Steady state theory of hot atom reactions

A simple steady state theory of hot atom reactions is developed based on the Boltzmann equation. The solution to this equation is approximated by a local Maxwell distribution involving the temperature of the hot atoms and steady state distributions are calculated by determining steady values of the hot atom temperature. General considerations imply the existence of steady state distributions with temperatures just below the ambient temperature and a simple model calculation indicates that very reactive systems should have steady or quasisteady states at temperatures much higher than ambient. An application of the theory to a photochemical reaction is shown to be compatible with more extensive computer calculations. If a hot atom distribution becomes steady, it is shown that the loss of hot atoms can be described by a pseudo-first-order rate equation with a rate constant differing from the equilibrium rate constant only by the appearance of the steady state temperature.