30iun'48 MDDC - 1088 UNITED STATES ATOMIC ENERGY COMMISSION ACTIVATION IN UNIMOLECULAR REACTIONS by O. K. Rice Clinton Laboratories This document consists of 2 pages. Date of Manuscript: Unlcnown Date Declassified: July 9, 1947 This document is issued for official use. Its issuance does not constitute authority to declassify copies or versions of the same or similar content and title and by the same author(s). Technical Information Division, Oak Ridge Directed Operations Oak Ridge, Tennessee ACTIVATION IN UNIMOLECULAR REACTIONS* By O. K. Rice The decomposition of nitrogen pentoxide remains first-order to extremely low pressures, of the order of 0.01 mm. KasseP 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 coUi- 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 NO3 + NO2 - NO2 + O2 + NO to give the decomposition. Working out this mechanism 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 N2O, 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,' 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_ ^11 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 fits into the scheme. The activated state of the molecule is actually the separated pair NOj + NO3 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.' MDDC - 1088 I 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. REFERENCES 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); O. K. Rice and H. C. Ramsperger, J. Am. Chem. Soc. 49, 1617 (1927). See also Kassel, reference 2, p 94. 4. O. K. Rice, J. Chem. Phys. 9, 258 (1941). UNIVERSITY OF FLORIDA 3 1262 08907 9544