A carbonized PVDC copolymer useful for the separation of an olefin from its corresponding paraffin may be made by heating a polyvinylidene chloride copolymer film or hollow fiber having a thickness of 1 micrometer to 20 micrometers to a pretreatment temperature of 100° C. to 180° C. to form a pretreated polyvinylidene chloride copolymer film and then heating the pretreated polyvinylidene chloride copolymer film to a maximum pyrolysis temperature from 350° C. to 750° C. A process for separating an olefin from its corresponding paraffin in a gas mixture is comprised of flowing the gas mixture through the aforementioned carbonized polyvinylidene chloride (PVDC) copolymer to produce a permeate first stream having an increased concentration of the olefin and a second retentate stream having an increased concentration of its corresponding paraffin.