Question

what property can be used to separate the gases in air

Answer 1

Part of the air liquefies to form a liquid that is enriched in oxygen. The remaining gas is richer in nitrogen and is distilled to almost pure nitrogen (typically < 1ppm) in a

high pressure (HP) distillation column.

Answer 2

In principle, I think density of gas (property) is used for separate each kind of gas following from PV=nRT equation. But if for practical, many kind of distillation can use for separate gases, such as fractional distillation of liquid air, or above answer.