I understand what basic,acidic and amphoteric oxides are. But how do we classify oxides on the basis of metallic nature?Explain how we can deduce if the oxide is metallic or not. For example,what does it mean when it is stated that "CrO2 is a metallic oxide."
This was an answer to one of the questions in an exam that I wrote recently.
'Metallic oxide' has nothing to do with basicity/acidity of the oxide and is about solid phisics.
Basically it means, that the solid is electrically conductive like a true metal. This involves a half-filled conductivity zone (that can be roughly imagined as a number of half-filled overlapping orbitals of same energy), so electrons can move freely through the crystal lattice.
There is no simple rule to guess metallicity of multi-element compounds, unfortunately; because this property is strongly tied to electronic structure of the solid and crystall lattice. As an example: of $\ce{TiO2}$, $\ce{VO2}$, $\ce{CrO2}$ and $\ce{MnO2}$ only $\ce{CrO2}$ is truly metallic, while $\ce{VO2}$ looses metallic conductivity at lower temperatures (it has two allotropes, one metallic and one insulating). For TiO2 it is, at the very least, expected, as it is a $d^0$ compound, but for other metallic oxides it is unclear, or, at least, aboive average chemist's level.
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As for acidic/basic classification of oxides, there are few solid rules. Generally, any oxide with oxidation state 5+ is a strong suspect for acidic nature, with 3-4 being anyware from acidic to basic and +1 usually basic except for halogens.
For an oxide to be basic, corresponding metallic cation must be reasonably stable. This implies relatively large radius, and moderate to low charge density. Consequently, +1 metal oxides are practically exclusively basic, +2 metal oxides are usually basic except for very small cations (Be and few late d-elements like copper and zinc) and +3 are usually amphoteric except for very large cations (like La) Anything of higher oxidation state is usually acidic or at most aphoteric, as corresponding cation has too high charge density to be stable in water solutions. The only true salts of +4 cation I can come with are $\ce{Zr(SO4)2}$ and $\ce{Hf(SO4)2}$ and even for them the corresponding hydroxide is classified as amphoteric.
Still, in some cases such oxides still may act as bases, but corresponding cation has lower charge. Probably, the simpliest examples are $\ce{VO2}$ and $\ce{UO3}$, with corresponding salts containing $\ce{VO^{2+}}$ and $\ce{UO2^{2+}}$ respectively. This, however, is not usually condidered as an excuse to classify these oxides as basic/amphoteric.
Some oxides are not acidic/basic/amphoteric as there is no 'simple' salt corresponding ot the oxide in question. This claim is usually debatable, as such a salt usually may be found (for example, NO, typically classified as not producing salt, may be tied to salts like $\ce{Na2N2O3}$ aka Angeli's salt), but for simplicity are not considered. There are reasons for it, as basic/acidic oxide classification is very rough, and should not be relied upon in extreme, borderline and simply too complicated cases.
