Let's analyze each option to determine which chemical equation represents a precipitation reaction. A precipitation reaction occurs when two aqueous solutions react to form an insoluble solid, known as a precipitate.
Option A:
[tex]\[ Mg(ClO_3)_2(aq) + 2 HCl(aq) \rightarrow MgCl_2(aq) + 2 HClO_3(aq) \][/tex]
In this equation, all the reactants and products are in aqueous states (aq), which means they are dissolved in water. No solid (s) is formed, so this is not a precipitation reaction.
Option B:
[tex]\[ AlBr_3(aq) + 3 Lil(aq) \rightarrow AlI_3(aq) + 3 LiBr(aq) \][/tex]
Similarly, in this equation, all reactants and products are in aqueous states. Again, there is no formation of a solid precipitate, so this is not a precipitation reaction.
Option C:
[tex]\[ NH_4NO_3(aq) + HBr(aq) \rightarrow NH_4Br(aq) + HNO_3(aq) \][/tex]
Here as well, all substances involved are in aqueous form, indicating that no solid precipitate is formed. This is not a precipitation reaction.
Option D:
[tex]\[ Li_2CO_3(aq) + FeCl_2(aq) \rightarrow 2 LiCl(aq) + FeCO_3(s) \][/tex]
In this reaction, we observe that [tex]\( FeCO_3 \)[/tex] is formed and it is in the solid state (s). This indicates that a precipitate is indeed formed during this reaction, making this a precipitation reaction.
Therefore, the chemical equation that represents a precipitation reaction is:
[tex]\[ \boxed{D} \][/tex]
