When concentrated hydrochloric acid is added to a red solution containing the \(\operatorname{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+}\) complex ion, the solution turns blue as the tetrahedral \(\mathrm{CoCl}_{4}^{2-}\) complex ion forms. Explain this color change.

The starting complex is \(\operatorname{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+}\), which has a red color. When concentrated hydrochloric acid is added, it results in the formation of the \(\mathrm{CoCl}_{4}^{2-}\) complex, which has a blue color.

When concentrated hydrochloric acid is added to the solution, its high concentration of chloride ions (Cl-) will replace the water molecules surrounding the cobalt ion. This results in the following reaction: \[ \operatorname{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+} + 4\mathrm{Cl}^{-} \rightarrow \mathrm{CoCl}_{4}^{2-} + 6\mathrm{H}_{2}\mathrm{O} \] In this reaction, the hexaaquacobalt(II) complex ion reacts with chloride ions to form the tetrachlorocobaltate(II) complex ion and releases water as a product.

The observed color change is due to the electronic transition occurring within the ligand field of the cobalt complex. In the original \(\operatorname{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+}\) complex, the cobalt ion is in an octahedral environment surrounded by water molecules. This arrangement causes the d-orbitals to split into two levels: t2g and eg. When hydrochloric acid is added and the complex changes to \(\mathrm{CoCl}_{4}^{2-}\), the cobalt ion now finds itself in a different, tetrahedral ligand field environment surrounded by chloride ions. This change in the ligand environment also changes the splitting of the d-orbitals, resulting in different energy gaps between the orbitals. As a consequence, the absorbed light's wavelength - and therefore the color that our eyes perceive - is different for the two complexes. The \(\operatorname{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+}\) complex absorbs blue light and appears red, while the \(\mathrm{CoCl}_{4}^{2-}\) complex absorbs yellow-orange light and appears blue.

To summarize, the concentrated hydrochloric acid leads to a replacement of water molecules in the \(\operatorname{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+}\) complex by chloride ions, forming the \(\mathrm{CoCl}_{4}^{2-}\) complex. The new ligand environment results in a change of the electronic transitions happening in the cobalt complex, leading to a different color being absorbed by the complex. The result is a color change from red to blue in the solution.