A chemical reaction is performed with separation of the product(s) and reactant(s) by pressure swing adsorption (PSA), using an apparatus having a plurality of adsorbers cooperating with first and second valve assemblies in a PSA module. The PSA cycle is characterized by multiple intermediate pressure levels between higher and lower pressure of the PSA cycle. Gas flows enter or exit the PSA module at the intermediate pressure levels as well as the higher and lower pressure levels, entering from compressor stage(s) or exiting into exhauster or expander stages, under substantially steady conditions of flow and pressure. The PSA module comprises a rotor containing the adsorbers and rotating within a stator, with ported valve faces between the rotor and stator to control the timing of the flows entering or exiting the adsorbers in the rotor. The reaction may be performed within a portion of the rotor containing a catalyst.