Disclosed herein is a process for separating components of a gas mixture using gas-separation copolymer membranes. These membranes use a selective layer made from copolymers of perfluorodioxolane monomers. The resulting membranes have superior selectivity performance for gas pairs of interest while maintaining fast gas permeance compared to membranes prepared using conventional perfluoropolymers, such as Teflon® AF, Hyflon® AD, and Cytop®.