Exercice II$.$ Inertia and Lability of cobalt complexes

The $[Co(N{H}_3{)}_{5}Cl{]}^{2+}$ complex was first synthesized by A$.$ Werner in $1893.$ This compound is still widely used as a single electron acceptor.

i$)$ Make an electron count of this complex named A $($oxidation state, $d^n$ configuration, total number of electrons$).$

ii$)$ Recall briefly the principles of the angular overlap theory.

iii$)$ This complex is in a low spin state. Give the spin value and fill the d$-$block for this complex in octahedral symmetry.

iv$)$ Calculate the total stabilization energy for the $[Co(N{H}_3{)}_{5}Cl{]}^{2+}$ complex considering the approximation that $e_{}$ is similar for the ligands $N{H}_3$ and $Cl-$

v$)$ We consider the exchange of the $Cl$ ligand in the coordination sphere of this complex by a water molecule. A dissociative mechanism will be assumed with an square

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pyramidal intermediate. Calculate the activation energy in term of required for this substitution.

vi$)$ Make a schematic energy diagram of the reaction path of this substitution reaction.

$2.$ The $[Co(N{H}_3{)}_{5}Cl{]}^{2+}$ complex $($A$)$ can be reduced by one electron to give a complex named B$.$

i$)$ Make an electron counting for complex B $($oxidation state, $d^n$ configuration and total number of electrons$)$

ii$)$ Give the spin value of the complex B considering it is high spin and fill in the orbitals of $d$ block.

iii$)$ Is there any change structural change $($bond length$)$ during this reduction process from $A$ to $B?$ Justify.

iv$)$ Calculate the activation energy required for the exchange of a ligand of $B$ by a water ligand. It will be assumed again that the intermediate has a square based pyramid $($note that e$\text{'}$ for $B$ is similar for an $N{H}_3$ and $Cl$ ligand$).$

v$)$ Comment on the relative values of $e_{}$ and $e_{}^{\text{'}}$ and justify.

vi$)$ Compare the activation energy to make the substitution reaction in the case of A and B $.$ Comment qualitatively on the inertia and lability of these complexes.