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Amphoteric means that the substance can act as either an acid or a base. Amphiprotic means that the the substance can both and accept donate hydrogen ions (aka protons). All amphiprotic substances are also amphoteric (donate hydrogen ions (act as an acid) or accept a hydrogen ion (act as a base)). But not all amphoteric substances are amphiprotic. Because sometimes a substance can act as an acid or base without donating hydrogen ions (aka the Lewis Theory with electron pair donors and acceptors).
Amphiprotic refers to the ability to donate or accept protons whereas amphoteric refers to the ability to act as an acid or a base. Something that is amphoteric is always amphiprotic, but something that is amphiprotic is not always amphoteric.
An amphiprotic substance, such as water, can both donate and receive protons while an amphoteric substance can act as either an acid or a base and can thus react with both acids and bases.
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