Question

\(X\) is the number of geometrical isomers exhibited by \([\mathrm{Pt(NH_3)(H_2O)BrCl}]\). 
\(Y\) is the number of optically inactive isomer(s) exhibited by \([\mathrm{CrCl_2(ox)_2}]^{3-}\). 
\(Z\) is the number of geometrical isomers exhibited by \([\mathrm{Co(NH_3)_3(NO_2)_3}]\). Find the value of \(X + Y + Z\). }

Answer 1

Correct Answer: 6

Step 1: Understanding the Concept:
Geometrical and optical isomerism depend on the coordination geometry (square planar vs octahedral) and the arrangement of ligands.
Step 2: Key Formula or Approach:
1. For square planar complexes of type \([\text{MABCD}]\), there are 3 geometrical isomers.
2. For octahedral complexes with bidentate ligands of type \([\text{M(AA)}_2\text{B}_2]\), there are cis and trans isomers.
3. For octahedral complexes of type \([\text{MA}_3\text{B}_3]\), there are facial ({fac}) and meridional ({mer}) isomers.
Step 3: Detailed Explanation:
1. Calculation of X:
\([\text{Pt}(\text{NH}_3)(\text{H}_2\text{O})\text{BrCl}]\) is a square planar complex with four different monodentate ligands.
This follows the \([\text{MABCD}]\) pattern, which gives 3 geometrical isomers (by keeping one ligand fixed and rotating the others).
\(\therefore X = 3\).
2. Calculation of Y:
\([\text{CrCl}_2(\text{ox})_2]^{3-}\) is an octahedral complex with two bidentate oxalate ligands and two chloride ions.
It exists as two geometrical isomers: {cis} and {trans}.
- The {trans}-isomer has a center of symmetry and plane of symmetry, making it optically inactive.
- The {cis}-isomer lacks a plane of symmetry and is chiral (optically active).
The question asks for the number of optically {inactive} isomers. Only the {trans}-isomer fits.
\(\therefore Y = 1\).
3. Calculation of Z:
\([\text{Co}(\text{NH}_3)_3(\text{NO}_2)_3]\) is an octahedral complex of type \([\text{MA}_3\text{B}_3]\).
It exhibits 2 geometrical isomers: the facial ({fac}) and meridional ({mer}) isomers.
\(\therefore Z = 2\).
Total Sum:
\(X + Y + Z = 3 + 1 + 2 = 6\).
Step 4: Final Answer:
The value of X + Y + Z is 6.