Facial (fac) and meridional (mer) isomers are types of geometric isomers found in octahedral complexes with the general formula \([MA_3B_3]\). In these complexes, three identical ligands can either be adjacent to each other forming a 'facial' configuration or adjacent to form a 'meridional' configuration.
Let's analyze why the other complexes do not show fac-mer isomerism:
Thus, the correct complex exhibiting facial-meridional isomerism is \([Co(NH_3)_3Cl_3]\).
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:
\([Co(NH_3)_3Cl_3]\)
Which one of the following graphs accurately represents the plot of partial pressure of CS₂ vs its mole fraction in a mixture of acetone and CS₂ at constant temperature?

Let \( \alpha = \dfrac{-1 + i\sqrt{3}}{2} \) and \( \beta = \dfrac{-1 - i\sqrt{3}}{2} \), where \( i = \sqrt{-1} \). If
\[ (7 - 7\alpha + 9\beta)^{20} + (9 + 7\alpha - 7\beta)^{20} + (-7 + 9\alpha + 7\beta)^{20} + (14 + 7\alpha + 7\beta)^{20} = m^{10}, \] then the value of \( m \) is ___________.