Question

Consider that the coordinating atoms of the ligands in cis-[Co(NH$_3$)$_4$Cl$_2$]Cl and mer-[Co(NH$_3$)$_3$Cl$_3$] octahedral complexes are at the vertices of an octahedron. The sum of total number of the triangular faces in both the complexes having one N atom and two Cl atoms at their corners is _______.

Hint:

In octahedral geometry, triangular faces are formed only by adjacent vertices. Trans ligands can never belong to the same triangular face.

Answer 1

Correct Answer: 6

Step 1: Understanding the Question:
We need to find the total number of triangular faces having one \(N\) atom and two \(Cl\) atoms at their corners in the following octahedral complexes: \[ \mathrm{cis\text{-}[Co(NH_3)_4Cl_2]Cl} \] and \[ \mathrm{mer\text{-}[Co(NH_3)_3Cl_3]} \] The coordinating atoms are located at the vertices of an octahedron.
Step 2: Key Concept or Approach:
In an octahedron:
Each triangular face is formed by three adjacent vertices.
We count only those faces containing: \[ 1\ N \text{ atom and } 2\ Cl \text{ atoms} \]
Also:
Trans vertices cannot belong to the same triangular face.
Only adjacent ligands can form a triangular face.
Step 3: Detailed Explanation:
(i) \(\mathrm{cis\text{-}[Co(NH_3)_4Cl_2]Cl}\) In the cis complex, the two \(Cl\) ligands are adjacent. Each triangular face containing these two adjacent \(Cl\) ligands can include one adjacent \(NH_3\) ligand. Number of such triangular faces: \[ 4 \] (ii) \(\mathrm{mer\text{-}[Co(NH_3)_3Cl_3]}\) In the mer complex:
Two \(Cl\) ligands are trans to each other.
One \(Cl\) ligand is cis to both.
Only adjacent \(Cl\) pairs can form triangular faces. Hence, number of triangular faces containing one \(N\) and two \(Cl\) atoms: \[ 2 \] (iii) Total Number of Faces: \[ 4+2=6 \] Step 4: Final Answer:
The required sum is: \[ \boxed{6} \]