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Amphiprotic means molecule can both accept and donate a proton. This makes it necessarily amphoteric as well, which is a molecule that can act as both an acid and a base. Acids and bases by Lewis definition do not have to donate or accept protons
This is because it depends on whether you use the Bronsted Acid definition- which states that any species that can donate a proton is an acid. Whereas a lweis acid is a species that can accept a nonbonding electron pair. Given this, in some situations, the difference in acid definitions do not correlate with the definition of amphiprotic- which is a substance that can donate or accept protons. Lewis acids, by definition, can be acid merely based on electrons. Therefore, not all amphoteric compounds can be amphiprotic because of the Lewis Acid definition.
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