Recycling hydrofluoric acid (HF) is a significant issue within the field of organofluoride chemistry. A key obstacle in this endeavor lies in the separation of azeotropic mixtures containing HF, such as the azeotropic mixture of HF and 1,1,1,3,3-pentafluoropropane (HFC-245fa), which exhibit similar boiling points. This study investigates the application of extractant distillation (ED) with ionic liquids (ILs) to achieve the separation of HF/HFC-245fa at the molecular scale, cell dimension, and systematic level (including the optimization and analysis of ED). COSMO-RS was employed to identify the suitable IL, with [Tf2N]-based ILs emerging as the most optimal extractants. Four representative [Tf2N]-based ILs were chosen based on their physical properties and thermodynamic behavior, and were applied in a continuous ED process simulation for the separation of HF/HFC-245fa using Aspen Plus, resulting in the production of 99.5 mol% HFC-245fa and 99.5 mol% HF. The determination of the optimal operational parameters was carried out through sequential quadratic programming, considering the purity requirements. An assessment of energy consumption analysis indicated that [C1Py][Tf2N] stands out as the most suitable IL for separation of HF/HFC-245fa, with heat and cooling duties of 467.82 kW and 304.80 kW, respectively. Economic analysis for the process with [C1Py][Tf2N] indicated that the annual operating costs and equipment costs are $ 5.58 x 104 and $ 3.75 x 106, respectively, of which the costs of IL are 93%, the total annual cost was comparable to that of the pressure-swing distillation process, suggesting that this ED process utilizing ILs for separating azeotropes is economically viable in terms of industrial application.