Reactions of Gaseous Molecule Ions with Gaseous Molecules. V. Theory

TLDR

Ion‑molecule reactions observed as secondary processes in mass spectrometry are described by modern kinetic theory, with rates expressed through reactant velocity distributions and reaction cross sections. A simple relation is provided that converts mass‑spectrometric data into the specific reaction rate under thermal conditions. The calculated cross section shows an inverse square‑root dependence on energy, the ion distribution function deviates from Maxwellian and is obtained from an explicit Boltzmann solution, and for simple molecules the a priori rate calculation agrees excellently with experiment.

Abstract

Ion-molecule reactions of the sort observed as secondary reactions in mass spectrometers have been treated by the methods of the modern kinetic theory; that is, the rate of reaction is expressed in terms of the velocity distribution functions of the reactants and the cross section for the reaction. The cross section, which is calculated by means of the properties of the classical collision orbits, is found to have an inverse square root dependence on energy. The ion distribution function, which is far from Maxwellian, is found by means of an explicit solution of the Boltzmann equation. A simple relation is given which relates the mass spectrometric data to the specific rate of the same reaction under thermal conditions. For the simpler molecules, this rate may be calculated completely a priori, with excellent agreement with experiment.