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 _______.
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 _______.
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In octahedral geometry, triangular faces are formed only by adjacent vertices. Trans ligands can never belong to the same triangular face.
Updated On: May 20, 2026
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Correct Answer: 6
Solution and Explanation
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: \[ \boxed{6} \]
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: \[ \boxed{6} \]
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