ANNUAL REPORTSON THEPROGRESS OF CHEMISTRY.GENERAL AND PHYSICAL CHEMISTRY.1. BOND INTERACTIONS.THERE are two main methods of obtaining information about bond inter-actions in polyatomic molecules. The first is to compare bond properties indifferent molecules. Thus the C-Cl bond is shorter in ClCN (1.67 A) 1 thanin CH&l (1.781 showing the effect of an adjacent triple bond (there isalso an increase in the force constant).4 The second is to study these inter-actions in a molecule as it vibrates; the usual way of doing this is to deter-mine from the vibration frequencies the function governing the variation ofpotential energy with distortion. For example Slawsky and Denni~on,~ andLinnett 6 found that, in the methyl halides, the C-X bond interacts withthe inter-bond angles in the methyl group, the potential-energy functionshowing that, as the C-X bond is lengthened, the HCH angle tends to in-crease. Analogous interaction effects have been found in ethylene,' formalde-hyde,8 keten,8 and dia~omethane.~ Recently other spectroscopic methods ofinvestigating bond interactions have been used.In this Report methods ofthe second kind will be specially considered.Potential-energy Functions.-Of the two basic force fields the Centralhas proved less useful than the Valency.lo In its simplest form the potential-energy function based on the latter involves squared terms in the bondlength and inter-bond angle changes but, in its complete form, " crossterms '' which take account of the interactions between different parts ofthe molecule are also included.Thus for the water molecule the completevalency force field (V.F.F.) potential-energy function is l1V = gkl(Ar12 + AvZ2) + *kaAuz + kla(Arl + AvZ)A# + klIAylAy2 . (1)where AY,, Ar2, and Act are the changes in the bond lengths and H-0-Hangle, k , and k, are the respective constants, k,, measures the interactionJ. Y . Beach and A. Turkevich, J . Amer. Chem. Soc., 1939, 61, 299.L. E. Sutton and L. 0. Brockway, ibid., 1935, 57, 473; S. L. Miller, L. C. Aamodt,A. D. Walsh, Trans. Faraday Soc., 1947, 43, 60.J. W. Linnett and H. W. Thompson, J., 1937, 1399.2. I. Slawsky and D. M. Dennison, J . Chem. Phys., 1939, 7, 509.J. W. Linnett, ibid., 1940, 8, 91.H. W. Thompson and J. W. Linnett, J., 1937, 1376.B. L.Crawford, W. H. Fletcher, and D. A. Ramsay, J . Chem. Phys., 1951, 19, 406.lo G. Herzberg, " Infra-red and Raman Spectra of Polyatomic Molecules," Vanl1 D. F. Heath and J. W. Linnett, Trans. Furaday SOL, 1948, 44, 550.G. Dousmanis, C . H. Townes, and J. Kraitchman, J . Chem. Phys., 1952, 20, 1112.Idem, ibid., p. 1384.Nostrand, New York, 1945, pp. 169-1868 GENERAL AND PHYSICAL CHEMISTRY.between the bonds, and k,, the interaction between the bonds and the angle.There are four independent constants in the complete quadratic potential-energy function. If there are n fundamentalvibrations in a symmetry class, the general potential-energy functiongoverning distortions of that symmetry will contain &n(n + 1) independentconstants.To obtain the number of independent constants for all distortionsof the molecule these must be summed over all symmetry classes. Thus, forwater, there are two fundamental symmetric vibrations ; for these distortionsthere are three constants. There is one fundamental antisymmetricvibration; for this there is only one constant. There are therefore fourconstants in all [cf. (l)].Determination of Force Constants.-The molecule H,O has only threevibration frequencies, so, from them alone, the four constants cannot befound. This difficulty may be overcome by using isotopes. Thus, for water,deuterium oxide which also has three fundamental frequencies may be used.However, for any pair of isotopic molecules, the Teller-Redlich productrule12 states that the ratio of the product of the frequencies of all thevibrations of a given symmetry class for one isotopic molecule to the corre-sponding product for the other is independent of the force field and equalto a function involving the atomic masses and molecular dimensions only.So, since the vibrations of H,O and D,O fall into two symmetry classes,D20 provides only one new independent frequency.This with the three ofH,O makes possible the determination of all four constants. The vibrationfrequencies of DOH might also be used but, because of relationships betweenthe frequencies of isotopic molecules , they provide no additional inform-ation. Decius and Wilson l2 have deduced certain sum rules relating thevibration frequencies of isotopic molecules.the summations being over all vibration frequencies.Decius l4 has alsoexamined what isotopic substitution is necessary in linear molecules toobtain a unique solution for the force constants.Hence, if the frequencies of a sufficient number of isotopic molecules areavailable all the constants may in principle be determined. However theuse of isotopic substitution is not always well suited for the accurate deter-mination of force constants. This may be illustrated with hydrogen cyanide.The valency vibration frequencies of HCN are 3312.0 and 2089.0 cm.'l.15The table lists the frequencies calculated for DCN and HC15N for threevalues of k,, in the functionAs one vibration frequency of DCN is 2629.3,15 k,, must have a small negativevalue.But the figures for HC15N show that it would be necessary toThis is so whatever its form.For example for water;Sv2(HOH) + CvZ(DOD) = 2Zv8(HOD) . . . . * (2)P' = &kl(AVm)' + &(A~CCN)' + ~ I ~ ( A ~ C ' C H ) ( A ~ O N ) * * - - (3)DCN HClSNL r 3 I > k,, ( x 10-6) -0.5 0 +0.5 -0.5 0 +O-5Frequency (crn.-l) 2648.0 2596.1 2548.6 3309-9 3310-8 3311.61881.4 1919.1 1954-9 2056.5 2056-0 2055.4l2 0. Redlich, 2. fibhysikal. Chem., 1935, B,. 28, 371 ; see also W. R. Angus e t aZ.,l4 J. C. Decius, ibid., 1952, 20, 511.J., 1936, 971. l3 J . C. Decius and E. B. Wilson, J . Chem. Phys., 1951, 19, 1409.l6 G. Herzberg, ref. 10, p. 279LINNETT BOND INTERACTIONS. 9determine the frequency shifts from HCI4N to HC15N very accurately tofix the value of kI2.The reason why the substitution of deuterium forhydrogen in hydrogen cyanide is so effective in determining k,, is that,while the CH " group " frequency is much greater than that of the C-Nbond, the CD " group " frequency is close to that of the C-N bond. Thecloseness of the " group " frequencies in DCN causes the effect of varyingk,, on the calculated frequencies to be large. Isotopic substitution shouldtherefore be used for calculating force constants only when it is clear thatit provides a reliable method.For H,O, and other bent AX, molecules, in the absence of isotopic sub-stitution there are only three frequencies to determine four constants. Aconvenient method of representation has been suggested by Duchesne, l6and Glockler and Tung,17 who proposed that the values of three constantsshould be plotted against values of the fourth which is regarded as an inde-pendent variable.It is then found that the graphs are ellipses, and thevalues of the constants are limited to certain ranges. Such graphical repre-sentations have been used by Burnelle and Duchesne,l* Torkington,lgThomas,20 and Linnett and Heath.21 However it is often impossible toselect from such inadequate data the correct set of values for the constantsand it is important that efforts be made to obtain, with complete certainty,all the constants in the general potential-energy function for as many mole-cules as possible so that reliable conclusions may be drawn from the values.Another method that has been used for overcoming the difficulty thatthe number of constants usually exceeds the number of observed frequenciesis that of transferring constants from other molecules containing similarbonds.Thus Crawford and Rrinkley 22 used the same values for the con-stant of the C-N bond in hydrogen cyanide and methyl cyanide. Thismethod has been used by Cleveland and Meister and their co-workers inextensive calculations on the halogen derivatives of methane,23 ethane,24and other molecules.25 However there are often variations in bond lengthsfrom one molecule to another (e.g. from methyl chloride to carbon tetra-chloride) so that there can be no certainty that force constants can betransferred in the above manner. Caution must be used in making suchtransfers.Thomas 26 has used constants from related molecules but hasmade allowance for bond changes on going from one to another. Forl6 J. Duchesne, Mesn. SOC. Roy. Sci., Lizge, 1943, 1, 429.G. Glockler and J. Y . Tung, J . Chem. Phys., 1945, 13, 388.J. Duchesne and L. Burnelle, ibid., 1961, 19, 1191.l9 P. Torkington, ibid., 1949, 17, 357.21 J. W. Linnett and D. F. Heath, Trans. Furaday Soc., 1952, 48, 592.22 B. L. Crawford and S. R. Brinkley, J . Chem. Phys., 1941, 9, 69.33 A. G. Meister, S. E. Rosser, and F. F. Cleveland, ibid., 1950, 18, 346; S. M.Ferigle, F. F. Cleveland, W. M. Bryer, and R. B. Bernstein, ibid., p. 1073; J . P. Zeitlow,F. F. Cleveland, and A. G. Meister, ibid., p. 1076; J. R. Madigan, F. F. Cleveland,W. M. Bryer, and R.B. Bernstein, ibid., p. 1081 ; J. R. Madigan and F. I;. Cleveland,ibid., 1951, 19, 119; C. E. Decker, A. G. Meister, and F. F. Cleveland, ibid., p. 784;P. F. Farlon, A. G. Meister, and F. F. Cleveland, ibid., p. 1561 ; A. Davis, F. F. Cleve-land, and A. G. Meister, ibid., 1052, 20, 454.24 F. F. Cleveland, J. E. Lamport, and R. W. Mitchell, ibid., 1950, IS, 1073; M. 2.El-Sabban, A. G. Meister, and F. F. Cleveland, ibid., 1951, 19, 855; P. 13. McGee,F. F. Cleveland, and S. I. Miller, ibid., 1952, 20, 1044.25 J. S. Ziomek and F. F. Cleveland, ibid., 1949, 17, 578; F. F. Cleveland, K. W.Greenlee, and E. E. Bell, ibid., 1950, 18, 355.26 W. J . 0. Thomas, ibid., 1951, 19, 1162.2o W. J. 0. Thomas, J., 1952, 238310 GENERAL AND PHYSICAL CHEMISTRY.example, the CO force constant in CO, is known exactly, and, from this andthe bond length, using Gordy’s form~lze,~~ Thomas calculated the bond orderin CO,. From the bond length in cyanic acid he calculated the CO bondorder in that molecule, and, from this, using Gordy’s formulz again, heobtained the CO force constant in cyanic acid.So, from the small observedchange in bond length (1-163 to 1.170 A) he determined the small change inthe force constant (from 15-5 to 15.0 x lo5 dynes/cm.). If accurate bondlength tralues are available from micro-wave or other data this probablyprovides the best means of making use of the known value of a force constantof a similar bond in a related molecule. It is to be preferred to transferringthe value uncorrected.With molecules having doubly degenerate vibrations there is a furthermeans of obtaining information about force constants.Such vibrations canpossess angular momenta by virtue of their internal motions, and the magni-tude of the vibrational angular momentum associated with a certain excitedlevel can, in favourable cases, be determined from the structure of the bandsassociated with the transition to that level from the ground state.28 Thisangular momentum is dependent on the force field and may be used todetermine force constants. Formulae for doing this have been publishedby Boyd and Longuet-Higgin~,~~ For the vibrations of a given symmetryclass (say the three of the degenerate class of methyl chloride) the sum ofthe angular momenta associated with all the first excited levels of thatclass has a particular value independent of the force field.Lord and Merri-field 30 and Boyd and Longuet-Higgins 29 have given some examples of themagnitude of this sum. So, for the degenerate vibrations of methyl chloridethere are only two independent angular momenta available for determiningthe force constants.As yet the so-called Coriolis coefficients which measure the angularmomentum associated with the vibration have not been widely used fordetermining iorce constants. Dennison 31 used them with ammonia andhe and Hansen3z used the frequencies of ethane and hexadeuteroethanetogether with values of the Coriolis coefficients to determine all 21 constants(excluding torsion) in the potential-energy function of that molecule. Lordand Venkatcswarlu33 have pointed out that for allene all ten potentialconstants associated with distortions corresponding to the degeneratevibrations could be obtained from the eight degenerate vibration frequenciesof allene and tetradeuteroallene (only seven are independent because of theTeller-Redlich relation) and the eight Coriolis coefficients (only six areindependent because of the sum rules),It has been assumed so far that the potential-energy function is quadratic27 W.Gordy, J . Chem. Phys., 1946, 14, 305; 1947, 15, 305.28 V. &I. McConaghie and H. H. Nielsen, Proc. Nut. Acad. Sci., 1948, 34, 455;D. R. J. Boyd, H. W. Thompson, and R. L. Williams, Discuss. Furuduy Soc., 1950, 9,154; D. R. J. Boyd, H.W, Thompson, and R. L. Williams, Proc. Roy. Sot., 1952, A ,213, 42; D. R. J. Boyd and H. W. Thompson, Trans. Faraday SOC., 1952, 48, 493;H. W. Thompson and R. L. Williams, ibid., p. 502; H. H. Nielsen, J . Chem. Phys.,1952, 20, 759.R. C. Lord and R. E. Mecrifield, J . Chenz. Phys., 1952, 20, 1348; M. Johnstonand D. M. Dennison, Phys. Review, 1935, 48, 868.29 D. R. J. Boyd and H. C. Longuet-Higgins, PYOC. Roy. Soc., 1952, A , 213, 55.3L D. M. Dennison, Review Mod. Phys., 1940, 12, 175.32 G. E. Hansen and D. M. Dennison, ./. Ckem. Phys., 1952, 20, 313.53 R. C. Lord and I?. VenkateswarIu, ibid., p. 1237LINNETT BOND INTERACTIONS. 11and anharmonicity can be neglected. When the aim is to obtain the completepotential-energy function this is not always justifiable.But only in rare cases(e.g. hydrogen cyanide,S5 nitrous oxide 36) can sufficient overtonesbe observed to obtain the zero-order frequencies. In other cases othermethods have to be adopted. For instance Dennison corrected the observedfundamentals of methane by assuming a relationship between the an-harmonicity coefficients of methane and tetradeuteromethane and by usingthe Teller-Redlich product rule. Hansen and Dennison treated ethanesimilarly.Calculating force constants from vibration frequencies is often tedious.Procedures for making such calculations have been proposed by El’yashe-v i ~ h , ~ ’ Wilson,38 and Torkingt~n.~~Results for Interaction Constants.-The simplest type are the bond-bondconstants of linear molecules [ e g .k,, in (3)] for in these the valency vibrationsoccur independently of the bending ones. In most cases the cross-termconstant is positive (e.g. in C0,,8 CS2,40 N3-,4* N,O,41 OCS,42 C1CN,20 BrCN,20ICNIz0 and also, regarding the NH as a unit, in HNC0,20 HNCS,20 and HN, 20).But in HCN,35 and the bent molecules H,O,ll H2SJM and H2Se,40 it is negative.The positive value of this constant has been ascribed to the effect of resonance.Thus in carbon dioxide there is resonance between (i) O=C=O, (ii) 6-C&,and (iii) 0sC-O. The lengthening of the left-hand bond, therefore, favours(ii) and the consequent shortening of the right-hand bond.s The potentialenergy increases less, therefore, when A Y ~ and AY, are opposite in sign thanwhen they are of the same sign and this accounts €or the cross-term constantbeing positive; but, when hydrogen is one of the atoms attached to thecentral atom, the constant is negative.Coulson, Duchesne, and Manne-back4, have suggested that this is due to a charge effect. Hoare andLinnett 40 pointed out that, when the cross-term constant is positive in atriatomic molecule, the diatomic molecule left on dissociating one bondwould be expected to be shorter than the corresponding bond in the triatomicmolecule. This is found to be so (e.g. rCs in CS, is 1.55 and in CS 1.53 A).When the constant is negative the reverse is to be expected; this is alsofound ( e g . roH in H20 is 0-958 and in OH 0-971 A). Thomas has confirmedthis in the molecules studied by him.20 The sign of the cross-term constantsin the mercury halides is still uncertain and more data for these would beinteresting.The positive cross-term constants are always larger than thenegative ones so interaction resulting from resonance effects must be greaterthan that occurring in hydrogen cyanide, water, etc. Heath, Linnett, and34 L. G. Bonner, Phys. Review, 1934, 46, 458; B. T. Darling and D. M. Dennison,ibid., 1940, 57, 128.35 W. Brookes, Trans. Faraday Soc., 1951, 47, 1152.3 6 G. Herzberg, ref. 10, p. 278.3 7 El’yashevich, Compt. rend. Acad. Sci., U.R.S.S., 1940, 28, 604.3 8 E. B. Wilson, J . Chena. Phys., 1939, 7, 1047; 1941, 9, 76; J. C. Decius, ibid.,39 I?. Torkington, ibid., 1949, 17, 357; 1950, 18, 93, 773; 1951, 19, 528, 979.4O M.F. Hoare and J. W. Linnett, Trans. Faraday SOC., 1949, 45, 844.4 1 W. S. Richardson and E. B. Wilson, J . Chem. Phys., 1950, 18, 604.42 H. J. Callomon, D. C. McKean, and H. W. Thompson, Proc. Roy. SOC., 1961,43 C. A. Coulson, J . Duschesne, and J. Manneback, Nature, 1947, 160, 793;+ -1948, 16, 1025.A , 208, 341.“ Contribution a 1’Etude de la Structure Moleculaire,” Liege, 1948, p. 3312 GENERAL AND PHYSICAL CHEMISTRY.Wheatley44 pointed out that in CH,, SiH,, NH,, PH,, H,O, and H,S thebond lengths were always less than in the diatomic molecules AH but,though the cross-term constants are not certain, it seems that they arepositive in the Group IV hydrides and in ammonia but negative in theGroup VI hydrides and in phosphine and arsine. The contrast betweenammonia and arsine has also been noted by Duchesne and Ottelet 45 whosuggest that it may be due to the opposing effects of hybridisation changesand H---H interaction which tend to lead to positive and negative cross-term constants, respectively.They also point out that the bond-bondinteraction constants involving bonds to hydrogen are small.From the three valency vibration frequencies of cyanogen and one ofthe molecule containing one 13C atom, Duchesne and Burnelle 18 have foundthat the (CN)(CC) cross-term constant is positive and the (CN)CN’) cross-term constant negative. The sign of both can be accounted for by theeffect of resonance between NC-CN and double-bonded forms, for a shorten-ing of one C-N bond favours the first canonical form and hence a lengtheningof the C-C bond (positive constant) and a shortening of the other C-N bond(negative constant) (cf.Longuet-Higgins and Burkitt 46).Torkington 47 has suggested a potential-energy function (omitting angleterms) for polyatomic molecules derived from that of Morse for diatomicmolecules. This includes bond-bond interaction terms and, for triatomicmolecules, Torkington relates the sign of the cross-term constant to thedifference between the heat of atomisation and the sum of the bond-dissoci-ation energies (cf. Duchesne 48). He also considers the sign of the higher-order terms in the potential-energy function.In methyl chloride the largest interaction constant is that between theC-Cl bond and the H-C-Cl.angle.It is positive showing that, as the H-C-C1angle is increased the C-C1 bond tends to shorten. It is noteworthy that,in cyanogen chloride, where a similar drawing together of the three pairs ofelectrons opposite to the chlorine atom must also have occurred (relative tomethyl chloride in its near-tetrahedral equilibrium configuration) , theC-Cl bond has become shorter. A similar effect appears to occur in methaneand hydrogen cyanide also.@ In methane the (CHi)(HjCHk) constant isnegative indicating that, as the HjCHk angle is reduced the CHi bond tendsto shorten. Also in hydrogen cyanide (and in acetylene) the C-H bond isshorter than in methane.50 The shortening of the C-Cl bond in cyanogenchloride is often ascribed to resonance, but objections have been made tothis explanation by Burawoy 51 and by D u c h e ~ n e .~ ~ Burawoy suggests thatit is due to changes in electron shielding and other inter-electronic effects,while Duchesne relates it to changes in hybridisation a t the chlorine atom.He has explained in a similar manner increases in bond length from carbontetrachloride to methyl chloride, from silicon tetrachloride to silyl chloride,44 D. F. Heath, J. W. Linnett, and P. J. Wheatley, Trans. Faraday Soc., 1950, 46,137.45 J. Duchesne and I. Ottelet, J . Chem. Phys., 1949, 17, 1354.46 H. C. Longuet-Higgins and F. H. Burkitt, Trans. Faraday Soc., 1952, 48. 1077.47 P. Torkington, J . Chem. Phys., 1952, 20, 1174.48 J. Duchesne, Mew. Acad. Roy. Betg., 1952, 26 (7), 1.4* J. W. Linnett, Proc.Roy. SOC., 1951, A , 207, 30.50 A. D. Walsh, ref, 3 ; J. W. Linnett, Trans. Favaday sot., 1945, 41, 223.6 1 A. Burawoy, Trans. Farnday SOL., 1943, 39, 79; 1944, 40, 537; “ Contribution aI’Etude de la Structure Moleculaire,” Li&ge, 1948, p. 73.52 J . Duchesne, Trans. Faraday Soc., 1950, 46, 187; J . Chem. Phys., 1953, 19, 246LINNETT : BOND INTERACTIONS. 13and from carbon tetrafluoride to methyl fluoride, giving nuclear quadrupolecoupling data in various molecules in support of this hypothesis. Thoughthe above effects in methyl chloride and cyanogen chloride correspond withthose in methane and hydrogen cyanide the bond-bond cross-term constantin the two triatomic molecules are different.The calculations by Hansen and Dennison32 for ethane are valuablebecause they provide a complete treatment of a relatively large molecule.The bond-angle are the largest interaction constants ; all the bond-bondconstants are small.As with the methyl halides the (CC)(CCH) constantis quite large and positive, but the biggest interaction constant is thatassociated with the term (CHi)(CCHi+,), the bond and angle being in thesame methyl group. It is negative, indicating that, as the C-Hi bond islengthened, the CCHi+ angle tends to increase. The constant associatedwith the (CHi)(Hi+ ,CHi-J cross-term is also negative, indicating that, asthe C-Hi bond is lengthened, the Hi+ ,CHi-, angle tends to increase. Thus,as the CHi bond is lengthened, the angles on the opposite side of the carbonatom tend to increase, so the effect is analogous to that produced by thelengthening of the C-C bond (and the C-Cl bond in methyl chloride 5).The interactions between the separate methyl groups are of interest becauseit may be possible to link these to the effects restricting rotation.Themolecule being in the staggered form, it is found that increasing one HCCangle tends to cause the opposite one in the other methyl group to increase,and that increasing a C-H bond length in one methyl group tends to causethe adjacent CCH angles in the other methyl group to decrease. The lattercould be due to repulsion between non-bonded atoms or between bonds butthe former is more difficult to explain, though it might be accounted for byhyperconj ugation effects.Torkington has studied ethylene 53 and its derivatives 54 extensively.Many of his conclusions are unaffected by modifications made to the fre-quency assignment by Arnett and C r a ~ f o r d , ~ ~ and Rank, Shull, and A ~ f o r d .~ ~For instance he finds that the interaction constant between adjacent C-Hbonds is negative (as in water, etc.) and between the trans-C-H bonds isprobably positive. The latter suggests that as one C-H bond is lengthenedthe C-H trans to it tends to contract. The (C=C)(C-H) interaction constantis positive, and Torkington suggests that this may be a consequence ofrepulsion between non-bonded hydrogen and carbon atoms (cf. Heath,Linnett, and Wheatley 57). Torkington also studied the out-of-planebending constant of the CH, group in CH,=CH,, CH,=CHX, and CH,=CX,,where X = methyl, halogen, cyano, etc.= He found that the effect onthe constant is twice as great for the CH,=CX, molecules as for the corre-sponding CH,=CHX molecules (using ethylene as the reference molecule)and also that ortho- and para-directing groups lower the constant whilewta-directing ones increase it.This surprising result appears to show that,1s electrons are drawn from the double bond, the constant increases. In alater paper 53 Torkington links this effect to the conclusion of Heath, Linnett,63 P. Torkington, Proc. Phys. SOL, 1951, A , 64, 32.54 Idem, Nature, 1949, 163, 96; Proc. Roy. Soc., 1950, A , 206, 17.5 6 R. L. Arnett and B. L. Crawford, J . Chew. Phvs., 1950, 18, 118.56 D. H.Rank, E. R. ShuII, and D. W. E. Axford, ibid., p. 116.6 7 D. F. Heath, J . W. Linnett, and P. J . Wheatlcy, Trans. Fnvadny .TOC , 19*9. 45. 114 GENERAL Ah’D PHYSICAL CHEMISTRE’.and Wheatley 57 that the out-of-plane bending of the ethylene molecule iseasier because the constant associated with the x-bond is negative. Tork-ington also studied the out-of-plane bending constant of the CH group inCH,=CHX molecules and found that the order was that of the electro-negativities of the attached groups X.%An important factor causing deviations from the simple valency forcefield is undoubtedly repulsion between non-bonded atoms as has been shownby Urey and Bradley 58 for various AX, molecules and ions, and by Sima-nouti 59 in a variety of substituted derivatives of methane and silane.Heathand Linnett also showed the importance of such repulsions in boron halidesJ6*various hexafluoridesJ61 Group IV halides,62 and such ions as SO,”, NO3-,e t ~ . ~ ~ (see also Coulson, Duchesne, and Manneba~k,~~ and Sehon andSzwarc 6*). Both Simanouti, and Linnett and Heath compared the repulsionconstants with those to be expected from the known van der Waals repulsionbetween inert gas atoms as calculated by Lennard- Jones.G5 Linnett andHeath,,l in a general survey, showed that the repulsion constants for a givenpair of non-bonded atoms varied regularly in a series of molecules with thedistance separating them. Wilson and Polo 66 find that the bond-bondconstant in nitrogen trifluoride is probably positive. This could be due torepulsions between the fluorine atoms.Caunt, Short, and Woodward 67have examined similar repulsion effects in germanium tetrafluoride.Dennison has determined the five potential constants of methane.31For those governing bending only, the main HCH constant is 0.42 x lo5(in dynes/cm.) and the (HfCHj)(H&Hz) interaction constant is -0.075 x lo5.The negative sign of the latter suggests that reducing one HCH angle tends tocause the opposite one to close up also. This would be an erroneous con-clusion, for the six HCH angles cannot be varied independently. Suppose(AHiCHj) = - (AH,CH,) and the distortion is symmetrical, the other HCHangles will not change, but if (AHiCHj) = + (AH,CH,) the other four anglesdecrease by an angle equal to half the increase in the other two.From thisit is easy to show that the potential energy increases more rapidly withchange in angle for the distortion in which (AH&Hj) = + (AH,CH,) thanfor the distortion in which (AHfCHj) = - (AHkCHz). So the closing of oneHCH angle favours the opening of the opposite one. This can be explainedby electron correlation effects 68 or by, what is essentially equivalent,hybridisation changes. Difficulties like the above provided one of thereasons for Heath and Linnett’s modifying the ordinary valency force fieldto their orbital force field (0.V.F.F.) in which the central atom is imagined5~3 H. C. Urey and C. A. Bradley, Phys. Review, 1931, 38, 1919.5s T. Simanouti, J . Chem. P h y s . , 1949, 17, 245, 734, 848; D.F. Heath and J. W.6o D. F. Heath and J. W. Linnett, Trans. Faraday Soc., 1948, 44, 873.61 I d e m , ibid., 1949, 45, 264.62 I d e m , ibid., 1948, 44, 561, 878.64 A. H. Sehon and M . Szwarc, Proc. Roy. Soc., 1951, A , 209, 110.65 J. E. Lennard-Jones, ibid., 1924, A , 106, 463; (‘R. A. Buckingham, ibid., 1938,Statistical Thermodynamics,”6 6 M. K. Wilson and S. R. Polo, J . Chem. Phys., 1952, 20, 1716.O 7 A. D. Caunt, L. N. Short, and L. A. Woodward, Nature, 1951, 168, 557; Trans.68 (Sir) J . E. Lennard-Jones, J . Chem. Phys., 1952, 30, 1024; H. Margenau, “ TheLinnett, ibid., 1950, 18, 147.63 I d e m , ibid., p. 884.A , 168, 264; R. H. Fowler and E. A. Guggenheim,C.U.P., 1939, p. 285.Faraduy SOC., 1952, 48, 873.Nature of Physical Reality,” McGraw-Hill, 1950, p.434LLNNETT : BOND INTERACTIONS. 15to have its valencies directed in particular directions relative to one another,and the angular deviation of each bond from their directions is used in thepotential-energy function.60 Force fields of the same type had been usedby Urey and Bradley 58 and by Howard and Wilson 69 but had never beendeveloped. By this approach difficulties like that for methane will notexist because the impossibility of varying angles independently does notoccur in using the O.V.F.F. In terms of cross-terms, a simple O.V.F.F.with no cross-terms, will correspond, in certain cases, to an ordinary V.F.F.including finite angle-angle cross-terms (and vice versa).Some wave-mechanical calculations of force constants and interactionconstants have been made.Examples are provided by W a r h u r ~ t , ~ ~ Coulsonand L~nguet-Higgins,~~ Parr and C r a w f ~ r d , ~ ~ Parr and Taylor,73 Wheatleyand L i ~ ~ n e t t , ~ ~ and Longuet-Higgins and Burkitt.46Intensities of Infra-red Bands.-Since 1945 an active start has beenmade in determining the intensities of infra-red bands and in using the dataobtained. The procedure is to determine the intensities of the fundamentalabsorption bands of the molecule and from these to calculate the rate ofchange of dipole moment with each normal co-ordinate, +/aQ (see Wilsonand Wells 7 5 ; Thorndike, Wells, and Wilson 7 6 ; Callomon, McKean, andThompson 77; and Penner and Weber 78). After a normal co-ordinatetreatment these may be converted into values for the rate of change of p withbond lengths and angles (+/h and ap/&).In most treatments the ap/&values have been related to a change of moment of a particular bond withlength and the &L/& values used to calculate bond moments supposing that,as the molecule bends, the bonds retain their constant moments whichremain directed along the line joining the atoms. The justifiability of thesefar-reaching assumptions seems to be doubtful. T h ~ r n d i k e , ~ ~ for example,stated that his results for ethane ‘‘ cast some doubt upon the whole conceptof additivity of bond dipole moments ” (see also Bell, Thompson, andVagoDipole-moment changes on distortion can also be obtained from measure-ments of refractive indices using infra-red radiation, as has been done byRollefson with RollefsonJ81 with Havens,sZ and with Kelly and Schurin.833ne important difficulty in the interpreting of the change of p on distortionis that the magnitude, but not the sign, can be deduced from the datalbtained from both refractive-index and absorption measurements.For carbon dioxide Thorndike 79 found that all‘/& for the C=O bond was6s J. B. Howard and E. B. Wilson, J . Chenz. Phys., 1934, 2, 630.70 E. Warhurst, Trans. Faraday Soc., 1944, 40, 26.7 1 C. A. Coulson and H. C. Longuet-Higgins, Proc. Roy. Soc., 1948, A , 193, 447.78 R. G. Parr and B. L. Crawford, J . Chem. Phys., 1948, 16, 526; 1949, 17, 726.73 R. G. Parr and G. R. Taylor, ibid., 1951, 19, 497.74 P.J. Wheatley and J. W. Linnett, Trans. Faraduy Sot., 1949, 45, 897.7 5 E. B. Wilson and A. J. Wells, J . Cltern. Phys., 1946, 14, 578.7 G A. h4. Thorndike, A. J. Wells, and E. B. Wilson, ibid., 1947, 15, 157.7 7 H. J. Callomon, D. C. McKean, and H. W. Thompson, Proc. ROT. Soc., 19517 8 S. S. Penner and D. Weber, J . Chem. Phys., 1951, 19, 807, 817, 974.79 A. M. Thorndike, ibid., 1947, 15, 868.8o R. P. Bell, H. W. Thompson, and E. E. Vago, Proc. Roy. Soc., 1048, A , 192, 498*l R. Rollefson and A. H. Rollefson, Phys. Review, 1935, 48, 779.82 R. Rollefson and R. Havens, ibid., 1940, 5’9, 710.83 R. L. Kelly, R. Rollefson, and B. S. Schurin, J . Clzeiw. Phys., 1951, 19, 1595.4 , 208, 33216 GENERAL AND PHYSICAL CHEMISTRY.+6.0 D/A (p and p’ are used for the dipole moments of molecules and bonds,respectively).This is much bigger than ap’/& for the C-H bond in methane(&0.55).82 He suggests that the large value in carbon dioxide arises be-cause, during the antisymmetric distortion, which is used in the measure-ment, there is a change in the relative contributions of the various canonicalforms which results in a large swing of charge across the molecule (cf. theearlier explanation of the cross-term constant 8). Such an effect will notoccur in methane. In effect, therefore, he ascribes the large value of ap‘/arto aE interaction between the two C=O bonds. Eggers and Crawford 84have investigated the intensities of some combination and overtone bandsof carbon dioxide and, by using Crawford and Dinsmore’s 85 theoreticaltreatment, have deduced the coefficients of higher-order terms in the expres-sion for the dipole moment.They find that “ electrical anharmonicityseems definitely the predominant factor accounting for the observed intensityof the 3614 and 3716 cm:l bands ” which is further evidence for interactionbetween the bonds. Unfortunately the sign of the coefficients of thesehigher-order terms cannot be fixed so that the data do not yet providedefinite information regarding the nature of the interaction, An examinationof the intensities of the bands of molecules like l60C18O might help in dis-coilrering more about electrical interactions between the bonds.86 Nitrousoxide has been studied by Thorndike, Wells, and Wilson 76 and by Callomon,McKean, and Thompson 77 who found that the values for in this mole-cule are large also.The explanation is probably similar to that for carbondioxide. Eggers and Crawford have measured the intensities of overtoneand Combination bands of nitrous oxide (see also Fraser and Price *’).Robinson 88 concluded that ap/arc, in carbonyl sulphide is -6.7&0-5compared with -6.0&0.6 in carbon dioxide and that i?p/arcs is --4.3,tO.r>in the iormer compared with -5.6&0.5 in carbon disulphide. He com-mented on the relative constancy of both these values. Callomon, McKean,and Thompson 42 give a higher value (8-55) for dp/drco in carbonyl sulphide.Hyde and Hornig 89 studied band intensities in hydrogen cyanide anddeuterium cyanide and found that p& and ap’/laruH are much greater inthe former than in methane.They ascribe this to changes in hybridisationof the bond orbitals. Kelly, Rollefson, and Schurin 83 also found pbTJ tobe greater in acetylene than in methane. However they found that ap’larcn:had about the same value in the two molecules (see Callomon, McKean, andThompson 42). Hyde and Hornig found that arc^ in hydrogen cyanidewas similar to that found by Nixon and Cross in cyanogen but much lessthan that found by them in cyanogen chloride. They ascribed the largevalue in the latter to the greater polarisability of the C-C1 bond; in effect,to interactions between the bonds (cf. interaction constant). They con-cluded that pbH in hydrogen cyanide decreases with bond length just asfor ~ H C I in hydrogen chloride (Bell and Coop 91),84 D.I;. Eggers and €3. L. Crawford, J . Chew. Phys.* p. 1554.85 B. L. Crawford and H. L. Dinsmore, ibid., 1950, 18, 983, 1682.B 6 B. L. Crawford, abid., 1952, 20, 977.R. D. B. Fraser and W. C. Price, Nature, 1952, 170, 490.D. 2. Robinson, J . Chenz. Phys., 1951, 19, 881.89 G. E. Hyde and D. F. Hornig, ibid., 1952, 20, 647.OO E. R. Nixon and P. C. Cross, ibid., 1950, 18, 1316.O1 R. P. Bell and I. E. Coop, Trans. Faraday SOC., 1938, 34, 1209LINNETT : BOND INTERACTIONS. 17Barrow and McKean92 have examined the methyl halides in detail.Only some of their results can be reported here. They found that ap’/aroxdecreases from the fluoride to the iodide, as would be expected, but that thevalues are surprisingly large especially for the C-F bond (4.7 D/A).Suchlarge values have only been observed previously in resonating systems.Robinson 93 has found that the dipole moment of hydrogen chloride dependscritically on the hybridisation of the bonding orbitals of the chlorine atom,and they suggest that a similar explanation may account for the large valuesof &L’/~Y,, in the methyl halides (cf. Duchesne 52). Barrow and McKeanalso deduce values for &L‘/&~H from the symmetric and degenerate vibrationsassuming no interaction between the bonds. In all the halides the valuesobtained from the symmetric are greater than those from the degeneratevibrations. The lack of agreement between the two values shows that, inall cases, bond interactions must occur.This is similar to the conclusionreached by Thorndike 79 from his study of ethane (cf. Francis 94). Theassumption of additivity of bond dipoles and an independent linear variationof bond dipoles with bond length seems to provide only a poor approxim-ati0n.9~ There is great need for some further theoretical developments inthis field.Other Possible Methods of Studying Bond Interactions.-The intensityand depolarisation factors of Raman lines may be used, together withmolecular polarisabilities, for calculating bond polarisabilities and theirchanges with bond length. This has been done by Wolkensteing6 for sub-stituted methanes. Cabannes and Rousset 97 have, however, approachedthe problem differently and regard changes of polarisability during molecularvibrations as resulting from changes in the interactions between centres ofpolarisability caused by changes in their separation.Further progress hererequires an extension of our knowledge of the intensities and depolarisationfactors of Raman lines.The determination of the quadrupole coupling constants provides avaluable means of obtaining information about the electron configurationaround a nucleus and changes in this from molecule to molecule caused bychanging environment. Examples of important applications o€ this methodhave been given recently by Townes and Dailey 98; Mays and Dailey *9;Westenberg, Goldstein, and Wilson loo ; Goldstein and Bragg 101 ; Gordy 102 ;Tetenbaum lo3 ; Simmons and Goldstein 104 ; and Duchesne.105J.W. L.9z G.93 D.94 s.95 J.207, 03;O 6 N835, 88397 J.9 8 c.99 L.loo A.lol J.102 w103 s.104 J.Io5 J .M. Barrow and D. C. McKean, PYOC. Roy. SOC., 1952, A , 213, 27.. 2. Robinson, J . Chem. Phys., 1949, 17, 1022.A. Francis, ibid., 1950, 18, 861.A. Pople, PYOC. Roy. SOC., 1950, A , 202, 323; C. A. Coulson, ibid.“ Valence,” O.U.P., 1952, p. 207.. V. Wolkenstein, Acta Physicochem, U.R.S.S., 1945, 20, 161, 174,; J . Exp. Theor. Phys., U.S.S.R., 1948, 18, 138.Cabannes and A. Rousset, J . Phys. Radium, 1940, 1, ( 8 ) , 138.H. Townes and B. P. Dailey, J . Chem. Phys., 1949, 17, 782.M. Mays and R. P. Dailey, ibid., 1952, 80, 1693.A. Westenberg, J. H. Goldstein, and E.B. Wilson, ibid., 1949, 17, 1H. Goldstein and J. D. Bragg, Phys. Review, 1949, 75, 1453.. Gordy, J . Chem. Phys., 1951, 19, 792.J. Tetenbaum, Phys. Review, 1952, 86, 440.W. Simmons and J. H. Goldstein, J . Chem. Phys., 1952, 20, 122.Duchesne, ibzd., p. 1894., 1951, A ,525, 544,31918 GENERAL AND PHYSICAL CHEMISTRY.2. SURFACE CHEMISTRY.The solid-liquid interface is the main theme of this section, and sincethis has not been reported on previously it is necessary to sketch in themain investigations of a decade and a half. Reasons of space have excludedreference to kinetic aspects, to flotation, and adsorption isotherms forsolutions. Two monographs, by Gregg la and Bikerman,l* have appearedin recent years, and there is considerable research in progress.Thermodynamics of the Solid-Liquid Interface.-The basis of modernwork remains the relations due to Young, Duprd, Gibbs, Hardy, and Lang-muir, set out in the textbooks on surface chemistry by Rideal 2a and Adam.2bHere we shall start with the work of Harkins and Dahlstrom and Banghamand R a ~ o u k , ~ who pointed out that arguments based on contact anglesmust take account of the adsorbed film of liquid on the free surface of thesolid.This consideration clarified many thermodynamic quantities,especially the work of adhesion. The equations of surface thermodynamicshave been systematically reviewed in numerous papers by hark in^,^* 6* 7¶ *and the following summary largely follows this author, using his nomen-clature. Let ysFo denote the surface free energy of the solid surface coveredwith an adsorbed film in equilibrium with the saturated vapour (pressure Po),yLV0 that of the liquid-vapour interface, and y y ~ that of the solid-liquidinterface.If a t equilibrium the liquid makes a contact angle eE with theplane surface of the solid, regarded as insoluble in the liquid, thenIf the solid surface has an adsorbed film corresponding to a pressure p < Po,the free energy isysv = y s t + yLv cos 0The work of adhesion is defined here as the work required to separate 1 cm.2of solid-liquid interface in vucuo,Here ys and yL denote surface tensions in zlacuo of solid and liquid, re-spectively. If (la) is substituted in (2), and if yLvo = 'yr; (except for liquidmetals, yL, the surface tension in vucuo, is equal to the usual value measuredin air), thenThe spreading pressure of an adsorbed film on a solid is defined byor for the adsorbed film at saturation pressure. .. . . . ysvo = ysL + y L v o ~ ~ ~ eE - (la). . . . . . . (1b)wA(8Z) = y8 + YZ - y8L - * - - * * - (2)w A ( S L ) = YS - YSV" + yL(1 + cos 8,) * * * * (3)l$ = ys - ysv . . . . . . . - (4a)t$h! = y&! - ysv" . . . . . . . - (4b)(a) S. J. Gregg, " Th?,Surface Chemistry of Solids," Chapman and Hall, London,1951 ; ( b ) J. J. Bikerman,( a ) E. K. Rideal, " An Introduction to Surface Chemistry," Cambridge Univ. Press,1930; ( b ) N. K. Adam, '' Physics and Chemistry of Surfaces," Oxford Univ. Press, 1941.W. D. Harkins and R. Dahlstrom, Im.d.Eng. Chem., 1930, 22, 897.D. H. Bangham and R. I. Razouk, Trans. Faraday SOC., 1937, 33, 1458.G. E. Boyd and W. D. Harkins, J . Amer. Chem. Soc., 1942, 64, 1190, 1195.W. D. Harkins, J . Chem. Phys., 1941, 9, 552.W. D. Harkins and H. I<. Livingston, ibid., 1942, 10, 342.W. D. Harkins and G. Jura, " Colloid Chemistry," Vol. VI, Chapter I (Ed., J .Surface Chemistry," Academic Press, New York, 1948.Alexander), Reinhold Publ. Corpn., New York, 1946ELEY : SURFACE CHEMISTRY. 19Substituting (4b) in (3) yieldswAcsL, = $rc + yL(i + case,) . . . . . * ( 5 )w2(8L,) = y L ( 1 f coS6,) . . . . . . (6)The equationyields the work required to separate 1 cm.2 of solid and liquid and leave anadsorbed film on the solid. Greg la calls this the work of adhesion, but inthe Reporter's opinion it is preferable to use (5).$E is appreciable for metalsand oxides, although for solids such as paraffin it may be very small.Eqn. (1) is Young's equation, (2) Duprk's equation, and eqn. (5) has beencalled the corrected Young-Duprk relation.Further definitions concern the spreading coefficient of a liquid on asolid to give thick (Harkins " duplex " 6, films. For the initial spreadingof a liquid on the clean solid surfacesL/S = ?'8 - y8,5 - Y& = $E e . . - * - (7a)Since the film adsorbed at saturation is a duplex film, i.e., has a lowersurface with energy ySL and an upper one with energy yL, S L , ~ is of courseequal to +E. The final spreading coefficient refers to the film-covered solid.s&,8i = ySVo - YSL - YL .- * * * . - (7b)As noted originally by Hardy, if SLIs is positive, the liquid will spread onthe solid.These equations may be adapted to the case where the solid is slightlysoluble in the liquid, if one puts the appropriate values ~ L ' V O and ~ S L 'into eqn. (1).for liquids and, with qualifications, for solids."free energy which omits the y A term, viz., G = U + PV - TS.Helmholtz free energy is F = U - TS.The surface tension may be equated to the free surface energy perHarkins employs a GibbsTheIn terms of these functions, we have eitherwhere small letters denote thermodynamic functions for 1Harkins usesf where the British use g, and E where the British use u.solid from a liquid into a vacuum isof surface.The Gibbs free energy change of emersion (reverse of immersion) of agE(SL) = g 8 - gSL = YS - y8L - * * * - (9)Physically Adsorbed Films on Solids.-Two topics of immediate interestare 4~ and the surface-area problem.In addition, the discussion of physicaladsorption is continued from the Annual Reports for 1950 and 1951.Bangham 10 suggested application of the Gibbsadsorption equation for calculating the spreading pressure of an adsorbedThe spreading pressure.@ W. D. Harkins, " Techniques of Organic Chemistry," Vol. I (Ed., A. Weissberger),lo D. H. Bangham, Trans. Faraduy SOC., 1937, 33, 805.* Thus, surface free energy is correct in eqn. ( ~ ) ( c f . R. Shuttleworth, Proc. phys.Intersci. Publ., New York, 1945.SOC., 1949, ea, A , 167)20 GENERAL AND PHYSICAL CHEMISTRY.film on a solid.adsorbed per cn~.2 of surface, thenIf I? is the " surface excess," i.e., the number of moles+ = p P 0and, if the perfect gas law can be assumed, then, (10a)where z, C.C.of gas are adsorbed on area A at pressure p , and V is the molarvolume of the gas. To obtain #E, the integration is taken up to the saturationvapour pressure PoRT *'v h =ml0 jjdp . . . . . . . . ( l o b )Bangham suggested that 4~ can only be regarded as a true lateral pressurewhen the film is mobile. Bangham and Razouk 11 applied graphical inte-gration to Coolidge's data for charcoal in order to evaluate +E. Harkins andJura have used this method extensively, and their +E values are listed in theTable on p. 25. A comparison of the third and the fifth column in thisTable show that +E may be 50% or more of the work of adhesion.Bafigham and Razouk11 found a dis-continuity when +a was plotted against ?/Po for water on charcoal, whichthey attributed to formation of a condensed phase.Here a = l/I' is thearea per molecule in the adsorbed film, assumed unimolecular. Gregg,12and later Harkins and Jura,*, 13914 have extended this analysis, findingcurves analogous to those found for monolayers on water.2* l5 FollowingDervichian, phase changes were classified according to Ehrenfest, viz., afirst-order change is a discontinuity in the v-$ isotherm, a second-orderchange a discontinuity in (%) -p, etc. First-order phase changes werereported for water on graphite, and for n-heptane on silver, ferric oxide, orgraphite.Smith l6 has repeated the work on the last two systems andfailed to find the transition points, so the matter is still open. However,as originally shown by R. H. Fowler, a first-order condensation processmay occur if attractive forces exist between neighbouring molecules in amonolayer. The theoretical aspects of phase changes in adsorbed filmshave been reviewed by Hi1l.l'Gregg and Maggs 18 plot the function p' against log p to reveal moreclosely the nature of the phase changes involved. p' is proportional to thecompressibility of the monolayer and isPhase changes in monolayers.av[Pl 1 D. H. Bangham and R. I. Razouk, Trans. Faraday SOC., 1937, 33, 1463.l2 S. J . Gregg, J., 1942, 696.l4 G. Juraetal., J .Chem. Phys,, 1945, 13, 535; 1946, 14, 117, 344.l5 W. D. Harkins, " Colloid Chemistry," Vol. V (Ed., J . Alexander), Reinhold Publ.l6 R. N. Smith, J . Amer. Chem. SOC., 1952, 74, 3497.3 7 T. L. Hill, Adv. i~ Catalysis, 1952, 4, p. 21 1,le S . J. Gregg and F. A. P. Maggs, Trans. Faruduv Soc., 1048, 44, 123.W. I). Harkins and G. Jura, J . Chem. Phys., 1944, 12, 112; J , Amer. Chem. SOC.,1944, 68, 1356.Corpn., New York, 1944ELEY : SUKPACE CHEMISTRY. 21where na& molecules are adsorbed per g. of solid. This method shows a veryfew true first-order changes, e.g., for n-heptane on silver, but most of thechanges occur over a range of pressure and fall into Mayer and Streeter’sclass of diffuse first-order ~hanges.1~ The changes are shown to occurbefore multi-layer formation sets in.Tompkins suggests that the changesare truly of first order, but blurred by surface heterogeneity.Coulter and Candela 21 attributed a phase transition, observed for wateron silver iodide, to the formation of a hydrate by an impurity. After sub-traction of this effect, a type I11 isotherm was obtained. Bowden andThrossel 22 found that a platinum foil, cleaned in V ~ C U O by electron bombard-ment, adsorbed only a unimolecular layer of water at PIPo = 0.9. Thethirty or so layers taken up before cleaning were attributed to traces ofhydrophilic impurities.Harkins and Jura 8 discuss empirical equations of state of adsorbedmonolayers, and use that for a condensed phase, 4 = a - bcc, as the basisfor their well-known surface area method (H.J. relative method 23).Thermodynamics and Surface Areas.-The theoretical aspects of physicaladsorption have been reviewed by Hill.17 He advocates 17¶ 24 the usefulnessof “ adsorption thermodynamics,” treating the adsorbed film as a pseudo-one-component system, yielding integral values of energies and entropiesof adsorption. Everett 25 discusses solution thermodynamics, treatingadsorbed gas and solid as a two-component system, which leads to differentialenergies and entropies. The thermodynamics of the solid-liquid interfaceyielding integral energies and entropies of immersion form a third system.Hill and Everett have clarified relations between the solution and adsorptionthermodynamics, and a discussion of immersion data has been promisedby Hill and Jura.17 The present approach to adsorption is predominantlythermodynamic. Thus, Hill, Emmett, and Joyner 26 have calculated fromisotherms differential and integral energies and entropies of adsorption fornitrogen on graphon. Drain and Morrison 27 have made similar calculations,using calorimetric data, for argon on rutile.The integral entropy of adsorp-tion goes through a minimum a t 0 = 1, an effect predicted by the Brunauer-Emmett-Teller (B.E.T.) equation for large c values, and considered by theauthors as justification for use of the B.E.T. equation for determinationof surface areas.I t is well known that the B.E.T. equation predicts too high an adsorptionfor $/Po > 0.35. Casse128 showed a related effect, that substitution of theB.E.T. isotherm into eqn.(10) yields + E = co. Hill 17 attributes thiscatastrophe to the configuration partition function, and stresses that a properapproach to multilayer theory can only be made through the difficult modernFurther work of this kind is urgently needed.Is J. E. Mayer and S. F. Streeter, J . Chem. Phys., 1939, 7, 1019.2o F. C. Tompkins, Tyans. Favadccy Soc., 1950, 46, 580.21 L. V. Coulter and G. A. Candela, 2. Elektrochem., 1952, 56, 449.22 F. P. Bowden and W. R. Throssel, Nature, 1952, 167, 601, 1038.23 W. D. Harkins and G. Jura, J . Amer. Chem. SQC., 1944, 66, 1366.24 T. L. Hill, J . Chem. Phys., 1949, 17, 520; 1950, 18, 246; Trans. Faraday SOC.,26 D. H. Everett, ibid., 1950, 46, 453.26 T.L. Hill, P. H. Emmett, and L. G. Joyner, J . Amel.. Chem. SOC., 1951, 73, 5102,27 L. E. Drain and J. A. Morrison, Trans. Faraday SOC., 1952, 48, 840.t 8 H. M. Cassel, J . Chem. Phys., 1944, 12, 115; J , Phys. Chem., 1944, 48, 195.1951, 47, 376.593322 GENERAL AND PHYSICAL CHEMISTRY.theory of liquids. He concludes I ‘ that, bearing in mind the confirmatorywork of Harkins and J ~ r a , , ~ B.E.T. areas are the best available at present.”The most recent papers do not disturb this conclusion. B.E.T. theory hasbeen applied to water on montmorillonite.30 Molecular cross-sectionalareas O’ have been obtained by determination 31 of VM for anatase of knownarea (H. J. absolute method 29) and their deviations from the liquid density anoted, e.g., CO, -8-1%, CO, +43.5%.The k of the H. J. relative methodwas found to be 0.2510. Anderson and Emmett 32 compare the B.E.T.method, its modifi~ation,3~ and the H. J. relative method 23 for variousgases on a range of carbon blacks. Barrer et aZ.* have produced a numberof modified B.E.T. equations which fit data up to higher pressures and giveconsistent Vrm values. Corrin, using a solid of known area, has comparedH.J. relative areas and B.E.T. a r e a ~ , ~ 5 and Huttig and B.E.T. areas.36Theimer3’ proposes a semi-empirical equation of the B.E.T. type. Achemisorbed film, depending on its nature, may reduce,38 or leaveunchanged,39 the isotherm for physical adsorption.The thermodynamic properties of argon on rutile upto 8 = 0.6 may be satisfactorily interpreted on the basis of a localisedmonolayer on a heterogeneous surface without interaction^.^^ The plot ofheat of adsorption against 8 for argon on the (1 11) face of potassium chlorideagrees with calculations, and differs markedly from the values for the (100)face.*1 This supplements data on the effect of crystal face on adsorptionalready advanced by Rhodin 42 for nitrogen on copper.Halsey43 notesthat a comparison of Rhodin’s data for single crystal faces and polycrystallinecopper, points to intercrystalline boundaries as an important source ofheterogeneity. In a review, Halsey43 concludes that the usual B.E.T.nitrogen isotherm with the well-marked point B corresponds to a state ofintermediate heterogeneity. The Sips distribution is different for nitrogenon rutile from that for oxygen and argon.a4 Huttig and Theimer45 havediscussed lateral interactions and heterogeneity, using the expanded Lang-muir equation.Porous Solids.-The pore-size distribution is generally measured 46 byapplication of Kelvin’s equation to the desorption branch of the isotherm.Thus, if the saturation vapour pressure of a liquid be Po, molar volume V ,Heterogeneity.29 W.D. Harkins and G. Jura, J. Amer. Chem. SOC., 1944, 66, 1362, 1366.3o R. W. Mooney, A. G. Keenan, and L. A. Wood, ibid., 1952, 74, 1367,3 l H. L. Pickering and H. C . Eckstrom, ibid., p. 4775.32 R. B. Anderson and P. H. Emmett, J. Phys. Chem., 1952, 56, 753, 756.33 R. B. Anderson, J. Amer. Chem. SOC., 1946, 68, 686.34 R. M.Barrer, N. Mackenzie, and D. McLeod, J.. 1952, 1736.35 M. L. Corrin, J . Amer. Chem. Soc., 1951, 73, 4061.313 Idem, J . Phys. Colloid Chenz., 1951, 55, 612.37 0. Theimer, Trans. Faraday Soc., 1952, 48, 326.38 F. S. Stone and P. F. Tiley, Nature, 1951, 167, 654.sS A. S. Joy and T. A. Darling, ibid., 1951, 168, 433.*O L. E. Drain and J . A. Morrison, Trans. Farnday SOC., 1952, 48,316; J. A. Morrison,J . M. Los, and L. E. Drain, ibid., 1951, 47, 1023.41 D. M. Young, ibid., 1952, 48, 548.42 T. N. Rhodin, Jr., J. Amer. Chem. SOC., 1950, 72, 5692.43 G. D. Halsey, Adv. Catalysis, 1952, 4, 259.44 J . M. Honig and L. H. Reyerson, J. Phys. Chenz., 1952, 56, 140.46 G. F. Hiittig and 0. Theimer, 2. EEektrochem., 1952, 56, 490.413 A. G. Foster, Trans.Faraday SOC., 1932, 28, 645; Proc. Roy. SOC., 1934, A , 146,129ELEY : SURFACE CHEMISTRY. 23and surface tension y, across a plane surface, then across a meniscus in acapillary, of radius r and with a contact angle 8,Foster 47 assumed that 8 = 0, and that a bimolecular layer of thickness 20is adsorbed on the capillary, so that Y = ro - 2 ~ , where yo is the actualradius of the capillary. Some success has been achieved in applying thistheory to data for ferric oxide gel, where seven liquids lie on a commonr0-v curve (v = volume adsorbed). Pore-distribution curves, dvldr against r,are disc~ssed.~7 Wheeler 48 has proposed a theory combining B.E.T.muitilayer and capillary-condensation viewpoints with Y = ro - t, t beingthe multilayer thickness at pressure p .Shul149 points out that B.E.T.theory predicts excessively thick multilayers for gases on plane surfacesand recommends obtaining t from experimental data on non-porous solids.This procedure has been followed recently by Juhola, Palumbo, and Smith ;they compare pore-size distribution for carbon blacks (1) from nitrogendesorption data 51 and (2) from water desorption data.52 Since the carbonblacks are free from hydrophilic groups, it is assumed adsorption is negligible,t = 0, and 0 = 60". The distributions agreed approximately over the22-300 A range, and method (2) was found applicable to the whole rangeof pores. The importance of pore-distribution in catalytic work has beenstressed in an important article by Wheeler.53The open-pore theory of hysteresis 46 has been developed by Cohan,54who considers condensation to start by formation of a cylindrical meniscusradius ro - G, at pressure pa, and desorption at pressure p, to follow theusual Kelvin equation with Y = yo.ThusHysteresis commences a t pd = pa, and thus a t ro = 2s. This theoryhas been discussed by Brunauer 55 and again recently by F0ster.~6 Cohan'stheory does not consider an adsorbed layer in desorption (eqn. 13b), andFoster 56 endeavours to improve this. He considers the adsorption potentialas made up of a term for capillary condensation and one for multilayeradsorption. The theory predicts that hysteresis will occur when productVylRTo for the adsorbed liquid exceeds unity. Pierce and Smith 57 haveconsidered hysteresis in charcoal adsorption, where adsorbed patches areformed on active spots.Everett and Whitton 58 consider the properties ofa mechanical model for hysteresis similar to the well-known bimetallic-strip4 7 A. G. Foster, Discuss. Faraday SOC., 1948, 3, 4.48 A. Wheeler, Catalyst Symposia, Gibson Island A.A.A.S. Conference, June, 1945,49 C . G. Shull, J . Amer. Chem. SOC., 1948, 10, 1405.50 A. J. Juhola, A. J. Palumbo, and S. B. Smith, ibid., 1952, 74, 61.51 E. P. Barrett, L. J. Joyner, and P. P. Halenda, ibid., 1951, 73, 373.52 A. J. Juhola and E. 0. Wiig, ibid., 1949, 71, 2069.53 A. Wheeler, Adv. Catalysis, 1951, 3, 249.E4 L. H. Cohan, J . Amer. Ckem. Soc., 1944, 66, 98.s5 L. Brunauer, " The Adsorption of Gases and Vapours," Vol.I, Oxford Univ.56 A. G. Foster, J., 1952, 1806.57 C . Pierce and R. N. Smith, J . Phys. Chenz., 1950, 54, 784.5 9 D. H. Everett and W. I. Whitton, Trans. Faraday SOC., 1952, 48, 749.June 1946.Press, London, 194524 GENERAL AND PHYSICAL CHEMISTRY.thermostat control (cf. also Gregg la). Freezing-point depressions have beenmeasured for liquid held in capillaries.59y60 The Kelvin equation has beenapplied to the contact zones of anatase powder.61Bartell and Bower 62 have applied eqn. (9a) to a porous gel (silica gel).They evaluated A+ by graphical integration and plotted log A# against-log$/$,. They obtained a curve which was interpreted as two straightlines cutting at a point fib, where liquid was formed in the capillaries. Thearea of the gel was determined bywhere everything except A was known.Contact Angle and Work of Adhesion.-To calculate work of adhesionone must insert the equilibrium contact angle eE into eqn.( 5 ) , and frequentlyvery large differences have been found between advancing and recedingangles, making evaluation of 8 3 impossible. Adam and Jessop 63 ascribethe difference formally to a frictional force opposing motion of the interface.Adam,2b and Bartell and Cardwell,6* suggest that the relatively largeadvancing angle arises from the need for the liquid to displace lyophobicadsorbed films from the surface. An additional factor is the roughness ofthe surface.2 Wenzel 65 writes a modified version of Young’s equation fora surface of roughness factor v (ratio true : apparent areas),and a thermodynamic proof has recently been advanced for eqn.(15) byGood.66 An analysis has been made of porous surfaces.67 Shuttleworthand Bailey 68 show that, on solids whose roughness is formed by isolated pits,subsidiary minima exist apart from that given by eqn. (la), and so hysteresisof the contact angle arises. Cassie G9 attributes hysteresis to a number ofpossible states of the adsorbed multilayer, which must be in the form ofmolecular clusters rather than a continuous film. Adam, in the discussionfollowing the last two papers, considered that factors other than roughnessmust cause hysteresis with varnished surfaces. Hysteresis of the contactangle has been reported at the mercury-benzene-water interface. 70 Soh-tions of surface-active agents show a unimolecular change of 8 with time,associated with adsorption of the agent.‘1Fowkes and Harkins 72 claim true equilibrium 83 values, using a develop-ment of Adam’s tilting-plate method.63~ 73 Harkins and Livingston59 M. J. Brown and A. G. Foster, Nature, 1952, 169, 37.6o I. Higuti and M. Shimizu, J. Phys. Chem., 1952, 56, 198; I. Higuti and Y. Iwa-61 I. Higuti and H. Utsugi, J. Chem. Phys., 1952, 20, 1180.62 F. E. Bartell and J. E. Bower, J . CoZZoid Sci., 1952, 7 , 80.O3 N. K. Adam and G. Jessop, J., 1925, 1863.O4 F. E. Bartell and P. H. Cardwell, J. Amer. Chem. Soc., 1942, 64, 494.O 5 R. N. Wenzel, Ind. Eng. Chem., 1936, 28, 988.O 6 R. J. Good, J . Amer. Cltem. Soc., 1962, 74, 5041.6 7 A. B. D. Cassie and S.Baxter, Trans. Favaday SOC., 1944, 40, 546.O 8 R. Shuttleworth and G. L. T. Bailey, Discuss. Faraday Soc., 1948, 3, 16.O9 A. B. D. Cassie, zbzd., p. 11.7O F. G. Bartell and C. W. Bjorklund, J. Phys. Chem., 1952, 56, 453.71 G. A. Wolstenholme and J. H. Schulman, Trans. Faraday Soc., 1950, 46, 488.72 F. M. Fowkes and W. D. Harkins, J. Amer. Chem. Soc., 1940, 68, 3377.7 3 N. K. Adam and R. S. Morrell, J. Soc. Chenz. Ind., 1934, 53, 2 5 5 ~ .v(ysvo - y8L) = y A v ~ ~ s e . . . . . . - (15)gami, ibid., p. 921ELEY : SURFACE CHEMISTRY. 25:alculated values of W(alsL from eqn. (5), and showed the importance of + E .The most modern data are in the annexed Table.Free energies of solid-liquid interaction, erg/cm.2 (Harkins)Solid Liquid,, * ............Nitrogen,, 8 ............ %-Butane,, * ............ n-HeptaneAnatase 8 ............ WaterCopper 74 ............Silver 7* ...............Lead 71 ............... ,Iron 7 x ............... I ,Graphite ‘I ............ , t>Spreadingcoeff.190564346293749534 E-Free energyof emersionfiE(8-L)26264586649576973-Work ofadhesionWAWL)3347273866977897369Low-energy Surfaces.-Fox, Zisman, and their co-workers are publishingm important series of papers on “ The Spreading of Liquids on Low EnergySurfaces.” To date, the following have appeared : I, Polytetrafluorethylene(TFE) 75; 11, Copolymers of TFE 7 6 ; 111, Hydrocarbon surfaces 77; IV,Monolayer coatings on platinum 78 ; V, Perfluorodecanoic acid monolayers.79In each case a very large number of pure liquids was found to give finitevalues of OB, measurable by the sessile-drop method to &2” or better. Itwas found that the contact angle was unchanged, whether measured in air,3r in air saturated with the vapour of the liquid, at least for the less volatileliquids. Thus it was concluded that these low-energy solids did not appre-ziably adsorb the vapours concerned, i e . , that +E = 0 in eqn. (5). It wasEurther found that for each homologous series of liquids and a given solid,EOS Ox decreased linearly with the surface tension of the liquid yLvo. Extra-polation to 0 = 0 yielded a parameter ye, regarded as the critical surfacetension, below which spreading of the liquid occurred on the solid concerned,typical values being 33 dynes/cm.for Polythene, and 17-5-206 dynes/cm.€or TFE. The following order of wettability of groups in the solid surfacewas found, @OF, > OGF, > OCH, > &H,. Another interesting result wasthat a monolayer of a long-chain compound effectively changed platinuminto a “ low-energy ” (non-spreading) surface ‘‘ demonstrating beyond doubtthe short-range nature of the forces involved in wetting.’’Elton has suggested combining Antonoff’s lawwithto givewhere ysa, y L A , refer to the surfaces mutually saturated with respect toEach other in air. Thus he calculated a value of Y ~ A for paraffin wax of74 W. D. Harkins and E. H. Loeser, J . Chew. Phys., 1950, 18, 556.75 H.W. Fox and W. A. Zisman, J . CoEloid Sci., 1950, 5, 514.7 6 Idem, ibid., 1952, 7, 109.78 E. G. Shafrin and W. A. Zisman, ibid., p. 166.79 F. Schulman and W. A. Zisman, ibid., p. 465.8o G. A. H. Elton, J . Chem. Phys., 1951, 19, 1066.7 7 Idem, ibid., p . 42826 GENERAL AND PHYSICAL CHEMISTRY.27 dyneslcm., values for water, glycerol, and ethylene glycol agreeing verywell. Fox and Zisman 76 point out that the correct equation isYS = 4~ + + Y L F O ( ~ + cos 0x1but since +E z 0 for their solids, presumably this introduces little error.They note that ys varies from 18 to 30 ergs/cm.2 for TFE, and reject themethod. Elton 81 concludes that evidence for mutual saturation of phases islacking and in any case that real differences in ys may exist.Fowkes andSawyer 82 assume that y8vn and y8L are the same for a solid perfluorinatedoil as for liquid fractions of the same material. Using Young's equation,they calculate OE values for the solid in good agreement with those observedfor a number of liquids. They also test the use of Antonov's rule, calculatingvalues of ysvg of 18.3-23.5 erg/cm.2 compared with 22.4 experimentally.Displacement Pressure.-The rate a t which a liquid penetrates a capillaryis of course determined by yL cos 8, but since this quantity is no longergenerally equal to yx - ysL, but toys - ysL - +E, Harkins and Livingstonsuggested that the use of Freundlich's term, adhesion tension, should beabandoned. Bartell and his co-workers 83 have described a method forrelating the pressure required to stop liquid 1 from displacing liquid 2 froma solid, which assumes that= ys - ysl = y1 cos eW .. . . . - (16)As2 = ys - ys2 = y2 cos osa- = ys2 - ysl = y 1 2 c 0 s e12 . . . . . (17)for the separate liquids displacing air from the powder, andfor liquid 1 displacing liquid 2.the correct equation derived from (5) isHarkins and Livingston have shown thatAS1 - A82 = (YSV," - Y S V z o ) + (YSl - 782)= y1 cos esl + yz COS eS2 . . . . . * (1st.- In one case, eqn. (17) gave 242 ergs/cm.2 while the correct eqn. (18) gave51 ergs/cm.2 for the difference of two adhesion tensions. Again, the equationy12 cos el, = 242 is impossible since y12 for the system concerned is 51.The experimental aspects of the method have also come under 85and a recent worker reports unfavourably on it.86 A D.C.potential isreported to affect adhesion tension.8'Heats of Wetting.-The heat of immersion per cm.2 qi(Ls) of a solid fromvacuo into a liquid, which is the enthalpy change of emersion, h,,, is *3 53 *G. A. H. Elton, J . Colloid Sci., 1952, '4, 450.F. M. Fowkes and W. M. Sawyer, J . Chem. Phys.. 1952, 20, 1650.See, e.g., F. E. Bartell and H. J. Osterhof, I n d . Eng. Chem., 1927, 19, 1277;Symposium on Wetting and Deter-F. E. Bartell and H. Y. Jennings, J . Phys. Chem., 1934, 38, 495.gency," Harvey, London, 1937, p. 19.84 N. S. Davies and H. A. Curtis, Ind. Eng. C k m . , 1932, 24, 1137.85 S. H. Bell, J. 0. Cutter, and C. W. Price,8 6 N. J. de Lollis, J. Phys. Chem., 1952, 56, 193.87 2.Laszlo, J . Chew. Plays., 1952, 20, 1807ELEY : SURFACE CHEMISTRY. 27If the solid has an adsorbed filmTo determine qi(L4 an evacuated bulb of solid is broken under the liquid,whereas if the solid is first equilibriated with vapour at pressure 9 and thenimmersed, qi(LJlf) results. In modern work the surface area of the powderis determined, usually by the B.E.T. method, and results are given inergs/cm.2. Laporte gives a bibliography.88 Most modern data are due toHarkins, who neglects PV and classifies results as zt~(s~) (he writes zE(s~)).*The liquids examined may be arranged in order of decreasing uE(gL), which isthe same for all the solids examined. If I z ~ ~ ~ a , ) is the enthalpy change ofdesorption of the adsorbed film containing n moles, the heat of evaporationfrom liquid being A, then 8,89an equation of use in linking heat of wetting to heats of adsorption.Harkinsand Jura 89 have plotted h,(S,L) for water on anatase as a function of filmthickness. There is an exponential decrease of 3 2 ~ ( a ~ ~ ) , which becomes con-stant after five molecular layers. At this stage, i.e., for the saturated film,the heat of emersion is just the surface enthalpy hL of the bulk liquid, forwater 118.5 ergs/cm.2 at 25". This forms the basis of the H.J. absolutemethod of surface area determinati0n.~3~~ It gives the specific area of asolid non-porous powder as the ratio of Qi(Ls,), heat of wetting per g. ofsolid with saturated film, to hL, Le., A = QqLalfIihL. Incidentally, themethod seems to have been foreseen in a way by Patrick and GrimmWin their work on the heat of wetting with silica gel, but the method is now-adays not recommended for porous solids.Heats of wetting for water-graphite confirm discontinuities observed on isotherrn~.~lHeats of wetting on alumina and silica gels have been reported to changewith absorbability of the and with molecular size.93 The effectsmay be associated with the failure of larger molecules to penetrate pores(cf. Gregg la). Stowe 94 examined the effect of surface coverage with alumina,and displacement of hydrocarbons by water. The heat of wetting of somesurfaces by water is high enough to suggest chemical reaction.95 The tem-perature of outgassing of the solid is important, and a balance is usuallystruck between removal of adsorbed layers and sintering of the internalsurface, e.g., with silica gel.96 It seems that many of the miscellaneousdata on heats of wetting apply to porous solids and therefore are difficult tointerpret.hUCVSf) = h[E)SL - h E ( S f S +D.D. E.8 8 F. Laporte, Ann. Physique, 1950, 5, 5 .89 W. D. Harkins and G. Jura, J . Amer. Chem. SOC., 1944, 66, 919.90 W. A. Patrick and F. V. Grimm, ibid., 1921, 43, 2144.91 P. R. Basford, G. Jura, and W. D. Harkins, ibid., 1948, 70, 1444.92 L. Robert, Compt. rend., 1951, 233, 1103.93 J . G. Miller, H. Heinemann, and W. S. W. McCarter, Ind. Eng. Chem., 1950, 42,84 V. M. Stowe, J . Phys. Chem., 1952, 56, 484, 487.g6 F. Howard and J . 0. Culbertson, J .Amer. Ckem. SOC., 1952, 72, 1185.g6 D. T. Ewing and B. T. Bauer, ibid., 1937, 59, 1648.* hE(8Z) = ~ ~ ( 8 5 ) + PV, where V is the associated volume change of emersion.15128 GENERAL AND PHYSICAL CHEMISTRY.3. ELECTROLYTES.Strong Electrolytes.-GeneraZ theory. In the Debye-Hiickel theory ofelectrolytic solutions, the calculation of the ionic atmosphere surroundingan ion is based on a Boltzmann distribution : nr = n exp(- ze+?/kT),where nr and $r are respectively the number of ions per unit volume andthe potential at a distance r from the central ion. According to this, thecharge density increases indefinitely with potential, but Wicke and Eigenpoint out that the space requirements of the ions cannot be neglected exceptin very dilute solution, and, taking account of these, they derive a newdistribution function which departs from Boltzmann’s at moderate concen-trations, bending over to a limiting saturation value for the charge density.The effect can account for the observed minima in activity data and, withreasonable assumptions concerning ion-hydration, gives good agreementwith experiment up to 1~ for the alkali halides in water.Falkenhagen isreported as having explained the conductance curves of some alkali halidesup to IM on the same basis, and extensions of the theory to multivalentelectrolytes are promised.Kramers’s derivation by statistical mechanics of the Debye-Hiickellimiting laws has been modified by Berlin and M~ntroll,~ and the new treat-ment eliminates the low critical concentration a t which Kramers’s derivationbroke down.has derived a relationbetween concentration (c) and the velocity (u) of sound in electrolytes; bycombining the equations of the interionic-attraction theory for the apparentmolar volume and isothermal compressibility of the dissolved salt, he obtainsfor very dilute solutions a relation of the form u = G~ + Fc - Gc4.Thecomparison of this with experimental results is reminiscent of the findingstwenty years ago with apparent molar volumes : plots of Au/c are linearagainst c* even up to 4 ~ , but F and G must be replaced by empiricalconstants. As the experimental data are not accurate below 0.3h1, nocomparison with the theoretical slope is yet possible. A substantial contri-bution on polarisation 5 extends Jaffk’s earlier theory 6 to electrolyticsolutions, and presents results for water and salt solutions with variouselectrode metals over a wide range of frequencies.The properties of purerare-earth salts should be of great interest owing to the close similaritiesbetween the compounds ; the predominating variable in their electroIyticproperties will be the radius of the ion.have now published a number of papers on the subject, giving data for theconductivities, transport numbers, and activity coefficients of many of thechlorides and bromides.The equivalent conductances conform with theOnsager limiting slope, and the mobilities derived for the rare-earth ionsE. Wicke and M. Eigen, Naturwiss., 1951, 38, 453; 2. Ebktrochem., 1952, 56, 551.H.A. Kramers, Proc. Roy. Acad. Amsterdam, 1927, 30, 148.T. H. Berlin and E. W. Montroll, J. Chem. Phys., 1952, 20, 76.S . Barnartt, ibid., p. 278.5 H. C. Chang and G. Jaff6, ibid., p. 1071; G. Jaffk and J. A. Rider, ibid., p. 107’7.G. JaffC, Ann. Physik, 1933, 16, 217, 249.F. H. Spedding, P. E. Porter, and J. M. Wright, J , Amer. Chem. SOC., 1952, 74,For graph summarisingTurning to more specialised topics, BarnarttCoizductivity, tvansport, and dzj@sion phenomena.Spedding and his associates2055,2778,2781 ; F. H. Spedding and I. S. Yaffe, ibid., p. 4751.mobility data, see p. 4753DAVIES AND MONK : ELECTROLYTES. 29increase regularly with decrease in atomic number up to a flat maximum forcerium, with the value for lanthanum slightly lower.The direction of thecurve implies that the effective hydration number is the larger the smallerthe ion; the maximum suggests that the larger radius of the first membersof the series enables them to accommodate an additional molecule of waterin the first hydration sphere, a view to which crystallographic and calorimetricdata * offer some support.Gordon and his co-workers have made precision transport-number andconductivity measurements on sodium chloride and potassium chloride inpure methanol at 25" and derive the limiting mobilities : C1-, 52.38; Na+,45.22 ; K+, 52-40. Moving-boundary studies have been made by Dismukesand King,lo and by Spiro and Parton l1 who have investigated and improvedBrady's 12 analytical boundary method.MacInnes and Dayhoff l3 havemodified the E.M.F. centrifuge and record new results for sodium iodideand potassium iodide. Measurements continue to appear both of saltdiffusion l4 and of tracer-ion diffusion; l5 a novel method has been intro-duced by Wall, Grieger, and Childers.16 For a review of the field up to1950 see Harned.1'The Wien effect 18 was discovered twenty-five years ago and, althoughsince then the theory of the increase in conductivity at high field strengthshas been worked out, the experimental data remain meagre.l9 Fortunately,new work in the field has now begun at Yale,20 taking advantage of the recentgreat advances in techniques a t high voltages, and systematic study by thenew method should make valuable contributions to electrolyte theory.Acompletely dissociated electrolyte undergoes a conductivity increase a thigh voltages because the normal ionic atmosphere, with its retarding effects,virtually disappears at the high ionic velocities engendered. With weakelectrolytes there is an additional mass-action increase, since the localconcentration of oppositely charged ions is reduced for each ion by the dis-appearance of its atmosphere, and dissociation proceeds further.21 Pattersonand his co-workers 20 have shown that new results for magnesium, zinc, andcopper sulphates are incompatible with the theory for completely dissociatedelectrolytes, but are in gratifying agreement with theory when the knowndissociation constants of the sulphates are taken into account.F.H. Spedding and C. F. Miller, J . Amer. Chem. SOC., 1952, '94, 3158.J . A. Davies, R. L. Kay, and A. R. Gordon, J . Chem. Phys., 1951, 19, 749; J. P.lo E. B. Dismukes and E. L. King, J . Amer. Chew. Soc., 1952, 74, 4798.l1 M. Spiro and H. N. Parton, Tram. Furuday Soc., 1952, 48, 263.l2 A. P. Brady, J . Amer. Chem. Soc., 1948, 70, 911.Is D. A. MacInnes and M. 0. Dayhoff, J . Chem. Phys., 1952, 20, 1034.l4 R. A. Robinson and C. L. Chia, J . Amer. Chem. Soc., 1952, 74,2776; H. S. Hamerl6 JI M. Nielson, A. W. Adamson, and J. W. Cobble, ibid., 1952, 74, 446; J. TI.l7 H. S. Harned, Ann. Rev. Phys. Chem., 1951, 2, 37.l8 M. Wien and J. Malsch, Ann. Physik, 1927, 83, 305.lS For review and references see H. C. Eckstrom and C . Schmelzer, Chem. Reviews,1939, 24, 367.2o J.A. GledhilI and A. Patterson, Jr., J . Phys. Chem., 1952, 56, 999; F. E. Bailey,Jr., and A. Patterson, Jr., J . Amer. Chem. SOC., 1952, 74, 4426, 4428; D. Berg andA. Patterson, Jr., ibid., p. 4704.21 G. S. Hartley and J. W. Roe, Tvans. Favaday Soc., 1940, 36, 101.Butler, H. I . Schiff, and A. R. Gordon, ibid., p. 752.and R. S. Hudson, ibid., 1951, 73, 5083.Wang, zbzd., p. 1182; J. H. Wang and S. Miller, ibid., p. 1611.P. T. Wall, P. F. Grieger, and C . W. Childers, ibid., p. 356230 GENERAL AND PHYSICAL CHEMISTRY.Thermodynamic $ro$erties. Partial molal heat capacities and heatcontents have been recorded by Spedding and Miller * for aqueous solutionsof cerium trichloride and neodymium trichloride at 25". MacInnes and hisco-workers 22 have developed the magnetic float method of density deter-mination, and report partial molal volumes of potassium chloride and iodideand sodium iodide in water at 25".Salt effects for various organic gasesand liquids have been studied,23 and current theories are analysed in a reviewby Long and McDevit 23; the solvation of uranyl nitrate has been examinedby both distribution 24 and calorimetric methods,25 and the activity co-efficients in aqueous silver nitrate-nitric acid mixtures have been measuredby Davidson and his collaborators 26 using a cell with silver and glass elec-trodes. E.M.F. measurements have also been used to obtain activities inliquid ammonia 27 and liquid hydrogen fluoride 28 as solvents.Incomplete Dissociation in Salt Solutions.-The applicability of mass-action considerations to ionic association in salt solutions is now widelyaccepted and a considerable amount of work in this field is being reported,partly filling gaps in the data previously accumulated for the commonersalts and partly supplying information about salts of the new or rarerelements.There is no major theoretical advance to report, but it is clearthat the experimental results now being derived from a wide variety ofdifferent properties will add to our understanding of the short-range forcesbetween ions. Measurements, unfortunately, are still being largely confinedto one temperature, and some, being made in mixed electrolytes at highnominal ionic strengths, cannot be safely used for theoretical comparisons.Most of the methods so far used are exemplified in the results underreview.Conductivity measurements on dilute solutions have yieldeddissociation constants for barium thiosulphate 29 and for SrI03+.30 Con-ductivities on mixed solutions are applicable where extensive association isexpected, and this method and the solubility method have both been appliedto a number of ferricyanides 31 and tri- and tetra-metaph~sphates.~~ Parryand Dubois 33 have used E.M.F. measurements, with copper and glasselectrodes, to investigate the interactions of cupric and citrate ions ; concen-tration cells have been used to study the association of stahnous with C1-and Br- ions 34 at a nominal ionic strength of 3.0 ; and equilibrium constantsof many bivalent cations with iminodiacetic and related acids 35 have beenB1 D.A. MacInnes, M. 0. Dayhoff, and B. R. Ray, Rev. Sci. Instr., 1951, 23, 642;D. A. MacInnes and M. 0. Dayhoff, J. Amer. Chern. SOC., 1952, 74, 1017.23 T. J . Morrison, J., 1952, 3814, 3819; W. F. McDevit and F. A. Long, J. Amev.Chem. Soc., 1952, 74, 1773; A. P. Altshuller and H. E. Everson, J. Phys. CoZZoid Chem.,1951, 55, 1368; H. A. C. McKay, Trans. Faraday SOL, 1052, 48, 1103; J . H. Saylor,A. I. Whitten, I. Claiborne, and P. M. Gross, J. Awzev. Chew. SOC., 1952, 74, 1778.For review see F. A. Long and W. F. McDevit, Chem. Reviews, 1952, 51, 119.24 A. W. Garner, H. A. C. McKay, and D. T. Warren, Trans. Faraday SOC., 1952,48,997.25 L. I. Katzin, D. M. Simon, and J.R. Ferraro, J. Amer. Chem. SOC., 1952, 74, 1191.26 0. D. Bonner, A. W. Davidson, and W. J. Argersinger, Jr., ibid., p. 1047.2 7 J . Sedlet and T. de Vries, ibid., 1951, 73, 5808.z 8 G. G. Koerber and T. de Vries, ibid., 1952, 74, 5008.2s T. 0. Denney and C. B. Monk, Trans. Paraday Soc., 1951, 47, 992.30 C. A. Colman-Porter and C. B. Monk, J., 1952, 1321.31 C. W. Gibby and C. B. Monk, Trans. Faraday Soc., 1952, 48, 632.32 C. B. Monk, J., 1952, 1314, 1317.33 R. W. Parry and F. W. Dubois, J , Amer. Chem. SOC., 1952, 74, 3749.34 C. E. Vanderzee and D. E. Rhodes, ibid., pp. 3552, 4806.35 S. Chabarek, Jr., and A. E. Martell, ibid., pp. 5052, 5057, 6021DAVIES AND MONK ELECT-ROLYTES. 31determined by J. Bjerrum’s method. A new departure is the use of cellswithout transference for studying ion-pair formation in salts.36 The methodis well adapted for work over a range of temperature and should lead to theaccumulation of reliable data for the entropy and heat content changes(AS, AH) of the dissociation process.The values so obtained, with thoseof some related compounds are (Ma1 = malonate) :MgSO, MgMal ZnMal37 LaSO,+ LaFe(CN), 38AH, kcal. ....,....... -5.7 - 3.2 -3.1 -2.5 -2.0AS, cal./deg. . . . . . . . . . -31.0 -23.9 -27.5 - 26.0 - 23.9Spectrophotometric measurements in the visible and ultra-violet regionsare being increasingly employed to study ionic equilibria. The method isexperimentally simple and the interpretation straightforward so long as it isremembered that foreign ions which do not affect the absorption may never-theless interact with the system being studied, especially at high ionicstrengths.By measurement of optical densities, Gordon and Schreyer 39have shown that the deep blue colour given by cobalt in concentrated alkaliis due to Co(OH),-, and by a similar method Yaffe and Voigt 40 find thatRU(III) and (IV) both give RuCNS2+, RU(IV) being reduced by the thiocyanate.They determine an equilibrium constant for the ion-pair at an ionic strengthof approximately 1, and Farrington,4l in a similar way and a t the same ionicstrength, has measured the extent of CuBr+ formation. King and Pandow 42have carried out further work on the ionic state of Ce(1v) in perchloric acidsolutions; Beer’s law is not obeyed a t H+-ion concentrations of 1-2.5~,and the spectra give evidence of polymerisation-presumably dimerisationthrough oxide or hydroxyl bridging.Anderson and his co-workers 43 haveused the method of continuous variations to study the interaction of sulpho-salicylic acid with aluminium, nickel, and chromium ; a maximum in opticaldensity is given for the 1 : 1 ratio. The copper salt was used as indicatorwith aluminium, and in a rather similar way Wilson and Taubea havestudied the interaction of chromium and gallium with the fluoride ion,using ferric ion as indicator.Raman spectra have been used45 to study the aluminate and zincateions; the experimental data are found to be in good agreement with cal-culations for the tetrahedral ions Zn(OH),2- and Al(OH),-.The interactionbetween thorium and various anions has been studied by distributionmeasurements using the thenoyl-trifluoroacetone complex.46 Finally,Schubert 47 has continued his application of ion-exchange resins, utilisingradio-tracers, to the determination of equilibrium constants, and his most36 H. W. Jones and C. B. Monk, Trans. Fwaduy SOC., 1952, 48, 929; J . I. Evans38 C. W. Davies and J. C . James, Proc. Roy. SOC., 1948, A , 195, 116.39 S. Gordon and J . M. Schreyer, J . Amer. Chem. SOC., 1952, 74, 3169.40 R. P. Yaffe and A. F. Voigt, ibid., p. 2500.4 1 P. S. Farrington, ibid., p. 966. 42 E. L. King and M. L. Pandow, ibid., p. 1966.4s A. M. Liebman and R. C. Anderson, ibid., p. 2111 ; M. B. Lasater and R. C.4 5 E. R. Lippincott, J .A. Psellas, and M. C. Tobin, J . Chem. Phys., 1952, 20, 536.46 E. L. Zebroski, €3. W. Alter, and F. K. Heumann, J . Amer. Chem. Soc., 1951, 73,47 J . Schubert, ibid., p. 113.and C. B. Monk, ibid., p. 934.J . C. James, J., 1951, 153.Anderson, ibid., p. 1429.5646; W. C. Waggener and R. W. Stoughton, J . Phys. Chem., 1952, 56, 1.44 A. S. Wilson and H. Taube, ibid., p. 350932 GENERAL. AND PHYSICAL CHEMISTRY.recent contribution also reviews earlier work in this field. This completes thelist of methods used in the period under review, but, varied as the list is, it isworth noting in addition that conductivities at high field strengths promiseto provide a sensitive method of detecting and estimating ion-pairs, and thatthe same applies, to a lesser degree, to diffusion rneas~rernents.~~In the main, the measurements enumerated fall well into line with earlierwork. In the summary below, numerical values quoted are equilibriumconstants for the dissociation process.Some recent writers give the reci-procals of these, but this seems a pity even in cases where it may be themore logical procedure, partly because it is confusing in relation to all theearlier literature and partly because it creates an artificial distinction betweenacids and other electrolytes.Ion-pair formation is appreciable but not extensive in cupric bromide,41in agreement with data for the chloride.49 It is somewhat more marked, asmight be expected, in RU(III) thiocyanate; K, = 0.017 for RuCNS2+ a t 40an ionic strength of approximately 1.An approximate value, K = 0.04, forThCP+ is quite high for this valency type 46 and suggests ion-pair formationof the Bjerrum kind between hydrated ions. At M-chloride concentrationand an ionic strength of 4.0, however, Waggener and Stoughton46 reporthigher association products to be present in the following proportions :Th4+, 33.8; ThCP+, 57.5; ThC122+, 4.7; ThC13+, 3.4; ThCl,, 0.6%. Therelative figures are not what would be expected from electrostatic theory,and suggest that the further association of C1- ions is governed rather byconsiderations of co-ordination chemistry ; this conclusion must be treatedwith reserve however, in view of our complete ignorance of the activitycoefficients and the sensitivity of the results to small experimental errors.The fluorides of metals of high valency are weaker than the other halides,and the dissociation constant 44 of GaF2+ is about the same as that of FeF2+ ;the corresponding chromium complex is about five times as strong, so thedifficulty in removing water from the hydrated Cr3+ ion has no discernibleinfluence here.The dissociation constants of a number of bivalent metal thiosulphatesare normal,29 being somewhat higher than those of the sulphates, but thecadmium salt is weak (K = 1.2 x and complex-anion formation isappreciable even in dilute solutions.The sulphosalicylates 43 of copper(K = 0.0022), aluminium (K = 5 x and chromium (K are ofthe order of magnitude to be expected for normal ion-pair formation, butthe nickel salt (K = 4 x The dissociation constantsfor the ion-pairs of the ferricyanides 31 and tri- and tetra-metaphosphates 32of the alkaline earths are given in the following Table :is distinctly weak.Mg Ca Sr BaFerricyanides ( x los) .....................1.63 1-47 1.41 1-32Trimetaphosphates ( x lo*) ............... 4-89 3-56 4.43 4.50Tetrametaphosphates ( x 106) ......... 6.7 3.9 7.0 10.3It seems that the trimetaphosphate ion, unlike the ferricyanide ion, isable to replace hydration water from the cation, thus giving much smaller4 8 H. S. Harned and R. M. Hudson, J. Anzev. Chem. SOC., 1951, 73, 3781.49 W. H. Banks, E. C. Righellato, and C. W. Davies, Tuuns. Furaday SOL, 1931,27, 621DAVIES AND MONK : ELECTROLYTES. 33K's, and reversing the order Ca, Sr, Ba.The magnesium trimetaphosphateis still the strongest salt, presumably because the inner hydration shell ofthis small ion is particularly stable. This further emphasises the importanceof geometrical considerations in any final analysis. Lanthanum trime ta-phosphate 32 (K = 2-0 x(K = 1-82 x lo-*) and again the non-hydrated cation may be involved.The dissociation constant 32 of the lanthanum tetrametaphosphate ion-pairis 2.2 x lo-'; this valency product of twelve is the highest yet studied.Analogous considerations concerning the stabilities of complexes involvingorganic ligands have received active consideration over the past few years.Williams,5o who has taken the alkaline-earth cations for detailed discussion,shows that the relation between the pK values and ionization potentials,which has so far provided the most satisfactory explanation, fails for mag-nesium.He considers that short-range repulsion forces must also beconsidered. In a study of the alkaline earth monocarboxylates by Colman-Porter and Monk,51 magnesium is again found to be anomalous, and it issuggested that, as detailed above for inorganic salts, the hydration ofmagnesium may account for this difference.has re-moved a former discrepancy between the dissociation constant at varioustemperatures obtained by this method and by other methods ( K = 0.0103at 25"); the Bureau of Standards 53 have added tartaric and 5 : 5-diethyl-barbituric acids to their series of precise E.M.F. data; sulphamic acid hasbeen carefully examined by King,54 and Jones and Parton 55 have obtainedsatisfactory results for benzoic acid by using the quinhydrone in place of thehydrogen electrode.A further article on an individual acid is that ofWaring,56 who reviews the thermodynamic properties of formic acid, andtwo papers devoted to a study of series of acids have been given by Bother-Byand Medalia 57 on some substituted benzoic acids and by Peek and Hill 58on some dicarboxylic acids in 20% methanol; both of these interpret theirresults in terms of current theories. As opposed to these E.M.F. methods,a spectrophotometric method has been developed for determining the over-lapping constants of dibasic acids 59; this has been applied to severalexamples and the results are compared with previous data.In the field ofnon-aqueous solvents, formamide, which is a good solvent of higher dielectricconstant than water (109 at room temperature), has been used by Dawsonand Griffith 6o for freezing-point studies of several organic acids. Theirsemi-quantitative calculations suggest that ionization is roughly 10% greaterin this solvent than in water.Two further contributions to the study of base equilibria are those ofis also much weaker than the ferricyanideAcids and Bases.-A recent E.M.F. study of the HSO, ion50 R. J. P. Williams, J., 1952, 3770.5 1 C. A. Colman-Porter and C. B. Monk, ibid., p. 4363.5% C. .W. Davies, H. W. Jones, and C. B. Monk, Trans. Faraduy SOC., 1952, 48, 921.63 R. G. Bates and R.G. Canham, J . Res. Nut. Bur. Stand., 1951, 47, 343; G. C .Manov, K. E. Schuette, and F. S. Kirk, ibid., 1952, 48, 84.64 E. J. King and G. W. King, J . Amer. Chew. SOC., 1952, 74, 1212.5 5 A. V. Jones and H. N. Parton, Trans. Faraday SOC., 1952, 48, 8.5G W. Waxing, Chem. Reviews, 1952, 51, 171.5 7 A. K. Bother-By and A. I. Medalia, J . Amer. Chem. SOC., 1962, 74, 4402.58 H. M. Peek and T. L. Hill, ibid., 1951, 73, 5304.69 B. J. Thanier and A, F. Voigt, J . Phys. Chem., 1952, 66, 226.Go L. R. Dawson and E. J. Griffith, ibid., p. 281.RE P,-VOL. XLIX . I34 GENERAL AND PHYSICAL CHEMISTRY.Everett and Wynne- Jones who used a hydrogen electrode for temperaturestudies of the ammonium and methylammonium ions in 60% aqueousmethanol, and a solubility investigation of strontium hydroxide ; 30 here(K = 0.11 for SrOH+) the value fits an equation 62 which relates crystallo-graphic cation radii with the pK’s of strong hydroxides.Redox Systems.-Potentials of some of the valency systems ofneptunium,m americium and praseodymium,64 and ruthenium 65 havebeen reported during 1952, and an interesting system, namely, that of the2 : 2’-dipyridyl derivatives of OS(II-111) has been investigated.66 The effectof varying the ionic strength ( I ) by indifferent electrolytes gave plots ofE.M.F.against I* which deviate from those predicted by the Debye-Huckeltheory. The authors suggest that the changing nature of the ligand-metalbonds with ionic eiivironment can explain this; however, a consideration ofthe possible ion-pairs present may well provide a more logical interpretation.C.W. D.C. B. M.4. THE KINETICS OF HOMOGENEOUS REACTIONS.There has been no substantial change in the theory of rate processes.Most of the published work has been based on experiment and Concernedeither with the elucidation of the mechanisms of various reactions or with thedetermination of the specific rate constants and energies of activation ofsimple unimolecular or bimolecular reactions involving ions, molecules, andradicals. The ready availability of suitable radioactive isotopes of most ofthe common elements has led to an increased understanding of electron- andgroup- or atom-transfer processes in solution, and also of the nature of thechemical reactions which ensue when nuclear radiations are absorbed bymatter. A noteworthy conference has been held on each of these twosubjects and the large amount of work which has been carried out is reflectedin the size of the appropriate sections of this Report.Three other symposiaconcerned with (1) the reactivity of free radicals (see ref. 56), (2) combustionand flame, and (3) ionic polymerisation (see ref. 300) have also taken placebut the Proceedings of none of these have yet been published.We have presented the topics in order of increasing complexity of mechan-ism, and have deliberately omitted any mention of certain fields of work.Thus, oxidation and combustion have not been referred to, but it is hopedthat this subject will be covered in next year’s Report when the paperssubmitted to the Boston conference (no.2 above) will have been printed.Work on reactions in the solid phase and investigations relating to the morephysical or dosimetric aspects of radiation chemistry have been omitted asbeing of only minor interests to chemists.General and Theoretical.-Most reactions which have been reported havebeen investigated by conventional experimental methods, or by slight61 D. H. Everett and W. F. K. Wynne-Jones, Trans. Faraday Soc., 1952, 48, 531.62 C. W. Davies, J . , 1951, 1256.63 D. Cohen and J . C. Hindman, J . Anzer. Chem. SOC., 1952, 74, 4679, 4682.64 L. Eyring, H. R. Lohr, and B. B. Cunningham, ibid., p. 1186.65 R. E. Connick and C. R. Hurley, ibid., p. 5012.6 6 G. T. Barnes, F. P.Dwyer, and (Miss) E. C . Gyarfas, Trans. Faruduy Soc., 1962,48, 269BETTS et al. : THE KINETICS OF HOMOGENEOUS REACTIONS. 35variants of these. One new method is that of Heitler who used a modifiedCottrell apparatus, with a suitably aged thermistor in place of a thermometerto detect the changes of boiling point of the solvent accompanying the chang-ing concentration of a dissolved reactant. By using acetone as the solvent itwas possible to record the course of reactions with half-lives of less than oneminute. A number of authors developed the mathematical treatmentappropriate to the kinetics of complex reactions, such as those involving twoconsecutive second-order steps,2 accompanied by diff u ~ i o n , ~ and auto-synthetic reaction^.^The principal difficulty in the calculation of velocity constants a priori,by the methods of the transition-state theory, is that of obtaining an accuratevalue for the increment in internal energy at absolute zero in passingfrom the reactants to the complex.At best the calculation is semi-empiricaland can only be carried through to completion for the simplest systems.There is therefore considerable incentive to find good empirical relationsbetween measured energies of activation and experimentally accessibleproperties of the reactants. Eyring and Smith have recently shown thatthere is a linear relation between the activation energy of the reaction ofsodium atoms with chlorinated hydrocarbons and the ratio of the net chargeon the halogen atom to the polarisability of the carbon-halogen bond whichis broken.It has often been pointed out that there is a simple proportion-ality between the change in activation energy (AE) and the change in bonddissociation energy (AD) for certain series of simple bimolecular reactions.Bernstein has pointed out, for the case of the reactionCX* - + M +M-X + CX, -- , t Y nwhere TZ = 0, 1, 2, or 3, and X is a halogen, that, if all the bonding andnon-bonding contributions to the heat of atomisation of the substitutedmethane CX, - ,Y, are additive, and if the same is also true for the activatedcomplex, then not only is AE proportional to ADc-x but both are proportionalto changes in the heat of formation and in the heat of atomisation of thesubstituted methane.It is a feature of the transition state theory that, since In A = aAS*,variations of the frequency factor (A) can be associated with variations of theentropy of activation (AS*).Rollefson has drawn attention to the factthat the A values of many bimolecular gas and solution reactions are within-loll or =lo7 1. mole-l min.-l, corresponding to AS* values of 21-10and --30 cal. deg.-l mole-l respectively. The second value of A S isof the same order as the translational entropies of many molecules at roomtemperature, and it is therefore suggested that in the first case the two mole-cules comprising the activated complex are only loosely bound and that theonly condition for formation of the complex is approach of the molecules towithin a certain distance, so that only one degree of vibrational freedom islost; however, in the second case the molecules are tightly bound in the1 C.Heitler, Chem. alad I n d . , 1952, 875.2 H. G. Higgins and E. J. Williams, Australian J . Sci. Res., 1952, 5, A , 572.3 F. J . W. Roughton, Proc. Roy. SOC., 1952, A , 214, 564; J. Crank, Phil. Mag., 1952,5 H. Eyring and R. P. Smith, J . Amer. Chem. Soc., 1952, 74, 229.6 R. B. Bernstein, J . Chem Phys., 1952, 20, 524.7 G. K. Rollefson, J . Phys. Chem., 1952, 56, 976.43, 811. 4 (Sir) Cyril Hinshelwood, J., 1952, 74536 GENERAL AND PHYSICAL CHEMISTRY.complex and all three degrees of translational freedom have gone. Thechemical nature of the reactions in the two groups is considered to be broadlyin accord with this view.Another simple deduction from transition-statetheory which can readily be demonstrated concerns equilibria.8 When areversible reaction is displaced from equilibrium so slightly that the free-energy change is less than the value of RT, the rate of approach to equili-brium is directly proportional to the free-energy difference between thereactants and the products.The transition-state theory has little of quantitative value to offerconcerning the pressure dependence of the rate constant of unimolecularreactions, and in the attempts to refine the Lindemann collision theory thereare signs of a revived interest in this field and in the problems which underliethis theory. Johnston9 has carried out a general summation over allquantum states of the individual steps in the Lindemann scheme, whence heobtains the expression.where ai, bi, and ci are respectively the average values of the rate constantsin proceeding from any quantum state of the molecules on the left-handside of reactions (l), (2), and (3) below, to any quantum state of the moleculeson the right-hand side :.. . . . . M + M A M + A * (1)M + A & M + - M . - (2)A 4 C . . . . . . . . * (3). . . . .and A denotes an activated molecule, C a product molecule, and N thereactant molecule. By assuming these averages to be constant it is possibleto set a limit on the value of the rate constant a t low concentrations of Mfrom data on the value of the rate constant at high concentrations and viceversa. Theory and experiment have been compared for the pyrolyses of nitrousoxide and nitrogen pentoxide.Benson lo has combined Slater's theory 11with the Lindemann hypothesis and concludes (a) that for molecules con-taining more than 6 atoms the rate constant is unlikely to change withdecreasing pressure until at least 1 mm. Hg is reached and (b) that formolecules of identical atomicity but differing shape the fall in rate constantwill occur at pressures higher for linear than for non-linear molecules.First-order and Unimolecular Gas Reactions.-Several pyrolytic andisomerisation reactions have recently been shown to be non-chain first-orderhomogeneous reactions. Notable amongst these are the dehydrohalogen-ation reactions of halogenated hydrocarbons. Howlett l2 has shown thatethyl chloride, 1 : I-dichloroethane, isopropyl chloride, and isobutyl chloridedecompose in this manner. Furthermore, below a certain pressure (5 mm.Hg for ethyl chloride a t 456') the order of reaction exceeds unity, but in thepresence of sufficient quantities of either product, or added inert gases suchas nitrogen and helium, the first-order character can be maintained down to8 V51.R. Gilkerson, M. M. Jones, and G. A. Gallup, J . Chem. Phys., 1952, 20, 1188.H. S. Johnston, zbid., p. 1103. lo S. W. Benson, ibid., p. 1064.l1 N. B. Slater, Proc. Roy. Soc., 1948, A , 184, 112.l2 K. E. Howlett, J . , 1952, 3695, 4487; Chem. and Ind., 1952, 1176XETTS ct a/. THE KINETICS OF HOMOGENEOtTS REACTIONS. 37lower pressures. The pyrolysis of 1 : 2-dichloroethaneJ though a chainreaction, shows similar effects below 20 mm.Hg pressure.13 This author hasexamined the results in the light of Rice and Ramsperger's theory and hasshown that they are in agreement with the idea that the transformationprobability of an activated molecule is a function of the energy possessed inexcess of the minimum required for reaction. The relations between thefrequency factors and energies of activation of these reactions are regarded asbeing in accord with the notion that the slow step is the localisation of theenergy in the activated molecules. By employing carbon-coated reactionvessels Barton, Head, and Williams l4 have succeeded in suppressing anyheterogeneous reaction in the decomposition of (-)-menthy1 chloride anddemonstrated the unimolecular nature of the residual homogeneous reaction.The usual stereospecificity was observed, the ratio of A2- to A3-olefin in theproducts being about 0.3.The isomerisation of diisopropenyl ether to allylacetone has been followedspectrophotometrically by Stein and Murphy.15 At temperatures between143" and 194" and pressures between 20 and 760 mm.the first-order rateconstant has the value 5.4 x loll exp (-29.3 kcal./RT) sec.-l, very closeto the value which they obtained earlier for ally1 vinyl ether. A preliminaryaccount has been given of the kinetics of the isomerisation of cyclopropaneto propylene between 10 and 0.1 mrn.l6 The reaction is quasi-unimolecular,and reasonably good agreement of the data with the predictions based onKassel's equation l7 is obtained, if in applying the latter, it is assumed thatthe collision diameter is 3.94 A and 13 oscillators are involved.Sir Cyril Hinshelwood and his collaborators have published a series ofpapers l8 on the decomposition of various straight-chain and branched-chainparaffins in the presence of sufficient nitric oxide to suppress the concurrentchain reaction, and their results are summarised in a final paper.lQ Re-actions of hydrocarbons such as ethane, propane, isobutane, isopentane,neopentane, and neohexane show a single transition from first to secondorder as the pressure is reduced, and the energy of activation is independentof pressure.Reactions of other hydrocarbons, including n-butane, PZ-pentane, n-hexane, 2 : 3-dimethylbutane, and 2- and 3-methylpentane,change from first to second order, return to first order and finally becomesecond order as the pressure is reduced from 1600 to 0.1 mm.This effectcould be ascribed to the coexistence of two unimolecular reactions withdifferent pressure dependence, and in agreement with this two distinctactivation energies are observed, but the products of these two reactionsappear to be the same in the case of n-butane. Hydrocarbons in the firstcategory have a frequency factor for decomposition in the normal range ofl O l a to 1014 sec.-l, as also do the hydrocarbons in the second category whenthe pressure is high. The low-pressure first-order frequency factors for thel3 K. E. Howlett, Tram. Furaday Soc., 1952, 48, 25.l4 D.H. R. Barton, A. J . Head, and R. J. Williams, J , . 1952, 453.l5 L. Stein and E. W. Murphy, J . Amer. Chem. Soc., 1952, 74, 1041.l6 H. 0. Pritchard, R. G. Sowden, and A. F. Trotman-Dickinson, J . Amer. Chena. SOC.,1952, 74, 4472.l7 L. S. Kassel, " Kinetics of Homogeneous Reactions," Chem. Catalog. Co., NewYork, 1932, p. 93.F. J. Stubbs, K. U. Ingold, B. C. Spall, C. J. Danbv, and (Sir) Cyril Hinshelwood,Proc. Roy. SOG., 1952, A , 214, 20; M. G. Peard, F. J . Stubbs, and (Sir) Cyril Hinshelwood,ibid., p. 330, 339. I* Idem, ibid., p. 47138 GENERAL AND PHYSICAL CHEMISTRY.latter group of hydrocarbons are however very much higher. A similarhigh-frequency factor is suggested for the dissociation of vinylcyclohexene intobutadiene.20 A comparative study of the pyrolysis of nine olefins has beenmade by Molera and Stubbs21 All these reactions are of first order duringthe initial stages.Marcus 22 has surveyed existing data on atomic crackingreactions and on the deuteration of free radicals, and has deduced thevelocity constants for the dissociation of various vibrationally excited alkanes.As would be expected, the rate constant increases with increasing number ofdegrees of freedom of the decomposing molecule.The kinetics of decomposition of diethyl peroxide have been investigatedin a flow system in the presence of excess of toluene.23 The products aremainly ethane and formaldehyde with smaller amounts of methane anddibenzyl. The results are interpreted in terms of a non-chain, radicalmechanism and the overall first-order constant [=2.1 x 1013 exp (-31.7kcal./RT) sec.-lJ is shown to refer to the initial break into two ethoxy-radicals.However, the value 31.7 kcal. is rather smaller than the expectedvalue of the bond dissociation energy DE~o-oE~. The possibility that thisreaction may be more complicated than has hitherto been supposed has beensuggested by Style and Jenkins; 24 and Mortlock and Style 25 have drawnattention to the fact that diethyl peroxide reacts with nitric oxide to formethyl nitrite. Clearly the nitric oxide method cannot be used to isolateany non-chain decomposition products of this peroxide. The pyrolysis ofdi-terf.-butyl peroxide has been studied mass spectrometrically by Lossingand Tickner at very low pressures (approx.2 p) and temperatures up t o350°.26 These results were combined with those obtained by Vaughan andSzwarc at lower temperatures, and the first-order constant was calculatedto be 7.1015 exp (-38 kcal./RT) sec.-l. Brinton and Volman 27 havecarried out the reaction at much lower temperatures and higher pressuresin the presence of ethyleneimine and give values for the rate of fission ofthe peroxide link in fair agreement with those of Lossing and Tickner.Szwarc and his co-workers have continued their measurements of bonddissociation energies by pyrolysis of the parent compound in a flow system,using toluene as a carrier gas and radical reagent.28 An interesting pointwhich has emerged from studies of this kind on alkyl and aryl bromides isthat, although the rate constants of two C-Br bond dissociation processesmay be in the ratio lo5 : 1, the frequency factors are of the same order ofmagnitude.29Bimolecular Gas Reactions.-Many bimolecular association reactions are“ slow,’’ i.e., have a P factor very much less than unity, and this is attributedto a loss of entropy during formation of the activated complex.Anotherexample of this behaviour is the simple reactions between olefins and ozone20 N. E. Duncan and G. J. Janz, J. Chem. Phys., 1952, 20, 1644.21 M. J. Molera and F. J . Stubbs, J., 1952, 381.22 R. A. Marcus, J . Chem. Phys., 1952, 20, 352, 359, 364.23 R. E. Rebbert and K. J . Laidler, ibid., p. 574.24 A. D. Jenkins and D. W. G.Style, Nature, 1952, 170, 706.25 H. N. Mortlock and D. W. G. Style, ibid., p. 706.26 F. P. Lossing and A. W. Tickner, J. Chem. Phys., 1952, 20, 907.2 7 R. K. Brinton and D. H. Volman, ibid., p. 25.M. Ladacki, C . H. Leigh, and M. Szwarc, Proc. Roy. SOC., 1952, A , 214, 273;C. H. Leigh and M. Szwarc, J . Chenz. Phys., 1952, 20, 403, 844; M. Szwarc and D.Williams, ibid., p. 1171. 29 M. Szwarc and D. Williams, Nature, 1952, 170, 290RETTS et al. : THE KINETICS OF HOMOGENEOUS REACTIONS. 39which are characterised by frequency factors of the order lo3 to lo4 1. mole-lsec.-1.30 The dimerisations of tetrafluoro- and chlorotrifluoro-ethylene arealso “ slow,” with frequency factors similar to those for the dimerisation ofdienes, viz., -lo7 1. mole-1 ~ec.-l.~l In marked contrast to these are theaddition of butadiene to cyanogen : 32and the addition of boron trifluoride to the mono-, di-, and tri-methyl-amines33 for which the frequency factors are respectively 1.6 x lo1, and - 1013 1.mole-l sec.-l. The latter reactionis particularly interesting in that noenergy of activation is required, and it is therefore as rapid as the combinationof two methyl radicals.34The expectation for bimolecular metatheses is that the P factor should beclose to unity. This appears to be almost the case in the very rapid reactionNO,C1 + NO + NO, + NOCl which was investigated over the widerange of pressure, 0-2 to 384 mm. Hg, by Freiling, Johnston, and Ogg 35 andfor which the velocity constant is lo9 exp (-6.9 kcal./RT) 1.mole-l sec.-l.This is a particularly interesting reaction in that it is not known whether achlorine or an oxygen atom is transferred.Atomic and Free-radical Reactions.-Some atomic and free-radicalreactions are dealt with in the section on photochemistry. In many casesthe photolysis of a compound has been used as a source of free radicals forthe purpose of studying the kinetics of inter-radical, and radical-moleculereactions.Much attention continues to be devoted to the reactions of hydrogenatoms and simple alkyl radicals. Berlie and LeRoy 36 claim to have elimi-nated the difficulties inherent in previous investigations of reaction (1) andgive preliminary values of El = 6-2 & 0.1 kcal. and P, = 3-3 xThe energy of activation is consistent with the work of Wijnen and Steacie 37on the reverse reaction (2), where deuterium is used in place of hydrogen.They find that the value E, = 13.3 & 0.5 kcal./mole, which after allowancefor the difference in zero-point energy of deuterium and hydrogen, leadsto El = 7 & 1 kcal./mole.Wijnen and Steacie did not detect any C,H,D,in their products, but in another system it is claimed3* that the exchangereaction CH,*CH,* + D, + CH,*CHD- + HD can occur.30 R. D. Cadle and C. Schade, J . ‘4mer. Chem. SOC., 1952, 74, 6002.31 J. R. Lacher, G. W. Tompkin, and J. D. Park, ibid., p. 1693.32 P. J. Hawlrins and G. J. Jam, ibid., p. 1790.33 D. Garvin and G. B. Kistiakowsky, J . Chem. Phys., 1952, 20, 105.34 R. Gomer and G. B. Kistiakowsky, ibid., 1951, 19, 85.35 E.C. Freiling, H. S. Johnston, and R. A. Ogg, ibid., 1952, 20, 327.38 M. R. Berlie and D. J. LeRoy, ibzd., p. 200.37 M. H. J . Wijnen and E. W. R. Steacie, ibid., p. 205.3* V. V. Voevodskii, G. K. Lavrovskaya, and R. E. Mardalekhvili, Dokl. Akad.Nauh. S.S.S.R., 1951, 81, 215; Cham. Abs., 1952, 46, 1852.Such reactions are reported mainly in this section.H +C2H6-+C2H5 + H, . . . . . * (1)CZH, + D,--+C2H5D + D . . . . . * (240 GENERAL AND PHYSICAL CHEMISTRY.Conflicting values continue to be reported for the energy of activation ofthe reactionMajury and Stea~ie,,~ using the photolysis of acetone as source of radicals,find E, = 9.7 & 0.6 kcal./mole; Davidson and Burton,m using photolysisof acetone and acetaldehyde as sources, find E, >13 kcal./mole; andAnderson and Taylor,41 using the photolysis of dimethylcadmium as source,find E, = 13 & 2 kcal./mole. It is assumed by all the authors that theenergy of activation for the combination of two methyl radicals is zero.Majury and Steacie have shown that substitution of D, for H, in reaction (3)causes an increase in activation energy of the order to be expected from thedifferent zero-point energies, while replacement of CH,.by CD,* causes arelatively slight reduction in rate.Lossing and Tickner 26 have developed a mass-spectrographic method formeasuring the partial pressure of methyl radicals in thermally decomposinggases. The method differs from previous similar methods in that relativelyhigh-voltage electrons (50 ev) are used, the effect of ionisation of speciesother than methyl being allowed for by assuming a 100% carbon balance.The combination reaction of methyl radicals was studied and the collisionefficiency at 850" estimated as 2-3 x 1W2.A redetermination of thecollision efficiency of the reaction between methyl radicals and nitric oxidehas been made,42 by using a radioactive tellurium mirror method. This leadsto a collision efficiency of for the combination of methyl radicals atroom temperature. Durham and Steacie conclude, from a comparison of theavailable data, that the true value is between 0-5 and 0.05. The problem hasalso been discussed theoretically.22The thermal decomposition of di-tert.-butyl peroxide has been used as asource of the methyl radical in studies of its reactions with acetone,43 acet-aldehyde, and acraldehyde.44 The energy of activation of the reaction withacetone was found to be 9.5 & 1.5 kcal./mole in agreement with otherwork, while for the reaction with acetaldehyde E = 7-5 & 0.3 kcal./mole.Acraldehyde polymerises as well as decomposing in the presence of radicals.The hydrogen abstraction reactions of methyl radicals with various halo-genated methane derivates have been found 45 to have the following activ-ation energies : CH,F, 8.7 ; CH2F2, 6.2 ; CH,Cl, 9.4 ; CH2CI2, 7.2 ; CHCl,, 5.8 ;CH3Br, 10.1; CH2Br2, 8.7 kcal./mole.The steric factors lie in the range10-2 to 10-4. The reactions of methyl radicals with oxygen46 and withsec.-butyl chloride 47 have also been studied.The Combination, disproportionation, hydrogen-abstraction, and de-composition reactions of the ethyl radical have been reviewed.48 Thereappears to be a real discrepancy between the relative extent of dispropor-tionation and combination of ethyl radicals produced by different methods.CH,-+H,-+CH,+H .. . . . . (3)39 T. G. Majury and E. W. R. Steacie, Canad. J . Chem., 1952, 30, 800.40 S. Davidson and M. Burton, J . Amer. Chem. SOG., 1952, 74, 2307.4 1 R. D. Anderson and H. A. Taylor, J. Phys. Chem., 1952, 56, 498.42 R. W. Durham and E. W. R. Steacie, J. Chem. Phys., 1952, 20, 582.43 M. T. Jaquiss, J. S. Roberts, and M. Szwarc, J . Amer. Chem. SOL, 1952, 74, 6005.4 3 D. H. Volrnan and R. K. Brinton, J. Chem.Phys., 1952, 20, 1764.4 5 F. A. Raal and E. W. R. Steacie, ibid., p. 578.4fi F. B. Marcotte and W. A. Noyes, J . Amer. Chem. Soc., 1952, 74, 783.4 7 A . S. Kenyon, ibid., p . 3372.4 5 K. J. Ivin, M. H. J. Wijnen, and E. W. R. Steacie, J. Phys. Chem., 1952, 56, 967BETTS d fll. THE KINETICS OF HOMOGENEOUS REACTIONS. 41Bevington 49 has calculated the differences in the heat content, entropy,and free energy of the products resulting from the disproportionation andcombination of ethyl and other radicals. It does not follow that the reactionleading to the greatest decrease of free energy will necessarily predominate,since it follows from the work of Wijnen and Steacie185 that the two reactionsare quite independent and do not proceed via the same transition complex.Paneth and Hollis 5O have shown by a radiochemical method that ethylradicals react a t every collision with a bismuth mirror.The frequency factors for a number of hydrogen-abstraction reactionshave been calculated 5 l from the theory of absolute reaction rates and shownto be in fair agreement with experimental values.The reactions of sodium vapour with ethyl chloride 52 and trifluoro-halogenomethanes 53 have been studied by the diffusion flame method andthe following energies of activation found : C,H5Cl, 10.2 & 0.5 ; CF,I, 1.7 ;CF,Br, 2.3; CF,Cl, 7-4 kcal./mole.In the CF,X compounds it is the X atomwhich is preferentially removed. In the case of ethyl chloride the stericfactor is unity within experimental error.In solution the phenyl radical reacts with aromatic compounds to givediphenyl derivatives :Ph- + PhX --+ PhC,H4X + Hbut in the gas phase at high temperature and low pressure, hydrogen ab-straction is preferred in the case of compounds such as toluene :This difference in behaviour has been investigated by Jaquiss and Szwarc 54who conclude that the effect is real and advance a tentative explanation.Kooyman and Farenhorst 55 hgve given a preliminary account of anexperimental study designed to provide a broad test of the predictions ofCoulson ct al.that the free valence number calculated for a given carbonatom in a compound should be related to its ability to interact with a freeradical. The correlation is found to be remarkably good for velocity con-stants varying over a range of more than lo5.A summary of the Toronto conference on the Reactivity of Free Radicalshas been published.56Reactions in Solution.-General.-Kacser 57 has given a theoreticalaccount of the probability factor in uncomplicated ion-dipole reactions. Anequation for the " effective shape " of a polar molecule in the field of an ionis developed, which determines the success of reactive approaches of the ionfrom any given direction. If the field around the molecule is markedlyanisotropic, there will be favoured directions of approach for the ion, whichwill be reflected in the non-exponential factor of the Arrhenius equation,When these concepts are applied to exgerimentaI data (reactions of methylPh. + PhMe --+ PhH + PhCH,.-> (PhCH,),43 J . C. Bevington, Trans. Faraday SOC., 1952, 48, 1045.60 F. A. Paneth and A. Hollis, Nature, 1952, 169, 618.j1 S. Bywater and R. Roberts, Canad. J . Chenz., 1952, 30, 773.j2 R. J . Cvetanovic and D. J. LeRoy, J . Chem. Fhys., 1952, 20, 1016.53 J. W. Hodgins and R. L. Haines, Canad. J , Chem., 1952, SO, 473.64 M. T. Jaquiss and M. Szwarc, Nature, 1952, lY0, 312.55 E. C. Kooyman and E. Farenhorst, ibid., 1952, 169, 153.56 H. W. Melville, zbzd., 1952, 170, 819.5 7 I-I. Kacser, J . Phys. Chem., 1952, 58, 110142 GENERAL AND PHYSICAL CHEMISTRY.halides with halide ions), they yield the approach distance of reacting mole-cules, and give infomation concerning the steric course of the reaction.The differential rate equations for the kinetics of competitive reactions ofthe type A + B + C + E, and A + C + D + E have been integrated forthe special case where [A] = [B].58 Measurements of the rates of hydrolysisof ethyl adipate and ethyl succinate were made and used as an illustration ofthe theory.Pearson 59 has made a theoretical study of the influence of the solvent onthe heats and entropies of reactions in which ions are formed from neutralmolecules. Changes in the entropy term appear to be decisive in relatingthe rates of similar reactions in different solvents.Curme and Rollefson 6o have compared the rate of quenching of fluor-escence of p-naphthylamine by carbon tetrachloride in the gas phase, and insolution in isooctane and cyclohexane. Values of the entropy of activationfor the process in these three media are essentially identical.They concludethat the rate a t which these molecules come together and react is not greatlydifferent in solution in an inert solvent, from what it is in the gas phase.Franklin has calculated the entropy and heat of formation of alkyl-carbonium ions in solution from corresponding values for the gaseous ions,using Latimer's method. These values are used for calculations of ASsand AHs for hydrolysis of alkyl halides in aqueous ethanol, and also of therate of hydration of isobutene and dehydration of tert.-butanol. The cal-culations of the rates of these processes are in good agreement with experi-mental values.IsotoPic Exchange Reactions in Solution. Many reactions in solutioncan be detected only by the use of suitably labelled isotopic species.Theincreasing availability of both radioactive isotopes of many of the elements,as well as stable isotopes, e.g., l 8 0 and 15N, has led to a considerable expan-sion in the number and variety of studies in this field.Adamson 63 has suggested that a relationexists between the rate of one-electron transfer and the magnetic propertiesof the ions concerned. The criterion of this correlation is that if the productof the sum and the difference of the magnetic moments of the couple is high,electron transfer between the couple will be slow. The theoretical basis forthis relation is admitted to be obscure.Libby 64 has considered the probability of isotopic electron transfer fromthe point of view of the Franck-Condon principle.He suggests that thehydration atmospheres around the ions are unable to move in the time re-quired for electron transfer, thus causing formation of ions in incorrectenvironment. This requires the later movement of hydration energy fromone site to another, and thereby constitutes a barrier which inhibits electrontransfer. For large co-ordinated ions such as the ferro- and ferri-cyanides,the energies of hydration are smaller, and the barrier is greatly reduced.Catalysis by small negative ions is explicable on the basis of formation of alinear complex with the anion between the two exchanging cations. This will(a) Electron-transfer processes.6 8 A. A. Frost and W. C. Schwemer, J . Amer. Chem.Soc., 1952, 74, 1268.59 R. G. Pearson, J . Chem. Phrvs., 1952, 20, 1478.60 H. G, Curme and G. K. Rollefson, J . Amer. Chern. Soc., 1952, 74, 3766.6 1 J. L. Franklin, Trans. Furaday Soc., 1952, 48, 443.62 W. M. Latimer, K. S . Pitzer, and C. M. SIansky, J . Chem. Phys., 1939, 7, 108.63 A. W. Adamson, J . Phys. Chem., 1952, 56, 858. 64 W. F. Libby, ibid., p. 863BETTS et al. : THE KINETICS OF HOMOGENEOUS REACTIONS. 43result in a sharing of the water molecules in the hydration spheres of thecations, with a consequent reduction in height of the energy barrier forelectron transfer. As an example of this predicted catalytic effect of smallanions, Hornig and Libby 65 have shown that concentrations of fluoride ionas low as 1 0 - 6 ~ exert an accelerating effect on the rate of electron transferbetween Ce(II1) and Ce(1v) in 6~-nitric acid.Silverman and Dodson 66 have published a definitive paper on thekinetics of electron transfer between ferrous and ferric ions in aqueousperchloric-hydrochloric acid media.In perchloric acid, the main contri-bution to exchange comes from the ions FeOH2+ and Fe2f ; the rate constantfor exchange between Fe3+ and Fe2' is about 1000-fold less. Chloride ionproduces a slight catalytic effect, and rate constants were measured forelectron transfer between the couples FeCT+-Fe2+, and FeC12+-Fe2+.Perchlorate ion plays no specific part in any of the reactions. Molecularoxygen 67 does not affect the rate of electron transfer, and the mechanismsuggested by Weiss 68 therefore cannot be operative.Furman and Garner 69 have found that the rate of electron transferbetween V(III) and V(IV) is given by :The mechanism suggested is : Vf3 + H20 VOH2+ + H+, VOH2+ +*VO2+ + Z4+ --+ *VOH2+ + V02+, where Z4+ is a quadruply chargedactivated complex of unspecified structure.The exchange between VII andVIII is complete within one minute at 2" c . ~ *Bonner and Hunt 71 have reported that the half-time for electron transferbetween CO(II) and CO(III) in aqueous perchloric acid a t 0" varies from 4.8 to22 minutes, depending on the molarity of the solution in the region 0.7to 3.0 x 10-3~. The exchange is not catalysed by glass surfaces or byordinary daylight.The electron transfer 72 between EU(II) and EU(III) in perchloric-hydro-chloric acid solutions is of first order in each of the valency states of euro-pium, and also of first order in chloride ion.The over-all energy of activationis 20.8 kcal./mole.Wolfgang and Dodson 73 have confirmed earlier work that exchangebetween Hg(1) and Hg(I1) is very rapid in perchloric acid solution. Theyfind, however, that addition of cyanide causes the exchange to become slowand measurable. Preliminary kinetic data suggest that the rate-controllingstep may be reaction between Hg22+ and a cyanide complex of Hg(I1).Electron transfer between K,Mo(CN) and K,Mo(CN), has been invest-igated with 99Mo as the radioactive tracer.74 The exchange is complete atall pH values between 1 and 11, and at total molybdenum concentrations aslow as lo-".R = 4.5 x 1012 exp (- ~O,~OO/RT)[V(III)][V(IV)~/[H+] mole 1.-1 sec.-l6 6 H.C. Hornig and W. F. Libby, J . Phys. Chem., 1952, 56, 869.6 7 L. Eimer, A. I. Medalia, and R. W. Dodson, J . Chem. Phys., 1952, 20, 743.6 8 J. Weiss, ibid., 1951, 10, 1066.70 W. R. King, Jr., and C . S. Garner, ibid., p. 3709.'1 N. A. Bonner and J. P. Hunt, ibid., p. 1866.'2 D. J . Meier and C . S. Garner, J . Phys. Chem., 1952, 56, 853.73 R. L. Wolfgang and R. W. Dodson, ibid., p. 872.74 R. L. Wolfgang, J . Anzer. Chem. SOC., 1952, 74, 6144.J . Silverman and R. W. Dodson, ibid., p. 846.S . C. Furman and C. S . Garner, J . Atner. Chem. SOC., 1952, 74, 233341 GENERAL AND PHYSICAL CHEMISTRY.By separating Cr(n) from Cr(m) by an ion-exchange resin, Haissinsky 75has shown that electron transfer between these ions is complete in hydro-chloric acid in the time taken for separation (3-7 minutes).There aresome indications that the exchange may not be complete in sulphuric acidin the same time.The electron transfer between the tris-5 : 6-dimethyl-1 : 10-phenanthro-line complexes of ferrous and ferric ions is complete within 15 seconds atO", a t concentrations 2 x 1 0 - 5 ~ in each species.76Jenkins and Yost 77 have investigated thekinetics of exchange of tritium between hypophosphorous acid and water,and their results indicate that in solution, two forms of this compoundexist which differ in position of the hydrogen atom in the H,PO, molecule.lPC-Labelled acetate has been used in a study of the exchange reactionsamong sodium acetate, acetic acid, and acetic anhydride in anhydrousacetic acid solutions. 78 Rapid exchange occurs between sodium acetateand the solvent, by direct proton transfer.Only slow exchange occursbetween acetic anhydride and acetic acid. Rapid acetate exchange isfound between both Pb(I1) and Pb(1v) acetates and the solvent. However,contrary to earlier results,79 no electron exchange occurs between Pb(11) andPb(1v) in acetic acid at 80" in four hours.Bonner and Bigeleisen *ci report no exchange of l80 between water andN20 in either concentrated alkali or concentrated acid media. No exchangewas found between water and sodium hyponitrite a t pH above 7.0, or inacid solution, in which this salt slowly decomposes.Similarly, no exchangewas observed during the decomposition of sodium " nitrohydroxylamite ' '(oxyhyponitrite) (Na2N20,) in either acid or alkaline media.Two independent investigations have shown that there is no exchangebetween either CN- or S= with CNS- in the pH range 0-5-12-7.81Based on the observations that ozone, H,O,, and 0, do not exchange1 8 0 with water, but that addition of hydrogen peroxide to water in presence ofozone causes exchange between water and ozone, Forchheimer and Taube 82suggest that OH radicals probably undergo exchange with water. Thisconclusion is reached from a consideration of the mechanism of interactionbetween hydrogen peroxide and ozone, according to which oxygen atoms inOH radicals finally emerge as oxygen gas.Atkins and Garner 83 have investigated the exchange of radioactive zincbetween zinc ions and seven zinc chelate complexes in pyridine.All " non-fused ring " complexes (e.g., the complex with 8-hydroxyquinoline) showedcomplete exchange in less than 0-5 minute, while the only " fused ring "complex examined (zinc phthalocyanine) showed no exchange in 35 days.This behaviour is in agreement with earlier predictions relating to theexchange lability of metallo-organic complexes.(b) Atom and group transfer.7 5 M. Haissinsky, J . Chim. Phys., 1952, 40, C 133.7 6 L. Eimer and A. I. Medalia, J . Apner. Chew. SOC., 1952, 74, 1692.7 7 W. A. Jenkins and D. M. Yost, J . Chem. Phys., 1952, go, 538.7 8 E. A. Evans, J . L. Huston, and T. H. Norris, J .Amer. Chem. Soc., 1958, 74, 4985.79 G. von Hevesy and L. Zechmeister, 2. EEektrochem, 1920, 26, 151.80 F. Bonner and J. Bigeleisen, J . Amer. Chem. SOC., 1952, 74, 4944.8l A. W. Adamson and P. S. Magee, ibid., p . 1590; G. E. Heisig and K. Holt, ibid.,83 D. C. Atkins, Jr., and C. S. Garner, ibid., p. 3627.84 S . Ruben, M. D. Kamen, M. B. Allen, and P. Nahinsky, ibid., 1942, 84, 2297.p. 1597. 82 0. L. Forchheinier and H. Taube, ibid., p . 3705BETTS et U l . THE KINETICS OF HOMOGENEOUS REACTIONS. 45Exchange of radio-chromium between the ion Cr( H20)63+ and thecomplexes (Cr en3)3t, Cr(~rea),~+, and CrF,(H,O), were found to be veryThe complex with fluoride ion showed some exchange whichincreased a t lower acidities.West 86 has continued his studies on the relation between bond type andrate of exchange for cobaltous and cobaltic complexes of the bidentate type.The results in general support the view that covalent bonds display slowexchange of the central metal atom with cobalt ion, and ionic complexesshow rapid exchange.Jones and Long 87 have investigated several exchange reactions betweenferrous and ferric ions and their complexes with ethylenediaminetetra-aceticacid (H4Y).Fey= and Fe2+ exchange instantaneously, while the corre-sponding ferric couple Fey- and Fe3+ exchange slowly. The pair FeOH2+-Fey- exchange a t a rate tenfold slower than the couple Fe3 '-Fey-.14C has been used by Harris and Stranks 88 to follow the kinetics ofexchange between carbonate ion in solution and the carbonate ion in thecomplex [Co (NH,) ,CO,]+.Exchange occurs by two mechanisms, dependingon the concentration of carbonate (or bicarbonate) ion in solution. Onemechanism involves the ions [CO(NH,)~,HCO,,H,O]~+ and HC0,-, and theother the equilibrium :H,O + [CO(NK,),HCO,H,O]~~ G+ CO(NH,),(H,O),+~ + HC0,-In a later paper, the effects of ionic strength on the rate of the ion-dipolemechanism and the ion-ion mechanism were in~estigated.~~ In the con-centration range for which the ion-dipole reaction is operative, the equationof Amis and Jaff6 accurately described the results up to ionic strength 1.0.For the ion-ion interaction, the Bronsted relation did not describe the effectof the ionic strength on the rate of reaction.The exchange reaction between water as H2180 and Cr(H20),+, is firstorder in Cr(IrI), and the rate increases with concentration of the anionpi-e~ent.~l With C1- as the only anion present, the rate of exchange of watergreatly exceeds the rate of formation of the complex ion [Cr(W20),C1]2+.The rate of exchange is markedly increased by Cr2+, and only slightly byCr,0,2-, and is induced by the reaction between Ce(1v) and Cr(r1r).Theresults suggest that electron transfer between Cr(I1) and Cr(1rI) is rapid, andthat exchange of water takes place a t the Cr(I1) stage. The exchangebetween free and bound water in the complex ion [Co(NH,),H20I3+ wasfound to be of first order with respect to the complex ion, and was independentof acidity. A dissociation mechanism is favoured over a bimolecularmechanism involving water as the second reacting speciesg2Bernstein and Katz 93 have measured the gas-phase exchange betweenfluorine and the interhalogen compounds ClF,, BrF,, and IF,.Homo-geneous exchange occurs at a measurable rate about loo", probably by$ 5 W. R. Icing, Jr., and C. S. Garner, J . Amer. Chem. SOC, 1952, 74, 5534.b G B. West, .I., 1952, 3116.8 7 S. S. Jones and F. A. Long, J . Phvs. Chacin., 1952, 56, 25. ** G. M. Harris and D. R. Stranks, Tians. Faraday SOC., 1952, 48, 137.89 D. R. Stranks, Trans. Faraday Soc., 1952, 48, 911.99 E. S. Amis and G. Jaffe, J. Chem. Phvs., 1952, 10, 598.91 R. A. Plane and H. Taube, J. Phys. Chew., 1952, 56, 33.9: A. C. Rutenberg and H. Taube. J. Chenz. Phys., 1952, 20, 825.KI R.I3. Bernstein and J. J. KaEz, J . Phys. Chem., 1952, 66, 88646 GENERAL AND PHYSICAL CHEMISTRY.reversible dissociation for the chlorine and iodine compounds, and by anassociation mechanism for BrF,.The exchange of 1311 as sodium iodide has been investigated for the follow-ing compounds : (i) ally1 iodide in ethyl alcohol; 94 (ii) iodobenzene insec.-octyl alcohol ; 95 (iii) 9-iodophenol in octan-2-01; 96 (iv) 2-iodo-naphthalene in acetyl alcohol; 97 (v) ethyl iodide in acetonitrile 9* and9-iodonitrobenzene in octan-2-01 and in acet~nitrile.~~Exchange between periodate and iodine loo is slow compared with thatreported lol for exchange between iodate and iodine. The rate varies withacidity in the same way as the chemical reaction between iodide ion andperiodate, and the temperature coefficients for the two processes are similar,suggesting similar mechanisms.The exchange between iodate and periodateis very slow and is catalysed by molecular iodine.Non-isoto9ic Reactions in Solution.- (a) Electron transfer reactions inaqueozcs solution. Dainton lo2 has reviewed both thermal and photochemicalelectron transfers between various cations and anions, on the one hand, andwater, hydrogen peroxide, and formic acid, on the other.Two independent studies have been made of the kinetics of the reactionTI(III) + 2Fe(11) ---+ Tl(1) + 2Fe(111).lo3 The hydrolysed forms T10H2+and TIOf take part in rate-controlling electron transfers from Fe(I1). T~(II)is suggested as an intermediate in the process.Carter and Davidson lo4 have shown that the oxidation of ferrous ion bybromine in a two-stage process involves the radical-ion Br2-.The kineticsof the reaction agree with the scheme :Fez+ + Br,-Br,- + Fe2-b +Fe+3 + 2Br-Fe3+ + Br- + Br2-Fudge and Sykes lo5 have shown that the thermal electron transfer betweenFe(m) and iodide ion probably occurs by the sequence : Fe3+ + I- FeI2+,FeI2+ + I- Fe2+ + I,-, and Fe3 + I,- Fe2+ + I,. Ferrous ioninhibits the reaction, by competition with ferric ions for the radical-ion 1,.In a second paper, Sykes loG relates the retarding effects of various anionson the process to complex-ion formation with Fe(m), and from the kineticdata, deduces the association constants for formation of the complex ionsFeOH2+, FeSO,+, and FeNO,,+.Adamson G3 has examined the kinetics of oxidation of cyanide ion byFe(CN)G3-, and suggests a mechanism involving the radical ion (CN),-.A preliminary account has appeared of the reactions of Hg(1) and Hg(r1)with formic acid.lo7 The rate-controlling steps involve electron transferfrom formate ion to Hg(1) or Hg(II), with formation of the free radical94 S.May, P. Daudel, J. Schottey, M. Sarraf, and A. Vobaur6, J . Chiin. phys.,1952, 49, 64.96 S. May, M. Sarraf, A. Vobauri., and P. Daudel, Compt. rend., 1951, 233, 744.913 S. May and B. Girandel, ibid., 1952, 234, 326.97 I. EstellCs and S. May, ibid., p. 433.98 S. May and B. Girandel, ibid., 1952, 235, 953.100 M. Cottin, M. Haissinsky, and D. Peschanski, J. Chirn. phys., 1951, 48, 500.101 0.E. Myers and J . W. Kennedy, J . Amer. Chem. SOL, 1950, 72, 89.102 F. S, Dainton, J . , 1952, 1533.103 C. E. Johnson, Jr., J . Amer. Chem. SOC., 1952, 74, 959; 0. L. Forchheimer and R. P.lo4 P. R. Carter and N. Davidson, J . Phys. Chew., 1952, 56, 877.106 A. J . Fudge and K. W. Sykes, J., 1952, 119.lo6 K. W. Sylres, ibid., p. 124. lo' A. R. Topham and A. G. White, ibid., p. 105.gs I d e m , ibid., 1952, 234, 2280.Epple, ibid., p. 5772BETTS et al. : THE KINETICS OF HOMOGENEOUS REACTIONS. 47H-CO*O*. Another thermal electron-transfer reaction leading to freeradicals is that between Fe(I1) and the isopropylcumene and tert.-butyl-cumene hydroperoxide.108 The rate-controlling step is Fe2+ + R-O*OH --+ Fe3+ + ROO- + OH-.Evidence for a two-electron transfer process has been given by Haight andSager,lo9 arising from their studies of the molybdate-catalysed reduction ofperchlorate ion by Sn(I1).The reaction is very complex, and appears toproceed via quadrivalent molybdenum formed by two-electron transferfrom Sn(I1).In continuation of his studies ofoxygen-transfer reactions involving the use of l80, Taube and his co-workers 11* have found that only part of the oxygen in HOCl is transferred tosulphite in this reaction to form C1- and SO,2-. He suggests two modes ofattack of the hypohalite on SO,,- : C10- + SO,,- -+ C1- + ;OC1- + SO,,- + Hf + ClSO,- + OH-, followed by ClSO,- + H20 --+SO4,- + 2H+ + 2C1-. In the first, oxygen transfer is direct, whilst in thesecond the oxygen atom transferred to the sulphite is derived from thesolvent.It was also shown that two atoms of oxygen are transferred to502- per molecule of hydrogen peroxide reactinglll When the samereaction is catalysed by molybdate, only one atom is transferred from H20,to SO,2-. In the former case, permonosulphurous acid is postulated as anintermediate. In the other reaction, oxygen atoms may be transferred frompermolybdic acid to SO,,-, with rupture of the 0-0 bonds in the per-molybdate. Transfer of oxygen from Mn0,- to SO,,- is very inefficient, andTaube suggests that pennanganate acts mainly by electron transfer.In alkaline solution, pentathionate ion decomposes to thiosulphate,according to 2S,0,2- + 60H- + 5S2OS2- + 3H20.112 The reaction is offirst order in S,0G2- and OH-, and displays a kinetic salt effect corre-sponding to that predicted for a reaction between a singly and a doublychanged anion.The slow stage in the reaction is postulated as S,0G2- +OH- --+ S2032- + HOS*S,O,-, followed byHOS=S,O,- + OH-+ S(OH), +S2032-.Peschanski 113 has made a detailed study of the kinetics of the oxidationof I, by periodate ion. The mechanism proposed involves successive oxygentransfers from periodate to I-, 10-, 10,- (or HOI and HIO,). Iodide ionis present at low concentrations provided by the hydrolysis of iodine.Abel 114 has discussed the mechanism of the permanganate-oxalatereaction in terms of the relative reactivities of the oxalate ion (C02)?2-and the radical-ion (C02)2-. He suggests that reaction of Mn in oxidationstates 6, 5, 4, and 3 is fast with either reagent, and that reaction of Mn04- isslow with (C02),2-.The ion-radical is thus the main catalyst, which slowlyaccumulates during the induction period. Catalysis by Mn(I1) is due toreaction with Mn04- to give intermediate oxidation states, which then reactrapidly with (C02)22- to give (C02),-. Malcolm and Noyes 115 suggest that(b) Reactions of oxygenated anions.lo8 R. J. Orr and H. L. Williams. Canud. J. Chem., 1952, 30, 985.log G. P. Haight, Jr., and W. F. Sager, J . Amer. Chem. SOC., 1952, '94, 6056.112 J. A. Christiansen, W. Drost-Hansen, and A. E. Nielsen, Acta Chem. Scand.114 E. Abel. Monutsh., 1952, 83, 695.116 J . M. Malcolm and R. M. Noyes, J . Anrev. Chem.SOC., 1962, 74, 2769.J. Halperin and H. Taube, ibid., p. 375. ll1 Idem, ibid., p. 380.1952, 6, 333. 113 D. Peschanski, J. Chim. phys., 1951, 48, 48948 GENERAL AND PHYSICAL CHEMISTRY.the kinetics of the Mn0,--oxalate reaction are consistent with a reactionbetween Mn0,- and an oxalate complex of Mn(II), to give Mn(vz), whichis rapidly reduced to Mn(1Ix) by either Mn(I1) or oxalate. The subsequentreaction involves decomposition of Mn( 111) complex oxalates, according to themechanism suggested by Taube.l16The kinetics of the reaction between Mn(I1) and periodate have beeninvestigated by Waterbury, Hayes, and Martin.l17 The scheme proposed toaccount for some aspects of their kinetic results involves oxidation-reductionequilibria between the pairs Mn(n)-MnO,-, Mn(Iv)-Mn(II), accompanied byreaction between Mn(1r) and Mn(v1) to form Mn(1v).With these postulatedequilibria, together with the assumption that [M~(II)] > [M~(III)] > [Mn(~v)],an expression was obtained which fits the experimental rate law, R =k[Mn0,-]0'5[Mn(~~)][H510,].A study of the reaction between nitrous acid and hydroxylamine to formnitrous oxide and water has been made by Bothner-By and Friedman.l18By examining the isotopic composition of the products formed from I5N-enriched nitrite and l*O-enriched water, they conclude that the earliermechanism involving NOH (nitroxyl) is untenable. Hyponitrous acid(HO-N:N*OH) is proposed as the intermediate in neutral solution, and N-nitrosohydroxylamine (HO-NH-NO) as the intermediate in acid solution.A mechanism based on kinetic studies has been proposed for the de-composition of nitrosyldisulphonate ion in water.lls It involves theformation of OH radicals as an intermediate by reaction of hydrogen-ionwith (S0,)2NO*2-, followed by reaction of OH with nitrosyl disulphonateion to produce N20, nitrous acid, and sulphate ion.Lister 120 has shown that the decomposition of HOCl is a second-orderreaction, and suggests that the rate-controlling step involves dispro-portionation of HOCl to chloride and chlorite ions. The reaction HOCl $-OC1- + C1- + Hf + C10,- also occurs, but is much slower than the reactionbetween un-ionised HOCl molecules. Oxygen is generated by a first-orderreaction, possibly by reaction of HOCl and water to form H,02, followed bya rapid reaction between OC1- and H20,.Taube 121 has published a comprehensivereview of the rates and mechanisms of substitution in inorganic complexes insolution.He stressed the importance in this connection of the electronicstructure of the complex ion.Bjerrum and Poulsen 122 have reported a preliminary study of the rate offormation of several types of complex ions, ,e.g., the reaction of Ni(11) withdimethylglyoxime and the reaction of Fe(II1) with thiocyanate. By usingmethanol as the solvent, they were able to examine the kinetics of suchreactions at temperatures down to 180" K, where the rates are no longer" instantaneous." The results support the idea of a connection betweenthe rate of complex formation and the valency and electron configuration inthe transition elements ; thus for the same electron configuration, e.g.,(c) Reaction of complex ions.116 H.Taube, J . Amev. Chenz. SOC., 1948, 70, 1216; 1947, 69, 1418.11' G. R. Waterbury, A. M. Hayes, and D. S . Martin, Jr., ibid., 1952, 74, 15.118 A. Bothner-By and L. Friedman, J . Chem. Phys., 1952, 20, 459.120 M. W. Lister, Cauaad. J . Chew., 1962, 50, 879.lZ1 H. Taube, Chem. Reviews, 1952, 50, 69.132 J. Bjerrum and K. G. Poulsen, Natwre, 1952, 189, 463.J. H. Murib and D. M. Ritter, J . Amer. Chem. Soc., 1952, 74, 3394BETTS et a2. : THE KINETICS OF HOMOGENEOUS REACTIONS. 49Feat and Mn2+, the higher valency state reacts more slowly. For equalvalency, ions with half-completed or completed electron shells give a muchhigher rate of complex formation.Approximate measurements of thekinetics indicate that most reactions leading to formation of complex ionsare instantaneous at room temperature because of a high value of thefrequency factor rather than a low value of the activation energy.Wilmarth and Baes 123 have shown that the paramagnetic complex ionsof Cr(m) with water, thiocyanate, urea, ammonia, and other ligands willcatalyse the conversion of para- to ortho-hydrogen. By using Wigner'sformula relating the approach distance of the paramagnetic ion to the rateof the conversion, deductions regarding the size of these ions were made. Itappears likely on this basis that hydrogen must penetrate through most ofthe atoms in the ligand groups surrounding the central Cr(m) ion.The mechanism of the acid-catalysed aquation of the complex ionCo(NH,),CO,+ has been investigated, by means of H2180.124 By analysingthe l*O content of the complex ion before and after aquation, it was shownthat at least 99% of the change leaves the Co-0 bond intact.have measured the rates of hydrationand hydrolysis of a series of C-substituted acetato-pentammino-cobalt (111)ions in solution.The rates of both processes were dependent on the basestrength of the acid ligand, but independent of its size. The authors concludethat the incoming groups approach the complex from a position opposite tothe outgoing groups, or that substitution occurs by dissociation. In asecond paper,126 the rate of aquation of the complex ions [Co(AA),Cl,]+were measured, where AA represents compounds of varying complexity,containing two amino-groups.Increased crowding around the centralatom, arising from longer hydrocarbon skeletons in AA, did not retard thereaction, which suggests that aquation does not occur by a seven-co-ordinatedSN2 mechanism, but rather by a S N 1 mechanism in which the activatedcomplex is penta-co-ordinated.Price 127 has examined the kinetics of the metal-ion catalysed decarboxyl-ation of acetonedicarboxylic acid, and has shown that the undissociatedacid, the univalent anionic form, and the bivalent enol anion react at differentrates. Hesuggests that the catalytic activity of cations is due to chelation of theactivated complex by the metal ion.In support of this, a relation was foundbetween the catalytic coefficient and the association constant of the chelatecompounds formed by these ions with nialonate ion. Further, ions whichdo not form chelate compounds display no catalytic effects.Brandt and Gullstrorn 12* have calculated the stabilities of some 5-substituted 1 : 10-phenanthroline-Fe(11) complexes from the rates of forrn-ation and dissociation of the complexes, and also from equilibribium data.The stabilities of the complex formed with Fe(I1) decreases in the ordermethyl, phenyl, chloro, and nitro, Values for the equilibrium constantsdetermined by the two methods for each system were in good agreement.Basolo, Bergmann, and PearsonThe last process is most strongly influenced by metal ions.123 W.K. Wilmarth and C. F. Baes, Jr., J. Chem. Phys., 1952, 20, 116.184 J. P. Hunt, A. C. Rutenberg, and H. Taube, J . Anzer. Chem. SOC., 1952, 74, 268.125 F. Basolo, J. G. Bergmann, and R. G. Pearson, J . Phys. Cheun., 1952, 58, 22.126 R. G. Pearson, C. R. Boston, and F. Basolo, J . Amev. Chem. Soc., 1952, 74, 2943.127 J . E. Prue, J., 1952, 2331.128 W. W. Brandt and D. K. Gullstrom, J . Amer. Chem. SOC., 1952, 74, 353250 GENERAL AND PHYSICAL CHEMISTRY.(d) Reactions of hydrogen peroxide. During the year, a review hasappeared of the reactions of hydrogen peroxides with " donor particles,''e.g., Br03-, IO,, I-.129 At least three papers have been published relatingto the source of oxygen evolved from the decomposition of hydrogen peroxidein aqueous solutions containing a variety of other reagents including Fe(Ir),Fe(m), Ce(Iv), MnO,-, Br2.130-132 In all cases examined, oxygen comescleanly from hydrogen peroxide, indicating that the 0-0 bond in the per-oxide remains intact.Measurements of the relative rates of evolution of1 8 0 and l60 have led to several interesting speculations regarding thedetailed mechanism of some of the reactions; thus, Cahill and Taube 131suggest that a two-electron transfer between Fe(I1) and H202 is an importantchain-carrying step in the Fe( 11) -induced decomposition of this substance.Reactive isomers of H02-, arising from decomposition of FeO*OH2+, havebeen suggested as intermediates in this reaction. 1339 134The reaction between nitrous acid and hydrogen peroxide has beenstudied by Halfpenny and R0bins0n.l~~ The scheme proposed to accountfor the kinetics involves peroxynitrous acid (H0,NO) as an intermediate,which decomposes to HO and NO,, followed by reaction of these speciesto form nitric acid.Shilov also suggests peroxynitrous acid as the inter-mediate in this r e a ~ t i 0 n . l ~ ~The reduction of sodiumanthraquinone-2-sulphonate by Ti3+ is a composite reaction involvingsimultaneous reduction of the semiquinone, the semiquinone dimer, and amolecular complex of one molecule of quinone and one of semiquinone.The ratio of reduction of the quinone itself is insignificant compared withthese other react ions. l3Turgeon and LaMer 138 have published a comprehensive account of thekinetics of formation of the carbinol of crystal-violet. The reaction followsquantitatively the Bronsted-Debye law for primary kinetic salt effects.The energy of activation is 0.9 kcal./mole higher in 40% acetone-water thanin pure water.This is contrary to the decrease expected due to the loweringof the coulombic activation energy in a solution of lower dielectric constant.A specific solvent effect may be involved, resulting in preferential solvation ofthe crystal-violet cation by the organic solvent rather than by water.Derbyshire 139 has reviewed recent results relating to the rates of bromin-ation and iodination by hypobromous and hypoiodous acid in acid solutions,and suggests that the active entity in such solutions is the halogen cationco-ordinated with a molecule of water, rather than siinply a cation hydratedby electrostatic solvation.CH,I + Br- have been investigated in ethylene glycol for comparison with(e) Kinetics qf other reactions in sobution.The kinetics of the non-isotopic exchange reaction CH3Br + I-lZ9 J.0. Edwards, J . Phys. Chem., 1952, 56, 279.130 C. A. Bunton and D. R. Llewellyn, Research, 1952, 5, 142.131 A. E. Cahill and H. Taube, J . Amer. Chem. Soc., 1952, 74, 2312.132 M. Dole, D. P. Rudd, G. R. Muchow, and C. Comte, J . Chem. Phys., 1952, 20, 961.133 V. S. Anderson, Acta Chem. S c a d . , 1952, 6, 1090.13p J. A. Christiansen, ibid., p. 1056.135 E. Halfpenny and P. L. Robinson, J . , 1952, 928.1 3 ~ E. A. Shilov, Chem. Abs., 1952, 46, 2946.137 C.E. Johnson, Jr., and S . Winstein, J . Amer. Chem. Soc., 1962, 74, 3105.158 J. C. Turgeon and V. K. LaMer, ibid., p. 5988.139 D. H. Derbyshire, Research, 1952, 5, 240BETTS et Ul. : THE KINETICS OF HOMOGENEOUS REACTIONS. 51earlier measurements of the same system in water, methanol, and acetone.140The rates in this solvent were three times greater than in methanol, andfour times as great as in water. Values of AG and A S for the equilibrium, asreflected in the ratio of the rate constants, are -1-62 kcal./mole and 17.3cal. mole-1 deg.-l, respectively.Glew and Moelwyn-Hughes have investigated the kinetics of the alkalineand acid hydrolysis of methyl fluoride in water.141 The first-order reactionwith water is retarded by hydrogen fluoride and by methanol, and kineticanalysis suggests the scheme CH3F CH3*F CH3*OH + HF. Thealkaline hydrolysis is a second-order process, vix., CH,F + OH-+ CH,*OH +F-.The energy of activation for alkaline hydrolyses of methyl bromide andfluoride are the same within experimental error, and thus the difference inbond energies of some 30 kcal. is not reflected in this quantity. The authorssuggest that the solvent plays an important part in these reactions, and thatthe energy of activation refers to the escape of the ion from its solventsheath. For the first-order reaction, this analysis suggests a simultaneousattack by six water molecules surrounding the methyl halide, with re-organisation necessary for the ionisation of a seventh water molecule.The rate-determining step is then the simultaneous ionisation of water andattack on CH3X by OH- so formed.Bell and Clunie 142 have described a thermal method for following fastreactions in solution, which they have used to investigate the kinetics ofhydration of a~eta1dehyde.l~~ The results do not support the view 144 that thereaction mechanism involves simultaneous attack by acidic and basic species.Meadows and Darwent 145 have shown that in neutral and buffered solu-tions, hemiacetal is the only important product in the reaction betweenacetaldehyde and methanol ; in strongly acid solution, acetal is formed nearlyquantitatively. The former reaction exhibits general acid-base catalysis,whilst the latter is catalysed only by hydrogenSeveral papers have appeared during the year relating to the kinetics ofthe reaction of formaldehyde in aqueous solution with urea 147, 148 N-methyl-urea,149 and phenol.lMBell and Skinner 151 have investigated the kinetics of depolymerisation ofparaldehyde in ethereal solutions of proton acids and Lewis acids.TheLewis acids (e.g., BCl,, SnCl,, TiC1,) showed in general more marked catalyticactivity than even a very strong proton acid such as HBr. Moreover,these substances appeared to act as catalysts without the co-operation ofproton acids. The reactions were initially of first order in paraldehyde andsecond-order in catalyst.Bell and Goldsmith 152 have shown that the iodination of 2-ketocyclo-j4* J. S. McKinley-McKee and E. A. Moelwyn-Hughes, J ., 1052, 838.141 D. N. Glew and E. A. Moelwyn-Hughes, Proc. Roy. SOC., 1952, A , 211, 254.142 R. P. Bell and J . C. Clunie, ibid.. 1952, A , 212, 16. lp3 Idenz, ibid., p. 33.144 C. G. Swain, J . Anter. Chew,. SOC., 1950, 72, 4578.145 G. W. Meadows and B. de B. Dai-went, Canad. J . Chem., 1952, 30, 501.146 B. de B. Darwent and G. W. Meadows, Trans. Faraday SOC., 1952, 48, 1015.147 J. I. de Jong and J . de Jonge, Xec. Tvav. chirn., 1952, 71, 643, 890.148 G. Smets and A. Borzee, J . PoJyiner Sci., 1952, 8, 371.14s L. E. Srnythe, J . Anaey. Chew. Soc., 1952, 74, 2713.150 L. M. Oebing, G. E. Murray, and R. S. Schatz, Igzd. Eng. Chew., 1052, 44, 354, 366.151 R. P. Bell and F. G. Skinner, J . , 1952, 2955.152 R. P. I3ell and H. L. Goldsmith, Pvoc.Roy. Soc., 1958, A , 210, 32252 GENERAL AND PHYSICAL CHEMISTRY.hexanecarboxylic acid is of first order with respect to the ester, and zeroorder in iodine, The reaction is catalysed by water and by anions of carb-oxylic acids. Catalytic constants for four carboxylic acids obey a relationof the Bronsted type. This ester is iodinated 100--400 times more slowlythan the &membered analogue. This result is unexpected on the basis ofring-strain considerations, which suggest that the 6-membered ring should bethe more reactive of the two compounds.Isotope Effects.-At least three papers have appeared during the year,which consider the theoretical aspeets of the effects of isotopic substitutionon the rates of chemical reacti0n.1~~ In some cases, an arbitrary choice ofmodel appears necessary to account for the experimental results.154The isotope effect in the hydrolysis of triphenylsilane in moist piperidinehas been studied with tritium.155 The ratio k ~ / k ~ of the rate constants forthe isotopic reactions was 0.8, whilst earlier work with deuterium gaveThe 12C-12C bond in carboxyl-labelled malonic acid is broken about 10%more frequently than the 12C-14C bond by decarboxylation at 138".15'This is an intramolecular isotope effect.The temperature coefficient of theintermolecular isotope effect for the same reaction is zero 158 in the tempera-ture range 137-196". The intermolecular isotope effect is slightly greaterin the decarboxylation of [C02H-14C]malonic acid than it is for the corre-sponding reaction with [a-14C]-acid.159Stevens, Pepper, and Lounsbury I6O have measured the relative isotopeeffects of 13C and 14C arising from decarboxylation of mesitoic acid.Byusing 0.8 mole-% 14C-compound labelled in the carboxyl position, they wereable to measure W02, 13C02, and 14C02 in a mass spectrometer. The14C isotope effect was more than twice the 13C isotope effect (1.101 and 1.038respectively) which is unexpected in view of current theories. 153The 12C-carboxyl group 154 is lost as 12C02 about 10% more frequentlythan in the %-groups in both a-naphthyl- and phenyl-malonic acid. De-carboxylation of 1%-labelled anthranilic acid,161 either by heating it aboveits melting point, or by boiling it in water, shows no isotope effect.This isconsidered explicable on the basis of the mechanism proposed, which in-volves a proton attack on the a-carbon of the zwitterion.The relative isotope effects in the thermal decomposition of oxalic acidhave been investigated with l4,C and 13C; the isotopes were measured byradiochemical and mass-spectrometric technique, respectively. The 13Cisotope effect was about one-half of the 14C isotope effect. A small tempera-ture coefficient was noted in the region 80-100".162 Bunton and Llew-ellyn have investigated 13C isotope effects in the chemical reactionsKDIFZN = 6.156153 J. Bigeleisen, Canad. J. Chem., 1952, 30, 443; J . Phys. Chem., 1952, 56, S23;H. Eyring and F. W. Cagle, Jr., ibid., p. 589.154 A. Fry and M. Calvin, ibid., p.901.155 L. Kaplin and K. E. Wilzbach, J. Amer. Chem. SOC., 1952, 74, 6152.166 G. E. Dunn, H. Gilmour, and G. S. Hammond, ibid., 1951, 73, 4499.157 P. E. Yankwich, E. C. Stivers, and R. F. Nystrom, J . Chem. Phys., 1952,20,344.158 J. G. Lindsay, A. N. Bourns, and H. G. Thode, Canad. J . Chem., 1952, 30, 163.159 G. A. Ropp and V. F. Raaen, J. Amer. Chem. SOC., 1952, 74, 4992.160 W. H. Stevens, J . M. Pepper, and M. Lounsbury, J. Chem. Phys., 1952, 20, 192.161 Idem, Canad. J . Chem., 1952,30, 529.162 A. Fry and M. Calvin, J. Phys. Chem., 1952, 56, 897.163 C. A. Bunton and D. R. Llewellyn, Research, 1952, 5, 443BETTS et al. : THE KIXETICS OF HOMOGENEOUS REACTIONS. 53between oxalic acid and bromine, hydrogen peroxide, potassium perman-ganate, and KMn0,-Mn2+. Formation of l2CQ, is preferred to that of13C02, but the effect varies from 1-8 to 3-6%, depending an the reagent used,and appears to be related to the mechanism of attack on oxalic acid by thesereagents.The thermal deammoniation of phthalamide shows an isotope effect,14NH, being formed more readily than 15NH,.16, The results are related tothe effect of isotopic mass of the nitrogen atom in the C-N bonds which areboth broken and formed in the reaction.Schmitt, Myerson, and Daniels have shown that an isotope effect existsin the hydrolysis of urea by u r e a ~ e .1 ~ ~ 12C02 is evolved 1% more readilythan 13C0,, and 3.2% more readily than 14C02.Ropp and Raaen 166 have examined the efiect of ring substitution on theisotope effect in hydrolysis of ethyl [C02Et-14C] benzoates.The isotopeeffect may be greatest in the hydrolysis of those esters in which the largestcontributions to the normal state are made by resonance forms of the type+ R:C,H,YC(OEt)*O-. Other organic systems for which isotope effectshave been detected include (i) the reaction between 14C-labelled benzo-phenone and 2 : 4-dinitrophenylhydrazine ; 167 (ii) Cannizzaro reaction of14C-labelled formaldehyde ; 168 (iii) reaction of 14CH20 with dimedone ; 169and (iv) reaction of [l-14C]acetonc with alkaline hypoiodite.170 The lastreaction is of particular interest, since the isotope effect appears to beopposite to that ordinarily found : the I2C-l4C bond is more easily brokenthan the I2C-l2C bond.Yankwich and McNamara 171 find no isotope effects on the equilibriuniCo(en),CO,- + H*CO,- HCO,-- + Co(en),*CO,+, but find that thelighter isotopes of carbon are exchanged more readily than the heavier.Stranks and Harris 172 have observed just the reverse behaviour in thesystem Co(NH,),CO,' : 14C becomes concentrated in the anion at equili-brium, while no discrimination is found between 12C and 14C in the kineticsof the process.Photochemistry.-Light Sources and A ctiizometers.-The influence ofseveral variables on the output of light of wave-length 2537 A from a quartz-mercury vapour lamp of the low-pressure type has been studied by Heidt and130yles,l~~ who conclude that the output is particularly sensitive to theexternal temperature and is a maximum at about 45".The uranyl oxalate actinometer has been shown to be suitable for measur-ing intensities up to 1000 times the highest previously used.174 The quantumyields, at 3650 A, for the photolysis of seven aromatic diazonium salts 175 havebeen accurately measured and found to lie in the range 0.20-0.74.Thel C 4 F. W. Stacey, J . G. Lindsay, and A. N. Bourns, Canad. J . Chon., 1952, 30, 135.165 J. A. Schmitt, A. L. Myerson, and 1;. Daniels, J . Phys. Chem., 1952, 56, 917.166 G. A. Ropp and V. F. Raaen, J . Chenz. Phys., 1952, 20, 1823.167 F. Brown and D. A. Holland, Canad. J . Chem., 1952, 30, 438.168 A. M. Downes and G. M. Harris, J . Chem. Phys., 1962, 20, 196.160 A. M. Downes, Austral. J . Sci. Res., 1952, 5, A , 521.170 A. Roe and E. L.Albenesius, J . Amer. Chem. SOC., 1952, 74, 2402.171 P. E. Yankwich and J. E. McNamara, J . Chem. Phys., 1952, 20, 1325.172 D. R. Stranks and G. W. Harris, J . Phys. Chem., 1952, 56, 906.173 L. J. Heidt and H. B. Boyles, J . Amer. Chem. Sot., 1951, '73, 5728.174 M. I. Christie and G. Porter, Proc. Roy. SOC., 1952, A , 212, 390.175 J. de Jonge, R. Dijkstra, and G. L. Wiggerink, Rec. Trav. chinz., 1952, 71, 84654 GENERAL AXD PHYSICAL CHEMISTRY.photolysis of phenylaminobenzenediazonium sulphate , $ = 0.36, has beenproposed as an actinometer for 3650 A. It has the merits (i) that 100%decomposition gives the theoretical amount of nitrogen, (ii) that the nitrogenproduced may be blown off by a stream of carbon dioxide and used as adirect measure of the light absorption, and (iii) that the diazonium salts havea high extinction coefficient and lOOyo absorption of light is easily achieved.The malachite-green leucocyanide actinometer has been reinvestigated.176An improved method of preparation has been described, and it has beenconfirmed that at all wave-lengths the quantum yield is 1.00, provided theintensity is sufficiently low and the stirring rate sufficiently high.A new type of Draper-Bunsen actinometer has also been described.177Direct Photochemical Reactions.-(a) Ketones and aldehydes.The photo-lysis of keten has been the subject of two papers. By means of 13C0 it hasbeen found that the CH, formed by the rupture of the keten moleculereadily combines with carbon monoxide to re-form keten.A study of theproducts of the reaction between CH, and (CHD), indicates the inter-mediate formation of the trimethylene diradical which then rearranges togive pr0py1ene.l'~ Norrish and his co-workers 179 have investigated theflash photolysis of keten and discuss attempts to obtain the absorptionspectrum of the methylene radical.Further evidence for the complete free-radical photolysis of acetonevapour, at all temperatures, and wave-lengths between 2300 and 3400 A, hasbeen published.180-182 Using radioactive l3lI3 as radical " catcher,"Martin and Sutton have investigated the photolyses of acetone lS2 and ethylmethyl ketone.183 They find that at 3130 A the relative rates of the twopossible primary radical processes, (1) COMeEt I_, MeCO + Et and (2)COMeEt + EtCO + Me, is RJR, = 21 6 2 compared with Blacet andPitts's value of 40, while at 2537 A the ratio is considerably lower.The photolysis of diethyl ketone vapour has been extensively investigatedbetween 25" and300" by Kutschke and by Wijnen and Steacie.Their results,which are in good agreement, are published in a joint paper and supportthe following mechanism :( 1 )( 2 ) 2C2H5. -+ C,Hlo(C,H,),CO + hu 4 C2H5*CO* + C,H,* +X,H,- + CO(3)(4)2C2H5. --+ CZH4 + CzH,CZH,. + (C,H,),CO _3 C&, + .C&4*CO*C&,,( 7 ) .C,H,*CO*C,H, + C2H4 + CO + CZH,.The results indicate that k3/k2 - 0.10 at all temperatures, i.e., E3 - E, = 0,E , - = 7-4 kcal./mole, and that reaction (7) only becomes important athigh temperature and/or low intensity.The photolysis of (CH,*CD,),COhas confirmed this mechanism and has provided the additional inform-176 J. G. Calvert and H . J. L. Rechen, J . Amer. Chem. SOC., 1952, 74, 2011.177 E. Crerner and H. Margreiter, 2. physikul. Chem., 1952, 199, 90.178 G. B. Kistiakowsky and W. L. Marshall, J . Amer. Chem. SOC., 1952, 74, 88.1 7 9 K. Knox, R. G. W. Norrish, and G. Porter, J . , 1952, 1477.180 S . W. Benson and C. ?V. Falterman, J . Chern. Phys., 1952, 20, 201.181 D. H. Volman and W. M. Graven, ibid., p. 919.182 G. R. Martin and H. C . Sutton, Trans. Furaday Soc., 1952, 48, 812.183 Idem, ibid., p. 823.184 K. 0. Kutschke, M. H. J. Wjnen, and E. W. R. Steacie, I . Amev. Chem. SOC. 1952,74, 714. 185 M. 13. J . Wijnen and E. W. R.Steacie, Canad. J . Chefn., 1951, 29, lb92BETTS et al. : THE KINETICS OF HOMOGENEOUS REACTIONS. 55ation that E , - 17 kcal./mole, that the disproportionation reaction occursby a head-to-tail mechanism :and that the energy of activation for reaction (4) is greater for the abstractionof a methyl hydrogen than that of a methylenic hydrogen atom.In the photolysis of di-n-propyl ketone, Masson lS6 has concluded thatabout 50% of the activated molecules ultimately decompose by one of thefollowing two processes :CH,*CD,. + CH,*CD,* --+ CH,CD,H + CH,:CD,> C,H, + CH,.COC,H,(C,H,*CO*C,H,)*(2) 2C,H, + COFor the reaction C,H, --+ C,H, + CH,, E = 20 kcal./mole was obtained.At 113", 17% of the propyl radicals disproportionate and 83% combine togive n-hexane.The photolysis of propaldehyde has been studied with steady and inter-mittent light,lS7 and Blacet and Pitts lS8 have deduced the relative im-portance of four possible primary processes from the products obtained inthe presence and the absence of iodine.In the photolysis of the hydrogenhalides the energy of the light absorbed may be considerably greater than theenergy required to break the hydrogen-halogen bond.Part of the excess ofenergy will appear as kinetic energy of the hydrogen atom* and might beexpected to affect the rates of the reactions, (1) H + HI -+ H, + I, and(2) H + I, --+ HI + I. However, in the presence of sufficient inert gas theexcess of energy will be removed by collision before these reactions occur.Schwarz and his colleagues 189 have interpreted, on the basis of this theory,their results on the photolysis of hydrogen iodide, deuterium iodide, andhydrogen bromide in the presence of helium and hydrogen.They find that,in the presence of inert gas, k,/k, is reduced to a limiting value which isindependent of the nature of the inert gas, and for thermal hydrogenatoms, E, - El f 4.5 -+ 0.8 l<cal./mole.Burns and Dainton lgo have made a complete investigation of the photo-chemical formation of carbonyl chloride in the presence and absence ofnitrosyl chloride as inhibitor, using light of wave-length 3660 A, between25 and 55". Their results confirm the Bodenstein mechanism and thefollowing values for the individual frequency factors ( A ) and energies ofactivation (E) have been obtained :(b) Reactions involving halogen atoms..,log,, A E(1. mole-* sec.-l) (kcal. mole.-')1% A,IA,- c1, + h v ---j 2CI co -b c1-4- COClCOCl--+ co + c1COCl + c1, --+ coc1, + C1 ............C1 + NOCl-+ XO + C1, ............ 10-06 1-06- ............................................. E, - E ,..................... = 6.31 = 2-8062.96COCl + c1--+ co + c1, ............ 11.6 0.83COCI + NOCl+CO + C1, + NO 10.68 1.14I{9.4> {(or COCI, + NO)186 C. R. Masson, J . Amer. Chent. SOC., 1952, 74, 4731.1 8 7 R. E. Dodd, J . , 1952, 878.188 F. E. Blacet and J . N. Pitts, J . Amey. Chew,. SOC., 1952, 74, 3382.1 8 9 H . A. Schwarz, R. R. Williams, and W. H. Hamill, ibid., p 6007.190 W. G. Burns and F. S.Dainton, Trans. Faraday SOC., 1952, 48, 39, 52. * Such atoms are designated as " hot " by the authors56 GENERAL AND PHYSICAL CHEMISTRY.The results lead to the following heats of reaction :CO + C1+ COCl + 6.3 kcal.COCl + C1-> COC1, + 74.9 kcal.The big difference in thc magnitude of the C-Cl bond strengths is in accordwith the high energy of reorganisation for the change : >C=O --+ lCC0.The authors have discussed their results in terns of the theory of absolutereaction rates.Other photochemical reactions involving halogen atoms which have beeninvestigated are the reaction between iodine monochloride and hydrogen,lglchlorination of toluene, 192 a-deutero toluene , lg3 and 2-deu teroisobu t ane(CH3),CD,lg3 bromination of n-pentane,l94 formation of acyl chlorides fromoxalyl chloride and paraffins,lg5 and reaction of a mixture of chlorine andsulphur dioxide with paraffins.lg6 In the liquid-phase photochlorination of(CH,),CD at -15" equimolar amounts of (CH,),CCl and DC1 are formed,indicating that no significant rearrangement of free radicals or hydrogenexchange between radicals and hydrocarbon occurs during chlorination. lg3Kharasch and his co-workers lg4 dispute Williams and Hamill's claim lg7that lower bromides are formed in the photobromination of ut-pentane.The formation of the H2+ ion has been postulated to explain the effect ofpH in the photochemical reactions of aqueous iodide 19* and ferrous solu-tions 1g9 respectively.(c) Other reactions. A further study of the photolysis of aqueous hydro-gen peroxide has been made at relatively high intensity.2mA mechanism of photolysis of methyl nitrite has been put forward whichis in complete accord with all work on the decomposition of this com-pound; 201 the unstable HNO molecule is postulated as an intermediate.it has been shown that 75% of theheavy liquid which is formed consists of a cyclic trimer of CH3*N:CH2, andthat both the radicals CH2*NH* and *CH,*NH, are formed either in the primaryprocess or in a secondary reaction.Booth and Norrish 203 have demonstratedthat the photolysis of aliphatic primary and secondary amines gives productsarising mainly from a primary process involving rupture of a N-H bondto give free radicals. The same authors have studied the photolysis ofamides and conclude that two main types of primary process occur which aremolecular, rather than free-radical, in nature.A novel light-induced reaction of diazomethane with carbon tetrachlorideto give C(CH,Cl), has been reported.204 A free-radical mechanism is pro-posed.Analogous reactions were observed with chloroform and bromo-trichloromethane, the halogens in each case being replaced by a (CH,Hal)group.In the photolysis of methylaminel g l G. G. Palmer and E. 0. Wiig, J . Amer. Chew. SOC., 1952, 74, 2785.132 S. Miyazalii, J . Chern. SOC. Japan, 1951, 73, 459, 641.Ig3 H. C. Brown and G. A. Russell, J . Amer. Chem. SOC., 1952, '74, 3995.lg4 M. S. Kharascli, W. Zimmt, and W. Nudenberg, J . Chem. Phys., 1952, 20, 1659.Ig5 F.Runge, 2. EEektrochem., 1952, 56, 779. lg6 F. Povenz, ibid., p. 746.Ig7 R. R. Williams and W. H. Hamill, J . Amer. Chem. SOC., 1950, 72, 1857.Ig8 T. Riggand J. Weiss, J., 1952,4198. IgS Idem, J. Chem. Phys., 1952, 20, 1194.Zol J . A. Gray and D. W. G. Style, Trans. Faraday Soc., 1952, 48, 1137.zo2 J. S. Watson and B. de €3. Darwent, J . Chem. Phys., 1952, 20, 1041.203 G. H. Booth and R. G. W. Norrish, J . , 1952, 188.204 W. H. Urry and J. R. Eiszner, J . Amer. Chem. SOC., 1952, 74, 5822.J. P. Hunt and H. Taube, J . Amer. Chern. Soc., 1952, '74, 5999BETTS et al. : THE KINETICS OF HOMOGENEOUS REACTIONS. 57The action of light on diazoaminobenzene in on mesoazanaphth-acene and its angular benzogues,206 on phosphotungstic acid in the pre-sence of isopropyl alcohol,m7 and on aqueous solutions of sodium meta-periodate,206 has also been studied.Some work on the photolysis of solid systems has also been reported.Jacobs and Tompkins 209 have shown that the photolysis of potassium azideinvolves the reaction of pairs of trapped excited azide ions (excitons) oflife-time approximately 2 x see.; and Linschitz and Rennert 210have investigated the reversible photobleaching of chlorophyll in glassysolvents at low temperature.Much recent work is summarised in a symposium on Photochemistry andPhotography held in Germany.211Photosensitised Reactions.-The merc~ry(~P~)-sensitised reaction ofethylene has been reinvestigated 212 and the results are compatible with thesuggestion that a significant fraction of the quenching collisions of ethyleneleads to the formation of metastable (3P0) atoms.Such atoms have beendetected directly not only for ethylene but also when nitrogen, hydrogen,or ethane is the quenching gas.212aThe cadmium(3Pl)-sensitised decomposition of propane at 300" has beenstudied.212b The mercury-sensitised decomposition of nitric oxide has beenshown to be caused by (6 lP,) atoms (1849-A resonance radiation). It issuggested that Noyes's observation of photosensitised decomposition by lightof wave-length 2537 A was due to " stepwise absorption," i.e., absorption of4047 A by (6 3P,) atoms or of 4359 A by (6 3P,) atoms to give (7 3S1) atomswhich then transfer their energy to the nitric oxide mole~ules.~1~The products of the mercury-photosensitised reaction of tetrafluoroethyl-ene at 30" are reported to be mainly hexafluorocyclopropane and a linearpolymer.The kinetics appear to fit a mechanism involving the rupture ofthe ethylenic bond to give two difluoromethylene r a d i ~ a l s . ~ l ~The kinetics of reaction of various dimes, furfurylamine, and thioureawith oxygen, photosensitised by fluorescent pigments, have been de-scribed.215 Uri 216 has found it possible to sensitise the polymerisation ofmethyl methacrylate, using chlorophyll and red light. The rate is enor-mously increased by certain organic reducing agents such as ascorbic acid,and quantum yields with respect to monomer of the order of 100 may beachieved.Fluorescence and Phosphorescence.-The fluorescence emitted by formicacid, carbonyl chloride, and methylene iodide has been described 217 and206 H.C. Freeman and R. J. W. Le Fkvre, J., 1952, 2932.208 A. gtienne and A. Staehelin, Compt. rend., 1952, 234, 1453.207 L. Chalkley, J . Phys. Chem., 1952, 56, 1084.208 F. S. H. Head and H. A. Standing, J., 1952, 1457.209 P. W. M. Jacobs and F. C. Tompkins, Proc. Roy. Soc., 1952, A , 215, 254.210 H. Linschitz and J. Rennert, Nature, 1952, 160, 193.211 Idem, 2. Elektrochem., 1952, 56. 705.512 B. de B. Darwent, J . Chem. Phys., 1952, 20, 1673.21z0 B. de B. Darwent and F. G. Hurtubise, ibid., p. 1684.212h P. Agius and B. de B. Darwent, J . Chem. Phys., 1952, 20, 1679.213 J. D. McGilvery and C. A. Winkler, Canad. J . Chem., 1952, 30, 194.214 B.Atkinson, J.. 1952, 2684.215 G. 0. Schenk and K. Kinkel, Naturwiss., 1951, 38, 355.216 N. Uri, J . Amer. Chem. SOC., 1952, 74, 5808.2 1 7 P. J. Dyneand D. W. G. Style, J . , 1952, 212258 GENERAL AND PHYSICAL CHEMISTRY.discussed.21s In the case of formic acid, the emitter is the radical H.CO.0..In the case of methylene iodide no evidence has been obtained for the emis-sion of the methylene radical in the region 2400-5000 A.The quenching of the fluorescence of p-naphthylamine by carbon tetra-chloride in the gas phase has been studied2I9 and the phosphorescenceemission of benzophenone in light petroleum has been examined and re-corded.2m Two types of emission have been found, the proportion of eachdepending on the concentration of benzophenone.Polymerisation and depolymerisation.Nomenclature.-The Inter-national Union of Pure and Applied Chemistry have issued a report 221 onnomenclature in the field of macromolecules. One of the recommendations isthat the term " intrinsic viscosity " be replaced by " limiting viscositynumber,'' and that the units in which it is expressed be changed fromdecilitres/g. to ml./g.The term " depropagation reaction ' I has been introduced to denote theexact opposite of the normal propagation reaction in addition polymerisa-Condensation Polymerisation.-In some condensation-polymerisationreactions, condensation is preceded by the addition of one reagent to theother, e.g., urea and formaldehyde. References to work on the kinetics ofsuch preliminary reactions are given in another section (p.51). Work onthe kinetics of polycondensation of phenolic alcohols 225 has been publishedand it is shown that the kinetic treatment of condensation developed byFlory in polyesterification reactions is also applicable to the polyetheri-fication of phenolic alcohols.Free-radical Polymerisation.-(a) Some aspects of the kinetics ofradical polymerisation are summarised in the Tilden lo3 and Liversidge 226lectures of the Chemical Society.The first-order velocity constant forthe decomposition of ad-azodiisobutyronitrile (I) at 82" has been found to beNC.CMe,-N : N*CMe,.CN (I)practically independent of the solvent.227 By using this initiator for thepolymerisation of methyl methacrylate it has been conclusively shown thatonly about 50% of the radicals produced are effective in initiating poly-merisation and that the termination process must be by combination oftwo radicals.It is inferred that the RN2* radical is capable of initiating thepolymerisation of methyl methacrylate but that the R* radical is not?However this cannot be true for the polymerisation of styrene by (I), sincethe rate of evolution of nitrogen, as calculated from Breitenbach and Schind-ler's results,228 is actually slightly greater than that in the solvents used bytion.222-224(b) Initiators and initiation rates.218 D. W. G. Style and J. C. Ward, J., 1952, 2125.219 H. G. Curme and G. K. Rollefson, J. Amer. Cherr,. SOC., 1952, 74, 28.220 J . Ferguson and H. J . Tinson, J., 1952, 3083.221 J .Polymer Sci., 1952, 8, 257.222 F. S. Dainton and K. J. Ivin, Proc. Roy. SOC., 1952, A , 213, 207.223 W. G. Barb, ibid., p. 66.224 P. R. E. J . Cowley and H. W. Melville, ibid., A , 210, 461.325 H. Kammerer, Makromol. Chem., 1952, 8, 72, 85.226 H. W. Melville, J., 1952, 1547.227 L. M. Arnett, J. Amer. Chem. SOC., 1952, 74, 2027.228 1. W. Breitenbach and A. Schindler, Monatsh., 1952, 83, 724RETTS et al. : THE KINETICS OF HOMOGENEOUS REACTIONS. 59Arnett.227 The initiator efficiency in various systems has been shown byradioactive tracer 229 and other methods 228, 230 to be generally between 0-5and 1.0.The rates of decomposition of the following initiators have also beenmeasured : aa-azobis-( ay-dimethylvaleronitrile) in ~ y l e n e , ~ ~ ~ 1 : 1'-azobis-cyclohexanecarbonitrile in ~ y l e n e , ~ ~ ~ benzoyl peroxide, cumenyl hydro-peroxide, and tert.-butyl hydroperoxide in methyl methacrylate and styrenerespectively,230 benzoyl peroxide in ally1 ethers,231 and para-substitutedtert.-butyl perbenzoates in diphenyl ether.232 The effect of structure ofdiacyl peroxides on the rates of initiation of polymerisation of styrene, andon their radical-induced decomposition has been in~estigated.~33 Tipper 234has studied the effect of water on the decomposition of benzoyl peroxide infour solvents. A comparative study has been made 235 of persulphates andbenzoyl peroxide as initiators in solution polymerisation.For some time it has been generally assumed that in the direct photo-chemical polymerisation of a vinyl monomer, the initial act of absorptionwould produce a diradical which would then grow in both directions bythe addition of monomer.However there is now clear evidence230>236that, in the cases of styrene and methyl methacrylate, photopoly-merisation proceeds via chains growing in one direction only. There isinsufficient evidence to say whether purely thermal polymerisation proceedsby diradicals, and Zimm and Bragg 237 have even suggested that, if there is notransfer process, self-termination of the biradical by cyclisation wouldprevent the formation of long-chain polymer. However it is possible thatthe polymerisation of styrene photosensitised by dyes such as trypaflavin,Illuminol RII, and Illuminol U proceeds via diradicals.238(c) Polymerisation of single monomers.Vaughan 239 has investigatedthe kinetics of the bulk polymerisation of styrene up to 100% conversion andsuggests that the termination and propagation reactions in turn becomediff usion-controlled. It has been shown that growing polystyrene chainsare terminated mainly by combination.236 The chain-transfer constants ofpolystyrene radicals with various halides have been determined.2403 241Iodides are more active than bromides which are more active than chlorides.Acid halides are exceptionally active.240 A preliminary account has beengiven of a method for the determination of the extent of self-branching inpolystyrene and other polymers.242 14C-Styrene is polymerised in thepresence of inactive polymers of high molecular weight (500,000). Transferwith the dead polymer occurs and the inactive polymer radical so formedproceeds to add active monomer.The polymerisation is performed under229 L. M. Arnett and J. H. Peterson, J . Amer. Chem. SOC., 1952, 74, 2031.230 B. Baysal and A. V. Tobolsky, J . Polymer Sci., 1952, 8, 529.231 N. G. Gaylord and F. R. Eirich, J . Amer. Chem. SOC., 1952, 74, 334.232 A. T. Blomquist and I. A. Berstein, ibid., 1951, '93, 5546233 W. Cooper, J., 1951, 3106; 1952, 2408.235 R. Sengupta and S. R. Palit, J., 1951, 3278.236 D. €3. Johnson and A. V. Tobolsky, J . Amer. Chem. SOC., 1952, 74, 938.237 B. H. Zimm and J. K. Bragg, J . Polymer Sci., 1952, 9, 476.238 M. Koizumi, 2. Kuroda, and A. Watanabe, J .Inst. Polytech. Osaka City Univ.,239 M. F. Vaughan, J . Appl. Chem., 1952, 2, 422; TtTans. Faraday Soc., 1952, 48, 576.240 J . A. Gannon, E. M. Feites, and A. V. Tobolsky, J . Amer. Chem. Soc., 1952, 74, 1854 .241 J . W. Breitenbach, Makromol. Chem., 1952, 8, 147.442 J . C. Bevington, G. M. Guzman, and TI. W. Melville, Nature, 1952, 170, 1026.234 C. F. H. Tipper, J., 1952, 2966.Ser. C., 1951, 2, 1; Chem. Abs., 1952, 46, 491560 GENERAL AND PHYSICAL CHEMISTRE*.conditions such that the polymer produced directly from monomer has arelatively low molecular weight (50,000), and the polymer originallyadded may then be isolated at the end of the experiment and itscontent of active monomer units determined. The transfer constant withdead polymer is found to be similar in magnitude to that of other transferreactions. Preliminary results are also given for vinyl acetate.A detailed branching mechanism has been proposed for the polymerisationof vinyl acetate, and a simplified kinetic analysis gives an expression for thedegree of branching in terms of six ratios.243 Four of these ratios have beenevaluated from experimental results.It appears that part of the branchingoccurs through ester linkages and that on hydrolysis of the polymer suchlinkages are broken.244 No such linkages are present in the polymer initiallyformed. The kinetics of the bulk and suspension polymerisation,Ms and theinhibited and retarded polymerisation of vinyl acetate have also beenstudied.246The chain-transfer reaction has been investigated in the catalysed poly-merisation of methyl metha~rylate,~~' and Matsumoto 248 has discussed thederivation of the mechanism of the termination process in the bulk poly-merisation, from the molecular-weight distribution in the polymer.The rate of the persulphate-catalysed polymerisation of methacrylicacid has been shown by Pinner 249 to decrease with decreasing acidity, andthis result is interpreted in terms of copolymerisation of the undissociatedacid with its less reactive anion.The polymerisation of vinyl chloride has been studied in solution bybenzoyl peroxide initiation,250 and in the gas phase 251 by means ofphotochemical initiation.In the polymerisation of allyl esters, termination takes place mainly bydegradative chain transfer with the monomer, a hydrogen atom being ab-stracted from the or-methylene group.It has been shown that abstraction ofhydrogen atoms from the acid-derived portion of the ester may also occurto a small extent.252 isoPropeny1 acetate behaves as an allyl compound,252whereas methyl isopropenyl ketone, containing a conjugated carbonylgroup, behaves like methyl m e t h a ~ r y l a t e . ~ ~ ~The rate of oxygen uptake in the inhibited polymerisation of acrylo-nitrile has been measured in four different systems.254 The products ofreaction in aqueous solution were quantitatively analysed and a highlyunstable peroxide isolated from non-aqueous systems.The photo-polymerisation of acetylene has been shown to yield small243 0. L. Wheeler, E.Lavin, and R. N. Crozier, J . Polymer Sci., 1952, 9, 157.244 R. Inoue and I. Sakurada, Chem. High Polymers, Japan, 1950,7, 211 ; Chem. Abs.,245 K. Noma and K. Irnai, ibid., 1951, 8, 44; Chem. Abs., 1952, 46, 11762.246 P. D. Bartlett and H. Kwart, J . Amer. Chem. Soc., 1952, 74, 3969.247 S. Basu, J. N. Sen, and S. R. Palit, Proc. Boy. Soc., 1952, A , 214, 247.248 M. Matsumoto, J . Polymer Sci., 1952, 8, 657.249 S. 13. Pinner, ibid., p. 282.250 G. V. Tkachenko, P. M. Khomikovskii, and S. S. Medvedev, Zhur. Fiz. Kkim.,251 M. Koizumi and K. Nakatsuka, J . Chem. Soc., J-n, Pure Chem. Sect., 1951, 78,162 N. G. Gaylord and F. R. Eirich, J . Amer. Chenz. SUG., 1952, 74, 337.253 G. Smets and L. Oosterbosch, Bdl. SOC. chim. Belg., 1952, 61, 139.264 K.C. Smeltz and E. Dyer, J . Amer. Chem. SOC., 1952, 74, 623.1952, 46, 4843.1951, 25, 823; Chem. Abs., 1952, 46, 3379.431; Chem. Abs., 1952, 46, 4916BETTS et al. : THE KINETICS OF HOMOGENEOUS REACTIONS. 61amounts of cycl~octatetraene.~~~ A review of the polymerisation of form-aldehyde has been The kinetics of polymerisation of methylacrylate have been 1 : 2-Dichloroethylene has been polymerisedby the application of high pre~sure.~~8 The inability of methyl a-tert.-butylacrylate to polymerise under a variety of conditions has been ascribedto potential steric hindrance in the polymer.a59Some aspects of the kinetics of polymerisation in systems in which polymeris precipitated have been discussed.260(d) Copolymerisation. Studies of the composition of copolymers as afunction of the composition of the monomer mixture have continued to giveinformation about the relative reactivity of monomers with polymer radi-cals.261-26* One of the most interesting reactions investigated was thecopolymerisation of ethylene with carbon monoxide at high pressure.2esCarbon monoxide behaves like maleic anhydride and the copolymer nevercontains more than 50% of carbon monoxide.The kinetics of copolymerisation of four further monomer pairs have been:investigated : methyl methacrylate and $-methoxystyrene, styrene andm-hydroxy~tyrene,~~~ but-l-ene and sulphur di~xide,~~O and styrene andsulphur dioxide.271 In the first system it has been shown that d,[=kt, 12/(kt, ll;kt, 22)0'5], which is a measure of the " cross-termination "process, varies from 12 to 27 as the concentration of P-methoxystyrene isincreased, whereas in the second system a value 4 < 1 fits the results quitewell. In both copolymerisations involving sulphur dioxide it has beenfound necessary to assume that one of the effective monomers is a 1 : 1complex, the presence of which has been demonstrated in each case bylight-absorption measurements. The ceiling temperature effect in thesulphur dioxide-olefin systems has been shown to be caused by the onset ofthe depropagation reaction, and the kinetics permit evaluation of theequilibrium constant, and hence of the heat and entropy changes, of thepropagation-depropagation reaction.Gee 272 has subjected to detailed analysis existing data concerning thephysical properties of liquid sulphur and has shown that the sudden increasein viscosity at 159" is due to the onset of polymerisation of (principally)S, molecules. The heat and entropy changes, unlike the values in normal255 2.Kuri and S. Shida, Bull. Chem. SOC., Japan, 1952, 25, 116.256 R. Sauterey, Ann. Chzm., 1952, 7, 5.2 5 7 P. S. Shantarovich, lzvest. Akad. Nauk, S.S.S.R. Otdel. Khiiiz. NauJz, 1952, 243;259 J. W. C. Crawford and S. D. Swift, J . , 1952, 1220.f60 C. H. Bamford, W. G. Barb, and A. D. Jenkins, Nutuve, 1952, 169, 1044.261 H. C. Haas and M. S. Simon, J . Polymer Sci., 1952, 9, 309.262 C. C. Price and R. D. Gilbert, ibid., p. 577.263 W. S. Port, E. F. Jordan, J . E. Hansen, and D. Swern, ibid., p.493.264 S. P. Mitzengendler and V. A. Chekhovskaya, Zkzw. Przklad. Khim., 1951, 24,Z65 S. N. Usliakov, S. P. Mitzengendler, and B. M. Polyatskina, ibid., p. 289; Chcnz.2 6 6 J . W. Vanderhoff, Macrofilm Abs., 1951, 11, 541; C h e w Abs., 1952, 46, 772.2 6 7 M. Yoshida and I. Sakurada, Chenz. High Polymers, Japan, 1950, 7, 334; Chem.268 D. D. Coffman, P. S. Pinkney, F. T. Wall, W. H. Wood, and H. S. Young,J . Amer. Chem. Soc., 1952, 74, 3391.269 E. P. Bonsall, L. Valentine, and H. W. Melville, Trans. Furaduy Soc., 1952, 48, 763.270 F . S. Dainton and K. J. Ivin, Pvoc. Roy. SOC., 1952, A , $319, 96, 207.2 7 1 W. G. Barb, ibid., pp. 6G, 177. 272 G. Gee, Tvans. Faraday Soc., 1962, 48, 515,Chem. Abs., 1952, 46, 9384. 258 K. E. Weale, J., 1952, 2223.485; Chem.Abs., 1952, 46, 9885.Abs., 1952, 46, 774.14bs., 1952, 46, 484462 GENERAL AND PHYSICAL CHEMISTRY.polymerisations, are both positive and a '' floor temperature " rather thana ceiling temperature is therefore found with sulphur.A general account of the degradation of polymershas been given by Burgess; 273 and Simha 274 and Madorsky 275 have sum-marised the behaviour of different polymers in terms of the percentagemonomer in the volatile products and the rate of change of molecular weightof the residue. Polymethyl methacrylate is one of the few polymers inwhich clean reversal to monomer occurs. In this case it has been shown thatthe depolymerisation can be induced photochemically above 130" andinvolves initiation, depropagation, and, in most circumstances, mutualtermination of chains.276 Using intermittent light to determine the lifeof the kinetic chains, and a retarder method to determine the initiation rate,Cowley and Melville 276 were able to deduce, for the first time, an experimentalvalue for a depropagation velocity constant.The value of this is in reason-able agreement with theoretical predictions and leads to an acceptable valuefor the change of entropy during polymerisation. On the other hand kt isabnormally small compared with radical-termination reactions in dilutesolution and this is attributed to the fact that the reaction is occurring ina highly viscous polymer. Simha 277 has discussed these results in terms ofhis theoretical treatment.278 Jellinek 279 has also derived theoreticalkinetic equations for the degradation of polymers, and has published apreliminary account of some experiments on the degradation of poly-styrene.280 The products of degradation of polystyrene 281 and polyvinylacetate 2g2 have been investigated.In the latter case acetic acid is evolvedby a chain reaction proceeding without the agency of free radicals, and aresidue of polyacetylene is left. Smets and Tasset 283 have reported data onthe degradation of four polymers in the presence of benzoyl peroxide.Ionic Polymerisation.-(a) Cationic polymerisation. When Friedel-Crafts catalysts (A) are employed as initiators, it appears that the presenceof a trace of a co-catalyst (BC), e.g., water, is generally required for thecatalyst to be effective.The catalyst and co-catalyst interact by a reactionsuch as A + BC ,--+ AB- + C+ to give a cation C+ which initiates polymeris-ation. A " system " will therefore be defined by monomer-catalyst-co-catalyst-solvent, It is extremely difficult to remove the last traces of waterfrom any system and where there is a possibility of a trace being presentthis is indicated below by H20(?).In the system isobutene-TiC14-CC1,*C02H-hexane, it has been shown 284by infra-red analysis that, in agreement with earlier work, the predominantend group is the methylene group. Trisubstituted double bonds andtrichloroacetate groups were also found. This suggests that termination(e) Depolymerisation.273 A. R. Burgess. J . Afifil. Chem., 1952, 78.274 R.Simha, Trans. N.Y. Acad. Sci., 1952, 14, 151.s y b S. L. Madorsky, J . Polymer Sci., 1952, 9, 133.276 P. R. E. J . Cowley and H. W. Melville, Proc. Roy. Soc., 1952, A , 210, 461; A ,278 R. Simha and L. A. Wall, J . Phys. Chem., 1952, 56, 707.279 H. H. G. Jellinek, J . Polymer Sci., 1952, 9, 369.280 H. H. G. Jellinek and L. B. Spencer, ibid., 1952, 8, 573.B. G. Achhammer, M. J. Reiney, L. A. Wall, and F. W. Reinhart, ibid., p. 555.282 N. Grassie, Trans. Faraday Soc., 1952, 48, 379.288 G. Smets and G. Tasset, Chim. Peintures, 1952,15,281; Chem. Abs., 1952,46,11762.384 M. St. C. Flett and I?. H. Plesch, J . , 2952, 3355.211, 320. 277 R. Simha. J . Polymer Sci., 1952, 9, 465BETTS et al. : THE KINETICS OF HOMOGENEOUS REACTIONS. 63occurs by loss of a proton from two possible positions a t the end of thegrowing cation, and by interaction with the trichloroacetate anion.Although Jordan and Mathieson 285 have reported the consumption ofcatalyst in the systems M-AlC1,-H20(?)-CCl, where M is styrene or M-methylstyrene, there is no evidence that the catalyst fragment is incor-porated in the polymer molecule.On the contrary, there is clear evidence 288that the catalyst is not incorporated in the polymer in the systems : styrene-SbC1,-H20 -nitrobenzene and styrene- SbC1, - H20( ?) - cyclohexane. Noradioactivity was detectable in the polymer when radioactive SbC1, wasused as catalyst. Williams and Bardsley 289 have studied the systemstyrene-SnCl,-HCl-CCl, a t low concentrations of styrene where the mainproduct is l-phenylethyl chloride.However, although the kinetics areconsistent with a carbonium ion mechanism, it is not possible to say whetherinitiation is by interaction of the catalyst with hydrogen chloride or withstyrene.Jordan and Mathieson have discussed their results on styrene286 andhave made a quantitative comparison with the results on a-methylstyrene.285They have also concluded 287 from molecular-weight distribution data 2mthat in the latter case termination is by monomer deactivation and solventtransfer.Norrish and Russell 291 have reported kinetic and molecular-weightmeasurements in the system isobutene-SnC14-H20-C2H,C1. Water wasshown to be essential for reaction. It was concluded that further work wasrequired with very highly purified materials before the mechanism could kefully elucidated.Further work has been published on the iodine-catalysed polymerisationof vinyl ethers.292 The effect of a number of side groups has been examinedwith results which accord with expectation.Wooding and Higginson 293 have made thefirst detailed kinetic study of anionic polymerisation.The results forpolymerisation of styrene in liquid ammonia, catalysed by potassamide, arein accord with a mechanism involving addition of the amide ion NH2- to themonomer, propagation, and termination by reaction of the growing chainwith the solvent leading to re-formation of the amide ion. A qualitativesurvey has been made of the reactivity of various anion bases, and theobserved correlation between base strength and reactivity is in accord withthe anionic mechanism of polymerisation.The interesting suggestion has been made that the formation ofrhodizonic acid when carbon monoxide reacts with liquid ammonia in thepresence of sodium, occurs through an anionic polymerisation in which sixcarbon monoxide molecules are added to an amide ion.294The relative ease of addition of two mono-mers to a growing polymeric entity may be expected to vary according to(b) Anionic polymerisation.(c) Ionic copolymerisation.286 D.0. Jordan and A. R. Mathieson, J., 1952, 611, 2354.28E Idem, ibid., p. 621. 287 Idem, ibid., pp. 2358, 2363.288 R. 0. Colclough, J . Polymer Sci., 1952, 8, 467.289 G. Williams and H. Bardsley, J., 1952, 1707.290 A.B. Hersberger, J. C. Reid, and R. G. Heiligmann, I n d . Eng. Chem., 1945, 37, 1073.291 R. G. W. Norrish and K. E. Russell, Trans. Faraday Soc., 1952, 48, 91.292 D. D. Eleyand J. Saunders, J., 1952, 4167.293 N. S. Wooding and W. C. E. Higginson, J., 1952, 760, 774, 1178.294 F. Leonard and P. Fram, Science, 1952, 118, 22864 GENERAL AND PHYSICAL CHEMISTRY.whether such an entity is an anion, a free radical, or a cation, and thishas been verified experimentally.295 The anionic copolymerisation ofbutyl vinyl sulphone with acrylonitrile 296 and the effect of reaction con-ditions on the monomer reactivity ratios for the system styrene+-chloro-styrene-SnC1, have been investigated.297 Other systems have also beenstudied 298b 299 and it has been found that for the cationic copolymerisation ofa given monomer with a series of substituted styrenes, the reactivity ratio is afunction of Hammett’s G value.298It is clear from the report 3oo of a conference held at Stoke that interestingdevelopments are to be expected in this field.Eliltulsion PoZynze~isatiolz.-This does not strictly come into thecategory of homogeneous reactions but it should be noted that it has beenpossible to derive from the kinetics,301 on the basis of Smith and Ewart’stheory,302 values for propagation velocity constants which are similar tothose obtained by the more usual methods.Radiation Chemistry.-(a) Primary Processes.-Most of the experimentaldata available on primary products has been obtained by the use of the massspectrometer.Therefore, strictly speaking, such data apply only to thecase of low-energy electron bombardment. Investigations of this kindinclude the measurement of appearance potentials of ions formed from~yclopropane,~~ cyanogen and methyl cyanide,304 and hydrogen peroxide.305Norton5O6 has studied the ionisation produced in water vapour in the pres-ence of an excess of hydrogen. An unusually sharp maximum is obtainedin the positive current at mass 19. This is due to the ion H,O+ formed in thefollowing process :H,O + H20t + H 4 OH (”+) 7 OH(27r)OH(21;+)H30Electron3 3 3 0 impact H3O+ + eThere is still no experimental information on the nature of the primaryproducts of high-energy bombardment processes. Until such results areavailable it will not be clear to what extent the different radiation chemicaleffects of, say, cr-particles and electrons are due to the different spatial dis-tribution of the entities formed or to differences in the entities themselves.There has also been very little direct experimental investigation of theprocesses immediately subsequent to the primary act.In the gas phase theprobability of electron exchange in hydrogen has been measured.307 The296 F. R. Mayo and C. Walling, Chem. Reviews, 1950, 46, 277.296 F. C. Foster, J . Aluter. Chem. SOC., 1952, 74, 2299.297 C. G. Overberger, L. H. Arond, and J. J. Taylor, J . Anzer. Chenz. Suc., 1952, ’73,298 C. G. Overberger, L. W. Arond, D. Tanner, J. J. Taylor, and T. Alfrey, ibid.,2g9 Y.Landler, J . Polymer Sci., 1952, 8, 63.300 P. H. Plesch, Nature, 1952, 169, 828.301 M. Morton, P. P. Salatiello, and H. Landfield, J . Polymer Sci., 1952, 8,111,215, 279.302 W. V. Smith and R. H. Ewart, J . Chem. Phys., 1948, 18, 592.3m F. H. Field, J . Chew. Ph sics, 1952, 20, 1734.304 C. A. McDowell and J. J W a r r e n , Trans. Faraday Soc., 1952, 48, 1084.305 A. J. B. Robertson, ibid., p. 228.306 F. J. Norton, Phys. Review, 1952, 85, 154.397 E. E. Muschlitz and J. H. Simons, J . Phys. Chem., 1952, 56, 837.5541.p. 4848BETTS et aE. : THE KINETICS OF HOMOGENEOUS REACTIONS. 65ions H,+ and Hf do not exchange appreciably with the H, molecule but theion H,+ does so readily. In hydrocarbon gases all the ions H,", H2+, and H+exchange readily, the explanation probably being that the large moleculescan absorb considerable amounts of energy as vibrational energy.It hasbeen found that the formation of the H,+ ion in hydrogen occurs by theprocess, H,+ + H, -+= H3+ + H, the H,+ ion being dissociated.308Hasted 309 has studied the charge-exchange cross-sections of severalprocesses, including that of Of ions in water, and cross-sections for processesof the type A- + B -+ A + B + C have also been measured. Suchcross-sections are expected to be negligible unless very energetic ions andatoms are presentJ31* but for 0-, Cl-, and F- in various gases unexpectedlylarge cross-sections were found. This is interpreted as due to the presence ofexcited states of these ions having low electron affinities.It has been sug-gested that electron-capture processes in polyatomic molecules generallyfall into two classes : 311AB + e -+A + B- . . . . . . . - (1)AB+e--jA++B-+C . . . . . . (2)Examples of type (1) are cyanogen and methyl cyanide, whilst type (2) isexemplified by carbon tetrachloride. Processes of type (1) are resonanceprocesses necessitating a suitable crossing in the potential-energy curves ofthe relevant electronic states of the molecule AB and the ion AB-. Studiesof the type of electron capture occurring in given cases may thus yieldinformation about the potential-energy curves of polyatomic molecules.The fact that processes of type (1) are resonance processes is significant in thatit opens up the possibility of investigating the ultimate fate of the ion B-in solution.312 A review of the reactions of gaseous ions has been presentedby Ma~sey.~lOI n a series of papers Magee and Burton have discussed certain initialprocesses in radiation chemistry.Semiquantitative treatments of simplecases followed by qualitative extension to more complex systems have led tothe following general conclusions, and the relevance of each of these toradiation chemistry, is discussed. (i) Thermal electron capture by a com-plex molecule positive ion should lead in most cases to immediate dissoci-ation into two particles, one of which is excited. The particles are morelikely to be radicals than molecules.313 (ii) Under suitable conditions low-energy electrons tend to form negative ions via capture by neutral molecules,rather than to neutralise positive i0ns.~1~ (iii) Charge transfers occurringby a resonance process, e.g.,may have large cross-sections ; non-resonant processes of the typenecessitate the crossing of two potential-energy curves of the system (A + B)+A' + A + A + A+A++B-+AfB+308 R.L. Murray, J. Appl. Phys., 1952, 23, 6.309 J. B. Hasted, Proc. Boy. Suc., 1952, A , 213, 235.310 H. S. W. Massey, Discuss. Faraday SOC., 1952, la, 24.311 J. D. Craggs, C. A. McDowell, and J . W. Warren, Trans. Faraday SOC., 1952, 48,312 F. S. Dainton, Discuss. Faraday SOL, 1952, 12, 10.313 J. L. Magee and M. Burton, J. Anzer. Chem. Soc., 1950, 73, 1965.314 Idem, ibid., 1951, ?3, 523.1093.REP.-VOL. XLIX. 66 GENERAL AND PHYSICAL CHEMISTRY.and are accompanied by vibrational excitation or dissociation ; 316 in general,complex formation is involved, lifetimes may be of the order of seconds, andother processes may therefore compete before the charge transfer is com-~ l e t e .~ ~ ~ (iv) Simple changes of the typeA+ + B- --+ C + Dare not expected to occur since charge transfer takes place a t a rather largedistance. Highly excited states of A + B are expected and the end pro-ducts should commonly be radicals.317Considerable interest was recently aroused by the work of Dee andRichards.318, 319 These authors claimed to have shown that an ultra-violetlight emission is produced by the a-particle bombardment of liquids. Thelight is strongly absorbed by the irradiated material and the wave-lengthinvolved probably lies between 1500 and 1700 A.The emission of this lightand its subsequent absorption were suggested as a mechanism for the for-mation of chemically active radicals. Miller and Brown 320 have attemptedto confirm these results, without success. They conclude that no appreciableemission of light of wave-length greater than 1800 A takes place when wateris bombarded with =-particles and that appreciable emission of light ofshorter wave-lengths is unlikely. Other workers have also been unable toobtain results consistent with those of Dee and Richards.321, 322 It isinteresting that although the ultra-violet light emitted from water exposed toy- or p-radiation is purely due to the Cerenkov effect 3z33 324 and that noultra-violet emission is found when high-intensity 50 kvp X-rays areice a t a temperature of -100" to -170" does emit ultra-violet light underthe latter type of irradiation and the emission is not of Cerenkov origin.325The light intensity is linear with dose rate over a large energy range and has amaximum energy at 3400 A.In support of these observations tritium-iceis found to be self-l~minescent.~~~~ 326A new conception of the processes occurring in liquids upon irradiationhas been suggested.327 Chemical activity is considered to be due to twotypes of excited species, M* and Mf. The M* species is produced in primaryprocesses occurring either in the main particle track or in its " spurs "(&ray tracks). It has a much smaller energy than MS and is persistent.The M* species is considered to result from ion neutralisation.It decomposesnear its production site into uncharged radicals. Most of the M* speciesare in the lowest excited state but can participate in reactions by excitonor photon transfer if energy traps are present in the solution.s15 J. L. Magee, J . Phys. Chem., 1952, 56, 555.316 M. Burton and J. L. Magee, ibid., p. 842.317 J. L. Magee, Discuss. Faraday SOC., 1952, 12, 33.318 P. I. Dee and E. W. T. Richards, Nature, 1951, 168, 736.319 E. W. T. Richards, Discuss. Faraday SOC., 1952, 12, 45.320 See N. Miller, Discuss. Faraday SOC., 1952, 12, 46.a21 See M. Magat, ibid., p. 48.322 31. A. Greenfield, A. Norman, and P. M. Kratz, U.S. Atomic En. Cornmiss.323 M.A. Greenfield, A. Norman, A. H. Dowdy, and P. M. Kratz, US. Atomic324 F. S. Dainton, Discuss. Faraday SOC., 1952, 12, 44.325 L. I. Grossweiner and M. S. Matheson, J . Chem. Phys., 1952, 20, 1654.326 W. M. Jones, ibid., p, 1974.327 M. Burton, J. L. Magee, and A. H. Samuel, ibid., p. 760.Report, 1952, UCLA-218.En. Commiss. Report, 1952, UCLA-211BETTS et al. : THE KINETICS OF HOMOGENEOUS REACTIONS. 67(b) A ctinometry. Owing to their comparative straightforwardness andease of handling, chemical methods of dosimetry are tending to be almostuniversally adopted. Of the numerous systems proposed for such measure-ments the ferrous sulphate system appears to be the most generally satis-factory and has been the subject of the most detailed calibration as yet.328A useful review and assessment of the various systems which have beenproposed for chemical dosimetry has been given.329 It is suggested that theterm “ chemical dosimetry ” should be replaced by “ actinometry,” followingthe nomenclature of photochemistry.It is unfortunate that a lack ofagreement exists between different workers as to the value of the oxidationyield of ferrous ion in aerated solutions which are conventionally 0 - 8 ~ insulphuric acid. Most authors agree that for X- and y-radiation, at doserates of up to 1000 r,/min., the yield for ferrous oxidation is of the order of20 molecules oxidised per 100 ev energy absorbed (G = Z O ) , and Miller andWilkinson have rechecked this result under varying conditions. However,using W o y-radiation, Hochanadel 330 obtained a value of G = 15.5 & 0.3,the method of calibration employed being a calorimetric one.As Hocha-nadel’s range of dose rates (1500--15,000 r./min.) was larger than that of theother authors, and since there is general agreement that the yield ultimatelyfalls on increasing the dose rate, it was thought that this may be an ex-planation of the discrepancy. However, Hardwick 331 found the yieldunchanged up to a dose rate of at least 4200 r./min. with 2000 kvp X-raysand Rigg, Stein, and Weiss,s2 using a dose rate of -3000 r./min., foundG = 19.9. Allen,333 moreover, found a constant yield over a dose-raterange of 100--10,000 r./min. with 2 Mv X-rays. It seems clear thereforethat this discrepancy is only to be settled by further experiment.Anothereffect observed in this system, which is confirmed by two investigator^,^^^ 335is that the yield falls when low-energy p-radiation is used. For high-energyp-radiation the yield remains the same as for X-radiation,336 and the fallingyield for low-energy p-radiation has been explained in terms of the differenceof ion density between the two types of r a d i a t i ~ n . ~ ~ This explanationreceives support from the fact that the yield for a-radiation in aeratedsolution is even lower, viz., G = 6-7-59 337 (depending on the exact value ofW for argon). A very marked fall in yield has been observed on increasingthe dose rate with 0.92-Mv electrons from lo3 to lo6 r./min.338 It has beenclaimed that ferrous sulphate actinometry is suitable for a-radiati~n,~~’ pileradiati0n,~3~, 340 and 24 Mevp X-raysM1 Evidence has been quoted to showthat a-radiation and lithium recoil particles do not behave additively to theferrous system.342 Though a reason for this has been suggested343 the32* N.Miller, J . Chem. Phys., 1950, 18, 79.32* N. Miller and J. Wilkinson, Discuss. Furuduy Soc., 1952, 12, 50.330 C. J. Hochanadel, J . Phys. Chem., 1952, 56, 587.331 T. J. Hardwick, Discuss. Faraday SOC., 1952, 12, 112.332 T. Rigg, G. Stein, and J. Weiss, Proc. Roy. SOL, 1952, A , 211, 375.333 A. 0. Allen, Discuss. Furuduy SOC., 1952, 12, 114.334 T. J. Hardwick, ibid., p. 203.335 E. J . Hart, U.S. Atomic En. Commiss. Report, AECU-1534.336 T. J. Hardwick, Cunad. J .Chem., 1952, 30, 39.337 N. Miller, Discuss. Furaday Soc., 1952, 12,110.3sD E. Saeland and L. Ehrenberg, Acta Chew. Scund., 1952, 6, 1133.340 J. Wright, Discuss. Faraday SOC., 1952, 12, 60.341 R. W. Hummel and J. W. T. Spinks, J . Chem. Physics, 1952, 20, 1056.342 J. Wright, Discuss. Furaday SOC., 1952, 12, 116.338 C. B. Amphlett, ibid., p. 272.843 M. Burton, ibid., p. 11768 GENERAL AND PHYSICAL CHEMISTRY,proposal is hardly borne out by the fact that a-radiation and 50 kvp X-radiation appear to be additive in their effects.337Another actinometer which has been investigated in some detail is theceric sulphate system.w When X - or y-radiation or high-energy p-radia-tion 336 was used this reaction was found to have a lower yield than the ferrous-ion actinometer.However the yield is independent of dose rate up to atleast 45,000 r./min. for 2000 kvp X-rays or 140,000 r./min. for 50 kvp X-rays,independently of the presence or absence of oxygen and independently of theceric-ion concentration down to the lowest limits which can be studied.It suffers the disadvantages of being more sensitive to impurities, and ofexhibiting an increasing yield with decreasing electron energy.334Compared with these two systems the benzene-water system 345 hasseveral disadvantages. Thus the concentration independence of yield isless well fulfilled than for the ferrous system, the yield is much lower, theanalysis is clumsy, and the reaction may exhibit a post-irradiation effect.346On the other hand this actinometer may prove useful at higher dose-rates.Other possible systems which have been proposed for actinometry arethe formic acid system,347 the diphenylpicrylhydrazyl systemYw8 a phosphateester s y ~ t e m , ~ 9 and the use of polyvinyl chloride Many systemshave been investigated for possibilities as chemical a~tinometers.~~~ Kan-wisher s62 has developed an ingenious method of measuring dose rates withthe chloroform-water system.In order to obtain reasonable standardisation of dose measurementsand expressions of yield it has been proposed that : 353 (i) Yields should beexpressed as molecules converted per 100 ev energy absorbed.This shouldbe designated by G where the actual energy input is measured. (ii) Theyield should be written as G’ if energy inputs are obtained from chemicalactinometry; in this case full details of conversion factors should be given.(iii) The yield should be written as Gm if ferrous sulphate actinometry isemployed, the value of G(Fe2+ ,--+ Fe3+) being provisionally taken as 20.(iv) The change to which G refers should be indicated, e.g., G(H20,).It isgenerally felt that the ferrous sulphate system would be the best for universaladoption in the X - and y-ray dose-rate range from 0 to at least103 r./min.3as 355Since the suggestion byEyring, Hirschfelder, and Taylor 356 it has. been commonly assumed thatboth ionisation and excitation processes play a part in radiation chemicalreactions, and the investigations by Essex and his co-workers 3g7-360 supportthis view.Nevertheless the polymerisation of acetylene by or-particles(c) Non-aqueous vapour and liquid systems.344 T. J. Hardwick, Canad. J . Chem., 1952, 30, 23.345 M. J. Day and G. Stein, Nature, 1949, 164, 671.346 J. Wright, Discws. Faraday Soc., 1952; 12, 114.34* A. Chapiro, ibid., p. 115.350 E. J. Henley and A. Miller, Nucleonics, 1951, 9, No. 6, 62.351 Illinois Univ. Progress Report No. 2, 1951 ; Nuclear Sci. Abs., 1952, 6, No. 4004.352 J. W. Kanwisher, Nucleonics, 1952, 10, No. 5, 62.353 M. Burton, Discuss. Faraduy SOC., 1952, 12, 317.354 F. S. Dainton, ibid., p. 10.356 H. Eyring, J. 0. Hirschfelder, and H. S. Taylor, J . Chem. Phys., 1936, 4, 479.357 C. Smith and H. Essex, ibid., 1938, 6, 188.3 5 * A. D. Kolumban and H.Essex, ibid., 1940, 8, 450.359 N. T. Williams and H. Essex, ibid., 1948, 16, 1153.360 Idem, ibid., 1949, 17, 995.347 E. J. Hart, ibid., p. 111.*49 B. E. Conway, ibid., p. 250.865 N. Miller, ibid., p. 318BETTS et al. : THE KINETICS OF HOMOGENEOUS REACTIONS. 69seems to provide an exception to this generalisation inasmuch as the wholeeffect can be accounted for on the basis of i ~ n i s a t i o n . ~ ~ ~A striking contrast between the chemical effects produced by irradiationin the liquid and the gaseous state is provided by a study of the a-particleirradiation of n-hexane, cyclohexane, and benzene.362 In the gaseous phasethe yields for each substance differ by a maximum factor of three, a com-pletely different result from the effect of electrons on the liquids.363In contrast to earlier findings for the effect of =-particle irradiation onethylene, an investigation of the y-irradiation of this gas showed no sub-stantial yield of hydrogen gas or of saturated hydrocarbons.364 The mainreaction is a chain polymerisation having an ionic yield of about 30.365The synthesis of ammonia by y-irradiation of nitrogen-hydrogen mixtureshas also been In this reaction the glass surface area is an im-portant factor.Three methods have now been used to obtain information concerningthe chemically active species produced in organic liquids under the influenceof ionising radiations.The first method comprises the use of iodine having :Ihigh specific activity of 1311.367 Radicals formed during radiolysis combinewith iodine to give iodides in small yield. To this product appropriateinactive alkyl iodide carriers are added and fractional distillation , followedby radioactivity measurement, permits an estimation of relative free-radicalyields.This method has been applied to the radiolysis of alkanes and alkyliodides in both the liquid and the gaseous p h a ~ e . ~ ~ 8 Almost all the radicalsformed are considered to react by the process R + I, -+RI + I. Ahigh yield of the parent substance in the case of the vapourised iodidesindicates that the C-I bond is that most frequently broken, whilst in theliquid state there is a greater ratio of C-C to C-I bond rupture. Very littlehydrogen iodide is formed, indicating only a small probability of C-Hbond rupture.With alkanes the radical corresponding to the parent sub-stance is no longer predominant except for methane. The results hereobtained are complementary to mass-spectral data.369 For example, themost important peak in the mass-spectrum of neopentane is C,H,+, whilst onradiolysis a large yield of CH, radical is found. Hence an important primarystep appears to beC(CH3)4 -f C(CH3)3+ 4- CH3 + eDose rate variation had no effect on the decomposition patterns but in thecase of ethyl iodide there were differences in the ratios of products for 2 MvX-radiation, y-radiation, and 50 kvp X-radiation. In experiments of thiskind an increase of yield at high iodine concentrations can be explained onthe basis of higher energy absorption by the heavy iodine atoms.370361 S.C. Lind, J . Phys. Chem., 1952, 56, 920.362 V. P. Henri, C. R. Maxwell, W. C. White, and D. C. Peterson, ibid., p. 153.363 M. Burton, ibid., 1948, 52, 564.364 Yale Univ. Progr. Report, No. 3, 1952, NYO-3309.365 Yale Univ. Progr. Report, No. 2, 1952, NYO-3310.3 6 6 mi. A. Selke, C. Kardys, E. V. Sherry, and R. C. Jagel, U.S. Atomic En. Commiss.367 R. R. Williams and W. H. Hamill, J . Amer. Chem. SOC., 1950, 73, 1857.368 L. Gevantman and R. R. Williams, J . Phys. Chem., 1952, 56, 569.369 A. Langer, ibid., 1950, 54, 618.370 C. C. Schubert and R. H. Schuler, J . Chem. Phys., 1952, 20, 518.Report, 1952, NYO-332770 GENERAL AND PHYSICAL CHEMISTRY.The other two methods so far used in following radical production are thetrapping of radicals by (a) the initiation of polymerisation, and (b) the re-action with diphenylpicrylhydrazyl (DPPH) radicals.Both of thesemethods have recently been employed for the determination of the numberof free radicals produced in a series of organic liquids by given doses ofy - r a d i a t i ~ n . ~ ~ ~ , 3729 373 Under the conditions of experiment the radical-trapping reaction is considered to be much more probable than radical-recombination reactions and energy yields for radical formation have beenevaluated on this basis. Results obtained by the two methods agreereasonably well in most cases, though it has been pointed out that owingto possible breakdown of the hydrazyl radical itself one would not reallyexpect to be able to count the radicals formed with accuracy greater than afactor of 2.374Manion and Burton have studied the radiolysis of mixtures of hydro-carbons in the liquid state.375 The results are consistent with a mechanismin which both ionisation transfer and excitation transfer play significantroles.Owing to this effect, radiolysis of mixtures yields products which arenot predictable on a simple law of averages. In a mixture of two com-ponents, whichever component is first ionised, there is known to follow a rapidtransfer of ionisation to the species of lower ionisation potential. Manion andBurton’s results indicate that excitation transfer usually behaves similarly,this effect being most readily appreciated in the case of radiolysis ofcyclohexane-benzene mixtures in which the two effects appear to act inopposition.Fundamental differences in mechanism are shown to existbetween radiolyses in the gaseous and the liquid state for cyclohexane-benzene mixtures.*A mass-spectrometric examination of benzene and deuterobenzeneindicated that the ratio of ions C,H,+/C,D,+ was constant for different valuesof m and n, whilst the ratio C6H,+/C6D,+ tended to increase as n decreased.376A different mechanism of formation of the two types of ion was thus in-dicated. Radiolysis of the two substances by 1.5 Mv electrons gave theresult G(H,)> G(C,H,) for benzene, and G(D,) < G(C,D,) for deutero-benzene, again indicating that at least two mechanisms are involved in theradiolysis of benzene and that these do not contribute to the same extent forC6H6 and C6D6.The results have been explained in terms of bond ruptureand rearrangement of the parent ion, and the difference in zero-point energybetween C-D and C-H bonds. It is also shown that the molecules C,H, andCGD6 exhibit mutual protection in a mixture and the implications of this arediscussed.The rate of polymerisation of styrene by y-radiation, in the dose-rate range2400-5500 r./min., has been found to be proportional to the dose rate.381This is contrary to earlier rep0rts.38~~ 371 Minder and Heydrich 383 haveinvestigated the radiolysis of halogenated hydrocarbons in alcohol andacetone solution. Halogen acids are formed in amount depending on the371 A. Chapiro, J . Chzm. phys., 1950, 47, 747.372 Idem, Compt. rend., 1951, 233, 792.373 A.Prevot-Bernas, A. Chapiro, C. Cousin, Y . Landler, and M. Magat, Discuss.374 W. Wild, ibid., p. 127.375 J. P. Manion and M. Burton, J . Phys. Chem., 1952, 56, 560.376 S. Gordon and M. Burton, Discuss. Furuday Soc., 1962, 18, 88.Faraday Soc., 1952, 12, 98.* Cf. ref. 362BETTS et al. : THE KINETICS OF HOMOGENEOUS REACTIONS. 71concentration, the number of halogen atoms in the compound, and the typeof binding. It is claimed that, in order to effect decomposition of chloroformby y-radiation alone or in solution, oxygen must be present.377, 378 Goodyields of salicylic acid are produced on irradiation of benzyl alcohol in ethylalcohol with l-Mev electrons.379 A bibliography on the effect of a-, p-, y-,and X-rays on organic compounds has been compiled.3mA widespread interest continues tocentre upon radiation effects induced in aqueous systems, consequently noapology is made for devoting most attention to their discussion.Althoughit has been accepted for some time that the ultimate formation of H atomsand OH radicals seems to offer the most convenient explanation of the be-haviour of irradiated water, nevertheless as more experimental data becomeavailable there is an increasing feeling that our conceptions regarding thenature of the primary reacting entities, and for that matter the particularform of the substrate with which they react, are too rudimentary. Despitethe fact that almost every possible radical or ion has now been invoked toexplain this or that aspect of radiatian chemical effects in water, togetherwith almost every possible permutation of kheir formation and breakdown,results continue to appear which meet with no explanation on existingconcepts, or which seem incompatible with those of other workers.Justhow far the sensitivity of some of the systems to very small changesin experimental conditions is responsible for the discrepancies it wouldbe hard to say at present, but the recent Faraday Society Discussion384indicated that several anomalies may in fact be due to this cause.It has several times been pointed out that the majority of radiationchemical reactions in aqueous solutions are 386 and the usualvalue of the equivalent reduction potential (e.r.p.) of irradiated water, asjudged from published experimental results, indicates that the oxidisingpower of irradiated water cannot be due to a mixture of H atoms and OHradicals alone in equal proportions. It has been shown387s 388 that anyargument based on a difference of distribution of H atoms and OH radicalscannot explain this effect, but the existence of the ions Hz+ 389 and HO+ 387(or 0 atoms) may help to give the observed result.It has also been suggestedthat all cases of radiation reduction so far observed can be explained by theaction of OH radicals or hydrogen peroxide.3w This indicates that H atomsappear to be very unreactive, and in fact raises the suspicion that they maynever have independent existence. From this point of view it has been(d) Water and aqueous solutions.377 J.F. Suttle and J. W. Schulte, Discuss. Furaday SOC., 1952, 12, 317.378 J. W. Schulte, J. F. Suttle, and R. Wilhelm, US. Atomic En. Commiss. Report,379 B.P., 1952, 665,263.380 F. Sachs, Literature Search for Carbide Chemicals Co., 1952, Co(Y-12).381 B. Manowitz, R. V. Horrigan, and R. H. Bretton, U.S. Atomic En. Commiss.382 A. Chapiro, Corn@. rend., 1949, 228, 1490.383 W. Minder and H. Heydrich, Discuss. Furaday Soc., 1952, 12, 305.384385 M. Haissinsky and M. Lefort, Compt. rend., 1949, 228, 314.388 M. Haissinsky. Discuss. Faraday SOC., 1952, 12, 133.387 F. S. Dainton and E. Collinson, Ann. Rev. Phys. Cham., 1951, 2, 99.388 E. Collinson and F. S. Dainton, Discuss. Furaduy Soc., 1962, 12, 251.38D J.Weiss, Nature, 1950, 165, 728.390 M. Haissinsky and M. Lefort, Compt. rend., 1950, 230, 1166.1952, LA-1438.Report, 1951, BNL-141.Radiation Chemistry,” Discuss. Furaduy Soc., 1952, 1272 GENERAL AND PHYSICAL CHEMISTRY.suggested that instead of the H,O- ion breaking down in the usually acceptedmanner :the breakdown occurs by one of the following processes :H,O-+HO-+H . . . . . . (3)H,O- -0- + H, . . . . . . . (4) 391followed by O-+H,O+HO-+OH . . . . . * (4a)followed by H- + H,O+OH- + 13, . . . . . * (5a)H,O-+H-+OH . . . . . . - ( 5 ) orSupporting arguments for reactions (5) and (5a) have recently beenadvanced 393 but (5) seems a less likely process energetically than either (3)or (4). It has been argued that process (4) is energetically to be preferred toprocess (3),392 but it has also been pointed out that if (4) is energeticallyfavoured with respect to (3) then it cannot be followed by (4a).394 It hasbeen claimed that process (4) offers an alternative explanation to the " hotspot '' hypothesis (see next section) for the production of hydrogen gas innearly constant initial yield and that it also indicates a decreased reducingpower of irradiated solutions.Against such a hypothesis the followingarguments may be advanced : (a) The difficulty of finding a suitable processto follow (4). ( b ) The fact that there is some direct evidence of the partici-pation of D atoms in polymerisations induced in deuterium oxide solution.395(c) The fact that hydrogen peroxide has been found in greater initial yieldthan hydrogen in the ferrous sulphate system.396 (d) The fact that it isdifficult to explain the reduction of certain organic dyes on this basis.It iscertainly not true to assume that reduction occurs by H atoms formed in theprocessas is shown by the enhanced yield produced by the addition of sodiumbenzoate to such systems.397, 398The theory of Burton, Magee, and Samuel327 suggests a mechanismsomewhat different from that usually accepted for H atom and OH radicalformation and it seems likely that the present position may be summarisedby the overall expressionH,O ---+ H,O* + H + OH + other species as yet ill-defined.The excited species H20* may be able to oxidise or reduce or play no chemicalpart, depending on the substrate concerned, and this may be an explanationof the differences in .G (solute) and G (free radical) values found frominvestigations on different solutes.(i) MoZecuZar and radical yield.The postulate, first advanced by Allen,399that the primary effect of ionising radiation on water could be regarded asconsisting of two processes :. . . . . OH+H,+H+H,O - (6). . . . . H20--+3H,0, +&H, - ( F )H,O I _ f OH + H + (R) . . . . . . .391 M. Haissinsky and M. Magat, Compt. rend., 1951, 233, 954.392 M. Magat, Discuss. Faraday SOC., 1952, 12, 244.393 G. W. R. Bartindale, ibid., p. 246.395 E. Collinson and F. S. Dainton, ibid., p. 212.396 F. S. Dainton and H. C. Sutton, ibid., p. 121.398 G. Stein, ibid., p. 243.3D4 F. S. Dainton, ibid., p.245.3*7 M. J. Day, ibzd., p. 280.A. 0. Allen, J . Phys. Chem., 1948, 62, 479BETTS et aZ. : THE KIXETICS OF HOMOGENEOUS REACTIOSS. 73has received considerable direct support from measurement of initial hydro-gen peroxide 401s 402, m3 and indirect support from the factthat certain results are explicable on mechanisms involving this postu-late.404im5* 406 On the other hand there have been some dissensions onexperimental grounds,407$ hydrogen yields having been found to vary.It is not clear whether or not the yields in these last cases are initial yields.Several attempts have been made to measure the yield for each of theprocesses ( F ) and (R). H o ~ h a n a d e l , ~ ~ ~ using y-radiation from a %o source,has examined the rate of production of hydrogen peroxide in acid de-aerated potassium bromide solutions and in water containing hydrogen andoxygen.Johnson and AllenN3 found a constant initial yield of hydrogenduring the irradiation of several solutions with 2 Mev X-rays, and used theirresults to evaluate the yield due to ( F ) . In 0-8~-sulphuric acid lower yieldsof hydrogen were found, probably owing to direct energy absorption by theacid. Johnsonm9 has estimated the percentages of radicals used in theprocesses ( F ) and (R). Hart 406 has made similar estimates from the resultsof oxidation of formic acid in aerated solution by 6oCo y-irradiation andby irradiation with tritium p-rays. This worker also employed the oxidationof ferrous sulphate, in aerated and in air-free solutions, to obtain relativeyields of (R) and ( F ) 410 forOther workers have made estimates of the radical-pair yield alone.Dainton and Rowbottom 411 achieved this by comparison of radiation andphotochemical yields for the decomposition of hydrogen peroxide in aqueoussolution.Rigg, Stein, and Weiss332 made an estimate from work on they- and tritium @-radiation.ferrous sulphaie system. The data obtained frompresented in the table below.Reference Radiation330 goco y406 6OCo y406 TB4 10 6OCo y410 TP330 Y + n411 "CO y332 200 kv X403 2 Mev X412 2 Mev eleztrons413 30 kv XGP GR G H ~ O0.46 2.74 3.660.35 2-78 3-483-351.18 1.57 3.9313.40.395 *12.3these investigations areev perRadicals (yo) radicalR F pair75 25 2779 21 30.570 30 20.862 3853 4740 60 25.57.619.4* Assuming G(Fe2 + Fe3 +) = 20.80 208-1400 A.0. Allen, Discuss. Faraday SOC., 1952, 12, 79.401 P. Bonet-Maury, ibid., p. 72.402 A. 0. Allen, C. J. Hochanadel, J. A. Ghormley, and T. W. Davies, J . Phys.403 E. R. Johnson and A. 0. Allen, J . Amer. Chem. Soc., 1952, 74, 4147.404 E. J. Hart, ibid., p. 4174.405 E. R. Johnson, U.S. Atomic En. Commiss. Report, 1952, BNL-1209.406 E. J. Hart, J . Phys. Chem., 1952, 56, 594.*07 M. Haissinsky, Discuss. Faraday Soc., 1952, 12, 123.OoD E. R. Johnson, U.S. Atomic En. Commiss. Report, 1952, BNL-1209.E. J. Hart, J . Anzer. Chem. SOC., 1951, 73, 1891.F. S. Dainton and J . Rowbottom, Nature, 1952, 169, 370.*12 E. R. Johnson, J .Chem. Phys., 1951, 19, 1204.*13 M. Haissinsky and M. Lefort, J . Chim. phys., 1951, 48, 368.Chem., 1952, 68, 575.408 T. Rigg, ibid., p. 11974 GENERAL AND PHYSICAL CHEMISTRY.All such values can only represent lower limits to the free-radical yield,owing to the possibility of recombination of some of the radicals to form water.This would account for the different values obtained for different systems,even when the work has been carried out by the same investigator. Fromthis point of view the highest value obtained for the free-radical yield, ifsubsequently confirmed, bids fair to be the most likely value. Anotherpossible source of variation is the effect of the excited water molecule H20*,as discussed earlier.It has been suggested that the products hydrogen and hydrogen peroxidefrom ( F ) are formed in regions of high density of energy release (hotspots) .400-402 Bonet-Maury 401 regards each radiation as having some of theproperty of X-radiation and some of the property of a-radiation, the transi-tion from predominantly a-behaviour to predominantly X-behaviour occurr-ing at a mean ion density of 200 ion pairs per micron.Such considerationslead to the expectation that an increase in ionisation density of the radiationemployed will increase the molecular yield (GF) and decrease the free-.radical yield (GR), and that the steady state level of decomposition in purewater will rise.399 These expectations have been fulfilled experimentally.The steady state level of decomposition of water rises as we pass fromX-radiation through proton and deuteron radiation to x-radiation," thisbeing the order of increasing ionisation density.The changing ratios ofradicals produced by (R) and ( F ) for different radiations as given in the Tableare also in agreement with this hypothesis, and Hardwick 334 has shown thaton these considerations a correlation between the apparently anomalousresults of various workers on the ferrous-ferric and cerous-ceric systems canbe achieved.In view of the importance of this systemfrom the point of view of chemical dosimetry it is natural to find that con-tinued attention is paid to it. The effect of several variables on yield in theoxidation of ferrous sulphate produced by X-irradiation has been studied byRigg, Stein, and Weiss 332 who conclude that the effect of increasing pH inreducing the oxidation yield, in air-free solution, can be accounted for bythe mechanism :(ii) The ferrous-ferric system..Fe2* + OH+Fe3+ +OH- .. . . . . ( 7 ). . . . . . . . H + H+ H,+ ( 8 )(9)H + Fe3++Fe2+ + H* - (10). . . . . . Fez+ + H2++Fe3f + H,. . . . .The limiting yield in acid solutions is considered to be due to completeremoval of OH radicals and also the complete removal of H atoms, asH2+acl., in oxidation of ferrous ions. At high pH the competing backreaction (10) causes non-linearity of yield. In aerated solutions all hydrogenatoms function as HO, radicals and the kinetic scheme proposed consists ofprocess (7) together with the following steps :.. . . . . . H + 0, -+ HO, - (11)HO, + Fe2+-jFeJt- + H0,- - (12)H,O, + 2Fe2++2Fe3+ + 20H- * (13)Fe3+ + 0,-+Fe2+ + 0, (14). . . .. . . .. . . . .* Ref. 401, p. 75, Table IBETTS et al. : THE KINETICS OF HOMOGENEOUS REACTIONS. 75The fall in yield found on increase of pH is attributed to the back-reaction(14), a reaction established by independent w0rk.4~~ The proposed schemeswill account for the effect of changing the ferrous-ion concentration in bothaerated and deaerated solution and also explains the authors’ finding thatthe limiting yield in aerated acid solutions is about double that in deaeratedacid solutions. This experimental result is not in agreement with thefindings of several other workers, a value of about 2.8 being more commonlyaccepted.410 The reduction of yield caused by addition of hydrogen indeaerated solutions is explained on the basis of the back-reaction (6), asuggestion supported by the fact that hydrogen increases the rate ofreduction of ferric ions in deaerated solution.Though the above mechanism suffices to explain these authors’ results,it fails to account for results found by other investigators.Thus Daintonand Sutton396 have found that hydrogen peroxide is formed during theX-irradiation of solutions of ferrous ion at concentrations less than 1 0 - 5 ~ .This tends to support the reaction ( F ) whereas no possible mechanism forthe formation of hydrogen peroxide arises from the above postulates.Amphlett 415 has examined the effect of pH on the initial yield of the oxidationof ferrous ions in aerated solutions by X - and y-irradiation.He finds evidenceof a back-reaction as the pH is increased and of an ultimate steady state.The data are not in agreement with those of earlier workers.416 It is shownthat pH effects can only arise from some effect on the HO, radical, and theprocesswhich is equivalent to process (14), is suggested as the pH-dependent step.On the other hand it is found that the pH-dependence of the yield is notfully explained on this basis, and the suggestion is made that possibly theratio (R) : ( F ) changes with pH. Other results still requiring a satisfactoryexplanation are the steady states at high pH and the fact that the yield offerric ion produced does not begin to fall immediately after the start of thereaction.So far the suggested kinetics have failed to fit the results com-pletely and it is suggested that there may be a fundamental inadequacy ofthe proposals. Baxendale 417 has suggested that some of the discrepanciesmay be cleared up by assuming a non-uniform distribution of radicals.It should be noted here that Collinson and Dainton 395 have also found itnecessary to postulate a non-uniform distribution of radicals in order toexplain results on the polymerisation of acrylonitrile in aqueous solution byX- and y-radiations. However, the ferrous oxidation problem is complicatedby the fact that Dewhurst 418 was unable to find stationary states and couldnot obtain reduction of ferric ions, though confirming the effect of pH onboth aerated and deaerated solutions.He also found, contrary to Amphlett,that low concentrations of chloride ion had no effect on the reaction, thishaving been checked on samples of solution from other laboratories. Otherwork which has appeared on the irradiation of the ferrous-ferric system(apart from that discussed in the section on actinometry) concerns irradiation414 W. G. Barb, H. J. Baxendale, P. George, and K. R. Hargrave, Trans. FaradaySOC., 1951, 48, 462.416 H. Fricke and E. J. Hart, J . Chem. Phys., 1935, 3, 60.417 J. H. Baxendale, Discuss. Faraday Soc., 1962, 12, 253, 256.*18 H. A. Dewhurst, ibid., p. 255.Fe3+ + HO,+Fe,+ + H+ + 0, . . . . . (15)415 C. B. Amphlett, Discuss. Farada-y SOC., 1952, 12, 14476 GENERAL AND PHYSICAL CHEMISTRY.in the presence of other substances.Dewhurst 419 has studied the effect ofalcohols on the ferrous oxidation initiated by y-radiation, Hart 420 hasexamined the mechanism of the y-ray-induced oxidation of ferrous ion in thepresence of formic acid and oxygen, and Cottin, Haissinsky, and Ver-meilP219 422 have investigated the effect of hydrocarbons on the yields offerric ion produced in aerated aqueous solutions by y-rays and 24 kv X-rays.The last authors have also examined the effect of alcohols on the X-ray-induced oxidation. In each case the yields of oxidation in aerated solutionsare appreciably higher than the yields without the added material. In thecase of the addition of formic acid the kinetics can be explained on the basisof a chain mechanism including the radical HCO-0.Both alcohols andhydrocarbons appear to give rise to radicals capable of reaction with oxygento form peroxides. These then oxidise the ferrous ions by chain mechanisms,which in the case of alcohols can be inhibited by the addition of chlorideion.419 The increase in rate of oxidation due to the presence of primaryalcohols is greater the longer the alcohol chain.Garrison and Rollefson 423 examined the effect of high-energy a-particleson aqueous solutions of ferrous ions and carbon dioxide containing 14C0,.The aim of this work was to attempt a removal of all the OH radicals byFe2+ ions and hence to study the effect of H atoms on carbon dioxide, thesetwo being assumed to be the active species.The principle products wereferric ions and hydrogen, but a small fraction of the H atoms were used informing reduction products of carbon dioxide, mainly formic acid, with someformaldehyde and oxalate. A mechanism is given which fits the data overthe whole range of observations, and an estimate of the effective concen-tration of H atoms gives this as N ~ O - ~ M .The formation and destruction -of hydrogenperoxide has been the subject of several investigations.401* 4113 424-428Hart and Matheson 424 find the rate of decomposition by ‘j0Co y-radiation tobe unmistakably proportional to [H20&* and (dose rate)*. A mechanismwhich satisfies the results is proposed which, however, contains an unusualthird-order termination step :The special efficiency of hydrogen peroxide as a third body in this reaction,rather than water which is present in much greater amounts, is attributed toa hypothetical ring-complex intermediate between HO, and H202 for whichit would seem there is some indirect supporting evidence.429 Propagationand termination rate constants have been measured in intermittent radiationexperiments.Dainton and Rowbottom411,430 point out that a rate pro-portional to [H202]+ is contrary to their own findings and to the results of(iii) Other aqueous systems.2H0, + H20,+2H,0, + 0, . . . . . (16)419 H. A. Dewhurst, Trans. Faraday SOC., 1952, 48, 905.420 E. J. Hart, J . Amer. Chem. SOC., 1952, 74, 4174.421 M. Cottin, M. Haissinsky, and C. Vermeil, Compt. rend., 1952, 235, 642.422 C.Vermeil, M. Cottin, and M. Haissinsky, J . Chim. phys., 1952, 49, 437.423 W. M. Garrison and G. K. Rollefson, Discuss. Faraday SOC., 1952, 12, 155.424 E. J. Hart and M. S. Matheson, ibid., p. 169.425 M. Ebert and J. W. Boag, ibid., p. 189.426 M. Haissinsky and J. Pucheault, J . Chim. phys., 1952, 49, 294.427 J. Pucheault, M. Lefort, and M. Haissinsky, ibid., p. 286.428 &I. Carmo Anta and M. Haissinsky, Compt. rend., 1952, 235, 170.429 N. M. Luft, Discuss. Farada-y SOC., 1952, 12, 266.430 F. S. Dainton and J . Rowbottom, ibid., p. 264BETTS et d. : THE KINETICS OF HOMOGENEOUS REACTIONS. 77most of the work which has been done on the photolysis of hydrogen peroxide.They find that the rate of decomposition is proportional to [H,O2Ip0 x (doserate)05 for 1-22~-solutions. This is a major discrepancy only to beresolved by further experimentation. Ebert and Boag 485 have investigatedthe formation and decomposition of hydrogen peroxide in aqueous solutionsby the action of 1 Mev electrons, and 1.2 Mev and 200 kv X-radiation.Inaerated solutions a higher initial yield of hydrogen peroxide was found withelectrons than had previously been found by Lefort 431 with 30 kv X-irradi-ation. Experiments with 200 kv and 1-2 Mev X-radiation confirmed that adifference existed between the effect of X-rays and of 1 Mev electrons. Asubsequent investigation by a group of workers 432 confirmed these findingsand showed that for 1 Mev electrons the initial yield of hydrogen peroxidewas Go = 1.10, whilst for 30 kv and 220 kv X-radiation Go = 2.28.More-over a limiting value was attained for the hydrogen peroxide concentrationproduced by 1 Mev electrons whereas no limit to the yield was reached forthe X-irradiations. The results meet with an explanation on the differenceof ion density arising from the two types of radiation and it seems possiblethat the different effects found may arise from a difference in decompositionrate. The effect of pH on the formation and decomposition of hydrogenperoxide in aerated solutions indicates that the effective back-reaction is :0,- + H,O,+OH + OH- + 0, . . . . . (17)The yields of hydrogen peroxide produced in boric acid solutions by pileirradiation are lower than those produced by or-particle irradiation withradon.426 The effects of adding various electrolytes in these experimentshave also been s t ~ d i e d .4 ~ ~ An investigation of the formation and decom-position of hydrogen peroxide in water by irradiation with a-rays of poloniumshowed that the results varied according to the acid In the pre-sence of @8~-sulphuric or -perchloric acid a limiting concentration of hydro-gen peroxide, which depends on the polonium concentration, is reached.In @8~-nitric acid, no hydrogen peroxide is formed. The effect of poloniumand radon in similar experiments is very different, but it is not clear whetherthis is due to a difference in the radiation emitted or to some effect of thepolonium, which was dissolved in the solutions in these experiments. In aninteresting extension of earlier work 4B3 it has been shown that the yield ofhydrogen peroxide produced by the a-radiation from radon is the same fromboth water and a 0.1% solution of carb~xypeptidase.~~~ This confirms theview previously suggested that hydrogen peroxide production occurs in thecore of an a-track and that the small inactivation of carboxypeptidase bya-irradiation is entirely due to &rays arising from the main cc-track. Weisshas discussed possible results which may arise from the photolysis andradiolysis of hydrogen peroxide with particular reference to reaction in andbetween tracksu5The exchange reaction between oxygen and water initiated by y-radiationhas been studied by using oxygen enriched in the isotope 180.436 The rate431 M. Lefort, J . Chim. plays., 1950, 47, 624.492 T. Alper, M. Ebert, L. H. Gray, M. Lefort, H. C. Sutton. and F. S. Dainton,433 TV. M. Dale, L. H. Gray, and W. J. Meredith, Phil. Trans. 1949, A , 242, 33.434 W. M. Dale, J - V. Davies, C. W. Gilbert, J. P. Keene, and L. H. Gray, Biochem. J . ,436 E. J . Hart, S. Gordon, and D. A. Hutchison, J . Amev Chem. SOC., 19 52, 74,5548.Discuss. Faraday SOC., 1952, 12, 266.1952, 51, 268. 435 J. Weiss, Discuss. Faraday SOC., 1952, 12, 16178 GENERAL AND PHYSICAL CHEMISTRY.of exchange was found to increase with pH and concentration of 16, l80 2and was inhibited by hydrogen peroxide. The exchange proceeds by achain mechanism, as many as 40 oxygen molecules being exchanged per freeradical pair formed at pH >9. The chain is terminated by hydrogenperoxide. An equilibrium is proposed : HO 6 0- + H+, exchange beingthen effected by reaction of 0- ions with oxygen molecules and OH- ions.H0,- and 0,- ions act as chain terminators.Hardwick437 has studied the reduction of ceric sulphate in varyingconcentrations of sulphuric acid, using y-rays from and radium, and2000 kv X-rays. The yield of cerous ion (G = 3.2) remained constant overa wide range of dose rates, ceric ion concentration, and pH, and was indepen-dent of the presence or absence of oxygen. The addition of hydrogen gasto air-free solutions increased the yield of cerous ion to G = 6.2. Theseresults, which can be explained on the basis of reduction by H atoms onlyor by H atoms and hydrogen peroxide, differ markedly from the results ofother workers.438 However the radiation used by Haissinsky et aLU8 was14 kv X-radiation and an attempt has been made to account for theseapparent anomalies, and to correlate other results obtained for this systemand the ferrous-ferric system, on the basis of the difference in energy of theionising electrons arising from the different radiations employed.334 Suchan explanation necessitates the assumption that a greater proportion of thereduction of ceric ions proceeds by hydrogen peroxide in the case of the low-energy X-rays than in the case of y-radiation. It has been pointed out,however, that no such corresponding effects arise in the irradiation of purewater.439 The effect of radiations ranging from y-rays to infra-red rays onmethylene-blue in water or glycerol is claimed to be different in the twosolvents.u6 Spectrophotometric evidence is given to show that bleaching ofthe dye takes place via the leuco-dye in glycerol; in aqueous solution noleuco-dye is formed, bleaching is much slower and is never complete.In view of other work which has recently been done on this system 3973 440s 441it seems certain that the effects in aqueous solution were in fact due toincomplete deaeration.A study has been made of the exchange between deuterium gas and liquidwater under the action of 60Co y-rays,a, but the full results are not yetavailable. Experiments have also been started u2 on the mode of formationof hydrogen peroxide in the y-ray-induced water-oxygen reaction, with theisotope l80 as a tracer. The X-irradiation of linoleic acid in aqueoussolution leads to a chain reaction.a3 Decrease of dose rate or increase ofconcentration of the substrate both tend to increase the ionic yield. Thisis a further demonstration that radiation chemical chain reactions showgreater sensitivity to changing conditions than do single molecular changes.*It is suggested that similar reactions may account for the large effectsproduced by small doses of irradiation in animals. Experiments on the437 T. J. Hardwick, Cavtad. J . Chew., 1952, 30, 23.438 M. Haissinsky, M. Lefort, and M. Le Bail, J . Chim. phys., 1951, 48, 209.439 M. Lefort, Discuss. Faraday Soc., 1952, 12, 273.440 M. J. Day and G. Stein, Nature, 1950, 166, 146.441 E. Collinson, Discuss. Faradav SOC., 1952, 12, 285.442 S. Gordon, E. J . Hart, and P. D. Walsh, U.S. Atomic En. Commiss Report,* Cf. ref. 395.1951, AECU-1742. 443 J . F. Mead, Science, 1952, 115, 470BETTS et nl. : THE KINETICS OF HOMOGENEOUS REACTIONS. 79change in viscosity produced in solutions of polymethacrylic acid under theaction of X-radiation and " nitrogen mustard " indicate that the mechanismis different in the two cases.& The change is brought about by coiling ofthe chains in the case of " nitrogen mustard " and by degradation of thechains with X-rays in aerated solution. The fact that there is no appreciablechain breakdown during X-irradiation of deaerated solutions seems toindicate that the effective chain-breaking radical may be the HO, radical.It is suggested that effective biological protective agents function by ab-stracting an oxygen atom from HO, since the same agents protect thepolymethacrylic acid degradation.445The X-irradiation of potassium iodate showed an interesting variationin the ratio of the products formed (iodine and hydrogen peroxide) and inthe after-effect observed according to whether the solutions were aerated ordeaerated.u6Other aqueous systems which have been studied are the decolorisation ofchlorophenol-red by X-radiation,M' the X-irradiation of ammonia solu-tions,u* perchloric acid,449 mercuric and i n d ~ l e , ~ ~ l the y-irradi-ation of cysteine 452 and benzene:453 the electron-irradiation of tryptophan,tyrosine, phenylalanine, and c y ~ t i n e , ~ ~ and of fats,455$ 456 the pile-irradiationof ~ y s t i n e , ~ ~ ~ and the a-irradiation of formicvarious aspects of the radiation chemistry of aqueous solutions have appearedduring the past year.459-462Alder and Eyring 463 have presented a kinetic analysis of irradiations insolution. Their treatment is not essentially different from that given earlierby Dainton464 but they have been able to use the resulting expression forionic yield in terms of solute concentration to fit the curves of, experimentalresults. This means that certain parameters in the expression can beevaluated and the yield of water molecules decomposed per 100 ev ofenergy absorbed can be estimated for each set of experiments. The highestvalue of G(H,O) so obtained is 5.9. This is derived from results on the X -irradiation of carb~xypeptidase.~~ Formation of hydrogen and hydrogenperoxide is neglected in the treatment. A treatment which is claimed toOther reviews of.444 P. Alexander and M. Fox, Nature, 1952, 164, 572.445 Idem, ibid., 1952, 170, 1022.446 N. Todd and S. L. Whitcher, J . %hem. Phys., 1952, 20, 1172.447 E. N. Weber and R. H. Schuler, J . .4mer. Chenz. SOC., 1952, 74, 4415.448 T. Rigg, G. Scholes, and J . Weiss, J., 1952, 3034.44Q B. Milling, G. Stein, and J. Weiss, Natzire, 1952, 1'70, 710.450 G. Stein, R. Watt, and J . Weiss, Trans. Favaday Soc., 1952, 48, 1030.461 C. B. Allsopp and J. Wilson, Discuss. Faraday Soc., 1952, 12, 299.452 A. J . Swallow, J . , 1952, 1334.453 T. J. Sworski, J . Chem. Phys., 1952, 20, 1817.454 B. E. Proctor and D. S. Bhatia, Biochem. J . , 1952, 51, 535.455 R. S. Hannan and J. W. Boag, Nature, 1952. 169, 152.458 R. S. Hannan and H. J. Shepherd, ibid., 1952, 170, 1021.457 M. Lipp and H. Weigel, Naturwiss., 1952, 39, 189.4 5 * W. M. Garrison, D. C. Morrison, H. R. Haymond, and J. G. Hamilton. J . Amer.45g G. Stein, Discuss. Faraday SOC., 1952, 12, 227.460 L. H. Gray, J . Cellular Comp. Physiol., 1952, 39, Suppl. l., 57.461 W. M. Dale, ;bid*, p. 39.462 A. 0. Allen, Ann. Reviews Phys. Chem., 1952, 3, 57.463 M. G. Alder and H. Eyring, Nucleonzcs, 1952, 10, KO. 4, p. 54.464 F. S. Dainton, A n n . Reports, 1948, 45, 5.Chem. Soc., 1952, 74, 421680 GENERAL AND PHYSICAL CHEMISTRY.be simpler 465 and is based on Dee and Richards’s theory 318 yields the sameexpression for the ionic yield as does that of Alder and Eyring. The muchlower radical yields deduced for a-irradiations by this method are explainedas being due to local quenching of primary photons by molecules directlydamaged by the radiation.R. H. B.E. C.F. S. D.K. J. I.R. H. BETTS.E. COLLINSON.F. S. DAIKTON.C. W. DAVIES.D. D. ELEY.K. J. IVIN.J. W. LINKETT.C. B. MONK.4135 J. B. Binks, J . Chem. Phys., 1952, 20, 1655