Several methods for chemical energy storage have been discussed recently in the context of fluctuating energy sources, such as wind and solar energy conversion. Here a compression–expansion process, as also used in piston engines or compressors, is investigated to evaluate its potential for the conversion of mechanical energy to chemical energy, or more correctly, exergy. A thermodynamically limiting adiabatic compression–chemical equilibration–expansion cycle is modeled and optimized for the amount of stored energy with realistic parameter bounds of initial temperature, pressure, compression ratio and composition. As an example of the method, initial mixture compositions of methane, ethane, hydrogen and argon are optimized and the results discussed. In addition to the stored exergy, the main products (acetylene, benzene, and hydrogen) and exergetic losses of this thermodynamically limiting cycle are also analyzed, and the volumetric and specific work are discussed as objective functions. It was found that the optimal mixtures are binary methane argon mixtures with high argon content. The predicted exergy losses due to chemical equilibration are generally below 10%, and the chemical exergy of the initial mixture can be increased or chemically up-converted due to the work input by approximately 11% in such a thermodynamically limiting process, which appears promising.