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I have read about the Brønsted-Lowry and Arrhenius concepts to define a substance as an acid or a base. Our teacher told us that there are substances which behave both as an acid and a base, using water and ammonia as examples. He also asked us to find other substances with the same behavior. Does anyone know any more substances which are amphoteric in nature?

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First, it may be worth elucidating the nomenclature a bit and distinguishing between amphiprotic and amphoteric substances. The former are those that can react as either acids or bases in the Brønsted-Lowry sense, while the latter are those that react in either manner per the broader Lewis definition. As you mention, water and ammonia are amphiprotic (and thus also amphoteric by definition), which is evident even from the fact that both undergo auto-ionization:

$$ \ce{H2O + H2O <=> H3O+ + OH-}\\ \ce{NH3 + NH3 <=> NH4+ + NH2-} $$

In fact, a large number of protic substances exhibit this type of behavior to an appreciable degree, including concentrated solutions of various acids (e.g., sulfuric, hydrofluoric, etc.). Another canonical example of an extremely common amphiprotic molecule prevalent in nature is bicarbonate, which you find in countless consumer products, as well as within the human body as a physiologic buffering agent.

Under the right conditions, a very wide array of molecules of diverse types can be amphoteric. The two necessary and sufficient criteria for amphoterism are:

  1. The molecule possesses lone pairs, so that it can act as a base.
  2. The molecule can accept electron pairs, so that it can act an acid.

Those are not rare properties, hence amphoterism isn't really an exotic phenomenon.

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    $\begingroup$ To drive the point home, every single neutral and anionic species we know exergonically receives a free proton, acting as a base (even many cations should accept protons, but sufficiently small and highly charged cations will likely electrically repel the proton). The pinnacles of unreactivity, helium and neon, will quite gladly react with a free proton to form the hydrohelium and hydroneon cations $\ce{HeH+}$ and $\ce{NeH+}$. I suspect the situation is not analogous for acids; even some neutral species have endergonic electron affinities, such as manganese atoms and benzene. $\endgroup$ – Nicolau Saker Neto Dec 28 '13 at 20:45

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