The present invention relates to the synthesis of linear aromatic polyimides and the production of membranes for the separation of gases. Specifically, polyimides featuring in their chemical structure, in the part derived from a diamine, 4-fluoro-4′,4″-diaminotriphenylmethane, and an aromatic dianhydride derived from tetracarboxylic acid. Polyimides are soluble in amidic solvents such as N,N′-dimethylformamide, N,N′-dimethylacetamide, N-methyl-2-pyrrolidone, etc., which are processed as dense membranes by controlled evaporation of the solvent. The resulting membranes are capable of separating at least a gaseous mixture constituted by two components such as H2/CH4, He/N2, H2/CO2, O2/N2, CO2/CH4 and CO2/N2.