check the box before each formula that represents a ligand that is likely to form a complex with a…

Brief Explanations:

A ligand is a molecule or ion that can donate a pair of electrons to a transition metal to form a coordinate bond.

• $\ce{NO^-_{2}}$: The nitrite ion has lone pairs (on N or O) to donate, so it can act as a ligand.
• $\ce{KBr}$: It is an ionic compound that dissociates into $\ce{K+}$ and $\ce{Br-}$. $\ce{K+}$ is a cation and not a ligand, and $\ce{Br-}$ is a spectator ion here (KBr is a salt, not a ligand - forming species in this context as it's a strong electrolyte that dissociates, and K+ is not a transition metal, and Br- alone doesn't typically act as a ligand in the context of KBr's role here).
• $\ce{FeO}$: It is an ionic compound (iron(II) oxide), a solid, and not a ligand (it's a metal oxide, not a species that donates electrons to a transition metal to form a complex; it's more of a compound with a transition metal, not a ligand for another transition metal).
• $\ce{H_{2}O}$: Water has lone pairs on the oxygen atom, so it can act as a ligand (e.g., in aqua - complexes like $\ce{[Cu(H_{2}O)_{6}]^{2+}}$).

So $\ce{NO^-{2}}$ and $\ce{H{2}O}$ are ligands. But let's re - evaluate KBr: KBr is a salt, and when dissolved, $\ce{K+}$ is a cation (not a ligand - donor) and $\ce{Br-}$: while $\ce{Br-}$ can be a ligand in some cases (e.g., in complexes like $\ce{[CuBr_{4}]^{2-}}$), in the context of KBr as a compound, it's not acting as a ligand here (since KBr is a separate ionic compound, not a species that donates to a transition metal to form a complex; the $\ce{Br-}$ from KBr would be a free ion, but KBr itself is not a ligand). FeO is a metal oxide, not a ligand. So $\ce{NO^-{2}}$ (has lone pairs, can donate) and $\ce{H{2}O}$ (has lone pairs on O, can donate) are ligands. But the question is to check the boxes for ligands likely to form a complex with a transition metal. So $\ce{NO^-{2}}$ and $\ce{H{2}O}$ qualify. Wait, but let's check again:

Wait, the options are to check the box before each formula. Let's re - assess each:

1. $\ce{NO^-_{2}}$: Nitrite ion, has electron pairs to donate (Lewis base), so ligand - yes.
2. $\ce{KBr}$: Ionic compound, dissociates into $\ce{K+}$ and $\ce{Br-}$. $\ce{K+}$ is not a ligand, $\ce{Br-}$: while $\ce{Br-}$ can be a ligand, KBr as a compound is not a ligand (it's a salt, not a species that donates to a transition metal to form a complex; the $\ce{Br-}$ from KBr is a free ion, but KBr itself is not a ligand - forming species in this context). So KBr is not a ligand.
3. $\ce{FeO}$: Metal oxide, not a ligand (it's a compound with a transition metal, not a ligand for another transition metal).
4. $\ce{H_{2}O}$: Water has lone pairs on O, so it's a ligand (e.g., in complexes with transition metals).

So the correct boxes to check are for $\ce{NO^-{2}}$ and $\ce{H{2}O}$. But let's confirm the definition again: a ligand is a species that can donate an electron pair to a transition metal (Lewis base). $\ce{NO^-{2}}$ (electron - pair donor), $\ce{H{2}O}$ (electron - pair donor on O). KBr: no, FeO: no.

Answer:

$\boldsymbol{\ce{NO^-{2}}}$ (check the box before $\ce{NO^-{2}}$), $\boldsymbol{\ce{H_{2}O}}$ (check the box before $\ce{H_{2}O}}$)