Problem 73 - Chemistry The Molecular Science

Question

\(\mathrm{Fe}^{3+}\) forms octahedral complexes with \(\mathrm{NCS}^{-}\) and with \(\mathrm{NO}_{2}^{-}\) ligands. One complex displays a greater paramagnetism than the other. (a) Write the formula for each of these complex ions. (b) Use the spectrochemical series to predict whether the complex ions are high-spin or low-spin. (c) Identify which complex ion is more paramagnetic. (d) Draw the crystal-field splitting diagram, including delectrons, for each complex ion.

Step-by-Step Solution

Answer

The high-spin \\([\text{Fe}(\text{NCS})_{6}]^{3-}\\) complex is more paramagnetic.

Step 1: Write the Formula for Each Complex Ion

The oxidation state of Fe in both complexes is +3, making it \( \text{Fe}^{3+} \). For the \( \text{NCS}^{-} \) ligand, the complex will be \([\text{Fe}(\text{NCS})_{6}]^{3-}\). For the \( \text{NO}_{2}^{-} \) ligand, the complex will be \([\text{Fe}(\text{NO}_{2})_{6}]^{3-}\).

Step 2: Predict High-Spin or Low-Spin Using the Spectrochemical Series

The spectrochemical series lists ligands in order of their ability to split the d-orbitals. \( \text{NCS}^{-} \) is a weak field ligand, typically producing high-spin complexes, while \( \text{NO}_{2}^{-} \) is a stronger field ligand, often resulting in low-spin complexes. Therefore, \([\text{Fe}(\text{NCS})_{6}]^{3-}\) is high-spin, and \([\text{Fe}(\text{NO}_{2})_{6}]^{3-}\) is low-spin.

Step 3: Identify the More Paramagnetic Complex Ion

A high-spin complex has more unpaired electrons and is thus more paramagnetic than a low-spin complex. \([\text{Fe}(\text{NCS})_{6}]^{3-}\) is high-spin with five unpaired electrons, whereas \([\text{Fe}(\text{NO}_{2})_{6}]^{3-}\) is low-spin with one unpaired electron. Thus, \([\text{Fe}(\text{NCS})_{6}]^{3-}\) is more paramagnetic.

Step 4: Draw the Crystal-Field Splitting Diagram for Each Complex Ion

Fe is in the +3 oxidation state, resulting in a \([\text{Ar}]3d^5\) electron configuration. In \([\text{Fe}(\text{NCS})_{6}]^{3-}\), being high-spin, the electrons are arranged as up-arrow in the three lower energy \( t_{2g} \) orbitals and two in the \( e_{g} \) orbitals. For \([\text{Fe}(\text{NO}_{2})_{6}]^{3-}\), being low-spin, electrons fill the \( t_{2g} \) orbitals first (all paired in \( t_{2g} \)) before any populate \( e_{g} \), leading to mostly paired electrons.

Key Concepts

Paramagnetism

Paramagnetism refers to the magnetic property of a material that has unpaired electrons. When these unpaired electrons are present, the material is attracted to an external magnetic field. The more unpaired electrons there are, the stronger the paramagnetism observed. In coordination chemistry, the presence of unpaired electrons in metal complexes can be predicted by looking at the electron configuration. For instance, in the case of the octahedral complex \([\text{Fe}(\text{NCS})_{6}]^{3-}\), the high-spin configuration leaves electrons unpaired. This results in stronger paramagnetism compared to low-spin arrangements, like in \([\text{Fe}(\text{NO}_{2})_{6}]^{3-}\), where electrons are more likely to be paired.Understanding paramagnetism is crucial for interpreting magnetic susceptibility experiments, which can help determine the number of unpaired electrons in a complex. Hence, complexes with more unpaired electrons, like \([\text{Fe}(\text{NCS})_{6}]^{3-}\), appear more paramagnetic.

Spectrochemical Series

The spectrochemical series is a key concept in crystal field theory, ranking ligands based on their ability to split d-orbitals. This series guides us in predicting the electron configuration within metal complexes and whether they will adopt a high-spin or low-spin state.

• Weak field ligands, like \(\text{NCS}^{-}\), cause a small splitting in the d-orbitals, promoting a high-spin configuration where electrons tend to remain unpaired.
• Strong field ligands, such as \(\text{NO}_{2}^{-}\), lead to a larger splitting, encouraging a low-spin state where electrons pair up in lower energy orbitals.

These interactions between ligands and metal ions are pivotal for predicting the properties of a complex. Knowing where a ligand stands in the spectrochemical series allows chemists to anticipate the electronic, magnetic, and even color properties of a complex. Therefore, \([\text{Fe}(\text{NCS})_{6}]^{3-}\) is high-spin, displaying greater paramagnetism due to its weaker field. Meanwhile, \([\text{Fe}(\text{NO}_{2})_{6}]^{3-}\) is low-spin due to the stronger field of \(\text{NO}_{2}^{-}\).

High-spin vs Low-spin Complexes

High-spin and low-spin configurations are determined by how electrons distribute themselves among the d-orbitals in a metal complex, based largely on the field strength of the ligand.High-spin Complexes:

• Formed with weak field ligands.
• Result in maximized unpaired electron count.
• Usually increase the paramagnetic character of a complex.

For example, \([\text{Fe}(\text{NCS})_{6}]^{3-}\) has five unpaired electrons due to the weaker field of the \(\text{NCS}^{-}\) ligand, leading to a high-spin configuration.Low-spin Complexes:

• Formed with strong field ligands.
• Minimize the number of unpaired electrons by pairing as many as possible in the lower energy set of orbitals.
• Usually exhibit less paramagnetism compared to high-spin complexes.

In the case of \([\text{Fe}(\text{NO}_{2})_{6}]^{3-}\), only one electron remains unpaired due to the strong field of \(\text{NO}_{2}^{-}\), resulting in a low-spin arrangement.By understanding the distinction between high-spin and low-spin states, one can infer various physical and chemical properties of coordination complexes, such as magnetism and reactivity.