Question #44580

The racemization of the chiral complex $\Delta\text{-}[Co(en)_3]^{3+}$ (where en = ethylenediamine) in aqueous solution at $298\text{ K}$ proceeds via an intramolecular Bailar twist mechanism, passing through a trigonal prismatic ($D_{3h}$) transition state. The purely steric activation barrier ($\Delta E_{\text{steric}}$) to deform the ligand backbone into the $D_{3h}$ geometry is $45\text{ kJ mol}^{-1}$. However, the total activation energy ($E_a$) must account for the 'hidden' electronic barrier due to the loss of Crystal Field Stabilization Energy (CFSE) during the geometric transition. Given:

• The octahedral crystal field splitting parameter for $[Co(en)_3]^{3+}$ is $\Delta_o = 25,000\text{ cm}^{-1}$.
• The complex is low-spin in its ground state.
• In the $D_{3h}$ transition state, the d-orbital splitting yields a net stabilization energy of $-1.8 \Delta_o$ (ignoring pairing energy changes).
• Conversion factor: $1\text{ kJ mol}^{-1} \equiv 83.33\text{ cm}^{-1}$.

Calculate the total activation energy ($E_a$) for the racemization process.