To address the problem, we must determine the relationship between the complex ions \([Co(NH_3)_5(NO_2)]^{2+}\) and \([Co(NH_3)_5(ONO)]^{2+}\).
1. Complex Ion Analysis:
Both complexes share the same elemental composition: Cobalt, five ammonia ligands, and a nitro group, with an overall charge of 2+. The distinction arises from the ligand's coordination mode:
- In \([Co(NH_3)_5(NO_2)]^{2+}\), the \(\text{NO}_2\) ligand attaches through the nitrogen atom (nitro, \(\text{-NO}_2\)).
- In \([Co(NH_3)_5(ONO)]^{2+}\), the \(\text{NO}_2\) ligand attaches through an oxygen atom (nitrito, \(\text{-ONO}\)).
2. Isomerism Identification:
The two complexes possess identical molecular formulas but differ in the atom through which the \(\text{NO}_2\) ligand binds to the metal center. This form of isomerism, characterized by a ligand connecting via different atoms, is termed linkage isomerism. The \(\text{NO}_2\)/\(\text{ONO}^-\) ligand is ambidentate, enabling coordination through either its nitrogen or oxygen atom, thus generating these two distinct isomers.
3. Consideration of Other Isomerism Types:
- Coordination isomerism involves ligand exchange between cationic and anionic parts; however, both species here are cations with identical ligands.
- Geometric isomerism (e.g., cis-trans) is inapplicable because \([Co(NH_3)_5X]\) (with five identical ligands) lacks the requisite symmetry for such isomerism.
Therefore, linkage isomerism is the accurate classification.
Conclusion:
The complex ions \([Co(NH_3)_5(NO_2)]^{2+}\) and \([Co(NH_3)_5(ONO)]^{2+}\) are classified as linkage isomers.