Which of the following is colourless?

[Sc(H₂O)₆]³⁺

The correct answer is option 4. \([Sc(H_2O)_6]^{3+}\).

Let us delve deeper into why \([Sc(H_2O)_6]^{3+}\) (hexaaquascandium(III) ion) is colorless compared to the other complex ions listed:

1. \([Fe(H_2O)_6]^{3+}\) (hexaaquairon(III) ion):

Iron in the +3 oxidation state \(([Fe(H_2O)_6]^{3+})\) typically appears yellow in aqueous solution. The yellow color arises due to d-d transitions within the iron(III) ion. These transitions involve absorption of light in the blue and green regions of the spectrum, resulting in the complementary color yellow.

2. \([Fe(CN)_6]^{3-}\) (hexacyanidoferrate(III) ion):

Iron in the +3 oxidation state \(([Fe(CN)_6]^{3-})\) appears deep red in color. This red color is due to ligand-to-metal charge transfer transitions between the cyanide ligands and the iron(III) ion. These transitions absorb light in the green region of the spectrum, leading to the observed red color.

3. \([Ti(H_2O)_6]^{3+}\) (hexaaquatitanium(III) ion):

Titanium in the +3 oxidation state \(([Ti(H_2O)_6]^{3+})\) typically appears purple in aqueous solution. The purple color results from d-d transitions within the titanium(III) ion. These transitions absorb light in the yellow-green region of the spectrum, resulting in the complementary color purple.

4. \([Sc(H_2O)_6]^{3+}\) (hexaaquascandium(III) ion):

Scandium in the +3 oxidation state \(([Sc(H_2O)_6]^{3+})\) is colorless in aqueous solution. Scandium(III) ions do not have d-electrons in the ground state, and therefore, they do not undergo d-d transitions that absorb visible light. As a result, \([Sc(H_2O)_6]^{3+}\) does not absorb any specific wavelength in the visible spectrum, and thus, it appears colorless to the human eye.

In summary, the reason why \([Sc(H_2O)_6]^{3+}\) is colorless is because scandium(III) ions lack d-d electronic transitions in the visible light range. Therefore, they do not absorb any visible light wavelengths, resulting in a complex ion that appears colorless in aqueous solution.