In this paper the considerations of the previous paper have been developed further and compared with the theory of reaction rates as formulated in terms of a specifically defined activated complex by Eyring. The theory has been applied to a discussion of various unimolecular reactions. A number of cases have been treated by considering the reverse bimolecular or trimolecular association and discussing the extent to which rotational degrees of freedom must be frozen out in order for the associations to occur. Other cases have been treated by the activated complex method, which involves discussion of the number of free rotations and the frequency of the vibrations in the complex. It has been shown that it is possible to account for the rates of a considerable number of unimolecular reactions by making reasonable assumptions and that there is a considerable class of unimolecular reactions which conform to what is designated as the ``hypothesis of exact orientation,'' the only necessary assumption being that the rotational degrees of freedom of the fragments which recombine in the reverse reaction must be frozen out just sufficiently so that they correspond as regards their entropy terms to the resulting vibrational degrees of freedom of the molecule formed.

Topics
Entropy, Vibrational spectra, Chemical reaction dynamics
1.
Parker Traveling Fellow of Harvard University.
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O. K.
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4.
The rate of reaction for the unimolecular reaction is written in the form A1 exp(−εa/kT), where εa is the energy of activation according to the definition of Tolman (Statistical Mechanics (Chemical Catalog Co., 1927), p. 261–2). This is the value obtained by plotting the logarithm of the rate constant against the reciprocal of the absolute temperature. The theoretical value of A1 is not independent of temperature but may, for comparison with experiment, be evaluated for the middle of the experimental range of temperatures, as noted in the following paper.
5.
They do assume that, if there is spin degeneracy in the electronic and nuclear states, all these degenerate states are equally available for reaction, and that the degeneracy is the same for M1 and for the system M2 plus M3. This may not always be true but we may in general assume that spin does not affect the probability of a decomposition, so that (3a) will always hold. As noted in footnote 13 of Part I, however, the spin state may affect the possibility of association, since the relative orientations of the spins of M2 and M3 will determine whether they will attract or repel each other. So, in general, if the association involves free radicals, or systems not in S states, (3b) will not hold, but needs to be multiplied by a constant factor. This, however, will not affect considerations of the present paper, as we are interested in the unimolecular decomposition, to which (3a) applies.
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Compare Part I, p. 860.
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If kT≫hν1 then in the case of exact orientation A1 becomes equal to ν1, in which case it is like Rodebush’s expression. A similar result was also obtained by Polanyi and Wigner, Zeits. f. physik. Chemie, Haber Band, 439 (1928). The latter authors also gave a comparison of experiment and theory. In the following pages we shall give a more detailed comparison of the theory with a number of gas phase unimolecular reactions.
See also
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8.
Gershinowitz and Eyring, submitted to J. Am. Chem. Soc.
9.
Two of these vibrational degrees of freedom are the carbon‐nitrogen stretching vibrations, while two will be bending vibrations of the carbon‐nitrogen skeleton. Of the degrees of freedom not included in the collision factor, the rotations of the methyl group will correspond in part to free rotations in the azomethane molecule and in part to carbon‐hydrogen bending vibrations, while corresponding to the rotation of the nitrogen will be the other skeletal bending vibration and the rotation about the long axis of the kinked chain.
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(b) Der Smekal‐Raman Effekt (Springer, 1931), p. 154.
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Kohlrausch, reference 11b, p. 188.
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a The mechanism assumed here implies either the immediately subsequent shift of a second hydrogen atom or the formation of dimethyl cyclopropane. It would thus be of interest to ascertain whether any of the latter substance were present in the reaction products.
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Kohlrausch, reference 11a, and reference 11b, p. 206.
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Kassel, Kinetics of Homogeneous Gas Reactions (The Chemical Catalog Co., 1932) pp. 192, 196.
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See the discussion, last part of §1.
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25.
Reference 21, p. 199.
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It may be of interest in this connection to note that in many of these cases, for example, the decompositions of nitryl chloride (
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and dimethyltriazene (
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and the isomerization of dimethyl maleate (
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1935
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