Problem 66 - Chemistry: The Central Science in SI Units, Global Edition

Question

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?

Step-by-Step Solution

Answer

In conclusion, \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}\) is a low spin complex due to its strong-field ligand \(\mathrm{CN}^{-}\) and one unpaired electron, while \(\left[\mathrm{Fe}(\mathrm{NCS})_{6}\right]^{3-}\) is a high spin complex due to its weak-field ligand \(\mathrm{NCS}^{-}\) and five unpaired electrons. In the spectrochemical series, \(\mathrm{NCS}^{-}\) should be placed earlier than \(\mathrm{CN}^{-}\).

Step 1: Recall the principles of Crystal Field Theory (CFT)

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.

Step 2: Identify high spin or low spin based on unpaired electrons

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.

Step 3: Compare the ligands and determine the placement of NCS- in the spectrochemical series

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.

Key Concepts

High Spin Complexes

High spin complexes are characterized by having a larger number of unpaired electrons. This happens when the ligands surrounding the central metal ion cause a smaller splitting of the d-orbitals. In simpler terms, the energy gap between the lower (t2g) and higher (eg) energy levels is quite small. This small energy gap allows electrons to populate higher energy orbitals instead of pairing up in lower ones.
For example, in the complex \(\left[\mathrm{Fe}(\mathrm{NCS})_{6}\right]^{3-}\), the presence of five unpaired electrons indicates it is a high spin complex. The \(\mathrm{NCS}^{-}\) ligand causes a weaker splitting, leading to unpaired electrons in several d-orbitals.
When analyzing any complex:

• Check the number of unpaired electrons
• More unpaired electrons typically indicate a high spin configuration

Low Spin Complexes

Low spin complexes are distinguished by having fewer unpaired electrons. The ligands in this case exert a strong field, causing a significant splitting of the d-orbitals. This large energy gap encourages electrons to pair up in the lower energy levels (t2g) before filling the higher ones (eg).
In the given example of \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}\), the presence of only one unpaired electron indicates a low spin complex. The \(\mathrm{CN}^{-}\) ligand is responsible for a stronger field and larger splitting of the d-orbitals, facilitating electron pairing.
To determine if a complex is low spin, consider:

• Fewer unpaired electrons often mean a low spin configuration
• Look for ligands known to cause significant splitting

Spectrochemical Series

The spectrochemical series is an incredibly insightful lineup of ligands arranged according to the field strength they generate. This list helps predict whether a given ligand will form high spin or low spin complexes.
Key points about the spectrochemical series include:

• Strong-field ligands: Located towards the end, cause significant d-orbital splitting, typically forming low spin complexes.
• Weak-field ligands: Found earlier in the series, they cause minimal splitting and often lead to high spin complexes.

When evaluating \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}\) and \(\left[\mathrm{Fe}(\mathrm{NCS})_{6}\right]^{3-}\), we observe that \(\mathrm{CN}^{-}\) produces a stronger field leading to low spin, while \(\mathrm{NCS}^{-}\) forms a weaker field indicating a high spin. Hence, \(\mathrm{NCS}^{-}\) appears earlier in the spectrochemical series compared to \(\mathrm{CN}^{-}\). Recognizing where ligands stand in this series provides a predictive edge in understanding complex behaviors.