= Solution
\b[<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:
$$
\boxed{2\mathrm H_2+\mathrm O_2\longrightarrow2\mathrm H_2\mathrm O.}
$$
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.
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