 Solution

Chemical elements are the constituents from which ordinary chemical compounds are built; many familiar materials are mixtures of those chemical compounds and sometimes free chemical elements. In the historical operational definition, a chemical element could not be resolved into simpler substances by chemical means. In the modern definition, its chemical atoms all have the same atomic number. Ordinary chemical reactions rearrange those chemical atoms rather than creating a new chemical element.

Air is a mixture, chiefly of nitrogen and oxygen, whose components can be separated or selectively consumed. For example, burning phosphorus in a suitable enclosed sample removes most of the oxygen and leaves chiefly nitrogen; the residual gas has different properties from the original air. Air also contains carbon dioxide, variable water vapour and smaller amounts of other gases. Its variable composition is incompatible with treating it as one elementary substance.

Water is a chemical compound: electrolysis produces molecular hydrogen and molecular oxygen, approximately in the volume ratio $2:1$ at the same temperature and pressure. Their recombination produces water again:Thus water has fixed composition but is chemically decomposable, whereas air has no fixed single chemical formula. Neither belongs with the chemical elements merely because it is common and widespread on the Earth's surface.