To determine which complex shows facial-meridional isomerism, we first need to understand what these terms mean:
Now, let's evaluate the given complexes:
\([Co(NH_3)_3Cl_3]\): This complex can display facial-meridional isomerism as it is an octahedral complex with three amine ligands and three chloride ligands, allowing for both fac-arrangement (three Cl or NH3 occupy one face) and mer-arrangement (three Cl or NH3 in a plane).
\([Co(NH_3)_4Cl_2]^+\): This complex cannot exhibit this isomerism as it lacks three identical ligands that could form a face.
\([Co(en)_3]^{3+}\): This complex is homoleptic, consisting of three ethylenediamine (\(en\)) ligands that do not allow for facial-meridional distinction.
\([Co(en)_2Cl_2]^+\): Similar to the above, this complex cannot show facial-meridional isomerism as it has only two Cl ions, preventing the formation necessary for fac-mer isomerism.
Thus, the correct complex that shows facial-meridional isomerism is:
\([Co(NH_3)_3Cl_3]\)