The rigorous statistical thermodynamics of mixtures of polyatomic species adsorbed on one-dimensional substrates is presented. The thermodynamic functions calculated for a monomer–dimer mixture are applied to describe the adsorption of methane–ethane mixtures in zeolites. The theoretical formalism reproduces the main features of the system, showing that the displacement of ethane by methane at higher pressures, a phenomenon known as Adsorption Preference Reversal, is the result of the difference of size (or number of occupied sites) between the adsorbed species.