A nanocomposite membrane including an α-Al2O3 membrane support, a γ-Al2O3 intermediate layer that is 300-1200 nm thick and coats a surface of the membrane support, and a nanocomposite layer including SiO2 and Y2O3 that is 25-150 nm thick and coats a surface of the intermediate layer, wherein the nanocomposite layer is porous with an average largest radius micropore of 0.2-0.6 nm. A method of manufacturing the nanocomposite membrane, whereby the membrane support is coated with the γ-Al2O3, a silica source is hydrolyzed with a mixture of water, an alcohol solvent, and a Y source with a sol-gel technique to yield a Si/Y sol-gel, the membrane support is dip coated with the Si/Y sol-gel, and the nanocomposite membrane is calcined. A method of separating a mixture of gas, whereby the mixture of gas is introduced into a permeance cell and fed through the nanocomposite membrane.