Analytical expression for the modeling of hydrogen sorption isotherms on LaNi4.75Fe0.25 alloy at three temperatures (293 K, 303 K and 313 K) is developed using statistical mechanics formalism. Our objective in this modeling is to select the adequate model that presents a high correlation with the experimental curves in order to obtain new physicochemical interpretations at a molecular level. The parameters involved in the model, such as the number of sorbed hydrogen atom per site, n, the receptor sites' density, N-M, and the energetic parameters, P-1 and P-2, were determined directly from the experimental sorption isotherms by numerical simulation. The results of fitting are interpreted. A dynamic study of the a and 13 phases of sorption was carried out by focusing on the formation of one of these phases in relation to the other, depending on the pressure and the evolution of the adjustment parameters. Then, the model is further applied to calculate thermodynamic functions which govern the sorption mechanisms such as entropy, free enthalpy of Gibbs and internal energy. (C) 2016 Elsevier B.V. All rights reserved.