An Application of Mechanics to Chemistry: the Dynamic Behaviour of Coupled Chemical Reactions Compared to that of the Two-Body Oscillator

Abstract

The dynamic behaviour of a chemical system made of two coupled reactions is compared with that of a mechanical system consisting of two oscillating bodies connected by springs. First, the principle of energy departure from equilibrium is employed to derive the motion equations of both systems. Subsequently, the relevant characteristic frequencies and the amplitude parameters are obtained and analysed in terms of “Normal Modes”. The results show that systems belonging to different branches of science can be analysed using the same methodologies. To elucidate the application of Normal Modes to chemistry, the dynamic analysis of a system consisting of a proton transfer reaction coupled to a complex formation reaction is described in the Supporting Information: the procedure enables the evaluation of rate constants, equilibrium constants and reaction enthalpies of a reacting chemical system made of two coupled reactions. The method is then extended to a cycle of three reactions.