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From Wikipedia-1, and from an answer here on Stack-Exchange, I can list at least the following elements which will dissolve in aqueous $\ce{NH4OH}$:

  • $\ce{Cr(III), Co(III), Ni(II), Cu(I, II), Zn(II), Ag(I),}$ along with "several platinum group metals"

From reading Wikipedia-2, I also suspect the following elements to dissolve in liquid ammonia:

  • $\ce{Mg, Ca, Sr, Ba, Eu, Yb, Li, Na, K}$ and $\ce{Rb}$

As a matter of fact, according to Wikipedia "almost all metal ions bind ammonia as a ligand." I thought it would be interesting, and potentially very useful, to find out which metal ions are NOT soluble in $\ce{NH4OH}$.

I can list two for now:

  • $\ce{Fe(OH)3}$
  • $\ce{Mg(OH)2}$ with a solubility product of only $5.61×10^{−12}$ (credit to Oscar Lanzi)
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    $\begingroup$ There is a huge difference in pure liquid $\ce{NH3}$ and an aqueous solution of $\ce{NH4OH}$. I can't imagine any of the metals Mg, Ca, Sr, Ba, Li, Na, K or Rb forming amine complexes. $\endgroup$ – MaxW Jul 11 at 0:34
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For the case of magnesium ion, at least, it seems a stretch to say it dissolves in ammonia solution. Assume that the ammonia solution has $\mathrm{pH}$ of $11$ and magnesium hydroxide has a solubility product of $5.61×10^{-12}$. We infer that the magnesium ion solubility at equilibrium with the hydroxide in ammonia solution is only $\pu{5.6μM}$ which is not really all that soluble.

Magnesium ion is appreciably soluble not in an ammonia solution but in a buffered solution of ammonia and an ammonium salt.

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