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When 3+ hexaaqua ions react with hydroxide ions, the following set of reactions occurs:

Reacting hydroxide ions with aluminium ions (ChemGuide)

When we get to stage 3, a neutral ion has formed, and a white precipitate is created. Now, we know that for amphoteric species, adding $\ce{H+}$ ions will reverse this process, hence removing the precipitate. Surely this is an effective test for amphoteric nature?

However, according to my exam board, if you add an excess of hydroxide ions (hence forming a negative ion) after initially adding a small volume of hydroxide ions, and then the precipitate dissolves, this proves that the metal is amphoteric. This does not make sense to me because the definition of an amphoteric species is one that reacts with both acids and bases; yet, in this test, the species has only reacted with hydroxide ions; no acid - so there is no proof of amphoteric nature.

So, why is a species amphoteric if it forms a white precipitate after reacting with hydroxide ions, then dissolves after adding an excess?

An example of a problem is: "how do you prove lead (II) hydroxide is amphoteric, whereas magnesium hydroxide is not?" The answer is: add an excess of $\ce{NaOH}$ - magnesium forms a white precipitate, whereas lead(II) hydroxide forms a white precipitate, then dissolves. There is no mention of acid, so how does this prove amphoteric nature?

If anybody can clear my doubts or explain where I am wrong in thinking, I would be very grateful.

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    $\begingroup$ :/ And you know any hydroxide that doesn't react with acids? No? I guess not - that's a given, just reaction with the base needs to be checked. $\endgroup$
    – Mithoron
    Jul 2 at 21:56
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    $\begingroup$ The definition of an amphoteric species that you are using is akin to the definition of a dog as a furry creature that runs and bites. It is not wrong per se, but relies on a good deal of prerequisites to be understood correctly. $\endgroup$ Jul 2 at 22:12
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    $\begingroup$ @Mithoron I don't see how the comment is helpful, it just potentially adds to the confusion of the OP. $\endgroup$
    – Buck Thorn
    Jul 3 at 4:32
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    $\begingroup$ @IvanNeretin I think the OP has a right to be confused. A more helpful comment would provide some guidance or ask for clarification. $\endgroup$
    – Buck Thorn
    Jul 3 at 4:34
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According to IUPAC Goldbook:

A chemical species that behaves both as an acid and as a base is called amphoteric. This property depends upon the medium in which the species is investigated: $\ce{H2SO4}$ is an acid when studied in water, but becomes amphoteric in superacids.

Most common example for amphoteric compound is water, which can act either as an acid or base depending on the solute present:

$$\ce{HCl + H2O -> H3O+ + Cl-} \tag{acting as an base}$$ $$\ce{NH3 + H2O -> NH4+ + OH-} \tag{acting as an acid}$$

OP describes the problem as: "This does not make sense to me because the definition of an amphoteric species is one that reacts with both acids and bases; yet, in this test, the species has only reacted with hydroxide ions; no acid - so there is no proof of amphoteric nature".

The problem is the question does not clarify which compound is the amphoteric. The starting compound, $\ce{[M(H2O)6]^3+}$, is not amphoteric for sure. I choose the most suitable amphoteric compound in this senario as the neutral precipitate, $\ce{M(H2O)3(OH)3}$ because it can shows the rest of amphoteric compounds in the series. For instance, according to the IUPAC description, this precipitate is an amphoteric compound because it will react with both acids and bases (as Mithoron pointed out in the comment) as follows:

$$\ce{M(H2O)3(OH)3 ->[H3O+] [M(H2O)4(OH)2]+ ->[H3O+] [M(H2O)5(OH)]^2+ ->[H3O+] [M(H2O)6]^3+}$$ $$\ce{M(H2O)3(OH)3 ->[OH-] [M(H2O)2(OH)4]- ->[OH-] [M(H2O)(OH)5]^2- ->[OH-] [M(OH)6]^3-}$$

Note: Strictly speaking, according to the IUPAC description, all of these metal hydroxides except for $\ce{[M(H2O)6]^3+}$ and $\ce{[M(OH)6]^3-}$ are amphoteric compounds since each can go either way with an acid or a base.

For more examples of amphoteric compounds including lead(II) hydroxide, read here and here. For example, lead(II) hydroxide is an amphoteric compound, which shows following reactions with both acids and bases: $$\ce{Pb(OH)2 (s) + 2HCl (aq) -> PbCl2 (aq) + 2H2O}$$ $$\ce{Pb(OH)2 (s) + 2NaOH (aq) -> Na2Pb(OH)4 (aq)}$$

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  • $\begingroup$ Thank you for the response. I understand why the species is amphoteric. I just don't understand why if a species reacts with an excess of NaOH and dissolves, it is amphoteric. Could anyone help to clarify this? $\endgroup$
    – Matthew
    Jul 3 at 11:26
  • $\begingroup$ An example from my text book is: paste.pics/D2MUR Apparently, the second reaction proves that lead hydroxide is amphoteric...? $\endgroup$
    – Matthew
    Jul 3 at 12:28
  • $\begingroup$ @Matthew: I edited according to your concern. Hope you understand it better now. $\endgroup$ Jul 3 at 12:39
  • $\begingroup$ @MathewMahindaratne Thank you, this helps a bit more; I now understand that M(H2O)3(OH)3 is the amphoteric species. However, I am still unsure as to why only adding an excess of NaOH (and seeing if M(H2O)3(OH)3 dissolves) proves amphoteric nature. Surely, like you described, you would also need to add acid to prove that M(H2O)3(OH)3 reacts with both acids and bases and is thus amphoteric? $\endgroup$
    – Matthew
    Jul 3 at 13:33
  • $\begingroup$ Here is a reference question from my exam board which explains why I have concerns over this: paste.pics/D2NVH $\endgroup$
    – Matthew
    Jul 3 at 14:00

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