GENERAL AND PHYSICAL CHEMISTRY.1. INTRODUCTION.THE choice of subjects in this Report has of necessity been dictatedby personal, as well as by scientific, considerations. The chemistryof deuterium compounds continues to attract attention, and a reporton this subject appears inevitable. The price of “ heavy water ”has fallen so considerably during the current year as to make thesubstance a relatively cheap reagent. Attention may be called totwo publications : a review, with about 400 references, by H. C.Urey and G. K. Tea1,l and a book by A. Farkas.2 The successfulseparation of deuterium has stimulated interest in other isotopes,and it is not improbable that waters enriched with H3 and with0ls will shortly be available for experimental investigation. Mentionmust be made of the fact that the artificial radioactive isotopes oflight elements are already being used in the study of chemical andbiological problems.Articles on aspects of spectroscopy have appeared in the twoprevious Reports : in the present Report the spectra of polyatomicmolecules and of deuterium compounds are the main considerations,since important advances have been made in these directions.The publication of two books on the subject likely to be of interestto chemists, by Frl.H. Sponer and by R. de L. K r ~ n i g , ~ must berecorded.Statistical methods for calculating thermodynamic functionshave been known for some time, but only in recent years, as a resultof developments in wave-mechanics and in spectroscopy, has itbecome possible to evaluate quantities of direct use t o the chemist.The principles involved in the calculations have become especiallyimportant in the study of isotopic exchange processes and for theoriesof reaction velocity, and a report on the subject is overdue.Thenecessity for an annual report on chemical kinetics is obvious inview of the interest being taken in the subject by workers in suchwidely different fields of chemical activity. Two books on kinetics, by1 Rev. Mod. Physics, 1935, 7, 34.2 “ Ortho-Hydrogen, Pars-Hydrogen, and Heavy Hydrogen,” Cambridgea “ Molekulspektren,” Springer, Leipzig, 1935.4 ‘‘ The Optical Basis of the Theory of Valency,” Cambridge UniversityUniversity Press, 1935.Press, 193640 GENERAL AND PHYSICAL CHEMISTRY.F. 0.Rice and K. K. Rice,5 and by N. Semenoff,G have been publishedduring 1935, and are likely to have an important influence.There has been no specific consideration of surface chemistry forsome years, and consequently certain aspects are discussed in thepresent Report. The enunciation of a theory of optical rotatorypower, by M. Born,‘ which marks a definite advance, and theappearance of a book, likely to become a classic, by T. M. L o w r ~ , ~during the current year, indicated that a short review of opticalactivity, from the physical, rather than the organic, standpointwould not be out of place. Dipole-moment data have been used todetermine the angles between the valency bonds, especially foroxygen and sulphur, but the situation has been confused: theintroduction of new concepts has done much to clarify the positionand it is now possible to consider the value and the limitations ofthe method.I n conclusion attention may be called to the issue of a new journal,in English, French, and German, vix., the Acta Physicochimica,U.R.S.X.The Reporter feels that some apology is necessary forthe omission of such topics as the quantum theory of valency,electron diffraction, photochemistry, the physical chemistry ofsurface films, and colloids, but these must be left for a subsequentoccasion. S. G.2. ISOTOPES.The electrolytic method of preparingdeuterium has continued to attract attention, because, not only isit still the best means of obtaining the heavy isotope of hydrogen,but also the separation involves matter of great theoretical interest.A number of arrangements have been described for carrying out theelectrolysis,l and although alkaline electrolytes have been mostlyused, it appears that equally good results can be obtained with acidDeuterium.-Separation.5 “ Aliphatic Free Radicals,” Johns Hopkins Press, Baltimore, 1935.6 “ Chemical Kinetics and Chain Reactions,” Oxford University Press,7 Proc.Roy. SOC., 1935, [ A ] , 150, 84.8 “ Optical Rotatory Power,” Longmans, 1935.1 &I. Harada and T. Titani, Bull. Chem. SOC. Japan, 1934, 9, 457; A . ,1935, 44; E. W. Washburn, E. R. Smith, and F . A. Smith, J . Res. Nat. Bur.Stand., 1934, 13, 599; A., 1935, 175; P. Goldfinger and J. Scheepers, J .Chim. physique, 1934, 31, 628; A., 1935, 311; B.Kamieriski, Rocz. Chem.,1934, 14, 401; A., 1935, 311; W. G. Brown and A. I?. Daggett, J . Chem.Physics, 1935, 3, 216; A . , 723; H. C. Urey and M. H. Wahl, PhysicalRev., 1935, [ii], 45, 566; A., 1329; H. Erlenmeyer and H. GZirtner, HeEz).C h i w ~ Acta, 1935, 18, 419; A., 589.1935GLASSTONE : ISOTOPES. 41solutions.2 The previous theoret icnl treatments of the separationcoefficient have been based on the view that an energy barrier pre-vents the passage of electrons from the cathode into the solution :it has now been shown that separation factors of the correct order,vix., 10 -+ 5, may be calculated by assuming the rate of productionof gas on electrolysis to be dependent, a t the current densities used,on the speeds of recombination of hydrogen and deuterium atoms,to form molecules, on the ele~trode.~ It is becoming increasinglyevident that the differing experimental values for s obtained underapparently identical conditions are due to variations in factors notyet fully understood which occur during the process of electrolysis.5For different metals, s appears 60 vary from 2.7 to 17 : there is noobvious connexion between the separation factor and the over-voltage of the cathode.Anodic prepolarisation of the latter increasess, and addition of a-naphthaquinone decreases it. By raising theC.D., the value of s is generally increased, but this is not alwaysthe case.6 A fundamental difficulty which may account for dis-crepant observations is the tendency towards the establishmentof the equilibrium H, + HDO e H , O + HD, since this wouldlead to a factor of about 3.8 in every case.Slight variations in thecatalytic activity of the electrode material for this process wouldbring about marked changes in the experimental results.As the deuterium content of the electrolyte is increased, s evidentlytends towards the value required by the complete establishmentof equilibrium, even at nickel cathodes. With only slightly enrichedwater, however, containing 1 part of deuterium oxide in about 3000parts, a factor as high as 100 has been claimed, based on the assump-tion that normal water contains 1 part of deuterium oxide in 5500.This result 8 is of great importance, since theoretical considerations,in which the possibility of quantum-mechanical leakage throughan energy barrier-the " tunnel effect "- is neglected, lead to theexpectation of a value of s less than 20, whereas much higher factorsshould be possible if " tunnelling " can occur.g Although somea A.I. Brodski et al., Compt. rend. Acad. Sci. U.R.S.S., 1934, 3, 615; A.,1935, 44.9 Ann. Reports, 1934, 31, 20; W. W. Sawyer, Proc. Cnmb. Phil. SOC., 1935,31, 116 ; A., 456.4 H. C. Urey and G. K. Teal, Rev. Mod. Physics, 1935, '7, 44; 0. Helpernand P. Gross, J . Chem. Physics, 1935, 8, 452; A., 1210; see also H. Eyringand J. Sherman, ibid., 1933, 1, 345.8 Private communication from Mr. J. H. Wolfenden.6 A. Eucken and K. Bratzler, 2. physika2. Chem., 1935, 174, 279.7 Ann.Reports, 1934, 31, 16.8 M. P. Applebey and G. Ogden, J., 1936, 163.9 C. E. H. Bawn and G. Ogden, Trans. Paraday Soc., 1934, 30, 432; A.,B 21934, 60242 GENERAL AND PHYSICAL CHEMISTRY.authors 10 regard this as one of the first proofs that the leakageeffect is an important factor in the reactivities of hydrogen anddeuterium atoms, the conclusion must, for the present, be acceptedwith reserve. The high factor is based on the supposition thatnormal water contains 1 part of deuterium oxide in 5500, whereasa value of 1 to 4500 for the isotopic ratio would give a normalfactor.8 The proportion of 1 part in 9000 reported last year l1appears to be definitely excluded by the new work, and even theproportions of 1 part of D,O in 5000 or 6000 obtained from densitymeasurements l2 and by the mass spectroscope l3 may eventuallyprove to be too low : experimental work of high precision is clearlynecessary.Further experiments on the fractional distillation of water haveconfirmed the possibility of enrichment in this manner.14 Desorp-tion of electrolytic hydrogen from charcoal a t liquid-air temperaturesgives a 3- to 5-f0ld,~~ and diffusion through palladium a 4-fo1d,lGenrichment of deuterium over that originally present.Partialseparation of hydrogen and deuterium also results because of thepreferential adsorption of deuterium oxide vapour by charcoaland by silica gel.17 The claim has been made18 that, in spite ofreports to the contrary,lg in the formation of crystal hydrates thereis some selectivity in favour of deuterium oxide.Analysis.The thermal conductivity method for determiningthe deuterium content of hydrogen gas has been improvedY20 per-lo J. Horiuti and M. Polanyi, Acta Physicochimica U.R.S.S., 1935, 2, 522.11 (Mrs.) E. H. Ingold, C. K. Ingold, H. Whitaker, and R. Whytlaw-Gray, Nature, 1934, 134, 661; A., 1934, 1317.12 H. L. Johnston, J . AmeT. Chem. SOC., 1935, 57, 484; A., 590; A. J.Edwards, R. P. Bell, and J. H. Wolfenden, Nature, 1935,135, 793 ; A., 841.13 W. Bleakney and A. J. Gould, Physical Rev., 1933,44,265; A., 1933, 994.14 M. Harada and T. Titani, Bull. Chem. SOC. Japan, 1935, 10, 39, 41; A.,458; W. N. Christiansen, R. W. Crabtree, and T. H. Laby, Nature, 1935,135,870; A., 815; M. H. Wahl and H. C. Urey, J . Chem.Physics, 1935, 3, 411;A., 1064; N. Morita and T. Titani, B d l . Chem. SOC. Japan, 1935, 10, 257;A., 1087; P. Jaulmes, Chim. et Ind., 1935, 33, 1045; B., 609; see also B.Kamieriski, loc. cit., ref. (1).l5 H. S . Taylor, A. J. Gould, and W. Bleakney, Physical Rev., 1933, [ii],43, 496; A., 1934, 1316.l6 0. Luhr and L. Htzrris, ibid., 1934, [ii], 45, 843; A,, 1935, 1336.17 A. King, F. W. James, C. G. Lawson, and H. V. A. Briscoe, J., 1935,1545.1* K. Okabe, M. Harada, and T. Titani, Bull. Chem. SOC. Japan, 1934, 9,460; A., 1935,48.l9 H. Erlenmeyer and H. Gartner, Helv. Chim. Acta, 1934, 17, 970; A . ,1934, 1303; E. H. Riesenfeld and H. E. Riesenfeld, Ber., 1934, 67, [B], 1659;A . , 1934, 1327; see also Ann. Reports, 1934, 31, 89.2o H.Sachsse and K. Bratzler, 2. phyeikal. Chem., 1934, 171, 331; A.,1935, 20ULASSTONE : ISOTOPES. 43mitting of a precision of 0.02'70 with 0.5 C.C. of gas at 1 atm. Twonew methods for estimating D/H ratios, depending on the measure-ment of the freezing point of water l7 and on observations of itsvapour pressure,21 have been described.Studies of interchange reactions betweendeuterium and compounds containing hydrogen have been con-tinued, partly because of their general interest and partly in order toelucidate reaction mechanisms. Direct introduction of deuteriuminto benzene has been observed22 on shaking with 90% sulphuricacid of enhanced deuterium content : the significance of the resulthas been discussed.23 Exchange also occurs wibh methyl- anddimethyl-amineY2* as their hyckochlorides, when dissolved indeuterium-enriched water, and confirmation of the reaction betweendeuterium oxide in alkaline solution and acetylene has been claimed,25although it has been stated that exchange does not occur.26 Slowexchange takes place between sodium acetate and deuterium oxide,24and a rapid interchange between hydrogen peroxide and deuteriumoxide has been observed; 27 no reaction is noted when potassiumhypophosphite is dissolved in water containing deuterium oxide.27Water obtained from the combustion of various carbohydrates,of natural origin, has been found to contain more deuterium thannorma1.28 A number of hexoses and their glycosides, etc., havebeen observed to undergo isotopic exchange in 11-30y0 and in80-96% deuterium oxide ; the results indicate that all the hydroxylgroups take part in the exchange.29 The investigation of the directintroduction of deuterium into acetone in aqueous alkaline solutionhas been the subject of further study, and the reaction resulting inthe replacement of the fist hydrogen atom is found to be pseudo-unimolecular with a high temperature coefficient .30 Completeinterchange between deuterium and the hydrogen in the NH, groupsExchange reactions.21 0.Reitz and K. F. Bonhoeffer, 2. physikal. Chon., 1935,174, 559.22 C. K. Ingold, C. G. Raisin, and C. L. Wilson, Nature, 1934, 134, 734;23 J. Horiuti and M. Polanyi, ibid., 1934, 134, 847; A., 1935, 74; C. K.24 P. Goldfinger and V. Lasarev, Coqnpt.rend., 1936, ROO, 1671 ; A., 965.2 5 L. €I. Reyerson, J . Amer. Chem. SOC., 1935, 57, 779; A., 713; L. H.26 R. P. Bell, ibid., p. 778; A., 713.2 7 H. Erlenmeyer and H. Gartner, Zoc. cit., ref. (19).5 8 T. Titani and M. Harada, Bull. Chem. SOC. Japan, 1935, 10, 205, 261;29 W. H. Hamill and W. Freudenberg, J . Amer. Chem. Xoc., 1935, 57,30 J. 0. Halford, L. C. Anderson, J. R. Bates, and R. D. Swisher, ibid.,A., 1935, 74.Ingold, C. G. Raisin, and C. L. Wilson, ibid., p. 847; A., 1935, 74.Reyerson and B. Gillespie, ibid., p. 2250.A., 944, 1212.1427 ; A., 1212.p. 166344 GENERAL AND PHYSICAL CHEMISTRY.of metal ammines occurs when the latter are dissolved in watercontaining deuterium 0xide.~1 Atomic deuterium enters into ex-change reactions with water vapour, ammonia, and acetylene, butnot with methane,32 contrary to results previously reported.33Catalytic exchange reactions between D, and H,O and betweenH, and D,O on the surfaces of chromium sesquioxide, zinc oxide andchromite, alumina and platinised asbestos have been observed : thevariation of the former reaction velocity with temperature on thefirst catalyst has been determined approximately and the mechanismhas been discussed?* Methane exchanges35 with deuterium on anickel catalyst at 184-305", and ammonia similarly reacts withdeuterium on a Pe-Al2O3-K,O catalyst at room temperature ; 36 thebearing of the latter observation on the kinetics of the ammoniasynthesis is discussed.Benzene and deuterium oxide exchangereadily at 200" on nickel-kieselguhr, the product consisting of anequilibrium mixture of various deuterobenzenes 37 (see also p.48).A serious source of error in exchange experiments has been indicatedas being caused by hydrogen remaining adsorbed on quairtz vesselsand platinum wires even when apparently thoroughly o~t-gassed.~sThe melting points of hydrogen and deuterium havebeen determined as 13.95" and 18-59' Abs., respectively, and thecorresponding heats of fusion are 28.0 and 47.0 g.-cals. The charac-teristic (Debye) temperatures, for Cp, of the solids are 91" and 89",respectively.39 The heats of evaporation 4O of liquid hydrogen anddeuterium a t 19-65' Abs., and the vapour pressures of o- and p -deuterium a t 20.38" Abs., of o- and p-hydrogen at 17-13' Abs.,41and of n- and e-deuterium over the range 15-20-4" A ~ S .~ ~ havebeen measured. Differences in the properties of hydrogen and31 H. Erlenmeyer and H. Glirtner, Helv. Chim. Acta, 1934, 17, 1008; A.,1934, 1321; H. Erlenmeyer and H. Lobeck, ibid., 1935,18,1213; A., 1332.32 K. H. Geib and E. W. R. Steacie, 2. phy8ikal. Chem., 1935,29, [B], 215;9., 1087.33 H. S. Taylor, K. Morikawa, and W. S. Benedict, J . Ainer. C'hem. SOC.,1935, 57, 383; A., 457.34 H. S. Taylor and H. Diamond, ibid., p. 1256; A., 1086.35 H. S. Taylor et al., loc. cit., ref. (33).36 H. S. Taylor and J. C. Jungers, ibid., p. 660; A., 710; see also K. Wirtz,37 P. I. Bowman, W. S. Benedict, and H. S. Taylor, J . Amer. Chem. SOC.,38 A. Farkas and L. Farkas, Trans.FaracEay SOC., 1935,31, 821 ; A., 710.39 K. Clusius and E. Bartholom6, Physikal. Z., 1934, 35, 969; A., 1935,40 Idem, Z. physikal. Chem., 1935, [B], 30, 237.dl K. Clusius, ibid., 1935, [B], 29, 169; A., 925.42 F. G. Briokwedde ,R. B. Scott, and H. S. Taylor, J . Chem. Physics, 1935,Properties.2. physikal. Chem., 1935, [B], 30, 289.1935,57,960 ; A., 852.155.3, 653GLASST'ONE : ISOTOPES. 45deuterium are attributed partly to differences in zero-point energiesand partly to other fa~tors.~O The heat capacities43 of o- andn-deuterium have been determined and the entropy of n-deuteriumat 298.1" Abs. evaluated: 44 the result is compared with thatcalculated from spectroscopic data by the statistical method, andthe difference in the two values explained by the persistence ofrotation in the solid state (cf.p. 88). The thermal conductivity,45volume coefficient of expansion,46 molecular viscosity,47"and rates of diffusion of deuterium gas through palladium 48 andcopper 49 have been studied, and the results compared with thosefor hydrogen gas. The difference in adsorption of hydrogen anddeuterium on various surfaces has been investigated from boththeoretical 5O and practical standpoints; 51 one of the applicationsof the latter is in connexion wit,h the reaction with ethylene.52The ratio of the magnetic moment of the proton to that of thedeuteron has been determined at 83", 193", and 293" Abs. by themethod based on the rates of the paramagnetic ortho-para conversionof hydrogen and deuterium.53 Provisional mass-spectrographicvalues for the atomic weights of the two isotopes, based on OL6, havebeen published; accurate results are desirable, as they may help inthe estimation of the deuterium oxide content of normal water.54Deuterium oxide.The value of for pure deuterium oxide isnow reported 55 as 1.1071, which is lower than that previously43 K. Clusius and E. BartholomB, Naclz. Ges. Wiss. Gottingen, M&.-phys.44 Idem, ibid., 1935, [B], 30, 237.45 A. B. van Cleave and 0. Maass, Cnnadian J . Res., 1935,12,372; A., 691.4 6 J. B. M. Coppock, Tram. Paraday SOC., 1935, 31, 913; A., 1064.4 7 A. B. van Cleave and 0. Maass, Cunadian J . Res., 1935, 12, 57; A . , 432.4 7 ~ I. Amdur, J. Amer. Chem. SOC., 1935, 57, 588.48 W.Jost and A. Wid.mann, 2. physikal. Chem., 1935, [B], 29, 247; A.,1200; H. W. Melville and E. K. Rideal, Proc. Roy. Xoc., 1935, [A], 153, 89;0. Luhr and L. Harris, loc. cit., ref. (16); se0 also A. Sieverts and G. Zapf,2. physikal. Chem., 1935,174,559.Kl., 1934, [C], 1, 1 ; 2. physikal. Chem., 1935, [B], 29, 162; A., 573, 924.413 H. W. Melville and E. K. Rideal, Zoc. cit., ref. (48).50 J. E. Lennard-Jones and C. Strachan, Proc. Roy. SOC., 1935, [ A ] , 150,442, 456; A., 1070.61 J. Pace and H. S. Taylor, J. Chem. Physics, 1934, 2, 578; A., 1934,1181; R. Klar, Naturwiss., 1934, 22, 832; A., 1935, 27; H. W. Kohlschiitter,2. physikal. Chem., 1934, 1'70, 300; A., 1935, 27; R. Kler, ibid., 1935, 174,1 ; A., 1329; H. W. Melville and E. K.Rideal, Proc. Roy. SOG., 1935, [A],153, 77.52 R. Klar, loc. cit.; 2. physikal. Chem., 1934, [B], 27, 319; A., 1935, 175.53 L. Farkas and A. Farkas, Nature, 1935,135, 372; A , , 560.54 F. W. Aston, ibid., 1935,135, 541 ; A., 677.55 L. Tronstad, J. Nordhagen, and J. Brun, ibid., 1936, 136, 515; A.,131346 GENERAL AND PHYSICAL CHEMISTRY.accepted,56 the difference being probably due to the larger 0l8content : for water containing less than 1 part of deuterium oxide in2 x lo5, dii: is 0.9999815. Measurements have been made of theheat capacities 57 of liquid and solid deuterium oxide, of the heatsof fusion 5 7 5 58 and melting points of mixtures 59 of light and heavyice, of the heats of vaporisation and dilution,60 and of the vapourpressures 61 of mixtures of liquid water and deuterium oxide.Thegeneral P- V-T relationships of solid and liquid deuterium oxidehave been studied,62 and different forms of heavy ice identified.The differences in the thermal properties of water and deuteriumoxide cannot be accounted for by their zero-point energies only;the importance of angular vibration or " libration " of the moleculeshas also been ons side red.^^ Observations have also been describedof the refractive index,G4 dielectric constant,65 surface tension,66and critical temperature 67 of liquid deuterium oxide, of its diffusionin ordinary water,68 of the diamagnetism G9 of the liquid and solidstates, and of the cell-dimensions 70 of solid deuterium oxide.The ratio of the dissociation constants '1 of deuterium oxide andwater is said to be 0.16 to 1 at 2loY from measurements with cells56 H.S. Taylor and P. W. Selwood, J . Amer. Chem. SOC., 1934, 56, 998;A., 1934, 590; see also, ibid., 1935, 57, 642, footnote (4).5 7 R. S. Brown, W. H. Barnes, and 0. Maass, Canadian J . Res., 1935, 12,699; A., 1198; E. Bartholome and K. Clusius, Z. physikal. Chem., 1935,[B], 28, 167; A., 584.58 L. Jacobs, Trans. Paraday Soc., 1935, 31, 813; A., 704.5D V. K. LaMer and W. N. Baker, J . Amer. Chern. Soc., 1934, 56, 2641;A., 1935, 167.6o E. Doehlemann and E. Lange, 2. physikal. Chem., 1935, 178, 295 ; A.,935.61 W. F. K. Wynne-Jones, J . Ghem. Physics, 1935,3, 197; A., 694; M. H.Wahl and 13. C. Urey, Zoc. cit., ref. (14).62 G. Tammann and G.Bandel, 2. anorg. Chern., 1935, 221, 391 ; A., 302 ;J. Timmermans and L. Deffet, Compt. rend., 1935,200,1661; A., 815; P. W.Bridgman, J . Chem. Physics, 1935,3,897 ; A., 1454.63 J. D. Bernal and G. Tamm, Nature, 1935, 135, 229; A., 432; P. W.Bridgman, 106. cit., ref. (62).64 W. J. C. Orr, ibid., p. 793; A., 810.*5 P. Abadie and G. Champetier, Compt. rend., 1935, 200, 1590; A., 808.66 I. Minkow, Nature, 1935, 136, 186; A., 1059.67 E. H. Riesenfeld and T. L. Chang, 2. physikal. Chern., 1935, [B], 28,408; 30,61; A., 691.6 8 W. J. C. Orr and D. W. Thomson, Nature, 1934,134, 776; A,, 1935,25;M. Temkin, ibid., 1935,136, 552; A., 1313; W. J. C. Orr and J. A. V. Butler,J., 1935, 1273; A., 1313.69 F. W. Gray and J. H. Cruickshank, Nature, 1935, 135, 268; A., 435;B.Cabrera and H. Fahlenbrach, Anal. Pis. Quirn., 1934,32,538 ; A ., 1935,923.70 H. D. Megaw, Nature, 1934, 134, 900; A., 1935, 151.71 E. Abel, E. Bratu, and 0. Redlich, 2. physikal. Chem., 1935, 173, 353;cf. Ann. Reports, 1934, 31, 17GLASSTONE : ISOTOPES. 47involving deuterium electrodes in deuterium chloride and sodiumdeuteroxide solutions. The dipole moment of the deuterium oxidemolecule, measured either in the vapour state 72 or in solution inbenzene 73 or d i ~ x a n , ~ ~ is not more than 0.02 x PO-18 e.s.u. greaterthan for water, although a somewhat larger difference might havebeen expected the~retically.~~ A similar difference of 0.03 x 10-18e.s.u. exists between the dipole moments of ammonia and trideuter-ammonia.75 Freezing-point determinations of solutions of waterand of deuterium oxide in dioxan indicate that the latter is slightlymore associated in this solvent,76 and a similar conclusion is derivedfrom the difference in the heat capacities of the liq~ids.~7 Replace-ment of H,O by D,O in binary systems with organic compounds,e.g., phenol, acetonitrile, triethylamine, and propionic acid, raisesthe upper and depresses the lower consolute temperat~res.7~Deuterium compounds.The absorption spectra of the bromides 79and iodides *O of hydrogen and deuterium have been studied, and thereason for the differences considered. The vapour pressures andboiling points 79 (206.3" Abs.) of the two bromides are identical,but the vapour pressure of deuterium iodide is slightly greaterthan that of hydrogen iodide, and the boiling point of the former(237.0" Abs.) is consequently 0.5" lower. The higher vapourpressure of the deuterium compound is probably due to factorsdifferent from those which result in its fluoride having a highervapour pressure than that of hydrogen.According to an approxim-ate theoretical treatment,s1 the vapour-pressure curves of thecorresponding hydrogen and deuterium compounds should crossat some temperature: this is apparently often above the boilingpoint, and so the conditions under which the latter have the highervapour pressure are not often observable. The transition pointof sodium sulphate decadeuterate (Na,SO,,lOD,O) is 34-48'. 82Pure hexadeuterobenzene 83 has been obtained by distilling the72 L.G. Groves and S. Sugden, J., 1935, 971.73 F. H. Muller, Physikal. Z., 1934, 35, 1009; A., 1935, 148.74 R. P. Bell, Trans. Paraday Soc., 1935, 31, 1345; A., 1304.75 J. M. A. de Bruyne and C. P. Smyth, J . Amer. Chem. Soc., 1935, 57,76 R. P. Bell and J. H. Wolfenden, J., 1935, 822; A., 931.7' R. S. Brown, W. H. Barnes, and 0. Maass, Zoc. cit., ref. (57).78 J. Tirnmermans and G. Poppe, Compt. rend., 1935, 201, 524; A., 1314.7g J. R. Bates, J. 0. Halford, and L. C. Anderson, J . Chem. Physics, 1935,80 Idem, ibid., p. 415; A., 1064.81 H . C. Urey and G. K. Teal, Zoc. cit., ref. (4), p. 58.82 H. S. Taylor, J . Amer. Chem. SOC., 1934, 56, 2643; A., 1935, 447.88 H. Erlenmeyer and H. Lobeck, Helv. Ohirn. Acta, 1935, 18, 1464; A.1203 ; A., 1055.3,531 ; A., 1313.Klit and A.Langseth, Nature, 1935, 3135, 956 ; A., 80648 GENERAL ABD PHYSICAL CHEMISTRY.calcium salt of mellitic acid with calcium deuteroxide and also byappIying the Friedel-Crafts reaction to benzene and deuteriumchloride : it has f . p. + 6.8" and b. p. 79.4", the corresponding valuesfor benzene being + 5.5" and + 80.12". These results agree withsome previously published,84 but differ markedly from others inwhich the hexadeuterobenzene was made by passing dideuter-acetylene over a tellurium cataly~t.8~ Octadeuteronaphthalene issaid to be obtained as a by-product in the latter process.86 Theexchange between benzene and deuterium oxide on a nickel-kieselguhr catalyst, already mentioned (p. 44), has been used toprepare hexadeuterobenzene ; if the mixed benzenes are separatedafter equilibrium is attained, and re-heated with pure deuteriumoxide, it is claimed that hexadeuterobenzene of over 99% purity, d;?0-9417, can be obtained after four operation^.^^ Dideuteromalonicdeuteracid, CD2( CO,D),, results from the action of deuterium oxideon carbon suboxide ; on heating to 140-150°, trideuteraceticdeuteracid, CD,-C02D, 112.p. 15.75", is obtained. The latter sub-stance is more volatile than acetic acid.87 Catalytic reduction oflinoleic acid with deuterium yields 6 : 7 : 9 : 10-tetradeuterostearicacid,88 and the addition of deuterium to cholestenone gives 4 : 6-dideuterocopro~tanone,~~ which has been used as an " indicator "in biological experiments.Solutions in heavy water.The conductivities of potassiumchloride and of deuterium chloride in deuterium oxide are 17%and 2S%, respectively, less than the corresponding values in water ;the differences are chiefly due to a 23% increase in the viscosity ofthe solvent. Similar decreases in the conductivities of hydrochloricand perchloric acids in deuterium oxide solution have been noted.91The conductances of mixtures of the chlorides of hydrogen anddeuterium are less than the expected values : the discrepancy can beexplained by supposing that hydrogen and deuterium ions take partin Grotthuss conducti~n.~~ The ratio of the dissociation constantsof a weak acid in water and in deuterium oxide should be largerthe weaker the acid.92 The free energy of hydration of the hydrogenion is stated to be greater in deuterium oxide than in water; a84 C.L. Wilson, Nature, 1935, 136, 301; A., 1198.8 6 G. R. Clem0 and A. McQuillen, J., 1935, 881; A., 967.* 6 I d e m , ibid., p. 1325; A., 1358.8 7 C. L. Wilson, ibid., p. 492; A., 731.8 8 R. Schonhoimer and D. Rittenberg, J . Bid. Chem., 1935, 111, 163; A.,89 R. Schonheimer, D. Rittenberg, and M. Graff, ibid., p. 183; A., 1407.91 A. Fink, P. Gross, and H. Steher, Monatsh., 1935, 66, 111 ; A., 1324.92 0. Malpern, J . Chem. Physics, 1935, 3, 456; A., 1203.1407.W. N. Baker and V K. LaMer, J . Chem. Physics, 1935,3,406; A., 1078GLASSTONE : ISOTOPES. 49similar difference is supposed to exist for hydrogen- and deutero-a~ids.9~ The potential of the quinhydrone electrode in 0-001M-hydrochloric acid in deuterium oxide has been found to be 0.0345volt more positive than in water; the ratio of the products of thetwo dissociation constants in water to that in deuterium oxideis 3.84.94 The cathodic overvoltage a t mercury is greater for theliberation of deuterium than of hydrogen, as is to be expected;the temperature coefficient is greater for the former.95 Observationshave also been made with the dropping-mercury cathode in varioussolutions containing deuterium oxide.g6Kinetics, etc.The spectroscopy, reaction kinetics, and surfacechemistry of deuterium compounds are mainly treated elsewhere inthese Reports : mention may be made in addition of the followingtopics. Two papersg7 dealing with the application of quantummechanics to reactions involving hydrogen and deuterium haveappeared, and a review article 98 on the use of the latter in the studyof acid-base catalysis has been published.The catalytic decomposi-tions of nitroamine by hydrochloric acid 99 and of hydrogen peroxideby the iodide ion are slower in deuterium oxide than in water,although for the latter reaction the energies of activation are thesame for both media in spite of the differences in the zero-pointenergies of hydrogen peroxide and deuterium peroxide. Thecatalysis of H20 and D, exchange by enzymes has been investigated ;the enzymic fission of salicin by emulsin is 25% more rapid indeuterium oxide than in water.3 The photo-oxidation of the iodidesof hydrogen and deuterium shows that the reactions between H orThe rate of the mercury-photosensj tised decomposition of acetyleneis about 30% greater than for dide~teracetylene,~ and a similar93 P.Goldfinger and W. Jeunehomme, CYompt. rend., 1935, 200, 1387; A.,824.94 V. K. LaMer and S. Korman, J . Amer. Chem. SOC., 1935, 57, 1511; A.,1205.95 F. P. Bowden and H. F. Kenyon, Nature, 1935, 135, 105; A., 450.96 J. Heyrovskf and 0. H. Miiller, Coll. Czech. Chem. Comm., 1935, 7,97 R. A. Smith, Proc. Camb. Phil. Soo., 1934, 30, 508; A., 1935, 306; R. P.98 W. F. K. Wynne-Jones, Chem. Reviews, 1935, 17, 115.99 C. A. Marlies and V. K. LaMer, J . Amer. Chem. SOC., 1935, 57, 1812; A.,E. Abel, 0. Redlich, and W. Stricks, Monatsh., 1936, 65, 380; A., 939.3 G.33.. Bottomley, B. Cavanagh, and M. Polanyi, Nature, 1935, 136, 103 ;3 E. W. R. Steacie, 2. physikal. Chem., 1935, [B], 28, 236; A., 588.4 G. A. Cook and J. R. Bates, J . Amer. Chem. SOC., 1935, 57, 1775.J. C. Jungers and H. S. Taylor, J . Chem. Physics, 1935, 3, 338; A . , 943.D and oxygen are three-body processes, and kH+OI+OI N kD+ol+02. 4281; A., 1079; 0. H. Miiller, ibid., p. 321; A., 1208.Bell, Proc. Roy. SOC., 1935, [A], 148, 241; A., 560.1466.A., 108460 GENERAL AND PHYSICAL CHEMISTRY.difference is observed in the combination of oxygen with hydrogenor deuterium in the presence of a-particles.6 The rate of polymeris-ation of dideuteracetylene under the influence of a-particles is,however, the same as for acetylene.’ The decomposition of trideuter-ammonia, like that of ammonia, on a tungsten filament is approxim-ately of zero order, although the former reaction is the slower.*A comparison has been made of the rates of ortho-para hydrogenconversion and of the H, + D, = 2HD reaction on a nickel catalyst :the mechanism of both processes is evidently the same.gGraphical arrangements of the knownisotopes of elements of low atomic weight indicated the possibilityof the existence of an isotope of hydrogen of mass 3, now called“tritium ” and given the symbol T.It was claimed lo that thepresence of tritium oxide in water containing 2% of deuterium oxidecould be detected by the magneto-optic method, but band-spectro-scopic examination 11 showed that the upper limit of its concentra-tion was 6 parts in 106 of ordinary hydrogen ; by the aid of the mass-spectrograph l2 this limit was placed at 2 parts in 109 as a maximum.Working with 99% deuterium oxide, G.Hertz has definitely provedthe presence of tritium by its mass-spectrogram; 13 the T : D ratiowas 5 : lo6, indicating a proportion of 1 part, or less, of tritium inlo9 of natural hydrogen. Study of the impacts of high-speeddeuterons on deuterium nuclei had indicated the occurrence ofthe disintegration l4 D + D ---+ H + T, and the passage of apositive-ray discharge through deuterium is stated l5 to result in anincrease of the T/D ratio from 1/200,000 to l/S000 : the absoluteamount of tritium formed must, however, be very small. In spiteof the apparent hopelessness of the task, 75 metric tons of waterhave been electrolysed down to 0-5 c.c.,16 which was found to contain1 part of tritium oxide in 4000 : the abundance of tritium in ordinarywater is estimated as 7 parts in 1W0.Under the experimentalOther Isotopes.-Tritium.S. C. Lind and C. H. Schiflott, J . Amer. Chem. Soc., 1935, 57, 1051; A.,7 S . C. Lind, J. C. Jungers, and C. H. Schiflett, ibid., p. 1032; A., 943.944.J. C. Jungers and H. S. Taylor, ibid., p. 679; A., 710.E. Fajans, 2. physikal. Chern., 1935, [B], 28, 239; A., 710.W. M. Latimer and Ip. A. Young, Physical Rev., 1933,44, 690.l1 G. N. Lewis and F. H. Spedding, ibid., 1933,43,964.l2 W. Bleakney and A. J. Gould, ibid., 1934, 45, 281.xi W. W. Lozier, P. T. Smith, and W.Bleakney, ibid., p. 655; M. A. Tuve,14 Ann. Reports, 1934, 31,387.16 G. P. Harnwell, H. D. Smyth, S. N. van Voorhis, and J. B. H. Kuper,16 P. W. Selwood, H. S. Taylor, W. W. Lpzier, and W. Bleakney, J. Arner.L. R. Hafstad, and 0. Dahl, ibid., pp. 746, 840.Physical Rev., 1934, 45, 655.Chem. Soc., 1935,57, 780; A., 711GLASSTONE : ISOTOPES. 51conditions, apparently nickel electrodes in alkali, the Dz--T2 separationcoefficient is 2.0, in agreement with theoretical predictions.17 Itappears probable that small quantities of water enriched with tritiumwill soon be available for experimental work.Oxygen and Nitrogen Isotopes.-W ater containing 018 in excess ofthe normal has been obtained by a diffusion method,18 and a slightenrichment has been observed in oxygen obtained from liquid airby the fractionation process; l9 the difference 2O of 1.4% in thevapour pressures of H,016 and H,Ols has resulted in a partialseparation by the fractional distil1at)ion of water.21 Decompositionof 30% hydrogen peroxide by colloidal platinum yields a gas with a0l6/Ol8 ratio of 462 & 8, compared with 426 & 4 for the residue.22Conflicting reports on the ehticiency of electrolysis in bringing abouta concentration of 018 have been published: in early work noenrichment was observed,23 but the reason for this is now apparent(see below).More recently the concentration of 0 1 8 in the residualwater has been e~tablished,~~ although the separation factor appearsgenerally to be no more than 1.01 : the reduction of the volume ofwater 100,000-fold by electrolysis increases the 0l8 content ofordinary oxygen from 0.20 to only 0.22y0.25 A separation coefficientof 1.15 has been reported recently 26 for the electrolysis of 1.25N-sodium hydroxide with nickel electrodes, although a previous claim 27for a coefficient of the same order has now been revised 28 bo 1.05.Assuming the rate-determining step in the separation of 0, byelectrolysis is the passage of a O1*H or OleH complex over or throughl7 H.Eyring, quoted in ref. (16).la 2. P h p i k , 1932,79,108; see M. Polanyi and A. S. Szabo, Tram, ParadaySOC., 1934, 30, 508; A., 1934, 979.lS R. Klar and A. Krauss, Naturwiss., 1934,22,119; A., 1934, 377; E. R.Smith, J . Chern. Physics, 1934, 2,298; A., 1934, 855.2o M.H. Wahl and H. C. Urey, ibitl., 1935,3, 41 1.21 G. N. Lewis and R. E. Cornish, J . Arner. Chem. SOC., 1933, 55, 2616;22 H. S . Taylor and A. J. Gould, ibid., 1934, 56, 1823; A., 1934, 1082.23 G. N. Lewis and R. T. Macdonald, J . Chem. Physics, 1933, 1, 341 ; A..1934, 10; P. W. Selwood and A. A. Frost, J . Arner. Chem. SOC., 1933, 55,4335; A., 1933, 1233; W. Bleakney and A. J. Gould, Zoc. cit., ref. (12).24 E. W. Washburn, E. R. Smith, and M. Frandsen, J . Res. Nat. Bur.Stand., 1933, 11, 453; A., 1934, 156; E. W. Washburn, E. R. Smith, andF. A. Smith, ibid., 1934, 13, 599; A., 1935, 175; C. H. Greene and R. J.Voskuyl, J . Arner. Chem. SOC., 1934, 56, 1649; H. L. Johnston, ibid., 1035,57,484; A., 590; W. H. Hall and H. L.Johnston, ibid., p. 1515; A., 1330.26 P. W. Selwood, a. S . Taylor, J. A. Hipple, and W. Bleakney, ibid.,p. 642; A., 711.26 G. Ogden, Nature, 1935, 136, 912.27 E. W. Washburn, E. R. Smith, and F. A. Smith, Zoc. cit., ref. (24).28 E. R. Smith and M. Wojciechowski, J . Res. Nat. Bur. Stmd., 1935, 15,G. N. Lewis, ibid., p. 3502.187 ; A., 132952 GENERAL AND PHYSICaL CHEMISTRY'.an energy barrier, a separation coefficient of 1-1-16 can be cal-culated,26 according to the width and height of the barrier. Themost favourable value would lead only to a four-fold increase inconcentration of 0l8, whilst the deuterium concentration in waterwas raised from 1 in 5000 to 100%. Such an enrichment wouldprovide a, tool of value to chemists, but it is doubtful if even thisrelatively low efficiency could be attained, especially as an alternative,approximate, calculation indicates a probable factor of 1.06 for theratio of the rates of separation of Oi6 and Oi8 on ele~trolysis.~~Calculations by statistical methods 29 (p.70) of the equilibriumconstant of the exchange reaction 2H,018 (E) + Oi6 = 2H2016 (I) +Oi8 gives a value of 1.012, implying an enrichment factor of 1.006at 25' : this equilibrium, which opposes the normal electrolyticseparation, will tend to be attained in the evolution of oxygen,and may explain the different electrolytic separation coefficientsreported by different workers.25 The equilibrium constant of thereaction 2H2018 (Z) + COP = 2H2W ( I ) + C0i8 has been calc~lated,~gand the result shows that the carbon dioxide gas should alwayscontain a larger proportion of 0l8 than does the water : the theoreti-cal fractionation factor, i.e., the ratio 0 1 8 / 0 1 6 in the gas to that) inthe water, of 1.047 at 0" has been confirmed e~perimentally.~~A counter-current process, based on the establishment of theequilibrium, for obtaining carbon dioxide enriched with 0l8, hasbeen devised 29 and is being tested.It is the use of carbon dioxidefor the neutralisation of the alkali that had become concentratedon electrolysis, which was probably responsible for the failure todetect any change of 0 1 8 in the early work mentioned above.s2, 25An attempt has been made to concentrate N15 by the fractionaldistillation of liquid ammonia : the results so far are not veryencouraging, but they indicate that the method may be of some usefor increasing the N15/N14 ratio.31Art~~cially-rudiouctive Isotopes.-Mention may be made of theuse of these substances as indicators in chemical investigations.By taking advantage of the radioactivity induced in bromine byneutron bombardment, it has been shown that the bromide ionin sodium bromide undergoes exchange with elementary bromine inaqueous solution.32 Iodine and sodium iodide exchange readilyin a similar manner, as also does iodine with methyl and ally12g H.C. Urey and L. J. Greiff, J. Amer. Chem. SOC., 1935,57, 321 ; A., 446.3O L. A. Webster, M. H. Wahl, and H. C. Urey, J. Chern. Physics, 1935,81 M. H. Wahl, J. F. Huffman, and J.A. Ripple, J. C'hent. Physics, 1936,12 A. von Grosse and M. S. Aquss, J, Amer. Chcnt. Xoc., 1935,57, 591 ; A.,8, 129; A., 693; see also M. P. Applebey and G. Ogden, J., 1936, 163.3,434.595SUTHERLAND : SPECTROSCOPY. 53iodides ; ethyl, n-propyl, isopropyl, and methylene iodides andiodoform, however, exchange very slowly, if at all.33 Only theiodide ion of diphenyliodonium iodide undergoes exchange withiodine; the experimental results are used to throw light on themechanism of the decomposition of the iodide in iodobenzenesolution.34 The rate of exchange of elementary iodine with theiodine in sec.-octyl iodide is equal to the rate of racemisation of thed-iodide : 35 the significance of this result is discussed elsewhere inthese Reports (p.96). A start has also been made in what islikely to be an important development, namely, the use of theradioactive isotope P32 in the study of metabolic processes.36S. G.3. SPECTROSCOPY.Atomic Xpectra and the Spectra of Diatomic Molecules.--In neitherof these fields are there any striking advances to report. This isto be expected, since the fundamental and important steps in eachwere made several years ago, and all that remains is to fill in thegaps in our knowledge of the energy levels of the less common atomsand molecules. The results for atomic states have been tabulatedin a book by R. F. Bacher and S. G0udsrnit.l Recently, interesthas shifted towards the determination of nuclear magnetic momentsfrom the investigation of the hyperfine structure of Bpectral lines.This has already been dealt with in last year’s Reports and neednot be repeated here, especially since it is only of secondary interestto chemists.The corresponding collection of results regardingthe energy levels and electronic structure of diatomic moleculeshas just appeared in an excellent compilation by Frl. H. Sponer(see p. 39). For more general treatment, reference should be madeto earlier Reports3 or to the books of R. de L. Kronig4 and ofW. Jevons and to the reports of R. S. Mulliken.6Spectra of Polyatomic Molecules.-It is here that the most interest-ing advances have been made from the chemical standpoint. Instead33 F. Juliusburger, B. Topley, and J. Weiss, J. Chent. Physics, 1935, 3,437.34 Idem, J., 1935, 1295.35 E.D. Hughes, F. Juliusburger, S. Masterman, B. Topley, and J. Weiss,35 0. Chiewitz and G. von Hevesy, Nature, 1935, 136, 754.ibid., p. 1525.“ Atomic Energy States,” McGraw-Hill, 1933.Ann. Reports, 1934, 31, 372.“ The Optical Basis of the Theory of Valency,” Cambridge, 1935 ; “ Band“ Report on the Spectra of Diatomic Molecules,” Cambridge, 1932.Rev. Mod. Physic&?, 1930, 2, 60; 1931, 3, 89; 1932, 4, 1.a Ibid., 1933, 30, 68.Spectra and Molecular Structure,” Cambridge, 193054 GENERAL AXD PHYSI(xBL( UHlWISTRY.of giving detailed results, it would appear more valuable, however,to take stock of what has been done during the past few years,reviewing the principles and methods by which it has been accom-plished,’ in order that limitations on future progress may be clearlyrealised. The polyatomic molecule may best be approached byconsidering what it has in common with, and wherein it differs from,the diatomic molecule.Just as the energy of a diatomic moleculemay be divided into three (practically independent) parts, vix.,electronic, vibrational, and rotational, so may that of a polyatomicmolecule, and consequently the latter has three distinct spectra :a pure rotation, a vibration-rotation, and an electronic spectrum.The differences between a diatomic and a polyatomic moleculebecome evident as soon as we consider the structure of any one ofthese three types. This follows since the expression for the energyof a polyatomic molecule is considerably more complicated than thatfor a diatomic molecule, as well as the selection rules governing itsallowed changes.For example, a diatomic molecule has effectivelyonly one moment of inertia, whereas the general polyatomic moleculehas three different moments of inertia; the expression for therotational energy in the first case is consequently very simple,while in the second case no explicit expression exists for the energylevels, although these can be computed. Again, the diatomicmolecule has only one degree of vibrational freedom, or one funda-mental vibration frequency, whereas the polyatomic molecule ofn atoms has, in general, 3n - 6 fundamental frequencies with aset of selection rules governing the appearance of each in the differenttypes of spectra. Finally, the electronic energy states of a diatomicmolecule are usually characterised by the associated resultantangular momentum about the internuclear axis, whereas in apolyatomic molecule these have to be specified through the symmetryand transformation properties of the associated wave functions.Nevertheless, the apparently hopeless complexity which such factorsintroduce into the spectra of polyatomic molecules has proved to bemore capable of disentanglement than one would have at firstsupposed.Before passing to the consideration of the three main classes ofspectra, it should be mentioned that these are all normally observedin absorption.In the case of the first two, however, they may alsobe obtained by scattering (Raman although the selectionD. M.Dennison, Rev. Mod. Physics, 1931, 3, 280. Articles by R. Mecke,E. Teller, and 0. Reinkober in the ‘‘Hand- und Jahrbuch der ChemischenPhysik,” 1934, Band 9/11; G. B. B. M. Sutherland, “ Infra-Red and RamanSpectra,” Methuen, 1935.8 Ann. Reporto, 1934,31, 21SUTHERLAND : SPECTROSCOPY. 55rules differ from those operative in absorption, and we shall have toconsider the relation between them more fully in what follows.A. Pure rotation spectra. For convenience in this and other sec-tions, we shall immediately divide polyatomic molecules into fourclasses according to their degree of rotational symmetry. If thethree moments of inertia are denoted by I*, IB, Ic, then thereare four classes of molecules : (1) linear molecules, for whichla = IB, I.= 0; (2) spherical molecu{les, for which la = IB = I c ;(3) symmetrical top molecules, for which IA = Ig I,; and (4)asymmetrical top molecules, for which IA I IB Io. The corre-sponding energy expressions and selection rules have been collectedin Table I. By examination of this table and application of theappropriate selection rule, it is clear that the pure rotation spectrumof a linear polyatomic molecule is in no way different from that of adiatomic molecule. Next, we note that spherically symmetricalmolecules (such as methane, carbon tetrachloride, etc.) have nopure rotation spectra. The absorption spectrum of a symmetricaltop molecule is exactly like that of a diatomic molecule with amoment of inertia equal to that of the symmetrical top moleculeperpendicular to its axis of symmetry.Thus, the spacing of thelines in the pure rotation spectrum of a symmetrical top moleculeTABLE I.Rotational Energy Formulce and Selection Rules for the Four Classesof Polyatomic Molecules.Selection rules. - ( a ) ( b )Class of Expression for Infra-red Ramanmolecule. rotational energy, &',., spectra. spectra .19S,elAJ(J+l)J = O , 1, 2, . I . AJ=&,1 AJ=O, f 2h*Spherical snaI, J( J + 1 1 No active No activeI* = I B = I0 J=O, 1, 2, . . . transitions transitionsh2 J ( J + 1 ) + --A K2h2IA=IB + I c K<J; J = O , l , . . . AK=O AK=OSymmetrical top (:c la) 8a2 A J = & l A J = O , + l , & 2No simple explicit expressionAsymmetrical top in terms of J , the quantum A J = f l A J = O , & l , f 2.la =+ IB I 10 number for total angularmomentum.can yield no information regarding the moment of inertia about thesymmetry axis (for AK = 0 in the Raman spectrum too).TheRaman spectrum is slightly more complicated, containing an 0 and anX branch in addition to the usual P , &, and R ones. Although th56 GENERAL AND PHYSICAL CHEMISTRY.spacing of the lines is independent of Ic, the intensity of the linesis a function of Io/Ia, and it is interesting to note that it has beenpossible in this way to confirm the flat pyramidal model of theammonia molecule by a careful intensity measurement of its purerotation Raman spe~trum.~Theenergy levels are characterised by the quantum number J of thetotal angular momentum.Corresponding to each value of J(1, 2, 3 . . .) there are 2J + 1 sub-levels, the values of whieh maybe computed by solving certain algebraic equations. As some ofthese equations will only admit of numerical (approximate) solution,it means that the moment of inertia must be known in order to makethe computation. Usually a fair approximation to the values ofthe moments can be made from other evidence : the levels may thenbe computed and the agreement with observation tested. By aprocess of successive approximation, one finally arrives a t valuesfor the moment which give agreement with experiment. Such aprocedure is extremely laborious and requires very accurate ex-perimental data before it can be applied. In fact, no asymmetricaltop molecule has had its pure rotation spectrum analysed in thisidealised way, although for the H,O molecule R. Mecke has shownthat all of the known lines may be classified by treating the asym-metrical rotator as an imperfect symmetrical rotator.1°When one considers the experimental difficulties in obtaining thistype of spectrum (under high resolution), it does not seem probablethat it will ever become an important source of information for thestructure of molecules.All of the information derivable can beobtained from vibration rotation or from electronic spectra, both ofwhich are very much easier to observe. The only advantage of purerotation spectra is their comparative simplicity, but as spectro-scopists become more experienced this will not count for very much,since the degree of resolution of lines obtainable in the near infra-red and the visible region is a t present as high as or higher than thatobtainable a t longer wave-lengths.B. Vibration-rotation spectra.This is the class of spectra whichhas so far proved most productive of information about polyatomicniolecules. Such spectra are not so complex as electronic, and yetyield just as much information as the latter do regarding the groundstate of the molecule. Their investigation is almost a necessarypreliminary to the study of electronic spectra, and certainly aninvaluable concomitant. From their analysis, we can obtain thevalues of the fundamental vibration frequencies, the shape of thelo " Hand- und Jahrbuch der Chemischen Physik," 1934, Band 9/11.The asymmetrical top molecule presents serious difficulties.C.M. Lewis and W. V. Houston, Physical Rev., 1933, 44, 903SUTHERLAND : SPEU"E0SCOPY. 57molecule, its moments of inertia, and (in certain cases) the inter-nuclear distances.would not be of interest here, nor would the cataloguing of resultsfor a, large number of molecules. Such information is more con-veniently available elsewhere.lOa What is important is to realise thegeneral principles underlying these analyses, and to be able toestimate the limitations of such a mcthod of investigating molecularstructure. One is all too frequently confused by conflicting reportsof the assignment of the fundamental frequencies of a molecule andof its form and moments of inertia.It is hoped that this reportwill give the reader some criteria which he may apply to the workon any particular molecule.Suppose we have given the fact that a molecule absorbs in theinfra-red at wave-lengths corresponding to the frequencies vl, v2,v3 . . . . , and that it has Raman lines of frequency vll, vzl, v31 ; howdo we set about determining any of the information just quoted?We must first establish which are tlhe fundamental frequencies andwhich are the combinations and overtones of them. This is doneby the application of a judicious combination of semi-empiricalrules, together with strict selection rules derived from a quantum-mechanical treatment of the problem. The first of these empiricalrules concerns the magnitude of the frequency.Any moleculecontaining a hydrogen atom may be expected to have its highestfrequencies in the neighbourhood of 3500 cm.-l. Any molecule notcontaining a hydrogen atom is very unlikely to have any fundamentalfrequency higher than 2500 cm.-l. This enables one immediatelyto put an upper limit on which of the observed frequencies may,or may not, be fundamentals. Certain authors l1 have tended tocarry this principle still further, and to associate definite fre-quencies in the molecule with definite linkages such as the C-H,0-H, C-C, C-S, etc. This is permissible only so long as it is clearlyunderstood that it is at best a rough approximation to the truth.The C-H bond in a molecule cannot vibrate by itself and leave therest of the molecule unaffected.The molecule must vibrate as awhole, although it happens that for certain of the normal modes ofvibration the motion is principally confined to, and determined by,the force constants of one particular bond or group.The next empirical criterion is that of intensity. It usuallyhappens that the more intensely absorbed (or scattered) frequenciescorrespond to fundamental vibrations of the molecule. This, how-ever, is a rule which must be applied with even more caution than100 H. Sponer, '' Molekulspektren," Springer, 1935.11 E.g., I<. W. F. Kohlrausch, '' Der Smekal-Raman Effekt," Springer,A detailed description of the method of analysis1931 ; R. Mecke, in " The Structure of Molecules," Blackie, 193158 GENERAL AND PHYSICAII CHEMISTRY.the first.What exactly determines the relative intensities offundamentals and their corn binations is not yet clearly understood(for the selection rules give only those which are forbidden). Itfrequently happens that a fundamental is so weak as to be, to allintents and purposes, “ inactive,” although the selection rules giveit as an “ active ” frequency. This is the case in water l2 andprobably in ammonia and ph0~phine.l~ In other cases, e.g.,acetylene,14 the intensity of a combination band appears to beconsiderably greater than that of a fundamental.Another important fact is that combination frequencies are veryseldom observed in the Raman spectrum. In the particular caseof ‘‘ resonance ” with a fundamental, however, this no longer holds.Thus, in carbon dioxide l5 the overtone of the perpendicular vibra-tion (9 & 7) happens to coincide numerically almost exactly withthe symmetrical vibration (0 -> C +- 0) ; the result is that thesetwo energy levels lose their individuality, a certain proportion ofthe molecules in each vibrating in the first fashion and the remainderin the second.Thus, instead of one strong Raman line appearingcorresponding to the symmetrical vibration, and an extremelyweak one corresponding to the overtone of the perpendicularfundamental, we obtain two Raman frequencies of comparableintensity lying very close together. This phenomenon is probablypresent also in carbon tetrachloride and in the methyl halides.17Having made a provisional allotment of the possible fundamentalfrequencies, one next chooses the most likely model of the molecule,and tries to correlate the observed fundamentals with its normalmodes of vibration, the latter being deduced by classical mechanics.In this, one may apply strict selection rules, for as soon as the modelis chosen, and its vibrations determined, quantum mechanics yieldsselection rules predicting which vibrations are active in absorption,and which in Raman scattering.These rules have been derivedby several authors and are now conveniently collected in severalplaces.7918 It issufficient for our purpose to know that they depend solely on the12 E. K. Plyler and W. W. Sleator, Physical Rev., 1931, 37, 1493; also13 J. B. Howard, J .Chem. Physics, 1935, 3, 207.14 A. Levin and C. F. Meyer, J . Opt. SOC. Amer., 1928,16, 137.1 6 E. Fermi, 2. Physik, 1931, 71, 250; D. M. Dennison, Physical Rev.,16 J. Horiuti, 2. Physik, 1933, 84, 380.17 A. Adel and E. F. Barker, J . Chem. Physim, 1934, 2, 627.18 D. M. Dennison, Rev. Mod. Physics, 1931, 3, 280; L. Tisza, 2. Physik,They would take too long to reproduce here.ref. (26).1932, 41, 304.1933, 82, 48SUTWI(;LBND : SPECTROSCOPY. 50symmetry properties of the molecules, and do not involve specificassumptions about their internal structure. We may, however,consider some of their more general aspects. The appearance of afrequency in the infra-red absorption spectrum of a molecule dependson whether there is associated with that vibration of the moleculea changing electric moment.For example, the symmetricalvibration (0 I_$ C + 0) of the carbon dioxide molecule willclearly be inactive in absorption, whereas the unsymmetrical modeof vibration (0 + +- C 0 +) will be expected to cause achanging electric moment and so to be active. In the Ramanspectrum, on the other hand, it is the changing polarisability ofthe molecule which is important in determining if it will scatter lightinvolving a particular frequency; e.g., in the above two frequenciesof carbon dioxide, the selection rules for the Raman spectrum willbe the reverse of those for the infra-red. More generally, for a, mole-cule possessing a centre of symmetry, the same frequency can neverbe active both in infra-red absorption and in Raman scattering.This is of great value in assigning the fundamentals of such molecules.For molecules which have not such a, high degree of symmetry,the selection rules are more concerned with the " character " of thevibration, since, as the degree of symmetry decreases, one tends toget all frequencies active both in infra-red and in Raman scattering.The " character " of a vibration means those of its propertieswhich do not depend on tho particular force field in the molecule,but rather on its geometrical or symmetry properties, e.g., propertiessuch as whether the vibration is single or degenerate; what thedegree of degeneracy is in the latter case; whether the vibration issuch that the change of electric moment takes place only along aparticular axis of symmetry in the molecule.The last is of greatimportance, since the rotational fine structure of a vibration bandcan differ profoundly according to the direction of vibration of theassociated electric moment within the molecule.Although these selection rules will usually enable a definite modelt o be chosen for the molecule (vix., one having the required degreeof symmetry) the final assignment of particular fundamentalfrequencies to particular modes of vibration can only be madecompletely certain by an examination of the rotational fine structureof some of the observed bands. So far, this is only practicable inabsorption, since Raman scattering in the gas is too weak (withpresent methods) to give more than the central (Q) maximum of theband.Even in absorption, we are seriously limited by the lowresolving power of the spectrometer. Up to the present, the smallestline separation which can be resolved is of the order of 0-5 cm.-1.To realise the full import of this limitation, it is necessary to con60 GENERAL AND PHYSICAL CHEMISTRY.sider the rotational fine structure of the different classes of moleculein a little detail.There are two types of band, and two only, ac-cording as the vibration of the electric moment takes place along, orperpendicular to, the symmetry axis of the molecule. The line spacingin each is the same and is given by h / 4 x I ~ in frequency units. Thelinear molecules for which it has been possible to resolve this spacingare carbon dioxide, nitrous oxide, hydrogen cyanide, and acetylene.loaIt seems unlikely that many more complicated molecules can beinvestigated in this way since the spacing for nitrous oxide l9 isalready only 0.8 cm.-l.I n cases of heavier molecules, however, itis possible to make an estimate of the moment of inertia by measuringthe spacing between the intensity maximum of the P and the Rbranch of the band, which is given by the classical formula of Bjer-rum, ( ~ W ) / X . ~ O This has been done for carbon disulphide.21There are again two types of band.The first corresponds to vibration of the electric moment along thesymmetry axis of the molecule, and resembles very closely the per-pendicular type band of a linear molecule. The spacing of the linesis given by h/4x21*, and so gives no information about the moment,of inertia -lo.The other type of band associated with vibrationof the electric moment perpendicular to the symmetry axis of themolecule is very complicated indeed, consisting of sets of overlappingbands. The spacing between the lines depends on both of themoments of inertia, and so, knowing I A from the parallel bands,one might expect the deduction of I c from the perpendicular bandsto be an easy matter. That this is far from being the case is due fotwo causes: first, the excessive number of lines makes them in-capable of resolution except in a few favourable cases (vix., wherel A > l a ) , and secondly, the spacing (when it can be determined)is not found to be the same in the different bands.The latterphenomenon has long worried spectroscopists, and it is only in thepast year that this difficulty has been completely resolved. Thequalitative explanation was first given by E. Teller and L. Tisza,22who showed that it was due to the imperfect coupling which mayexist between rotation of the molecule and degenerate vibrations ofthis type in a symmetrical molecule. To put it very roughly, thevibration itself may have a characteristic angular momentumwhich can be coupled to that due to rotation of the molecule as aLinear molecules.Symmetrical top molecules.19 E. K. Plyler and E. F. Barker, Physical Rev., 1931,38, 1827.20 Here k is Boltzmann’s constant, and T the absolute temperature.21 C. R. Bailey and A.B. D. Cassie, Proc. Roy. SOC., 1931, [ A ] , 132, 236;22 2. Phyeik, 1932, ’73, 791.{bid., 1933, [ A ] , 140, 605SUTRERLAND : SPECTROSCOPY. 61whole. It is readily understandable that such a phenomenonwould lead to anomalous spacingx, as the coupling factor neednot be the same for each mode of vibration. More recently, E.Teller 23 gave a quantitative theory, in which he showed that althoughthe spacings in the separate bands could not be predicted withouta knowledge of the force constants controlling the vibrations, yetthe sum of the spacings in all the bands was a function only of themasses and of the inter-nuclear distances in the molecule.Unfortunately, Teller’s work contained some errors, but M. Johnsonand D. M. Dennison 24 have finally given the simplest expressionfor the sum of the spacings in terms of the moments of inertiaof the molecule.Thus, they were able for the first time to giveaccurately the moments of inertia of methane and the methylhalides. In cases where the moments of inertia are so large that itis impossible to resolve the individual rotation lines, a fair estimateof them may be obtained by a carefiil measurement of the separationand intensity of the two extreme maxima in the “ parallel ” bands.25For these molecules the positionis not nearly so simple. Here, as we have said, there is no explicitexpression for the rotational energy, but to each value of therotational quantum number J there correspond 2J + 1 levels, andthe selection rules governing transitions between all these levelscannot be given in a short space.The resulting band structure isextremely complex and apparently hopelessly irregular. However,given patience and a rough idea of the values of the moments ofinertia, there is no reason why it should not be analysed and thishas been accomplished successfnlly for waterySB hydrogen sulphide,27formaldehyde,28 and ethylene.29 It will be noticed that each ofthese molecules contains at least one hydrogen atom, and it is veryunlikely that any asymmetrical top molecule not containing ahydrogen atom will have its vibration-rotation analysed for along time to come. The resolving power of present spectrometerswill have to be improved by an order of magnitude before sufficientstructure will be obtained to justify an attempt at analysis.Yetthe position is not so hopeless as this sounds, for, as in the othertypes of molecule, the contour of the unresolved band gives someguide as to its f0rrn,~0 Thus, it appears that the contour of a band2.1 LOC. cit., ref. (7).2 5 S . L. Gerhard and D. M. Dennison, {bid., 1933, 45, 197.26 R. Mecke, 8. Physik, 1933, 81, 313; R. Mecke and W. Baumann, ibid.,p. 445; K. Freundenberg and R. Mecke, ibid., p. 465.27 P. C. Cross, Physical Rev., 1935, 47, 7.28 H. H. Nielsen, ibid., 1934, 46, 117.29 R. M. Badger, ibid., 1934, 45, 648.313 D. M. Dennison, Rev. Mod. Physics, 1931, 8, 280.AsynzmetricaE top molecules.24 Physical Rev., 1935,4’9, 93 ; 48, 86862 GENERA& AND PHYSIUAL CHEMISTRY.which corresponds to a vibration of the electric moment along thegreatest axis of inertia will exhibit a strong but rather broad central(Q) maximum together with symmetrically disposed minor (P andR) maxima.For a vibration along the middle axis of inertia, onewould expect the central (Q) branch to be absent, while for avibration along the least axis of inertia, a very sharp and well-defined Q branch is to be expected in addition to the '< P " and " R ''maxima. These qualitative rules are well exemplified in the spectraof water,31 hydrogen ~ulphide,~~ ethylene,33 and sulphur dioxide,34but attempts to apply them quite generally, e.g., to ozone35 andnitrogen peroxide,36 have led to difficulties. This is not surprisingseeing that they are only an extrapolation from calculations on thepossible transitions for J < 5.It may be that future theoreticalwork will lead to their being modified for heavier molecules.To sum up, it is now possible to determine the general form andfundamental frequencies of the simpler polyatomic molecules,and to assign each fundamental to a particular mode of vibrationof the model. Only in the hydrogen-containing molecules (and a fewlinear ones such as carbon dioxide or carbonyl sulphide) does itseem possible to obtain accurate values of the moments of inertiawithout a great increase in resolving power of spectrometers in theinfra-red. The only obvious line of advance would be t o observeovertones (instead of fundamentals), which fall in the photographicregion.Unfortunately, it is just those molecules whose overtoneshave a measurable intensity in the photographic region, v k , thehydrogen-containing ones, which are already amalysed.Although an immense amount of workhas been done on the electronic spectra of polyatomic molecules,there is remarkably little which can be said to be of significancefrom the true spectroscopic point of view ; in other words, very littleof it can be interpreted to yield the energy states of the absorbingor emitting molecule. This is not surprising, since the theory ofsuch spectra has only been developed in the last three years. Thefirst step was made by R. S. Mulliken 37 who showed how the elec-tronic levels may be classified by means of their symmetry properties,C.EEectronic spectra.31 E. K. Plyler and W. W. Sleator, Physical Rev., 1931, 37, 1493; and32 A. D. Sprague and H. H. Nielsen, ibid., 1933, 43, 375.33 A. Levin and C. F. Meyer, J . Opt. SOC. Amer., 1928, 16, 137.34 C. R. Bailey and A. B. D. Cassie, Proc. Roy. SOC., 1932, [A], 137, 622;35 G. Hettner, R. Pohlmann, and H. J. Schumacher, 2. Phpik, 1934,91,372.3C G. B. B. M. Sutherland and W. G. Penney, Nature, 1935,135,958.s7 Physical Rev., 1932, 40, 55; 41, 49; 1933, 43, 279; J . Chern. Physics,ref. (26).C. R. Bailey, A. B. D. Cassie, and W. R. Angus, ibid., 1930, 130, 133.1933, 1, 492; 1935,3, 375, 506, 514, 517, 564, 635, 720SUTHERLAND : SPEUTROSCOPY. 63and by extrapolating from close analogies with well-known diatomicspectra. G.Herzberg and E. Tellor, and others,38 have now con-sidered the selection rules which govern the associated vibrationaltransitions, while the rules for the rotational transitions followreadily from those applicable to vibration-rotation spectra. Togo into all these matters in detail is impossible in the space allotted,and we reserve their discussion for a future Report. We can nowonly mention a few of the more siiccessful attempts to apply andtest the theory.The first electronic spectrum to be analysed was that of formalde-hyde. The rotational structure of several bands was analysed byG. H. Dieke and G. B. Kistiako~sky,~~ enabling them to give themoments of inertia of the molecule in the ground and excited stateswith considerable accuracy.The interpretation of the electronictransition and the deduction of the nature of the electronic states isdue to R. S. M~lliken.~~ Another important success was achievedin the methyl halides,41 although in this case the rotational structurecannot yet be satisfactorily resolved. E. Eastwood and C. P. Snow 42have examined the spectra of a series of aldehydes; it appears fromtheir results that these are not due (as was formerly supposed) tothe excitation of an electron in the carbonyl bond, but to theexcitation of one of the non-localised electrons of the carbon atom.They also obtained some remarkably simple bands from acraldehyde,which could best be represented as isolated R branches fitting theusual parabolic formula. Unfortunately, these do not give consistentvalues for the corresponding " moment of inertia " and theirexplanation is at present obscure.Other molecules with whichsome progress has been made are S02,43 C2H2,44 C2H4,45 NH3,46CO,:' CS2,$8 HCN,49 and N2H4.49There is one very important advance on the experimental sideto be reported. This is the development of a new type of Lymancontinuum for the extreme ultra-violet by G. Collins and W. C.3* Z. physikal. Chem., 1933, [B], 21, 410. Also A. E. F. Duncan, J. Chem.Physics, 1935, 3, 384.Physical Rev., 1934, 45, 4. 40 Ibid., 1935, 47, 413.41 Refs. (38) and (40). 42 Proc. Roy. SOC., 1935, [ A ] , 149, 434.43 J. H. Clements, Physical Rev., 1935, 47, 224; R. K. Asundi and R.44 W. C. Price, Physical Rev., 1934, 45, 843; ibid., 1935, 47, 444; H.4 6 H.J. Hilgendorff, 2. Physik, 1935, 95, 781; see also refs. (38) and (44).4 6 A. B. F. Duncan, Physical Rev., 1935, 47, 822.47 Idem, J . Chem. Physics, 1935, 3, 384.4 8 W. W. Watson and A. E. Parker, Physical Rev., 1931, 37, 1013; and49 H. J. Hilgendorff, 2. Physik, 1935, 95, 781.Samuel, Proc. Indian Acad. Sci., 1935, 2A, 30.Gopfert, 8. wi8s. Phot., 1935, 34, 156.ref. (47)64 GENERAL AND PHYSICAL CHEMISTRY.P r i ~ e . ~ o As a result, W. C. Price 51 has been able to photographabsorption spectra of many polyatomic molecules as far down as300 A. He has found the very interesting result that most of thesimple molecules exhibit bands in this region which can be arrangedin Rydberg series. He has thus been able to find the ionisationpotentials of several of the simpler molecules such as acetylene,ethylene, water, hydrogen sulphide, and the methyl and ethylhalides.Spectra of Deuterium Compounds.-The early work on the spectraof deuterium and its simpler compounds has already been reviewed ;52this report is accordingly confined almost entirely to work which hasappeared during the past year.For the best documented anddetailed report of the early work the review of H. C. Urey and G . K.Teal 53 is, of course, the standard reference. Work on the spectraof deuterium compounds has, roughly speaking, one of four objectsin view : (1) the investigation of the accurate theory of the isotopeeffect in diatomic spectra and the elucidation of certain perturbationproblems in such spectra, (2) the determination and assignmentof doubtful fundamental frequencies in polyatomic molecules,(3) the determination of internuclear distances in polyatomicniolecules containing hydrogen, and (4) the determination ofpotential functions for polyatomic molecules.As regards (l), certain difficulties arose when it was found byW.Holst and E. Hulthkn 54 that the “ B values ” (these define thespacing of the rotational structure of the band) did not have theexpected ratio for A1H and A1D. These authors explained this asdue to the neglect of the moment of inertia of the electron cloud.R. de L. K r ~ n i g , ~ ~ however, gave an entirely different explanationbased on the fact that a certain interaction term giving the reactionof the nuclei to the precession of the electronic angular momentumhad been neglected.Unfortunately, Kronig’s theory cannot givethe whole truth for, according to it, there should be no anomalyfor DC1, LiD, or NaD. Now, although the first does not have thean0maly,~6 the other two do.57 The whole theory has been carefullyreviewed by G. H. Dieke,58 who has shown that Kronig’s theory50 Rev. Sci. In&+., 1934, 5, 423.51 Ref. (44); J . Chem. Physics, 1935, 3, 256.52 Ann. Reports, 1933 and 1934.54 2. Physik, 1934, 90, 712.5 8 J. D. Hardy, E. F. Barker, and D. MI. Dennison, Physical Rev., 1932,57 F. H. Crawford and T. Jorgensen, ibid., 1934, 46, 746; E. Olsson, 2.Physical Rev., 1935, 47, 661; 48, 606; G. H. Dieke and R. W. Blue,53 Rev. Mod.Physics, 1935, 7, 34.65 Phy8ica, 1934, 1, 621.42, 279.Physik, 1935, 93, 206, 816.ibid., 1935, 47, 261SUTHERLAND : SPECTROSCOPY. 65(supplemented by corrections for anharmonic factors) will accountcompletely for the isotope effect in the spectra of HD and D,, butthat it is not capable of explaining the defects of heavier molecules.Since then, more experimental work has been done,59 and the im-portance of anharmonic corrections demonstrated.GO The completetheoretical explanation is still, however, some way from achievement.The determination and assignment of doubtful fundamentalfrequencies by means of the isotope effect is likely to become oneof the more important applications of the discovery of deuteriumto spectroscopy. A very striking example is afforded by benzene,for which there has long been the anomaly that certain of the Ramanfrequencies appear to coincide with fundamental absorption fre-quencies in the infra-red. The apparent conclusion that thebenzene molecule does not have a centre of symmetry has not foundfavour in view of the theory of " resonance " between possibleKekul6 structures.If, however, this coincidence of infra-red andRaman frequencies were purely fortuitous, then it would not beexpected to occur for the isotopic form, hexadeuterobenzene.Recent work here 61 and in America,62 although not yet final, alltends to show that the agreement was indeed fortuitous, andthat benzene is symmetrical. Other applications towards theassignment and identification of fundamentals have been made inthe cases of water,63 ammonia, p h ~ s p h i n e , ~ ~ and chloroform.65In the third type of application we would mention the accuratedetermination of all the internuelear distances in the moleculesacetylene,6G hydrogen ~yanide,~ 7 methane,G8 and ammonia.68aThe final and possibly most important application is in connexionwith the determination of the most suitable potential function to69 F. H. Crawford and T. Jorgensen, Physical new., 1935,47,358,932 ; W. W.Watson, ibid., p. 27; A. Guntsch, 2. Physik, 1935, 93, 534; B. Grundstrom,ibid., 1935, 95, 574; Y. Fujioka and T. Wada, Sci. Papers I n s t . Phys. Chem.Res. Tok?yo, 1935, 27, 210.60 P. G. Koontz, Physical Rev., 1935, 48, 138.W. R. Angus, C. R. Bailey, C.K. Ingold, A. H. Leckie, C. G. Raisin,J. W. Thompson, and C. L. Wilson, Nature, 1935, 135, 1033 ; 136, 680.62 R. B. Barnesand R. R. Brattain, J . Chem. Physics, 1935, 3,446; R. W.Wood, ibid., 3, 444.G3 C. H. Cartwright, Nature, 1935, 136, 181; R. Ananthakrishnan, Mem.Ind. Inst. Sci., 1935, 2, No. 21, 291.64 J. B. Howard, J . Chem. Physics, 1935, 3, 207.65 R. TYV. Wood and D. H. Rank, Physical Rev., 1935, 48, 63.6 6 G. Herzberg, F. Patat, and J. W. T. Spinks, 2. Physik, 1934,92, 87.67 P. F. Bartunek and E. F. Barker, Physical Rev., 1935, 48, 516.6s N. Ginsburg and E. F. Barker, ibid., 1935, 47, 641; J . Chenz. Physics,685 R. B. Barnes, Physical Rev., 2935, 47, 658; E. F. Barker and M.1935, 3, 668.Migeotte, ibid., p. 702.REP.-vOL. XXXII.66 GENERAL AND PHYSICAL CHEMISTRY.represent the force field controlling the vibration of the atoms in apolyatomic molecule. Many attempts have been made to do this,69but none has been more than partially successful, since more con-stants are required to define the force field than there are frequenciesby which to determine them. The introduction of a deuterium inplace of a hydrogen atom leaves the force field unchanged (to thedegree of approximation involved here) while yielding a new set offrequencies. The problem then is no longer indeterminate. Con-versely, any force field which was chosen in an empirical way toagree with the earlier data, may now be tested by qeeing how wellit predicts the frequencies of the deuterium compound. Thegeneral theory of the isotope effect has been given by severalauthors ; 7* applications have already been made to acetylene,71waterY72 hydrogen cyanide,67 ammonia,73 phosphine,6* methane,aiid the methyl halides.74 G.B. B. M. S.4. THE DETERMINATION OF THERMODYNAMIC CONSTANTS FROMSPECTROSCOPIC DATA BY STATISTICAL METHODS.The energy of a molecule may be divided into two independentparts : one is concerned with translation only, and the other involvesall forms of internal energy. The portion, due to translation, of athermodynamic function, e.g., entropy, total energy, or heat capacity,of any molecule in the ideal gaseous state is virtually the whole ofthe value for a monatomic gas. This problem has been treated bya number of authors,l and the equation for the entropy of a mon-atomic gas-the well-known Sackur-Tetrode equation-may bewrittens = R [ ~ ~ ( Z ~ I ~ ~ T ) ~ / ~ V V / I L ~ N + ;-I .. . (1)See Ann. Reports, 1934, 31, 21 ; J. E. Rosenthal, Physical Rev., 1934, 45,426 ; 46,730 ; ibid., 1935,47,235 ; G. B. B. M. Sutherland and D. M. Dennison,Proc. Roy. SOC., 1935, [ A ] , 148, 250; A. B. D. Cassie, ibid., p. 87.70 E. Teller, loc. cit., ref. ( 7 ) ; 0. Redlich, 2. physikal. Chem., 1935, [B],28, 371 ; J. E. Rosenthal, loc. cit.71 G. B. B. M. Sutherland, Nature, 1934, 134, 7 7 5 ; W. F. Colby, PhysicalRev., 1935, 47, 388; Y. Morino, Sci. Papers Inst. Phys. Chem. Res. Tokyo,1935, 25, 232 ; 27, 39 ; see also ref. (66).72 L. G. Bonner, Physical Rev., 1934, 46, 458; J. E. Rosenthal, Eoc.cit.,ref. (69); R. Ananthakrishnan, loc. cit., ref. (63).73 M. F. Manning, J . Chem. Phyeics, 1935, 3, 136; see also ref. (64).74 M. Johnson and D. M. Dennison, Physical Rev., 1935, 47, 93; 48, 868.0. Sackur, Ann. Physilc, 1911, 36, 958; 1913, 40, 67; A., 1912, ii, 145;1913, ii, 128; H. Tetrode, ibid., 1912, 38, 434; 1913, 39, 255; 0. Stern,Physikal. Z., 1913, 14, 629; Z. Elektrochem., 1919, 25, 66; A., 1919, ii, 219;P. Ehrenfest and V. Trkal, Proc. K . Akad. Wetensch. Amsterdam, 1920, 23,162; Ann. Physik, 1921, 65, 609; A , , 1920, ii, 738; L. S. Kassel, Chem.Reviews, 1936, in the pressGLASSTONE : DETERMINATION OF THERMODYNAMIC CONSTANTS. 67where R is the gas-constant, k the Boltzmann constant, m the weightof a single molecule, T the absolute temperature, V the volume of1 g.-mol.in c.c., h the Planck constant, and N the Avogadro number.This expression represents the translational entropy of any idealgas, and for practical purposes at 1 atm. pressure, it may be put.in the formR is now expressed in calories, and M is the molecular weight ofthe gas. Similarly the translational energy of any gas has thevalue $BT per g.-mol., and the corresponding heat capacity isgB ; these results follow, of course, from the kinetic theory.For polyatomic molecules the portion of the various thermo-dynamic functions due to internal energy must now be considered .2If the Maxwell-Boltzmann distribution law applies to a system, thenthe number of molecules in any state represented by i, is piAe4"lkT,pi being the " a priori probability " or " statistical weight " of theith state, A the number of molecules in the state of lowest internalenergy, and ci the internal energy per molecule in the given state,with reference to the lowest energy state.* The statistical weightrepresents the degeneracy, or multiplicity, of the energy level underconsideration: in terms of wave mechanics it is the number ofproper values (eigenvalues) which satisfy the wave equation for themolecule in the particular quantum state.Actually these valuesdo not correspond to states of identical energy, but the differencesare so small that they may be grouped together in one state witha probability p equal to the number of eigenvalues. In 1 g.-mol.of a gas the total number of molecules, i.e., the Avogadro number,is equal to the sum of the molecules in the various states characterisedby i = 0, 1, 2, 3, .. . ; hence N = AXpe-e/kT. Similarly,the internal energy of all the molecules in a given state is &pAe-&lkT,and the total internal energy Eojnt. of 1 g.-mol. of gas, with referenceto the zero state, is A&pe-&IkT. Combining this relationship with theequation for N , it follows thatSotr. = &RlnM + &RlnT - 2.300 . . . (2)2 The treatment given here is essentially that of W. F. Giauque, J. Amer.Ghern. SOC., 1930, 52, 4808.* The convention adopted in the treatment given here is to take as thezero the energy of the molecule at rest and with vibrational and rotationalquantum numbers equal to zero ; i.e., the value of E is effectively the diflerencebetween the total engrgy and the zero-point energy (the energy a t 0" Abs.).It will be seen later (p.70) that some authors take the molecule in its dis-sociated state, i.e., in the form of atoms, t o represent the zero from whicht o take the E values. Whichever convention is adopted, the final resultxnuat be the same (compare R. H. Fowler, " Statistical Mechanics," 1929,p .26, footnote)68 GENERAL AND PHYSICAL CHEMISTRY.where Q is equal to Cpe-&IkT, and is known as the “ summation ofstate ” or “ state sum ” (“ Zustandsumme,” Planck) or “ partitionfunction ” (Fowler). Strictly speaking, the equation given appliesonly if the Maxwell-Boltzmann distribution holds, and this is cer-tainly not the case for real gases, especially a t low temperatures;the assumption of an ideal gas, however, permits the use of the.classical law, and in any case a t appreciable temperatures theBose-Einstein and Fermi-Dirac statistics lead to the same result .3The differentiation of Eoht.with respect to temperature givesan expression for the heat capacity of a perfect gas due to internaldegrees of freedom,4 thusAlternatively, this equation can be writtenwhere XA = Q ; U3 = ET2(dQ/dT); and XC = 2E2T3(dQ/dT) +k2T4( d2Q/dT2).By making use of the definition of internal entropy in the formdXint. = Cint. d In T , it follows that the entropy due to internaldegrees of freedom is given byXoint. = R[ln Q + T d In QldT] . . . . . .(7)= R[lnA + (l/kT)(CB/CA)] . . . . (8)= R[ln Cpe-&IkT + C ~ ~ e - & ‘ ~ ~ / k T C ~ e - & l ~ ~ ] . (9)From any of these equations it is possible to calculate the internalentropy of an ideal gas, and the addition of the translational entropy,equation (2), gives the value of Xo7 the total entropy a t atmosphericpressure. If necessary, a correction can be applied for deviationsW. F. Giauque, loc. cit.; G. N. Lewis and J. E. Mayer, Proc. Nat. Acad.Sci., 1929, 15, 208; A., 1929, 648; W. H. Rodebush, Chern. Reviews, 1931,9, 319; H. L. Johnston and M. K. Walker, J . Amer. Chem. SOC., 1933, 55,182 (footnote).Cf. F. Rciche, Ann. Physsik, 1919, 58, 657; H. C. Urey, J . Amer. Chem.Soc., 1923, 45, 1445; A . , 1923, ii, 533; R. C. Tolman and R.M . Badger,ibid., 1923, 45, 2277; A., 1923, ii, 830; H. C. Hicks and A. C. G. Mitchell,ibid., 1926, 48, 1520; A., 1926, 784.H. L. Johnston and A. T. Chapman, ibid., 1933, 55, 153; A., 1933, 229.H . C. Urey, Zoc. cit.; R. C. Tolman and R,. B!L Badger, Zoc. cit.; H. C.Hicks and A. C. G. Mitchell, loc. citGLASSTONE : DETERMINATION OF THERMODYNAMIC CONSTANTS. 69from ideal behaviour, but this is quite small, especially a t temper-atures high enough to be of chemical interest.'The free energy Po in the standard state, i.e., ideal gas a t I atm.pressure, may be expressedPo= E"+IZT-TS" . . . - (10)where E" and X" refer to the total energy and entropy, respectively,including the translational terms. The total energy E'" must alsoinclude the energy of the gas a t assumed zero state, i.e., the zero-point energy (Eoo), in addition to the energy of translation (gRT),and the internal energy (Eoint.) obtained from equation (3).Itfollows, therefore, thatF" - Eoo = - 4RT Jn M - SRT In T - RT In Q + 7.267T (11)By combining the F" - E," values for resultants and reactants,it is possible, provided Q be known, to determine A(F" - Boo) fora chemical reaction, and this is related to the thermodynamicequilibrium constant. By definition, in this case, AF" = - RT In Ifpwith pressures in atms., and hence- A(F" - Eoo) = RT In K p + AE," . . (12)The calculation of Kp for a reaction involves a knowledge of- A(F" - E,") for the substances concerned in the process,evaluated from equation (ll), and of AE," for the reaction as awhole.The latter quantity may be determined by combiningappropriate spectroscopic data for heats of dissociation, since theseare values for the lowest energy level, or by means of the zero-point energies of the molecules, including all modes of vibration,also obtained from band spectra. The Eoo for an atom must bestated on the basis of the assumed energy zero as a moZecuZe.Alternatively, if AH", the heat of reaction a t constant pressure, isknown, then since H" = E" + RT, it can be readily shown, by meansof equation (lo), thatAE," = AH" - A[-ZRT + RT2(dln&/dT)] . (13)The factor + 7-267 in equation (11) arises, as may be seen froma consideration of this and equations (1) and (2), from the termR In (2xk/h2N)3'2k/a, where a is the normal atmosphere in dynes persq. em., i.e., 1.0132 x 106, and if this is introduced into equation(1 1) it becomesF" - E," = - R T I n [$(2,m~T/h2)3/2k/'ja] .(14)7 See, e.g., W. IF. Giauque, J . Amer. Chem. SOC., 1930, 52, 4822; A. R.Gordon, J. Chem. Physics, 1933,1, 30870 GENERAL AND PHYSICAL CHEMISTRY.A further obvious modification leads toPo == - AT In ([e-"oo/"~Q(2xmrcT/h)3'2](kT/a)) . (15)- RTlnG(kT/a)* . . . . . . ' (16) -where G is equal to the term in the square brackets.it is evident, since AF" = - RT In K p thatFor anyreversible chemical reaction aA + bB . . . J --- mM + nN . . . ,where v = (m + n + . . .) - (a + b + . . .). Some authors omitthe factor (kT/a)', thus giving Ke with concentrations expressed inmolecules per c.c., whereas others omit a only, which gives Kpwith pressures in dynes per sq.em. instead of in atmospheres. If vis zero the IPS are, of course, all identical. The quantity G, whichmay be regarded as the complete partition function of any molecularspecies under given conditions, is made up of three separate terms.The portion (2mET/h2)3/2 is effectively the partition function fortranslatory motion with three degrees of freedom,s and Q is thefunction for vibration and rotation, including nuclear-spin effectsand internal rotation within the molecule ; there still remains the" zero-point '' factor e--Eo"/RT. If the zero of energy, for the purposeof calculating the vibrational and rotational partition function, istaken as the energy of the free atoms,g formed by the molecule whencompletely dissociated, at their lowest levels, then a quantitye-Eo''RT actually becomes included in the vibrational function, Eo'being the heat of dissociation of the molecule a t 0" Abs.The energyterm in the " zero-point " factor is altered by this same amount,thus leading to a value identical with G for the partition functi0n.t8 R. H. Fowler, " Statistical Mechanics," 1929, p. 114.* The corresponding equation for hydrogen given by E. Teller and B.Topley (J., 1935,877) should not contain the EOo term (private communicationfrom Mr. B. Topley). The position of the large bracket also appears to havebeen misprinted. t The subjects of equilibrium constants and partition functions have beendealt with at length because of the apparent confusion facing a newcomerto the literature.Writers who employ Q generally use it in the sense definedabove, and Q' is often used for e-Jo'IRT X Q , but not consistently. H. C.Urey and D. Rittenberg ( J . Chem. Phylsics, 1933, 1, 137) define Q withoutthe zero-point factor, but H. C. Urey and G. K. Teal (Rev. Mod. Physics, 1935,'7, 52) include it in some cases, although not in others. H. C. Urey and L. J.Greiff ( J . Amer. Chem. SOC., 1935, 57, 321) define the " summation of state,"given the symbol Q , to include the e-~oo/Rp term, and use f, which is equal toGkT, as the " distribution function." The " distribution function " f ofR. H. Crist and G. A. Dalin ( J . Chem. Phy8ic8, 1934, 2, 735) is virtuallyIdem, ibid., p.103BLASSTONE : DETERMINATION OF THERMODYNAMIC CONSTANTS. 71In order to apply the equations given above to evaluate thermo-dynamic constants, the essential point remaining is the determinationof Q : to calculate this quantity the pe-E/kT terms must be summedover all possible energy states of the molecule. The energy of eachstate can be obtained from spectroscopic data with the aid of thefundamental equation of the quantum theory, E = hcv, but there issome difficulty in the assignment of the correct statistical weights( p ) ; it was the use of incorrect values which invalidated the earlierapplications lo of some of the equations deduced here. The prin-ciples involved in the determination of the partition function, whichare based on wave mechanics, may be conveniently consideredseparately for (a) atoms and monatomic molecules, ( b ) diatomic,and (c) more complex molecules.Atoms and Monatomic Molecu.les.--The value of Q is given by theproduct of the function for nuclear-spin orientation and that forevery possible electronic configuration.The nuclear-spin functionis equal to the corresponding statistical weight, since E is zero, andis given by 2is + 1, where is is the number of units of nuclear-spin momentum; this quantity represents the total number ofpossible orientations, having nearly the same energy, of the nucleusin a perturbing field. The p factor for each electronic configurationis 2js + 1, where js(= I 5 s), which cannot be negative, resultsfrom the combination of the azimuthal quantum number (1) and theresultant spin (s) of the electrons; to obtain the partition functionthis weight must be multiplied by e-&lkT for the appropriate state,and summed over all possible configurations indicated by spectro-scopic data.This apparently impossible task is simplified by thefact that the quantity e-&lkT has a significant value only a t temper-atures exceeding hcv/4lc, where v in cm.-1 is the frequency separationof the given energy level above the ground level.ll Hence, it isonly at high temperatures that any level other than the groundstate ( E = 0) need be considered. With atomic hydrogen, foridentical with our C, and so also, apparently, is the G of E. Teller and B.Topley (J., 1935, 876), although the latter authors employ a different energy-zero convention.The partition function P employed by B. Topley and H.Eyring ( J . Chem. Phyt?/sics, 1934, 2, 217) is evidently e--Bo'/RE times the productof Q and the translational factor; since ABo' is equal to AE,', this function Ir'may replace C. in the calculation of equilibrium constants. The partitionfunction F used in chemical kinetics (see p. 94) is G with the zero-pointfactor omitted.10 H. C. Urey ; R. C. Tolman and R. M. Badger; H. C. Hicks and A. C. G.Mitchell, Eocc. cit., ref. (4); see also D. 5. Villars, Proc. iVut. Acad. Sci., 1929,15,705; 1930,16,396; A., 1929, 1236; 1930, 1121.11 J. E. Mayer, S . Brunauer, and M. C:. Mayer, J . Amer. Chem. SOC., 1933,55, 37; A., 1933, 218; H.Zeke, 2. Elektrochem., 1933, 39, 76272 GENERAL AND PHYSICAL CHEMISTRY.example,12 is = +, and so the corresponding partition function is2 ; the electronic ground level (n = 1) is a singlet state with j, = 4,and since E = 0, the electronic function is also 2. Since no higherlevel need be considered, the complete partition function is 4, therebeing no vibrational or rotational energy for an atom. The nuclearspin of the chlorine atom is $, and so the nuclear-spin function is 6 ;spectroscopic evidence indicates the ground state to be an inverted2P doublet, with js values of $- for the lower and 8 for the upperlevel, the frequency separation being 851 cm.-l. The statisticalweights for the two levels, i.e., 2js + 1, are 4 and 2, respectively,and hence the electronic partition function is 4 + 2e--881hc/kP;the complete function for the atom is then obtained by multiplyingby 6 for the nuclear spin.No other energy levels need be consideredfor all reasonable temperat~res.1~ The ground level of normalatomic oxygen is an inverted 3Y term, the js values being 2, 1, and0, respectively, and the frequency separations 157.4 cm.-l and226.1 cm.-l; the electronic partition function is thus 5 + 3e-157.4hc/k' + 1e-226.1hc/kP. At high temperatures it is also necessary to includethe contributions for the two metastable levels consisting of lDZand lX0 terms, respectively. Since the oxygen nucleus has no spin,is = 0, the complete partition function is the same as the electroniccontribution.l* The literature may be consulted for other cases,which present no novel features.15Diatomic Molecules.-The Q value for a molecule containing twoor more atoms involves summation over every possible electronic,vibrational, and rotational state ; in general, electronic levels abovethe ground state necd no$ be considered, for reasons already given.The multiplicity, if any, of the ground level must, however, be in-cluded. Most diatomic molecules have 12 ground terms, and sothere are no multiplet levels; nitric oxide, oxygen, hydroxyl, andthe cyanide radical, amongst others, are, however, exceptional.16The energy separation of successive vibrational levels is relativelysmall, and so it is necessary to sum the pe-&lkF terms over severallevels; unless approximation methods are used (see below), only afew of the lowest states are actually included, especially at low12 W.3'. Giauque, J . Amer. Chem. SOC., 1930, 52, 4816; A., 1931, 294.l3 W. F. Giauque and R. Overstreet, ibid., 1932, 54, 1731; A., 1932,695.14 H. L. Johnston and M. K. Walker, ibid., 1933, 55, 187; A., 1933, 229;G. van Elbe and B. Lewis, ibid., p. 507 ; A., 1933, 350.15 W. F. Giauque and J. 0. Clayton, ibid., p. 4875; L4., 1934, 135; H. L.Johnston and E. A. Long, J . Chem. Physics, 1934, 2, 389; A., 1934, 951;C. W. Montgomery and L. S. Kassel, ibid., 1934, 2, 417; A., 1934, 966; H.Zeise, 2. Elektrochem., 1934, 40, 665.l6 W. Jevons, '' Band Spectra of Diatomic Molecules," 1932, Appendix IIGLASSTONE : DETERMINATION OF THERMODYNAMIC CONSTANTS.73temperatures. For example, with hydrogen it is only the lowestvibrational level (v = 0) which contributes appreciably to thepartition function at temperatures below 900" Abs. ; even a t 2000"Abs. only the first four levels (v = 0, 1, 2, 3) nced be considered.17With oxygen and nitric oxide, however, five levels must be includedbelow 900" Abs., the number increasing up to 12 a t 2000" Abs., ineach multiplet.l*Each rotational state has, in addition to the rotational degeneracyresulting from nuclear spin, a statistical weight of 2J + 1, whereJ is the rotational quantum number. If the molecule has two,similar nuclei with spin is, the total statistical weight of each rota-tional level in a Cf state is obtained by multiplying the 2J + 1value by the nuclear-spin factor (i, i- a)(%, + l), for even values ofJ (including zero), and by i, (Zi, + 1) for odd values of J , if the nucleifollow the Bose-Einstein statistics, but the factors are reversedif the Fermi-Dirac statistics are followed.Ordinary hydrogenobeys the latter statistics, and since i, = 8, even levels have pvalues equal to 2J + 1, and for odd levels they are 3(2J + I),resulting in the well-known alternation of the spectral lines, and theproportions of o- and p-hydrogen in the normal gas. Deuteriummolecules, on the other hand, have is = 1, and follow the Bose-Einstein statistics; hence the statistical weights for even andodd levels are 2(2J + 1) and 2J + 1, respectively.The nuclear spin of the oxygen atom is zero, and consequentlyfor the symmetrical 0l6Ol6 molecule, the main constituent of oxygengas, alternate rotational levels have statistical weights of 2J + 1and zero; only alternate rotational levels, for odd values of J , areconsequently present, the normal state being 3C,- and the Bose-Einstein statistics being followed.20 The components of the tripletterm have been called the Fly F2, and F, coupling states (Hund'scase-b).The coupling energy of the %12 state is about 2 cm.-l(ca. 6 cals.) : this amount is so small that all three states may beregarded as having the energy of the lowest level, i.e., 6 = 0. Thevalue of J in calculating the rotational statistical weight is determinedby the rotational quantum numbers, which are K + 1, K , and K - 1,respectively, for the levels F,, F,, t-md F3, only odd values of Kbeing permitted ; the corresponding y values are, therefore, 2K + 3,2K -t 1, and 2K - 1, where K has the values 1, 3, 6, etc.The1 7 C. 0. Davis and H. L. Johnston, J. Amer. Chem. SOC., 1934, 56, 1045;18 H. L. Johnston et ul., ibid., 1933, 55, 153, 172; A,, 1933, 229.19 G. N. Lewis and M. F. Ashley, Physical Rev., 1933, 43, 837; H. C. Urey20 W. Jevons, op. cit., p. 290, etc.A., 1934, 722.and D. Rittenberg, J. Chem. Physics, 1933,1, 137; A., 1934, 30.c 74 GENERAL AND PHYSICAL CHEMISTRY.rotational contribution to the partition function is then given by thethree summations 21z(2K + 3 ) e - E m K W + C(2K + l ) e - & w K P T + C(2K - l ) e - E m K ) / k T .In addition to the ground state, two excited states, vix., lAg+ at 0.97e.v., and lEg+ at 1-62 e.v., above the ground level, must be con-sidered; the former 21 has a noticeable effect only at 1000" Abs.,and the latter 22 a t 2500" Abs.If a diatomic molecule has two dissimilar nuclei, having spinsis and ifs, the nuclear-spin factor, by which the 2J + 1 value forevery level is to be multiplied, is (2i, + 1 ) ( 2 i : + 1) to obtain thecomplete rotational statistical weight.For a 1Z molecule, theapplication involves no complications, but where other types ofground terms have to be considered the necessary factors must beincluded. Nitric oxide in itseground state is Qi7; (Hund's case-acoupling), with a frequency separation of about 120 cm.-l, whichis too large to be ignored; for the lower level the smallest value ofJ , here also the effective rotational quantum number, is 8, whereasfor the upper level it is G, subsequent values increasing in steps ofunity.Except in C states, each rotational level is split into twoslightly separated sub-levels, the phenomenon being known as A-typedoubling.23 The frequency separation of the doublet is generallyso small that the energies may be regarded as identical, so that theeffect is merely to double the statistical weights. The completerotational partition function for nitric oxide is thus : 24B = l , 3 , 5 . . . K = 1 , 3 , 6 . . . K = l , 3 , 6 . . .2 x 3C(2J + l)e-"JkT + 2 x 3 C ( 2 J + 1 ) e - Y k rwhere 2 and 3 are the A-type doubling and the nuclear-spin factor,and E J and E; refer to the energies in the 211t and the 2flG state,respectively, for various values of J .At 298.1" Abs., no more thanthree values of J need to be included in each sum.The hydroxyl radical has an inverted 211 ground term, so that the2II: is lower than the 211* level; the separation of rotational statesinto A and B sub-levels, due to A-type doubling, is unusually large,and so, except a t high temperatures, it is not sufficient merely todouble the statistical weights as is the case with nitric oxide. Therotational partition function is therefore obtained as the sum offour 2C(2J + l)e-EJ/kT terms, with different sets of EJ values for the21 H. L. Johnston and M. K. Walker, J . Amer. Chem.~Soc., 1933, 55, 172;A . , 1933, 229.22 Jdem, ibid., 1935, 57, 682; A., 690.z3 W. Jevons, op. cit., p. 126.24 H. L. Johnston and A. T. Chapman, t7. Amer. Chem. SOC., 1933, 55,J = l 3 5 2 ) '13 '1 . . . J = l 'I 'I 2, 2 , '1 . . .153, 229QLASSTONE : DETERMINATION OF THERMODYNAMIC CONSTANTS. 75A and B rotational levels of each constituent of the d0ublet.2~The factor 2 is the nuclear-spin contribution, since is is Q for hydrogen,and zero for oxygen.Since the cyanide radical has a 2C. ground term, there is noA-type doubling, although every rotational level is a duplet. Thevalue of J for one set (P,) is equal to K -t Q, and for the other (F2)it is K - Q, where K , the rotational quantum number, can haveany integral value, including zero ; when K = 0, however, the corre-sponding F2 level is missing.The p values of the P, and F2 seriesare, therefore, 2K + 2 and 2K, respectively, each being then multi-plied by the nuclear-spin factor 3, since the spins of the carbon andnitrogen nuclei are 0 and 1, respectively. The complete rotationalpartition function 26 for this radical is consequently3C(2K + 2)e-c~(m’kp + 3C.2Ke-Em~dk(rK = 0 , 1 , 2 , 3 . . . K = l , 2 , 3 . 4 . . .Energy Values.-In the early applications 27 of the partitionfunction for the determination of fhermodynamic constants, theenergies of the rotational levels were calculated from the actualfrequencies of the spectral lines of the molecules concerned, thelowest rotational level in the v = 0 vibrational band being taken asthe zero point.Recent analyses of band spectra, however, havepermitted the expression of the frequencies of the lines of a givenelectronic level, for diatomic molecizles, in the form of equations ofthe type 28v = VO + ae(v + Q) - xoe(v + Q)2 . . + B J ( J + 1) + D , J ~ ( J + i ) 2 + P,J~(J + 113 . . (18)where vo is the electronic frequency-separation, we the equilibriumvibration frequency, x the anharmonic vibration constant, and vand J (sometimes K ) are the vibrational and rotational quantumnumbers, respectively. The factors B, and D, vary with the vibra-tional level according to the relationshipsB, = Be - a(v + 8) -t y(v + $)2 . . .Dv = De + p ( ~ + Q)2 + 6(v + i)4 . . .Be, De, and a, p, 7,. and 6 being constants for the electronic level,which are determmed from the observed spectral frequencies.The quantity F, also depends on v, but as it is in any case very small,25 H.L. Johnston and D. H. Dawson, J . Amer. Chem. SOC., 1933, 55, 2744;A., 1933, 1005.26 Cf. F. A. Jenkins, Y. K. Roots, and R. 8. Mulliken, Phyaical Rev., 1932,39, 16; A., 1932, 145; see H. Zeise, 2. Ellektrochem., 1933, 39, 899.27 H. C. Hicks and A. C. G. Mitchell, loc. cit., ref. (4); W. F. Gianque andR. Wiebe, J . Amer. Chem. Soc., 1928, 50, 101; A., 1928, 228.28 W, Jevons, op. cit., Chap. 1176 GENERAL AND PHYSICAL CHEMISTRY.it may be assumed constant. The purpose of the correction factorsis to allow for changes in the moment of inertia of the molecule indifferent vibrational levels, and for the interaction of vibrationaland rotational energies.For a rigid molecule in which there is nointeraction D, and Fv are zero, and B, is constant and equal toh2/8x21, where I is the moment of inertia. By means of theseequations the frequencies of all the rotational lines can be calculatedand hence the total internal energy, including electronic and vibra-tional energy, of the corresponding levels can be determined; thevalue of E to be used in the partition function Q is then obtained bysubtracting the energy for the lowest level (v = 0, J = 0) in theground state, i . e . , the zero-point energy, (&me - &xoe)hc." Whenspectroscopic measurements are relatively limited, it is often possibleby means of the frequency equations to determine, with fair accuracy,the energies of levels giving rise tjo bands beyond the limit of actualexperimental observation ; such energies have frequently to beused in the calculation of thermodynamic quantities.Xurnrnation.-In the determination of &, the rotational portion,using the appropriate energies and statistical weights, is first deter-mined by summing the series for all possible rotational levels(see above) in the v = 0 vibrational level, for the ground state ofthe molecule.The process is then repeated for the v = 1, 2, 3,etc., levels, as long as they contribute appreciably to the partitionfunction. The same process is then carried out for every electronicstate of relatively low energy separation, and the various sumsadded to give the complete state sum.Since the separations ofsuccessive rotational levels are relatively small, it is evident that,except a t very low temperatures, such levels will contributeappreciably to the total partition function until high rotationalquantum numbers are attained. With nitric oxide, for example,the rotational contribution becomes negligible only after 81 levels,in the v = 0 state, a t 1000" Abs., and 168 and 200 levels must beincluded at 2000" and 3000" Abs., re~pectively.~4 It is evident,therefore, that the process of summation may become very tediousa t high temperatures, where several vibrational, and possiblyelectronic, states must be included. Various methods have beenemployed for simplifying the labour involved : by means of appro-priate frequency equations, of the type of equation (18), the internalenergy is expressed in the form of asymptotic series of exponentialterms, and summation is replaced by integration; provided thetemperature is not too low, the error involved in the determination ofQ is negligible.The method in its simplest form was first used for* The equation (18) for the frequency of spectral lines can be expressed insuch a form as to give the required energy c directlyGLASSTONE : DETERMINATION OF THERMODYNAMICJ CONSTANTS. 77rigid diatomic molecules,29 and was later modified 30 to allow fornon-rigidity in molecules having ground terms. It permittedthe determination of the rotational partition function for a givenvibrational state by summing a small number of terms in a series :the calculation had to be repeated for each vibrational level con-tributing materially to the total sum.Since the evaluations ofentropy and heat capacity require a knowledge of the first and secondderivatives of Q [equations (6) and (S)], these have also been expressedas a similar series which can be summed quite readily.31 If manyvibrational levels have to be taken into account, then the summationis still laborious, although the work can be simplified by utilisingthe observation that the rotational function &rot., and its derivativesdQ,,,,./dT and d2Qrot./dT2, for one vibrational level v bear a constantratio to the values for the v + 1 level.31 Further developments 32have eliminated even this summation, and have permitted theapplication of the mathematical methods to determine completepartition functions of 211 and 3X diatomic molecules,33 and evenof polyatomic non-linear molecules (see below).By means of suit-able tables, based on the formuh derived, the labour involved inthe calculation has been considerably diminished. These tables,and formulze, apply only t o unsymmetrical molecules in which thereis no alternation in the statistical weights of odd and even levels, andthey do not allow for nuclear spin: allowance can be made forboth these factors, as will be seen later (p. 78).Approximation Methods.Tf the different forms of internal energyof a molecule can be regarded as independent, the complete partitionfunction can be taken as equal to the product of electronic, vibrational,and rotational functions, QVik,,., and &rot., respectively, whereQel.= Cpel.e-EeI./kp ; Qvib. = Cpdb.e-Edb.lk* ; Qrot. = Cprot.e-erot-/krand the complete partition functionQ = &el. X &vib. X Qrot.In evaluating the separate terms, pel. may be taken as equal to themultiplicity of the particular electronic state, provided the energy39 H. P. Mulholland, Proc. Camb. Phil. Soc., 1928, 24, 280; G. B. B. M.Sutherland, ibid., 1930, 26, 402; A., 1930, 1244.80 W. F. Giauque and R. Overstreet, Zoc. cit., ref. (13) ; L. S. Kassel, J .Chem. Physics, 1933, 1, 576; A., 1934, 31.31 H. L. Johnston and C. 0. Davis, J . Amer. Chem. Soc., 1934, 56, 271;A., 1934, 354.33 A. R. Gordon and C. Barnes, J .Chern. Physics, 1933, 1, 297; A., 1934,31; L. S. Kessel, loc. cit., ref. (30); Phyaicd Rev., 1933, 43, 364.33 A. R. Gordon and C. Barnes, Zoc. cit.; L. S. Kassel, Zocc. cit.; E. E.Witmer, J. Chem. Physics, 1934, 2, 618; A , , 1934, 1165; see also C. Gregory,8. Physik, 1932, 78, 791; A., 1933, 1675 GENERAL AND PHYSICAL CHEMISTRY.of separation of the multiplets is not large, and the correspondingenergy of the level above the ground state, determined from thevalue of v0 in equation (18). In the Qvjb. term, (pvib. is alwaysunity for a diatomic molecule; &vib. may be taken as being the samein all electronic levels, and equal to ~ C C G ~ Z I above the zero-pointenergy, neglecting the anharmonicity constant, where oo is theequilibrium frequency in the ground state.The vibrationalpartition function is thus given by the expression(1 - e--7ccwo/kP 1 Qvib. = Ce-hWovlkf = W 1-v = oSince the rotational and vibrational energies are assumed independ-ent, the molecule may be taken as rigid and the moments of inertiaconstant ; the rotational energy of such a 1C diatomic molecule maythen be written J ( J + l ) h 2 / 8 ~ 2 1 , and consequentlywhere G = h2/8x21kT. In this equation the nuclear-spin factor isneglected, and it is also assumed that the molecule is heteronuclear,so that there is no alternation in the p values for successive rotationallevels, If 0 is small, i.e., for relatively high temperatures, andespecially for molecules having small moments of inertia, the sum-mation can be replaced by i n t e g r a t i ~ n , ~ ~ ~ ~ ~ with the result that= 1/0.For molecules in other than l Z states, analogousapproximate values for the rotational function, applicable atappreciable temperatures, can be deduced ; if necessary, the effectof A-type doubling must be included by means of a factor 2,the frequency separation being ignored. Allowance for multi-plicity due to nuclear spin is made (p. 74) by multiplying by(2& + l)(2ifS + 1) for a heteronuclear molecule.If the molecule has two identical atoms, the effect of nuclearspin should be obtained by multiplying the odd and even terms byis(.ZiS + 1) and (is + l)(2iS + l), as already explained (p. 73).In the summation of the (2J + l)e-uJJ'J+l) terms over all values ofJ from 0 to 00 , it can be shown that, provided a be small, the sum ofthe terms for which J is even is equal to that for the terms with oddJ values.35 The inclusion of the nuclear-spin factor is consequentlyequivalent to multiplying the Qrot.obtained above by (2i, + 1)2/2;for hydrogen this correction factor is 2, for deuterium it is p, and foroxygen 8. This last result is obviously in agreement with the factthat the alternate rotational levels of oxygen are missing, and the34 L. S. Kassel, J . Amer. Chem. SOC., 1933, 55, 1351; A., 1933, 661.35 See L. S. Kassel, Zoc. cit., ref. (30)QLASSTONE : DETERMINATION OF THERMODYNAMIC CONSTANTS. 79others show no nuclear-spin degeneracy. For molecules of thistype the approximate value of &rot. becomes 1/20 : this result hadbeen previously deduced by classical mechanic^,^^ the factor 2,called the " symmetry number," representing the number of equiv-alent orientations in space which the molecule is able to occupyas a result of simple rotation.37 Since the expression for entropy[equation (7)] involves R In &, the correction for symmetry and fornuclear-spin degeneracy with a diatomic molecule is 222 In (2is + 1) -Rln2; if i, = 0, as for oxygen, this becomes - Rln2.It should be noted that the equality of the odd and even terms inthe &rot.summation is .only approached when c is small : for mostmolecules, the temperature at which this occurs is quite low, butwith equilibrium hydrogen and deuterium it is not the case. Withthese substances 38 it only applies when the ratio of ortho- to para-forms has attained the values of 3 : 1 and 1 : 2, respectively, and thisis only the case at about 273" Abs.for hydrogen and a t 200" Abs.for deuterium. For " normal " hydrogen and deuterium theapproximations described are, of course, applicable. With otherhomopolar molecules possessing nuclear spin, the " normal " ratioof ortho- and para-states is reached at such low temperatures thatunder reasonable conditions the summation and correction factorsconsidered above are adequate.If the partition functions are required for the calculation ofequilibrium constants, then provided the temperatures are suchthat the approximations discussed are valid, it is permissible t oomit the nuclear-spin factor, both from atoms and molecules,although the '' symmetry number " must be included.39 Sincenuclear spins are not always known, it is customary to quoteentropy and Po - 8," values with the spin-multiplicity effectomitted, but with due allowance for symmetry; in fact, theseallowances must be made if the entropy values from spectroscopicdata are to be used in conjunction with others determined fromthermal measurements.These entropies have been called " virtual "entropies,40 and given the symbol S* ; if absolute values are required,36 Cf. P. Ehrenfest and V. Trkal, Zoc. cit., ref. (1).37 For full discussion, see J. E. Mayer, S . Brunauer, and M. G. Mayer, Zoc.cit., ref. (11).See W. F. Giauque, Zoc. cit., ref. (12); H. L. Johnston and E.A. Long,Zoc. cit., ref. (15).39 G. E. Gibson and W. Heitler, 2. Physik, 1928, 49, 465; H. Ludloff,ibid., 1929, 57, 227; W. F. Giauque and R. Overstreet, Zoc. cit., ref. (13);J. E. Mayer et al., Zoc. cit., ref. (11); see, however, H. Ludloff, 2. Physilc,1931, 68, 433; A., 1931, 675; D. 5. Villnrs, Physical Rev., 1931, 38, 1563.40 Idem, ibid., p. 1552; A., 1932,14; R. M. Badger and S.-C. Woo, J. Arner.Chem. SOC., 1932,54,3523; A . , 1932, 120580 GENERAL AND PHYSICAL CHEMISTRY.a factor R In (2i, + 1) must be added for every atom of spin is in themolecule.Isotope E#ect.-For substances containing isotopic forms, accuratespectroscopic data are generally available only for the moleculecontaining the predominant isotope ; the corresponding values forother forms can be readily calculated, however, by assuming thebinding forces between atoms to be independent of their isotopicnature.In the determination of the entropy of the normal mixturethe entropies of the separate forms are multiplied by their respectivemo1.-fractions, determined from the isotopic and chemical atomicweights, and the results are added, the entropy of mixing beingincluded. Thermally determined entropies do not involve thisfactor, and for use in conjunction with these, for calculation ofequilibrium constants, the entropy of mixing is omitted : if this isdone, then in the appropriate instance it is necessary also to neglectthe fact that the statistical weight of a heteronuclear molecule,e.g., C135C137, is double that of the symmetrical molecules, C135C135and C137C137.The same result, at least for chlorine, may be obtainedin a simpler manner by treating the substance as a homonuclearmolecule, each atom having an atomic weight 35.46, the energy ateach level being obtained by giving the proper proportional weightst o the corresponding levels for the three types of isotopic molecules ;this effect is believed to be general and to apply to all analogous~ases.4~ Hydrogen chloride may be treated as a mixture of definiteamounts of HCP5 and HCP7, although the entropy of mixing andthe nuclear-spin effect must not be included if the results are to beused in conjunction with thermal values.Polyatomic MoZecuZes. *-With such molecules precise calculationsare very difficult, partly because the spectra are complex anddifficult to analyse, and partly because of the labour involved inthe evaluation of the partition function when three, or more,moments of inertia and several types of vibration have to be con-~idered.4~ By replacing summation by integration and using41 W.F. Giauque and R. Overstreet, loc. cit., ref. (13); W. G. Brown, ibid.,1932, 54, 2394; A., 1932, 906; A. R. Gordon and C. Barnes, J . PhysicalChem., 1932, 36, 2292; A., 1932, 997.42 F. Hund, 2. Physilc, 1927, 43, 805; A., 1927, 809; W. Elert, ibid., 1928,51, 6 ; A., 1929, 11; D. S. Villars and G. Schultze, Physical Eeu., 1931, 38,998; A., 1931, 1216; D. S. Villars, ibid., p. 1552; A . , 1932, 14; D. P. Mac-Dougall, ibid., p. 2074; D. M.Dennison, ibid., 1932, 41, 304; A . , 1932, 982;A. AdelandD. M. Dennison, ibid., 1933,43,716; 44,99; A., 1933, 661, 885;Dennison, Rev. Mod. Physics, 1931, 3, 280; H. R. Nielsen, Physical Rev.,1932, 40, 445; T. E. Sterne, ibid., 1932, 39, 993; 42, 556; A., 1932, 666;1933, 118; D. S. Villars, Chem. Reviews, 1932, 11, 369; E. B. Wilaon, J .C‘hem. Physics, 1935, 3, 276; A., 810.* See report on “ Spectroscopy,” p. 53GLASSTONE : DETERMINATION OF TIIERMODYNAMIC CONSTANTS. 81methods of asymptotic e~pansion,~:~ it has been possible to diminishthe labour involved in obtaining the Q sum for relatively simplepolyatomic molecules, e.g., HCN, GO,, N20, C2H2, H20, SO,, CH,,and CD,, due allowance being made for anharmonicity and forstretching and interaction terms.In most cases, however, thesimplification is made of treating the molecule as rigid and ofassuming the different forms of energy to be independent : thecomplete partition function is then the product of the separateelectronic, vibrational, and rotational functions. At relativelyhigh temperatures the errors involved in these assumptions aregenerally small.The classification of polyatomic molecules according to theelectronic configuration of the ground state is only possible for arelatively limited number of substances which behave as quasi-diatomic ; in other cases it is assumed that there is only one electronicground level and that excited levels do not contribute to the totalstate sum. The electronic factor in the partition function is thusgenerally, unless there is direct evidence to the contrary, taken asunity.A molecule containing n atoms has in general 3n - 6 normal modesof vibration : for a linear molecule this is increased t o 3n - 5, andis decreased t o 3n - 7 for a molecule of the ethane type because ofinternal rotation.Of this total, n - 1 are stretching (valency),the others being bending (deformation) vibrations. If the energyof the vibrational levels 44 can be expressed in terms of a formulasimilar to the one used for diatomic molecules, it is sometimespossible t o make a reasonably accurate estimate of the vibrationalpartition function.45 For a complex molecule it is generally thepractice t o use for each type of vibration the approximate relation-ship obtained for a diatomic molecule, vix., Qyib. = (1 - e-hcoi'kr )- 1 :the vibrational function for the whole molecule is given by theproduct of these terms, one for every possible vibrational mode.46If any of the frequencies are degenerate, due allowance must bemade in the product, the corresponding term being included foreach component of the degenerate frequency.The vibrational43 A. R. Gordon, J . Chem. Physics, 1934, 2, 65; 1935, 3,259; A., 1934,355 ;1935, 811; I. E. Viney, Proc. Comb. Phil. SOC., 1933, 29, 142, 407 (correction);A., 1933, 206; L. S. Kassel, Eocc. cit., ref. (30), (34); J . Chern. Physics, 1935,3, 115; A., 437.** Cf. D. M. Dennison, Rev. Mod. Physics, 1931, 3, 280.45 L. S. Kassel, J. Arner. Chem. SOC., 1934, 56, 1838; A., 1934, 1300;R.W. Blue and W. F. Giauque, ibid., 1935,57,991; A., 924.46 See B. Topley and H. Eying, J . Chem. Physics, 1934, 2, 217; S., 1934,851 ; R. H. Crist and G. A. Dalin, ibid., p. 735 ; A., 1935,33 ; E. Teller and B.Topley, J . , 1935, 876; A , , 107682 GENERAL AND PHYSICAL CHEMISTRY.terms affect the complete Q value to a relatively small extent,except at high temperatures; 47 e.g., at 298" Abs. Qrot. for nitrousoxide is 496, whereas Qvib. is 1.1 ; the introduction of approximationmethods and the use of uncertain frequencies consequently resultin relatively small errors. The rotational factor is the more im-portant, and this may best be considered under the headings ofdifferent types of molecules.The rotationalenergy, at least in the lower vibrational levels, may be expressed bythe same formula as for a diatomic molecule,48 although this is notstrictly accurate.,*, 49 The moments of inertia being relativelylarge, it is permissible to replace summation by integration, and theapproximation already described (p. 78) may be used.For amolecule possessing symmetry, the appropriate symmetry factors must be introduced, giving Qrot. = 1/80, thus allowing for missinglevels. The value of I required to calculate t~ is generally obtainedfrom spectroscopic data, although it may be evaluated from theinteratomic dimensions if they are known. The result does notinclude the nuclear-spin factor, for which allowance need only bemade if the Q is required to calculate absolute entropy.Xphericul rotator (e.g., CH,, CCl,, but not CMe, because of freerotation). Molecules possessing tetrahedral symmetry may betreated as spherical rotators having three equal moments of inertia :the rotational energy may be expressed by the same equation as fora diatomic molecule.From quantum-mechanical considerations,it is sometimes possible to allow for the statistical weights of differentrotational levels, but if missing levels and nuclear-spin effects areignored, each level has a p value of (2J + 1)2 ; replacing summationby integrationYm then at appreciable temperatures Qmt. = +/st~3/2.The term t~ has the same significance as previously (p. 78), I beingassumed constant, and s is the symmetry number,51 vix., 12 forCH, and CC14, which allows for missing levels.The nuclear-spinfactor is not included.Xyrnrnetrical top. Under this heading may be considered twotypes of molecule : (a) single pyramidal, e.g., NH,, CHCl,, or ( b )double pyramidal, e.g., C,H,. I n molecules of this nature, two ofthe three moments of inertia are identical, I* = IB > Ic. Forthe single-pyramid type the rotational energy, assuming a rigidLinear molecuEes (e.g., HCN, N,O, CO,, C,H,).47 R. M. Badger and S.-C. Woo, loc. cit., ref. (40), p. 3527.4 * R. M. Badger and S.-C. Woo, loc. cit., ref. (40).49 L. S. Kassel, loc. cit., ref. (45).m H. P. Mulholland, loc. cit., ref. (29) ; L. S. Kassel, toc. cit., ref. (34).61 See J. E. Mayer et at., loc. cit., ref. (11); A. R. Gordon and C. Barnes,J . Physical Chem., 1932, 36, 2601; A ., 1932, 1203GLASSTONE : DETERMINATION OF THERMODYNAMIC CONSTANTS. 83molecule, may be written 52 in the form given on p. 55, whereK can have a series of 2J + 1 values, vix., J, J - 1 , . . . , 0, . . .- J + 1, - J , for every value of J . The multiplicity of eachrotational level is 2J + 1, but owing to the introduction of K eachlevel is (2J + 1)-fold degenerate. The application of the usualapproximation methods 53 leads to Qrot. = x ~ ’ ~ / Q G ~ c T # ~ , where CTA andoc involve I* and Io, respectively. Complete analysis, with fullallowance for statisticalweights, etc. , gives results very little different.For an ethane-like top, the rotational-energy equation is similarto that for the single pyramidal molecule, another term involvingK’ equal to K & 2n, where n is an integer, being included; 54 theapproximate value 55 of &rot.is then found to be X / S G A C T ~ .For the general case in which the moleculeis non-linear and has three different moments of inertia, the rotationalenergy cannot be expressed by a simple formula : the energies of thelower levels may be represented by a complex relationship 56 whichhas been actually used to calculake & for the water molecule.57A satisfactory approximation,53 at appreciable temperatures, assum-ing a rigid molecule, is obtained by substituting I A I B for Ia2 in theequation for a pyramidal moleciile, thus &rot. = ( ~ / O A . C T B ~ C ) ~ ’ ~ / ~ .For a planar molecule, e.g., H20 or C6H,, IA +- IB = 10; forH20, s = 2; for C,H6, s = 12; and for cyclohexene, 8 = 2, sinceit is non-planar.Complex Molecules.-By analogy with the formulae already given,it has been deduced 58 that for a molecule with several rotatingpartsAsymmetrical top.I*, IB, Ic .. . being the moments of inertia of the molecule andof its independently rotating parts; a, b, c . . . are the rotationaldegrees of freedom associated with the corresponding moments ofinertia, their sum being equal to n, the total number of rotationaldegrees of freedom; and s is the symmetry number, defined as thenumber of indistinguishable permutations produced by rotation ofthe molecule or of its parts. This relationship has been applied toG2 F. Reiche, 2. Physik, 1926, 39, 444; J.E. Mayer et al., loc cit., ref. (11).53 L. S. Kassel, Zoc. cit., ref. (34); A. R. Gordon, loc. cit., ref. (43); for54 H. R. Nielsen, Zoc. cit., ref. (42); J. E. Mayer et. al., loc. cit., ref. (11).5 5 I d e m , ibid.56 H. A. Kramers and G. P. Ittmann, 2. Physik, 1930, 58, 217; D. M.5 7 A. R. Gordon and C. Barnes, J. Physical Chem., 1932, 36, 1143; A.,68 J. 0. Halford, J. C’hem. Physics, 1934, 2, 694; A., 1934, 1300.classical treatment, see A. Eucken, Physikal. Z., 1929, 30, 818.Dennison, Zoc. cit., ref. (44).1932, 69684 GENERAL AND PHYSICAL CHEMISTRY.calculate the entropies of methyl alcohol, methyl ether, toluene,acetone, isobutane, P-methyl-AP-butene (CMe2:CHMe), and neo-pentane. The problem of complex molecules has also been examinedfrom a more fundamental point of view 59 which appears to haveconsiderable promise, especially in its application to normal paraffinhydrocarbons .GOSince in all the approximation methods the nuclear-spin factorhas been neglected, the partition function should be multiplied byZi, + I for every nucleus if absolute entropies are required; forthe calculation of dissociation constants or for combination withcalorimetric data this correction should not be applied.Applications.-The methods outlined above have been used inthe calculation of thermodynamic functions, e.g., entropy, heatcapacity, and the free-energy function, (Po - Eoo)/T, for the follow-ing molecules : hydrogen,62 hydrogen deuteride deuter-oxygenYs5 ozone,66 hydroxyl radical,67 water,68 methane,6959 M.L. Eiciinoff and J. G. Aston, J . Chem. Physics, 1935, 3, 379; A.,6o L. S . Kassel, private communication.For atoms, see refs. (12)-(15).62 D. M. Dennison, Proc. Roy. Xoc., 1927, [A], 115, 483; A., 1927, 817;R. H. Fowler, ibid., 1928, [A], 118, 52; A., 1928, 469; T. E. Sterne, ibid.,1931, [A], 130, 367; 133, 303; A., 1931, 295, 1222; F. Hund, 2. Physik,1927, 42, 93; A., 1927, 495; S. Daumichen, ibid., 1930, 62, 414; A., 1930,982; W. F. Giauque, loc. cit., ref. (12); C. 0. Davis and H. L. Johnston,ibid.,1934, 56, 1045; A., 1934, 722; A. R. Gordon and C. Barnes, J . PhysicalChem., 1932,36, 1143; A., 1932, 695; see also R. H. Fowler and T. E. Sterne,Rev. Mod. Physics, 1932, 4, 635.1064.63 H. C. Urey and D. Rittenbcrg, loc.cit., ref. (19).64 Idem, ibid. ; H. L. Johnston and E. A. Long, loc. cit., ref. (15); H. Motzand F. Petat, Monatsh., 1934, 64, 17; A., 1934, 480; K. Clusius and E.Bartholom6, 2. Elektrochem., 1934, 48, 524; A., 1934, 951 ; 2. physikal.Chem., 1935, [B], 30, 258.6 5 W. F. Giauque and H. L. Johnston, J . Amer. Chem. Xoc., 1929, 51,2300; A., 1929, 1137; H. L. Johnston and M. K. Walker, Zoc. cit., ref. (21);ibid., 1935, 57, 682; A., 690; B. Lewis and G. von Elbe, ibid., 1933, 55,511; 1935, 57, 1399; A., 1933, 343, 1198; A. R. Gordon and C. Barnes,J. Physical Chem., 1932, 36, 2292; A., 1932, 997.66 L. S. Kassel, J . Chem. Physics, 1933, 1, 414; A,, 1934, 30.67 H. L. Johnston and D. H. Dawson, J. Amer. Chem. Xoc., 1933, 55,2744; A., 1933, 1005.68 A.R. Gordon and C. Barnes, loc. cit., ref. (62) ; A. R. Gordon, J . Chem.Physics, 1933, 1, 308; 1934, 2, 65, 549; A., 1934, 30, 355, 1070.69 W. F. Giauque, R. W. Blue, and R. Overstreet, Physical Rev., 1931, 38,196; D. S. Villars and G. Schultze, loc. cit., ref. (42); D. S. Villars, loc. cit.,ref. (42); D. P. MacDougall, Zoc. cit., ref. (42); T. E. Sterne, ibid., 1932, 42,556; A., 1933, 118; L. S. Kassel, loc. cit., ref. (34); A. R. Gordon and C.Barnes, J. Physical Chem., 1932, 36, 2601; A., 1932, 1203; R. D. Vold,J . Amer. Chem. Soc., 1935, 57, 1192; A., 1064GLASSTONE : DETERMINATION OF THERMODYNAMIC CONSTANTS. 86ethylene, 70 acetylene, 71 ethane, 72 benzene, 73 cycZohexene, 73 nitrogen, 7*ammonia,75 nitric oxide, 76 nitrous oxide, 77 hydrogen cyanide,78sulphur (S2),79 hydrogen sulphideY8O sulphur dioxideY8l carbon di-sulphide and oxysulpliide,81a sulphur monoxide ( SO),s2 chlorine,s3hydrogen chloride, 84 deuterium chloridejs5 bromine,86 hydrogen70 L.S. Kassel, Zoc. cit., ref. (34) ; H. A. Smith and W. E. Vaughan, J .Chem. Physics, 1935, 3, 341; A., 934; A. V. Frost, J . Gen. Chem. Russia,1934, 4, 124; A., 1934, 843.71 L. S. Kassel, Zoc. cit., ref. (34); J. E. Mayer et aZ., Zoc. cit., ref. (11);A. R. Gordon, J . Chem. Physics, 1935,3,259; A., 811.72 H. A. Smith and W. E. Vaughan, loc. cit., re€. (70); J. E. Mayer et aZ.,loc. cit., ref. (11); A. V. Frost, Zoc. cit., ref. (70).73 J. E. Mayer et al., Zoc. cit., ref. (11) ; V. Deitz and D. H. Andrews, ibid.,1933,1, 62; A ., 1933,212.74 W. F. Giauque and J. 0. Clayton, loc. cit., ref. (15); H. L. Johnston andC. 0. Davis, loc. cit., ref. (31).7 5 W. F. Giauque et al., Zoc. cit., ref. (69) ; D. S. Villars, loc. cit., ref. (69) ;D. P. MacDougall, Zoc. cit., ref. (69); T. E. Sterne, Physical Rev., 1932, 39,993; A., 1932, 566; W. M. D. Bryant, J . Amer. Chm. Soc., 1931, 53, 3014;A . , 1931, 1127.7 6 H. L. Johnston and W. F. Giauque, J . Amer. Chem. SOC., 1929, 51,3194; A., 1930, 24; H. L. Johnston and A. T. Chapman, ibid., 1933, 55,153, 5073 (correction); A., 1933, 229; R. W. Blue and W. F. Giauque, Zoc.cit., ref. (45); A. R. Gordon and C. Barnes, Zoc. cit., ref. (32); E. E. Witmer,J . Amer. Chem. SOC., 1934, 56,2229; A., 1935, 21.7 7 R. M. Badger and S.-C. Woo, Zoc.cit., ref. (40); W. H. Rodebush,Physical Rev., 1932, 40, 113; R. W. Blue and W. F. Giauque, loc. cit.,ref. (45); L. S. Kassel, Zoc. cit., ref. (45); A. R. Gordon, Zoc. cit., ref.7 8 R. M. Badger and S.-C. Woo, Zoc. cit., ref. (40); A. R. Gordon, loc. cit.,ref. (71).'* C. W. Montgomery and L. S. Kassel, Zoc. cit., ref. (15); P. C. Cross, J .Chem. Physics, 1935,3, 168; A., 569; I. N. Godnev, Phpikal. 2. Sovietunion,1935, 7, 442; A., 1312.(72).8o P. C. Cross, Zoc. cit., ref. (79).n1 A. R. Gordon, J . Chem. Physics, 1936, 3, 367; A., 1204; P. C. Cross,Ila P. C. Cross, Zoc. cit.82 C. W. Montgomery and L. S. Kassel, Zoc. cit., ref. (15).83 W. F. Giauque and R. Overstreet, Zoc. cit., ref. (13); T. E. Sterno, Proc.Roy. SOC., 1931, [A], 131, 339; A., 1931, 674; A.1%. Gordon and C. Barnos,loc. cit., refs. (32), (65) ; H. M. Spencer and J. L. Justice, J . Amer. Chem. SOC.,1934, 56, 2311; A., 1935, 21.84 W. F. Giauque and R. Wiebe, Zoc. cit., ref. (27); E. Hutchisson, ibid.,1928, 50, 1895; A., 1928, 941 ; W. F. Giauque and R. Overstreet, Zoc. cit.,ref. (13); T. E. Sterne, Proc. Roy. Soc., 1931, [A], 133, 303; A., 1931, 1222;H. M. Spencer and J. L. Justice, Zoc. cit., ref. (83) ; A. R. Gordon and C.Barnes, locc. cit., refs. (32), (65).8 5 H. C. Urey and D. Rittenberg, Zoc. cit., ref. (19).8 G A. R. Gordon and C. Barnes, Zoc. cit., ref. (32); J. Ckem. Physics, 1933,1, 692; A., 1934, 30; W. G. Brown, J . Amer. Ghem. Xoc., 1932, 54, 2394;A., 1932, 906.ibid., p. 82586 GENERAL AND PHYSICAL CHEMISTRY.bromide,*' iodine,88 hydrogen iodide,B9 deuterium iodide,g0 iodinemonochloride,gl carbon monoxide,92 carbon dioxide,93 chloro-methane~,~4 the tetrachlorides of carbon, silicon, titanium, andarsenic and phosphorus trichl~rides,~~ arsenic g6 and phosphorustri ff uorides , p hosp hine,97 sulphur hexafluor ide , 98 nickel carb ony 1, 99methyl alcohol, dimethyl ether, acetone and various hydrocarbon^.^^Equilibrium constants 1 have been evaluated for the followingreactions : H, e 2H;2 D, =+= ZD; HD H + D;2HD =s= H, -t D2;4 0, 2 0 ; 0, =+= 0, + 0 ; H20 =+H, + 40,; 7 H,O &H2 + OH; 7 H,O + D20 G+ 2HDO;;HDO + H, HZO + D2; 9 D2O + H, H2O + D,; '0 N28 7 W.F. Giauque and R. Wiebe, J . Amer. Chem. SOC., 1928, 50, 2193; A . ,1928, 1083; A.R. Gordon and C. Barnes, Zoc. cit., ref. (32).88 W. F. Giauque, ibid., 1931, 53, 507; A . , 1931, 429.8f) W. F. Giauque and R. Wiebe, ibid., 1929,51, 1441; A . , 1933, 755.91 J. M. McMorris and D. M . Yost, ibid., 1932, 54, 2247 ; A., 1932, 906.92 J. 0. Clayton and W. F. Giauque, ibid., 1932, 56, 2610; 1933, 57, 5071(correction); A . , 1932, 906; L. S. Kassel, J . Chem. Physics, 1933, 1, 576;A . , 1934, 31 ; H. L. Johnston and C. 0. Davis, Zoc. cit., ref. (31) ; A. R. Gordonand C. Barnes, Zoc. cit., ref. (32).93 R. M. Badger and S.-C. Woo, Zoc. cit., ref. (40); L. S. Kassel, Zoc. cit.,ref. (45); H. M. Spencer and J. L. Justice, Zoc. cit., ref. (83); A. R. Gordon,J . Chem. Physics, 1933, 1, 308; A., 1934, 30.H. C. Urey and D. Rittenberg, Zoc.cit., ref. (19).94 R. D. Vold, Zoc. cit., ref. (69).95 D. M. Yost and C. Blair, J . Amer. Chem. SOC., 1933, 55, 2610; A., 1933,g6 D. M. Yost and J. E. Sherborne, J . ClLem. Physics, 1934, 2, 125; A . ,97 D. M. Yost and T. F. Anderson, ibid., p. 624; A., 1934, 1289.g8 D. M. Yost, C. C. Steffens, and S . T. Gross, ibid., p. 311; A., 1934, 830.Qg A. B. F. Duncan and J. W. Murray, ibid., p . 636; A . , 1934, 1289.784.1934, 473.For tabulated summaries, see H. Zeise, 2. EZektrochem., 1934, 40, 885 ;W. F. Giauque, Zoc. cit., ref. (12); re-calculated by H. Zeise, Zoc. cit.,H. L. Johnston and E. A. Long, Zoc. cit., ref. (15); ibid., 1934, 56, 710H. C. Urey and D. Rittenberg, Zoc. cit., ref. (19) ; F. Patat and H. Hoch,H. L. Johnston and M.K. Walker, Zoc. cit., ref. (14); G. von Elbe andL. S. Kassel, J . Chem. Physics, 1933, 1, 414; A., 1934, 30.A. R. Gordon, loc. cit., ref. (93).B. Topley and H. Eyring, Zoc. cit., ref. (46).R. H. Crist and G. A. Dalin, ibid., 1934, 2, 442, 548 (correction); A.,1934, 962, 1070; T. Forster, 2. p h y s i h l . Chem., 1934, 27, [B], 1 ; A . , 1935,33 ; see also, L. Farkas and A. Farkas, Trans. Paraday SOC., 1934, 30, 1071 ;A., 1935, 33.lo B. Topley and H. Eyring, Zoc. cit., ref. (46) ; R. H. Crist and G. A. Dalin,Zoc. cit., ref. (46).B. Lewis and G. von Elbe, J . Amer. Chem. SOC., 1935,57,612.ref. (1).(correction).Monatsh., 1934, 64, 229; A., 1934, 1153.B. Lewis, Zoc. cit., ref. (14)GLASSTONE : DETERMINATION OF THERMODYNAMIC CONSTANTS, 872N;ll NO =+ N + 0 ; 1 2 NO s *N2 + Q02;11 N,O Ge=N, + $0,; l3 c + CO, _-I 2co ; l 3 , l4 2c0, * 2co t o , *CO =+= C + &O,; l5 CO, + H, s CO + H,O; 13,16 C + 2H,+= CH4; '7 2C + 2H2 -+ C2H4 ; l7 2C + H2 =+= C,H,; 1.8C2H4 + H2 C 2 H 6 ; l9 CH, + 2H2O T+ CO2 + 4H2 ; 2o S2C1; 21 HC1 e QH, + QC12 ; 21 Br, =+= 2Br ; 22 HBr =s= QH, ++Br,;22 I, + 21;23 HI + iH2 + IBr =+ QI, + QBr;25ICl 41, + QC12; 26 H, + 2DC1 D, + 2HCI; 27 H, + 2DID, + 2HI ; 27 2C1, + 2HzO s 4HC1+ 0 2 ; 28 P2 +=2 ~ ; 2 9 S, =+= 2s; 82 SO + Q S ~ + Q0,; 82 SO, s= QS, + 0,; 30SO, SO + 40,; 30 3H, + SO, G H,S + 2H,O; 2C0, +$3, += 2CO + SO,; COS +H,S z+= CS, + H,O; CO + $3, COS; 2COS CO, 4-CS, ; CS, =+= C + S,; 81a and various interchange reactionsinvolving the isotopes of lithium, carbon, oxygen, nitrogen, chlorine,and br0mine.~1Discrepancies.-In general, there is excellent agreement betweenthermodynamic functions calculated from spectroscopic data andthe values obtained by direct experiment : in a few cases there are,l1 W.F. Giauque and J. 0. Clayton, Zoc. cit., ref. (15); recalculated by H.GO, f- H2S GS COS + H,O;Zeise, Zoc. cit., ref. (1) (p. 886).H. Zeise, loc. cit., ref. (1) (p. 886).l2 H. L. Johnston and A. T. Chapman, Zoc. cit., ref. (76);l3 L. S. Kassel, Zoc. cit., ref. (45).l4 A. R. Gordon, Zoc. cit., ref. (93); A. R. Gordon and C.l5 J. 0. Clayton and W. F. Giauque, Zoc. cit., ref. (92).l6 A. R. Gordon, Zocc. cit., ref. (68); A. R. Gordon and C.l7 L. S. Kassel, Zoc. cit., ref. (34); A.R. Gordon and C.la L. S. Kassel, Zoc. cit., ref. (34).ref. (69).ref. (62).ref. (69).recalculated byBarnes, loc. cit.,Barnes, Zoc. cit.,Barnes, Zoc. cit.,l9 H. A. Smith and W. E. Vaughan, Zoc. cit., ref. (70); A. V. Frost, Compt.rend. Acad. Sci. U.R.S.S., 1933, 4, 161 ; A., 1934, 254; see also E. Teller andB. Topley, loc. cit., ref. (46).2o A. R. Gordon and C. Barnes, Zoc. cit., ref. (69).21 W. F. Giauque and R. Overstreet, Zoc. cit., ref. (13).22 A. R. Gordon and C. Barnes, J . C'hem. Physics, 1933,1,692 ; A., 1934, 30.23 G. E. Gibson and W. Heitler, Zoc. cit., ref. (39) ; H. Zeise, Zoc. cit., ref.24 H. Zeise, loc. cit., ref. ( l ) , p. 887.25 Idem, 2. Elektrochem., 1935, 41, 267; A . , 702.2 6 J. McMorris and D. M. Yost, Zoc.cit., ref. (91); H. Zeise, Zoc. cit., ref. (l),27 H. C. Urey and D. Rittenberg, Zoc. cit., ref. (19).28 A. R. Gordon and C. Barnes, Zoc. cit., ref. (65).29 H. Zeise, Zoc. cit., ref, ( l ) , p. 888.30 A. R. Gordon, J . Chem. Physics, 1935, 3, 336; A., 1204.31 H. C. Urey and L. J. Greiff, J . Amer. Chem. Soc., 1935,457, 321; A., 446.(1) p. 887.p. 88888 GENERAL AND PHYSICAL CHEMISTRY.however, outstanding discrepancies which require consideration.The statistical entropy of hydrogen is 33.98 units, including thenuclear-spin contribution, compared with the accurate thermalvalue of 29.6-29.7 a t 298.1" Abs. : 32 there has been some contro-versy 33 over this difference, but it is now accepted as being dueto the persistence of rotation in the s0lid,~4 so that the thermalmethod, based on the third-law assumption of zero entropy, isincorrect.The calculated error, 4.39 units, is in excellent agree-ment with the observed discrepancy of 4.3-4.4 units. The correct(virtual) entropy of hydrogen to be used in conjunction with thevalues for other substances is obtained by subtracting R In 4, thenuclear-spin correction, from 33-98, giving 31.23 units. A similardifference exists between calculated and thermal entropies of deuter-ium, the values being 38.98 and 33.9, respectively : 35 this agreesexcellently with the calculated discrepancy (5.09 units). Thevirtual entropy of D2 is 38.98 - R In 9 (the nuclear-spin effect),giving 34.62 units a t 298.1" Abs. The calculated entropy of nitricoxide is about 0.75 greater than the thermal value : 36 since thisdifference is approximately +B In 2 it has been attributed to thepresence of N,O, in the solid, which exists either 36 in two formswith different coupling energies, or37 in a single form possessingtwo different possible orientations distributed at random.Fornitrous oxide the experimental value is 1.14 less than that obtainedfrom spectroscopic data : if in the solid the nitrous oxide moleculescould be oriented in a random manner either as NNO or ONN, thecrystal would possess an entropy of 1.38 instead of zero. If theorientation were not completely random, the discrepancy might besomewhat less than this amount.37 A discrepancy of the same order,1.1 units, for carbon monoxide has been attributed to a similarrandom, possibly not complete, arrangement of CO and OC in thecrystalline state.3* There also appears to be some difference betweenthe experimental and calculated entropies of water : this might wellbe due to the persistence of rotation in ice at temperatures as low32 W.F. Giauque, J. Arner. Chem. SOC., 1930,52,4816; A., 1931,294.33 H. L. Johnston and W. F. Giauque, ibid., 1928, 50, 3221; A., 1929,138; R. H. Fowler, loc. cit., ref. (62); R. H. Fowler and T. E. Sterne, loc. cit.,ref. (62); W. H. Rodebush, Proc. Nat. Acad. Sci., 1929, 15, 678; A., 1929,127; Physical Rev., 1931, 37, 221; D. MacGillavry, ibid., 1930, 36, 1398; A.,1931, 31 ; W. F. Giauque, ibid., p. 1592; loc. cit., ref. (31) ; W. M. D. Bryant,loc. cit., ref. (75).34 L.Pauling, Physical Rev., 1930, 36, 43; A., 1930, 1357; see also R. H.Fowler, Proc. Roy. SOC., 1935, [ A ] , 151, 1.35 K. Clusius and E. Bartholome, 2. physikal. Chem., 1935,30, [ B ] , 258.36 H. L. Johnston and W. 23. Girtuque, loc. cit., ref. (7G).37 R. W. Blue and W. F. Giauque, loc. cit., ref. (77).38 J. 0. Clayton and W. F. Qiauque, Zoc. cit., ref. (92)MOELWYN-HUGHES : CHEMICAL KINETICS. 89as 10" The disagreement between thermal and spectroscopicentropies of benzene has been ascribed to the possibility of deviationfrom flatness of the ring,4o but similar differences have been observedfor molecules the configurations of which are in no doubt.41 Theseeffects are probably due to incomplete knowledge of the vibrationalmodes of complex molecules.The uncertainty in treating theproblem of free rotation of the methyl group in ethane may accountfor the calculated equilibrium constants for C,H, e C,H, + H,being one-half the experimental values.42 It must be emphasisedin conclusion that, whenever detailed analysis of rotational andvibrational levels is possible and accurate spectroscopic data areavailable, the statistical thermodynamic constants are more reliablethan those determined thermally by measurements based on thethird law. S. G.5. CHEMICAL KINETICS.From the benefactions of the quantum theory to chemistry ingeneral, the subject of reaction kinetics has received a rich share.The resulting new theory of chemical change incorporates theclassical theory as a special case, and has the additional advantageof affording a more intimate glimpse into the actual mechanism ofreaction.The distinction between the two theories may be illus-trated by reference to bimolecular metatheses. The classicaltheory accepts the energy of activation ( E ) as a characteristic,experimentally ascertainable property of the reaction, and thenproceeds to examine the frequency of collisions of critical violence.1The watchful eye of the theorist follows, as it were, the approachof reacting molecules until they come to grips, whereupon the eyeis closed, to be opened again only when the chemical change is afuit accompli and the products of reaction are flying apart. Thequantum theory, on the other hand, is not content with acceptingE as a dynamic datum, but aims a t evaluating it from the staticproperties of the reactants and resultants.The idea of collisionalviolence is maintained, but the watchful eye is kept wide openduring the crash, in which old atomic allegiances are seen t o be tornand new ones forged. The methods hitherto adopted for thea priori calculation of E and of other related terms are admittedly39 W. F. Giauque and M. F. Ashley, Physical Rev., 1933, 43, 81 ; H. Zeise,2. Elektrochern., 1933, 39, 905; A. R. Gordon, J . Chern. Physics, 1934, 2, 65;A., 1934, 355.40 V. Deitz and D. H. Andrews, Zoc. cit., ref. (73).4 1 D. M. Yost and C. Blair, Zoc. cit., ref. (95).42 H. A. Smith and W. E. Vaughan, Zoc. cit., ref. (70).1 H. Goldschmidt, Physikal.Z., 1909,10, 206 ; M. Trautz, 2. anorg. Clzern.,1916, 96, 190 GENERAL AND PHYSICAL CHEMISTRY.of an approximate character, yielding results which are only inpartial agreement with experiment. The qualified arithmeticalsuccess of the quantum-mechanical theory is, however, more thancounterbalanced by the general correctness of the physical hypo-theses which make such calculations possible. For the purpose ofthe present report, some knowledge of the new theory is essential;current theoretical research subsumes it, and much of the experi-mental work is most conveniently discussed in its light.The Picture of Chemical Change Drawn by Quantum Hechani~.-We shall illustrate the method of H. Eyring and M. Polanyi2 bysetting ourselves the problem of evaluating the energy of activationof the reaction Br + H,+ HBr + H, which M.Bodenstein hasshown to be 17,700 calories. The perturbation theory of quantummechanics yields the following simple expression for the potentialenergy of a triatomic system, in terms of the Coulombic energies,A , B, and C, and of the exchange or resonance energies, a, p, and y :In general, the magnitude of the six separate contributions to thetotal energy is not known, but the quantities ( A + a), (B + p),and (C + y ) can be directly found from the Morse functions of therelevant diatomic configurations. The evaluation of E thus requiresa knowledge of the proportion of the total energy which is contri-buted by the Coulombic terms. The absence of a fixed or universalmethod of estimation and the approximate nature of the actualestimation are the first vulnerable points in the theory.Thepreviously accepted value of 3.5% is certainly too low ; and it is nowbelieved that 14%, which is known to hold for the hydrogen molecule,is nearer the mark. Adopting it, we may rewrite equation (1) thus :E = A + B + c + (*[(a - N2 + (P - r>2 + (a - 7421)* (1)= 0*14{(A + a) + (B + PI + (C + y)> + 0.61W + 4 - (B + P)I2+[(B+P)-((C+y)I2+[(A+a)-((C+y)l2)) (2)The theoretically justifiable step of considering only linear combin-ations of the three atoms, e.g.,II I A mII I - - - I -‘+--I 1 Q-t,introduces an obvious simplification, enabling us to write’ (3) I ( A + a) = DIH,[ 1 - e-aHsCrl - ro(WI]2(B + p) = DIHBr[1 - e-aHBr[rz - ro(HBr)l]2(C + y ) 3= DIHBr[ 1 - e- a ~ ~ ~ [ r a + r1 - rdHBr)I]2Z.physsikd. Chem., 1931, [BJ, 12,279.W. Heitler and F. London, 2. Physik, 1927, 44, 455MOELWPN-HUGHES : CHEMICAL KINETICS. 91where D‘ is the energy of dissociation (D) plus the zero-pointenergy (&v0). By combining equations (2) and (3), we obtain anexpression for the potential energy of the triatomic system in termsof two spatial co-ordinates, rl and r2 (Fig. 1).The initial system consists of a free bromine atom at an infinitedistance away from a stable hydrogen molecule, and is representedby a point [r2 = co ; rl = ro(Hz) ; E = D’Ha] in the top left-handcorner of Pig. 1. The final system corresponds to a free hydrogenatom, infinitely separated from a stable hydrogen bromide mole-cule, and is characterised by the point [r, = co ; r2 = ro(HBr);FIG.1.0.5 $0 2:or, (k).E = D’HBr]. The passage of the system from its initial to its h a 1state clearly corresponds to the occurrence of the chemical reactionBr + HH --j BrH + H, for which the heat of reaction is simplyD’HH - D’HBr. The easiest of an infinite number of such passages isthat traced by the broken line. If we imagine ourselves to take theplace of the representative point of the reacting system, we can gaina clearer view of what happens. Starting at x, we climb a gentleascent southwards in a valley flanked by mountains, those on ourright being the steeper. Round about the position y, there is avirtually horizontal walk, beyond which we descend into it secondvalley eastwards.The crux of the theory of Eyring and Polanyiis the identification of the height of the pass with the energy o92 GENERAL AND PHYSICAL CHEMISTRY.activation. The critically activated complex, represented by thepoint y, has certain definite probabilities of changing and of beingformed in either of two ways : H + HBr zz [H---H---Br] zzH, + Br. From the magnified contour of the saddle region(Pig. 2), the complex is characterised by rl = rz = 1.43 A. andE = 22,100 calories. The identity of rl and r,, though possiblyaccidental, fits in with the hypothesis of D. S. Villars that E isthe minimum energy of the system which is compatible with equalatomic separations. The discrepancy between the observed andcalculated vaIues of E is due partly to the approximate nature ofLondon’s equation, to the uncertainty about the Coulombic exchangeratio, and to the omission of statistical averaging.The energy-mountain model, in spite of its crudeness, is the rock upon whichFIG. 2.quantum-mechanical theories of chemical change are built. Itis believed to depict, at least in broad outline, the essential featuresof the mechanism of those simple chemical reactions which proceedwithout electronic transitions. Such reactions are said to beadiabati~.~General Considerations on the Pot en tial- energy Mountain .-Ahelpful aspect of the present theory is the light which it throwson some of the obscure factors which determine the course ofchemical change. Expressions similar to equation (1) have beenderived for systems consisting of more than three atoms.Eyringand Polanyi’s comparison of the theoretical energies of activation4 J. Amer. Chem. SOC., 1930, 52, 1773.6 F. London, 2. Elektrochem., 1929, 35, 552; J. H. van Vleck and A.Sherman, Rev. Mod. Physics, 1935, 7, 167; H. Hellmann, Acta Physico-chimica U.R.S.S., 1936, 1, 913.F. London, Sommerfeld Festschrift, p. 104, Hirzel, Leipzig, 1928MOELWYN-HUGHES : CHEMICAL KINETICS. 93of the two reactions H, + o-H, -+ H, + p-H, and H + o-H, _j.H + p-H, showed E to be smaller for the latter reaction, whichshould therefore, ceteris paribus, be the more likely to occur. Theconclusion is in agreement with the actual mechanism establishedby A. Farkas.7 A comparison of the calculated E's for the reactionsC2H41, --+ C2H4 + I, and C,H41, -+ I + C2H4 + I, + I revealedbut a trifling difference; hence the two reactions should occurconcurrently, as is found to be the case.9 The predominant, thoughnot exclusive,lo addition of bromine in the 1 : 4-positions of thebutadiene molecule has received a similar explanation.11 As themechanism of each reaction had been established by experimentbefore theoretical computations were made, it is evident that thefunction of the theory in this direction has, up to the present, beenone of interpretation rather than of prediction.Perhaps thesuitable note to strike at this juncture is not lament at the inabilityto predict, but delight at the ability to interpret.The velocity of chemical reaction is determined by the number ofmolecules which possess the necessary energy ( E ) and by the prob-ability (G) per unit time that the activated molecules will suffertransformation.E is represented by the height of the col, and Q bythe probability that the representative point surmounts it. Ourestimate of G depends on whether the process obeys the laws ofclassical or those of quantum mechanics. Consider a one-dimen-sional barrier with a height corrt:sponding to E. According toclassical mechanics, the chance that a freely moving particle willsurmount it is independent of its shape; particles with energy Wwill always pass the top provided W 2 E , and will never pass itwhen W <E. According to quantum mechanics, the probabilityof transit is finite even when W < E, and amounts to certaintyonly as W --+ CO. In principle, C can always be evaluated whenthe potential energy barrier has been expressed analytically.l2 Bymaking assumptions about the shape of the barrier, expressions canbe deduced l3 relating its permeability (G) with its height ( E ) andwidth. Numerical computations for barriers of plausible widths7 2. physikal. Chem., 1930, [B], 18, 419.8 A. Sherman and C. E. Sun, J . Amel.. Clzem. SOC., 1934, 56, 1096.9 L. B. Arnold and G. B. Kistiakowsky, J . Chem. Physics, 1933, 1, 166.10 G. B. Heisig and J. L. Wilson, J . Arner. Chem. SOC., 1935, 57, 859.11 H. Eyring, A. Sherman, and G. E. Kimball, J . Chem. Physics, 1933, 1,12 E. Wigner, 2. physikal.Chem., 1933, [B], 19, 203.13 D. G. Bourgin, Proc. Nut. Acad. Sci., 1929,15,357 ; R. M. Langer, PhysicalRev., 1.929, 33, 290; C. Eckart, ibid., 1930, 35, 1303; S. Roginsky and L.Rosenkewitch, 2. physikal. Chem., 1930, [B], 10, 47; E. Wigner, PhysicalRev., 1932, 40, 749; C. Zener, Proc. Roy. SOC., 1932, [A], 137, 696.58694 GENERAL AND PHYSIUAL CHEMISTRY.and heights 14 show that G approximates to the classical valueexcept when the mass, temperature, and energy of activation arelow. It is conceivable that certain reactions exist, the rate ofwhich is governed by the quantum-mechanical transmission ofa hydrogen atom or proton, rather than by the co-ordinatedevolutions of a system of atoms. Bell1* has shown that, adoptinga barrier of the shape postulated by Eckart l3 for an athermicreaction with E = 14,500 calories and a width of 2 8., G varieswith T in such a way that the Arrhenius E would be only 6,300calories.If the somewhat speculative computations approximateto the truth, large differences are to be expected between observedand theoretical values of E. However, the behaviour of reactionsinvolving massive particles may confidently be regarded as classical(G = 1 when W 2 E), particularly when E is appreciable.Recent classical treatments of the passage of the representativepoint over the col15 have been synthesised and elaborated into atheory of great attractiveness by H. Eyring,lG who considers thecritical complex to resemble a stable molecule in all respects exceptin the motion along the co-ordinate of decomposition. On accountof the flatness of the saddle region, the motion in this degree offreedom is regarded as classical.The governing idea is that thepassage over the col is associated with constancy in the number,but change in the nature, of the degrees of freedom. When, forexample, two atoms A and B collide to form a complex A .. . B,from which the stable molecule AB will ultimately emerge, thesix translational degrees of freedom (three for each atom) areconverted into three degrees of translation of the complex A . . . Bas a whole, two degrees of freedom of rotation, and-most importantof all-one degree of freedom of translation of the atoms A and Bwithin the complex, along the line of centres. The velocity ofreaction is largely a function of the energy in this special degree offreedom.Quantitative developments have recourse to a generaltheorem in statistical mechanics 1’ (see also p. 66) which relates theequilibrium constant ( K ) , for unit volume, with the energy change(E,) and the relevant partition functions ( F ) :K = F ~ B . e-Eo’RT/FaFB . . . . * (4)l4 R. B. Bell, Proc. Roy. SOC., 1933, [ A ] , 139,466 ; 1935, 148, 241 ; C. E. H.Barn and G. Odgen, Trans. Paraday Xoc., 1934, 30, 432.l5 E. Wigner and M. Polanyi, 2. physikal. Chem., 1928, 139, 439; H.Pelzer and E. Wigner, ibid., 1932, [B], 15, 445 ; 0. K. Rice and H. Gershino-witz, J. Chem. Physics, 1934, 2, 853; W. H. Rodebush, ibid., 1933, 1, 440;1935, 3, 242; M. G. Evans and M.Polanyi, Trans. Paraday Xoc., 1935, 31,875.l6 J . Chem. Physics, 1935, 3, 107.l7 R. H. Fowler, “ Statistical Mechanics,” Chap. V, Cambridge, 1929MOELWYN-HUGHES : CHEMICAL KINE’MCS. 95The evaluation of F is in general a difficult matter, unless the motionsare completely classical or completely quantised, and can be treatedas virtually independent. In such cases, F factorises into F1F2F3. . .Extracting from FAB the factor which takes account of the motionin the ‘‘ co-ordinate of decomposition,” and regarding this motion asone in a force-free field, we get :K = (FZ*/FAFB). e-EO/RT. dZnmkT/hThis expression gives the concentration of critical complexes a t thecol ; multiplication by the average velocity dLT/2nm of transit overthe col gives us Eyring’s general formula for the velocity of reaction :In the particular example discussed here, F,&/FA.FB becomeshZ/lcT, where Z is the kinetic-theory value for the frequency ofbinary collisions. The classical equation for the velocity of simplebimolecular processes is thus deducible from somewhat novelpremises. The theory has been helpful in elucidating severalproblems, including the rates of homologous unimolecular reactionsin gases,l* the negative temperature coefficient of the velocity oftermolecular reactions,lg and the variation of the steric factor withmolecular complexity.20 Its application to the problems of reactionsin solution21 makes appeal to the idea of entropy of activation.22Attention has been directed 23 to errors in the treatment of Wynne-Jones and Eyring.An extension of the energy-mountain technique has shown theway to the calculation of the energy of activation of simple ionicreactions.24 We shall illustrate the method by discussing thereaction CH,C1 + I’ -+ CH31 + C1’ in acetone solution.Thecharge on the attacking ion and the sign of the dipole predisposethe approach to take place in the manner indicated :k = (F&/FAFB) . e-EotRT . ET/h . . . (5)During chemical change, therefore, the methyl chloride molecule isturned inside out, like an umbrella in a strong wind. This mechan-l8 0. K. Rice and H. Gershinowitz, J . Chem. Physics, 1935, 3, 479.l9 H. Gershinowitz and H. Eyring, J . Amer. Chem. SOC., 1935, 57, 985.2O C. E. H. Brzwn, Trans. Paraday SOC., 1935, 31, 1536.21 W.F. K. Wynne-Jones and H. Eyring, J . Chem. Physics, 1935, 3, 492.22 F. G. Soper, Discussion on the Critical Increment, Chemical Society,23 E. A. Moelwyn-Hughes, ibid., in the press.24 R. A. Ogg and M. Polanyi, Trans. Paraday SOC., 1935,31, 604.1931, p. 45; V. K. LaMer, J . Chem. Physics, 1933,1, 28996 GENERAL AND PHYSICAL CHEMISTRY.ism was dictated by the facts of the Walden inversion, and isconsistent with Lowry's theorem that reaction takes place throughthe intermediate formation of a compound of higher symmetry.Direct support for it has recently been given by E. D. Hughes,F. Juliusberger, S. Masterman, B. Topley, and J. we is^,^^ who haveestablished experimentally the identity in the rate of inversion ofsec.-octyl iodide and the rate with which the iodine atom is exchangedby its radioactive isotope.Ogg and Polanyi's expression for thepotential energy of the reacting system may be writtenwhere rl is the separation of the iodine ion, and r2 that of the chlorineatom, from the carbon atom, the polarisability of which is CI.DCH3CI is the heat of dissociation, and a and ro are the Morse constantsfor methyl chloride. The heat of solvation (XI-) of the iodine ionis computed from the constants (b, and p ) of the repulsive field incrystals.26 The use of a similar expression for the potential energy(E,) of the product system allows an evaluation of the energy ofactivation ( E ) . Among the factorswhich are omitted from the treatment, one may mention theinfluence of the cation, the inclusion of which leads to a bettervalue of E.Several conclusions of a qualitative, or a t best asemi-quantitative, nature may be drawn from general considerationsof the solid geometry of potential-energy models. Some of theproblems relating to chemil~minescence,~~ prototropy 28 andexchange 29 have been approached from this angle. By a combin-ation of the methods of Eyring and Polanyi for non-polar systemswith those of Ogg and Polanyi 24 for ionic systems, potential surfaceshave been constructed for simple chemical changes where thereactants are of one kind and the resultants of an~ther.~OSince the velocity coefficient (Ic) is usually proportional toe-E'RT, any influence which lowers the energy of activation increasesthe velocity, and is thus positively catalytic.The introductionof an ion, a dipole, or a, polarisable atom or molecule into anelectrically neutral reacting system may, of course, increase ordecrease the potential energy; and the height of the col maythereby be raised or lowered. I n the former case, however, thedisturbance merely makes possible an alternative mechanism whichThe result is 50% too high.2 5 J., 1935, 1525.2 6 M. Born and J. E. Mayer, 2. Physilc, 1932, 75, 1.2 7 R. A. Ogg and M. Polanyi, Trans. Paraday SOC., 1935, 31, 1375.2 8 J. Horiuti and M. Polanyi, Acta Physicochirnica U.R.S.S., 1935, 2, 505.2o R. A. Smith, Proc. Camb. Phil. SOC., 1934,30, 508.30 A. G. Evans and M. G. Evans, Trans. Paraday Xoc., 1935,31,1400MOELWYN-HUGHES : CEEMICAL KINETICS.97is less likely to occur than the undisturbed process, and may there-fore be ignored. In the latter case, the disturbed mechanism isthe more facile, and may replace the original one. Steps towardsthe formulation of a quantum-mechanical theory of catalysis havealready been taken.31It is a matter of interest to inquire into the possible connexionbetween the processes of activation, as the term is understood inchemical kinetics, and of the excitation of vibrational quanta. Thestudy of the latter phenomenon is advancing rapidly.32 Quantitativeapplications of the theories presuppose a precise knowledge ofinteratomic force-fields, and are possible only in very simple cases.Approximate solutions to the problem being a~cepted,3~ it canreadily be shown, for example, that the chance of a hydrogen atomexciting the first vibrational quantum in the molecule of hydrogenbromide is negligible compared with the chance of chemical reaction,in all relevant collisions.On the other hand, with molecules ofslightly higher complexity, the interchange of translatory andvibrational energy is of some importance. C. N. Hinshel~ood,~~co-ordinating the salient facts relating to the catalytic decompositionof gaseous aldehydes, ethers, and nitrous oxide, points out that theefficient catalysts (e.g., iodine, halogen atoms, nitric oxide, andoxygen) possess the qualities (polarisability, free valency, oddelectron, and magnetic moment) which according to classicaltheory favour specific energy transfers.The distinction thusappears t o be due to the fact that, with an organic molecule,vibrational excitation occurs in bonds other than that which iseventually broken. Hinshelwood differentiates between a pre-activated molecule and a critically activated one : both possess thenecessary energy, but the former laeks the appropriate internaldistribution, while the latter possesses the necessary energy in theright spot, and will decompose in the course of the next completevibration. Further reference will be made to the question of theinternal redistribution of energy (see p. 108).Atomic Reactions.-The study of reactions involving the simplereplacement of one atom by another offers obvious advantages.31 H. M.James and A. S. Coolidge, J . C7~em. Phyaics, 1934, 2, 811; A. E.Stearn, J. Gen. Physiol., 1934, 18, 171 ; A. A. Schuchowitzky, Acta Physico-chimica U.R.S.S., 1935, 1, 901; R. M. Langer, loc. cit., ref. (13).33 0. Schmidt, Ann. Physlsik, 1934, 21, 241; H. 0. Kneser, Physikal. Z.,1934, 35, 983; A. Eucken and R. Becker, 2. physilcal. Chem., 1934, [B], 27,219; J. E. Lennard-Jones and C. Strachan, Proc. Roy. SOC., 1935, [ A ] , 150,442.33 N. F. Mott and H. S. W. Massey, “ The Theory of Atomic Collisions,”p. 248, Oxford, 1933.34 J., 1935, 1111.REP.-VOL. XXXII. 98 GENERAL AND PHYSICAL CHEMISTRY.A profitable approach t o the investigation of any given chemicalreaction, say A + BC --+ AB + C, is to examine it in conjunctionwith the sister reaction A + BD + AB + D, where C and Dbelong to the same family in the periodic table, Experience shows,however, that the study of the second reaction, instead of solving ourfirst difficulties, very often introduces new ones.We find ourselvest o be, in fact, very near the core of chemistry, which holds thesecret of the specificity of the various forms of matter. Aninvestigation of the twin reactions A + BD, + AB + D, andA + BD, --+ AB + D,, where D, and D, are isotopes of the sameelement, should take us a stage nearer the goal, because isotopicspecificity, for all chemical purposes, is confined to those propertieswhich are directly related t o their masses. Of these properties,zero-point energy is one of the most important.35 From accuratespectroscopic values of V, we have, for hydrogen, EoHI = 6,180, andfor deuterium, EoDz = 4,390 calories per g.-mol., hence EoEt - E*D, =1,800. The simplest known chemical reactions are (1) H + H, --+(4) D + H, 4 DH $- H.Kinetic information about them iswell-nigh complete.36 The first two are the ortho-para conversionof hydrogen and deuterium; the second two are the significantsteps in the reaction H, + D, 2HD. The difference in velocityof reactions (1) and (2) is due to two factors, vix., the difference inthe collision frequencies and that in activation energies, whichexperiment shows to be about 500 calories. Now the energy ofactivation ( E ) is defined as the difference between the energy (E*)of the activated state (HHH or DDD) and the energy (E") of theinitial state (H2 or D2); hence E&E - E z D D = (EOH, - EOD,) -/-(EE,,H - ED2,D) = 1,300.This quantity is in agreement with thedifference calculated for the energies of the systems HHH and DDDby making plausible assumptions about the force constants. Muchof the existing literature has been considered in this light. Theadditional data for HHD, HDD, HDH, DHD, HNBr, DDBr,HHC1, etc., make it appear probable that critical complexes do, infact, possess zero-point energy, and thus resemble stable moleculesat least in one respect. The difference in E for the reactions Na +H C l 4 NaCl + H (6,100 cals.) and Na + DCl-> NaCl + D(6,400 cals.) has been independently accounted for in the same way.37G. Schay has continued his work on the interaction of alkali atomsH,+H; (2) D+D,+D,+D; (3) H+D,---t.HD+D;3 5 (Frl.) E.Cremer and M. Polanyi, 2. physikal. Ci~em., 1932, [B], 19, 443.36 A. Farkas and L. Farkas, Proc. Roy. Soc., 1935, [A], 152,124; A. Farkas,(' Ortho-Hydrogen, Para-Hydrogen, and Heavy Hydrogen," Cambridge,1935.3 7 C. E. H. Bawn and A. G. Evans, Trans. E'araday Suc., 1935, 31, 1392MOELWYN-HUGHES CHEMICAL KINETICS. 99with molecules of halogen38 and of mercury halides.39 Except fora few details, the mechanism of reaction with potassium atoms isthe same as that established with sodium.40 The homogeneousreaction K + I,---+ KI + I + q1 cals. is followed by a wallreaction K + I + KI and by a second homogeneous reactionK, + I+ KI + K + 4, cals. The state of electronic excitationof the emergent potassium atom is governed largely by the magnitudeof the heat effect 4,.The violet doublet is absent from the flamespectrum, in agreement with thermodynamic anticipation. Fromthe temperature variation of one of the contributions to the totallight intensity, the heat of dissociation of the reaction K, zz 2K isfound t o be 18,700 cals. The rate and energy of activation for thereaction between sodium atoms and monohalogen derivatives ofbenzene have been measured and discussed,41 as well as thereactions 42343 0 + NO, -+ NO + 0, and Br + C1, + BrCl + C1.The actual union of two atoms to form a covalent molecule differsfrom the pictorial account discussed on p. 91, in that it requires thepresence of a third atom or molecule to render the collision effective.The third partner may be a part of the wall of the reaction vessel,or a free atom or molecule in the gas.W. Steiner, whose earlierwork44 on the mechanism of ternary encounters has received newconflrmati0n~4~ has elaborated his theory of the recombination ofhydrogen atoms.46 After allowing for the diffusion of hydrogenatoms to the wall, it appears that the reactions H + H + Molecule-+ H, + Molecule and H + H + Atom- H, + Atom havevelocities in the approximate ratio of 9 : 10. Hydrogen atoms havebeen found to combine 1.36 times as fast as deuterium atoms, inagreement with our knowledge of the identity in diameters andforce constant^.*^ G. M. Schwab 48 has shown that every collisionbetween a bromine atom from the gas phase and a similar atomadsorbed on the wall is effective.38 E.Roth and G. Schay, 2. physikal. Chem., 1935, [B], 28, 323.3g I. Bereger and G. Schay, ibid., p. 332.40 M. Krocsak and G. Schay, ibid., 1032, [B], 19, 344. References to stillearlier work have been given by E. K. Rideal, Ann. Reports, 1928, and byC. N. Hinshelwood, ibid., 1930, 1931.4 1 F. Fairbrother and E. Warhurst, Trans. Paraday SOC., 1935, 31, 987.42 M. L. Spielman and W. H. Rodebush, J . Amer. Chem. SOC., 1935,57,1474.43 G. Brauer and E. Victor, 2. Elektrochem., 1935, 41, 508.44 2. physikal. Chem., 1931, [B], 15, 249.45 L. Farkas and H. Sachsse, ibid., 1934, [B], 27,111 ; G. A. Cook and J. R.Bates, J . Amer. Chem. SOC., 1935, 57, 1775.46 W. Steiner, Trans.Faraday SOC., 1935, 31, 623, 962.47 I. Amdur, J . Amer. Chem. SOC., 1935, 5'9, 856.48 2. phyeikal. Chem., 1934, [B], 27, 452.IT. L. Lehmann, Trans. Paraday SOC., 1035, 31, 689.See also E. Rabinowitch an100 GENERAL AND PHYSICAL CHEMISTRY.As a matter of pure nomenclature, it may be pointed out that theterm “ exchange reaction ” is being accepted for changes involvingthe replacement of an atom by one of its isotopes. The mechanism,as we have seen, is usually an atomic one.More Complicated Reactions in the Gaseous Phase.-The repetition-perhaps inevitable-of some of the key experiments has con-solidated the territories gained during the last decade in this domain.A reinvestigation 49 of the reaction CH,*CHO -+ CH, + COunder the original conditions yields no evidence that it is appreciablyheterogeneous, as is the case a t lower temperatures50 or that itdepends upon a chain mechanism.It also appears 51 that thestationary concentration of hydrogen atoms is too low t o maintainthe type of chain mechanism mooted by F. 0. Rice and K. F.H e r ~ f e l d . ~ ~ The catalytic influence of oxygen and of two oxidesof nitrogen on this reaction has been st~died.5~ The decompositionof nitrous oxide, examined under pressures amounting to 40 atmo-s p h e r e ~ , ~ ~ confirms the conclusions of F. 3’. Musgrave and C. N.Hin~helwood.5~ For both these reactions, the apparent E increasesas the pressure is raised. The r81e of keten as the intermediatecompound in the unimolecular decomposition of acetone has beenquantitatively studied ; again, there is evidence for compositeactivation and for the absence of long chains.56 The thermaldecomposition of ozone has been the subject of repeated investig-ation 57 and discussion.58 Azomethane explodes a t temperaturesslightly higher than those a t which H. C. Ramsperger measured thequiet unimolecular decomposition.59 The study of the formation ofhydrogen sulphide from its elements continues to offer difficulties,but the r81e played by sulphur atoms is becoming clearer.60 Thereaction between hydrogen and oxygen attracts unabated attention.The influence thereon of replacing hydrogen by deuterium,61 of49 C. A. Winkler and C. N. Hinshelwood, Proc. Roy. SOC., 1935, [A], 149,50 M. W. Travers, Proc.Roy. Xoc., 1934, [ A ] , 146,284; Nature, 1935,135, Till.81 F. Patat and H. Sachsse, Naturwiss., 1935, 23, 247.62 J . Amer. Chem. SOC., 1934, 56, 284.s3 F. H. Varhoek, Trans. Paraday Xoc., 1935, 31, 1521; E. W. R. Steacie54 E. Hunter, Proc. Roy. SOC., 1934, [ A ] , 144,386. 55 Ibid., 1932,135,23.5 6 C. A. Winkler and C. N. Hinshelwood, ibid., 1935, [A], 149, 340.5 7 M. Ritchie, ibid., 1934, [A], 146, 848.58 H. J. Schumacher, ibid., 1935, [ A ] , 150, 220; M. Ritchie, Nature, 1935,355; M. Letort, Cornpt. rend., 1935, 200, 312.and R. D. Macdonald, Canadian J . Res., 1935, 12, 711.136, 221.A. 0. Allen and 0. K. Rice, J . Amer. (772,em. SOC., 1935, 57, 310.60 E. E. Aynsley, T. G. Pearson, and P. L. Robinson, J., 1935, 58.61 C. N. Hinshelwood, A, T, Williamson, and J, H.Wolfenden, PTOC. Rqy.SOC., 1934, [A]$ 147, 48MOELWYN-HUGHES : CHEMICAL KINETICS. 101salt-coating the walls,62 of passing electric dis~harges,~~ of intro-ducing tetraeth~l-lead,~~ and of the presence of a palladium catalyst 66have all been examined. Recent values of the lower explosionlimit 66 are somewhat lower than those found originally. The lowerexplosion limit for the oxidation of phosphine has been re-examinedunder a wide variety of conditions by S. C. Gray and H. W. Mel-~ i l l e , ~ ~ whose results, along with recalculated values for eight otherreactions, confirm the accepted t,heory. New data on the lowerexplosion limit for the oxidation of carbonyl sulphide and of silanehave been published by H.Gutschmidt and K. Clusius.67aThe number of recorded chemical phenomena which find theirreadiest interpretation in terms of the chain theory is rapidlyincreasing.67b For example, R. G. W. Norrish 68 has shown that theoxidation of hydrocarbons-now definitely established as a directattack by oxygen 69-which yields such complicated analyticaland kinetic results, can be represented in terms of quite a simplechain mechanism. A helpful summarising article on this subjecthas also been given by W. Jost.’O Polymerisation reactions offerspecial opportunities for displaying the power of the chain theory.71These interesting chemical changes are gaining a new importance ;but the time does not seem ripe for discussing them in these Reports.We shall, however, refer to them again in a later section.The chaintheory itself has been elaborated in two directions. To accountfor the widening out of the explosion limits consequent upon theintroduction of artificially generated chain centres, N. Semenoff 72has postulated a mutual interference of the chains. I n order toexplain the rapidity with which explosion waves travel in deton-ations, K. I<. Andrkew and J. B. Chariton 73 invoke the idea ofmacro-chains, New experiments to which the less elaboratetheory has been applied include those on the explosion of ethyl62 M. Prettre, C’ompt. rend., 1935, 200, 132.a3 G. Gorchakov and L. Lavrov, Actii Physicochimica U.R.S.S., 1934,1,139.64 H. G . Tanner, J . Amer. Ghem. Soc., 1934, 56, 2250.6 5 D. L.Chapman and G. Gregory, Proc. Roy. SOC., 1934, [ A ] , 14’9, 68.6 6 W. E. Garner and H. J. Willavoys, Trans. Paraday SOC., 1935, 31, 806.6 i b N. Semenoff, “Chemical Kinetics and Chain Reactions,” Oxford, 1935.6 8 Proc. Roy. SOC., 1935, [ A ] , 150, 36.09 W. A. Bone and J . Bell, ibid., 1934, [A], 144, 257.70 2. Elektrochem., 1935, 41, 186.7 1 H. Dostal and H. Mark, 2. physsilcal. Chem., 1935, [B], 29, 299; G. Geeand E . K. Rideal, Trans. Paraday SOC., 1935, 31, 969. A Report of theFaraday Society’s Discussion on Polymerisation is to be published in 1936.A preliminary survey (E. K. Rideal, Nature, 1935, 135, 626) has alreadyappeared.Ibid., p . 452. 67a Z. phyaikal. Chem., 1935, [B], 30, 265.72 2. physikal. Chem., 1935, [B], 28, 31.73 Trans. Paraday SOC., 1935, 31, 797102 GENERAL AND PHYSICAL CHEMISTRY.nzide, 74 the oxidation of pr~paldehyde,~~ the chlorination of pro-pane,76 the polymerisation of f~rmaldehyde,~~ the reaction betweencarbon monoxide and nitrous oxide,78 and the effect of hydrogenon the carbon monoxide flame.79Brief mention must be made of the increasing variety of decom-position reactions which have been recently studied.The followingcompounds decompose by a unimolecular mechanism in the homo-geneous gas phase : methyl 8* and sec.-butyl 81 iodides; nitro-methane ; methyl,83 mpropyl,84 and isopropyl s5 nitrites ; andb dyoxa1.86 Only the primary step in the decomposition of methyl-amine 87 is homogeneous; increased surface inhibits the rate ofdecomposition of propylamine,88 an effect which is apparentlyabsent in the case of trieth~lamine.~~ An interesting exampleof intermolecular conversion obeying the unimolecular law is the iso-merism of cis-methyl inna am ate.^^ Bimolecular behaviour is ex-hibited by the polymerisation and hydrogenation of a ~ e t y l e n e , ~ ~by the decomposition of nitrosyl and predominantly bythe decomposition of a~raldehyde.~~ The effect of iodine on therate of decomposition of chloral 9* is consistent with a bimolecularmechanism involving iodine atoms ; catalysis by nitric oxide issimilarly inter~reted.~5 The decomposition of nickel carbonyl 96follows a more complicated course.74 H.C. Campbell and 0. K. Rice, J . Amer. Chem. SOC., 1935,5'7,1044.7 5 E. W. R. Steacie, W.H. Hatcher, and S. Rosenberg, J . Physical Ckem.,7 6 S. Yuster and L. H. Reyerson, ibid., 1935, 39, 859.7 7 J. E. Carro%hers and R. G. W. Norrish, Nature, 1935, 135, 582.7 8 C. E. H. Bawn, Trans. Faraday SOC., 1935, 31, 461.79 W. E. Garner and F. H. Pollard, J., 1935, 144.80 E. W. R. Steacie and R. D. Macdonald, J . Arner. ClLem. SOC., 1935,57,488.81 R. A. Ogg and M. Polanyi, Trans. Faraday SOC., 1935, 31, 482.82 H. A. Taylor and V. V. Vesselovsky, J. Physical Chem., 1935, 39, 1095.83 14:. W. R. Steacie and G. T. Shaw, Proc. Roy. SOC., 1934, [A], 146, 388.8 4 Idem, J . Chern. Physics, 1935, 3, 345.6 5 Idem, Proc. Roy. SOC., 1935, [A], 151, 685.86 E. W. R. Steacie, W. H. Hatcher, and J. F. Harwood, J . Chem. Physiqv,87 H. J. Emel6us and L.J. Jolley, J., 1935, 929.88 D. V. Sickman and 0. K. Rice, J . Arner. Chem. SOC., 1935, 5'7, 22.s9 H. A. Taylor and E. E. Juterbock, J . Physical Chem., 1935, 39, 1103.90 G. B. Kistiakowsky and W. R. Smith, J . Amer. Chem. SOC., 1935,57,269.91 H. A. Taylor and A. van Hook, J . Physical Chem., 1935, 39, 811.92 G. Waddington and R. C. Tolman, J . Amer. Chem. SOC., 1935, 57, 698.93 H. W. Thompson and J. J. Frewing, J., 1935, 1443.g* F. H. Verhoek and C. N. Hinshelwood, PTOC. Roy. SOC., 1934, [A], 146,334.9 5 F. H. Verhoek, Trans. Paraday SOC., 1935, 31, 1521.96 A. P. Garratt and H. W. Thompson, J., 1934, 1822; C. E. H. Bawn,1934, 38, 1189.1935, 3, 291.Trans. Paraday SOC., 1935, 31, 461MOELWYN-HUGHES : CHEMICAL KINETICS. 103Reactions in Solution.-Advances in this field have dependedmore on the correct interpretation of existing data than on thediscovery of new reactions.Our virtual ignorance of the natureof interaction in the condensed phase, long used as an excusefor shunning the problem, is now recognised as a, reason forstudying it.Many of the reactions which proved helpful in instituting it co-ordinated theory of reactions in solution have been reinvestigated ,with confirmatory results. To the sole instance previously known,two others have been added (C,H,12 + I+ C,H4 + I, + I and0, + p-H, + 0, + o-H,) of bimolecular reactions which have beenmeasured in the gas phase and in solution : 97, 98 they have the sameE and li: in the two phases. These results afford the most directknowledge we have of the frequency of binary collisions in dilutesolution.They support the anticipations of Christiansen (1923)’Tolman (1927), and others that 2 is of the same order of magnitudein the two systems. A third example (COX + H,O --+ CO, +H,S) gives E = 25,700 for the predominantly homogeneous gasreaction, and E = 22,700 for the condensed reaction; collisionsin the latter case, however, are hetween solute and solvent mole-cules ; if their frequency is calculated by the equation ,Z, = 3xr)o/2m,E for the condensed reaction becomes 26,300 ~als.9~ Furtheranalogies between collision frequencies in the two systems may bedrawn from the work on quenching of fluorescence in gases andliquids.1 A. W. Chapman, has shown that the velocity of theBeckmann transformation of benzophenoneoxime picryl ether,catalysed by a variety of substances in carbon tetrachloride, has thesame value as that computed for the hypothetical gas reaction,the observed E’s and the gas kinetic collision formula being used.The assumption that reactions of the type R,ONa + R,Cl+R,0R2 + NaCl are chiefly ionic, involving R,O’ ions, has beenjustified by more reliable determinations of the degree of dis-sociation.3 The similarity of the k’s for homologous reactions hasbeen discussed in terms of the theory of coupled oscillators.4 Thedistinction drawn between these etherifications and reactions ofthe type R,R,R,N + R,Cl-+ R,R,R,R4NC1 has been heightenedby the response of the two to high pressures, which has been accur-9 7 LOC.cit., ref. (9), p. 93.9s L. Farkas and H. Sachsse, 2. physikal. Chem., 1933, [B], 23, 1.99 H. W. Thompson, C. F. Kearton, and S. A. Lamb, J., 1935, 1033.1 ,J. Franck and H. Levi, 2. physikal. Chem., 1934, [B], 27, 409.2 J . , 1934,1550 ; 1935,1223 ; see also K. D. Anderson and D. L1. Hammick,3 p. J. Hardwick, ibid., 1935, 141.4 H. Pelzer, 8. EZektrochem., 1934, 39, 608.ibid., p. 30104 GENERAL AND PHYSICAL CHEMISTRY.ately studied.5 The rate of formation of urea and of monomethyl-urea to form cyanate ions and the corresponding cations has beenthe subject of precise and extensive work in various media,6enabling the relation between critical increment and ionic strengthto be verified and elaborated.' The expected independence of Eof electrolyte concentration has been demonstrated for numerousreactions of zero ionic type, including the acid hydrolysis of diethyl-aceta18 and ethyl a ~ e t a t e , ~ and the basic hydrolysis of the acetyl-glycollate ion, for which over 300 values of E have been published.10The value of E recently found for the mutarotation of glucose inwater (18,000) l1 is in better agreement with the classical value of17,700 given by Hudson and Dale in 1917 than with the amendedvalue of 19,300 published by Kilpatriclr in 1931.The rates ofreactions of the type R1R2S + R,Cl _t R1R2R,SC1 have hithertobeen inferred quantities ; direct measurements have now been madein various solvents.12 Distinctly less attention is being paid to thestudy of reactions of the first and the third order.New instances ofthe unimolecular cleavage of carbon dioxide from acids have,however, been examined,13 and the alleged termolecular reactionbetween stannous and ferric chlorides has been shown to be fairlycomplicated.14 The latter change bears many of the distinguishingfeatures of a chain reaction, though it has not yet been discussed fromthis angle. The search is also being continued for a satisfactoryexplanation of the kinetics of those complicated reactions involvinghalide, hypohalite, halite, and halate ions in aqueous s01ution.l~E. W. Fawcett and R. 0. Gibson, J . , 1934, 386; R. 0. Gibson, E. W.(Miss) C. C. Miller, ibid., 1934, [ A ] , 145, 288; 1935, [ A ] , 151, 188.J . C. Warner and collaborators; with F.€3. Stitt, J. Amer. Chenb. SOC.,1933,55,4807; with E . L. Warrick, ibid., 1935,57, 1491 ; with W. J. Svirbely,ibid., p. 1883.L. C. Riesch and M. Kilpatrick, J . Physical Chem., 1935, 39, 561.W. Wylzafkowska, Rocz. Chcm., 1934, 14, 1118.Fawcett, and M. W. Perrin, Proc. Roy. Soc., 1935, [A], 150, 223.lo A. von Kiss and R. Kukai, 2. anorg. Chem., 1935, 223, 149; Rec. trav.l1 E . A. Moelwyn-Hughes, 33. Klar, and K. F . Bonhoeffer, 2. physiknl.l2 J. K . Syrkin and I. T. Gladischew, Acta Physicochiinica U.R.S.S.,l3 (Miss) J. MUUS, J . PhysicaZ Chem., 1935, 39, 343 ; K. Beniya, J . Biochem.14 R. A. Robinson and N. H. Law, Trans. Paraday ~ o c . , 1935, 31, 899.l5 H. A. Liebhafsky, J . Amer. Chem. SOC., 1934, 56, 2369; R. M. Chapin,ibid., p.2212; W. C. Bray and H. A. Liebhafsky, ibid., p. 51; R. 0. Griffithand A. RlcKeown, Trans. Faraday SOC., 1935, 31, 868; A. Skrabal and H.Schreiner, Monatsh., 1935, 65, 213; C. F. Prutton and S. H. Maron, J . Amel..Ghem. SOC., 1935, 57, 1652.chim., 1935, 54, 337.Chem., 1934, 169, 113.1935, 2, 291.J a p n , 1934, 20, 451MOELWYN-HUGHES : CHEMICAL KINETICS. 105Four of the directions in which the subject is advancing may beindicated roughly by the terms rapid reactions, radical reactions,exchange reactions, and film reactions.The application of Hartridge and Roughton's technique 16 offersa. means of extending the range of observable phenomena in solution.In the hands of H. von Halban and H. Eisner,17 preliminary con-clusions are already derived concerning numerous organic andinorganic reactions which are half completed in about 0.001 second,and further useful information may confidently be expected fromthis source.The methods of measuring the speed of reactions insolution have formed the subject of a recent biochemical discussion.18The part played by free radicals in solution becomes moreprominent. E. Abel and K. HilferdingI9 accept the mechanismproposed by Griffith and McKeown (1932) for the action of aqueousiodine on oxalic acid. One of the three rate-determining steps isI + C,O," + C204' + I f , with E = 19,000, and a chain lengthof a few million cycles. The function of HO, in the decompositionof aqueous hydrogen peroxide has been quantitatively studied.20J.R. Velasco 21 finds that the relative rates of reaction of ketoneswith diphenylsemicarbazide are exponentially related to theiroxidation potentials ; and a complementary relation apparentlyholds for the inhibitive action of foreign substances on the reductionof mercuric chloride by picric acid.22 The energetics of some of thesteps in radical chains thus become amenable to measurement.Experiments on the replacement of the hydrated proton by thehydrated deuteron showed that the ratio a = k~~o-/k=,O- is lessthan 1 for the mutarotation of glucose, and that daldT is positive ; 23for the inversion of cane sugar, a exceeds 1, and dct/dT is negative.24The hydrolysis of methyl acetate25 runs parallel to the case ofsucrose. By applying the theory of multiple catalysis, the valueof EHoD has since been estimated a t 25°.26 E for the pseudo-uni-16 See R.Brinkman, R. Magaria, and F. J. W. Roughton, Phil. Trans,,1933, [A], 232,65.1 7 Helv. Chim. Acta, 1935,18, 724.18 A. V. Hill, H. Freundlich, 13. Hartridge, G . Millikan, F. J. W. Roughton,E. K. Rideal, J. B. S. Haldane, 31. Polanyi, and McK. Cattell, Proc. Roy. SOC.,1934, [B], 116, 185.1s 2. physikal. Chem., 1935, 172, 353.20 G. Kornfeld, ibid., 1935, [B], 29, 205; J. Weiss, Trans. Paraday SOC.,1935, 31, 668; Naturwiss., 1935, 23, 64.21 Afial. Pis. Quim., 1935, 32, 345; cf. B. F. Chow, J . Arner. C'hem. SOC.,1935, 57, 1437.22 K. Weber, 2. physikal. Chem., 1935,172,459.23 E. A. Moelwyn-Hughes, ibid., 1934, [B], 26, 272.24 E. A.Moelwyn-Hughes and K. F. Bonhoeffer, Natumuiss., 1934, 22, 174.25 J. C. Hornel, Nature, 1935, 135, 909.26 W. IT. Hammill and V. K. LaMer, J . Chem. Physlsics, 1934, 2, 891.D 106 GENERAL AND PHYSICAL CHEMISTRY.molecular reaction CH3*CO*CH, + HOD ---+ CH3*CO*CH2D + HOHis 18,000 cals. ; 2' cc appears to be very nearly unity for hydroly-ticreactions catalysed by enzymes28-a result which allows us toeliminate one of the many explanations possible for the arrestingeffect of heavy water on the growth of organisms.29The relatively simple technique required to measure the surfacepotential of films 30 is a new and powerful implement in the handsof the investigator, enabling him, as it were, almost to touch themolecules which are reacting. With investigations of the hydrolysisof proteins,31 the oxidation of fatty the saponification ofe~ters,~3 and the polymerisation of unsaturated thesubject of chemical kinetics in two dimensions may be said to havebegun .35Remarks on the Semi-empirical Pactor, P.-The velocity constantfor bimolecular reactions may be written in the form li: = PZe-E/R1l,where 2 is the collision frequency.In the case of simple reactions,P gives the probability that an energetically satisfying encounterleads to chemical change. The meaning of P, often called the" steric " factor, is in other cases more obscure, and must be discussedbriefly. We shall accept the value of 2 given by the kinetic theoryof gases, although the use of formulae differing from it both inform 361 37 and in order of magnitude 383 l6 has been advocated.P is known to be unity for some hundreds of reactions in solutionand for some tens of reactions in gases.It may also be as highas lot9 or as low as 10-9. Reactions are said t o have normal,fast, or slow rates, according as P equals, exceeds, or is less than 1.When two comparable reactions have different rates, experimentshows that the difference may be due to a change in E, in P, or inboth. For example, when hydrogen chloride is replaced by hydrogenbromide in the chloroacetanilide reaction,39 the 20,000-fold increasein speed is due almost entirely to a, change in E . When an ionicreaction is compared with the corresponding non-ionic one, it oftenhappens that E remains constant while P, is about 1 and Po is2 7 L.J. Halford, L. C. Anderson, J. R. Bates, and R. D. Swisher, J . Amel..Chem. SOC., 1935, 57, 1663.28 E. W. R. Steacie, Z . physikal. Chem., 1934, [ B ] , 27, 6 ; 28, 236.z9 0. Reitz and K. F. Bonhoeffer, ibid., 1934, 17'2, 369; 1935, 174, 424.30 A. IT. Hughes, J. H. Schulman, and E. K. Rideal, Nature, 1932, 129, 21.31 J. H. Schulman and E. K. Rideal, Biochem. J., 1933, 27, 1581.32 A. H. Hughes and E. K. Rideal, Proc. Roy. SOC., 1933, [A], 140, 253.33 R. J. Fosbinder and E. K. Rideal, ibid., 1933, [ A ] , 143, 61.34 See Ref. 71. 35 Cf. E. J. Bowen, Ann. Reports, 1934.36 J. K. Syrkin, Acta Ph3sicochirnica U.R.S.S., 1935, 1, 855.37 R. S. Bradley, J., 1934, 1910.s8 M. C. Evans and M. Polanyi, Zoc. cit., ref. (16), p.94.$9 I. Jones and F. G, Soper, Proc. Roy, BOG, 1934, [A], 144, 643BlO.lkLWYN-HJJGHES : (IEEMICAL ICINETICS. 107lower by several powers of ten. Concurrent changes in P and Eare very common.There has been no lack of ideas in attempting to interpret P.Some of the earlier conjectures were disproved by the experimentsof Hinshelwood and Moelwyn-Hughes (19321, who pointed out newpossible meanings which may be attached to it. There are threeaspects of recent discussions.(1) The geometric factor, which aims a t allowing for orientationefTects. Opinions on the possible extent of this contribution varylargely. It should, perhaps, be pointed out that the effect is to someextent automatically allowed for in the dynamical formulation ofthe problem.@ J.M. SturtevantY4l on theoretical grounds, con-cludes that the orientation effect is not large enough to allow for therelatively minor deviations from the laws of Bronsted and LaMer.42With different experimental systems, on the other hand, A. T.Williamson and C. N. Hinshelwood43 consider that a factor of theorder of '' could reasonably be explained on the basis of thesimplest kind of steric considerations "-a view which is endorsedby R. P. Bell and (Sir) R. V. H. Levinge.44( 2 ) The transmission probability, G, which, according to H. Hell-mann and J. K. S ~ r k i n ? ~ can be considerably smaller than 1, evenfor massive particles, provided G is computed for each discretestate. Thus the ease with which the nitrogen atom in ammoniacan pass to and'fro through the plane of the three hydrogen atomsappears to be sensitive t o the degree of sharpness of the quantis-ation of vibrational energy.(3) The entropy change, S.Drawing on thermodynamicalanalogy, we may anticipate that E varies linearly with the temper-ature ( E = E, + XT), in which case P includes a term es/B. Inprinciple, X can be found from the temperature variation of E orfrom the postulated structure of the critical complex (Soper,22L;lrMer,22 Rodebush, l5 Wynne- Jones and Eyring 21). Provided welrnow the actual equilibrium data for reactants Z resultants,as distinct from the hypothetical equilibrium data for reactants zzreactive complex, we can eliminate the unknown term involvingthe entropy of activation, and obtain expressions for the velocity40 R.C. Tolman, " Statistical Mechenics," p. 67, 1927.4 1 J . Chem. Ph98iC8, 1935, 3, 295.42 A full account of these laws, and of salt effects in general, was given bySubsequent developments have43 Trans. Paraday SOC., 1934,30, 1145; A. C. Rolf0 and C. N. Hinshelwood,44 proc. Roy. SOC., 1935, [A], 151, 211.4s ACta Ph,yeico~himka U.R.S.S., 1935, 8,433.R. p. Bell in the Annual Reports for 1934.been hardly sufllcient to warrant discussion here.ibid., p. 935108 GENERAL AND PHYSICAL CHEMISTRY.of reaction which include only measurable entropy terms. A fairtest of the theory in this least speculative form has been carriedout by F. G. Soper 46 for bimolecular reactions in the gaseous phaseand in solution. There is satisfactory agreement for cases with Pdiffering as widely as 1 and 10-7. According to Soper, P alwaysapproximates to unity for reactions attended by an increase inentropy.The theory, therefore, applies in particular to slowreactions, the outstanding examples of which were shown, some yearsago, to be highly exothermic.A method of factorising the more complicated term P for uni-molecular reactions has been suggested by C. N. Hinshel~ood.~~In addition to the geometric contribution, and a correction termsuperimposed on the Boltzmann factor, a third term a/S is intro-duced, where CI. is the rate at which energy in the preactivated mole-cule flows into the requisite bond, and is the rate a t which it flowselsewhere, i.e., is dissipated.The internal redistribution of energyhas also been the topic of an organised discu~sion.~~Organic Reactions.-We must regrettably confine ourselves to amere categorical list of selected organic reactions which have beenstudied with sufficient care to allow the detection of even smallchanges in P or in E. Apart from the unimolecular decompositionof nitrites, and the cis-trans-isomerism of stilbene, methyl cinnamate,and methyl maleate,48 the study of reactions in families has been con-fined to bimolecular reactions in solution. In the following examples,each consists of about twelve members : reactions of aryl and alkylchlorides with ethyl alcohol in various solvents ; 49 saponification ofesters of different substituted phthalic 5* and crotonic acids; 51reactions between hydrogen bromide and alcohols in phenol solution ; 52reactions between bases and p-C,H4R*CH,Br in various solvents ; 53organic esterifications ; 54 the union of arnines with halides in benzenesolution ; 55 the hydrogen-ioii catalysed prototropy of nuclear sub-46 J ., 1935, 1393.4 7 C. N. Hinshelwood, J. E. Lennard-Jones, M. Travers, 31. Polanyj, C.Zener, E. J. Bowen, R. C . W. Norrish, H. W. Thompson, C. J. M. Fletcher,E. K. R$idenl, and A. R. Ubbelohde, Proc. Roy. Soc., 1934, LA], 146, 239.4 8 G. B. Kistiakowsky and W. R. Smith, J . Amer. Chem. Soc., 1935,57, 269.49 J. F. Norris, E. V. Vasee, and J. C. J. Staud, ibid., p. 1415; J. F. Norrisand H. H. Young, &id., p. 1420; J. F. Norris and E. C. Haines, ibid., p.1425.60 G.Semerano, Gazxetta, 1935, 65,252.5 1 E. Schjanberg, 2. physikal. Chem., 1935, 174, 465.52 G. M. Bennett and F. M. Reynolds, J., 1935, 131.53 J. W. Baker and W. S. Nathan, ibid., p. 519.54 C. N. Hinshelwood and A. R. Legard, ibid., pp. 587, 1588.6 5 C. A. Winkler and C. N. Hinshelwood, ibid., p. 1147MAXTRD : SURFACE CHEMISTRY. 109stituted acetophenones, 56 which affords an additional illustration ofNathan and Watson’s rule (1933) ; and the action of alkali on bromo.ethanes and chl~roethanes.~~ The theory of tlhe constitutional effectsupon the kinetics of organic reactions has been developed con-siderably in the light of new work.58 The distinction between organicand physical chemistry, perhaps seldom more than a convention,seems to vanish completely when we find that mesomerism, forexample, may be directly interpreted as a resonance effect betweenmolecules possessing normal and polar structure.69E. A.M.-H.6. SURFACE CHEMISTRY.A considerable and increasing amount of work has been done inthis field during the period under review. It is difficult to selectsections for special comment ; but outstanding interest is perhapsattached to the nature of adsorption processes of chemical or so-called “ activated ” type and to the degree to which those of slowerform are due to penetration effects; also to the recognition andmeasurement of the energy barriers which are involved in theactivated migration theory which has recently been put forward byE. K. Rideal. Further, in heterogeneous catalysis, the attemptedanalysis by H.zur Strassen and Q. M. Schwab of the factors whichare contributory to the apparent energies of activation appearsundoubtedly an important step towards the attachment of somedegree of precise significance to the experimental values of thoseenergy terms which are obtained on the basis of the temperaturecoefficient.Adsorption Components.-In certain cases of adsorption, theprocess is obviously composite and consists-in addition to low-temperature adsorption of van der Waals type-of a relativelyrapid component, which in all probability involves linkage of apurely chemical nature, and of a slower process which takes placeconcurrently with or subsequently to the primary process. Thissharply differentiated, very rapid component is especially character-istic of the adsorption of hydrogen and of certain other gases bymetals, such as platinum or nickel, which are active for catalytic66 D.P. Evans, IT. G. Morgan, and H. B. Watson, J . , 1935, 1167, 1174.6 7 W. Taylor, ibid., p. 1514; W. Taylor and A. M. Ward, J., 1934, 2003.5 8 J. L. Gleave, E. D. Hughes, and C. K. Ingold, J., 1935, 236; E. D.Hughes and C. K. Ingold, ibid., p. 344; E. D. Hughes, ibid., p. 255; C. K.Ingold and H. G. G. Mohrhenn, ibid., p. 1482 ; L. P. Hammett, Chem. Reviews,1935, 17, 125.59 C. K. Ingold, ibid., 1934, 15, 2 2 5 ; H. B. Watson, W. S. Nathan, andL. L. Laurie, J , Cltem. Physics, 1935, 3, 170110 GENERAL AND PHYSICAL CHEMISTRY.hydrogenation. In other cases, e.g., in the adsorption of manygases on adsorbents of oxide type, this distinct rapid component isless pronounced or absent.In the last Report in which a review of the progress of surfacechemistry was included (1931), an account was given of H.S.Taylor's conception of activated adsorption. This has in themeantime been developed in a number of papers ; and the treatmentof the subject has become less simple by the apparent presence, inmany cases, of more than one activated component. Thus H. S.Taylor and C. 0. Strother,l who continued the work of H. S. Taylorand D. V. Sickman,2 have put forward, in connexion with theadsorption of hydrogen on zinc oxide, evidence for two activatedadsorption processes, in addition to van der Waals adsorption.The first of these activated processes takes place between 0" andabout loo", and is associated with an activation energy of the orderof 5 kg.-cals.The second, which begins at about 100" and is stillmeasurable at about 300", has an activation energy of about 12 kg.-cals. Physical adsorption took place up to about - 80" ; and therewas no measurable adsorption of this type at or above room temper-ature. With zinc oxide promoted with chromium oxide, whichis a more active catalyst, the existence of only one form of activatedadsorption, beginning at - 78", was deduced; and this low initialtemperature is regarded as being indicative of an extremely lowactivation energy. The calculated values of these activationenergies vary with the conditions : for instance, J.Howard andH. S. Taylor 3 found that the apparent energy of activation of theactivated adsorption of hydrogen on chromium oxide varied, withthe sample of oxide studied, from 14 kg.-cals. to about twice thisvalue and increased with the degree of covering. A similar apparentincrease in the critical increment with the adsorbed concentrationhas been observed by P. V. McKinney for hydrogen on manganesechr omite .If the adsorption of hydrogen or of another reducing gas on anoxide is involved, the possibility of the reduction of the oxide isalways present. There appear, however, to be good grounds forassuming in many such cases the prior formation of an adsorptioncomplex, which breaks down, on being further heated, into thenormal reduction products; and the total reaction may thus beregarded as including an initial process of irreversible adsorption.McKinney has investigated from this standpoint the adsorption ofJ .Amer. Chem. SOC., 1934,56, 586; A,, 1934, 484.Ibid., 1932, 54, 602; A . , 1934, 458.Ibid., 1934, 56, 2259; A., 1935, 28.J . Physical Chem., 1933,37,381; A., 1933,471MAXTED : SURFACE CHEMISTRY. 11 1carbon monoxide by palladium which is only slowly reducedby this gas even at 100". At - 80" the adsorption was almostentirely of the physical type ; but irreversible activated adsorptionbegan at about 0" and increased with increasing temperature to amaximum at about 110", beyond which temperature adsorptiondecreased. The isobar thus showed all the normal characteristicsof activated adsorption.Evaporation of the adsorbed gas only tookplace in the form of carbon dioxide. McKinney calculated theapparent energy of activation of the adsorption process, but regardsthe wide variation in the values obtained (2.6-16 kg.-cals.) as anindication of the complex nature of the adsorption. The formationof irreversible adsorption complexes has also, for instance, beenpostulated by W. E. Garner and F. J. Veal in the adsorption ofcarbon monoxide on a zinc chromite catalyst ; and a slightly differenttype of irreversible activated adsorption is represented by thework of W. W. Russell and L. G. Ghering on the adsorption ofoxygen by nickel at low temperatures.'Since the subject is not complicated by the possibility of reduction,the investigation of activated adsorption +on metals is of specialinterest.R. W. Harkness and P. H. Emmett have adducedevidence for two types of activated adsorption, in addition tophysical adsorption, for hydrogen on promoted ammonia catalysts ;and J. Turkevich and H. S. Taylor9 have examined, from thestandpoint of an activated compoiient, the adsorption of ethyleneon hydrogenating catalysts both of metallic and of oxide type.With manganese chromite, the adsorption of ethylene at or below0" is principally of the van der W&als form. At 110" there was, inaddition, some activated adsorption. With copper, activatedadsorption occurs a t a much lower temperature, vix., even at 0".The isotherms for both types of catalyst were of the form in which theadsorption rises continuously with increasing pressure. A furtherexample of a somewhat similar nature to the already cited adsorp-tion of oxygen by nickel is its adsorption by platinum.H.Reischauer lo obtained, with compact platinum, indications of twotypes of activated adsorption, which are associated with differentactivation energies and occur at different ranges of temperature.The conception of activated adsorption, in which the interactionbetween the gas and the adsorbent is regarded as being composed ofactivated surface processes, has been criticised by many investig-J . Amer. Chem. SOC., 1933, 55, 3626; A., 1933, 913.7 J . Amer. Chem. SOC., 1933, 55, 4468; A., 1934, 22.Ibid., p. 3496; A., 1933, 1018; 1034, 56, 490; A., 1934, 371.9 Ibid., 1934, 56, 2254; A ., 1934, 28.10 2. physikaZ. Chem., 1934, [B], 26, 399 ; A,, 1934, 1303,J., 1936, 1487112 GENERAL AND PRYSICAL CKEMISTRY.ators. For instance, Garner and Veal l1 consider that there is butlittle evidence that this type of adsorption is controlled by activationenergy inherent in the adsorption process itself. Certainly, thedegree of significance of the widely varying values which areobtained, on thk basis of the temperature coefficient, for theapparent activation energy needs further definition ; and much is tobe said for Garner and Veal's preference for the older designation,chemisorption, to indicate the nature of the linkage and to dis-tinguish such processes from physical adsorption, rather than theapplication of the term '' activated " to processes for which therate-control by activation energy of adsorption is still a matter onwhich agreement has not been reached.In this connexion, the degree of influence of any penetrationef-fects in the total slow adsorption process is still to be considered.This aspect was discussed by E.W. R. Steacie,12 A. F. H. Ward,13and J. E. Lennard-Jones7l4 as already reported,l5 and also byS. Iijima,16 who concurs in the view that the rate curves obtainedfor hydrogen on, e.g., finely divided nickel indicate adsorptionfollowed by diffusion. The subject of penetration has more recentlybeen developed by E. K. Rideall' in collaboration with H. W.Melville.l* The total adsorption is regarded as consisting of a tleast three processes involving energy barriers, vix., the passagefrom van der Waals adsorption to chemisorption, migration fromjust outside to just inside the surface, and internal migration.Evidence was adduced, in the course of work with hydrogen andwith deuterium, for the existence of a definite energy barrier for thepenetration of these gases from the surface t o the interior of copper,as well as for migration within the metal.Accordingly, the slowadsorption process, which proceeds with an apparent energy ofactivation, is apparently a composite reaction; and any data,e.g., for the activation energy, only acquire significance if the degreeof incidence of each component can be determined. The surfacefactor in these composite processes may be recognised from manyobservations.J. Howard lg found that the high-temperaturechemisorption of hydrogen on chromium oxide gel markedly11 LOC. cit., ref. (6).l2 J . Physical Chem., 1931, 35, 2112; A., 1931, 904.l3 Proc. Roy. SOC., 1931, [ A ] , 133,506,522 ; A., 1931, 1365 ; T'runs. ParadaySOC., 1932, 28, 399; A., 1932, 688.l4 Ibid., p. 333; A., 1932, 688.l6 Sci. Pupers 1 s t . Phys. Chem. Res. Tokyo, 1933, 22, 285; 23, 34; A.,l7 Nature, 1935,135, 737; A., 818.Proc. Roy. SOC., 1935, [ A ] , 153, 77, 89.l9 Nature, 1933,132, 603; A., 1933, 1112.l5 Ann. Reports, 1931, 28, 37, 38.1934, 139, 358MAXTED : SURFACE CHEMISTRY. 113diminishes the van der Waals adsorption, from which he concludesthat the slow high-temperature process is a t least in part a surfacephenomenon.P. H. Emmett and R. W. Harkness20 reach thesame conclusion from the effect of previous high-temperatureadsorption on the rate of the ortho-para conversion of hydrogen onplatinum or nickel at - 190" and from a study of adsorption oniron-ammonia catalysts .21Heat of Adsorption.-In calorimetrically determined adsorptionheats, the effect measured will, in cases such as the adsorption ofhydrogen by metals, represent principally that due to the rapidcomponent; and, in view of the difficulty in previously removingthe last traces of adsorbed gases without exposure of the adsorbentto a temperature sufficient to modify its normal surface properties,the initially observed differential heat will not, in general, be thetrue threshold value. This is especially the case for hydrogenatingcatalysts such as platinum or nickel.If, on the other hand, theadsorption heat is calculated by means of the Clausius-Clapeyronequation, the significance of the result will depend on the attainmentof true equilibrium and on the effective simplicity of the adsorptionstudied.In exceptional cases, however, threshold values for the adsorptionheat may be measured. J. K. Roberts,22 who used the value ofthe thermal accommodation coefficient of neon as an indication ofthe degree of bareness of a tungsten filament, previously flashed ata temperature above 2000", has calculated a threshold heat ofabout 45 kg.-cals. per mol. of hydrogen for the adsorption of thisgas on tungsten.The adsorption heat subsequently decreases toa limit of about 18 kg.-cals. for a completely covered tungstensurface, the decrease being regarded as due to the nature of theadsorption process and not necessarily to any heterogeneouscharacter of the surface. The adsorption was practically instan-taneous, even at pressures of 10-4 mm. or less.Under the conditions which obtain when the adsorption heat ismeasured for a previously degassed catalytically active metal, thesurface is already, in general, partially covered ; and the apparentlyconstant values for the differential adsorption heat which havebeen obtained by various investigators 23 for hydrogen on copperor platinum, or for oxygen on platinum, may be due to the restrictedadsorption range imposed by the limitations of degassing, or to a2o J.Arner. Chern. SOC., 1935, 57, 1624; A , , 1329.21 Ibid., p. 1631; A., 1315.22 Proc. Roy. SOC., 1935, [A], 152, 445.2s A. F. H. Ward, Zoc. c i t . ; R. A. Beebe, Trans. Faraday SOC., 1932, 28,761; A., 1932, 1199; E. B. Maxted and N. J. Hassid, J., 1931, 3313; A.,1932, 118; Trans. Faraday SOC., 1933, 29,688; A., 1933, 911114 C,ENERAL AND PHYSICAL CHEMISTRY.difference in the adsorptive properties of finely divided metalliccatalysts and a previously heated compact metal filament. Forcarbon monoxide on reduced copper, R. A. Beebe and E. L.Wildner 24 observed an adsorption heat which decreased with tbeadsorbed concentration. It may be noted that, in a, compositeadsorption, an increased degree of incidence of slower and lessexothermic components as the adsorbed concentration is increased,would, under the conditions of calorimetric measurements, in itselfcause a fall in the observed heat as the degree of covering is increased.In any case, the direct determination of adsorption heats presentsconsiderable experimental difficulty. Possible sources of error havebeen discussed by Ward and by others of the above workers, alsoby G.M. Schwab and W. Brenne~ke.~b Note may also be made ofa particularly accurate form of calorimeter which has recently beendescribed by W. E. Garner and P. J. The direct measure-ment of the adsorption heat of hydrogen and of carbon monoxideon zinc oxide and on zinc chromite in this apparatus gave evidenceof two types of adsorption for the latter adsorbent, which was alsoemployed in the partially reduced state, namely, an irreversibleadsorption, associated with a heat of about 45 kg.-cals., whichtakes place on the oxidised surface, and, on the reduced surface, areversible adsorption having a heat effect of 10-15 kg.-cals.As an example of a system containing a metallic adsorbent andin which the conditions permit the thermodynamic calculation ofthe adsorption heat, the adsorption of oxygen on silver may bementioned.A. F. Benton and L. C. Drake27 have calculated inthis way a value of about 13 kg.-cals. for the adsorption at about190", at a pressure such that the formation of silver oxide is pre-cluded. Frequently, however, with metals, this indirect method ofcalculation is inapplicable owing either to non-attainment ofequilibrium or to lack of knowledge with regard to the effectivesimplicity of the adsorption.Calculation by means of the Clausius-Clapeyron equation can,however, be applied to many adsorbents of oxide type. H.S.Taylor and D. V. Sickman28 obtained by this method a value of1.1 kg.-cals. for the physical adsorption of hydrogen on zinc oxideat low temperatures, and about 21 kg.-cals. for the adsorptionprocess which takes place at about 450". Purther, as an instance ofa relatively high-temperature adsorption accompanied by a far24 J . Amer. Chern. SOC., 1934, 56, 642; A., 1934, 485.2 b 2. phyaikal. Chem., 1932, [ B ] , 16, 19; A., 1932, 459.ae J., 1935, 1436, 1487.a7 J .Amer. Chem. SOC., 1934,56,256; A , , 1934,370,28 Ibid., 1932, 34, 602; A. 1932,458MAXTED : SURFACE CHEMISTRY. 115smaller heat effect, B. Neumann and E. Goebel 29 have attemptedto estimate the influence of temperature on the heat of adsorptionof oxygen on iron oxide. Grebt accuracy was not possible, but theadsorption heat apparently fell from 2.2 kg.-cals. for a temperaturerange of 20-100" to 1-3 kg.-cals. when the upper temperature wasincreased to 300".Structure of Solid Adsorbing and Catalysing Surfaces.-In earlierReports reference has been made to H. S. Taylor's theory of surfaceheterogeneity based on the postulated occurrence of extra-latticeprojections or peak areas which are associated with special activity.This important conception of extra-lattice projections has beendiscussed by a number of workers.0. Schmidt 3O mentions in thisconnexion G. Tammann and W. Boehme's observation3l thatsmall particles of metals--e.g., small rods or films of gold, for instanceof an order of thickness of 4p, at 200O-have only a very short lifeand disappear through sintering, by virtue of differences in vapourpressure, an effect which must be even more intense with extra-lattice projections of molecular dimensions. Again, E. Fajans 32has shown, and it is a matter of general experience, that a veryshort sintering period is sufficient to stabilise a nickel surface insuch a way that it does not change in activity even on prolongedfurther exposure to temperatures up to the sintering temperature.Evidence for the effective uniformity of a metallic catalysingsurface has been put forward by E.W. R. Steacie and E. M. Elkin,33who have shown that there is no discontinuity at the melting pointin the activity of zinc when this metal is used as a catalyst for thedecomposition of methyl alcohol between 360" and 440°, from whichit is concluded that the whole surface is uniformly active and thatthe catalytic activity is not limited to a part only; for, if activecentres are involved in the catalytic reaction on solid zinc, it wouldbe expected that there would be a sudden and very large drop inthe activity at the melting point. The equivalence of the catalysingsurface elements has also been discussed by G.M. S~hwab,~* whoconsiders, on reaction-kinetic grounds, that catalysis is carried outby a range of energetically homogeneous points. Further evidencemay, moreover, be obtained 35 from the effect of progressive poison-2. Elektrochem., 1934, 40, 754; A., 1935, 28.30 Ber., 1935, [B], 68, 1098; A., 940.31 Ann. Physik, 1932, [v], 12, 820; A,, 1932, 452.32 2. physikal. Chem., 1935, [B], 28,252.33 Proc. Roy. SOC., 1933, [A], 142, 457; A., 1934, 38.34 2. physikal. Chem., 1934, 169, 81 ; 171, 421.35 E. B. Maxted and G. J. Lewis, J., 1933,502 ; E. B. Maxted and V. Stone,ibid., 1934, 26, 672; E. B. Maxted and C. H. Moon, ibid., 1935, 393; E. B.Maxted, J. SOC. Chem. Ind., 1934, 53, 102T; A., 1933, 680; 1934, 262, 607,851; 1935, 589116 GENERAL AND PHYSICAL CHEMISTRY.ing and of deactivation by heat treatment, and by a re-examinationof G.Vavon and A. Husson’s work 36 on step-wise deactivation.Although many observations apparently indicate the effectiveequivalence of the catalysing range of surface elements, yet theextension of this to equivalence throughout the whole range ofadsorbing points is bound up with the question as to whetherall adsorbing points are equally effective for catalysis. Steacieand Elkin’s work on the absence of discontinuity in activity atthe melting point of a solid catalyst would appear to show thatthis is so, a t any rate in the case investigated; but this extensionis not in conformity with Pease and Stewart’s observation 37 of thenon-correspondence between the depression of catalytic activityand adsorptive capacity which is caused by partial poisoning;and further investigation is undoubtedly still required.Thelimited degree of equivalence, namely, that of the catalysing points,is, however, not incompatible with the adlineation theory of Pietschand S ~ h w a b . ~ ~Heterogeneous Catalysis.-It is becoming more and more evident,that heterogeneous catalytic reactions are processes the mechanismof which is complicated, not only by the presence of a transitionstate, but also by composite adsorption effects. For this reason,activation energies calculated by applying the simple Arrheniusrelationship have little significance, unless the conditions are suchthat they refer to a dominant stage.In this connexion, attention may be drawn to an activationmechanism which has been proposed by E.C. C. B a l ~ , ~ ~ accordingto which the total critical increment required in a heterogeneouscatalytic reaction is supplied in two stages. G. H. Bottomley,B. Cavanagh, and M. Polanyi40 also consider that such reactionstake place in two stages, the second being the slower and thereforethe rate-determining process. This is suggested, further, in Horiutiand Polanyi’s treatment of the part played by nickel or anothercatalyst in the hydrogenation or hydrogen-deuterium exchange ofethylene or benzene.41 In any case, a mechanism which involves36 Compt. rend., 1922, 175, 277; A., 1922, ii, 631.37 R. N. Pease and L. Stewart, J . Amer. Chewi. Xoc., 1925, 4’4, 1235; A .,1926, ii, 691.3* E. Pietsch, A. Kotowski, and G. Berend, 2. physikal. Chem., 1929, [BJ,5, 1 ; A . , 1929, 1150; G. M. Schwab and E. Pietsch, 2. Elektrochem., 1929,35, 135; A . , 1929, 519; G. M. Schwab and L. Rudolph, 2. physikal. Chem.,1931, [B], 12, 427; A., 1931, 919.39 Nature, 1935, 136, 146; A., 1084.40 Ibid., p. 103; A., 1084; see also J. Horiuti and M. Polanyi, Proc.41 Trans. Parndciy SOC., 1934, 30, 1164; d., 1934, 1077.Jlnnchester Lit. Phil. SOC., 1934, 78, 50MAXTED : SURFACE CHEMISTRY. 117the formation of an intermediate adsorption complex appears to begenerally applicable. A surface may, in exceptional circumstances,promote reaction outside the adsorbed phase, for instance by theinitiation of chain reactions.42 The degree of gaseous chain initiationwhich was claimed by K.Bennewitz and W. Neumann 43 in ordinarycatalytic reactions such as in the hydrogenation of ethylene onplatinum appears, however, to be unfounded ; 44 and heterogeneouscatalytic reactions of the usual type may probably be regarded asbeing effectively confined to the adsorbed phase.The relative influence of the various adsorption components onthe reaction velocity has continued to receive attention, particularlyfrom the standpoint of the catalytic importance of the slowerforms of adsorption. Thus, J. Howard and H. S. Taylor 45 considerthat the activated adsorption of ethylene is the rate-determiningfactor in the hydrogenation of ethylene on catalysts of the oxidetype; and P. H. Emmett and 8.Brunauer46 regard the slowadsorption of nitrogen by various ammonia catalysts as being thecontrolling step in the synthesis. Chief interest is attached tocases where a relatively rapid and a relatively slow adsorptioncomponent, each of which constitutes a source of supply of the samemolecular species, occur concurrently. M. Polanyi’s theory of themechanism of catalytic hydrogenation 47 requires that the cata-lytically active adsorption should be not a strong, but an extremelyweak, activated adsorption; and, where there are, side by side, aslow activated adsorption, of high apparent activation energy, anda rapid adsorption, of low activation energy, on the same catalyst,the catalysed reaction should, according to the above conception,proceed through the latter and not through the former.An exampleof this is to be found in the observation of A. J. Gould, W. Bleakney,and H. S. Taylor 48 that the interaction of hydrogen and deuteriuma t low temperatures takes place far more rapidly than the rate ofactivated adsorption.The degree of influence of a dominant adsorbed species, togetherwith the utilisetioii of the heat of association as a contributoryfactor towards the activation energy, has been developed by H. zurStrassen 49 and by G. M. Schwab 50 in connexion with the passage42 See e.g., M. W. Travers, Nature, 1935, 136, 909.43 2. physikal. Chew&., 1930, [B], 7, 247; A., 1930, 715.44 K. Bennewitz and W. Noumann, ibid., 1932, [B], 17,457; A , , 1932, 818.45 J . Amer. Chem.Xoc., 1934, 56, 2259; A., 1935, 28.46 Ibid., p. 35; A., 1934, 262.47 J . SOC. Chem. Ind., 1935, 54, 1 2 3 ~ ; A., 711.48 J . Chem. Physics, 1934, 2, 362; A., 1934, 1074.49 2. physikal. Chem., 1934, 169, 81; A., 1934, 974.Ibid., 1934, 171, 421; A., 1935, 441118 GENERAL AND PHYSICAL CHEMISTRY.of a reaction velocity through a maximum value as the reactiontemperature is increased-with subsequent production of a negativetemperature coefficient-and as an alternative to ascribing thisnegative coefficient to a decrease in adsorbed concentration. Thus,in the hydrogenation of ethylene on nickel, the variation of thereaction velocity with temperature is represented by an expressionof the formin which 7c is the reaction velocity, E the activation energy ofthe hydrogenation reaction, QH2 and QCaH, the heats of adsorptionof the hydrogen and of the ethylene, and a st factor involvingadsorbed concentrations.According to the views of these authors,the reversal takes place at a temperature at which adsorption ofthe ethylene, together with its heat of adsorption, begins to be aneffective factor in the kinetics. A similar treatment has also beenapplied in connexion with the reversal in the sign of the temperaturecoefficient in the hydrogenation of crotonic and maleic acids in adissolved state in the presence of platin~m.~lWhile a further examination of the controlling mechanism postul-ated by zur Strassen and Schwab is obviously needed, since othermethods of control are possible, their treatment of these cases ofreversal appears both suggestive and-provided that it can beconfirmed-capable of wider application.Certainly, without somemodification in the Arrhenius equation for these heterogeneousreactions, the calculated values for the activation energy are ofrather indefinite significance.An alternative view to the above aspect of the reversal has beenput forward by T. Tucholski and E. K. Ridea1.52 These authorsfind that hydrogen and deuterium reduce ethylene a t equal ratesin the high-temperature region,53 from which it is pointed out thatthe rate is probably determined by some reaction involving thehydrogen which does not involve a zero-point energy difference;and control by activated migration, probably of hydrogen, issuggested.A further alternative, which Tucholski and Ridealconsider less probable, is control by a reaction involving identicalenergies of activation for the ethylene, the negative temperaturecoefficient being due to its desorption. R. Klar 54 also observed areversal in the hydrogenation of ethylene with both isotopes in thepresence of an iron catalyst. At temperatures up to about 100"= ae- KE - QHJ - QC2HJI RT51 J., 1935, 1190; A., 1210.53 See R. N. Pease and A. Wheeler, J . Amer. Chem. SOC., 1935, 57, 1144;54 2. physikal. Chem., 1934, [B], 27, 319; A., 1935, 175.Ibid., p. 1701.A., 938MAXTED : SURFA(!E CHEMISTRY. 119deuterium reacts with ethylene more slowly than hydrogen, but,above this temperature, a more rapid reaction with the heavyisotope took place.With deuterium, the maximum velocityoccurred at about 150°, whereas, with hydrogen, reversal tookplace at about 125".Some work has been done on the mode of activation of catalysts bysecondary constituents. For instance, an interesting study of thenature of the association between the constituents of a number oftwo-component catalysts has been made by G. Wagner, 0. M.Schwab, and R. Staeger.55 I n cases in which an abnormal increasein catalytic activity-compared with the activity of each of thecomponents separately-occurs, X-ray analysis shows evidence forchemical association between the components, in contrast to theoccurrence of the lattice structure of each of the componentsseparately in other cases. Thus, Cu0,ZnO and Cu0,MgO gavediagrams showing no association, whereas CuO,Cr,O, and CuO,Al,O,showed the formation of a new complex with the possibility of newadsorptive properties.Similarly, A. Mittasch and E. Keunecke 56have obtained evidence, on chemical grounds and as the result ofX-ray examination, of the formation of mixed crystals of alumina,and ferric oxide in the promotion of iron-ammonia catalysts withalumina. These authors infer that one function of the promoter isto inhibit the reduction of the iron oxide. J. Eckell 57 found thatthe apparent activation energy of an iron oxide catalyst promotedwith an increasing concentration of alumina decreased linearlywith the alumina concentration up to a content of about 25%, andthis was accompanied by a parallel change in the lattice structure.Of the catalytic reactions which have been studied during theperiod under review and which possess special general significance, abrief reference may be made to catalysed processes involvingdeuterium, for which, as would be expected, the same catalysts canbe employed as for the lighter isotope.The saturation of ethyleneby deuterium in the presence of metallic catalysts has already beennoticed. K. Morikawa, W. S. Benedict, and H. S. Taylor 58 haveused nickel for the deuterium-hydrogen exchange in methane.J. Horiuti, G. Ogden, and M. Polanyi 59 found that substitutiontook place on shaking benzene with deuterium in the presence ofnickel or platinum; although these substitutions also occur in theabsence of a catalyst.60 The somewhat similar process of exchange6 5 2.physikal. Chern., 1934, [B], a, 439; A., 1935, 455.56 2. Elektrochem., 1932, 38, 666; A . , 1932, 1004.5 7 Ibid., p. 918; 1933,39,855; A., 1933, 131, 1253.68 J . Amer. Chern. SOC., 1935,57, 592; A., 688.6Q Trans. Paraday SOC., 1934, 30, 663; A., 1934, 973,6o Nature, 1934, 134, 734; R., 1935, 74120 GENERAL AND PHYSICAL CHEMISTRY.of atoms between water and deuterium may also be catalysed byplatinum-black.6lI n the above review, no attempt has been made to deal with themany catalytic reactions which are of interest principally in relationto the process involved, rather than from a general standpoint,since such catalytic processes are more logically considered in thesection appropriate to the reaction in question.E.R. M.7. THE PHYSICAL BASIS OF OPTICAL ROTATORY POWER.The progress which has recently been made towards the elucid-ation of the problem of the origin of optical rotatory power hasculminated during the present year in an important paper byM. B0rn.l Current theories may be divided into two classes,“ electronic ” and “ molecular,” but they have a common basis inthe theory of coupled vibrators, proposed by M. Born in 1915,2according to which a molecule may be represented by a system ofelectrical particles which are more or less rigidly fixed relative toone another but become polarised (Le., undergo small displacements)under the influence of an applied electric field, such as the electricvector of a plane-polarised light wave.When one particle is setin vibration, it sends out secondary waves which act on the otherparticles just as the primary light wave does, and this process isrepeated from particle to particle. If the particles are isotropic,rotation of the plane of polarisation can appear as a third-ordereffect when not less than four of them have taken part in theresonance process, or when two have taken part if they areanisotropic; but only on the condition that the four particles donot lie in the same plane in the former case, and that, in general,the system has no plane or centre of symmetry. This is a mathe-matical statement of the principle of molecular dissymmetry,but unfortunately, the detailed analysis in the general case isextremely complicated, and involves parameters which are notdirectly accessible to physical or chemical measurement.Sub-sequent developments have therefore consisted in the introductionof simplifying assumptions, and the difference between the electronicand the molecular theory lies only in the nature of the simplificationswhich they involve.61 S. Horiuti and M. Polanyi, Nature, 1933,132, 819; A., 1934, 17.1 Proc. Roy. SOC., 1935, [ A ] , 150, 84.2 Physikal. Z., 1915, 16, 251, 437; Ann. Physik, 1918, [iv], 55, 177. Seealso M. Born and P. Jordan, “ Elementare Quantenmechanik,” 1930, 260 ;M. Born, “ Optik,” 1933ALLSOPP : PHYSICAL BASIS OF OPTICAL ROTATORY POWER. 121(i) W. Kuhn applied the principle of coupling to a molecularmodel consisting of two hear (i.e., completely anisotropic)vibrators which are constrained to move only in directions perpen-dicular to one another along axes separated by a vertical distance d(Fig.3a), the optically active medium being treated as a collectionof such models in random orientation. Under these conditions,optical activity is promoted from a third-order t o a first-ordereffect, with a consequent reduction in mathematical complexity.For wave-lengths remote from an absorption band, formulz areobtained which are identical with those of Drude or of Natanson,but they have the merit of being consistent with the model, whereasW. Kuhn4 shoked that Drude’s conception of spiral oscillatorsdoes not actually lead to rotatory power a t all. Kuhn’s model,however, itself needed modification, since the value of d derived forit from measurements of circular dichroism (see below) proved inmany cases to be incompatible with the known molecular dimensions ;but W.Kuhn and K. Bein were able t o show that activity of thecorrect order of magnitude can result so long as the axes of thevibrators are inclined, but not parallel, to one another, and accept-able values of d are then obtained when the angle between them issmall. Born criticises this model on the ground that “ it makesno attempt to reduce a priori the dimensions and location of theassumed resonators to other known properties of the molecule.”The conception of a linear vibrator, also, which implies that theradical to which it corresponds can never be polarised in any directioninclined to its one axis, seems remote from the relatively flexibleelectronic systems which seem to exist in chemical molecules,whilst, in the case of the simplest active molecule with a centralasymmetric carbon atom, the presence of four dissimilar radicalsseems to call for four vibrators, and the system of two anisotropicresonators must form part of a molecule containing at least fouratoms or radicals, since otherwise a plane of symmetry would bepossible.6Kuhn’s model does not therefore appear to be capable of directapplication to the asymmetric carbon atom, but there is a class ofcompound to which it bears a closer resemblance, i.e., those spiro-molecules which, though possessing no asymmetric carbon atom,have no plane of symmetry and can therefore be prepared in3 2.physikal. Chem., 1929, [ B ] , 4, 14; Trans. Paraday SOC., 1930, 26, 293;4 2. physikal. Chern., 1933, [B], 20, 325. See also M. Born, Ann. Physik,2. physikal. Chem., 1933, [B], 22,406.Ber., 1930, 63, 190.1918, [iv], 55, 177.6 M. Born, loc. cit., ref. (1); T. M. Lowry, Nature, 1935, 136, 191122 GENERAL AND PHYSICAL CHEMISTRY.optically active forms. Kuhn and Bein selected as an exampleerythritoldipyruvic acid (I), in which the niolecular dissymmetryarises from the fact that the planes containing the two systemsH0,C-C-CH, must be perpendicular to one another, as is indicatedby the dotted lines. If the two carboxyl groups are identifiedwith the two completely anisotropic resonators of the originalmodel (Fig.3a), this reduces to the form of Fig. 3b, where theresonators are displaced along their respective axes from the centralaxis of the model. Kuhn and Bein predicted that the configurationof Fig. 3b would be lzvorotatory, and they also investigated theabsolute configurations of the cobaltioxalates in a similar way,8but in neither case were their conclusions in agreement with thegeneral principles now developed by Born.FIG. 3.Kuhn achieved more success in the analysis of curves of rotatorydispersion inside an absorption band (the Cotton effect). Experi-ment shows that, as an absorption band is approached, the rotationrises to a maximum value (+ or -), returns to zero at the centre ofthe band, and then passes through a second maximum value ofopposite sign.This phenomenon was successfully treated byL. Natanson9 on the basis of Fresnel?s fundamental postulate ofcircular double refraction in an optically active medium and Cotton’sdemonstration of the corresponding phenomenon of circulardichroism (difference of absorbing power for light circularly polar-ised in left- and right-handed senses). The contribution of theabsorption band to the rotatory dispersion of the molecule (its“ partial rotation ”) can be predicted from a knowledge of the7 2. physikal. Chem., 1934, [B], 24, 335.8 2. anorg. Chem., 1934, 216, 321.9 Bull. Acad. Sci. Krakow, 1908, 7 6 4 ; J . Phys. Radium, 1909, [iv], 8, 321.See also Kuhn and Freudenberg, “ Handbuch der chemischen Physik,” 1932,8, 111, p.77ALLSOPP : PHYSICAL BASIS OF OPTICAL ROTATORY POWER. 123shape of the absorption curve ( L e e , its strength f as determinedfrom the area covered, which is E . & where E is the molecularextinction coefficient a t frequency v), and of the magnitude of itscircular dichroism, E, - E!, for the measurement of which at ultra-violet wave-lengths W. Kuhn and E. Braun10 have developed asimple method.Numerical calculation of partial rotations by Natanson’s methoddemands a knowledge of the relationship between E and v insideeach absorption band in order that the integral r . d v may becorrectly evaluated. Relationships which had been deduced byNatanson on a classical theory of damped oscillations were foundto be inadequate, but Kuhn and lBraun1l obtained more successwith an empirical exponential expression of a type which had beensuggested by J.Bielecki and V. Henri.12 This expression has beenfurther modified by T. M. Lowry and H. Hudson l3 and the partialrotations then deduced give excellent agreement with the curvesobtained experimentally. Striking examples of the applicationof this method of treating the Cotton effect are the analysis byW. Kuhn and H. L. Lehmann l4 of a very curious curve of rotatorydispersion obtained from p-octyl nitrite, and the demonstrationby H. Hudson, M. L. Wolfrom, and T. M. Lowry l5 that the rotatorypower of tetra-acetyl parabinose is contributed entirely by theultra-violet absorption band of the carbonyl radical, whilst thepartial rotations from the asymmetric carbon atoms entirely cancelone another.(ii) S.3’. in contrast to Kuhn, based his analysis on thesimplest chemical model which can show optical activity, anasymmetric carbon atom surrounded by four different radicals.This is a return to Born’s system of four isotropic resonatorsarranged tetrahedrally; but, instead of making use of the resultswhich had already been established, Boys attempted to calculatethe forced vibrations of the resonators directly, expressing theirpolarisabilities in terms of their refractivities instead of taking intoaccount their characteristic frequencies. This method is involved,and the results do not entirely agree with the rigorously establishedformulze of the general theory.They lead to an expression forthe rotatory power of the molecule in terms of the product of therefractivities of the four radicals, and of a complex function of theff10 2. physikal. Chem., 1930, [B], 8, 445. l1 Ibid., p. 281.12 Physikal. Z . , 1913, 14, 516. Phil. Trans., 1933, [A], 232, 131.14 2. Elektrochem., 1931, 37, 549; 2. physikal. Chem., 1932, [B], 18, 32.l5 J., 1933, 1179.16 Proc. Roy. Soc., 1934, [A], 144, 655.W. C. G. Baldwin, M. L. Wolfrom, and T. M. Lowryhave also found optical cancellation in penta-acetyl p-fructose ; J . , 1935, 696124 GENERAL AND PIiYSICAL CHEMISTRY.linear dimensions of the molecule which he deduced approximatelyfrom the “atomic” radii of the radicals, assuming them to beclose-packed spheres. A similar result was obtained, by differentreasoning, by R.de Ma1lemann.l‘ Since the characteristic frequen-cies of the radicals are only involved implicitly in their refractivities[which may be expressed in the form alc/(A2 - A ~ ~ ) , a/, being a constantand hk. the wave-length characteristic of the lcth absorptionfrequency], it follows that the rotatory power and refractive indexshould depend on wave-length in the same way; but this con-clusion must be invalid,l* since in the case of refractive dispersionthe constants ak are always positive, whereas in the case of rotatorydispersion some of them may be negative, and the general theoryrequires that Cak = 0, a result also obtained by Kuhn; andexperiment actually shows that absorption bands which give only atiny contribution to the refractive index often contribute verylargely indeed to the rotatory power of a molecule.At wave-lengths in the visible spectrum, Boys’s formula leads to values forthe specific rotations of simple alcohols and amines which are inexcellent agreement with experiment, but, as is to be expected, itdoes not give satisfactory values for their rotatory dispersions ;nor can it explain the Cotton effect, since the reversal of sign in therefractivity of the chromophoric radical, which is necessary toaccount for the observed reversal of the sign of the rotatory powera t the centre of its absorption band, does not occur.19 On the otherhand, for a given arrangement of the four radicals, Boys’s analysisleads directly to an unambiguous prediction of the sign of therotation, and he specified the absolute configurations of simpleoptically active molecules such as amyl alcohol.(iii) Born 2O has now reshaped his general theory in such it wayas to make it available immediately for chemical purposes.Hestarts from the simple model of the tetrahedral molecule, but, fortechnical reasons, he assumes the four resonators to be slightlyanisotropic on the ground that theory shows that such anisotropywill inevitably occur as LZ result of the coupling forces even if theresonators are initially isotropic. At present, he considers onlythose wave-lengths which are remote from an absorption frequency,since the complex (and often diffuse) band systems of real moleculesare beyond the scope of the method of analysis employed, and anyformulz which represent the variation of rotatory power insideabsorption bands must at best be semi-empirical in character;l7 Compt.rend., 1925, 181, 298; Trans. Faraday Soc., 1930, 26, 281.1* M. Born, loc. cit., ref. (1).Is T. M. Lowry and C. B. Allsopp, Proc. Roy. Soc?, 1934, [A], 146, 317.2o LOG. cit., ref. (1)ALLSOPP : PHYSICAL BASIS OF OPTICAL ROTATORY POWER. 125but with this restriction, he deduces a simple formula for rotatorypower which depends only on the frequencies and strengths of thefour resonators and on their arrangement in space. In general,this formula is only valid when no two of the resonators are equal,but there is a limiting case where it still holds even when two pairsof them are the same, vix., when the faces of the tetrahedron havethe form of congruent triangles (Fig.4a). Still greater simplificationresults when these tlwo pairs are so arranged that the lines joiningthem are perpendicular to one another and to the line joining thecentres of the corresponding edges of the tetrahedron (Fig. 4b).This, of course, is exactly the configuration of the erythritoldipyruvicacid molecule considered by Kuhn, but whereas Kuhn’s treatmentonly involved two of the four radicals (the carboxyl groups),Born’s formula takes account of all four of them. The formuladoes not implicitly include the sign of the rotation for a givenmolecular configuration, but this can be deduced from the generalFIG. 4.A B(a) (b)theory : ‘‘ The rotation of the plane of the polarisation is representedby the same screw motion which makes the two atom pairs coincide,if one pair is moved along the line connecting the centres of thepairs.” The model of Fig.4c is therefore lzevorotatory, althoughthe screw is right-handed, since chemists specify the sign of rotationwhen facing the on-coming light. This conclusion is the oppositeof that reached by Iiuhn for the qiro-acid; the dispersion factorin Born’s formula, however, is identical with that obtained byKuhn. Born’s formula was used to calculate the rotatory power ofdiaminospiroheptane (II),21 in which the dissymmetry arises fromthe spatial arrangement of the hydrogen atoms and amino-groups,which thus correspond with the pairs of resonators AB, AB in themodel.The parameters in the formula (the distances A-B and0-P in Pig. 4c, and the characteristic frequencies of the hydrogen21 Resolved by (Sir) W. J. Pope and S. E. Janson, Chem. and Ind., 1932,51, 316126 GENERAL AND PHYSICAL CHEMISTRY.atom and of the amino-radical) are not known, but appropriateguesses lead t o a value = 30°, which is in good agreementwith experiment.Born has provided chemists with a physical theory of opticalrotatory power which has a sound mathematical basis, and, whensufficient experimental accuracy in the determination of the variousparameters is attainable, will make it possible t o predict the absoluterotatory powers of molecules of known configuration; but theachievement of such accuracy will always be difficult, for Born’sformula involves the eighth power of the molecular dimensions andthe sixth power of the frequency and the square of the strength ofabsorption bands which lie in a region of the spectrum wheremeasurements are by no means simple.For the moment, there-fore, as T. M. Lowry has pointed out,22 the chief importance ofBorn’s work is that it can be applied to the prediction of the relativemagnitudes of the rotatory powers of related compounds, as functionsof three pairs of their fundamental physical constants, when theexperimental errors in the parameters may be of much lessimportance .23C. B. A.8. DIPOLE MOMENTS AND VALENCY ANGLES.In addition to being used in the qualitative determination ofmolecular structures,l dipole moments have been applied for thepurpose of calculating valency angles.The fundamental assump-tions involved are the constancy of bond moments, which aresupposed to act along the direction of the valency bonds, and theirstrict vector additivity without any interaction effects of onemoment on another.2 If the constituent bond moments, eithersingly or in the form of group moments, and the total dipolemoment of a compound are known, then clearly it should, in general,be possible to calculate the angles between certain individualmoments, i.e., between the corresponding covalency linkages.One of the simplest applications is t o determine the angles betweenthe o-, m-, and p-directions, respectively, in the benzene ring; ifthis is a plane regular hexagon, these angles should be 60°, 120°, and180°, respectively.As far as the rn- and p-positions are concerned,22 Nature, 1935, 136, 191.23 Reference must also be made to the appearance of T. M. Lowry’s“ Optical Rotatory Power ” (Longmans, 193!5), which contains a comprehon-sive detailed account of the development and significance of this recent work.(Sir) J. J. Thornson, Phil. Mag., 1923, 46, 513; A., 1923, ii, 682; see also1 Ann. Reports, 1931, 28, 387.I(. Hiijendahl, Phyeikal. Z., 1929, 30, 391; A . , 1929, 980GLASSTONE : DIPOLE MOMENTS AND VALENCY ANGLES. 127the results are in agreement with expectation, but the moments ofo-substituted compounds frequently imply that the angle betweenthe valency directions is greater than 60°.3 This discrepancy,known as the " ortho-effect," has been attributed to actual distortionof the molecule resulting from the size of the substituent groups:or to mutual interaction between the two dipoles,5 so that theassumption of the constancy of the group m.oments-or of theirstrict vector additivity-taken as equal to the values for thecorresponding monosubstituted benzene compounds, is no longervalid.It is probable that both factors are operative : measurementsof the C-I and 1-1 distances in o-di-iodobenzene by the electron-diffraction method indicate that the angle between the two C-Ibonds is at least 68°,6 and may be as high as A similardistortion of the molecule appears to oecur in the peri-substitutednaphthalene There is little doubt, however, that, inaddition, interaction between groups occurs : 9 in some cases this isprobably due to simple inductive polarisation, but in others it isconnected with the permanent electromeric, i.e., mesomeric,10 effectin the molecule.ll It is the error in the calculations resulting fromthe presence of such an effect which led to the conclusion l2 that themoment of the >C-CN system does not act in the directionof the C-C bond; there is now little doubt that this view isinc0rrect.1~In general, when two identical or different groups, or when threeC.P. Smyth and S. 0. Morgan, J . Amer. Chem. Soc., 1927,49,1030; A.,1927, 611 ; E. Bergmann and L. Engel, 8. physikal. Chem., 1930, [B], 8, 111 ;A., 1930, 979; E.Bergmann, L. Engel, and S. Shndor, ibid., 10, 106; A.,1930, 1501.4 C. P. Smyth and S. 0. Morgan, Zoc. cit.,5 H. M. Smallwood and K. F. Herzfeld, J . Amer. Chem. SOC., 1930, 52,6 H. de Laszlo, Trans. Paraday SOC., 1934, 30, 892.7 S. B. Hendricks, L. R. Maxwell, V. L. Mosley, and M. E. Jefferson, J .Chem. Physics, 1933,1, 549; A., 1934, 17.8 A. Weissberger, R. Sangewald, and G. C. Hampson, Trans. ParadaySOC., 1934, 30, 884; A., 1934, 1157.0 G. C. Hampson and L. E. Sutton, Proc. Roy. SOC., 1933, [A], 140, 562;A., 1933, 766; H. Poltz, 0. Steil, and 0. Strasser, 8. physikal. Chem., 1932,[B], 17, 155; A,, 677; E. G. Cowley and J. R. Partington, J . , 1935, 604; A.,809 ; K. Hiijendahl, Zoc. cit.1019; A., 1930, 84.10 C. K. Ingold, J., 1933, 1120; A ., 1933, 1151.11 G. M. Bennett, Ann. Reports, 1929, 26, 132; G. C. Hampson and L. E.Sutton, Zoc. cit.; G. M. Bennett and S. Glasstone, Proc. Roy. SOC., 1934, [A],145, 71 ; A., 1934, 831.12 E. Bergmann and M. Tschudnovski, 8. physilcal. Chem., 1932, [B], 17,116 ; A., 1932, 677.13 A. Weissberger and R. Sangewald, J., 1935, 856; A., 976; cf. alsoR. P. Cook and P. L. Robinson, ibid., p. 1001 ; A., 1064128 GENERAL AND PHYSICAL CHEMISTRY.identical groups, are attached to the same atom, it, is possible todetermine the valency angles, provided the individual groupmoments and the total moment of the compound are a~ai1able.l~For example, the angles between the C-X links in CH2X2 andCHX,, where X is a halogen, have been calculated in this manner ; 14, l5an allowance of 0.4D for the moment of the G H bonds can bemade, or alternatively, it may be assumed that the value for theC-X bond is equal to the moment of CH,X, the neglect of theC-H moment resulting in a cancellation of the errors involved.The angles for methylene chloride and for chloroform were foundto be about 130" and 116", respectively, in good agreement withthose obtained from X-ray diffraction measurements on thevapours,16 vix., 124" & 6" and 116" & 3".Analogous observationsof electron scattering show, however, that the latter valuesare probably in error,17 and that the valency angles in the twocompounds mentioned are 111" & 2", a result in agreement withcalculations based on wave mechanics.18 It is evident that in thechloromethanes there is considerable mutual interaction of thedipoles so that the C-C1 bond moments may be reduced by as muchas 30Y0.l9 Similar interaction probably occurs in the otherhalogenomethanes ; no measurements of interatomic distances inthe vapours, from which valency angles can be calculated, havebeen reported, but it is probable that, as the size of the halogenincreases,20 the valency angles become greater than the tetrahedralvalue, although it is unlikely they will prove to be as large as those-134" and 140" for methylene bromide and iodide, respectively-calculated from dipole moments.14 I n spite of statements to thecontrary, it now appears that inductive effects are also operativein cis-dichloroethylene : the presence of a double bond in thismolecule may, however, be a special contributive factor.21When one or more phenyl groups are attached to a central atom,valency angles may be calculated by making use of the fact that inl4 G.C. Hampson and L. E. Sutton, Zoc. cit., ref. (9).I s E. Bergmann, L. Engel, and S. S&ndor, Zoc. cit., ref. (3); E. Bergmann,L. Engel, and H. A. Wolff, 2. physikal. Chena., 1932, [B], 17, 81; A., 1932,677; see also F. R. GOSS, J., 1934, 1467; A., 1934, 696.16 L. Bewilogua, Physikal. Z., 1931, 32, 265; A,, 1931, 788.1' R. Wierl, Ann. Physik, 1931, 8, 521 ; A., 1931, 665; L. E. Sutton andl8 W. G. Penney, Trans. Faraday SOC., 1935,31, 734; A., 810.20 Cf. C. P. Smyth and H. E. Rogers, J . Amer. Chem. SOC., 1930, 50, 222;A., 1930, 1093.21 G.C. Hampson and L. E. Sutton, Zoc. cit., ref. (9), p. 565; see alsoE. C. E. Hunter and J. R. Partington, J., 1931, 2062; 1932, 2819; A., 1931,1113; 1932, 210.L. 0. Brockway, J. Amer. Chem. SOC., 1935, 57, 473.L. E. Sutton and L. 0. Brockway, loc. citGLASSTONE : DIPOLE MOMENTS AND VBLENCY ANGLES. 129the p-position to the point of attachment the moment of a groupsuch as a halogen, CN, NC, CH,, or NO, acts along the axis of thebenzene ring. The dipole moment p of a compound c6H5-A/Bis determined by the bond moments of C6H5-A (pl) and of A-B(p2), and by the valency angle (e), which are related by the usualequation p2 = p12 + p z + 2p1v2 00s 8, the correct signs being usedfor the directions of the individual moments.2 Another equationconnecting pl, p2, and 8 can be obtained from the measured momentof the compound p-X*C,H,*AB, the X-C,H, bond moment,assumed equal to the moment of the compound C6H5X, acting inthe line of the C,H4-A bond.In order to calculate 8 , it is necessaryto know the value of the bond moments pl and p2, or to be able toexpress pl as a function of p2; for practical purposes the lattercondition is best satisfied by making pl and p2 equal, i.e., B is also aphenyl group, and the compounds examined are diphenyl deriv-atives, C,H5eA*C,H,. By using either the moment of a mono-substituted compound, vix., p-X*C,H,*A*C,H,, or that of a pp’-disubstituted derivative, vix., pp’-X*C6H4*A*C6H4*X, independentvalues of the valency angle can be obtained; in the latter case,however, two solutions are possible, so that the result is not entirelyfree from uncertainty.Several fundamental assumptions are involved in these calcul-ations : (a) that the dipole moment of a compound is strictly thevector sum of the constituent bond or group moments, (b) thatthe valency angle of A remains unchanged by the introduction of thesubstituent X in the p-position of the phenyl group, and (c) thatthere is no interaction between X and the group AB, e.g., A*C6H5.The first assumption is implicit in all calculations involving bondmoments, and the second is reasona,bly probable, except in so faras substitution in two benzene nuclei may result in some repulsion,22but the third assumption requires further consideration.A testfor interaction between groups is to calculate from the moments ofC6H5*AeB, c6H5x, and p-X*C,H,*A*B, by means of a simple vectortriangle, or the equivalent equation, the so-called “ characteristicangle,” 4,23 between the resultani; moment of C,H,*A*B and theaxis of the benzene ring passing through A; for a series of sub-stituents X, the value of + should remain unchanged. It was atone time claimed that 4 was in fact constant for a number of sub-stituted anisoles and anilines,14, 22 except when the moleculecontained groups having large and opposed electromeric effects.29 E. Bergmann and $I. Tschudnovski, 2. phpilcal. Chem., 1932, [B], 1’7,107; A . , 1932, 677.2s E. Bergmann, L. Engel, and S. Shdor, ibid., 1930, [B], 10, 397; A.,1931,23.REP.-VOL.XXXII. 130 GENERAL AND PHYSICAL CHEMISTRY.As far as the anisoles are concerned, the apparent constancy of 4was shown to be due to the use of incorrect dipole moments; theactual values of the angle for different p-substituents follow thepolar sequence CR,, F, C1, Br, I, and NO,, and a similar variationprobably occurs with the corresponding p-substituted anilines.There is little doubt that interaction occurs between the groupsX and OCH, in the anisoles; this does not appear to be due toinductive effects, but to a permanent polarisation of the mesomerictype transmitted through the conjugated system of single anddouble bonds in the benzene ring.24 The same type of interactionappears to occur in all compounds in which a phenyl group isattached to oxygen, sulphur, or nitrogen.For the phenols, thevalue of +, with X = CH,, C1, or Br, appears to be constant,25 andhence it has been claimed that there is here no evidence for inter-action;26 in view of the fact that p-chloro- and p-bromo-phenolare virtually one case, and of the very small difference between themoments of phenol (166D) and p-cresol (1.57D), which leads toconsiderable uncertainty in the calculation of +, the evidence forthe constancy of this angle is very slight.The methods described above for determining valency angles indiphenyl derivatives have been used to calculate the oxygen andthe sulphur angle in diphenyl ethers and diphenyl sulphides,14~ 223 23,27but in view of the existence of interaction moments of considerable,although unknown, magnitude, the results are of no direct value.249 26An examination of the errors in the calculated angles, as a con-sequence of this interaction moment, supposed to act along the axisof the benzene ring passing through the p-positions occupied by Aand the substituent X, shows 28 that in certain cases, e.g., nitro- andbromo-diphenyl ethers, the errors in the two independent values of8 obtained from mono- and di-substituted compounds are ofopposite sign; i.e., one is greater and the other less than the truevalue.With other compounds, e.g., ditolyl ethers, the errors areboth in the same direction. If these limitations are borne in mind,and allowance is made for possible errors in observation and for24 G.M. Bennett, Trans. Paraday SOC., 1934, 30, 853; A., 1934, 1157;G. M. Bennett and S. Glasstone, Zoc. cit., ref. (11).25 H. L. Donle and K. A. Gehrckens, 2. physlsikd. Chern., 1932, [B], 18,316; A., 1932, 984.26 L. E. Sutton and G. C. Hampson, Trans. Paraday SOC., 1935, 31, 945;A , , 1056.27 C. P. Smyth and W. S . Walls, J . Amer. Chern. SOC., 1932, 54, 3230; A.,1932, 984; G. C. Hampson, R. H. Farmer, and L. E. Sutton, Proc. Roy. SOC.,1933, [ A ] , 143, 147; A., 1934, 131.2 8 G. C. Hampson, Trans. Paraday SOC., 1934, 30, 858; G. C. Rampsonet al., Eoc. c i t . ; L. E. Sutton and G. C. Hampson, Zoc. cit., refs. (9) and (26)GLASSTONE : DIPOLE MOMENTS AND VALENCY ANGLES. 131solvent effects, for atom polarisation, and for the fact that theinteraction moment operative along each benzene ring axis in adisubstituted ether may be less than the value for a mono-sub-stituted derivative, an examination of the available data for varioussubstituted diphenyl ethers leads to the conclusion that in thesecompounds the oxygen valency angle 26 is 128" & 4". This resultis in harmony with the fact that diphenylene dioxide has zeromoment, so that the molecule must be planar, and consequentlythe minimum oxygen valency angle in compounds of this typemust be 120"; 29 it also agrees with the calculations of deviationmoments, which necessitate a valency angle greater than the tetra-hedral value in diphenyl ethers, in order to yield a consistent set ofres~lts.~O It is of interest to note that the new calculations implyan interaction moment of about 0.7D for the nitro-group, 0.25D forbromine, and 0.1D for the methyl group, acting along the axis ofthe benzene ring, in substituted diphenyl ethers.Electron-diffractionmeasurements indicate an angle of 118" -+ 3" in pp'-di-iododiphenylether.31The data for diphenyl sulphides are not so extensive as for theethers, but the application of the limitations mentioned above tothe available measurements leads to a value 26 of 113" & 3" for thesulphur valency angle. The appreciable dipole moment of thi-anthren, about l6D, indicates that in this compound the valencyangle of the sulphur atom must be less than 120" ; 32 using the momentfor the C6H5-S bond, estimated from measurements on diphenylsulphide, the actual angle may be calculated to be about l10".33An angle of 110-120" is of the order proposed for the sulphur atomin the thiocyanate group34 and in alkyl sulphides35 to account forthe dipole moments of various compounds.It is perhaps surprising that the oxygen angle in the diphenylethers is markedly greater than the corresponding angle in otheroxygen compounds ; for instance, in water the value as determined59 G.M. Bennett, D. P. Earp, and S. Glasstone, J., 1934, 1179; A., 1934,1058.30 G. 31. Bennett and S. Glasstone, Zoc. cit., ref. (ll), p. 76.31 L. R. Maxwell, S. B. Hendricks, and V. M. Mosley, J . Chem. Physics,1935, 3, 699.32 E. Bergmann and M. Tschudnovski, Ber., 1932, 65,457; A,, 1932, 507;W. S. Walls and C.P. Smyth, J. Chem. Physics, 1933, 1, 337; A., 1934, 12;G. M. Bennett and S. Glasstone, J . , 1934, 128; A., 1934, 349.33 L. E. Sutton and G. C. Hampson, Zoc. cit., ref. (26), p. 951; cf. alsoG. M. Bennett, Zoc. cit., ref. (24), p. 858.34 E. C. E. Hunter and J. R. Partington, J., 1932, 2825; A., 1933,210.35 K. A. JenRen, 2. anorg. Chem., 1935, 225, 97; see, however, E. C. E.Hunter and J. R. Partingtan, J., 1932,3812; A., 1933,210132 GENERAL AND PHYSICAL CHEMISTRY.from spectroscopic measurements 36 is about 105", and in dimethylether the angle has been calculated as 118" from the Ramanspectrum 37 and as 111" & 4" from electron-diffraction measure-ment~.~8 By assuming the moment of the G O link to be the samein dimethyl ether as in ethylene oxide, in which the oxygen angle isdetermined by the known dimensions of the oxygen and the carbonatom, the angle in the ether has been calculated 39 to be 116" -+ 7";the objection that the inductive effect of one (3-0 bond on the othermay be different in the two compounds considered 40 does not appearto apply.The angle of 110" in dimethyl ether deduced by the" shadow area " method 41 should not be quoted as evidence, sincean application of the same principle led to the conclusion that theKaufler formula was applicable to diphenyl.42 The natural valencyangle of oxygen in water and in the simple ethers, and also inchlorine monoxide and oxygen fluorideF89 43 appears to be slightlyless than the tetrahedral value, whereas in diphenyl ethers andrelated compounds it is 120" or greater ; unless the result is due toa misinterpretation of the dipole moments, which appears improbable,8ome reason for this discrepancy must be sought.The importantsuggestion has been made 26 that in diphenyl ether8 resonance occursbetween the normal molecule (I) and two possible excited states (11) :(1.)The observations(If.)of Pauling and his co-workers44 indicate as anempirical fact that, when- resonance occurs between differentpossible structures of a molecule, the actual dimensions within themolecule approach more closely the values for the form having thegreater radial force constants ; i.e., the molecular configuration willfavour distances and angles required by double bonds over those36 R.Mecke, 2. Physik, 1933,81,313; A., 1933,445; see also E. F. Barkerand W. W. Sleator, J . Chem. Physics, 1935,3,660.3 7 N. G. Pai, Indian J . Physics, 1934, 9, 121; A., 1935, 283.3 8 L. E. Sutton and L. 0. Brockway, Zoc. cit., ref. (17).30 G. M. Bennett, Zoc. cit., ref. (24); see also N. G. Pai, Zoc. cit., ref. (37).40 L. E. Sutton and G. C. Hampson, Zoc. cit., ref. (26), p. 953.4 1 W.A.Hare andE.Mack, J . Amer. Chern.Soc., 1932,54,4272; A,, 1933,ll.42 E. Mack, ibid., 1925, 47, 2468; A., 1925, 1124.43 H. Boersch, Monatsh., 1935, 65, 311; A., 687; see also J. S. Allen andH. Hibbert, J . Amer. Chem. Soc., 1934,56, 1398; A., 1934, 831; M. M. Otto,ibid., 1935, 57, 693; A., 1192; C. R. Bailey and A. B. D. Cassie, Proc. Roy.SOC., 1933, [A], 142, 129; A., 1933, 1228.44 E.g., L.Pauling, Proc. Nut. Acad. Sci., 1932,18, 293; also L. E. Sutton,Trans. Faraday SOC., 1934,30,789; A., 1934, 1156GLASSTONE : DIPOLE MOMENTS AND VALENCY ANGLES. 133necessitated by single linkages. In the diphenyl ethers, therefore,resonance between (I) and either form of (11) will result in a tendencytowards an oxygen valency angle of 125" 16', the usual value betweena single and a double bond attached to a tetrahedral atom, insteadof the normal angle between two single linkages. The same factorshould be operative, to some extent, in phenols and phenolic ethers.If the two benzene rings in diphenyl ether are to lie in one plane, itwould be necessary for the oxygen valency angle to be widened toa value lying between 123" and 145", according as an allowance of0-0.5 8.was made for an envelope 45 around the hydrogen atomsin the o-positions to represent the repulsion of the electrons. Thepossibility of this factor influencing the measured value of thevalency angle has been ~onsidered,~~ and there is reason to believethat the resonance mentioned above may favour a configurationin which the two benzene rings are coplanar.The normal valency angle of sulphur appears to be definitely lessthan that of oxygen; analysis of the Raman and infra-red spectraof hydrogen sulphide leads to an angle of 90" 47 or 92" 20',48 and avalue of 100" has been proposed for dimethyl sulphide, based onits Raman spectrum.37 The angle of 113" & 3" for diphenylsulphide, obtained from measurements of dipole moments,26 maytherefore indicate resonance of a similar type to that postulated forthe diphenyl ethers.Nothing is known of the value to be expectedfor the angle between a single and a double bond attached tosulphur,48a but owing to the fact that the radius of the sulphuratom is greater than that of oxygen, a smaller valency angle wouldaccommodate two benzene rings in one plane.The principles used for calculating valency angles in compoundsof the type C6H5*A*C,H5 can also be applied in cases where otheratoms or groups are attached to the atom A, provided the momentof the compound still lies along the axis of symmetry of the mole-cule, e.g., diphen~lrnethane,4~ benzophenone ,50 diphenylsulphone,6145 N.V. Sidgwick, Ann. Reports, 1932,29, 70.46 Idem, ibid., p. 72; C. P. Smyth and TV. S. Walls, ref. (27), p. 3238.47 A. Dadieu and K. W. F. Kohlrausch, Physikal. Z., 1932, 33, 165; A.,1932, 320.P. C. Cross, Physical Rev., 1935, 47, 7.4 ~ 3 ~ See, however, P. C. Cross and L. 0. Brockway, J . Chem. Physics,1935, 3, 821.49 E. Bergmann, L. Engel, and H. A. WOW, loc. cit., ref. (15); G. C.Hampson, R. H. Farmer, and L. E. Sutton, loc. cit., ref. (27).50 E. Bergmann, L. Engel, and H. Meyer, Ber., 1932, 65, 446; A., 1938,506; L. E. Sutton and G. C. Hampson, Zoc. cit., ref. (26), p. 955; see also 0.Fuchs and H. L. Donle, 2. phyeikal. Chem., 1933, [B], 22, 1; A., 1933, 888;0. Hessel and E. Nseshagen, ibid., 1929, [B], 4, 217; A., 1929, 275.61 E. Bergmann and M. Tschudnovski, ZOC. cit., ref. (32)134 GENERAL AND PHYSICAL CHEMISTRY.aa-diphenylethylene derivative^,^^ and aayy-tetra~hsnylallene.~~In diphenylmethane and diphenylsulphone there is no possibilityof resonance, so that the angle between the phenyl groups is closeto the tetrahedral value, any small deviations being attributableeither to experimental error, to the influence of mutual induction onthe bond moments, or to steric effects; with benzophenone andaa-diphenylethylene the corresponding angles are about 130°, andin both cases resonance, which should result in the angle beinggreater than the tetrahedral value, is theoretically possible. Inthe aa-diphenylallene compounds the angle between the valenciesjoining the phenyl groups to the carbon atom is found to be 119";this increase over the tetrahedral angle is in conformity with theThorpe-Ingold valency-deflexion hypothesis, but it might also beaccounted for by resonance.A similar method to that adopted for diphenyl compounds can beapplied to triphenyl derivatives l4 in which the resultant momentof the molecule acts along its axis of symmetry; for triphenyl-methane and triphenylchloromethane the angle between the threephenyl groups has been calculated from dipole-moment data 54 tobe, as expected, about 110". The method is, theoretically, availablefor triphenylamine, but the requisite measurements have not yetbeen made. The application of a similar principle to the determin-ation of the nitrogen valency angle in triethanolamine appearsto be open to criticism, since no allowance has been made in thecalculations for the possibility of free rotation about the N-C andC-0 linkages.When the direction of the moment of an unsubstituted diphenylcompound is not collinear with the bisector of the angle betweenthe axes of the benzene rings, but is equally inclined to both of them,as in diphenylsulphoxide or diphenylamine, it is possible to calculatethe angle between the phenyl groups from a knowledge of themoments of the unsubstituted molecule and of a mono-p-substitutedand a di-pp'-substituted derivative containing the same sub-stituent.14 An alternative value of the angle can be obtained if,instead of the last two moments, the values are known for twodi-pp'-compounds, each with two identical groups, which are aswidely different as possible in the two compounds. Both thesemethods have been used to determine the configuration of diphenyl-s~lphoxide,~~ with the result that the angle between the two52 E. Bergmann, L. Engel, and H. Meyer, Zoc. cit., ref. (50).53 E. Bergmann and G. C. Hampson, J . , 1935,989; A., 1115.(i4 E. Bergmann, L. Engel, and H. A. Wolff, Zoc. cit., ref. (15).55 J. N. Pearce and L. F. Berhenke, J . Physical Chem., 1935, 39, 1005.56 G. C. Hampson, R. H. Farmer, mdL. E. Sutton, Zoc. cit., ref. (27), p. 164GLASSTONE : DIPOLE MOMENTS AND VALENCY ANGLES. 135C,H,-S bonds has been found to be 112" & 8" ; the close agreementbetween this and the tetrahedral angle is in harmony with the factthat from the chemical properties of the sulphoxide group there isno expectation of resonance of the type to which the widening ofthe valency angle in diphenyl ether has been attributed.26The alternative procedure for determining the valency angle in acompound of the type C6H5-A--B, involving a knowledge of oneof the group moments (p. 129), has been applied to compoundshaving the general formula C,H,*CH,X, wix. , benzyl chloride,bromide, and cyanide. In these substances no appreciable inter-action between the CH2X group and other groups substituted inthe p-position is to be expected, and so the dipole-moment methodshould give reliable results. The assumption is made that theresultant moment of the unsubstituted compound, C,H,*CH,X,acts in the direction of the C-X bond; this is equivalent toassuming that the bond moments of C H , in the methylene group,and of C,H,-C are zero, so that the only effectivemoment in themolecule is that of the C-X linkage, the value of which is equalt o the measured dipole moment of the compound. These postulatesare not strictly justifiable, but it is probable that the errors involvedeffectively cancel one another. From the moments of the benzylcompounds and of a number of p-substituted derivatives, the anglebetween the C,H,-C and C-X bonds was calculated as 114-119" :the departure from the tetrahedral angle is regarded as being nomore than the probable errors involved in the determination.57In the benzyl compounds no resonance, of the kind already con-sidered, is to be anticipated, so that there should be no widening ofthe valency angle.58Attempts have been made to estimate the oxygen angle in anisoleon the assumption that the moment of the O-CH, bond is the sameas in dimethyl ether; 59 the values of 140-150" obtained in thismanner are undoubtedly in error, because of group-interactioneffects in the p-substituted anisoles, the moments of which arerequired for calculating the valency angle.25, 6o A similar difficultyarises in connexion with the oxygen angle in phenol itself and inother phenolic ethers, but no dipole method appears available atpresent for overcoming it.57 C. P. Smyth and W. S . Walls, J . Amer. Chern. SOC., 1932, 54, 1854; R.,1932, 794.58 See, however, J. M. A. de Bruyne, R. M. Davis, and P. M. Gross, ibid.,1933,55, 3936 ; A., 1933, 1230.59 G. C. Hampson et al., Zoc. cit., ref. (27); see also C. P. Smyth and W. S.Walls, Zoc. cit., ref. (27), p. 3237.80 G. M. Bennett and S. Glesstone, Zoc. cat., ref. (11); L. E. Sutton and GI. C.Hampson, loc. cit., ref. (26)136 GENERAL AND PHYSICAL CHEMISTRY.The dipole moment of 2-13D for hydrogen peroxide was a t firstattributed 61 to its having the structure :>O+O, but it wasshown later that the result was in harmony with the ordinaryformula H*O*O*H, on the assumption that the oxygen valencyangle is tetrahedral and that there is free rotation of the OH groupsabout the 0-0 axis. From considerations of wave rnechanic~,~~however, it appears that free rotation is unlikely, although spectro-scopic considerations indicate the formula HOOH to be the correctone. It is concluded that the two OH groups, which are stationary,are not coplanar, and that the two H.0-0 planes in the moleculeare inclined at an angle of about 100" to one another. The calcul-ations indicate that the oxygen valency angle is also about loo",and these two values lead to a dipole moment of %OD, comparedwith the observed 2*13D, based on the assumption that the 0-Hbond moment is the same as in water, and that in the latter substancethe oxygen angle 3G is 105". Similar application of wave-mechanicalmethods 63 to the hydrazine molecule indicates that it has a structureanalogous to that of hydrogen peroxide ; the nitrogen valencyangle is about 110", and the two planes containing nitrogen atomsand bisecting one of the two N<H angles are perpendicular toone another. Prom the known dipole moment of ammonia and thedimensions of the molecule,G4 the moment of the N-H link isfound to be 1-3D, and the value being assumed to be the same inhydrazine, the moment of the latter is calculated as 1.70D, on thebasis of the co&guration suggested; this result is in satisfactoryagreement with the observed value 1.83D.Some confirmation of the stereochemistry of certain elements inthe second and third groups of the periodic classification has beenobtained from dipole-moment data. The moment of boron tri-chloride is zero in solvents with which it does not combine,65 andhence this compound probably has a symmetrical planar structure,the valency angle being 120". This conclusion is in agreement withthat reached from a study of the diffraction of electrons by borontrichloride.66 Aluminium bromide has a very small dipole momentH61 E. P. Linton and 0. Maass, Canadian J . Res., 1932, '9, 81 ; A., 1933, 8.c2 W. Theilacker, 2. physikal. Chem., 1933, [B], 20, 142; A., 1933, 338;see also E. C. E. Hunter and J. R. Partington, J., 1932, 2817; 'A., 1933, 210.W. G. Penney and G. B. B. M. Sutherland, Trans. Farachy SOC., 1934,30, 898; J . Chem. Physics, 1934, 2,492; A., 1934, 1158.64 D. M. Dennison and G. E. Uhlenbeck, Physical Rev., 1932, [ii], 41, 313;A., 1932, 982.6 5 H. Ulich and W. Nespital, Z. EleEtrochem., 1931,37,559 ; A., 1931,1213.66 R. Wierl, Zoc. cit., ref. (17)GLASSTONE : DIPOLE MOMENTS AND VALENCY ANGLES. 137in carbon disulphide solution,65, 67 but as it consists largely ofdouble molecules in this solvent,68 its structure is probablyrepresented by Br \ /A], rBr\ fX1\Br /Br although there is no means ofBr Brdeciding between planar and tetrahedral configurations. Themoments of beryllium chloride and bromide in benzene 65 are statedto be zero : if this is so, then in the bicovalent state the molecules arelinear. From observations with diethylmercury and diphenylmer-cury,09 it appears that these substances have small but probablydefinite moments ; it is suggested that the compounds have a linearstructure, but that flexibility of the bonds leads to the setting up ofa resultant moment. Some confirmation of this view is said to beobtained from the molecular dimensions of dibromodiphenylmercury,calculated from electron-diffraction measurements ; 70 the resultsare believed to be compatible with a swing of 30" of the -C,H,Brgroups on either side of a straight line through the mercury atom.The whole subject appears t o be worthy of further investigation.S. G.C. B. ALLSOP.S. GLASSTONE.E. B. MAXTED.E. A. MOELWYN-HUGHES.G. B. B. M. SUTHERLAND.67 W. Nespital, 2. physikal. Chem., 1932, [B], 16, 153; A., 1932, 447.68 H. Ulich, ibid., Bodenstein Festband, 1931, 423; A., 1931, 1229.60 E. Bergmann and W. Schutz, ibid., 1932, [B], 19, 401; A., 1933, 210;G. C. Hampson, Trans. E'araday SOC., 1934, 30, 877; A., 1934, 1157; W. J.Curran and H. H. Wenzke, J. Amer. Chew&. SOC., 1935, 57, 2162.'O H. de Laszlo, Trans. Faraday SOC., 1934, 30, 884.E