## Abstract

A theory which gave the high-pressure unimolecular reaction rate as K$_{\infty}$ = $\nu $ exp (- E$_{0}$/kT) is extended to find the decline of rate with pressure; the gas molecule is again a classical vibrating system which dissociates at a critical extension of an internal co-ordinate. The general rate K is found to be approximately $\frac{K}{K_{\infty}}$ = $\frac{1}{\Gamma (\frac{1}{2}n+\frac{1}{2})}\int_{0}^{\infty}\frac{\text{e}^{-x}x^{\frac{1}{2}(n-1)}\text{d}x}{1+x^{\frac{1}{2}(n-1)}\theta ^{-1}}$, where n is the effective number of normal modes of vibration; 0 is proportional to pT$^{-\frac{1}{2}n}$, but depends also on the molecular structure and size. For n $\leq $ 13, this integral is tabulated, and the pressures at which the rate declines from first order are estimated. The pressure tends to decrease as n increases; for E$_{0}$/kT $\sim $ 40, it is estimated that only molecules with six or more atoms should show rates approaching K$_{\infty}$ at normal pressures. The table of K/K$_{\infty}$ is not carried as far as the 'bimolecular' range, but a precise technique is developed for this region. The theory is compared with Kassel's classical theory of a molecule of s 'oscillators'. The low-pressure activation energy, and the shape of the curve of log K against log p, are similar in the two theories if n = 2s - 1; the absolute values of p for a given rate are also roughly comparable. Two results are proved, for the present severely classical model, concerning special cases. (i) A pair or triplet of degenerate modes with equal frequencies counts as one in assessing 'n' for the general rate K. (ii) If the dissociation co-ordinate q relates atoms m$_{1}$, m$_{2}$, and m$_{1}$ is replaced by an isotope m$_{1}^{\ast}$, the high-pressure rate changes in the ratio $\surd ${m$_{1}$(m$_{1}^{\ast}$ + m$_{2}$)/m$_{1}^{\ast}$(m$_{1}$ + m$_{2}$)}; for this, the internal potential energy V need not be quadratic, nor need q be isolated in V from other co-ordinates.