Step 1: Understanding the Complex - The chemical formula of nitropentammine chromium (III) chloride is: \[ {[Cr(NH}_3{)}_5({NO}_2)]Cl_2 \] This complex contains the nitro ligand (NO$_2$), which can bind through either the nitrogen or oxygen.
Step 2: Types of Isomerism Optical Isomerism: Seen in chiral molecules with non-superimposable mirror images. Not applicable here.
Ionization Isomerism: When exchange of anions leads to different compounds in solution. Not applicable.
Polymerization Isomerism: Occurs when two complexes have the same empirical formula but different molecular formulas. Not applicable.
Linkage Isomerism: Occurs when a ligand can bind through two different atoms. (Correct Answer)
Step 3: Linkage Isomerism in This Complex
The NO$_2$ group can bind via:
Nitro form (NO$_2$-N)
Nitrito form (ONO)
Final Answer: The correct isomerism is linkage isomerism due to NO$_2$ binding through either N or O.