Is it true for a pure substance that has two allotropes A and B; to have four possible phases, solid A, solid B, liquid and vapor that can coexist in equilibrium?
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Not on this planet .A phase is a state of matter. Allotropes have to do with the arrangements of the molecule.
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Three phases is the best you can do, not four. You typically have solid, liquid and vapor, but it is possible to have solid A, solid B and vapor. (In the unique case of helium, you can have two liquids and a vapor.)