A method of separating oxygen from an oxygen containing gas with a composite membrane capable of conducting oxygen ions and electrons. In accordance with the method, the composite membrane is subjected to an operational temperature and the oxygen containing gas at a cathode side thereof. The composite membrane has a dense layer, at least one active porous layer contiguous to the dense layer, and at least one porous support layer. The active porous layer has a thickness and a distribution of pore radii. The distribution of pore radii has a standard deviation from a theoretical radius that would produce a maximum operation flux through the thickness when the thickness is about equal to a product of a constant and the square root of the theoretical radius. The constant is a function of a material used to fabricate the active porous layer, the operational temperature and an oxygen partial pressure within the active porous layer, and a porosity and a tortuosity produced by the pore radii. The standard deviation of the log of the theoretical radius is equal to a product of 1.45 and a shape factor, the shape factor being greater than 0 and no greater than about 0.5.