A pervaporation membrane may be an acid-resistant polybenzidimazole (PBI) membrane. The acid-resistant PBI membrane may be a PBI membrane chemically modified by a process selected from the group consisting of sulfonation, phosphonation, cross-linking, N-substitution, and/or combinations thereof. The membrane may be thermally stabilized. A method for the dehydration of an acid material may include the steps of: contacting an acidic aqueous solution with a membrane of an acid-resistant polybenzidimazole; taking away a permeate stream rich in water; and taking away a concentrate steam rich in the acid material. The acidic aqueous solution may be acetic acid.