On the rate of maximum activation by collision for complex molecules with applications to velocities of gas reactions

Abstract

The difficulties of the theory of homogeneous unimolecular gas reactions are well known. The well known natural hypothesis on which to account for a unimolecular reaction such as the decomposition of N 2 O 5 is to assume that there exist in equilibrium in the gas N 2 O 5 molecules of two classes, active and inert, and that the active molecules are all those which contain internal energy greater than ϵ 0 . This idea of active and inactive molecules, due to Arrhenius, is demanded in order to account for the observed temperature coefficient of the reaction velocity. The equilibrium conditions must be maintained by some mechanism which allows inactive molecules to be activated and the reverse process to occur, the rates of change a t the equilibrium point of the reaction (N 2 O 5 ) active ⇄(N 2 O 5 ) inactive being, of course, equal. In order to account for the decomposition, as of N 2 O 5 , at a rate strictly proportional to the concentration of N 2 O 5 , a t least over a very wide range of concentrations, we have now merely to assume that the active N 2 O 5 -molecules have a certain chance of spontaneous decomposition, so that if at any time there are x such molecules present, Bxdt will decompose in the following interval dt . It is not necessary to look farther into the mechanism of this decomposition. We may recognise it as of a type made familiar to us by the phenomenon of the spontaneous emission of light by excited molecules. The coefficient B may, or may not, be an absolute molecular constant; it is only essential here that it should be independent of any concentration. These spontaneous decompositions will then proceed at a rate proportional to the concentration of active molecules and therefore at a rate proportional to the total concentration of N 2 O 5 , provided that the equilibrium ratio (active/total) is unaltered by the spontaneous decomposition. This will be true so long as the natural rate of activation and deactivation is large compared with the rate of decomposition.