Which of the following cannot show linkage isomerism?

The correct answer is option 4. \(H_2O\).

Linkage isomerism is a form of isomerism where a ligand can bind to a metal center through two different atoms. This is possible when the ligand has multiple potential donor atoms. Ligands Capable of Linkage Isomerism:

1. \(NO_2^-\) (Nitrite ion):

Binding sites: Nitrogen and Oxygen.

Linkage isomers:

Nitro: When nitrogen binds to the metal (M-NO\(_2\)).

Nitrito: When oxygen binds to the metal (M-ONO).

\(\text{M-NO}_2 \quad \text{and} \quad \text{M-ONO}\)

2. \(CN^-\) (Cyanide ion):

Binding sites: Carbon and Nitrogen.

Linkage isomers:

Cyanide: When carbon binds to the metal (M-CN).

Isocyanide: When nitrogen binds to the metal (M-NC).

\(\text{M-CN} \quad \text{and} \quad \text{M-NC}\)

3. \(SCN^-\) (Thiocyanate ion):

Binding sites: Sulfur andNitrogen

Linkage isomers:

Thiocyanato: When sulfur binds to the metal (M-SCN).

Isothiocyanato: When nitrogen binds to the metal (M-NCS).

\(\text{M-SCN} \quad \text{and} \quad \text{M-NCS}\)

Ligand That Cannot Show Linkage Isomerism:

4. \(H_2O\) (Water):

Binding site: Only Oxygen.

Water molecule has only one donor atom, which is the oxygen atom. It cannot form bonds with a metal through any other atom because hydrogen atoms are not capable of donating lone pairs for coordination with the metal. Therefore, water cannot exhibit linkage isomerism.

\(\text{M-H}_2\text{O} \quad \text{(only one binding mode through oxygen)}\)

Conclusion

\(\text{H}_2\text{O}\) (water) cannot show linkage isomerism because it has only one donor atom (oxygen), which binds to the metal center. In contrast, \(\text{NO}_2^-\), \(\text{CN}^-\), and \(\text{SCN}^-\) have multiple potential donor atoms, allowing them to exhibit linkage isomerism.