Definition of ambidentate ligand

An ambidentate ligand is a monodentate ligand that can coordinate to the central metal atom through two different atoms, but only one at a time.

Check each ligand

We examine the given ligands one by one:

(i) $\mathrm{NO}_2^-$

Nitrite ion can coordinate through:

• $N$ atom: nitro
• $O$ atom: nitrito

So, $\mathrm{NO}_2^-$ is ambidentate.

(ii) $\mathrm{SCN}^-$

Thiocyanate ion can coordinate through:

• $S$ atom: thiocyanato-S
• $N$ atom: thiocyanato-N

So, $\mathrm{SCN}^-$ is ambidentate.

(iii) $\mathrm{C}_2\mathrm{O}_4^{2-}$

Oxalate ion is a bidentate chelating ligand. It does not act as a typical ambidentate ligand.

So, $\mathrm{C}_2\mathrm{O}_4^{2-}$ is not ambidentate.

(iv) $\mathrm{NH}_3$

Ammonia coordinates only through the lone pair on $N$.

So, $\mathrm{NH}_3$ is not ambidentate.

(v) $\mathrm{CN}^-$

Cyanide ion can coordinate through:

• $C$ atom: cyano
• $N$ atom: isocyano

So, $\mathrm{CN}^-$ is ambidentate.

(vi) $\mathrm{SO}_4^{2-}$

Sulfate generally acts as a polyatomic ligand through oxygen atoms; it is not treated as a standard ambidentate ligand in this context.

So, $\mathrm{SO}_4^{2-}$ is not ambidentate.

(vii) $\mathrm{H}_2\mathrm{O}$

Water coordinates through oxygen only.

So, $\mathrm{H}_2\mathrm{O}$ is not ambidentate.

Count ambidentate ligands

Ambidentate ligands are:

• $\mathrm{NO}_2^-$
• $\mathrm{SCN}^-$
• $\mathrm{CN}^-$

Therefore, total number is: $3$