R. D. ANDERSON, S. DAVISON AND M. BURTON 143 THE THERMAL STABILITY AND REACTIVITY OF HYDROCARBON RADICALS BY M. SZWARC Received 12th February, 1951 The bond dissociation energies of some hydrocarbon radicals are calculated and the vpriation in their magnitudes discussed in relation to radical structure. Various types of reactions involving radicals are treated, special attention being paid to the problem of repulsion forces in metathetic reactions of the type R + XR* --f RX + R*. Some conclusions are drawn regarding the shapes of various repulsion curves. The problem of the temperature independent factors of radical reactions is examined. It is shown that the experimental findings can be well accounted for by the transition state theory. The behaviour of radicals in chemical reactions is somewhat different from that of ordinary molecules.The essential difference is caused by their low thermal stability and by their high reactivity. The Thermal Stability of Radicals.-The low thermal stability of many hydrocarbon radicals when compared with the parent hydrocarbons is due to the considerably decreased dissociation energy of some of their bonds. CH, . CH,*H + CH, : CH, + 11. Let us clarify this point by considering the dissociation processI44 REACTIVITY OF RADICALS In this reaction the extension of the C-H bond coincides with a coupling process in which the free electron of the radical couples with one of the electrons participating in the C-H bond. Consequently, the rupture of the C-H bond occurs simultaneously with the formation of a new T bond (the “ second half of the double bond ”) and the energy 1ibera.ted in the formation of the latter bond is utilized in the process of fission of the former bond.Hence, the C-H bond dissociation energy in the ethyl radical is lower than the C-H bond dissociation energy in ethane by the energy of the “ second half ” of the double bond. Table I presents some C-H and C-C bond dissociation energies in a series of simple hydrocarbon radicals. The listed values have been calculated by applying the equation D(R-olefine) = AHf(R) + AH, (olefine) - AHf (R . olefme). R . olefine denoting the relevant radical, and R a hydrogen atom or a smaller radical produced in the dissociation process. The required heats of formation of radicals have been taken from a previous article.1 TABLE I D(*CH,.CH,-H) = 38 kcal./mole D(‘CH”)CH-H) =-- 39 kcal./mole D(CH, . &t. CH,-H) =: 45 kcal./mole CH, *CH; ( 3 3 3 \CH-H) = 40 kcal./mole \c. CH2-H) = 4G kcal./mole D(*CH,. CH2-CH,) = 25 kcal./mole D(*CH,. CH2-C2Hs) = 26 kcal./mole *CH YC-13) = 68 kcal./mole *CH D( CH,/ \C-CH,) = 57 kcal./mole Although the quoted values are not altogether certain and should be taken with reservation, they do show definite regularities and enable one to draw interesting conclusions.* (I} In the series, CH, . CH2-H, CHZ . CH-H, *CH, . CH-H t H 3 &S we find a small increase in the C-H bond dissociation energy. other hand, in the series On the CH3. CH2-H, CH3. CH-H, CH, . CH-H 6H , i‘.2HS there is a definitz and quite considerable decrease in the C-H bond dis- sociation energies, the relevant values in kcal./mole being 98, 89 and 86 -f respectively .Szwarc, Chem. Rev., 1950, 47, 75. *The results for D[(CH,),CH-HI and D[(CH3),C-H] of Stevenson in this 7 D( cH3>H-H) was estimated by subtracting from the value of \CH-H), 3 kcal./mole, which is the difference between D(CH,. CH,-H) Discussion invalidate some of our conclusions. CZHS CH, D and D(C,H, . CH,-H). (CH3/M, SZWARC I45 A useful interpretation of these results can be given by considering the ( I ) (2) following series of reactions : CH, . CH, . H +CH,. CH,. + H - D(X. CH,. CH,-H) kcal.jmole, and CH, . CH. H + CH, . CH- + H - D(CH3 . CH-H) kcal./mole, x x k k 2 X denoting an alkyl or a q l radical. energy is not affected by the presence of the X group, i.e.I n the second case this assumption cannot be made since the proximity of the X group to the reacting centre certainly changes the CH, . CH-H Let us assume that in the case (I) the X . CH, . CH,-H dissociation D(CH3. CHS-H) w D ( X . CH, . CHZ-H). dissociation energy making k D(CH3. CH2-H) > D(CH3. CH-H). ;ri. This decrease in the C-H bond dissocistion energy might be attributed to the inereas? in the resonance energy of the CH, . CH- radical as com- pared with that of the CH, . CH2* radical.8 In another way, one might say that the delocalization of the free electron is greater in the radic.al CH, . CH- than in the radical CH, . CH,.. 2 k It is plausible that the same gain in delocalization energy would be observed if one compares the hypothetical processes (3) CH, .CH . H 4 CH, . CH* + H k ;;r CH2. CH, . H -+ CH8 . CH,* + H However, the energy gained in process (3) as compared lost in process (5). CH, . CH* 3 CH, : CHX . x and (4) (3) * (4) with (4) would be and if the delocalization of 7~ electrons in CH, : CHX is about the same a s that in CH, : CH,, the results would be D(CH2. CH2-H) D(*CH,. CH-H). k The resultc quoted in Table I seem, therefore, to indicate th3.t the sub- stitution of a group X for a. hydrogen on a carbon atom having a free electron has much greater effect on its delocalization energy than it hds on the delocalization energy of the T electrons of the corresponding olefin. one finds a considerable increase in the C-H bond dissociation energy. This effect is in agreement with the preceding discussion.The substituent X affects only slightly’ the dissociation energy of the hypothetical process (2) Comparing D(.CH2 ~ CH,-H) with D(CH, . dH . CH,-H) CH . CH, . H -+ CH . CH,. + H - E , kcal./mole CH, . CH, . H -+ CH, . CH,. + H - E , kcal./mole. x 5i i.e. E, w E,. Szwarc, J . Citem. Physics, 1950, 18, 1160REACTIVITY OF RADICALS However, in the coupling processes CH . CH,. -+ CH : CH, + E,’ kcal./mole, ;;c k and CH, . CH,. -+ CH, : CH, + E,,’ kcal./mole, the difference E,‘ - E,’ is approximately equal to the difference between D(CH,. CH,-H) and D(CH,. CHX-H) (i.e. the “ delocalization ” energy in the CH, . CH, radical is lost in the coupling process). A We conclude, therefore, that D(CH,. 6H. CH,-H) - D(&I.,CH,-H) w D(CH,. CH,-H) CH, - D ( cH3>H-H).Inspection of the experimental values shows that the former difference is 7 kcal./mole, whilst the latter is g kcal./mole. ( 3 ) The loss of considerable resonance energy of the allyl radical is the reason for a great increase in its C-H bond dissociation energy as compared with that in n-propyl radical. (4) The difference in D(R-H) and D(R-CH,) is only slightly smaller for radicals than for molecules. For example, D(CH,. CH,-H) - D(-CH,, CH,-CH,) = 13 kcal./mole. D(CH,. CH,-H) - D(CH, . CH,--CH,) = 16 kcal./mole. As mentioned previously the decrease in the thermal stability of a radical is due to the decrease in the relevant bond dissociation energy. Whenever the radical is stabilized by resonance the relevant bond dis- sociation energy increases, and therefore its thermal stability increases too (see, e.g., n-propyl radical as compared with allyl radical).For the sake of accuracy one has to point out that the thermal stability is measured not by the dissociation energy but by the activation energy of the dis- sociation process. The latter is larger than the bond dissociation energy by the activation energy of the addition process olefine + R --f olefine . R. If R is a hydrogen atom or a methyl radical the relevant activation energy of the addition process seems to be small, and most likely it does not change the gradation in the stabilities of radicals as obtained from con- siderations of bond dissociation energies. A great increase in the thermal stability of a radical is found foi all cases where the decomposition cannot lead to the formation of a double bond. For example, no double bond can be formed in the decomposition of benzyl radical, and this makes the benzyl radical thermally more stable than the allyl radical, although the resonance stabilization of the latter is perhaps even higher than that of the former (estimates quoted from ref.(2) lead to ca. 24 kcal./mole for the resonance energy of benzyl radical and to ca. 25 kcal./mole for that of allyl radical). On similar grounds a high degree of thermal stability might be expected for such radicals as CH,. I It would be interesting to investigate the thermal stability of cyclopropyl radical, since the formation of a double bond would lead in this case to a highly strained structure. Of course, this does not exclude the possi- bility of an easy isomerization of the cyclopropyl radical to an allyl radicalM.SZWARC 147 and the subsequent decomposition of the latter to allene and a hydrogen at om. The Reactivity of Radicals.-In discussing the reactivity of radicals we shall consider two aspects of this problem : (a) reactions between two radicals and (b) reactions between radicals and molecules. The reactions between radicals may lead either to their dimerization or to their disproportionation. I t seems that the dimerization of many radicals does not require any activation energy. Evidence favouring this opinion has been obtained recently by independent studies of Gomer,3 of Rice and Lucas,* and of Dodd.6 All these workers investigated the rate of dimerization of methyl radicals CH, + CH3 + C&&, and their findings show that this reaction takes place nearly at every collision,* i.e.its activation energy is negligible. Saying that a re- action takes place at every collision implies that we can calculate in- dependently the frequency of encounters among the particles (or that we know the relevant cross-sections). However, it seems that the concept of a collision may be interpretzd in more than one way. Whether an encounter is considered as a collision depends on the type of interaction in which one is interested. It is common practice in chemical kinetics, especially when the collision theory is applied, to calculate the number of collisions from data obtained in measurements of the viscosity or the heat conductivity of a gas.This implies, of course, that we are interested in such collisions in which the translation energy of colliding particles can be exchanged. It is not certain, however, that this type of collision is relevant when a chemical reaction is considered (see, e.g., Glasstone, Eyring and Laidler ).6 Hence, it appears that the normal value for 2 (i.e. collision number) used in chemical kinetics is chosen quite arbitrarily. A more analytical approach to the problem of chemical kinetics is provided by the transition state theory.', * J * Unfortunately this approach requires a knowledge of the structure of the transition state (also referred to as the activated complex), which is a hypothetical species, not accessible to direct experimental measurements.Consequently, any calculations based on the latter method must remain vague, and the a priori computa- tion leading to numerical values is a matter of intelligent conjecture of the structure of the transition state. Nevertheless, this treatment helps in the understanding of the trends which are actually observed and makes it possible to interpret them in terms of some molecular models. Returning to the problem of recombination of methyl radicals, we have to point out that the high value for the rate constant of about 5 x 1013 cm.3 moles-1 sec.-l, reported in the recent investigations, might indicate that the collision diameter for the recombination process is large. Thi: would mean that the interaction between two methyl radicals which lead: to the dimerization might take place at a greater distance than that a1 which, say, two methane molecules can exchange their kinetic energy.On the other hand, one would expect that the methyl radical has to approach quite closely the molecule RH in order to react with it according to the equation CH, + RH -+ CH, + R. The last statement requires some clarification. Gomer, J . Chem. Physics, 1950, 18, 998 ; Gorner and Kistiakowsky, ibid., Rice and Lucas, J . Chem. Physics, 1950, 18, 993. 1951, 19, 85. 5 Dodd, Trans. Faraday SOC., 1931, 47, 56. * See, however, Miller and Steacie, J . Chem. Physics, 1951, 19, 73. 6 Glasstone, Eyring and Laidler, Themy of Rate Processes (McGraw-Hill, 1940). 7 Eyring and Polanyi, Z. physzk. Chem. B, 1931, 12, 279. Eyring, J . Chem. Physics, 1935, 3, 107.Evans and Polanyi, Trans. Faraday SOC., 1935, 31, 875.148 REACTIVITY OF RADICALS If this view is correct then one would ascribe to the methyl radical a large collision cross-section when a recombination process is considered and a small collision cross-section when it reacts with RH. The purpose of this discussion is to show that one can, in principle, ascribe different cross-sections to the same species according to the type of reaction which is investigated, a point which has been realized for some time. For instance, it is known that in experiments in which the scattering of particles by some medium is measured, the cross-section of the particle depends on its energy. An example is provided by the recent studies of the scattering of hydrogen atoms by hydrogen molecules.lo Although it is likely that on the whole the recombination of radicals does not involve any activation energy, some radicals have to surmount an activation barrier before recombining, e.g. in the dimerization of tri- phenyl methyl radicals.11 It seems that in this process the activation energy arises due to the necessity of overcoming the steric hindrance between the bulky phenyl groups.l* The recombination of polar radicals was discussed by Weiss 13 who suggested that these reactions might re- quire activation energies to overcome the repulsion between the approach- ing dipoles. A mathematical treatment of such a problem has been given by Heitler and Rummer.14 It seems that our present knowledge is not sufficiently well advanced to allow us to make any definite statement about the relative rates of disproportionation of radicals as compared with their dimerization. The experimental facts reported in the literature are highly confusing, l5 and it appears that experiments with as simple systems as possible are needed before one can hope for the elucidation of this problem.From general considerations, it would be expected that the disproportionation of radicals would involve only a small activation energy, and that the probability of occurrence of such a process, i.e. the PZ factor, would be smaller than for the dimerization reaction. Reactions between radicals and molecules will be considered under two headings : the activation energy and the temperature independent factor (the PZ factor). In the methathetic reactions of the type R + XR, +RX + R, the exothermicity of the process is given by D(R-X) - D(R,-X).It was suggested that for some processes of this type, namely, RX + Na + R + X- Na+ there is a simple relation between the activation energy of the process and its exothermicity, 16 AE and AH denoting the increase in the activation energy and in the exothermicity of the sodium flame reaction when two reacting species RX and R,X are compared. In deriving this relation one has to assume that the sodium atom can approach the reacting centre without overcoming any repulsion, and that the repulsion curve for the R-CI- interaction is independent ot the nature of the radical R. These assumptions seem to be justified for sodium flame reactions (see, however, ref.(IZ)), but they might not be valid for such reactions as, e.g., RH + CH, + R + CH,. AE = a. AH, lo Amdur, Kells and Davenport, J . Chem. Physics, 1950, 18, 1676. l1 Ziegler, Trans. Faraday Soc., 1934, 30, 10. l2 Szwarc, Faraday SOG. Discussions, 1947, 2, 39. l3 Weiss, Trans. Faraday SOL, 1940, 36, 856. l4 Heitler and Rummer, 2. Plzysik, 1931, 68, 12. I5 See, e.g., Steacie, Atomic and Radical Beactions (Reinhold, 1946). * The disproportionation process is highly exothermic, since the dissociation energy of the bond formed is greater than the dissociation energy of the bond broken. l6 Evans and Polanyi, Trans. Faraday Soc., 1936, 32, 1933 ; 1938, 34, 22.M. SZWARC 149 In considering the variation in the activation energies of such reactions one has to bear in mind the changes of the resonance energy in the transi- tion state 17 which is not negligible for this type of process.It seems profitable to compare a metathetic reaction of the type RA + Rl -+ R + AR, with the thermal decomposition of RA into two fragments produced by the rupture of one bond only. In the latter case the bond ruptured is always the weakest bond, i.e. the bond which has the lowest dissociation energy. However, this need not be the case for methathetic reactions. For example, let us consider two methathetic reactions between a mole- cule AMB and a radical R, namely, AMB + R +AM + BR and BMA + R +- BM + AR. It is not sufficient to consider the dissociation energies of AM-B and BM-A bonds in order to say which of the two reactions is more likely to occur.The result depends very much on the values of D(R-A) and D(R-B), since the energy liberated in the process of bond formation provides the driving force for the reaction. This problem was treated by Evans and Polanyi,l* who also showed how important is the consideration of the repulsion forces for understanding these processes. Let us consider, e.g. a series of thermoneutral reactions of the type R , X + R* + R + XR* R . Y + R* + R + YR*. Evans and Polanyi suggested that this reaction can be considered as taking place in three steps : (i) R* approaches the rigid molecule RX until the distance R . . . R* is that in the transition state complex, without affecting the R-X bond length, i.e. the configuration obtained is R-X . . . R*. - (1) R . . . X-R* * (11) (ii) Keeping the R .. R* distance constant, we move X from the position shown in (I) to the position shown in (11) where X-R* is the normal R*-X bond length in the molecule R*X. (iii) R is removed to infiGity. Fig. I and 2 represent schematically the overall process, the arrows denoted by number I, z and 3 representing the three stages of the reaction suggested. The total activation energy E , can be considered as composed from two parts, E,. resulting from the repulsion forces and Et resulting from the extension of the bond which is ultimately broken, i.e. It is plausible to expect that Et increases with increasing R-X dissociation energy, and hence the knowledge of bond dissociation energies enable us to understand the trend in Et. However, our knowledge of E, is scanty’ and its variation with molecular structure is not known.Some observa- tions of Kharasch may shed light on this problem. investigated the addition of chloroform and bromoform to double bonds and it follows from their observations that radical R reacts with chloroform and bromoform according to eqn. E, = Et + E,. Kharash and his colleagues R + CHBr, -+ RBr + CHBr,. . 17 Evans and Szwrarc, Trans. Faraday Soc., 1949, 45, 940. 18 Evans and Polanyi, Trans. Furuduy Soc., 1938,34, 11. 19 Kharash, Jensen and Urry, J . Amev. Chern. Soc., 1947, 60, 1100.150 REACTIVITY OF RADICALS Data of bond dissociation energies indicate that in general D (C-H) > D (C-CI) > D (C-Br) . Therefore we would expect that for reactions R + CHCI, -+ RH + CCl, - (1) R + CHCl, -+ R .C1 + CHCI, (2) . Et, >Eb. On the other hand, the results of Kharash seem to indicate that E,< E,. To explain these observations one would assume t h a t the repulsion forces increase along the series H, C1, Br, i.e. E, < Er? < E,, the results of Kharash being then interpreted in terms of the diagram (Fig. 3). ET, < Er2 < Er, Et, > Et, > Et, Ea, < Ea, < EQ- I R-X d / ; h c e --+ FIG. I. c 4 I I 6 h A - - ---- x FIG. 2. TIT Our knowledge of repulsion forces is very scanty, and it is gratifying that the above discussion might furnish information about the shape of various repulsion curves. Fig. 3, taken from the paper of Evans and Polanyi,I* shows the method for finding the position of the transition state and for calculating the activation energy of the process.Curves I and I’ represent the repulsion potentials which hinder the approach of a radical R to a rigid molecule XR*, and of a radical R* to a rigid molecule XR. Curves z and 2’ represent the potential energies corresponding to X-R* and X-R bond extension processes. The position of curve I relative to curve I’ is fixed by the properties of the system investigated. To find the position of the transition state (point T in Fig. 3 ) one has to slide curves 2 and 2’ along the curves I and I’ respectively until their crossing point is as low as possible ; this crossing point then represents the transition state. Its elevation from the 0 line gives the required activation energy of the process.151 M. SZWARC Simple geometrical considerations show that when curves 2 and 2’ attain the required positions, the slope of curve z a t the crossing point T must be equal to the slope of curve I a t point A.If we replace atom X in the molecule XR* by an atom Y, and let D(R*-Y) be greater than D (R*-X) . The potential energy curve representing the extension of R*-Y bond would be steeper than the one corresponding to the R*-X bond. Consequently, if one uses the same repulsion curve for both pro- cesses (i.e. involving R*X and R*Y) one finds the RY curve (the dotted curve in Fig. 3 ) to be placed higher than the corresponding RX curve. Since E, is measured by the level on which point A (or A’) is placed, we conclude that E, would increase with increasing dissociation energy of the bond in question, if the same repulsion curve is used for both reactions : and R + XR* -+ RX + R* R + YR* -+RY + R*.,e-- I / FIG. 3 We have seen, however, that the results of Kharash suggest a decrease in E, for a series R-Br, R-Cl, and R-H, i.e. for a series in which the relevant bond dissociation energy increases. To explain these results we assume that the repulsion curves are different for different atoms (X, Y , etc.) transferred in the reaction. For example, for R approaching HR* the repulsion curve should have the shape of curve I in Fig. 4, i.e. the repulsion force, being negligible for the first stages of reaction, increases suddenly when R is sufficiently close to HR*. In this case not much work is performed in overcoming the repulsion forces while the system arrives at point A corresponding to a relatively steep slope (i.e.E, is small). On the other hand, the repulsion curve representing the interaction of R and ClR* would have the shape of curve I1 in Fig. 4. The repulsion force appears at a greater distance, but i t increases gradually, and in consequence, a considerable amount of work has to be done before the system arrives a t point B which corresponds to a comparatively flat slope (i.e. here E, is greater than in the previous case). The difference in the shapes of these two repulsion curves is plausible. One can say that the approach to a small but “compact” hydrogen demands a repulsion curve represented by I, while the approach to a bigger but more “ compressible ” chlorine would call for a repulsion curve repre- sented by 11.Although this representation is crude and highly ap- proximate it seems to be reasonable. At any rate, it gives us a glimpse into the problem of repulsion forces, which are of great importance for the understanding of chemical kinetics. Let us turn now to the problem of “ temperature independent ” fac- tors of radical reactions. This problem has recently caused some dis- cussion, and it seems profitable at this juncture to survey the questionREACTIVITY OF RADICALS again. A paper published by Steacie, Danvent and Trost 20 initiated a discussion on the magnitude of steric factors in reactions involving radicals or atoms. These authors tentatively suggested that the steric factors for the metathetic reactions of the type RH + X + R + HX, where X denotes a hydrogen atom or a methyl radical, are very small, e.g.a steric factor of the order of I O - ~ was suggested for the reaction The idea of low steric factors was taken up by Bamford and Dewar who stated : ‘‘ It seems reasonable to infer that organic radical reactions with activation energy less than 20 kcal./moIe in geneVal have frequency factors of the order of 107 and not 10l2 * as is commonly assumed.” C,H,o + €3 --f CIH, + Ha. FIG. 4 It seems that the above papers created an impression that a new approach is required in dealing with the rates of reactions involving radicals or atoms. It might appear that these reactions cannot be treated by the usual transition state method, and that this theory should be abandoned, or at least modified, if it is to cope successfully with radical reactions.The paper by Evans and Szwarc l7 attempted to point out that there is no justification for such an extreme conclusion. The review of the existing experimental data, collected in Tables I and IA of the latter paper, indicates that the steric factors in reactions involving atonzs are of the order 0.1, to within a factor of 10. It was pointed out that the transition state theory leads to lower steric factors if a reaction involves radicals. For example, a steric factor of the order I O - ~ (within one power of 10) would be expected for a reaction involving the comparatively small CH, radical (see p. 945 of their paper). For reactions involving more complex radicals, still lower steric factors are to be expected, examples being given by the recombination of triphenyl methyl radicals, the growth of a polymeric chain, or chain transfer reactions.In all these cases three degrees of rotational freedom are lost in the formation of the transition 20 Steacie, Darwent and Trost, Faraday SOC. Discussions, 1947, 2, 80. Bamford and Dewar, Nature, 1949, 163, 256. * These numbers refer to cm., mole. -l sec. -l units.M. SZWARC I 5 3 state complex, and in terms of this loss of rotational freedom steric factors as low as I O - ~ have been described and understood. In consequence, the paper concludes that “ . . . there is no justification for assuming abnorwuZZy low steric factors for such (radical) reactions. Small steric factors will occur in reactions involving two complex radicals or mole- cules.This is not new, and has frequently b2en discussed in terms of the loss of rotational freedom of the reacting centres.” The paper by Szwarc and Roberts 22 re-emphasized the conclusion of Evans and Szwarc. The former authors discussed the reaction CH, + CIH, . CH, --f CH, + C,H, . CH, and deduced that the magnitude of the steric factor in this reaction does not contradict the expectations of the transition state theory, i.e. the frequency of the effective collisions (the temperature independent factor, or PZ factor) for this reaction is of the order 10ll-10~~ cm., sec.-l mole-1 (see summary of their paper, p. 625). In calculating the magnitude of stsic factors one has to assume the magnitude of collision encounters (usually denoted by the letter 2) which, in turn, depends on the collision diameter.Evans and Szwarc pointed out, however, that there are some uncertainties in estimating the latter entity, since it depends on the type of phenomenon which is in- vestigated and this point has been discussed further in the present paper. Obviously, if a large collision diameter is chosen, one must derive a low steric factor. For example, Gomer and Dorfman 28 used the data of Szwarc and Roberts 22 for the reaction CH, + toluene, and assuming a collision diameter as large as 10 derived a steric factor as low as 7 x I O - ~ . The magnitude which is measured directly and which is indeed essential for reaction kinetics is the PZ factor, i.e. the temperature independent factor (or the effective collision frequency). It would be better to con- centrate attention on this entity, and so avoid the apparent controversy due to usage of various values for the collision diameter.The transition state theory enables us to calculate approximately the PZ factors. For example, for a reaction of the type RH + CH, - + R + CH, the calculation would lead to PZ of cu. 10ll-10~~ (within a power of 10). It is remarkable that the experimental results of various workers give this order of magnitude (see Table 11). TABLE 11* I I Reaction Investigators A = P Z cm.S/moles Sec. I I CH, + CH,. CO . CH, CH, + CH,. CO. CH, CH, + CH, . C,H, CH, + CH,. C,H, Trotman-Dickenson z4 and Steacie Jaquiss, Roberts 24 and Szwarc Trotman-Dickenson 24 and Steacie Szwarc and Roberts 22 5’7 x I011 3’3 x I011 1.6 x 10ll 6.4 x 1o12 Szwarc and Roberts, Trans. Faraday SOC., 1950, 46, 625. 23 Gomer and Dorfman, J . Chem. Physics, 1951, 19, 136. *The values for A listed in this Table were computed from the formulae taking for AC~H,, the value 7 x 1013 ~m.~/rnoles sec. as reported by G ~ m e r , ~ who assumed E . c ~ H ~ = 0.I 5 3 TRICHLOROMETHYL RADICALS We conclude, therefore, that all the experimental evidence reported recently for reactions of the type CH, + RH -+ CH, + R seems to be in concord with the requirements of the transition state theory. No new hypothesis seems to be required to account for the rates of these radical reactions. Of course, the PZ factors need not be constant, and the work of Trotman-Dickenson and Steacie 24 is of the greatest value in showing how the change of the reacting species affects the numerical value of these factors. It is important, however, that their order of magnitude remains within the range predicted by the transition state theory. It is a pleasure to express my thanks to Prof. M. G. Evans, F.R.S., for very helpful and stimulating discussions. Chemistry Department, Manchester University, Manchester, 13. z4 Trotman-Diekenson and Steacie, J . Amer. Chem. Soc., 1950, 72, 2310 ; 45 Jaquiss, Roberts and Szware, unpublished data. J . Chem. Physics, 1950, 18, 1097; 1951, 19: