Semiclassical versions of the statistical associating fluid theory for three- and two-dimensional chain molecules with attractive potentials of variable range (SAFT-VRQ) are applied to model selectivities and adsorption isotherms of mixtures containing hydrogen (H-2) and methane (CH4) onto metal-organic frameworks (MOFs). The theoretical model for mixtures relies on eight molecular parameters and their corresponding combining rules. Six of the eight parameters are obtained from the bulk properties of pure components and only the other two, related to the energy depth of the surface-particle potential, epsilon(w), and the surface area S, are determined from fitting to experimental data of adsorption isotherms of pure components. The obtained S values are in agreement with reported BET surface areas. Satisfactory results are obtained for the prediction of adsorption isotherms for pure substances and mixtures containing hydrogen and methane compared with experimental data. This molecular thermodynamic model is also able to describe adsorption selectivities in mixtures and the relevance of the quantum description as the molar fraction of hydrogen is increased. Finally, we include detailed information about all the mathematical expressions used to describe the adsorption isotherms of mixtures. (C) 2018 Elsevier B.V. All rights reserved.