The theoretical rate of isomerization of cyclo propane

The rate of isomerization of cyclopropane to propylene is calculated on a theory of unimolecular reactions, which treats a molecule as a classical vibrating system. Isomerization is assumed to occur when the vibrations carry any hydrogen too near to a carbon of another methylene group. The frequency factor found for the high-pressure rate is 4 $\times $ 10$^{14}$ s$^{-1}$, which is comparable with the experimental value 15 $\times $ 10$^{14}$. The decline of the rate K from K$_{\infty}$ with pressure shows a curve of log$_{10}$ (K/K$_{\infty}$) against log$_{10}$ p of the correct shape, down to the lowest pressures (under 0$\cdot $1 mm) of Pritchard, Sowden & Trotman-Dickenson's recent experiments; but the absolute values of the theoretical pressure for given K/K$_{\infty}$ are 3$\frac{1}{2}$ times those observed. As an alternative model, isomerization is assumed to follow the over-stretching of a carbon-carbon bond; here the high-pressure frequency factor found is only 6 $\times $ 10$^{13}$, and this limit is estimated to be approached only at excessively high pressures. In the course of the vibrational analysis, which is based on Saksena's calculation of the force constants, the detailed classical behaviour of the molecule is found in each of the twenty-one modes of vibration.