The ion \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}\) has one unpaired electron, whereas \(\left[\mathrm{Fe}(\mathrm{NCS})_{6}\right]^{3-}\) has five unpaired electrons. From these results, what can you conclude about whether each complex is high spin or low spin? What can you say about the placement of \(\mathrm{NCS}^{-}\) in the spectrochemical series?

Crystal field theory explains the interaction between the central metal ion and the ligands in a coordination complex. High spin and low spin complexes arise due to the difference in electron configurations that can be favored when the ligands approach the central metal ion. In a high spin complex, the ligands have a weak splitting effect, allowing the electrons to occupy higher energy orbitals. In a low spin complex, the ligands have a strong splitting effect, causing the electrons to pair up in the lower energy orbitals.

The given complexes are \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}\), which has one unpaired electron, and \(\left[\mathrm{Fe}(\mathrm{NCS})_{6}\right]^{3-}\), which has five unpaired electrons. A complex with fewer unpaired electrons, such as 1, is a low spin complex because it has a strong splitting effect, causing electrons to pair up in the lower energy orbitals. Therefore, \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}\) is a low spin complex. A complex with a higher number of unpaired electrons, such as 5, is a high spin complex because it has a weak splitting effect, allowing electrons to occupy the higher energy orbitals. Therefore, \(\left[\mathrm{Fe}(\mathrm{NCS})_{6}\right]^{3-}\) is a high spin complex.

The spectrochemical series is a list of ligands ordered by their ability to split the d-orbitals of the central metal ion. Strong-field ligands, which cause a large splitting of the d-orbitals and result in low spin complexes, are found towards the end of the spectrochemical series. Weak-field ligands, which cause a small splitting of the d-orbitals and result in high spin complexes, are found at the beginning of the series. Since \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}\) is a low spin complex, the \(\mathrm{CN}^{-}\) ligand is a strong-field ligand, and it is found towards the end of the spectrochemical series. On the other hand, \(\left[\mathrm{Fe}(\mathrm{NCS})_{6}\right]^{3-}\) is a high spin complex, so the \(\mathrm{NCS}^{-}\) ligand is a weak-field ligand. Therefore, \(\mathrm{NCS}^{-}\) must be placed earlier than \(\mathrm{CN}^{-}\) in the spectrochemical series. In conclusion, \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}\) is a low spin complex, and \(\left[\mathrm{Fe}(\mathrm{NCS})_{6}\right]^{3-}\) is a high spin complex. \(\mathrm{NCS}^{-}\) should be placed earlier than \(\mathrm{CN}^{-}\) in the spectrochemical series according to the information provided.