A process for separating a gas from a gas mixture containing the gas and a C3+ hydrocarbon vapor, using gas-separation membranes selective for the gas over the C3+ hydrocarbon vapor. The membranes use a selective layer made from a polymer having repeating units of a fluorinated polymer, and demonstrate good resistance to plasticization by the organic components in the gas mixture under treatment, and good recovery after exposure to liquid aromatic hydrocarbons.