Data is stored by establishing patterns on a material which may be dye on paper or magnetic domains on a magnetic material or dots on a reflective surface or some other fixed relationship in a material base. Air, like any gas, is a collection of molecules in fairly violent random movement with no established pattern in its motions. Not a stable base for laying down patterns that can be retrieved.

Interesting. If I were forced to use this medium of storage, I might investigate the following. This is not currently possible, that I know of, but it may be in the future.

Air contains nitrogen, oxygen, carbon dioxide, and other molecules. Develop a method to influence the spin of electrons (not actually a spin, its just a nuclear term). Encode within each molecule a unique address. Then as the molecules are randomly scanned, data can be read or written on other atoms of that molecule. The electrons at the lower potentials would need to be used because the higher potential electrons exchange randomly with other surrounding molecules.