the invention is a method of separating a gas comprising helium , oxygen , nitrogen or carbon dioxide from a mixture of gases containing helium , oxygen , nitrogen or carbon dioxide wherein the method comprises a . contacting the gas mixture with a thin , non - porous membrane comprising a polymer with a perfluorinated backbone and pendant ionomer moieties which contain cations of alkali metals , alkaline earth metals , or transition metals under conditions such that helium , oxygen , nitrogen or carbon dioxide selectively permeates through the membrane to the other side of the membrane ; and , b . removing the permeated helium , oxygen , nitrogen or carbon dioxide from the other side of the membrane . the membranes useful in the method of this invention demonstrate good selectivity for oxygen , helium , nitrogen , and carbon dioxide over other gases in gas mixtures containing such gases . furthermore , the permeabilities of oxygen , helium , and carbon dioxide through these membranes is quite good .