Quantum chemical hybrid MP2:PBE+D2 calculations in combination with molecular statistics are employed to calculate enthalpies and Gibbs free energies of adsorption for CH4 at Brønsted acid sites [bridging Si-O(H)-Al groups] and silica wall sites (Si-O-Si) of the proton form of zeolite MFI (H-ZSM-5) and its purely siliceous analogue Silicalite-1. A Langmuir model is adopted to calculate the amounts of CH4 adsorbed at each type of site from the Gibbs free energies. The combination of these results according to the ratio of silica wall sites and Brønsted acid sites in the sample yields adsorption isotherms for zeolites with different Si/Al ratios. The zero-coverage isosteric heats of adsorption, calculated as thermal averages of the adsorption enthalpies of the individual sites, vary between 20.2 kJ/mol for the pore wall site and 29.2 kJ/mol for the acid site and agree well within ±1 kJ/mol with experimental results.