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UNITED STATES ATOMIC ENERGY COMMISSION
ACTIVATION IN UNIMOLECULAR REACTIONS
0. K. Rice
Clinton Laboratories n &v ne
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Date Declassified: July 9, 1947
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ACTIVATION IN UNIMOLECULAR REACTIONS*
By 0. K. Rice
The decomposition of nitrogen pentoxide remains first-order to extremely low pressures, of the
order of 0.01 mm. Kassel2 has shown that to account for this it is necessary, using the most probable
model for the system of oscillators comprising the molecule, to suppose that the diameter for colli-
sional activation and deactivation is about 20 x 10-' cm. Recently Ogg' has made an ingenious sugges-
tion which appears to account for this characteristic of the reaction, as well as a number of other
features, without any excessive collision diameters. It is supposed the equilibrium
is established, and that the dissociated products of this equilibrium can occasionally react
NO, NO, NO, 0O, + NO
to give the decomposition. Working out this mernanism shows that the reaction should be first-order
to arbitrarily low pressures; the apparent observed falling off in the rate constant at very low pres-
sures presumably indicates that an appreciable fraction of the N0, is dissociated.
A brief historical note, which will indicate where this explanation stands in relation to the theory
of unimolecular reactions, may be in order. In the early days of the discussion of these reactions, it
was supposed that the equilibrium fraction of activated molecules would'be given by the simple expo-
nential e-Q RT, where Q is the activation energy. The rate of activation could not be faster than the
rate of deactivation which would occur if there were no reaction and consequently no draining away of
activated molecules. This in turn would be equal to the number of collisions made by the activated
fraction of molecules, e-Q RT, with other molecules. It was in general impossible, on this basis, to
account for a sufficiently rapid rate of activation to maintain the reaction. It was soon pointed out,3
however, that in the case of a molecule with many internal degrees of freedom, the fraction of mole-
cules with energy greater than Q is much greater than e-Q RT. All this energy may be considered as
activation energy if the molecule is capable of transferring energy between the internal degrees of
freedom, and.in particular, to the bond which is to break in the reaction. Thus it is possible to
account for much larger rates of activation. This comes about because there are many ways in which
the excess energy necessary for activation can be distributed among the various oscillators of the
molecule, thus increasing the probability, or the entropy, of the activated molecules. Anything which
increases this entropy may increase the rate of activation. For example, if the energy levels of an
activated molecule are much closer together, on the average, than those in the normal state of the
molecule, the rate of activation is increased. This can be important when the number of degrees of
freedon is small.'
It is now apparent how Ogg's suggested mechanism lits into the scheme. The activated state of the
molecule is actually the separated pair NO, NO, which has an extremely high entropy. The rate of
A remark on the note "The Mechanism of Nitrogen Pentoxide Decomposition,"-by R. A. Ogg, Jr.1
2 ] MDDC 1088
activation can, therefore, be large. In fact, the difference in entropy between the activated and normal
states increases with decreasing pressure in such a way as to render the rate of activation independent
of the pressure. But the assumption that activation occurs while the parts of the molecule are sepa-
rated is essentially a device for increasing the rate of activation.
1. R. A. Ogg, Jr., J. Chem. Phys. 15, 337 (1947).
2. L. S. Kassel, The Kinetics of Homogeneous Gas Reactions pp 182 ff Reinhold Publishing Corp.,
New York, 1932.
3. G. N. Lewis and D. F. Smith, J. Am. Chem. Soc. 47, 1514 (1925); J. A. Christiansen, Proc.
Cambridge Phil. Soc. 23, 438 (1926): C. N. Hinshelwood, Proc. Roy. Soc. London 113A, 230
(1926); 0. K. Rice and H. C. Ramsperger, J. Am. Chem. Soc. 49, 1617 (1927). See also Kassel,
reference 2, p 94.
4. 0. K. Rice, J. Chem. Phys. 9, 258 (1941).
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