Solutions of $\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+},\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}$ (both octahedral), and \(\left[\mathrm{CoCl}_{4}\right]^{2-}(\) tetrahedral) are colored. One is pink, one is blue, and one is yellow. Based on the spectrochemical series and remembering that the energy splitting in tetrahedral complexes is normally much less than that in octahedral ones, assign a color to each complex.

In an octahedral complex, the energy of the d orbitals splits into two levels: the lower energy t2g level (consisting of dxy, dxz, and dyz orbitals) and the higher energy eg level (consisting of dx^2-y^2 and dz^2 orbitals). The energy difference between these two levels is called ∆o. In a tetrahedral complex, the energy splitting of d orbitals is inverted compared to octahedral complexes, with the higher energy level being t2 and the lower energy level being e; this energy difference is called ∆t. It is important to note that ∆t is usually much smaller than ∆o.

The spectrochemical series is a ranking of ligands based on their ability to split the d orbitals. Ligands that cause a large splitting are called strong-field ligands, and those that cause a small splitting are called weak-field ligands. The series is as follows: I- < Br- < Cl- < F- < OH- < H2O < NH3 < en < bipy < phen < CN- < CO Here, NH3 (ammine) and H2O (aqua) are both moderate-field ligands, while Cl- (chloride) is a weak-field ligand.

For the two octahedral complexes: 1. \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+}\) - Coordination geometry: Octahedral - Ligand: NH3 (moderate-field) - Energy splitting: Moderate ∆o 2. \(\left[\mathrm{Co}\left(\mathrm{H}_{2}\mathrm{O}\right)_{6}\right]^{2+}\) - Coordination geometry: Octahedral - Ligand: H2O (moderate-field) - Energy splitting: Moderate ∆o For the tetrahedral complex: 3. \(\left[\mathrm{CoCl}_{4}\right]^{2-}\) - Coordination geometry: Tetrahedral - Ligand: Cl- (weak-field) - Energy splitting: Small ∆t

The absorbed photon's energy determines the electron's transition between the split d orbitals, which also determines the color of light absorbed. Based on the relationship between energy and wavelength (E = hν = hc/λ), a shorter wavelength corresponds to a higher energy, and vice versa. The complementary color of the absorbed light is the observed color, which is the color we associate with the complex. Thus, the complex absorbing the lowest-energy light will appear with the highest-energy complementary color, and vice versa. The energy of absorbed light in the visible spectrum follows the order: Red < Orange < Yellow < Green < Blue < Violet The corresponding complementary colors, which are the observed colors, follow the reverseorder: Violet < Blue < Green < Yellow < Orange < Red

Comparing the energy splitting of the complexes, we can order them as follows: Small ∆t: \(\left[\mathrm{CoCl}_{4}\right]^{2-}\) (tetrahedral) Moderate ∆o: \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+},\left[\mathrm{Co}\left(\mathrm{H}_{2}\mathrm{O}\right)_{6}\right]^{2+}\) (both octahedral) Since there are three colors given in the problem (pink, blue, and yellow), we can assign the colors based on the energy order for complementary colors: - \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+}\): Pink (lower energy absorption compared to the other octahedral complex due to slightly stronger field ligand) - \(\left[\mathrm{Co}\left(\mathrm{H}_{2}\mathrm{O}\right)_{6}\right]^{2+}\): Blue (higher energy absorption compared to pink) - \(\left[\mathrm{CoCl}_{4}\right]^{2-}\): Yellow (highest energy complementary color due to the smallest energy splitting) Thus, the color assignment is: \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+}\): Pink \(\left[\mathrm{Co}\left(\mathrm{H}_{2}\mathrm{O}\right)_{6}\right]^{2+}\): Blue \(\left[\mathrm{CoCl}_{4}\right]^{2-}\): Yellow