Question

Rank the following complex ions in order of an increasing wavelength of light absorbed.

$\mathbf{\text{Co}}{{\mathbf{\left(}{\mathbf{H}}_{\mathbf{2}}\mathbf{O}\mathbf{\right)}}_{\mathbf{6}}}^{\mathbf{3}\mathbf{+}}\mathbf{,}\mathbf{}\mathbf{Co}{{\mathbf{\left(}\mathbf{CN}\mathbf{\right)}}_{\mathbf{6}}}^{\mathbf{3}\mathbf{-}}\mathbf{,}\mathbf{}\mathbf{Co}{{\mathbf{\left(}\mathbf{I}\mathbf{\right)}}_{\mathbf{6}}}^{\mathbf{3}\mathbf{-}}\mathbf{,}\mathbf{}\mathbf{Co}{{\mathbf{\left(}\mathbf{en}\mathbf{\right)}}_{\mathbf{3}}}^{\mathbf{3}\mathbf{+}}$

Short answer

$\text{Co}{{\text{(CN)}}_6}^{3-}<\mathrm{Co}{{\left(\mathrm{en}\right)}_3}^{3+}<\mathrm{Co}{{\left({\mathrm{H}}_2\mathrm{O}\right)}_6}^{3+}<\mathrm{Co}{{\left(\mathrm{I}\right)}_6}^{3-}$

Step-by-step solution

Step 1:  Weak-field complex ion has low splitting energy ∆, that means it absorbs light of higher wavelengths.

The iodide ligand forms weak-field complex while cyanate ligands form strong-field complex according to the spectrochemical series.

The iodide complex of cobalt absorbs at higher wavelengths than cobalt complexes formed by ethylene diamine, aqua and iodide ligands.

Step 2: Strong-field complex ion has high splitting energy  ∆ , that mean it absorbs light of shorter wave lengths.

The cyanate complex of cobalt absorbs shorter wavelengths than the cobalt complexes formed by ethylene diamine, aqua and iodide ligands.