Complex Hybridization and Geometry

The metal complex has $sp^3d^2$ hybridization. This hybridization corresponds to an octahedral geometry around the central metal atom ($M$) with a coordination number of 6.

Complex Structure Determination

The formula given is $MCl_4.3NH_3$. Given the coordination number is 6, the central metal atom $M$ must coordinate to a total of 6 ligands. The formula suggests the presence of 3 ammonia ($NH_3$) molecules and 4 chlorine ($Cl$) atoms associated with the metal. Ammonia ($NH_3$) is a neutral ligand, and chlorine ($Cl$) typically acts as an anionic ligand ($Cl^-$) in coordination complexes. A plausible structure consistent with the formula and coordination number 6 is that 3 $NH_3$ molecules and 3 $Cl^-$ ions act as ligands, while one $Cl^-$ ion remains outside the coordination sphere as a counter ion. The complex can be represented as $ [M(NH_3)_3Cl_3]Cl $. This arrangement utilizes 3 neutral $NH_3$ ligands and 3 anionic $Cl^-$ ligands, totalling 6 coordination sites, and leaves one $Cl^-$ as the counter ion, consistent with the overall stoichiometry.

Identifying the Isomer Type

The coordination entity within the complex is $ [M(NH_3)_3Cl_3] $. This is an octahedral complex of the general formula $ Ma_3b_3 $, where 'M' is the central metal atom, 'a' represents the $ NH_3 $ ligands, and 'b' represents the $ Cl $ ligands.

Number of Geometrical Isomers

Octahedral complexes of the type $ Ma_3b_3 $ exhibit geometrical isomerism. There are two possible arrangements for the ligands:

• Facial (fac): The three identical 'a' ligands ($NH_3$) occupy positions on one face of the octahedron. The three identical 'b' ligands ($Cl^-$) occupy the positions on the opposite face.
• Meridional (mer): The three identical 'a' ligands ($NH_3$) are arranged such that one ligand is opposite (trans) to another along one axis, while the third ligand is in a plane perpendicular to this axis.

Therefore, the complex $ [M(NH_3)_3Cl_3] $ exhibits 2 geometrical isomers.