Consider that the coordinating atoms of the ligands in cis-[Co(NH_3)_4Cl_2]Cl and mer-[Co(NH_3)_3Cl_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 ____.
A. A
In an octahedral complex, the six coordinating atoms are located at the vertices of an octahedron, which has 8 triangular faces. Each face is formed by 3 vertices, and any two adjacent (cis) vertices form an edge that is shared by exactly two faces. For the cis-[Co(NH_3)_4Cl_2]^+ complex: The two Cl atoms are at adjacent (cis) positions, forming exactly one Cl-Cl edge. This edge is shared by two triangular faces. Since the remaining four vertices are occupied by N atoms, the third vertex of each of these two faces must be an N atom. Therefore, there are 2 faces with exactly two Cl atoms and one N atom. For the mer-[Co(NH_3)_3Cl_3] complex: The three Cl atoms are in a meridional arrangement, meaning two Cl atoms are trans to each other and the third is cis to both. This arrangement forms exactly two Cl-Cl edges. Since the three Cl atoms do not occupy the vertices of the same face (unlike the fac isomer), no face contains three Cl atoms. Each of the two Cl-Cl edges is shared by two faces, yielding 2 2 = 4 distinct faces that contain exactly two Cl atoms. The third vertex in all these 4 faces is an N atom. Therefore, there are 4 faces with exactly two Cl atoms and one N atom. The sum of the total number of such faces in both complexes is 2 + 4 = 6. Answer: 6
Related: Chemistry — Coordination Compounds · All PYQ Banks