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SOME COMPARISONS BETWEEN PHOTOCHEMICAL PROCESSES IN GASES AND SOLUTIONS1 2 ROSCOE G. DICKINSON Department of Chemistry, California Institute of Technology, Pasadena, California Received May 25, 1988 The chief purpose of the present section of this report is a comparison of photochemical reactions in the gaseous state with those in solution or in the liquid state. It is not proposed to enter into a detailed discussion of photochemical processes in solution but rather to indicate the relation of such processes, when possible, to those occurring in the gaseous state. This section accordingly contains a brief statement of viewpoints involved in comparing gaseous and solution or liquid reaction, together with some discussion of pertinent experimental results. In recent years theories of the liquid state and of various phenomena occurring in liquids have undergone active development; this may, for example, be seen in the general discussion of the liquid state published by the Faraday Society (43) as well as in other papers to which specific refer- ence will be made. Theoretical approaches to the liquid state have some- times started with the gaseous state and have sometimes started with the crystalline state; Bernal (4), however, has given reasons for believing that liquid structure, while having points of close resemblance to the crystal- line, is of a character that can not be reached by continuous transition from the crystalline state. Current views are that a liquid, at not too high a temperature, aside from differing from a gas in the matter of coherence, possesses a somewhat quasi-crystalline structure. This does not necessarily show itself in any large regions with crystalline regularity but appears rather in the char- acter of the distribution function perk, where 4,rr2p~r~dr gives the probability of finding a second molecule within the distance range r to r + dr of a chosen molecule. This distribution function has been investigated by x-ray diffraction methods (25, 42, 5, 11, 29) and by experiments with models (30~. The function does not show the monotonic character ex- pected for a dilute gas, but rather exhibits maxima and minima which ~ Contribution No. 4 to the Third Report of the Committee on Photochemistry, National Research Council. 2 Contribution No. 643 from the Gates and Crellin Laboratories of Chemistry, California Institute of Technology. 41

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42 ROSCOE G. DICKINSON become less pronounced with increasing r but are evident for a distance of several molecular diameters. The structure, at least in the case of simple non-polar liquids, may be thought of as such that a chosen molecule has immediately coordinated about it a number of other molecules at a distance corresponding to the first maximum of part, others more loosely coordinated at a distance corresponding to the next maximum, and so on. The chosen molecule is accordingly closely confined in a "cage" of surrounding mole- cules, so that its motion becomes in part a pseudo-oscillatory one within this cage. (One estimate (8) places the mean displacement between the extremes of oscillation at about 0.5 A.) This suggests that, for diffusion to occur, the molecule must acquire sufficient energy to break through the wall of immediately surrounding molecules (8), i.e., to move to the center of a new coordination complex (33~. In calculating numbers of collisions of solute molecules with each other, the custom has been to treat the solute as if it were gaseous with solvent absent; in the calculation the molecules have been ordinarily regarded as rigid. In recent theories the occurrence of collisions has been modified both as to distribution in time and as to average number per unit time. In view of the cage effect of the solvent molecules, once two solute mole- cules have made collision there is a greater probability of further collision between the same pair than would be the case in a gas. Thus a given solute molecule undergoes collisions with other solute molecules in sets. The occurrence of such collision sets has been found in experiments with models (35~. For thermal bimolecular reactions between solutes, the number of sets per unit time is important when there is high probability of reaction at any collision, but the total number of collisions per unit time rather than the number of sets becomes important when any considerable activation energy is required (8, 33, 46~. Present estimates of the total collisions per unit time between solute molecules give values rather higher (five to twenty times) than those from a gas calculation. In view of the present state of flux in these ideas, it would be premature to recommend any one mode of calculating collision numbers. Specific information concerning primary absorption processes is con- siderably more abundant and certain for gaseous substances than for substances in the liquid state or in solution. This arises partly from the relative simplicity of the phenomenon in the gaseous state, where the absorption is by fairly isolated molecules, and partly from the related fact that in condensed states the fine structure of absorption spectra is lost, together with the detailed information derivable from such structure. Aside from the smoothing out of fine structure into a continuum in solu- tion, dissolved substances frequently show spectra differing from those of the same substances in the gaseous state, both as to magnitude of absorp- tion coefficient and as to position of absorption maxima. This is not

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PHOTOCHEMICAL PROCESSES IN GASES AND SOLUTIONS 43 surprising, since solution may be accompanied by such processes as solva- tion, dissociation, or ionization producing essentially new absorbing mole- cules. However, when interactions between molecules in the solution are not too great, the solution absorption spectrum becomes essentially a blurred copy of that of the gas. For example, the absorption coefficients of the halogens in non-polar solvents such as carbon tetrachloride differ little from values for the gases. In cases where this close similarity exists, it is usual to presume that absorption is accompanied by the same elec- tronic transition in both cases, and to draw inferences concerning the primary process in solution from a knowledge of that in the gas. When a molecule in solution absorbs a quantum of radiation, there is initially produced an excited molecule for which there exists a variety of conceivable fates. Among these are the following: The molecule may (a) immediately lose its excitation energy through collision of the second kind with solvent molecules, whereby the absorbed energy becomes ineffectively distributed through the solution, or it may (b) retain its excitation (in part at least) in spite of collisions with the solvent molecules and later fluoresce or enter into reaction; again, (c) the absorbing molecule may immediately enter into chemical reaction with an adjacent solvent molecule; and finally, (d) the molecule, after a lapse of time possibly dependent on whether a true continuous or a predissociation spectrum is involved, may dissociate. Since molecules in solution are practically continuously in the process of collision with solvent, the effect of collisions of the second kind in degrading activation energy from light absorption may be expected to be of greater importance in solution than in the gaseous state. Indeed, the ability of a molecule to retain its excitation in solution sufficiently to fluoresce or to react with a second molecule of solute implies a considerable insensitiveness toward collisions of the second kind. Among inorganic substances only a few, such as the uranyl salts and compounds of the rare earths, are known to fluoresce in solution; among organic substances the phenomenon is largely confined to various ring compounds. The view has been that, in substances showing fluorescence in solution, the electronic transition was one protected from outside influences either because of occurring in the interior of an atom or because of occurring in a protected part of a compli- cated molecule. Frank and Levi (17) have remarked that this view is in- complete and does not explain how some substances may fluoresce yet have their fluorescence strongly suppressed by the addition of various substances to the solution. Using the idea that the electronic excitation energy of the absorbing molecule can be easily transformed only when it is approximately equal to that of a new electronic state (of the absorbing molecule, the collision partner, or both), Franck and Levi have discussed the conditions for fluorescence? quenching? and reaction in terms of po- tential energy curves. The retention of electronic excitation permitting

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44 ROSCOE G. DICKINSON reaction with a second molecule of solute is probably somewhat exceptional, most photochemical reactions occurring as a result of reaction with the solvent or of the formation of atoms or free radicals. In connection with these considerations, attention should be given to cases where sensitization of solute reaction by the solvent occurs. In the conversion of o-nitro- benzaldehyde into o-nitrosobenzoic acid in acetone solution (45), the gross quantum yield (molecules transformed per quantum absorbed by the system) for 3130 A. remains near 0.5 for acetone solutions containing from 2 per cent to 0.02 per cent of aldehyde, although, at the lower concentra- tion, 96 per cent of the absorption is due to the acetone. Again, the de- composition of ethyl iodide at a mean wave length of 2610 A. gives a quantum yield (48) in 0.03 molar solution in benzene of 0.52, although only 1/180 of the absorption is due to the ethyl iodide; moreover in hexane solution, where the absorption is all due to the ethyl iodide, the yield is substantially the same. The mechanisms of these sensitizations are not known. If, in the gaseous state, an induced predissociation occurs in competition with fluorescence, then, in solution, the dissociation may evidently be favored. However, even if the molecule does dissociate, there exists a possibility that the dissociating partners, in view of the fact that they are closely hemmed in by solvent molecules, will frequently immediately recombine. The greatly increased probability of this occurrence in solu- tion has been emphasized by Franck and Rabinowitsch (18~; they have called the process "primary recombination" to distinguish it from the "normal" recombination process which involves the uniting of atoms or radicals which were not previously partners. It has long been recognized that the Einstein photochemical equivalence law does not, in general, apply to the overall photochemical reaction, but frequently only to the primary process. The effect of a dissipation accompanying the absorption, or of primary recombination, would operate to prevent the occurrence of an integral relationship between the number of quanta absorbed and the number of primary products of the absorption process. Existing~experimental evidence which might be expected to have a bearing on the question of primary recombination may for the most part be divided into three classes: (~) experiments in which the stationary con- centration of the primary products of dissociation is estimated by measure- ment of the light transmission of the solution while under irradiation; (~) photochemical experiments in which a reaction proceeds by a chain, with the rate of reaction interpreted as depending on the stationary concentra- tion of transient substances resulting from the absorption process; and (~) photochemical experiments in which no chain is presumed to be involved and in which the stationary concentrations of transients are of secondary interest.

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PHOTOCHEMICAL PROCESSES IN GASES AND SOLUTIONS 45 Extensive experiments of the first type have been carried out by Rabino- witsch, Wood, and Lehmann. In these the stationary decrease in con- centration of halogen molecules under a measured strong irradiation was determined. With iodine in carbon tetrachloride or hexane solution (34), the processes apparently involved were only the photodissociation of the molecules and recombination of the atoms. If the fraction ,8 of absorbed photons gives dissociation Is + he- > 2I so that the rate of production of atoms by dissociation is 2`B(I3ba.~' and if the atoms disappear only by recombination 2I ~ Is with a rate 2k(I)2, the value of B is evidently given by ~ = k(I)2/(labs.) at the steady state. Corresponding values of (I) and (Ian.) have been measured experimentally; the value derived for ~ then depends on what is assumed concerning k. If a pair of normally diffusing iodine atoms are assumed to combine on their first collision, and if it be assumed that the specific rate, Z. of such collisions may be calculated with the gas kinetic expression Z= 2/d2~/RT/M then this specific collision rate may be set equal to k and ,B may be ob- tained. Taking d = 5.0 X 10-8 cm., the data lead to average values of of 0.7 at 0.3 for Is in carbon tetrachloride and 1.0 ~ 0.3 in hexane. How- ever, if in the absence of combination, collisions between normally diffusing iodine atoms were to occur in sets of, on the average, n collisions each, then, with combination at the first collision, k becomes Z/n and the cal- culated values of ,6 become the former values multiplied by 1/n. Again if, in accord with ideas mentioned earlier, the total number of collisions between solute molecules is somewhat greater than the value given by the gas formula, say m times that value, then the calculated values of ~ become m/n times the values given above. Thus, while values of ~ of the order of magnitude of unity are compatible with the experimental results, more definite independent knowledge of the recombination rate is necessary in order to make a definite determination of ~ from the stationary concen- trations. The assumption that two particles just leaving a photodissociation have the same probability of immediate collision as two particles leaving an ordinary collision is doubtful when (as is usually the case) the dissociating partners have considerable excess kinetic energy. Rollefson and Libby (36) have urged that "such atoms have an excellent chance of forcing their way between the solvent molecules" so that the two probabilities would

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46 ROSCOE G. DICKINSON not be equal. Rabinowitsch and Wood (35) had considered such a dys- symmetry of cage eject possible when the molecules of the solvent were smaller in mass than the dissociation products but not when the solvent was greater since, from conservation of momentum, the dissociating prod- ucts would be brought to rest by their first collision with the heavier particle irrespective of their kinetic energy. However, this consideration applies primarily to head-on collisions and may not seriously affect the contentions of Rollefson and Libby. In this connection it may be re- marked that activation energies for diffusion of 3000 cat. and less have been calculated (8~; at least this excess is often possessed by dissociating partners in photochemical experiments. If it be admitted that the probability of separation is greater for a pair of photodissociating atoms than for a pair in normal collision, then an effect of wave length on stationary concentrations becomes possible. Such an effect was sought (34) but not certainly found. Turning now to photochemical evidence concerning primary recombina- tion, there are various photochemical chain reactions to which mechanisms have been assigned which are such that the rate of reaction is proportional to the steady concentration of transients produced immediately or in- directly by the light absorption process. Simple examples are the sensi- tized decomposition of ethylene iodide and the iodine-sensitized transfor- mations of geometrical isomers. Attempts to draw inferences concerning primary recombination from the rates of such reactions encounter the same ambiguities, inter alia, as discussed above in connection with the experi- ments of Rabinowitsch and Wood. However, here again, if the solvent eject is not the same for primary and secondary recombination, a wave length effect is possible; for, whereas the secondary recombination is pre- sumably unaffected by wave length, the kinetic energy of the dissociating partners will be smaller at longer wave lengths with possibly more primary recombination and a smaller rate of reaction. Reactions of the type under discussion often proceed at rates proportional to the square root of the intensity of illumination. In such cases the total material reacting per unit time depends not only on the rate of absorption of radiation but on the distribution of absorption through the reacting medium (1~; this point has, unfortunately, been frequently ignored. A rather small wave length eject has been reported (14) for the iodine-sensitized ethylene iodide decomposition; the primary quantum yields for the wave lengths 4358, 5461, and 5780 A. were found to stand in the ratios 1:0.87:0.75. Other halogen chain reactions in which yields somewhat smaller at longer wave lengths than at shorter have been reported are the following: the bromina- tion of cinnamic acid in carbon tetrachloride solution (2~; the bromination of liquid benzene (32~; the bromination of maleic ester and its sensitized rearrangement to fumaric ester (15~; the iodination of various olefins in

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PHOTOCHEMICAL PROCESSES IN GASES AND SOLUTIONS 47 chloroform solution at55C. (16~. It is to be noted that similar wave length effects have been reported absent in the following gaseous reactions: the formation of hydrogen bromide (22~; the bromination of acetylene (6~; the bromination of cyclohexane (23~; the bromine-sensitized decom- position of chlorine dioxide (40, 41~. Considerable wave length effects in the same sense are often found in aqueous solution reactions, but caution must be exercised in attributing them to varying primary recombinations as opposed, for example, to reaction with solvent or to the occurrence of different electronic transitions on absorption. The situation can be somewhat different in the case of certain reaction mechanisms not involving a chain. If conditions are such that the atoms or radicals formed in the primary process always react with some solute to give products without the intervention of a chain, then the gross quantum yield may be used to give indications of the primary quantum yield. A necessary experimental condition is evidently a constancy of gross quantum yield over a range of concentrations of reactant. Reactions which may be of this type have not been very thoroughly examined. The decomposition of ozone in carbon tetrachloride solution sensitized by chlorine has been reported (7) to occur with a quantum yield of 2O3 decomposed per quan- tum absorbed at the wave length 3660 A. If the mechanism be such as the following (38), Cl2 + he > 2Cl Cl + 03 > C10 + O2 2ClO > Cl2 + 02 the observed quantum yield would indicate absence of primary recom- bination. The gaseous reaction is complicated (211. Again the chlorina- tion of trichlorobromomethane in carbon tetrachloride was reported (20) to proceed with a yield of 0.9 mole of bromine per quantum absorbed (wave lengths); if the mechanism is the following (38), Cl2 + he > 2 Cl Cl + CCl3Br ~ CC14 + Br 2Br ~ Br2 the quantum yield indicates little primary recombination. However, the compound BrCl was not known and its formation not considered in these experiments. In the gaseous reaction, chains have been found (44~. The oxidation of carbon tetrachloride to phosgene by dissolved oxygen brought about by radiation (2537 A.) absorbed by the carbon tetrachloride has been reported (28) to occur with a yield of 1 mole of carbon tetrachloride oxi- dized per quantum absorbed. But in the absence of dissolved oxygen

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i: 48 ROSCOE G. DICKINSON the quantum yield of decomposition of carbon tetrachlor~de was found to be less than 0.01. Taken together, these results could mean either (~) no primary recombination but a low specific rate for the reaction 2CCl3 C2C1~ as compared with reactions leading to reformation of carbon tetrachloride or (2) large primary recombination with a long chain oxida- tion. The second possibility would make the apparently simple yield of oxidation fortuitous. A similar result has been obtained (48) in the oxida- tion of ethyl iodide by oxygen in solution under the influence of radiation absorbed by the ethyl iodide. In the presence of oxygen a 1.38 molar solution of ethyl iodide in hexane irradiated with a wave length of 2610 A. yielded "exactly 2 atoms of iodine for every quantum absorbed." In the absence of oxygen the yield was only 0.58. Franck and Rabinowitsch (18) pointed out how primary recombination might fail to operate through reaction of the dissociating molecule with the solvent. With the aid of radioactive chlorine Rollefson and Libby (36) have shown that, when chlorine absorbs visible radiation in carbon tetrachloride solution, little if any reaction with the solvent occurs. A possibility of obtaining further information concerning primary re- combination, that does not seem to have been exploited, is offered by the photochemical intermittency effect. To illustrate this possibility, suppose a photochemical solution reaction to proceed with the mechanism: I2 + hv~2I I + A > I + B 2I ~ Is (1) (2) (3) This mechanism involves the same processes as those occurring in the experiments of Rabinowitsch and Wood (34), and, in addition, an iodine atom catalysis of the conversion of A into B. The steady-state rate of this process is evidently k2~/`B(Iabs.~/k' where ,B and k have their former significance. If, however, the illumination is not steady but is carried out in regularly spaced periods of light and dark of measured duration, then it can be shown3 that for the measurable reaction A ~ B. the ratio of the 3 Complete details are too lengthy to be given here. However, the considerations are simply as follows: that in the light do = 2~B(IabS.) 2k(112 that in the dark and that at all times d(~) = - 2k`Iy2 d(A) = _ k2(I) (A)

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PHOTOCHEMICAL PROCESSES IN GASES AND SOLUTIONS 49 rate under steady illumination to that under intermittent illumination Is given by a complicated but known function of the measurable quantities (Iabs.~, blight and Clark (the periods of light and dark in the intermittency experiments and the unknown quantity ilk. The points of importance are that, in the theory of the intermittency eject, the product of ,B and k occurs and may be rendered measurable by absolute measurements of (Ian ), whereas steady-state experiments involve the ratio of B to k; com- bination of results from both types of experiment may thus give ,B and k separately. The idea of primary recombination has been employed (31) to account for some of the special complications arising in the decomposition of ke- tones in hydrocarbon solvents where reaction with the solvent occurs. It has also been employed in the discussion (47) of the decomposition of ethyl iodide, which occurs with a larger quantum yield in the liquid state than in the gaseous, and in a discussion (12) of the decomposition of ethylene iodide in carbon tetrachloride solution. When a comparison of gaseous and solution photochemical reactions with respect to processes subsequent to the primary one is undertaken, the ordinary problems of chemical kinetics of thermal reactions are encoun- tered. The literature on the erect of solvent on thermal reaction rate is, of course, large (see, for example, the symposium on the kinetics of reac- tion (10~. There are, however, two very simple ways in which the kinetics may undergo large apparent alteration in passing from the gas to even an inert solvent. If the gaseous reaction involves some wall reaction (for example, a chain-breaking step) this process will hardly occur in solu- tion; the kinetics (including, for example, the dependence on light intensity) may then be considerably altered. If the gaseous reaction involves a three-body combination of two atoms or simple radicals, this process can be strongly favored in solution, owing to the abundant supply of third bodies by the solvent; if the combining bodies are sufficiently compli- cated, however, a third body is of little advantage (249. In 1935, a collection was made (13) of photochemical reactions which had been examined in both the gaseous and the liquid or solution states. It was found that when the same reaction occurred in the gaseous state as in the liquid or in an inert solvent, the reaction was usually as fast or faster in the gaseous state. Additional cases for which this is true are the bromination of dichloroethylene (19), the chlorination of chloroform (9, 37, 39, 3), and the conversion of o-nitrobenzaldehyde into o-nitrosobenzoic acid (45, 26, 27~. REFERENCES (1) ALLMAND, A. J.: J. Chem. Soc. 1929, 1557. (2) BASER, W. H., AND DANIELS, F.: J. Am. Chem. Soc. 66, 384 (1934~. (3) BEEZHOLD, W. F., AND ORNSTEIN, L. S.: Physica 3, 154 (1936~. 1'

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50 ROSCOE G. DICKINSON (4) BERNAL, J. D.: TranS. Faraday SOC. 33, 27 (1937~. (5) BERNAL, J. D., AND FOWLER, R. H.: J. Chem. PhYS. 1, 515 (1933~. (6) BOOKER, J. E., AND ROLLEFSON, G. K.: J. Am. Chem. SOC. 66, 2288 (19341. (7) BOWEN, E. J., MOELWYN-HUGHES, E. A., AND HINSHELWOOD, c. N.: PrOC. ROY. SOC. (LOndOn) A134, 211 (1931~. (8) BRADLEY, R. S.: TranS. Faraday SOC. 33, 1185 (1937~. (9) CHAPMAN, A. T.: J. Am. Chem. SOC. 66, 818 (19341; 67, 416 (1935). (10) Chem. ReV. 17, 43-137 (1935). (11) DEBYE, p., AND MECKE, H.: PhYSik. Z. 31, 797 (1930~; 33, 593 (1932~. (12) DERIGHT, R. E., AND WIIG, E. O.: J. Am. Chem. SOC. 67, 2411 (1935~. (13) DICKINSON, R. G.: Chem. ReV. 17, 413 (1935~. (14) DICKINSON, R. G., AND NIES, N. P.: J. Am. Chem. SOC. 62, 2382 (1935~. (15) EGGERT, J., AND BORINSKI, w.: z. PhYSik 26, 865 (1925~. (16) FORBES, G. S., AND NELSON, A. F.: J. Am. Chem. SOC. 59, 693 (1937~. (17) FRANCK, J., AND LEVI, HILDE: z. physik. Chem. B27, 409 (1934). (18) FRANCK, J., AND RABINOWITSCH, E.: Trans. Faraday soc. 30, 125 (1934~. (19) GHOSH, J. C . ~ AND BHATTACHARYYA, s. K., AND BHATTACHARYYA, s. CH.: Z. physik. Chem. B32, 145 (1936~. (20) GRUSS, H.: Z. Elektrochem. 29, 144 (19231. (21) HEIDT, L. J., KISTIAKOWSKY, G. B., AND FORBES, G. S.: J. Am. Chem. soc. 66, 223 (1933~. (22) JOST, W. Z. physik. Chem. 134, 92 (1928~. (23) JOST, W.: Z. physik. Chem., Bodenstein Festband, p. 291 (1931~. (24) KASSBL, L. S.: J. Am. Chem. soc. 63, 2143 (1931~. (25) KEESOM, w. D., AND DESMEDT, J. Proc. Acad. Sci. Amsterdam26, 118 (1922~; 26, 112 (1923~. (26) KUCHLER, L., AND PATAT, F.: Monatsh. 68, 275 (1936). (27) LEIGHTON, p. A., AND LUCY, F. A.: J. Chem. Phys. 2, 756, 760 (1934~. (28) LYONS, E. H., JR., AND DICKINSON, R. G.: J. Am. Chem. soc. 56, 443 (1935~. (29) MENCKE, H.: Physik. Z. 33, 593 (1932~. (30) MORRELL, w. E., AND HILDEBRAND, J. H.: J. Chem. Phys. 4, 224 (1936~. (31) NORRISE, R. G. W.: Trans. Faraday Soc. 33, 1521 (1937~. (32) RABINOWITSCH, E.: Z. physik. Chem,B19, 190 (1932~. (33) RABINOWITSCE{, E.: Trans. Faraday Soc. 33, 1225 (1937~. (34) RABINOWITSCH, E., AND WOOD' w. C .: Trans. Faraday Soc. 32, 547 (1936~. (35) RABINOWITSCH, E., AND WOOD, w. c.: Trans. Faraday Soc. 32, 1381 (1936~. (36) ROLLEFSON, G. K., AND LIBBY, w. F.: J. Chem. Phys. 6, 569 (1937~. (37) SCHWAB, G. M., AND HEYDE, u.: z. physik. Chem. B8, 147 (19301. (38) scHlrMAcHER, H. J., AND WAGNER, c.: z. physik. Chem. B5, 205 (19291. (39) SCHUMACHER, H. J., AND WOLFF, K.: Z. physik. Chem. B25, 161 (1934). (40) SPINES, J. W. T.: J. Am. Chem. soc. 66, 428 (1933~. (41) SPINKS, J. W. T., AND PORTER, J. M.: J. Am. Chem. soc. 66, 264 (1934~. (42) STEWART, G. W.: Rev. Modern Phys. 2, 116 (1930~. (43) Trans. Faraday soc. 33, 1 (1937). (44) ~ESPER, H. G., AND ROLLEFSON, G. K.: J. Am. Chem. soc. 56, 1455 (1934~. (45) WEIGERT, F., AND PRUCKNER, F.: z. physik. Chem., Bodenstein Festband, P. 775 (1931~. (46) WEISS, J.: Naturwissenschaften 23, 229 (1935~. (47) WEST, w.' AND GINSBURG, E.: J. Am. Chem. soc. 56, 2626 (1934~. (48) WEST, w.' AND PAUL, B.: Trans. Faraday soc. 28, 688 (1932~.