 L. E. Sutton and L.0. Brockway, Zoc. cit., ref. (4).34 J . Arner. Chem. SOC., 1935, 57, 2693.56 L. Pauling, L. 0. Brockway, and J. Y. Beach, ibid., p. 2705.36 Nature, 1935, 135, 474.97 R, W, Dornte, J. Chem. Physics, 1933, 1, 03076 GENERAL AND PHYSICAL CHEMISTRY.0.05A. for the C-I distance in methyl and ethyl iodides, and formethylene iodide, 3'9 38 has now been replaced by 2-12 A. in iodoform,2.10 A. in tram-di-iodo- and tetraiodo-ethylene, and 2.03 A. indi-iodoacetylene. It is clear from these results that further accurateinvestigation on the halogeno-ethylenes a,nd -acetylenes will haveto be undertaken before the suggestion of resonance involvingdouble-bonded halogen can be regarded as proved or disproved :it is important to bear in mind that the tendency to form thedouble bond might be expected to increase in the series C1, Br, I ,but there is hitherto no evidence that this is the case.In aromatic compounds the carbon-halogen distances are lessthan in the halogenomethanes, as the following results (in A.) show :-Ca1.--X.3 6 v 39 >Car,-X. 24$ 2 5 Additive. x = c1 1.76 1-69 1.76Rr 1.93, 1.91 1.88 1.91I 2.12 2-05, 2.00 2.10The observed values for the aliphatic compounds are in goodagreement with those calculated on the assumption of additivity ofcovalent bond distances by using the best data in the literature,aObut with the aromatic compounds a distinct shortening of thebond distance is evident. Here again resonance between two states,>C,,-X and >Car.rX, has been suggested35*41 to account for thedifference; resonance of this type, however, not only appears to beout of harmony with chemical reactivity and other properties ofaromatic halogen derivative^,^^ but the results seem to be capableof another interpretation.It may be noted in the first place thatthe > C,,.-Cl distance recorded is for hexachlorobenzene, in whichthe double-bond character can be divided amongst six atoms :the actual shortening should thus be very small. Further, the same>C,,,-Br distances have been found in di-, tri-, and hexa-bromo-benzenes, whereas a steady increase might have been anticipated.Prom general considerations, the difference between additive andobserved bond distances might be expected to increase through theseries C1, Br, I, but there is no evidence that it does so.It is notimpossible that the conjugated resonating system of single anddouble linkages in the benzene nucleus can bring about a " tighteningup " of external bonds, and so produce a small discrepancy from the38 L. Brh, Anal. Pis. Quirn., 1933, 31, 115.39 Unpublished, see L. 0. Brockway, Zoc. cit., ref. ( l l ) , pp. 260-261.40 Data from N. V. Sidgwick and E. J. Bowen, lor. cit., ref. (30), pp. 401,402; N. V. Sidgwick, op. cit., ref. (30), Chap. 111; L. Pauling, Zoc. cit., ref. (30) ;I;. Pauling and M. L. Ruggins, 2. Krist., 1934, 8'9, 205.*l See, e.g., H. P. Klug, J. Chem. Physics, 1935, 3, 747; N. V. Sidgwick, J.,1936, 533 (537).42 G. Baddelcy, G. M. Bennett, S. Glasstone, and B. Jones, J., 1935, 1827GLASSTONE : ELECTRON DIPFXACTION.77additive carbon-halogen distance ; there would then be no necessityto postulate resonance and double-bond formation. Some evidencefor this view is to be found in the fact that the Cal.-Car. distance,obtained from X-ray observations on crystals of durene and di-berm~yl,*~ are 1-47 A. compared with the value of 1.54 A. for theCal.-Ca,. bond. The electron-diffraction method gives the Cal.-Car.distance as 1-50 A. in di-, tri- and hexa-methyl benzene^,^^ whichis again less than the normal value. The suggestion might be madethat this was due to resonance 45 involving the structures >C-CH,and >C=GH,H, but if this were so, some difference in the C-Cdistance might be expected according to the number of methylgroups substituted in the nucleus.The C-F distance in methyl fluoride 46 is 1.42 A., in excellentagreement with the spectroscopic value (1.43 A.) and that based onadditivity (1.41 A.), but in carbon tetrafluoride 14* 22 the bond lengthis 1-36 A., similar values being found in dichlorofluoromethane anddich10rodiAuoroniethane.~~ It was a t one time suggested 22 thatthe shortening of the bond was due to the partially ionic characterof the C-F link resulting from the difference in the electronegativityof the two elements.It should be noted, however, that the ionicdistance Cj-F- is about 1.53 A., which is actually greater than thecorresponding covalent distance ; further, the dimensions of the ionsare such as to make the structure C4t(F-)4 irnpr~bable.~' Analternative view has been proposed by L.Pa~ling,~* who considersthat, in addition to the single-bonded structure of carbon tetra-fluoride, the molecule resonates among structures having an F- ionbound electrostatically to a CF3+ ion in which there is a double.. bond, as shown in the inset, so that a shortening of: F : the C-F bond distance, determined by the double-bond character which should be shared by all four 'F"C' :jl:- . bonds, would be observed. This resonance would:P: .. not be possible in methyl fluoride, since only onefluorine atom is present. If this explanation for thelength of the C-F bond in tetrafluoromethane is correct, then, it mustbe pointed out, the shortening of the distance is unexpectedly large.This fact is brought out more clearly by considering the bond dis-.... .. . ..43 J. AX. Robertson, Proc. Roy. SOC., 1933, A , 141, 594; 1934, A, 146, 473.44 P. L. F. Jones, Trans. li'araday SOC., 1935, 31, 1036.4 5 Compare J. W. Baker and W. S. Nathan, J . , 1935, 1844.46 Unpublished, see L. 0. Brockway, Zoc. cit., ref. ( l l ) , pp. 260, 261.4 7 N. V. Sidgwick, Ann. Reports, 1933, 30, 118; see also M. L. Huggins,Quoted by L. 0. Brockway and H. 0. Jenkins, J . Amer. Ghem. SOC.,Chem. Rez&zus, 1932, 10, 427.1936, 58, 2036 (2043)78 GENERAL AND PHYSICAL CHEMISTRY.tances in SiF4,22 PF3,22 and A S F ~ , ~ ~ which are as follows, the additivefigures being given below each measured value :Si-F 1.54 P-F 1.52 As-F 1.72Additive 1.81 1.74 1-85The maximum decrease due to the complete formation of doublebonds, ie., 10% of the single bond distances, would be 0.18,0-17, and0.18 respectively, whereas the actual differences are 0.27, 0.22, and0.13.The subject evidently requires further consideration. It hasbeen mentioned in a previous Report 49 that the discrepanciesbetween observed and additive distances in the hexafluorides ofsulphur, selenium, and tellurium 5 0 p 51 have been interpreted asimplying a tendency towards ionic linkage in all these bonds, but insulphur hexafluoride, at least, it is not possible to accommodatesix fluorine ions (radius 1.33 A.) about the S6+ ion (radius 0-3 A.) 5 2 ;even if the latter were extended to 0-55 A., so that the bond distancewas equal to the measured value, 1-88 A., this would still not bepossible.Resonance of the type postulated above, involving theelectrostatically bound structure SF5+F-, with one fluorine atomdoubly bound, might account for the results, but again the effects arevery large.With chlorides there appears to be no tendency for ionisation ofthe chlorine, since the GC1 distance in carbon tetrachloride isexactly equal to the additive value; hence the shortening of thebond in SiC1, (0-16 A.),10p22* 51 GeCl, (0.13 A.),lO> 53 SnCI, (0.09 A.),Io1 22PCl, (0.09 A.),22 and AsC1, (0.04 A.),22 must be explained in anothermanner. It was originally suggested 22 that this might be due to thedifference in the electronegativity of the two atoms forming thebond, but this view was disposed of by the fact that in the methylderivatives of silicon, germanium, tin, nitrogen, and sulphur thedistance between each of these atoms and the carbon atom is almostexactly equal to the additive value, in spite of the difference ofele~tronegativity.~~ An alternative explanation is that double-bond formation can occur between the halogen and the centralatom, as a result of the latter holding five, or more, pairs ofelectrons.22p54 There is no reason to believe that this increase canoccur in the flrst row of the periodic classification, and for theseelements the decrease is not found.In fact a discrepancy in theopposite direction appears to exist between the observed and the48 Ann. Reports, 1933, 30, 93.6o L. 0. Brockway and L.Pauling, Proc. Nut. Acad. Sci., 1933, 19, 68.51 H. Braune and S. Knoke, Zoc. cit., ref. (32).52 For data, see N. V. Sidgwick, Zoc. cit., ref. (47); M. L. Huggins, Zoc. cit.,53 L. 0. Brockway, J . Amer. Chena. Soc., 1935, 57, 958.5* L. 0. Brockway and H. 0. Jenkins, Zoc. cit., ref. (48).ref. (47)GLASSTONE : ELECTRON DIFFRACTION. 79additive distances for the 0-F and the 0-C1 bonds in oxygenfluoride and chlorine rnono~ide,6~ respectively ; the values are asfollows :0-F . 0-c1.Observed, A. . , . . , . 1.36 f 0.10 ; 65 1.41 f 0.05 l4 1.7 1 & 0.02 55 ; 1.68 f 0.03 66Additive, A. ...... 1.30 1.66The difference in the case of the fluoride may be due to experimentalerror, but it is believed not to be so for the 0-C1 bond; L. E.Sutton and L.0. Brockway 55 have suggested tentatively that theaccepted value for the radius of the singly-linked oxygen atom,0*66A., may actually be low by 0*06A., but it is neverthelessconcluded that the rule of additivity of atomic radii is only approx-imate. It is of interest to note here that the G O distance invarious compounds 551 5' has been found to be between 1.42 and1.45 A.,? in good agreement with the additive value 1.43 A. :this result lends support to the accepted oxygen radius. TheC1-0 distance in chlorine dioxide 58 is 1.53 A., a value not verydifferent from that to be expected for a double bond betweenchlorine and oxygen, vix., 1.48 A. The measurements have beenused to suggest a structure for chlorine dioxide involving tworesonance states, vix., : 0 C1: 0 : and : 0 : C1: 0 : ; the argumentsare based on the probable assumption that the 0 : C1 distance liesbetween those for a single and a double bond, since the three-electron linkage is generally equivalent to a single-electron bond.The distance between singly linked carbon atoms in aliphaticcompounds has been found 59 to be 1.60-165 A,, whereasbetween adjacent atoms in the benzene nucleus it is 1-39-1.42249 25* 44 The C=C double-bond distance in ethylene deriv-atives is apparently 1-38 34, 60, 61 in agreement with expectation(see, however, p.45). The C-C distance in acetylene lo anddiacetylene 62 is given as 1.20-1-22 A., the latter figure being. . . . . *** . .. . . . . . . . . . . . ...5 5 L. E. Sutton and L. 0.Brockway, Zoc. cit., ref. ( 4 ) .6 6 L. Pauling and L. 0. Brochvay, Zoc. cit., ref. (28), recalculated by tho57 D. C. Carpenter and L. 0. Brockway, J. Amer. C'hem. Xoc., 1936, 58,5 8 L. 0. Brockway, Proc. Nat. Acad. Sci., 1933, 19, 303, 874.59 R. Wierl, Ann. Physik, 1932, 13, 453; R. W. Dornte, loc. cit., ref. (31);80 L. 0. Brockway and P. C. Cross, Zoc. cit., ref. (57).61 R. W. Dornte, J. Chena. Physico, 1933, 1, 666.62 L. 0. Brockway, Proc. Nat. Acad. Sci., 1933, 19, 868.f The observed distance 1-34 &- 0.07 A. proposed for dimethyl and diethylradial distribution method.1270; L. 0. Brockway and P. C. Cross, ibid., p. 2406.L. 0. Brockway, Zoc. cit., ref. (46).ethers (L. Brh, Anal. Pis. Quirn., 1932, 30, 486) is probably in error80 GENERAL AND PHYSICAL CHEMISTRY.identical with the length generally attributed to this linkage; theobsemed value for the E N linkage in cyanogen 49 G2 and in aceto-nitrile,63 1-16-1.18 A., is also in excellent agreement with theadditive distance 1-16 A.The use of additive values for the carbon-nitrogen and the nitrogen-nitrogen bond in methyl azide 6* givescalculated electron-scattering curves in harmony with the experi-mental maxima and minima, and the C-N and N-0 distances innitromethane and in a-methylhydroxylarnine, respectively, con-firm the concept of a d d i t i ~ i t y . ~ ~It has been mentioned that the measured length of the singly-linked C-0 bond is very close to the additive value, but the measure-ments on the C=O bond were at one time confusing, since distancesof about 1.13 A.were reported in carbonyl and acetyl chloride andbromide 65 and in formaldehyde,66 as compared with the expectedvalue of 1-28 A. New measurements on carbonyl chloride,34however, give the C=O distance as 1-28 A., and a similar result isreported from observations on the dimeric form of formic acid.66Distances of the same order, 1-25-1-29 A., have been obtained bythe X-ray study of crystals of carbonates, oxalic acid, urea, and basicberyllium acetate G7 : it is somewhat surprising, however, to finda distance of 1.14 A. reported for the C=O bond in solid benzo-quinone,G8 The carbon-oxygen distance in carbon dioxide lo andin carbon oxysulphide14~ 65369 is 1.13 A., according t o electron-diffraction measurements, a result in agreement with the value cal-culated from Raman spectra and from X-ray scattering of theformer compound.The marked difference between this distanceand the additive C=O bond value of 1-28 A. has been attributed 7Oto resonance between the normal state O=C=O and the twoexcited states -O-CEO+ and + 0 3 Y O - , for then the carbon-oxygen distance would approach that for the CEO bond, namely,1.13 A. Similar resonating states apparently take part in thestructure of carbon oxysulphide and of carbon disulphide,68although there is less tendency for the formation of the - C 3 3bond, than for the corresponding oxygen link.-a3 L. 0. Brockway, J. Amer. Ghem. Soc., 1936, 58, 2516.64 L. 0. Brockway and L. Pauling, Proc. Nnt.Acad. Sci., 1933, 19, 860;see also N. V. Sidgwick, Trans. Paraday Soc., 1934, 30, 801.66 R. W. Dornte, J. Anaer. Ghem. Soc., 1933, 55, 4126.6 6 L. Pauling and L. 0. Brockway, Yroc. Nu,t. Acad. Sci., 1934, 20, 336:the results differ from those given by L. Hmgst,enberg and L. Brb, Zoc. cit.,ref. (31).6 7 For summary, see H. P. Klug, Zoc. cit., ref. (41), p. 750.6 8 J. M. Robertson, Proc. Roy. SOC., 1935, A, 150, 106.69 P. C. Cross and L. 0. Brockway, J . Cihern. Physics, 1935, 3, 821.' 0 L. Pauling, Zoc. cit., ref. (30)GLASSTONE ELECTRON DlFFRACTION. 81The length of the C-H bond as used by different authors variesfrom 1.06 to 1.10 A. in aliphatic 4137955*64 and from 1.06 to 1-14 A. inaromatic substances ; 18a25* 64 the additive distance is at least 1-06 A.,and agreement between the results is as good as could be expected,especially as the electron scattering of the hydrogen atom is sosmall that it is frequently neglected (p.72).Nolecular conjiqurutions. Electron-diffraction measurementshave been applied in a number of different ways to throw light onthe structures of various molecules. The diffraction pattern ofmethyl azide vapour is quite incompatible with IL ring structurefor the azide group, and a linear structure is indicated : 64 theconfiguration and distances in A. favoured may be represented by1.26 1.10 $/ N ~ N - N * This structure is taken to imply resonanceHaC 135°&150.between the forms -N=&=N and -N-kN, for the twonitrogen-nitrogen bond distances would then approach the values forN=N, i.e., 1-26 A., and N 3 , i.e., l-lOA., respectively.Thenitrogen valency angle of 135" & 15" is in reasonable agreementwith the value of 126" to be expected €or a tetrahedral nitrogenatom. Striking confirmation of the proposed structure for theazide group has been obtained from X-ray measurements oncrystalline cyanuric azide;71 the azide group is found to be linear,as in alkali azides, the bond distances between successive nitrogenatoms being 1.26 A. and 1.11 A. respectively. The nitrogen bondangle is, however, stated to be 114", and the C-N distance is givenas 1-38, compared with 1.47 A. indicated by bond additivity.The commonly written ring structure for diazomethane is rejectedfrom an examination of the electron-diffraction pattern given bythe vapour ; l4 the carbon-nitrogen and ni trogen-nitrogen distancesof 1.34 and 1.13 A.suggest resonance between the structuresH2C=kN and H26-kN. As might be expected, azomethaneis a conventional azo-compo~nd,~* CH,*N=N*CH,, the methylgroups being in the trans-position ; this formulation is compatiblewith the small dipole moment of pp'-dibromoazobenzene. Thecis- and trans-forms of other substances, e . g . , A2-butenes andpy-epoxybutanes,6° have been distinguished by means of electron-diffraction measurements.The carbon-oxygen and carboil-carbon distances in carbonsuboxide 149 64 have been given as 1-18-1-20 A, and 1.27-1.30 A.respectively, whereas the normal formula 0:C:C:C:O would requirethe double-bond values of 1-28 and 1-38 A.This result is interpreted7 1 (Miss) I. E. Knaggs, PTOC. Roy. SOC., 1935, A , 150, 576$2 GENERAL AND YHYSICAL CHEMISTItY.as implying resonance between the normal state and two excitedstructures kC-C=C-6 and O-C33-C=bJ so that all thebond distances would approach the values for trebly-bound atoms.Early work 72 on cyanogen and dincetylene indicated a non-linearstructure for these molecules, but later study62 has shown thisconclusion to be incorrect, a result in harmony with ordinarystereochemical considerations. The diffraction pattern forcyanogen agrees with a carbon-nitrogen distance of 1.16 A., thesame as the accepted additive value for the CEN bond, but thecarbon-carbon distance is only 1.43 A., which is somewhat closerto that for C=C than for cl-C.This suggests that the normalstate of cyanogen, N33--CE-N, which is the most important, isin resonance with other states, e.g., %=C=C=N and &=C=C=N,containing doubly-bound carbon atoms. It is of interest to recordhere that the terminal carbon-nitrogen distances in methyl cyanideand isocyanide have been found to be almost identical 63 (1.16 A.),thus providing strong evidence for the view that the form R*N=Cis an important contributor to the structure of isocyanides. Thestructure of diacetylene is believed to be analogous to that ofcyanogen: the carbon-carbon distances at the two ends of themolecule are 1.21A., as expected for the CEC bond.62 The dis-tance between the central carbon atoms is, as with cyanogen,1-43A., a result implying resonance, to some extent, of thenormal structure H*CEEC-C33H with the excited statesH&=C=C=C*H and H&C=C&H.Electron-diff raction results are incapable of distinguishing 73between the structures of NNO and NON for nitrous oxide, becauseof the small difference in the scattering powers of oxygen andnitrogen atoms, but the first of these formulae is generally favouredas being in harmony with the chemical properties, spectrum, anddipole moment.The extreme nitrogen-oxygen distance is found 73to be 2.38 5 0.06 A., which is in fair agreement with the sum ofthe bond distances for NEN, i.e., 1.10 A., and N=O, i.e., 1.22 A.,and also corresponds with the known moment of inertia of themolecule. The interpretation 709 74 of this result is that in nitrousoxide there is resonance between N=N=O and FTFl-0.Thethird possible state N-NGO is definitely excluded since thiswould reduce the shorter nitrogen-oxygen distance to 1.07 A., ar,dthe extreme distance would be 0.21 A. less than actually observed.f _--- + +7% R. Wierl, Zoc. cit., ref. (59).73 L. R. Maxwell et aZ., Eoc. cit., ref. (17).74 L. Pauling, Proc. Nat. Acad. Sci., 1932, 18, 498GLASSTONE : ELECTRON DIZ'FRACTION. 83The electron-diffraction patterns of nitrogen dioxide, tetroxide, andpentoxide have also been examined, but the results are notsufficiently precise to permit of an unequivocal interpretation : 73it is certain, however, that the linear model for nitrogen dioxide isnot correct, the nitrogen valency angle being between 90" and 120".The evidence for the planar configuration of benzene is so over-whelming that there is little need for further confirmation : it issatisfactory to note, however, that the scattering of electrons bybenzene derivatives can only be accounted for on this ba~is.l0*18*~4~4*The compound B,N,H,, known as boron amide, gives an electron-diffraction pattern similar to that of benzene, and the molecule isevidently a flat, regular hexagon with alternate boron and nitrogenatoms round the ring.75 The boron-nitrogen distance is uniformly1.47- & 0.07 A,, which is much smaller than that required for thesingly-linked B-N bond, vix., 1-59A., but reasonably close to theB=N value, 1.43A.; it is probable that in boron amide, as inbenzene, there is resonance between two alternative structures ofthe Kekul6 type, so that all the boron-nitrogen bonds are effectivelydouble.Mention may be made of the fact that X-ray diffractionmeasurements of crystalline cyanuric triazide 54 indicate that inthe cyanuric ring alternate carbon-nitrogen distances are 1.38and 1.31 A., corresponding approximately to the C-N and C=Nbond values, 1.47 and 1.32 A., respectively ; in spite of the apparentsimilarity to benzene and to boron amide, there is in this caseevidently no resonance, the single and double bonds occupyingfixed positions. Electron-diffraction measurements have beenused to determine the structure of pentaborane, B,H9 7 6 ; itappears to consist of a square four-membered ring, made up ofthree BH, groups and a boron atom, the fifth boron group, as BH,,being attached to the latter, almost coplanar with the ring.The structure of nickel carbonyl, Ni(CO),, presents an interestingproblem which has now been solved by means of electron diffraction.The dipole moment of this compound is zero, so that it is not cyclic,as had been suggested, but the four CO groups must either be a t thecorners of a square, that is planar, or else arranged tetrahedrally.The diffraction pattern definitely favours the latter structure, 77in agreement with Pauling's views.The carbon-oxygen distanceis 1-15 A., which is close to the value in carbon monoxide and to thatexpected for the C Z O bond; hence the triply linked carbonylstructure probably predominates in nickel carbonyl, as it appearsto do in carbon monoxide.Paraldehyde has been shown to con-7 6 A. Stock and R. W i d , 2. anorg. Cltem., 1931, 203, 228.76 S. H. Bauer and L. Pauling, J . Arner. Chm. SOC., 1936, 68, 2406.7 7 L. 0. Brockway and P. C. Cross, J . Chem. Physics, 1935, 3, 82984 GENERAL AND PHYSICAL CHEMISTRY.sist of a staggered six-membered ring of alternate oxygen andcarbon atoms : the angles are all approximately tetrahedral.15~ 78Valency angles. Measurements with carbonyl chloride andbromide 65 are in harmony with an angle of 110" & 5" between thetwo carbon-halogen bonds in each case; the same result was foundfor the angle between the carbon-carbon and carbon-halogenbonds in acetyl chloride and bromide.65 The experimental valueis close enough to 109" to confirm the tetrahedral configuration ofthe carbon atom concerned; the value of 125" & 10" found for theangle between the C-0 and the other bonds also provides supportfor this The angles between the C-C1 bonds inmethylene chloride and in chloroform were at one time believed tobe markedly in excess of the tetrahedral value :lo* 79 more recentwork 55 has shown these results to be in error, and it now appearsthat the angles are 111" & 2".The oxygen bond angle in chlorine monoxide 55 is 111" & 2", andin oxygen fluoride 55 it is somewhat less, 105" & 5" or 100 & 3" ;in dimethyl ether 55t the oxygen angle is 111" & 4", allowing forfree rotation of both methyl groups about the C-0 bonds, and aclosely similar result has been obtained with a-methylhydroxyl-amine.3* These results might a t first sight be taken as supporting thetetrahedral value as the natural oxygen valency angle, but this con-clusion may not be justified.The distance between the chlorineatoms in chlorine monoxide, 2.82 A., is appreciably less than the nor-mal distance of closest approach of two non-bonded chlorine atoms,Blvir,., 3.7 A. ; similarly in dimethyl ether the carbon atoms areonly 2-39A. apart, although the minimum distance of approach ofnon-bonded atoms s2 is normally 3.4A. It is evident that in boththese compounds there must be considerable repulsion between thechlorine atoms and the methyl groups, respectively, so that theobserved valency angles may well be greater than the "natural"value.It may be noted that the approach of the methyl groups indimethyl ether is not sufficient to interfere with free rotation, evenafter allowing an envelope 0.5 A. thick 83 round each hydrogenatom. 5", andthe same factor of repulsion of the groups attached to the oxygenatom arises here as with the compounds just considered. TheThe oxygen angle in dioxan is stated t o be 110"7 8 D. C. Carpenter and L. 0. Brockway, Zoc. cit., ref. (57).79 L. Bewilogua, PhysikaZ. Z., 1931, 32, 865.80 The value given by L. Br6, Anal. Pis. Quirn., 1932, 30, 486, is probably81 R. (2. Dickinson aiid C. Billiukc, J. Ainer. Chern. Xoc., 1928, 50, 764;82 S. B. Hendrieks, ibid., 1931, 7, 430.a3 N.V. Sidgwick, Ann. Reports, 1932, 29, 70.incorrect.M. L. Huggins, Chern. Reviews, 1932, 10, 447GLASSTONE : ELECTRON DIFFRACTION. 85observations with dioxan show that in the vapour state, a t least,the Z, or trans-, form predominates; this configuration agreeswith the zero dipole moment of the liquid. In pp'-di-iododiphenylether the oxygen valency angle,l6 according to elect,ron-diffractionresults, is 118" j, 3"; as previously indicated,g4 a larger anglethan in aliphatic ethers is not unreasonable. The ordinary methodfor interpreting electron-diffraction data does not permit of adetermination of the configuration of sulphur dioxide with suffi-cient certainty to give the sulphur valency a11gle,~9 but by meansof the radial distribution method the distance between the twooxygen atoms, as well as between sulphur and oxygen, can beevaluated, a t least approximately.The results indicate an angleof 124" &- 15°728 in agreement with the value obtained from Ramanand infra-red spectra. This angle and the sulphur-oxygen distancesuggest that in sulphur dioxide there are a t least two resonatingstructures, vix., 6-6=0 and O=$-O. In sulphur vapour itself,containing complex molecules, the sulphur angle is about 100".85Apart from the uncertain interpretation of the observations onmethyl azide (p. 81) and on azomethane, which suggest a valuegreater than the tetrahedral, there is no definite quantitative evidencefrom electron scattering concerning the valency angle of tervalentnitrogen J in PCl,, PF,, and AsCl,, however, the angles are 100" & 2",99" 5 4" and 101" j, 4", respectively.22 According to calculationsby wave mechanics,*6 the bond angles in nitrogen and its congenersin the tervalent state should lie between 90" and 109" 28', theformer value being approached as the atomic weight increases ; theresults quoted above are in general agreement with this expectation,since there is reason to believe that the nitrogen angle is close tothe tetrahedral value.*' I n nitroniethane the valency angle hasbeen found to be 127" & 3" ; 34 this is in harmony with the structure-Nq0 as one of the resonating forms of the nibro-group, the + Onitrogen, in the quadrivalent state, being tetrahedral.S. G.8* Ann.Reports, 1935, 32, 132.8 5 L. R. Maxwell, V. M. Mosley, and S. B. Hondricks, PhysicaZ Rev., 1936,8 6 L. Pauling, J . Amcr. Chem. SOC., 1931, 53, 1367.87 See, e.g., R. €3. Barnes, W. S. Beiiedict, and C. M. Lewis, Physiccd Rev.,50, 41.1934, 45, 34786 GENERAL AND PHYSICAL CKELWSTR;Y.5. CHEMICAL KINETICS.Though numerous ideas in the subject of chemical kinetics havebeen profitably pursued again during the current year, we mustrestrict attention in the present report to the major developments inthe study of thermal reactions in homogeneous systems. The yearhas witnessed important advances in theory and an increased rateof accumulation of experimental material.The Quanta1 Theory of Chemical Change.lThe quantal theory of chemical change, which was briefly out-lined in last year’s report,2 has been in itself refined and elaboratedby thermodynamic 3,4 and statistical 5 ~ 6 methods, and has beenapplied with marked success to a number of diversified problems,including diabatic unimolecular transformations,! ternary atomiccollisionsYs calculation of the energy ol triatomic s y s t e m ~ , ~ ~ re-actions between hydrogen atoms and moleculcs,lo* reactionsbetween hydrogen and the halogens,ll the ortho-para conversionof hydrogen under the influence of cx-particles,l2 the radiochemicalsynthesis of hydrogen brornide,l3 reactions involving four atoms,14and the addition of atomic and molecular halogens to ethylene andits derivatives.15 That the theory is capable of accommodatingsuch diversity without distortion of its general features is in itselfsignificant.The object of the quantal theory of chemical change is anambitious one, namely, to predict the absolute magnitude of thevelocity of chemical reactions of all kinetic orders in homogeneousand heterogeneous systems.Though still in its infancy, it may besaid to have succeeded, at least as far as elementary chemicalchanges are concerned. Its present protases will doubtless be1 We adopt the words “ quantal ” and “ quantally,” following the sug-gestions of C. G. Darwin (Nature, 1936, 138, 908), instead of the cumbrous‘ ‘ quantum-mechanical,’ ’ etc.E. A. Moelyn-Hughes, Ann. Reports, 1935, 32, 89.M. G. Evans and M. Polanyi, l‘rams. Paraday SOC., 1936, 32, 1333.4 W.H. Rodebush, J. Chem. Physics, 1936, 4, 744.L. Farkas and E. Wigner, Trans. Faraday SOC., 1936, 32, 708.H. Eyring and numerous collaborators (vide infra).A. E. Stearn and H. Eyring, J . Chem. Physics, 1936,3, 778.J. Hirschfelder, H. Eyring, and N. Rosen, ibid., 1936, 4, 121.* 13. Eyring, H. Gershinowitz, and C. E. Sun, ibid., p. 786.l o J . Hirschfelder, 13. Eyring, and B. Topley, ibid,, p. 170.11 A. Wheeler, B. Topley, and H. Eyring, ibid., p. 178.l a H. Eyring, J. 0. Hirschfelder, and H. S. Taylor, ibid., p. 479.l4 W. Altar and H. Eyring, ibid., p. 661.l6 A. Sherman, 0. T. Quimby, and R. 0. Sutherland, ibid., p. 732,Idem, ibid., p. 570MOELWYN-HUGHES : CHEMICAL KINETICS. 87replaced by others less drastic, but there can be no doubt that itsfundamental conception constitutes a permanent acquisition tothe science of chemical dynamics.The theory treats the approachof reactant molecules, their interaction during chemical change,and their separation thereafter as (z continuous process, depicted bythe movement, in phase space, of the representative point for thesystem. Occurrence of chemical change coincides with the passageof tillis point over an energy barrier, the height of which corresponds,roughly, with the energy of activation. Experiment demandsthat the velocity of chemical change shall generally be expressibleas the product of two terms [equation (I)], of which the first, ifnot absolutely independent of temperature, is far less dependentupon it than is the second term :(1) k* = A .e - E A / f < y ’ . . . .The problem thus resolves itself into a determination of the twoquantities, A and EA, which, although not strictly separable, mayconveniently be treated as if they were. Ea must be evaluatedquantally, A either quantally or classically according to circum-stances. A is determined by the average velocity with which therepresentative point surmounts the col.The quanta1 theory of reaction velocity has been applied in detailto reactions between two atoms, reactions between atoms anddiatomic molecules, and to reactions between two diatomic mole-cules. In order t o illustrate the principles involved, we shallselect for discussion a reaction of intermediate complexity, namely,that occurring between an atom, a, and a diatomic molecule, bc :@ + @-@ _3 @****@****@ 4 @-@ + @f*Tab Tbc”f---3f---,Tab TbcThe method of determining the height, E,, of the pass was outlinedin last year’s report.2 It is due to H.Eyring and M. Polanyi,16whose treatment we have now to reconsider, paying attention tosome of its finer points. For generality, rectangular co-ordinatesmust be replaced by co-ordinates inclined at an angle +, such thatsin 4 = - (mamb/(ma + mb)(mb + mc)}* * . (2)The resulting model enables us to represent the potential energyof the triatornic system, pictorially at least, as a function of a specialspatial co-ordinate, which is usually termed the reaction path(see figure). Now the height (Zm) of the summit is the differencebetween the potential energies of the reactants (at the point x)and the activated complex (at the point y), both being, of course,16 5.physikal. Chew., 1031, B, 12, 27088 GENERAL AND PHYSICAL CHEMISTRY.static values. According to the quanta1 theory, both systemspossess residual energies, which, at; the absolute zero of temperature,are S&, and Z-ihv* respectively. I f , therefore, we choose to defineour energy of activation (E,) as the difference between the actualDecomposition co- ordinate.energies of reactant and activated systems a t T = 0, we have therelationOf the quantities in this equation, v, and E, are known experimentallyfrom spectroscopic and kinetic data respectively; Em and v* maybe calculated from the theory under discussion.Since activated complexes usually contain an odd number ofelectrons and are not molecules in the ordinary sense, the vibrationfrequencies which characterise their internal motions are notamenable to direct measurement, but must be obtained by indirectmeans.is a directapplication of the classical equations of motion to the movementof a point particle in the neighbourhood of the co1, where the forcefield is assumed to be expressible by a function of the formE, = Em - (C$hv0 - X-$hv*) . . . - (3)The method commonly adopted 16* 17* l 8 1 8* l 1 pI n this equation) 8 denotes the small difference produced in thepotential energy (v), in the interatomic separations (rab and Tbc)and in the deformation angle (a) for systems displaced very slightlyfrom the equilibrium system, for which = Em; Tab = r*ab;rbc = r*bc; The desired frequencies may be calculatedfrom a knowledge of the masses and of the force constants (f).An important distinction is afforded by this analysis between thebehaviour of normal triatomic molecules and activated triatomiccomplexes, since one of the f values for the latter is negative, with1 7 H.Pelzer and E. Wigner, ibid., 1932, B, 15,445.18 Cf. the treatment of stable triatomic systems, discussed by W. G. Penney0: = 0.alld G. B. B. If. Sutherland, Proc, Roy. SOC., 1936, A , 156, 654MOELWYN-HUGHES : CHEMICAL KINETICS. 89the result that one of the frequencies of transverse vibration (whichwe shall call v-) has an imaginary value. The frequency ofdeformation (va) and the frequency of the other transverse motion(vT) have real values for complexes as for normal molecules.I n order t o illustrate the principles involved, we shall considerthe specific example discussed in last year's Report,2 attempting,a t the same time, to show the relation of the new theory to the old,and of both to the facts.The Kinetics of the Reaction Br + H, --j BrH + H.-(1)Experimental facts.The results of M. Bodenstein and S. C. Lind l9yield the following values for the constants of equation (1) :-B = 1.20 x 10-lo C.C. per molecule-second; EA == 17,640 cals./g.-mol. Extending the temperature region, and employing a totallydifferent technique, F. Bach, K. F. Bonhoeffer, and E. A. Moelwyn-Hughes 2o found A = 1-17 x 10-lo and EA = 17,740, thus fullysubstantiating the earlier work.I n round figures, therefore, andfor the temperature region T = 576' 2 75'Abs., A has a value of1.2 x 1 V 0 and Ea of 17,700 in these units.According to the collision theoryin its simplest form, the rate of reaction is equated to the fractionof the total number of collisions for which the energy exceeds acritical value E, the theoretical expression for the velocity constantbeing k* = (ra + rbc)2(8X~T/EL)le-~'~~. It follows that Ea = E- $RT;hence the kinetic value of (ra + rbc) is 1.57 A. In this manner,M. Trautz 21 found values of the same reasonable order of magnitudefor the present reaction and for many others, thus establishing theclassical collision theory for gases. If we regard the energy of activ-ation as a critical value of the component of the relative kineticenergy referred to the line of centres,22 we may proceed one stagefurther along classical lines.The above theoretical expressionmust now be multiplied by the factor (1 + EIRT), so that, towithin less than 3%, E = EA + ART. Solving for (ra + rbc)now gives us the value 0-38 A., showing that the greater the imposedrestriction on the direction of approach, the sma'ller becomes thetarget area derived from kinetic measurements. Hence the classicalinterpretation is consistent, though inadequate.(3) Quanta1 interpretation. With a constant resonance factorof 0-14, we have seen that Em = 22,100 cals. For the sake ofsimplicity, we now assume a strictly linear structure for the threeatoms throughout the chemical change, i.e., we take fa of equation(2) Classical interpretation.l9 Z.physikal. Chem., 1906, 57, 168.a. Ibid., 1934, B, 27, 71.21 2. anorg. Chem., 1916, 96, 1.23 It. C, Tolman, " Statistical Mechanics," New York, 192790 GENERAL AND PHYSICAL CHEMISTRY.(4) as zero. We then find -&hv,. = 2,730 and - iihv- = 160; &hvbci s known t o be 6,180 cals./g.-mol. Henoto, by equation (3), Eo ==18,650 cals., which, though not directly comparable with E d , liesvery near to it. From the imaginary frequency v-, we may estimatethe value of E. Wigner’s factor,23 for quanta1 transits (“ tunnelling ”),which is [l - 4 ( $ h ~ - / k T ) ~ ] = 1.0052. The correction thusamounts in the present case to about 0-5%, and can be ignored.The application lo.l1 of H. Eyring’s general formula 24 to thepresent case gives results in agreement with previous treatments,l7~and proceeds as follows. The formula for the velocity constant isThe transmission coefficient ( K ) is the average value of the absolut’eprobability that the representative point, having reached the 001,shall pass over i t ; its, maximum value, according to classicaltheory, is 112. Leakage through the potential barrier may increaseK by an amount given approximately by the Wigner factor. c isa, symmetry term, which is integral for both reactant and activatedsystems. I n the following account, we shall include all these factorsin the term K*, which must be of the order of magnitude of unity.v* is the average velocity of transit over the barrier, and will begiven the classical value of dSk’P/rp*.The partition function,Pa, for the atom, a, is due entirely to translation, and is therefore(2.xmaET)3’2/h3. The corresponding function for the molecule ,bc, includes additional terms to account for rotation and qiiantisedvibrations ; Fbe is accordingly-___IThe nine degrees of freedom for the reactive complex, taken inorder, are three for translation of the complex as a whole, two forrotations, one for the symmetrical transverse vibration, two forthe degenerate deformation, and one for the relative translatorymotion of the component parts of the decomposing complex,referred to the ordinate of decomposition. These motions, con-sidered as separable, enable us to write23 Z.physiknl. Chem., 1932, B, 19, 303,z4 J . Chenz. Phyeica, 3935, 3, 107MOELWYN-HUGHES : CHEMICAL KINETICS. 91Substituting in equation (5), and combining the result with equation( 3 ) , we have the theoretical expression for the velocity constantp is hI2ET.relationEm, of the niountsin pass (No being the Avogadro number) :Comparison with equation (1) leads to the followingbetween the Arrhenius constant, Ea, and the height,Ea = Em - &RT - *iVohVbe coth pubc + $Nohv+ coth PV I- +Nohv,coth pu, . . (7)Introducing the numerical values quoted above, we obtain thefollowing theoretical results : Ed = 18,090 cals./g.-mol., andA = 1.11 x 1W0 C.C. per molecule-second. Both are in goodagreement with experiment.A.Wheeler, B. Topley, and H. Eyring l1 have made calculationson the same reaction, assuming the resonance factor to be 0.20,and making allowance for the deformation of the triatomic system.The theoretical value of A [equation (l)] so obtained is 1.06 x 10-lo,so that the quanta1 theory, like its classical predecessor, guaranteesa fairly reasonable value for the collision frequency. The reasonin both cases is to be traced to the high magnitude of interatomicrepulsive forccs a t low separations. On the other hand, it is nowfound that E,rA = 25,100 and that IN, = 1,309 cals./g.-mol. Sub-stituting into equation (7) , the calculated value of tho Arrheniusactivation energy, ELI, becomes 23,630. Thus the present methodof evaluating the energy of activation is sensitive to the proportionof the total potential energy which is ascribed to the Coulombicterms-which raises the following questions.Is the Londonprocedure for estimating the potential energy of triatomic con-figurations in itself a sufficiently good approximation ? Can we, asone of the authors asks, regard the existence of a dip round the col(shown by the dotted line wqx in the figure, p. 88) as a virtue or adefect in the Eyring-Polanyi theory? If the activated complexsiiffers marked bending, how far are we justified in constructingan energy surface in terms of oizly two spatial co-ordinates ? Whilethese and similar questions must await authoritative answers, themethod may confidently be applied as a self-consistent, semi-empirical procedure, justified a posteriori.Reactions in the Gaseous Phase.Increasing attention is being paid to simple processes, especiallythose involving Eree atoms, and to the elucidation of the detaile92 GENERAL AND PHYSICAL CHEMISTRY.simultaneous mechanisms which together are responsible for thenet observed velocity of the decomposition of polyatomic molecules.A.Parkas 25 has studied the exchange of hydrogen and deuteriumatoms between the corresponding molecules and ammonia. Therate-determining step is D $- NH, __z NH,D -t H, for whichEd = 11,000, and the absolute rate is about 35 times as slow asthat of the reaction D + H, --+ DH + 13. The exchange re-actions of water and of methane have similarly been investigatedby A.Farkas and H. W. Melville.26 W. Heller and M. P~lanyi,~'measuring the rate of reaction between sodium atoms and numerousinorganic halides, find an instructive parallelism between the velocityand the restoring force-constant as estimated from the Ramanfrequency of the halide molecule. En has a value of about 6,000for the reaction 28 0 + 0, -+ 20,. Atomic mechanisms are verycommon in photochemical reactions, as for example, in the chlorine-sensitised oxidation of chloromethane, where the step C1 + CH2C1,--+ HC1 + CHC1, has been detected.29The reaction D, + HC1--+ DH + DCl proceeds as a homogeneousbimolecular with En = 27,000. Equally simple examplesare afforded by the rate of formation31 and decomposition31aof deuterium iodide, D, + I, 2DI.The data for these reactionsare summarised in Table I.M. Bodenstein and W. Kraus have made a complete study ofthe reaction of nitric oxide with oxygen, chlorine, and brominemolecules.32 Essentially t,ermolecular mechanisms control thereactions between nitric oxide and hydrogen,33 and between oxygenatoms and molecules.28 I<. H. Geib's conclusion (1924) that mostof the reactions undergone by the hydroxyl radical are termolecularhas been confirmed by A. A. Frost and 0. Ol~lenberg.~~The chain theory has again been applied to EL number of reactions,including the oxidation of methane,35 ~entane,,~ a~etylene,~'25 J., 1936, 26.27 Trans. Paraday SOC., 1936, 32,633.28 A. Eucken and F. Patat, 2. physikal. Chern., 1936, B, 33, 459.29 W.Brenschede and H. J. Schumacher, ibid., 1936, A , 177, 245.30 P. Gross and H. Steiner, J . Chern. Physics, 1936, 4, 165.31 K. H. Geib and A. Lendle, 2. physikal. Ckern., 1936, B, 32, 463.31a J. C. L. Blagg and G. M. Murphy, J . Chern. Physics, 1936, 4, 631.32 2. physikal. Chem., 1936, A , 1'75, 294.33 C. N. Hinshelwood and J. W. Mitchell, J., 1936, 378.34 J . Chem. Physics, 1936, 4, 642.3 5 H. Sachsse, 2. physikal. Chem., 1936, B, 33, 229; W. A. Bona and J. B.Gardner, Proc. Roy. SOC., 1936, A , 154, 297; R. G. W. Norrish and S. G.Foord, ibid., 1936, A, 157, 503.2 G Proc. Roy. SOC., 1936, A , 157, 625.36 A. Aivazov and M. Neumrtnn, 2. physikal. Chem., 1936, By 33, 319.37 E. W. R. Steacie and R. 0. Macdonald, J . Chern. Physics, 1936, 4, 75MOELWYN-HUGHES : CHEMICAL KINETICS.93TABLE I.*EA for IZT*In E* for R'*In -theH 5 1. theH 5Reaction. reaction. k~ \ pD' Reaction. reaction. ku *pz'H + H2 5,500A 1,050 H + N20 13,800D 0'D + D,D + D2Br + D,Na +- HC1 6,100C 300 H2 + H2 + NO 45,00033 0Na + DCl D, + D2 + NO42,5OO3l 580 H + H + H OG 0 H2 + I2D2 + I 2D + N2OH + ND,D + PJ3,n + H2 4,850A 1,160 D + NH, 10,80026 1,230Br + H, 17,70020 1,440 H + PH, 14,400E 60043, lOOF 1,490 c1+ H2 ca. 6,000B 1,400 H, + C2H,c1+ D2 D2 + C2H4D + D + D40,000 31a 1,240 HI f HIDI + DI* After H. W. Melville, Science Progress, 1936, No. 123, p. 499.A. A. Farkas and L. Farkas, Proc. Roy. Xoc., 1935, A , 152, 124.B. G. K. Rollefson, J . Chem. Physics, 1934, 2, 144.C. C. E. H. Bawn and A. G.Evans, Trans. Paraday SOC., 1935, 31, 1932.D. H. W. Melville, J., 1934, 1243.E. H. W. Melville and I. L. Bolland, Proc. Roy. SOC., in press.F. R. A. Pease and A. Wheeler, J . Amer. Chem. SOC., 1936, 58, 1665.G. I. Amdur, ibid., 1935, 57, 856.benzeneF8 rneth~lamine,~~ and silane,4°g 41, 42 and the decompositionof alkali azides 43 and divinylPolymerisation processes formed the topic of a discussion organisedby the Paraday Society. The kinetic aspects of the general treat-ment have been discussed by A. Abkin and s. Medvedev ; C. E. H.Bawn, J. E. Carruthers, and R. G. W. Norrish; H. Dostal and H.Mark; K. Freudenberg; G. Gee; M. W. Melville and S. C. Gray;E. A. Moelwyn-Hughes; M. W. Perrin; E. K. Rideal; G. Salomonand W. F. K. Wynne-J~nes.~~ The earlier theory of polymerisationreactions has been generally developed, and modified 46 to allowfor the specific influence of promoters and inhibitors.The decompositions of azomethane?' ethylene oxideY4* ethyl-38 3%.M. Griffith and S. G. Hill, Trans. Ir'araduy Xoc., 1936, 32, 829.39 H. J. Emelhus and L. J. Jolly, J . , 1936, 1524,*O P. S. Schantarowitsch, Acta Physicochim., U.R.S.S., 1935, 2, 673.41 H. Gutschmidt and K. Clusius, 2. p h y s i b l . Chem., 1935, B, 30, 265.4 2 H. J. Emelbus and K. Stewart, J., 1935, 677.43 W. E. Garner and D. J. B. Marks, J . , 1936, 657.4 4 H. A. Taylor, J. Chem. Physics, 1936, 4, 116.45. Trans. Paraday SOC., 1936, 32, pp. 1-412.46 G. Gee and E. K. Rideal, ibid., p. 666; Proc. Roy. SOC., 1936, A, 153,4 7 D.V. Sickman and 0. K. Rice, J. Chem. Physics, 1936, 4, 236.4 8 C. J. M. Fletcher and G. K. Rollefson, J. Amer. Chem. SOC., 1936, 58,2129; R. V. Seddon and M. W. Travers, Proc. Roy. SOC., 1936, A, 156, 273;H. W. Thompson and M. Meissner, Trans. Paraday SOC., 1936, 32, 1451.11694 GENERAL AND PHYSICAL CHEMISTRY.amine 49 and diethyl ether have all been carefully rc-examinedunder wide ranges of conditions. I n connexion with the lastreaction, L. A. K. Staveley and C. N. Hinshelwood 51 have deter-mined the conditions under which nitric oxide may act either as acatalyst or as an inhibitor. The reaction B,O, -> F, + 0,proceeds by a simple unimolecular mechanism.52 The kineticsof the decomposition of benzylideneazine and o-azotoluene 53yield values of EA which are consistent with the greater stabilityof the azo-nitrogen bond, compared with the azine bond.Thehomogeneous unimolecular deconlposition of silane 53a is moreconsistent with the mechanism SiH,+ SiH, + H,, proposedby Kassel (1933), than with the mechanism SiH, ---+ SiH, + Hanticipated by analogy from nice and Dooley’s work (1934). Acommon energy of activation has been found for the homogeneousunimolecular decomposition of tert.-butyl and tert. +my1 ~hlorides.~~bTwo further examples may be added to the not very abundantinformation available j 4 3 on the direct experimental comparisonbetween the kinetics of reactions in the gas phase and in solution.The unimolecular racemisation of 2 : 2’-diamino-6 : 6’-dimethyl-diphenyl has roughly the same velocity and the same Ed valuein the homogeneous gas phase as in solution in diphenyl ether:Me Me <2H52 -+ cx3 NH, MeThe same observation applies to the bimolecular addition ofacraldehyde to cyclopentadiene in the gas phase 56 and in benzenesolution.Reactions in Solution.The greater difficulties in the way of interpreting the kineticsof reactions in solution are to some extent offset by the greater49 H.A. Taylor and J. G. Ditman, J . Clzem. Physics, 1936, 4, 212.60 E. W. R. Steacie, W. H. Thatcher, and S. Rosenberg, ibid., p. 220;5 1 Proc. Roy. SOC., 1936, A , 154, 335; J., 1936, 812.52 P. Frisch and H. J. Schumacher, 2. physikal. Chem., 1936, B, 34, 322.53 G. Williams and A. S. C. Lawrence, Proc.Roy. Xoc., 1936, A , 156, 444.5 3 ~ T. R. Hogness, T. L. Wilson, and W. C. Johnson, J . Amer. C‘lzem. Xoc.,53b D. Brearly and G. 13. Kistiakowsky, ibid., p. 43.54 E. A. Moelwyn-Iluglies, “Kinetics of Reactions in Solution,” Oxford, 1933.6 5 G. B. Kistiakowsky and W. R. Smith, J. Amer. Chem. SOC., 1936, 58,1042; cf. C. C. Li and R. Adams, ibid., 1935, 57, 1565; VV. H. Itodebush,J . Chem. Physics, 1936, 4, 744.56 CX. B. Kistiakowsky and T. R. Lachor, J . Amw. C‘hem. Soc., 1936,58, 123.57 A. Wassermann, J., 1936, 1027.C. J. M. Fletcher and G. K. Rollofson, Zoc. cit., ref. (48). .1936, 58, 108NOELWYN-HUGHES : CHEMICAL KINETICS. 96wealth of experimental material. Unless we adopt a quasi-thermo-dynamic approachy2> 3* 4p 58 we must be content with making step-wiseprogress, by examining, for example, reactions in groups, selectedso as to reveal the effect of a single variable factor.When dealingwith fairly complicated molecules, the homologous groups of organicchemistry are eminently suitable. On the other hand, a classific-ation of chemical reactions based on the nature of the interatomicforces concerned s9 offers certain advantages.I n some respects, the simplest known reactions in solution arethe bimolecular reactions between ions and polar molecules, mostof which have normal velocities.2* 54 Ogg and Polanyi’s method forevaluating their energies of activation was described in the lastreport.2 Further instances of great interest have been studiedby E. D. Hughes, F. Juliusberger, A.D. Scott;, B. Topley, and J.Weiss,60 by E. Bergrnann, M. Polanyi, and A. L. Szabo,61 by D. P.Evans,62 and by A. R. Olson and collaborator^,^^ who have attemptedan interpretation of the slight differences in P values for reactionsinvolving halide ions in terms of their entropieq of solution. J. W.Baker and W. S. Nathan have, independently, given a, statisticalexplanation of the relative reactivities of halide and nitrate ionsin terms of their shapes (spherical and planar, respectively), andof their absolute dimension^.^^ C. K. Ingold and W. S. Nathan,65in a study of the hydrolysis of esters, have chosen a series of re-actions in such a way as to eliminate the direct electrostatic inter-action between the hydroxyl ion and the carboxylic group, and toisolate the induced polar effects.For a series of p-substitutedderivatives of ethyl benzoate, the P factor remains constant, whilethe absolute velocity varies by a factor of about 5,000, which isreflected in a change of Ed values amounting to 5,500 calories.The results are in good agreement with Nathan and Watson’srule.66 The problem of hydrolysis has also been studied by W. B. S.Newling and C. N. Hin~helwood,~~ chiefly from the point of viewof discovering the comparative behaviour of esters towards acidand basic attack. They find that a 10,000-fold change in k is to6 8 E. A, Moelwyn-Hughes, Trans. E’uraday SOL, 1936, 32, 1723.69 E. A. Moelwyn-Hughes and A. Sherman, J., 1936, 101.60 Ibid., p. 1173.6 1 Trans. Paraday SOC., 1936, 32, 843.62 J., 1936, 785.63 A.R. Olson and F. A. Long, J . Amer. <!hem. SOC., 1936, 58, 383; M. J.64 J . , 19’36, 230.Young and A. R. Olson, ibid., p. 1157.c 5 Ibid., p. 222.Cf. C. N. Hinshalwood, Ann. Reports, 1933, 30, 43.6 7 J . , 1936, 135796 GENERAL AND PHYSICAL CHEMISTRY.be attributed almost entirely to a change in EA. It is noteworthythat (Ex+ - EOH-) in aqueous acetone seems to be about 1,000calories less than in .pure water.6s Another interesting series ofreactions which have been measured and discussed, by G. N.Burkhardt and collaborator^,^^ is the hydrogen-ion catalysis ofthe hydrolysis of alkyl hydrogen sulphates. An isolated exampleof an unusual kind is afforded by Yun-Pu Liu and Tien-Chi Wei'sstudy 70 of the rate of hydration of methylethylethylene underthe influence of acids. A theory of reactions between ions and polarmolecules has been advanceda7lContinued attention is being paid to the kinetics of reactionsbetween two polar molecules.A. W. Chapman and I!. A. Yidler 72conclude, from a, study of the effects of substituents on the Beck-mann transformation of picryl ethers in carbon tetrachloride solu-tion, that the change is an intramolecular conversion of a complexformed from the reactant and the catalyst. Cyclisation reactionshave been studied in great detail by G. Sal~rnorr,~~ who resolvesthe semi-empirical term, P, into two factors, one of which is quantit-atively related to the surface energy. This, in turn, is calculatedfrom Langmuir's formula for capillary forces, which differ accordingto the geometric configuration of the halogeno-amine.Furtherexamples of the Menschutkin reaction have also been examined byJ. W. Baker,'* by N. J. T. Pickles and C. N. Hinshel~ood,~~ and byA. Singh and D. H. Peacock,76 while the kindred change involvedin sulphonium-salt formation has been studied by N. H e l l ~ t r o m . ~ ~The theory of reactions between ions in solution has been furtherdeveloped,78 yielding the following relations for the factor P and€or the variation of E A with temperature and with ionic strength :(3LT - 1). X*X*E2L Z*X*&2 lnP=------+- kDr 2DkT(LT - 1)(1 - 3 K r )E * = E - A E L N Z Z E 2Dr6 8 Cf. Moelwyn-Hughes, op. cit., p. 253.O9 G . N. Burkhardt, W. G.N. Ford, and E. Singleton, J., 1936, 17; G. N,Burkhardt, A. G. Evans, and E. Warhurst, ibid., p. 25; G. N. Burkhardt,C. Horrex, and (Miss) D. I. Jenkins, ibid., p. 1649.70 J . Chinese Chern. SOC., 1936, 4, 297.71 E. A. Moelwyn-Hughes, Proc. Roy. Xoc., 1936, A , 157, 667.72 J., 1936, 448.7 3 Trans. Paraday SOC., 1936, 32, 153 ; Helv. Chirrb. Acta, 1936, 19, 743.74 J., 1936, 1448.7 5 Ibid., p. 1353.7 6 J . Physical Chern., 1936, 40, 669.7 7 Z. physikal. C'lbern., 1936, A , 177, 337.7 8 E. A. Moelwyn-Hughes, Proc. Roy. SOC., 1936, A , 155, 308MOELWYN-HUGHES : CIZENICAL KINETICS, 97Both equations are in substantial agreement with experiment,the former being capable of accounting for the extremely highvalues of P found when the charges of thereacting ions are unlike and like respectively.The principles and method of the technique for measuring rapidreactions have been described in detail by F.J. W. Roughton andG. A. iUillikan,79 and have been applied by G. A. Millikan todetermine the rates of combination and dissociation of musclehzmoglobin with oxygen and with carbon monoxide. H. vonHalban and H. Eisner have continued their investigation ofinorganic reactions by the same method.H. M. Dawson has extended his well-known work on individualcatalytic coefficients to include the influence of temperature onthe hydrolysis of aqueous solutions of monochloroacetate.82Different values of EA have been found for the three simultaneousmodes of decomposition of isopropyll bromide in alkaline solution,which, according to Ingold’s theory, are denoted by the symbolsSN2 (bimolecular substitution), E 2 (bimolecular elimination) andSK1 (unimolecular dissociation). 83 A composite mechanism seemsprobable also in the acidolysis of numerous phenolic ethers, whichhave been studied by R.P. Ghaswalls arid 3’. G. D ~ n n a n , ~ ~particularly in view of their discovery that the Arrhenius equationis not applicable to the pseudo-unimolecular constants obtained.Two modes of decomposition of the ether-hydrogen halide complexare thus postulated.M. Buboux and R. Farre 85 have supplied further confirmationof Bredig and Fraenkel’s standard work on the hydrogen-ioncatalysis of diazoacetic ester. C. A. Marlies and V. K. LaMer 86have added to our knowledge of the catalytic decomposition ofnitroamine.Catalyses by hydrosulphide ions 87 and in sulphuricacid solution 88 have also been the subject of investigation. Amongmore complicated systems must be noted the reaction betweenferric ions and the oxy-acids of nitrogen,sg and between bromineand ally1 alcohol.go E. F. Caldin and J. H. Wolfenden 91 have madeand low?* E. A. Moelwyn-Hughes, Proc. Roy. Soc., 1936, A , 155, 258.81 Helv. Chim. Acta, 1936, 19, 916.82 H. M. Dawson and E. R. Pycock, J., 1936,153.83 E. D. Hughes, C. K. Ingold, and U. G. Shapiro, J . , 1936, 225.s4 Ibid., p. 1341.s6 J . Amer. Chem. SOC., 1935, 57, 1812.s7 E. Friedmann, J . p r . Chem., 1936,146,179.8 8 H. C. S. Snethlage, Rec. trav. chim., 1936, 55, 712, 874.89 E.Schroer, Akademische Verlagsgesellschaft, Lcipzig, 1936.QO M. Schar and L. C. Riesch, J . Amer. Cheni. SOC., 1936, 58, 667.91 J . , 1936, 1239.Ibid., 1936, By 120, 366.8 s Helv. Chim. Acta, 1936, 19, 1177.ItEEP.-VOL. XXXIII. 913 UENERAL AND PEYSICAL CHEMISTRY.an interesting study of the cyclisation of a charged molecule.R. Livingston and E. A. Schoeldgz have confirmed the work ofLivingston and Bray (1923) on the reaction between bromine andhydrogen peroxide, and have demonstrated the absence of a chainmechanism.The Influence of Pressure on the Velocity of Reactions in Solution.The quasi-thermodynamic treatment of reaction velocity wasgiven first by 5. H. vaii’t NofK93 Within the restricted limitsimposed by the suppositions underlying the treatment, it can beshown that, just as the increase (AE.) in heat content betweenpassive and active molecules may be found from the temperaturevariation of E, so may the increase (AV) in volume betwecn passiveand active molecules be found from the pressure variation of k.The values of the term A V given in the table have been calculateddirectly by means of the equation dlnkldp = - AV/RT, fromReaction. Solvent.c.c./g.-mol.A v,Hydrolysis of methyl acetate, catalysed byReaction between acetic anhydride and ethylN-HC1 ................................................ Water - 9.0alcohol ................................................ Ethyl alcohol - 16.5Hydrolysis of sucrose, catalyscd by AT-HC1 ... Water + 2.79 9 9 9 9 , 9 ,7, 9 , Y , 9 ,Toluene - 12.5Hexane - 4.16the early data quoted by van’t Hoff , and from the recent and moreextensive data obtained by E.G. Williams, M. W. Perrin, and R. 0.Gibson .94Beactions imolving Deuterixm in Solution.T. M. . L ~ w r y ~ ~ proposed the name “prototropy” to describechemical changes which may be represented by the migration ofa proton. Hydrolytic reactions in general Come under this category,as do also catalyses by acids and bases. Hydrolyses are amongthe most studied and least undersbood oi chemical changes. Thediscovery of deuterium quickened general interest in the problem,and, although relatively little quantitative work has yet been carriedout on deuterolysis,96 it is quite clear that the new isotope is to be92 J .Amer. Chern. SOC., 1936, 58, 1244.93 ‘‘ Vorlesungen uber theoretische und physikalische Chemie,” Vol. 1,94 Proc. Roy. Soc., 1936, A, 154, 684.95 Chem. Reviewa, 1927, 4, 231.96 Yellowing K. F. Bonhoeffer (see below), wc shall adopt the termsprotolysis and cleuterolysis for roac tions ii lioroiii tho molocdes H,O andD,O, respectively, are participating.p. 236, Braunschweig, 1901; cf. refs. 2, 6, snd 68MOELWYN-HUGHES : CHSMICGL KINETICS. 99regarded more as a useful tool than as a golden key. We shalltherefore refer only to some of the established experimental facts.When aliphatic compounds are dissolved in heavy water, thereoccurs a ready exchange between the deiaterium atoms o€ the solventand hydrogen atoms of the solute.M. Harada and T. Titani 97have confirmed the findings of Bonhoeffer and Brown (1933) onthe exchange of deuterium atoms between D,O and certain hexoses.After establishment of equilibrium, the distribution coefficientof deuterium atoms between solute and solvent is 0 . 8 7 4 . 7 0 inthe case of acetone,98 0.88 for acetylacetone,9!3 and 0.78 for nitro-methane.l The hydroxyl ion is often found $0 induce, or at leastto accelerate, the exchange. Thus K. Wirtz arid K. F. Bonhoefferfind that the hydrogen atoms in the hydrogen molecule exchangewith the deuterium atoms of heavy water in tlze prcsence of alkaliat 100". They formulate the following mechanism, in conformitywith the Lowry-Bronsted definition of bases as proton-acceptors :!D-6z--+--@-;JX + D:OD -j DON: + H-D + OD-Were all the deuterium atoms replaced by protium atoms, thechange would be described as the alkaline hydrolysis of the hydrogenmolecule.Other solutes for which exchange bas been eitherattempted or effected are chloroform: the dihydroxybenzenes:and formaldehyde .The ionic product of D,O in the neighbourhood of %Go has beendetermined electrornetrically by W. I?. I!. Wynne- Jones,6 wlioseresults, which confirm the earlier value given by E. Abel, E. Rratu,and 0. Redlich at 21", are given in the following form :(H20) ; - loglo K = 14.00 - 0.0331 (to - 25) -+ 0-00017(t0 - 25)2I.----------'! -------- _----- I.- --------AH = 13,460 - 42.5 (to - 25)(D2O) ; - loglo K == 14-71 - 0.0354 (to - 25) + 0*00017 (to -- 26)'AH = 14,420 - 42.8 (to - 25)The quantity AHl - AH2 is thus 970 calories.Ka,o = [H+][OH-] = 1-00 x l W 4 ;At 2 5 O , we haveKn,,, = [D'-][OD-] == 1.95 xJ.0. Halford, L. C:.Anderson, J. R. Bates, and R. D. Swisher, J. Amer. Chew. SOC., 1935, 57,1663.97 33ukl. Chem. SOC. Japan, 1936, 11, 65.9 8 1%. Klar, 2. physiknl. Chein., 1934, By 26, 335;99 R. Klar, Zoc. cit., ref. (98).1 0. Reitz, 2. physikal. Chem., 1936, A , 176, 363.3 J. Horiuti and Y. Sakamoto, Bull. Chem. SOC. J a p n , 1936, 11, 627.4 F. K. Miinzberg, 2. physik02. Chem., 1936, B, 33, 39.6 K. Wirtz and K. F. Bonhoeffer, ibid., 32, 108.6 [I'raw. Faradccy SOC., 1936, 32, 1397.7 Z. physikul. Chem., 1936, A , 173, 363.!4 IbicE., 177, 1100 GENERAL AND PHYSICAL CEEMISTRY.10-15 (mols./l.)2. The equilibrium constant X = [EtOD][HOH]/[EtOH][HOD] has the value 1.11 a t 25", and the rate a t whichthe equilibrium is reached has also been determined.*The principal kinetic data on reactions in deuterium oxide referto the following changes.(1) Mutarotation of glucose, uncatalysed.E. Pacsu publishedthe first datum on the velocity of chemical change in pure heavywater. It referred to an 18% solution of glucose at 20°, and,although the corresponding velocity in ordinary water under theseconditions has not been measured, a sufficiently close estimatemay be obtained by interpolation from the classical work of Hudsonand Dale. The comparison yields a ratio kD,OlkHaO 0.328. I nmore dilute solutions of glucose in heavy water, a slightly lower valueof 0.317 was found by E.A. Moelwyn-Hughes, R. Klar, and K. F.Bonhoeffer lo to hold, within the limits of error, over a temperaturerange of 30". Hence, there is no difference in the two EA values.If , however, collisions between solute and solvent molecules deter-mine the rate, both EA values must be corrected for the temperaturecoefficient of the collision frequency, which has a different valuefor the two solvents. On the simplest basis, EDao - EHaO becomes750 calories. These figures refer, of course, to velocities of mutarot-ation in the two pure media. For solvents of intermediate com-position, it seems reasonable to ascribe catalytic efficiency to themolecule HOD also. To do so requires a knowledge of theequilibrium constant K = [HQD]2/[HOH][DBD], the values forwhich have been estimated by B.Topley and H. Eyring.11 I nthis way, W. H. Hammill and V. K. LaMer l2 find itHoD to have avalue intermediate between those for kHoH and kDOD, while the ratioof the latter is concluded to be 1/0.263 at 25'.(2) Hutarotation of glucose, catalysed by protons and deuterons.With hydrochloric acid as catalyst, the following values have beenobtained for the ratio of the catalytic coefficients at varioustemperatures : l3t ........................ 9-00' 14.80' 20.69' 25.19' 30.39" 35-24'k D s ~ + / k ~ 8 ~ + ......... 0.53 0.56 0.63 0.64 0.68 0.77(3) Inversion of sucrose, catalysed by acids. A ratio kD30+/kHao+greater than unity holds for this reaction, and for a number ofothers, discussed below. With sulphuric acid as the source ofW.J. C. Orr, Trans. Paraday SOC., 1936, 32, 1033.Q J . Amer. Chew&. SOC., 1934, 56, 745.10 2. physikal. Chem., 1934, A , 169, 113.l1 J. Chem. Physics, 1934, 2, 381.l3 E. A. Moelwyli-Hughes, 2. phy8ikaZ. Chem., 1934, By 26, 272.l a Ibid., p. 891MOELWYN-HUGHES CHEMT.CAL KINETICS. 101protons the ratio 1-66 was obtained l4 for kD,,+/E,,,+ at 40°, andan approximate value of 1.67 at 30.7". B. Gross, H. Suess, andH. Steiner,15 studying the same system, obtain a value nearer 2.The discrepancy may be due, as they note, to the difference inconcentration of catalyst employed in the two cases. The di-basicity of the acid introduces complications which may be avoidedby using HCl and DC1.With these catalysts,13 the followingfigures are found :t ........................... ... 18.71" 24.27" 30.02" 37-13'a = I C ~ ~ O f / k x ~ o f ......... 1.80 1.77 ' 1.75 1.55(4) Hydrolysie of esters, catalysed by acids. K. Schwarz l6 foundthat methyl and ethyl acetates were hydrolysed by acids about50% more rapidly in heavy than in ordinary water. J. C. Horneland J. A. V. Butler,17 using sulphuric acid as catalyst, have foundthe ratios for the rates of deuterolysis and protolysis of methylacetate to be a = 1.85 a t 15' and a = 1.68 a t 2 5 O , in striking agree-ment with the data, for the inversion of sucrose, and indicatingthat the term AE is mainly responsible for the difference in rates.(5) Decomposition of diazoacelic ester, catalysed by acids.Againthe heavy isotope has the faster velocity,18 a being about 3.( 6 ) Neutralisation of nitroethane. A ratio of 1.5 holds forkOD-JjkOH-- in the case of the reaction between the two ions andnitroethane, and a ratio of 10 for the relative rates of reaction ofthe common ion OD- with %-nitro- and with a-nitro-aa-dideutero-ethane. l9According to Pedersen (1932),the rate of substitution of bromine in nitromethane is governedby the rate of conversion from the keto- $0 the enol form. Bromineand chlorine are introduced at the same rate, which is independentof their concentration and is proportional to that of any basiccatalyst. The rate-determining step may thus be regarded as therate of transference of a proton from the substrate to the base.0.Reitz20 finds that, in water a t 25", nitromethane passes on itsfirst proton to the acetate ion 6.5 times as rapidly as its trideutero-analogue passes on its first deuteron to the same base. Smallervalues of the same ratio are found when the proton- or deuteron-acceptor is the water molecule or the monochloroacetate ion.14 E. A. Moelwyn-Hughes and K. F. Bonhoeffer, Naturwiss., 1934, 11, 174.1 5 Ibid., p. 662; Trans. Paraday SOC., 1936,'32, 883.16 Anzeiger Alcad. W&3. Wien, 1934, 26, 4.17 J., 1936, 1361.18 P. Gross, H. Stoiner, and F. Krauss, Trans. Faraday Xoc., 1936, 32,19 W, F. K. Wynne-Jones, J . Chem. Physics, 1934., 2, 381.20 Z . physikd. Chem., 1936, A , 176, 363.(7) Enolisation of nityomethane.877102 GENERAL AND PHYSICAL CHEMISTRY.(8) Hydrolysis of the monochloroacetate ion.The ratio kDZO/kHzOappears to be 1.2 in both ordinary and heavy waLer as media, butaccurate analysis of the complete reaction presents c~rtaindifficulties.21(9) Hydrolysis of acetal and of ethyl orthoformate, catalysed byacids. Hornel arid Butler l7 find, for the two reactions respectively,the ratios kD30+/kx30+ = 2.66 and 2.05, both being independentof the nature of the buffer.Interesting information is accruingon the rate of growth of moulds in culture media containing D,Q,bui; we must be content with merely citing the references.2zHypothetical energy differences which may be held responsiblefor the die'erence in rates are shown in the following table :(lo) BiochemimZ processes.Catalysed reaction.RZ' . In kH/kD (cals./g.-mol.).a t 15" ............... + 325Mutarotation of glucose ............... + 255at 35" ............... + 180j at 15" ...... - 360.................. - 340.................. - 270at 18" Hydrolysis of sucrose ( at 3,0...... - 280 Hydrolysis of methyl acetate at 250Neutralisation of nitroethane .................. - 240Hydrolysis of acetal ..............................Hydrolysis of ethyl orthoformate ............- 570- 430It may be noted that, if Ic were regarded as proportional t o theviscosity of the medium, the energy terms would be small positivevalues, increasing with temperature a t such a rate as to be com-parable with the energy terms found for reactions in the gaseousphase at high temperatures.The mechanism of proton transfer rea,ctions has been discussedtheoretically from very differciit standpoi:ita.23 I n all discussions,however, the importance of Bronsted's empirical relation betweencatalytic coefficient and dissociation constant is fully appreciated.The Frequency of Collisions in Liquid Systems.I n view of the forthcoming discussion which is being arranged b:ythe Fara,day Society on the kinetics of reaction in solution, it will21 0.Reitz, 2. physikal. Chem., 1936, A, 177, 85.22 A. Farkas, L. Farkas, and J. Yudkin, Proc. Roy. Soc., 1934, B, 115, 373;B. Cavanagh, J. Noriuti, and M. Polanyi, Nature, 1934, 133, 797; K. H.Geib and K. F. Bonhooffer, 2. physikal. Chem., 1936, A, 175, 459; 0.Reitz,ibid., p. 257; F. Salzer and K. F. Bonhoeffer, ibid., 176, 202,z3 J. Horiuti and M. Polanyi, Acta Physicochim. U.R.S.S., 1935, 2, 505;R. P. Bell, Proc. Roy. Soc., 1936, A, 154, 414; E. A. Moelwyn-Hughes, ActaPhysicochim. U.R.S.S., 1936, 4, 173; J. C. Hornel and J. A. V. Butler, Zoc.cit., ref. (17)ADAM : SURFACE CHEME3TRP AND COUOIDS. 103serve no useful purpose to eirter into any detail on this highlycomplicated problem. Mcntion must be niade, however, of thecontinued attention which has been paid to it during the prcscntyear,2* and to the desirability, well exemplified by the work ofW. A. of applying as many of the formuh as are extantto the new experimental results. E. A. M.-H.6. SURFACE CHEMISTICY AND C:OLLOID.S.The vast range of these two subjects has rendered it impossibleto touch on more than a fraction of the work being published;instead of attempting to cover mnch ground, two restricted fieldshave been selected for this year’s Report,, and an attempt made topresent a readable account of thc more important advances duringthe last few years in these fields.The reporter is only too wellaware that even in these fields much has been deliberately, andperhaps much more inadvertently, omibted.Great advances have been made during recent, years in our know-ledge of aqueous solutions of substances containing, a t the endof a long hydrocarbon chain, a water-soluble and electrolyticallydissociated group. Besides the soaps, this class of substance includesmany with strongly dissociated, non-hydrolysable end groups, givingions such as R-XO,’, R*O*SO,’, R-NMe,’. These substances havelately come into great prominence industridly on account of theirpowerlul wetting mnd detergent action, cornpounds with manydifferent end groups having been synthesised 2nd patented, a d not afew placed on the market.The whole class, inchding soaps, hasrecently been called by G. S. Ilartley the “paraffin-chain salts,”a name perhaps preferable to the alternative “ long-chain salts,yyas the latter would be applicable to numerous classes of highlypolymerised compounds containing long chains with oxygen ornitrogen atoms coderring considerable water-attracting power onthe chains. The peculiar properties of these substances, whichrender them so active as depressants of surface or interfacial tension,are due to their unsymmetrical structure, with the very stronglyhydrophilic group at one end of a great length of hydrophobicchain.24 B.I. Sve6niBov, Compt. rend. Acad. Sci. U.R.S.S., 1936, 3, 61; T. S.Wheeler, Proc. Indian Acad. Sci., 1936, 4, 291 ; K. S. G. DOSS, ibid., p. 23;E. Rabinowitch and W. C. Wood, Tmm. Paraday SOC., 1936, 32, 1381.25 J., 1936, 1014; “ Physical Aspects of Organic Choinistry,” JEoutledge,1935104 GENERAL AND PHYSICAL CHEMISTRY.F. Krafft’s early studies 1 showed that the soaps have such lowosmotic activity as to be rightly called colloids in aqueous solution.J. W. McRain’s recognibion 2 in 1913 t’hat their simultaneous highelectrical conductivity and low osmotic act>ivity require the presenceof large electrical charges on the “ micelles ” or colloidal particleswas the commencement of his well-known researches with manycollaborators 3 on soap solutions, which have established the ionicmicelle as perhaps the most characteristic feature of these solutions.In the same year A.Reychler4 independently concluded thatcetanesulphonic acid forms charged aggregates with the paraffinchains in the centre and the sulphonic groups outside, from consider-ations of the water-attracting power of the different parts of themolecules, and in 1921. N. K. Ada= assigned the same structureto the. ionic micelle from considerations of the forces which orientmolecules of this general constitution a t surfaces.In a series of papers,g-lon and one short monograph,ll G.S. Hartleyand others have established beyond doubt that the ionic micelle isformed from the paraan-chain ions, a t dilutions much greater thanthose formerly associated with the ionic micelle, and that its form-ation is fairly sudden, as the concentration increases, and is accom-panied by (a) a marked decrease (not an increase, as had previouslybeen supposed) in the t’otal equivalent conductivity l2 of the solution,( b ) an increase in the mobility of the parafin-chain ions, (c) anenormous increase in the solubility of the whole salt in water, andcertain other changes. A good deal Q€ light has also been shed onthe structure of the ionic micelles, on the way in which the smallions (called the “gegenions”) of opposite charge to the paraffin-Ber., 1894, 27, 1747; 1895, 28, 2566; 1896, 29, 1328, 1344.Cf.J., 1919,115,1279; 1922,121,2325; 1923,123,2417; J . Amer. Chern.SOC., 1920,42,426 ; 1928, 58,1636; 1933,55,545, 2250, 2762 ; 1935,57, 1905,1909, 1913, 1916; Proc. Roy. SOL, 1920, A, 97, 44; 1933, A , 139, 26.2 Trans. Paraday SOC., 1913, 9, 99.KOllOid-Z., 1913, 12, 283.5 Proc. Roy. SOC., 1921, A, 99, 348.J. Mdsch and G. S. Hartley, 2. physikal. Chern., 1934, A, 170, 321.7 33. C. Murray and G. S. Hartley, T’ram. Paraday SOC., 1935, 31, 183.J. L. Moillet, B. Collie, C. Eobinson, and G. S. Hartley, ibid., p. 120.G. S. Hartley, ibid., p. 31.lo G. S. Hartley, B. Collie, and C. S. Samis, ibid., 1936, 32, 795.10a G. 8. Hartley, J .Amer. Chern. Soc., 1935, 58, 2347.11 G. S. Hartley, “ Aqueous Solution of Paraffin Chain Salts,” Actua1iti.sScientifiques et Industrielles, Paris, 1936.12 The expression “ total equivalent conductivity ” is here used instead ofthe more usual “ equivalent conductivity,” t o distinguish it from tho “ equi-valent conductivity of the paraffin-chain ions,” zc term which Hartley hasused in place of “ mobility ” as it is more informative; the last two will beused interchangeably hereADAM : SURFACE CHEMISTRY AND COLLOIDS. 10 5chain ions adhere to the micelles, partially neutralising their charge,and on the solvent properties of the interior of the ionic micelles,whic;;h appear to be a,lrnost the same as those of liquid para’ffmsin bulk, and account, for tlie curious solvent properties of solution8of soaps.It has also been shown that there is no need to postulate‘‘ neutral micelles ” as well as “ ionic micelles ” to account fort,he properties of these solutions.The total equivalent conductivity of a paraffin-chain salt changeswith increasing concentration in the manner of curve I of the--figure. The curve given is for cetylpyridinium bromide ; similarcurves were first obtained with all the important details on the alkylsodium sulphates by A. Lottermoser and E”. Piischel; l3 the cetane-sulphonates, trimethylcetylammonium salts, and some otherparaffin-chain salts with 16 carbon atoms in the chain show closelysimilar curves.The main features are : below about N/1000, the curve (plottedagainst the square root of the concentration) is the ordinary linearone of a uni-univalent electrolyte ; beyond this concentration ( A ) ,the conductivity falls very sharply ; with increasing concentration,the fall becomes gradually less steep and finally ceases.At stilll3 KolZOid-Z., 1933, 63, 175206 GENERAL AND PHYSICAL CHEMISTRY.higher concentrations (from N/20 to N12 usually), the total equivalentconductivity increases more often than not ; in the partictilarcase shown, and in some others, however, there is almost no rise.This rise in the conductivity curves att higher concentrations isalways gradual, and is much smaller than the fall commencing at A .Salts with longer or shorter chains give similar curves, but theconcenhrations at which the various features, particularly the suddenfor a 12-carbon chain A occurs at about; N/100, instead of N/1000for a 16-carbon chain.The specific nature of the end groupsmakes minor differences only; the " critical concentration " A issome 30% lower for *O-SO,K than for -80,K; l5 it is intermediatefor *NMe,Br. Rise of temperature increases the critical concentra-tion somewhat.l3* l4 Bivalent positive gegenions (e.g., in thezinc alkyl sulphafes) give a decidedly lower critical concentrationthan univalent .I3 Addition of ordinary uni-univalent salts to thesolution lowers the critical concentration, but little quantitat'iveevidence is available yet on the amount of this lowering.With solutions of soaps, hydrolysis of the end groups complicatesmatters in very dilute solutions, so that the curve rises above thelinear one for uni-univalent salts at dilutions considerably belowthe critical.The most careful measurements show the presence ofthe discontinuity a t A , however.16G. S. Hartley brings ample evidence that the discontinuityat A is associated with t'he start of aggregation of the paraffin-chain ions into ionic micellcs. There are three main consequencesof this aggregation : (1) a diminished viscous resistance to flowof a given number of these ions through the water, by Stokes'slaw, as McBain pointed out in 1913 ; (2) a much increased " braking "effect of the Debye-Hiickel atmospheres of oppositely chargedgegenions, and (3) a considerable diminution of the total chargeon the aggregated ions through the adherence of gegenions suffi-ciently closely to travel with the niicelles, in the opposite directionto that which they would take if free.Under ordinary conditions,(2) and (3) predominate over (l), so the equivalent conductivityfalls when micelles are formed.If, however, the conductivity is measured at extremely high fieldstrengths, as in curve 11: (200 kV./cni.), the conductivity risesinstead of falling at A.6 M. Wien has shown that at these highfield strengths the effects of ionic atmospheres are very much reduced,14 0. R. Howell and €1. G. B. Robinson, Proc. Roy. Soc., 1936, A , 155, 386.z.fall at A , take plaoe are lower the longer the chain ; 11* l 3 ~ l4 e4.YG. 8. Hartley, op. cit., p. 36.P. K.Ekwall, Acta Acad. h o e n s i s (17lath. Phys.), 1927, 4, 40;physikal. Chem., 1932, A, 161, 195ADAM : SURFACE CHEMISTRY AND COLLOIDS. 107because the ions move so rapidly that the atmospheres have nottime to form pr0per1y.l~ This diminishes (2); and owing to thediminished concentration of gegenions near the micelle, the equili-brium between adherent and free gegenions is probably so alteredthat many of the adherent gegenions leave the micelle, so that effect(3) is also much diminished. Consequently the effect (l), the diminu-tion of resistance t o motion resulting from aggregation, now pre-dominates, and the conductivity rises a t the eoncentration wheremicelles begin to form. The later fall of the curve is due to themuch increased stability of the ionic atmospheres as the concen-tration increases, sothat theeffects (2) and (3) againpredominate, evenunder the maximum field strength attainable short of actual sparking.The total equivalent conductivity, including effects due to thegegenions equally with those due to the paraiiin-chain ions, is notthe best quantity to employ for detecting changes in aggregationof the latter.Curve 111 shows Olio mobility, or equivalent con-ductivity, of the paraffin-chain ions, obtained as usual from measure-ments of conductivity and transport number ; the latter weremeasured by an interesting new method, the “ balanced boundary ’’method.18 I n all cases yet examined lo* l1 the mobility of theparaffin-chain ions increases suddenly a t the critical concentration.At the same time, the mobility of the gegenions decreases even moremarkedly than the total equivalent conductivity, and soon becomesnegative.The change of sign of the mobility of the gegenions canonly mean that a large proportion of them adhere to the pamffin-chain micelles and travel with them in the opposite direction tothat which they would take if free.The effects due to the ionic atmospheres have been estimated,but only semi-q~antitatively,~- lo on account of hhe difficultieswhich the Debye-Huckel theory presents when applied to ions of thevery high valency of the micelles. The braking effect is certainlymuch greater than would be found with uni- or bi-valent ions.Whether or not these is any sharp distinction between the gegenionsin the atmospheres and those adhering sufficiently closely tomove with the micelles is not certain, so perhaps the effects (2)and (3) above are not sharply distinguishable; but that adherenceoccurs and that the effective charge on the micelles and theircurrent-carrying capacity are very much diminished is beyonddoubt, on account of the transport-number measurements.17 J.Malsch and M. Wien, Ann. Physilc, 1927, 83, 305; M. Wien, ibid.,p. 327; 1928, 85, 795; 1929, 1, 400; Physikal.Z., 1027, 28, 834; 1929, 30,196; cf. G. Joos, Physikal. Z., 1928, 29, 765; M. Blumentritt, Ann. Physik,1928, 85, 812.18 G. S. Hartley, B. Collie, and E. Drew, Trans. Ir’araday SOC., 1934, 30, 648108 GENERAL AND PHYSICAL CHEMISTRY.The number of paraffin-chain ions and gegenions which go tomake up an ionic micelle can only be provisionally estimated atpresent.The most probable size of the micelle, i.e., the numberof paraffin-chain ions, may be estimated from considerations of thedimensions of the single ions.l0u l1 A 46-carbon chain is about18 A. long; 3 A. being added for the end group, the length of thewhole ion is about 21 A. The attraction between the end groupsand water is so much greater than that between the latter and thechains that it is very unlikely the micelles will contain hydrophilicend groups in their interior ; the largest micelles of 16-carbon-chainions must be 42 A. in diameter, if a sphere; this implies about 50paraffin-chain ions. If the micelles are not spherical, but elongated,they may be longer than this when they have reached their maximumsize, and contain more paraffin-chain ions.G. S. Hartley has calcul-ated that the surface energy of the various parts of these ions ismore than sufficient to bring this number together against the re-pulsive electrostatic forces which arise from bringing together thecharged end groups on the surface of the micelles.The number of adherent gegenions could be found from themobilities, if the effects of the Debye-Hiickel atmospheres couldbe exactly calculated; an approximate estimate lo gives, for thefraction of the gegenions adhering, in the dilute solutions in whichthey are first formed, about 0.74; this gives as the net charge on amicelle of 50 paraffin-chain ions, about 13 units, no fewer than about37 gegenions being dragged along with the micelle.had observed some of the curious changesin transport number with increasing concentration, and concludedfrom these and other observations that there is present, in additionto the ionic micelle, neutral colloid.Their theory involved, origin-ally, the presence of a certain proportion of uncharged colloid andionic micelle car‘sying the full number of charges associated withthe number of single paraffin-chain ions in the micelle. It was,unfortunately, worked out without full consideration of the ionicatmospheres; and many diagrams oE the constitution of soapsolutions with the proportions of uncharged colloid and entirelyun-neutralised ionic micelle required by this theory have appeared.20G.S. Hartley lo* 21 has shown that these diagrams can be replacedby much simpler ones, in which there is no ‘‘ neutral colloid,” butthe ionic micelle is partially neutralised by the adherent gegenions,whose number varies somewhat with variation in concentration ofthe solutions. This appears far more probable than that two sharply10 Cf. particularly J. W. McBain and R. C. Bowdon, J., 1923, 123, 2417;20 Cf. “ International Critical Tables,” 1929, 5, 448. 21 O p . cit., p. 56.McBain and othersMcBain, J . Amer. Chem. SOC., 1928, 50, 1636ADAM : SURFACE CHEMISTRY AND COLLOIDS. 109distinguished types of colloidal micelle exist simultaneously, oneuncharged and the other bearing the full charge of all its paraffin-chain ions.The suddenness of the discontinuity a t the critical concentrationfor micelle formation indicates that the proportion of micellesincreases very rapidly as the concentration increases; this is evenmore striking if the " differential equivalent conductivity " dK/dc,or A + c .dh/dc, where K is the specific and A the equivalent con-ductivity, is plotted against concentration (curve V). Considerationof the mass-action equilibrium between the single ions and micellescontaining a large number of single ions shows that there is reasonto expect 7, 22 a very sudden change from infinitesimal micelleconcentration to a solution consisting almost entirely of micellts,if as many as 50 ions unite to form one micelle. If there were aninfinite number of single ions in the micelles, the change would beentirely abrupt, as with any other phase change.G. S. Hareleyconsiders that the discontinuity is not quite so abrupt as if nothingbut 50-ion micellcs were formed from the start, and suggests thata proportion of smaller micelles, containing perhaps about 10 ions,is formed at first. When the concentration has reached from twoto five times the critical, it is thought that practically the wholeof the salt is in the form of ionic micelles, with about 50 ions.Fairly sudden changes in other properties of the solution, besidesthose associated with the transport of electricity, would be expectedwhen micelle formation commences. Perhaps the most remarkableof these is in the solubility of the paraffin-chain salts, which changeswith temperature in a characteristic and very unusual manner.Below a certain temperature, which depends both on the lengthof the chains and on the nature of the end group, the solubilityincreases with temperature in a normal manner.Above thistemperature, the solubility increases extremely rapidly, so much sothat only 5" or 7" above a temperature at which the solubility is buta small fraction of 1%, the paraffin-chain salt may be almostindefinitely soluble, solutions of 50 yo and upwards being easilyobtainable. This is explained by the ionic micelle's being extremelysoluble, whereas the single ions are but slightly soluble; as thetemperature rises, the solution becomes gradually richer in singleions, until a critical concentration is reached a t which the equilibriumshifts quickly over to the side of ionic micelles, so that there is noimpediment; to very high solubilities.G. S. Hartley and R. C.Murray 7 show theoretically that the rate of increase of solubilitywith temperature should be rather less abrupt than the actualtransition between single ions and micelles.22 Op. cit., pp. 23 ff110 GBNERAL AND PHYSICAL CBXMISTRY.C. a. Bury has found appreciable changes in the density and thepartial specific volume of paraffin-chain salta as the critical con-centration is passed ; 23 this work includes observations on the octo-atecr and the laurates, Some tendency to micelle formation isfound even iii butyric acid solutions.24Another effect of ionic micelle formation is a displacing effeaton the equilibrium point of various acidimetric indicators.25 Ifparaffin-chain salts are gradually added to buffered solutions con-taining indicators, there is little colour change until the concentrationis sufficient for micelles to form, whereupon it may change by asmuch as corresponds to 1 or 2 units of pR.The sign of the chargeson the ionic niicelle and the indicator ions determines whether ornot the equilibrium is displaced; and G, S. Hartley has givenrules for the choice of indicators not subject to displacement fromthis cause, which leads to oonsiderable errors in pH determinationby colorimetric methods.The activity and osmotic coefficients of the solutions are verymuch lowered, naturally, by micelle formation.26 The aggregationreduces the osmotic activity of the paraffin-chain ion to practicallynil ; and that of the gegenions must also be lowered very considerablyby the Debye-Hiickel effeot and the adherence of gegonions tothe rni~lles.~' J.W. &IcBain and M. 14. Retz2* bave demon-strated the very great decrease in the activity of the hydrogen ionin solutions of various paraffin-chain sulphonic acids, its the con-centration rises above the critical; but it should be mentioned thathere the sharp discontinuity a t the critical concentration has beenmiwed. No one appears a8 yet to have obtained sufficientlyaccurate osmotic measurements in dilute solution to detect thediscontinuity due to incipient micelle formation, sxcept perhapswith potassium o ~ t o a t e .~ ~It remains to account for the changes in conductivity and mo-bility at ooncentrations sbove those at which the formation of theionicz micelle is complete, according to the theory given above.With the 16-carbon chains, the total equivalent conductivity mayrise a little above 8/20; this rise was, at one stage of McBain'stheories, attributed to ionic micelle formation in addition to alarge amount of neutral colloid. The mobility of the pmaffin-chainp3 D. G. Davies mid C. R. Bury, J., 1030,2263 ; C. R. Bury- and G. A. Parry,24 J. Grindley and C. R. Bwy, J., 1929, 679.25 G. S. Hartley, Tram. Paraclay Soc., 1934, 3Q, 444.e 6 Cf. McBain et al., ref. (3).27 G. S. Hartley, B. Collie, and C. S . Samis, ref.(lo), p. 812.2g J . Amer. Chem. SOC., 1935, 57, 1913.J., 1935, 626.J. W. McBain, M. E. Laing, and A. F. Tifley, J . , 1919, 115, 1291ADAM : SIJRB’ACE CHICXIYTRY AND COI&OIDS. 111ions begins to decrease (see figure) a t about 0.005N, and simul-taneously that of the gegenions begins to increase, and these changesgo on steadily up to above N/10. Increase of concentration wouldbe expected, if no other changes occurred in the solution, to decreasethe mobility of all the charged particles, owing to the increasedbraking effects of the ionic atmospheres. The observed increase inmobility or equivalent conductivity of the gegenions indicates thatsome of the adherent gegenions corn(: off the micelles as they becomemore crowded in the solution.Albhough conditions in such con-centrated solutions are so complex that exact calculation seemsimpossible, some effect of this kind seems very probable. AtX / l O , the micelles occupy some 3% of the total volume, so that closeapproach must occur frequently; and when this takes place, thecharges on the surface of one micelle will tend to pull off the gegenionsadhering to the other.Soap solutions have, in addition to their emulsifying power,considerable solvent power for organic compounds in soluble, or veryslightly soluble, in water. S. U. Piekering 30 and E. Lester Smith 31have called attention to this, which indeed can scarcely be overlookedby anyone conducting organic preparations in the course of whichany quantity of soap is formed.6. S. IPartley makes the mostinteresting suggestion32 that this solvent property is due to thcsolute’s going into the interior of the ionic micelles, which is almostprecisely sirnila’r to a liquid paraffin in nature. It has been shownthat the amount of azobenzene which will go into a solution of aparaffin-chain salt consisting mainly of micelles is proportionalto the amount of the salt present. As this substance, and manyothers which dissolve similarly in solutions containing ionic micelles,are very soluble in Liquid paraffins, but insoluble or very slightlysoluble in water, and also do not form solid solutions with para,ffins,it is concluded that the interior of the ionic rnicelles is a chaoticarrangement of hydrocarbon chaks possessing all the propertiesof a liquid.The very pronounced elastic properties of many paraffin-clnaiiisalt solutions are ascribed by H a r t l e ~ , ~ ~ following a suggestion ofA.S. C. to adhesion between micelles; as this adh3 monis by the exterior of the micelles, the nature of the end groups isof great importance. Adhesion such as this may perhaps havesomething to do with the explanation of the results of ultrafiltration30 J . , 1917, 111, 86.31 J . Physa’cal Chem., 1932, 36, 1401, 1672.s2 Op. cit., pp. 41 ff,34 Trans. If’arudcty Soc., 1935, 31, 189.33 Im., pp. 5s fn”112 GENERAL AND PHYSICAL CHEMISTRY.measurements of soap solutions carried out by J. W. McBain andothers .35Recent Work on Unimolecular Pilrns.The structure of the ‘‘ liquid-expanded ” type of unimolecularfilm of long-chain fatty substances on water has been explainedat last by I.L a n g r n ~ i r , ~ ~ who uses the very bold conception thatthe upper, hydrocarbon parts of the molecules adhering to the waterby their lower, soluble, end groups form a liquid layer with sufficientof the properties of a phase in bulk to have both an upper and a lowersurface tension; the upper surface is supposed to have the sametension as that of a paraffin in bulk; the lower is similar to aninterface between a paraffin oil and water, containing a few fatty-acid molecules in addition to the paraffin. Such films form, accord-ing to Langmuir, the limiting case of an oil caused to spread on waterthrough the presence of water-attracting groups in the water-oilinterface.These films had proved exceedingly difficult of inter-pretation; the work of N. K. Adam and G. J e s ~ o p , ~ ~ in particular,having shown that they have an area and a compressibility inter-mediate between that of the condensed films, in which the moleculesstand nearly upright and are closely packed, and that of moleculeslying flat. It was obvious that there was some considerable degreeof tilt in the molecules; it was supposed that the thermal agitationproduced a state of chaotic agitation in the hydrocarbon chains,but there seemed no reason why the film should cohere, instead ofspreading to unlimited areas, like the “ gaseous ” type of film,or why the area should so often be about 2; times that of the mole-cules standing upright.Langmuir points out that the relationbetween the outward spreading force or ‘‘ surface pressure ” of theseliquid-expanded films is identical with the spreading force of a thinlayer of a hydrocarbon oil on water, when a certain number of fattyacid molecules are present in the interface between the oil and thewater. The theory appears to meet all the facts, and provides anexplanation for the failure to spread indefinitely in the cohesionof the “ liquid ” layer formed by the hydrocarbon portions of themolecules, a, liquid layer only some four-fifths of a molecule thick !If a layer of this thickness only can possess the properties of a liquid,there can be no objection to the interior of the ionic micelle possessingthem also, as suggested a t the end of the preceding section.35 J.W. McBain and W. J. Jenkins, J., 1922,121, 2325; J. W. McBain, Y.Kawakami, and H. P. Lucas, J. Amer. Chem. SOC., 1933, 55, 2762.313 J . Chem. Physics, 1933, 1, 756; cf. also 3rd Colloid Symposium Mono-graph, 1925, 71 ; Alexander, “ Colloid Chemistry,” 1926, vol. 1, 625.37 Proc. Roy. SOC., 1926, A, 112, 362; cf. also N. K. Adam, IfT. A. Berry,and H. A. Turner, ibid., 1928, 11’7, 532; N. K. Adam, ibicl., 1930, 128, 366ADAM. : SURE’ACX CHEMISTRY AND COLLOIDS. 113The transition between liquid-oxpanded and condensed filmspresents some curious features, resembling in some ways, but notexactly, a phase change in the surface; Langmuir considers that itindicates a condensation of the molecules into surface “ micelles ”of from five to thirteen single molecules-the numbers cannot beestimated with great accuracy, though they are probably not thesame for all different types of end group in the molecules-and thatthese micelles have a constant surface vapour pressure, but themselvesbehave as the units in a ‘‘ gaseous ’’ type of film.This part ofthe theory is more difficult to test experimentally than that dealingwith the expanded films alone, hut appears to fit the surface-pressure measurements.The transition region between the expanded and the condensedfilms appears, however, from measurements of the surface potentialtaken at different parts of the surface, to consist often of at leasttwo types of film in patches large enough to give a fluctuatingpotential as the exploring air electrode moves over the surface.It will be remembered that the surface potential, or the changein contact potential between the water and the air caused by thepresence of a unimolecular film a t the surface, is measured with ametallic wire just above the water, the end of the wire being coatedwith a little radioactive material 60 render the air condu~ting.~~A film consisting of patches appears inhomogeneous to a movingair electrode.J. H. Schulman and A. H. Hughes39 found smallfluctuations with films of myrisfic acid, and N. K. Adam and J. B.Harding 4O found fairly large oncs with margaronitrile, in the tran-sition region. Such patches must be of the order of millimetresacross, as the air electrode is usually about 1 mm.above the surface,and can scarcely be accounted for by micelles consisting of a fewmolecules only. The transition region appears to require furtherinvestigation, in order t o account for this patchy struckure. Apartfrom this obscure point, the structure of unimolecular surfacefilms of long-chain fatty substances on water now appears to befairly well understood.A beginning has been-made with the investigation, by F. A.Askew and 5. P. Danielli,41 by methods analogous to those used forinsoluble films at water-air surfaces, of films a t the interface betweenan aqueous and a non-aqueous, immiscible, liquid. Preliminary38 Cf. J. Guyot, Ann. Phgsique, 1924, 18, 506; A. Frumkin, 2. physikal.Ghem., 1925, 116, 486; J.H. Schulmari and E. K. Rideal, PYOC. Roy. SOC.,1931, A,‘130, 259; N. K. Adam and J. B. Harding, ibid., 1932, 138, 411;l’raw. Faraday Soc., 1933, 29, 837.Proc. Roy. Soc., 1932, A, 138, 443.40 Ibid., 1933, A , 143, 107. Ibid., 1936, A , 165, 696I14 GENERAL AND PHYSICAL CHEmSTRY.results at the interface between bromobenzene and water indicatethat, for long-chain aliphatic compounds, the lateral adhesionin the films, due to hydrocarbon chains, is much less when these areimmersed in a non-polar or slightly polar liquid than at the water-air interface. This is because the chains are moved about amongthe molecules of the liquid ; their surface energy does not have to besatisfied, as in the case of a water-rtir surface, by close adhesion tothe hydrocarbon chains of other molecules in the film, but is satisfiedby adhesion to the molecules of the non-aqueous liquid, which are inconstant translatory motion.As a general rule: mere presence at a liquid surface does not appearto alter the intrinsic reactivity or energy of activation of a molecule.In fhis respect liquid surfaces differ, of course, from solid.Never-theless, it has been shown that the rate of reaction of a substanceat a liquid surface may be influenced by the special conditions gre-vailing at; the surface, through change in the accessibility of the re-acting groups in the molecules at the surface to reagents in thesubstrate or underlying liquid. A striking instance of this wasfound by A. M. Hughes and E. K. Ridea142 in the oxidation ofacids containing a double bond in the middle of the hydrocarbonchain, such as oleic or petrsselinic acid, by permanganste in theunderlying water.The rate of oxidation is nearly ten times asgreat when the film is under low compression, so thaf the moleculesfrequently lie nearly flat, as when the film is highly compressed andthe double bonds in the molecules have less chance of reaching thewater. These films are of the expanded type, i.e., the moleculesare oscillating in a chaotic manner, so that probably all parts of thehydrocarbon chain come into contact with the water a t one time oranot'her ; but the chance of the upper and middle parts of the chainsreaching the water is much greater if the film is not too highlycompressed.Similar results have been obtained on the morehighly unsaturated addition compouiid of elaeostearin and maleicanhydride by G. Gee and E. K. Rideal; 43 A. H. Hughes44 findsthat snake venoms in the substrate hydrolyse the oleyl chains offlecithin in a unimolecular film on the surface more easily if thelecithin film is not highly compressed; Le., if the double bonds inthe oleyl chains can easily reach the water.In ell such work, as indeed in all work on surface films, there is arisk of changes in the surface being due, not to actual chemicalchanges in the substance originally spread in the film, but to thearrival, often accidental, of other substances at the surface from the42 Proc. Roy. soC.7 1933, A , 140, 233; cf. dso A. €I. Hughes, J b , 1933, 338,48 PTOC.Roy. SOC., 1935, A , 153, 116.4b Bwchpm. J., 1935, 29, 437ADAM : SURFACE CHEMISTRY AXD COLLOIDS. 116solution. In this connexion the veyy slow rates of adsorption ofdilute solutions of certain paraffin-chain salts may be of interest :N. K. Adam and H. L. S h ~ t e , ~ ~ also R. C. Brown 46 by a differentmethod, found that the final surface tension in extremely dilutesolutions may not be reached for days, A curious fact is that, if theconcentration is high enough for ionic micelles to be present, thefinal tension is reached almost a t once. Incidentally, R. C. Brownfinds that the (‘ ripple ” method for determining surface tensiongives values as low as the usual static methods, proving that whenripples pass over the surface of an aqueous solution there is no dis-placement of the solute from the surface.It has been shown byJ. H. Schulrnan and A. H. Hughes 47 that some soluble but stronglysurface-active substances, especially soaps and other paraffin-chain salts, will displace such substances as tripalmitin from aunimolecular film on the surface, by reason of their own tendencyto pass from the interior of the solution to its surface. Proteinfilms also may be displaced.Besides the long-chain fatty substances, the sterols,48 and manyallied complex ring structures,4g* 50* 51 form very stable unimolecularfilms, which have been investigated €or several years by N. M.Adam, F. A. Askew, J. F. Danielli, and others. Very frequentlythe principal or the only water-soluble group is found at the extremeend of the molecule, any aliphatic side chain, if present, being at theopposite end; and usually surface films of such substances have themolecules standing upright in the surface, closely packed and form-ing very coherent films.Exceptions do, however, occur, the mostnotable being with coprostenone, the ketone formed by oxidation ofthe sterol cholesterol. The change cuf the CN(0MI) group into COYwithout any change of position, results in the molecules becomingvery much tilted to the vertical, and the area increasing by nearly50%. Some other substances, particularly ketonic derivatives of46 Trans. Paraday SOC., 1936, 31, 204.46 Ibid., p. 206; Proc. Physical SOC., 1936, 48, 312.47 Biochem. J., 1935, 29, 1236, 1243.48 Sterols : N.K. Adam, Proc. Roy. Soo., 1928, A , 120, 473; N. K. Adamand 0. Rosenheim, ibid., 1929, A, 126, 25 j 1929, B, 105, 422; J. F. DanielliandN. K. Adam, Biochem. J., 1934,28, 1583; N. K. Adam, F. A. Askew, andJ. F. Danielli, ibid., 1935, 29, 1786.49 Oestrin derivatives: N. K. Adam, J. F. Danielli, G. A. D. Haslewood,and G. F. Marrian, ibid., 1932, 26, 1233; Danielli, Marrian, and Haslewood,ibid., 1933, 27, 311.60 Sapogenins: F. A. Askew, S. N. Farmer, and G. A. R. Kon, J., 1936,1399.s1 Resinols : F. A. Askew, ibid., p. 1595; W. D. Harkins, H. E. Ries, andE. F. Carun, J. Amer. Chem. Xoc., 1935, 57, 2224; 1936, 58, 1377; J .Chem. Physics, 1936, 4, 228116 GENERAL AND PHYSICAL CHEMISTRY.sterols, show the same effect in lesser degree.Irradiation of ergo-sterol produces the same effect. The cause remains a completemystery, and the fact, with the possibility of tilt of the moleculesoccurring even when there is only one water-soluble group at theextreme end of the molecule, renders it much more difficult to makedeductions as to the constitution of new members of this class ofcompound from surface-film measurements than had been hoped.The oestrin group has proved interesting, in so far as derivativesof the same parent substance, differing only in the number andposition of certain water-soluble groups, stand on one or the otherend of the ring system, in the surface films; and may also, withappropriate distribution of water-soluble groups, lie flat in the surface.These results are quite simply interpreted in the light of the coii-stitution of the molecules.49The surface-film measurements give a measurement of the sizeof organic molecules in certain packings and orientations on thewater surfaces, and have been used as an aid in determining theconstitution of various substances; the size and properties of thesurface films to be expected for a given constitution can often beforetold from measurements on nearly related compounds, or evenon models of the molecules.It was shown by B. C . J. G. Knight,52for instance, that batyl alcohol, known to be an ether of glycerolwith one molecule of octadecyl alcohol, has the long chain on oneof the terminal hydroxyls in the glycerol, not on the centre one,by a comparison of surface films of this substance with those ofa-monopalmitin ; the films are very closely similar, but quite differentfrom those to be expected if the long chain were attached to thecentral hydroxyl group.This conclusion, disputed a t first, wasafterwards confirmed by more ordinary 1nethods.~3 Surface-film measurements on the sterols are quite inconsistent with theolder formulae, but consistent with the new and now universallyadopted formulae of 0. Rosenheim and H. King.Cellulose derivatives ,54 proteins J55* 56 and highly polymerisedsynthetic substances containing numerous hydroxyl groups in the62 Biochem. J., 1930, 24, 257; cf. N. K. Adam, J., 1933, 164.53 W. H. Davies, I. M. Heilbron, and W. E. Jones, J., 1933, 165; 1934,1232.ti4 N.K. Adam, Trans. Fwraday Soc., 1933, 29, 90; N. K. Adam and J. El.Harding, ibid., p. 837.55 E. Gorter and others, Proc. A’. AEwd. Wetensch. Amsterdam, 1925, 28,371 ; 1926, 29, 1262 ; 1929, 32, 770; 1932,35, 838; 1933,36, 922 ; 1934, 3’7,20, 355, 788; J . Gen. Physiol., 1935, 18, 431 ; Biochem. J., 1935, 29, 38, 48.li6 A. H. Hughes and E. K. Rideal, Proc. Roy. Soc., 1932, A , 137,62; A. H.Hughes, Tram. Paraday SOC., 1933, 29, 214; J. H. Schulman and A. H.Hughes, Biochem. J., 1935, 29, 1236GLASSTONE : SOLVENT AND MEASUREMENT OF DIPOLE MOMENTS. 117chains 57 generally lie flat. in the surface, if they can be spread a t all.Complete spreading is decidedly difficult to obtain, and practicallyno spreading is obtained if the protein is first denatured.5* Whenspread, the protein films, and the cellulose films, may be compressedor expanded somewhat without collapsing ; in the case of the proteinfilms this is considered by A.H. Hughes and E. K. Rideal to be afolding of the chains without leaving the surface, similar to thosecaused by stretching protein fibres. N. I<. Adam 54 considers thatthe compressibility of cellulose derivatives is due to a tilt of theunit glucose rings slightly away from the surface on lateral com-pression.Finally, some interesting work on the transference of orientedfilms 01 Iong-chain molecules from water surfaces to solids must bementioned.59 By repeatedly dipping r2 clean glass, or polishedmetal, plate into water covered by unimolecular films, layers may bedeposited one by one.Generally, the first layer has the polargroups oriented towards the glass or metal, the next has themoutwards, and so on alternately. The structure is very similarto that of crystals of these paraffin-chain compounds. If the outerlayer has the hydrocarbon ends of the molecules outwards, thesurface is not easily wetted by water ; but if it has the water-attract-ing groups outwards, it is perfectly wetted. I n certain circum-stances successive layers can be deposited all with the hydrocarbonchains pointing outwards.Even one of these layers, as 1. Langmuir showed in 192OY6O hasa considerable lubricating effect on the solid.N. K. A.7. THE EFFECT OF THE SOLVENT IN THE MEASUREMENT OFDIPOLE MOMENTS.Although it was realised before 1932 that, when determined insolution, the dielectric polarisation of a compound possessing a result-an6 dipole moment varied somewhat with the nature of the solvent,even when the results were extrapolated to infinite dilution, it wasgenerally believed that the differences were not considerable and thatthe dipole moments calculated from data obtained in this manner5 7 W.D. Harkins, E. F. Carman, and H. E. Ries, J . Chern. Physics, 1935,3, 692.5 8 H. Neurath, J . Physical Chem., 193G, 40, 361.be K. B. Blodgett, J. ,4?ner. Chern. SOC., 1934, 56, 495; 1935, 57, 1007; I.Langmuir and V. J. Schaefer, ibid., 1936, 58, 254; G. L. Clark, R. R. Sterrett,and P. W. Leppb, ibid., 1935, 57, 330.60 Trans. Furadny SOC., 1020, 15, 68118 GENEBAL AND PHYSICAL CHEMISTRY.were in good agreement with those derived from measurements onthe vapour.The results of F. H. Miiller f on the polarisation ofchlorobenzene in a number of solvents called attention, however, tothe possibility that the solvent influence might be appreciable, andthat dipole moments estimated from measurements in dilute solutionmight require reconsideration. I n the past three years manystudies of the solvent influence on dielectric polarisation have beenmade, from both theoretical and experimental points of view, andMiiller’s results have been substantiated and extended. One of theobjects of this work has been to discover a, relationship between themoment determined in solution and the true value, it being assumedthat the latter is given by the vapour-temperature method based onthe well-known Mosotti-Clausius-Debye equation.The treatmentmay be divided very roughly into three sections: (a) empiricalmethods for correcting for the solvent influence, (b) theoretical con-sideration of factors not included in the Debye equation, (c) funda-mental modifications of this equation. It will be assumed, for thepresent, that the deviation from ideal behaviour is to be ascribedto electrical interaction between solvent and solute, and that nochemical action occurs.(a) Empirical Corrections for the Solvent Influence.--In order toaccount for the results with a number of substances, F. H. Miiller 2proposed the relationshipwhere P, and R represent the total polarisation and molecularrefractivity respectively of the solute and E is the dielectric constantof the solvent.The value of cQ P, in solution is obtained by extra-polation to infinite dilution. If the atom polarisation is negligible,then equation (1) can be written, to a first approximation, in theform- (2) = 1 - 0.038 (E - 1)’ . . . tR*h a p .This equation implies that the dipole moment measured in solution isless than the vapour value, the discrepancy increasing with increasingdielectric constant of the solvent. To obtain the true momentit is necessary to extrapolate the results in solution to the valuefor a medium of dielectric constant unity. The facts were explainedqualitatively by supposing that the intense electrical field of a dipolemolecule produced saturation of the dielectric in its vicinity, so that2 Ibid., 1933, 34, 659; Trans.Faraday Soc., 1934, 80, 729.PJ.,ysilcccl. Z., 1932, 88, 732GLASSTONE : SOLVENT AND MEASUREMENT OF DIPOLE MOMENTS. 119the polarisability of the non-polar solvent is decreased below itsvalue in the pure state. The decrease in polarisation of the solution,which is evident as an apparent decrease of moment of the solute, is,according t o Miillcr, due t o the solvent. By adapting the methodemployed for the interpretation of dielectric phenomena in electro-lytic solutions, an expression was deduced for the expected change inpolarisation of the solvent. It has been pointed however, thatthe almost exact additivity of refractivities in solution argues againstthe postulate of dielectric saturation.The empirical equation (1)is satisfactory for calculating pmp, in certain instances, but it failsin other^,^ and in any case it can only have limited applicability,since it is now evident that, although for the majority of compoundsthe apparent dipole moment decreases with increasing dielectricoonstant of the solvent, yet for some substances, e.g., alcohols, themoment is almost independent of the medium, whereas for others,e.g., chloroform, the moment in solution is greater than that of thevapour .6suggested that ,nPz in various media is a linearfunction of 1 /E, thuswhere A and B are constants. By altering the sign in front of theB/c term, equation (3) could be used to represent both positive andnegative solvent effects.This empirical relationship has the advan-tage of covering a wider range of dielectric constants than equation(1) and appears to be applicable to nitrobenzene, chlorobenzene, aridp-nitroaniline in a number of solvents, both polar and non-polar,It fails, however, in certain instances to give the correct value for thepolarisation when the results are extrapolated to E = 1. In itssimplest form the relationship proposed by S. Sugdeq8 that Pd 0 1s * izlinear function of the volume polarisation, may be writtenH. 0. Jenkinsa P , = A &B/E . . . . . . (3)P z = A & B ( & - 1 ) / ( & + 2 ) . . . . (4)so that it covers both types of solvent influence: as will be seenshortly, an equation of this type has a theoretical basis.It has beenfound to be of the correct form to represent the variation of polarisa-tion with dielectric constant of the medium for a number of dipolarsolutes, but it is doubtful if the significance originally attached to d ,H. Sack, Phyeikat. Z., 1927, 28, 199.C. P. Smyth et nl., J . Chem. Physics, 1935, 3, 55, 347, 557; E. G. CowloyK. Higesi, Bull. Inst. Phys. Chent. Re. Tokyo, 1934, 13, 1167.4 F. C. Frank, Proc. Roy. SOC., 1935, A, 152, 171 (172).and J. R. Partington, J., 1936, 1184; 1937, 130.7 Nature, 1934, 133, 106; J., 1934, 480.8 Natirre, 1934, 133, 415; 12‘mn.s. Paradcsy Soc., 1934, 30, 720120 GENERAL AND FZIYSICAL CHEMISTRY.as the sum of e p - and a small constant, and to B , as the orienta-tion polarisation (Po) of the solute, can be substantiated either theor-etically (see below) or from actual measurements.By Sugden'sequation the plot of P, against (E - 1)/(& 4- 2 ) for various solvents, orfor different concentrations in the same solvent, should be a straight,line, which on extrapolation to (E - l ) / ( ~ + 2) = 0, that is E = 1,should give e p . , but this procedure does not always yield satis-factory result^.^ F. Fairbrother lo has tested equation (4) by plot-ting 9, against (& - l ) / ( ~ + 2) for nitrobenzene in solution a t severaltemperatures, and found, as required, that straight lines convergingto a common point for ( E - l ) / ( ~ + 2) = 1 are obtained. Promthe slope of the lines, assumed equal to Po, the moment was foundto be 4-24 D, in excellent agreement with the vapour value.A com-prehensive test of equation (4), however, has led H. 0. Jenkins andL. E. Sutton to conclude that it is only approximately correct : thevalue of B is often very different from Po, and the agreement ob-served by Fairbrother for nitrobenzene is regarded as fortuitous.Another type of semi-empirical equation is that of R. J. W. LeF&vre,ll vix.,PJP; = I<(&' -1 2)/(&' + 2) . . . . (5)where Po and Pi represent the orientation polarisations for a givensolute in two media of dielectric constant E' and E' ' , respectively, andK is a constant approximately equal to unity for a number of sub-stances. If one of the solvents is regarded as a vacuum (E" = I),then it follows that- (6) p",ol. f p 6 p .- X3/(& + 2) . . .The use of this equation is restricted by the uncertainty in the valueof K , and also because it only applies to negative solvent effects,that is, when polarisation decreases with increasing dielectric con-stant. In spite of their limitations, and the fact that they cannot beusedfor accurate extrapolation to E = 1 , one or other of the equationsgiven above may be employed for interpolation purposes, for ex-ample, when it is required to compare polarisations of differentsubstances under analogous conditions, e .g. , in media of the samedielectric constant. Por this purpose a function of E giving a linearrelationship against P, is to be preferred : the volume polarisation(E - l)/(& + a), or its square, appears to be best for this purpose.l29 H.0. Jenkins and L. E. Sutton, J., 1935, 609; E. G. Cowley and J. R.10 J . , 1934, 1846.11 J., 1935, 773.12 D. P. Earp and S. Ghsstone, ibid., pp. 1709, 1720.Partington, low. cit., ref. ( 5 ) GLASSTONE : SOLVENT AND MEASUREMENT OF DIPOLE MOMENTS. 121(b) Theoreticnl Consideration of Factors not included in the DebyeEquntimz.--Soon alter the publication of &fiiller’s work on the polari-sation of chlorobenzene, an attempt) ~;lras made by J. Weigle l 3 toexplain the results theoretically. Two factors not included in theDebye treatment of dipolar molec~tles were considered, namely,(i) the polarisation of the medium by the dipolar molecules of solute,and (ii) the orienfation of optically anisotropic solvent moleculessurrounding the dipole.The second of these factors should producea moment Apt, acting in the same direction as the primary moment,given bywhere A is a numerical constant, p is the moment of the dipolarmolecule, assumed to be spherical, and a is its radius ; a’ and a” arethe polarisabilities along the two chief axes of the anisotropic solvcntmolecule, assumed to be an ellipsoid of revolution. Since a’ - a”is involved, Ap’ is evidently small, and for most solvents it is pro-bably of the order of 1 yo of the primary moment. The main influ-ence of the solvent is attributed to the polarisation of its moleculesby the dipoles. If the molecules are spherical, Weigle finds themoments induced by the solut’e in surrounding molecules shouldcancel one another, so t,hat the resultant effect is zero.For non-spherical solvent molecules, however, the resultant induced momentis generally not zero : its value and sign depend on the actual shapeof the molecules. Weigle considered only the case of a moleculeconsisting of a cone terminating at its point in a spherical surface,and found the resultant induced moment Ap, in the direction of theprimary moment, to be given by the following equation, in whichsmall terms have been ignored, viz.,Ap‘ = A ( p 3 / t 6 ) ( ~ ’ - E”)~//cT . . . . ( 7 )Ap = Bp(a‘ + 2 ~ ” ) . . . . ’ (8)where the magnitude and sign of B dt:pend on the shape of the solutemolecule and a’ and a” are the polarisabilities of the solvent.‘Thisis virtually the form in which Weigle left his deductions, but furtherconsiderationshows that it can be written in another way so as t obring out more explicitly the influence of the dielectric constant ofthe medium. If the difference in a‘ and a” is not great, equation (8)reduces to Ap = SBpcc, where a represents the mean polarisabilityof the solvent molecules, and for a non-polar substance this is givenN(& - l)/d(& + 2) = 4 / 3 X i V E . . . . (9)bYso thatAp = ~ C ( E - 1)/(& + 2)or ~sol./pvap. = 1 + C(E - I)/(& + 2 ) . .la Helv. Physlsica Acta, 1933, 6, 68122 UiENERAL AND PHYSICAL CHEMISTRY.where C is a constant, dependent on the shape of the solute molecule.The relationship between this and Sugden’s equation (4) is evident.K.Higasi has shown that Weigle’s theory predicts a negativesolvent effect for molecules elongated along the dipole axis, and apositive effect for molecules having their elongation perpendicularto this axis. The latter type of molecule should have negativeKerr constants, and it was in fact found thak with such substances,only a limited number of which are known, the dipole moment insolution is greater than in the vapour.The calculation of the moment induced in the solvent by the di-polar solute has been extended by P. C. Prank,l* who has given LLvery complete discussion of the solvent effect in the measurement ofdipole moment, and independently by K. Higasi.15 Frank makesuse of the relationship I = E(& - 1)/4~e for the induced moment perunit volume, where B is the field strength in the given volumeelement : the field strength at any point in the vicinity of the dipole,assumed t o have no finite length, can be readily calculated.I norder to obtain the resultant induced moment it is convenient todivide the space round the dipole into elementary shells of uniformfield, aiid each of these is further divided into elementary rings inwhich the uniform field is uniformly inclined t o the dipolar axis,The induced moment is calculated to beAp = LIE/,(€ - l ) / ~ . . . . . (11)or E-L.sol./~vap. == 1 -t- - l>/& ’ - - * (12)where A is a quantity determined by the shape of the molecule andthe position of the dipole within it : the value of A may be positiveor negative and is evalu:$ted by a process of graphical integration.Actual dipolar molecules may be divided roughly into four cate-gories according to their geomstry, with characteristic solventeffects.(i) Small molecules with no large group attached, e.g., HC1,H20, for which A is about + 0.1, so that the solvent effect should bepositive. (ii) Molecules with a radical on the dipole axis, e.g., CH,Cl,C6H5*N0,, C,H,Cl; nearly all the substances considered by F. H.Miiller fall into this category. The solvent effect is negative, andFrank’s calculations give results in approximate agreement withMuller’s rule (equation 2). (iii) Molecules with a single radical noton the dipole axis, e.g., CH,*OH; with such substances the effectdepends largely on the angle 0 representing the polar co-ordinate ofthe radical with respccb to the dipole axis, the position of the dipolebeing the origin.If 8 is less than 55”, Ap is negative and of appreci-14 LOC. cit., ref. (4), p. 171.l5 Sci. Papers Inst. Phys. Chm. Res. Tokyo, 1936, 28, 884GLASSTONE : SOLVENT AXD MEASUREMEST OF DIPOLE MOMENTS. 123able magnitude, but if 0 is greater than 55" then Ap tends to becomepositive although it, is oidy appreciable when 0 is about 90°. Foralcohols, the solvent effect might be expectcd to be small. (iv) Mole-cules with radicals off the dipole axis but possessing axial symmetry,e.g., CH,*O*CH,, (CHE,),N, (CM,),CO ; the induced moment in thesolvent is, as in case (iii), negative or positive according as 8 is lessor greater than 65". For dimethyl ether it should be small, for tri-methylamine it shonld be positive, whereas for acetone it should benegative but not large.The anticipations are in general agreementwith experimental observations. It is of interest to record that3'. H. Muller and P. Mortier,16 as a result of measurements with anumber of compounds, have divided molecules into groups corres-ponding closely to those proposed by Frank from theoretical con-siderations : the former authors also emphasise the importanceof the position of the dipole in the molecule, which is determined byFrank's angle 8. Since equation (12) may be writtenp.soI./pvap. = 1 + L4~vap. - A ~ v a p . / c * (13)it follows that the plot of peal. against 1 / E should be linear, and whenextrapolated to E = 1 the result should give the true moment, in thevapour state.As far as the available data are concerned theseanticipations are only realiscd very approximately, the extrapolatedvalue of pvap being higher than that 0bserved.l' Although it isapparcnt that the main solvent effect is to be attributed to inducedpolarisation in the solvent molecules, other factors, e.g., distortionof the field surrounding the dipole, various forms of interaction be-tween the molecules of solvent and the solute, and orientation of thesolvent molecules on account of their anisotropy, must be taken intoconsideration. It may be no-ted that since Po is proportional top2, equation (13) reduces to one similar to that ol Jenkins [equation(3) 1, if the term involving 1/z2 is neglected.The treatment of K.Higasi l5 is based on the relationship A p =aE, where cc is the polarisability of the solvent molecule, as given byequation (!I), and E is the field strength. The value of Ap is cal-culated asorwhich is identical in form with that obtainable from Weigle's treat-ment : this is to be expected, as Hipsi's method is a direct extensionof that of Weigle. The sign and value of A depend on the shape ofthe solute molecule, and a number of cases are considered. (I) Ifl6 Physikal. Z., 1935, 36, 371.1 7 See, however, E. G. Cowley and J. R. Partington, J., 1936, 1184 (1189).Ap = ~A(E - l ) / ( ~ -1- 2) . . . * (14)P80l./P.,,P. = 1 + -4. - + 2) - * * (15224 GENERAL AND PHYSICAL CHEMISTRY.the molecule is spherical, then A is zero and ps.l.= p,,,.. (11) Thedipolar molecule has the shape of an ellipsoid of rotation with adipole at its centre along its axis of symmetry : if a is the radius alongthe dipolar axis and c the value at right angles, then there are twopossibilities, according as (a) a > c (Fig. 1A) or ( h ) a < c (Fig. 1B).For case (a) , the value of A is given bywhere li: is equal to alc, the ratio of the radii, which is greater thanunity : the value of A,,, is a'lways negative, so that for moleculesof this type the solvent effect should always be negative. For case( 6 ) it is calculated thatwhere k is now less than unity, and AIIb is always positive, as also isthe solvent influence. (111) The solute molecule is an ellipsoid ofrotation but the dipole is not a t its centre (Fig.2) : several cases are00FIG. 1. FIG. 2.possible.A, and A,, where(a) I€ a, > c and a2 > c, then A,,,, is the sum of two termsand A, has an analogous value with a2 replacing a1 : both A, and A ,are always negative. ( b ) If a, > c and a2 < c, then AIIIb is thesum of A,, as above, and B,, wherGLASSTONE : SOLVENT AND MEASURICMENT OF DIPOLE MOMENTS. 125which is always positive. The actual solvent effect will therefore beeither negative or positive according as A, is greater or less than B,.(c) If a1 < c and a2 < c, thenAuIC=Bl+B2 . . . . a (20)where B, is as already given and B, is the corresponding value whenal replaces a2 : both terms are positive.< c and az > c,thenwhich may be negative or positive, according t o the relative values ofA, and Bl. Provided the dipole is not situated far from the centreof the molecule, the results of Higasi may be summarised, in general,by the statement(d) IfA1m=Bjl+Az . . . . * (21)> <psol. 7 pvap. according as a cwhere a and c are measured along the dipolar axis and perpendicularto it, respectively. The main difficulty in the application of theequations given above to determine pvap. from measurements insolution lies in the determination of the shape of the molecule and theposition oEthe dipole in it. This is done approximately from theknown atomic dimensions and from stereochemical considerations,the molecule being assumed to be equivalent in shape to an ellipsoidof rotation. Where the necessary data are available, Higasi hasshown the calculated values of Ap to be in good agreement withps,,l.- pvap., and the same conclusion has been reached by E. G.Cowley and J. R. ParfingtonY5 who have made measurements onbenzonitrile, propionitrile, bromobenzene, and ethyl bromide in sixnon-polar solvents. The theory of the electro-optical Kerr effect l8indicates that positive Kerr constants are, in general, to be expectedfor molecules in which the dipole lies in the direction of the longeraxis, so that they should show negative solvent effects : most com-pounds have positive Kerr constants, and hence the dipole momentsin solution are usually smaller than the vapour values.When theKerr constant is negative, e.g., for chloroform, the solvent effect ispositive : for such substances the dipole is perpendicular to the longeraxis of the molecule.6 Before proceeding, attention may be calledto a difference between the equation of Frank and those of Weigleand of Higasi : both the last two involve (E - I)/(& + 2), but thefirst gives Ap as a function of (E - l)/e. Since E for most non-polarsolvents is about 2, the general results are not very different, but thediscrepancy requires further investigation.An entirely different approach has been outlined by P. Debye,lSSee, e.g., H. A. Stuart, “ Molekciilstruktur,” 1934, p. 197 et seq,l@ Physilcal. Z., 1935, 36, 100; Chem. Reviews, 1936, 19, 171126 GENERAL AND PH'YSICAL CHEMISTRY.based on the theory of quasi-crystalline structure of liquids : theaxis of the dipolar molecule is supposed to rotate relatively slowly, sothat an additional term is to be added to that of thermal agitationhindering the orientation of dipoles in an external field.The expres-sion for the orientation polarisation per molecule should then bewrittenwhere F(y) is a fuxtion of y = E/k[i', E being regarded as the coup-ling energy between solvent and solute molecules which preventsrapid rotation. The treatment so far has been qualitative; itaccounts only for negative solvent effects but does not explain itsvariation with dielectric constant. It has been suggested that thetheory may prove more useful lor polar than for non-polar solvent^.^(c) Fundamental Modijcations of the Debye Eqmtion.-TJnless a,molecule is optically isotropic, i.e., equally polarisable in all direc-tions, neither the Mosotti-Clausius equation nor its extension byDebyc to polar molecules can be strictly applicable.(Sir) C. V.Raman and K. S. I(rishnan20 have pointed out that there is muchevidence to show that actual molecules are not isotropic ; they haveconsidered the general case of a pure liquid consisting of anisotropicmolecules and have derived the equationPo r= (47q491cT). F(y) . . * . . (22)E - 1 E - 4 r N p + g ) + E - l N ( y+-- &) * (23)& + 2 ' d -3 3 312 E + 2where Zx = a' + a" + a"', the polarisabilities along three axes, andY and 0 give the effects of anisotropy on the induced and the orient-ation polarisation, respectively, which can be determined, approxi-mately at least, from mea.surements ol light scattering and from thegeometry of the molecule.21 The equation has been extended toliquid mixtures,22 then becomingwhere the subscripts 1 and 2 stand for solvent and solute respectively.M. A.Govinda Rau 23 has considered the special case when one of thef O Proc. Roy. Soc., 1928, A , 117, 689.2 1 See (Sir) C . V. Raman and K. S. Krishnan, Phil. Mag., 1928, 5, 498;K. S. Krishnan and S. R. Rao, Indian J . Physics, 1929-30,4,39; M. Raman-adham, Proc. Indian Acad. Sci., 1934, 1, A , 281; H. 0. Jenkins and 8. H.Bauer, J . Amer. Chm. Soc., 1936, 58, 2435.22 D. S. Subbaramaiys, Proc. Indim Acad. ScL, 1934, 1, A , 355.23 [bid., 1935, 1, A , 498; see also H.0. Jenkins and S. li. Eauer, koc. tit.,ref. (21)GLASSTONE : SOLVENT AND MEASUREMENT OF DIPOLE MOMENTS.components, i.e., the solvent, is non-polar, that is pl = 0 and 0,so that127= 0,The molar polarisation of the non-polar solvent in tho gaseous statcis - n i ~ ~ l , and according to equation (23) this can bc put equal to 4x3 3-___ --___ -c 1 + 2 ' d ~ 1 + 2 NY1; further, {,'he molar polarisatioii of the &1- 1 nf4 x 2 \N (z? + -k), so that 31cT solute in thc vapour state is equal 60substitution in equation (25) givesthe fir& term on the right-hand side being .*I.. I n very dilutesolutions it may be assumed that the dielectric constant and thedensity vary in a linear manner with the concentration, thusE = E 1 ( 1 + &> and dl,2 = q a + bf2)It can then be showii 24 that in the limit as infinite dilution isapproached, when the first term in equation (26) becomes ,P2, the33& second term becomes A'\k:, -1 and iii the third E bocomes thevalue for the solvent, i.e., so that(El + a2In fhis equation the quantity 'r, applies to the pure solvent, butY2 and 0 are those applicable tQ the solute molecule in a state ofin$nite dilution in the solvent, and not those for the pure homogeneoussolute.Of the correction terms in -the square bracket of equation(27) the first two are generally small and negative, but the third,which is the most important, can be negative or positive accordingas the dipole moment of the solute molecule lies along the axis ofgreatest polarisability or not : that if;, according as the solute has apositive or negative Kerr constant, the sign of which is oppositc to24 G.Hedestrand, Z . phyeikal. Cyhena., 192!4 €3, 2, 428128 GENERAL AND PHYSICAL CHEMISTRY.that of 0.25 This result is, therefore, in qualitative agreement withexperiment and with Higasi’s treatment. By assuming the soluteto be represented by an ellipsoidal cavity of the same shape as ben-zene, M. A. Govinda Rau 23 was able to apply equation (27) tomeasurements 26 on nitrobenzene in various solvents, and therebyobtained a value of P, in good agreement with that observed for thevapour : for dioxan as solvent, however, there was an appreciabledifference. have tested theequation with measurements on benzonitrile, bromobenzene, andethyl bromide ; the calculated G P .values are of the correct order,and almost constant for data from different solvents, but they differsomewhat from the experimeatal vapour values. It is importantto note that for carbon disulphide as solvent, the molecules of whichare anisotropic, the discrepancies are considerable. The funda-mental diEculty in the exact application of equation (27) lies in theevaluation of the important quantity 0 for the solute : not only isthe basis of its calculation from optical and other data uncertain,but the result so obtained is for the pure solute, whereas, as emphas-ised above, it is the value at infinite dilution in the particular solventwhich is required.By using experimental Ppp- data 0 can becalculated, and the results so obtained are different from thoseevaluated for the pure solute ; 27 further, the 0 values vary appreci-ably from one solvent to anothcr.28 The fundamental arguments ofRaman and Krishnan, upon whose treatment Govinda Rau’sequation is based, have also been subjected to criticism.29(Mrs.) C. G. Le FBvre and R. J. W. Le Fb~re,~O following F. R.G o s s , ~ ~ have shown that the relationshipE. G. Cowley and J. R. Partington. (28)may be derived from the Raman and Krishnan equation for a pureliquid, and there is reason to suppose that a similar equation willapply if Pp is replaced by Pi’. determined from measurements25 M. A. Govinda Rau, Zoc. cit., ref. (23), p. 505; (Mrs.) C.G . Le FBvre26 M. A. Govinda Rau and B. N. Narayanaswamy, PTOC. Indian Acad.27 M. A. G. Rau, Zoc. cit., ref. (23), p. 507; F. C. Frank, Chem. and Ind.,2 8 R. J. W. Le FBvre and P. Russell, ibid., 1936, 491 (492); H. 0. Jenkins29 H. 0. Jenkins and 2. E. Sutton, J., 1935, 609 (614); H. Miiller, Physical3o J., 1935, 1747.81 J . , 1934, 696.and R. J. W. Le FBvre, J., 1035, 1747 (1748).Sci., 1935, 1, A, 489.1936, 55, 37; E. G. Cowley and J. R. Partington, J., 1937, 130.and S. H. Bauer, Zoc. cit., ref. (21).Rev., 1936, 50, 547; H. 0. Jenkins and S. H. Bauer, Zoc. cit., ref. (21)QLASSTONE : SOLVENT AND MEASUREMENT OF DIPOLE MOMENTS. 129in solution after extrapolation to infinite dilution. It must bepointed out, however, that the argument is not exact, since 0, p, andE in equation (28) for the pure liquid refer to the same substance;when the equation is applied to a solution, however, 0 and p refert o the solute and E to the solvent.By making use of the equationPrp* = 45;Np2/9kT, it is seen that the relationship of Le FBae andLe FBvre is identical with equation (27) with the first two terms in thesquare bracket omitted : it can only be regarded, therefore, asapproximate. If 0 is assumed to bt: equal to - 4xp2/3, then equa-tion (28) becomes identical with the empirical relationship, equation(6), with K equal to unity (p. 120). By making the same assumption,M. A. Govinda Rau 32 has shown that equation (27) may be reducedto the form of equation (4) with A and B having the significanceattributed to them by Sugden (see p.119). It has been emphasised,however, by F. R. Goss 31 that it is very unlikely that 0 should bcequal to - 4xp2/3 ; this only occurs when p is zero. Further, at thecritical point 0 vanishes, whereas p retains its normal value. Men-tion may be made of the fact that, even before Rau had applied theRaman-Krishnan equation to dilute solutions, F. R. G O S S ~ ~ hadused it to calculate vapour dipole moments from measurements insolution : the treatment is, however, not entirely justifiable, since thesame equation was assumed to apply to dilute solutions as well as topure liquids. It should be noted that Goss, Rau, and Le Fbvre haveall obtained relationships which can be written in the form ofSugden’s equation (4), and by utilising the fact that p is proportionalto no they all reduce to the same type as equations (10) and (15)of Weigle and of Higasi, respectively, provided small terms are neg-lected : the constant factor preceding (E - l)/(s + 2) is in each caserelated to the shape of the molecule.Apart from the modifications of the Mosotti-Clausius-Debyeequation described above, attention must be called to a, number oftheoretical investigations; some of these have not yet reached thestage of being of practical value, but they may have an importantinfluence on future developments.Amongst other factors, theDebye treatment neglects the force on a polar molecule due to thesurrounding molecules being polarised by the molecule considered.M. Kub0,34 E.A. G~ggenheim,~~ and L. Onsager 36 have independ-ently attempted to take into consideration what is called by Onsagerthe ‘‘ reaction field,” as distinct from the “ cavity field ” treated by32 LOC. cd., ref. (23), p. 508.38 LOC. cit., J., 1935, 502, 727; see also F. Fairbrother, J., 1934, 1846.34 S&. Papers Inst. Phye. Chem. Rea. Tokyo, 1935, 27, 295.85 Nature, 1936, 137, 459.36 J . Amer. Chent. SOC., 1936, 58, 1486.REP.-VOL. XXXIII. 130 GENERAL AND PHYSICAL CHEMISTRY.&bye, following Mosotti and Clausius. Kubo has applied hisargument to gases only, and finds. . (29) E - 1 &! 4 X 2xctp2vE+2' d= VN [a + &(I + mdlwhere v is the number of molecules per c.c., a is the polarisability,and p is the radius of the " sphere of action " of the molecules.In apreliminary report, Guggenheim gives the result of a treatmentbased on the use of a model for polar solutions similar to that em-ployed by Debye and Huckel for electrolytes : the solvent molecule isassumed to be spherical and the solvent is regarded as a continuousmedium. It is deduced that[ ( E - &J2 - (no" - n2)]/c0 = 4xp%,/3i%T . . (30)where E and n are the dielectric constant a'nd refractive index of thesolution, and c0 and no are the values for the solvent ; v, is the num-ber of solute molecules per C.C. of solution, and p is here defined asthe total electric moment between the plates of a, large parallelcondenser filled with the solvent containing one single molecule ofsolute with its polar axis normal to the plates.The values of pobtained from equation (30) are somewhat lower than those given bythe Debye formula, but the results are independent of concentration,so that the decrease of polarisation often observed with increasingconcentration cannot be due to association, as has been frequentlysuggested (see below). According to Guggenheim, the variationof p with solvent should be given byp(a0 + &i) = constant . . . * (31)where ( E ~ - 1)/4x is the polarisability per unit kolume of the solutcsphere. The treatment is preliminary and is only applicable tospherical molecules, for which the solvent correction should, accord-ing to the views described above, be zero. Onsager has given asomewhat fuller report of his deductions : he finds for a pure dipolarliquidE - 1 n 2 - I E ( n 2 + 2 ) 4 d p O 2E + 2 n2 + 2 - ( 2 ~ + n2)(& + 2) * 3Ll'where the symbols have their usual significance, and vo is the dipolemoment as vapour.For a dilute solution of a polar solute in anon-polar solvent the relationship deduced isP . (32) ----where E and n refer to the solution, and the subscripts 1 and 2 to thGLASSTONE : SOLVENT AND MEASUREMENT OF DXPOLE MONENTS. 131solvent and solute respectively. Further, the relationship betweenpsol. as measured and pvap. is given byAccording to this equation, the solvent effect for a spherical molecule-the deductions so far only apply to such molecules-should benegative. It may be pointed out that the treatments of Guggen-heim and of Onsager should lead to the same equations, and it is notyet evident why the discrepancy e ~ i s t s . 3 ~ J. G. K i r k w o ~ d ~ ~ hasinvestigated the polarisation of a non-polar dielectric in a homo-geneous field from the molecular point of view, and has shown thatthe Mosotti-Clausius equation can hold only if every molecule hasthe same induced moment throughout all phases of its thermalmotion. Statistical calculations show that the fluctuations fromthe mean value of this moment lead to deviations from ideal be-haviour, and it is possible to deduce the equation(E - 1)M/3d P[1 + (1 + y $- ~)Pd/lcf + . . . 1. . (36)wlicro P is the polarisation, y is approximately equal to P/4vm,v, being the volume of a single molecule, and (I is a correction foranisotropy. This may be compared with the ordinary Mosotti-Clausius equation written in the form(C - 1)M/3d PL1 + PdIM . . . 3 (36)The treatment has not so far been extended to polar molecules.Temperature and Concentration EfSeects.-?Xow that it is realised thepolarisation of a solute frequently depends on the dielectric constantof the medium, it is possible to account for the fact that the tempera-ture method, used for determining the dipole moment of a gas orvapour, has not been found applicable to solutions.39 Since thedielcctric constant of the solvent changes with temperature, an addi-tional factor is introduced, and it has been found that the productPOT, which should be constant if there were no solvent effect, oftenfalls off steadily with increasing ternperat~re.~~ Further, the markeddecrease in polarisation sometimes observed with increasing con-centration of a polar solute in a non-polar solvent, e.g. , nitrobenzenein benzene, and which had been attributed to association of the37 Private communication from Mr. E. A. Guggenheim.38 J. Chem. Physics, 1936, 4, 592.39 Cf. C. P. Smyth, ibid., 1933, 1, 247; C. P. Smyth and IS;. B. McAlpine,40 F. H. Miiller, Physilcal. Z., 1934, 35, 346; E. a. Cowley and J. R.ibid., 1935, 3, 347 ; H. 0. Jenkins, Trans. Paraday Soc., 1934, 30, 739.Partington, Zocc. cit., ref. ( 5 ) 132 GENERAL AND PHYSICAL CHEMISTRY.solute,4l is probably to be attributed almost entirely to an increasein dielectric constant. A. E. van Arkel and J. L. Snoek 42 have shownthat, apart from other considerations, the Debye equation can onlyapply to solutions if vsp2<kT, where v, is the number of dipolemolecules per C.C. ; for substances having high moments this occursonly in very dilute solution, and so it is proposed to apply an em-pirical correction to the Debye equation, thuswhere c is a constant. It can be shown43 that this equation isvirtually identical with equation (4) for the variation of polarisationwith the dielectric constant of the medium. It should be noted thatthe remarks made above concerning association do not apply to allsubstances : with the alcohols, for example, it is certain that thevariation of association with concentration is an important factor.44A brtorml Solvent EfSects .-The exceptionally high dipole momentsobtained for aluminium and boron trichlorides in certain solvents 45are undoubtedly due to the formation of compounds containingsemi-polar links, and the results obtained with mixtures of halogeno-methanes or -ethanes and ether, acetone, or quinoline are probablyto be ascribed to some kind of association between the two constitu-e n t ~ . ~ ~ It is a striking fact that the dipole moment of ethylenedichloride is almost the same in a number of solvents, in spite of thepossibility of free rotation, but in benzene the value is exceptionallyhigh.47 This may also be due to a type of attraction between soluteand solvent in which other than van der Waals forces are involved.Another type of abnormality has been found in connection with thehydrogen halides ; 48 the moments in solution are invariably higher41 Cf. J. Rolinski, Physikal. Z., 1028, 29, 658; L. G. Davy and N. V.S i d s c k , J . , 1933, 281.42 Tram. Paraday SOC., 1934, 30, 707.48 J. L. Snoek, ibid., p. 721.44 See, e.g., K. L. Wolf and W. Harold, 2. physikal. Chem., 1934, B, 27,58; C. Hennings, ibid., 1936, B, 28, 267.46 H. Ulich, ibid., 1931, Bodenstein Festband, p. 423; H. Ulich and W.Nespital; 2. Elektrochenz., 1931, 37, 659; W. Nespital, 2. physikal. Chem.,1932, B, 16, 153.46 0. Hassel and A. H. Uhl, ibid., 1930, B, 8, 187; F. H. Miiller, loc. cit.,ref. (2); M. Kubo, Bull. I n s t . Phys. Chem. Res. Japan, 1934,13, 1221; D. P.Earp and S . Glasstone, Zoc. cit., ref. (12).47 A. E. Stearn and C. P. Smyth, J . Amer. Chem. Soc., 1934, 58, 1667; cf.also M. A. G. Rau and B. N. Narayanaswamy, Proc. Indian, Acad. Sci., 1934,1, A , 14; M. Kubo, loc. cit., ref. (46).4s F. Fairbrother, J., 1932, 43; 1933, 1541; Trans. Paraday SOC., 1934,30, 862 ; S. Mizushima, K. Suenaga, and K. Kozima, BulI. Chem. SOC. Japan,1936, 10, 167GLASSTONE : SOLVENT AND MEASUREMENT OF DIPOLE MOMENTS. 133than for the gas. This has been explained by postulating that thesolvent brings about a change towards an ionic linkage,*S or byassuming that there is a small displacement of the protonY5O but F. C.Frank 51 has expressed the view that the observations are adequatelyaccounted for by reflex induced polarisation in the hydrogen halidemolecules brought about by the induced moments in the solvent.These will always act in the same direction as, and so will enhance,the primary moment. The normal solvent effect for an almost spheri-cal molecule of hydrogen halide is in any case probably positive.The marked increase of moment of iodine chloride in solution hasalso been attributed to an increase in the ionic contribution to thelinkage,52 but normal solvent effects have not been entirely excluded.A number of compounds containing symmetrically situated polargroups, e.g., p-nitrobenzene, have appreciable moments in certainsolvents : this has been explained 53 by assuming that, as a result ofsolvent-solute forces, the moment of each group is not constant butfluctuates, independently of the other, about a most probable value.The resultant moment is then not zero, and by postulating a Gaussiandistribution la6 54 an expression for the effective moment of theniolecule, in terms of the most probable value of the group moment,can be derived. This explanation requires the period of fluctuationto be long in comparison with the time of relaxation of tlie solutemolecule in tlie electrical field, but some preliminary calculations byL. E. Sutton and F. C. Frank 55 indicate that this may not be thecase. A possibility being considered by these authors is that thedistribution of the solvent around the dipole is affected by the appliedelectrical field in such a way as to influence the measured moment.Polar Solvents.-In the theoretical discussion of solvent effects,only non-polar solvents were considered : when the solvent is polaronly a qualitative Oreatment is possible.56 There are a number ofresults in the literature 5 7 which suggest that certain polar solventsmay be used in the measurement of dipole moments, provided acorrection is made for the dielectric constant of the medium, gener-49 F. Fairbrother, Zocc. cit.51 LOC. cit., ref. (4), p. 183.52 F. Fairbrother, J., 1936, 847.63 H. 0. Jenkins, ibid., p. 862.54 See S. H. Bauer, J . Chern. Physics, 1936, 4, 459.5 5 Private communication from Dr. L. E. Sutton.68 See, e.g., F. C. Frank, Zoc. cit., ref. (2), p. 190.51 H. Higasi, Sci. Papers Inst. Phys. Chern. Res. Tokyo, 1934, 24, 57;H. 0. Jenkins, J., 1034, 480; 1936, 862; R. J. W. Le FBvre et d., ibid.,1935, 957; 1936, 491, 496; D. P. Eerp and S. Glasstone, loc. eit., ref. (12),p. 1719; A. E. Stearn and C. P. Smyth, Eoc. cit., ref. (47).J. D. Bernal, Trans. Paraday SOC., 1934, 30, 872.134 GENERAL AND PRYSICAL CHEMISTRY.ally by an empirical procedure. It is not certain, however, that thegeneral use of polar solvents is permissible. (Mrs.) C. G. Le FQvrcand R. J. W. Le FBvre 5* have measured the polarisations ofsome non-polar compounds in polar solvents, and have obtainedvalues of considerable magnitude, e.g., a moment of 1.5 D is indicstedfor benzene in nitrobenzene solution. The observations have beeninterpreted in terms of induced polarisations brought about by thepolar molecule of solvent, but the results must be accepted withcaution until due allowance can be made in the calculations for therelatively large change in the dielectric constant of the polar solventresulting from the addition of the non-polar solute.59 An interestingqualitative discussion of the influence of polar solvent moleculeson a polar solute is given by R. J. W. Le FBvre : 60 if molecules maybe divided approximately into two types, similar to those consideredby Higasi (p. 124), according as the principal moment lies along theaxis of maximum polarisability (A) or perpendicular to it (B), thenit is considered that a solvent of type A will be more effective inreducing the polarisation of a solute of its own type.than in increas-ing that of a type B molecule, and a solvent of type B will cause asmaller diminution of polarisation of an A molecule than it will in-crease the polarisation of one of the B type. The actual effects willdepend on the polarisabilities and moments of solute and solvent,on the distance apart of the molecules in the solution, and often oninternal distances between dipoles. S. G.N. K. ADAM.G. J. KYNCH.E. A. MOELWYN-HITGEES.W. G. PENNEY.8. GLASSTONE.G. R. B. M. SUTHERLAND.68 J., 1936, 487.69 See D. P. Earp and X. Glasstone, Zoc. cit., ref. (12)) p. 1721.60 J., 1935, 1747; 1936, 491