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Aqueous ammonia readily dissolves $\mathrm{AgCl}$ because
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The correct answer is:
a soluble complex $\mathrm{Ag}\left(\mathrm{NH}_3\right)_2^{+}$is formed
$\mathrm{AgCl}$ is soluble in ammonia because it forms complex $\left[\mathrm{Ag}\left(\mathrm{NH}_3\right)_2\right]^{+}$with ammonia. Formation of this complex make it like ionic, therefore it is soluble in aqueous ammonia.
$$
\mathrm{AgCl}+2 \mathrm{NH}_4 \mathrm{OH} \longrightarrow \mathrm{Ag}\left(\mathrm{NH}_3\right)_2^{+}+\mathrm{H}_2 \mathrm{O}+\mathrm{Cl}^{-}
$$
(Highly soluble)
$$
\mathrm{AgCl}+2 \mathrm{NH}_4 \mathrm{OH} \longrightarrow \mathrm{Ag}\left(\mathrm{NH}_3\right)_2^{+}+\mathrm{H}_2 \mathrm{O}+\mathrm{Cl}^{-}
$$
(Highly soluble)
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