Problem 66 - Chemistry The Central Science In Si Units

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

The complex \([\mathrm{Fe}(\mathrm{CN})_{6}]^{3-}\) is low spin, while \([\mathrm{Fe}(\mathrm{NCS})_{6}]^{3-}\) is high spin. \(\mathrm{NCS}^{-}\) is weaker than CN\(^-\) in the spectrochemical series.

Step 1: Determine Oxidation State and Electronic Configuration of Iron

Both \([\mathrm{Fe}(\mathrm{CN})_{6}]^{3-}\) and \([\mathrm{Fe}(\mathrm{NCS})_{6}]^{3-}\) have iron in the complex. The oxidation state of iron in both complexes is +3, as can be deduced from their charges and the fact that CN\(^-\) and NCS\(^-\) are both monodentate ligands. So, iron is in the \(\mathrm{Fe}^{3+}\) state. In this state, iron has the electronic configuration \[\text{Fe}^{3+}: 3d^5\].

Step 2: Evaluate Splittings for \([\mathrm{Fe}(\mathrm{CN})_{6}]^{3-}\)

For the \([\mathrm{Fe}(\mathrm{CN})_{6}]^{3-}\) complex, there is one unpaired electron. This implies that CN\(^-\), a strong field ligand, causes a large splitting of the d-orbitals (known as \(\Delta_0\)), which leads to pairing of electrons in the lower energy orbitals (t\(_{2g}\)). This means the complex is low-spin.

Step 3: Evaluate Splittings for \([\mathrm{Fe}(\mathrm{NCS})_{6}]^{3-}\)

For \([\mathrm{Fe}(\mathrm{NCS})_{6}]^{3-}\), having five unpaired electrons suggests no pairing of electrons has occurred; indicating that the crystal field splitting is small. NCS\(^-\), therefore, is a weaker field ligand as it does not cause enough splitting for electrons to pair up, resulting in a high-spin complex.

Step 4: Placement of \(\mathrm{NCS}^{-}\) in Spectrochemical Series

CN\(^-\) is established as a strong field ligand that causes low-spin complexes, so it is high in the spectrochemical series. Since NCS\(^-\) in the \([\mathrm{Fe}(\mathrm{NCS})_{6}]^{3-}\) complex results in a high-spin state, it must be lower in the spectrochemical series compared to CN\(^-\), indicating it is a weaker ligand.

Key Concepts

high spin complexes

The concept of high spin complexes revolves around the arrangement of electrons within an atomic structure. At its core, a high spin complex occurs when the d-orbitals in a transition metal split due to the presence of ligands, creating different levels of energy but only causing weak splitting. In high spin complexes, the energy provided by the crystal field splitting is not sufficient to pair the d-electrons, resulting in a greater number of unpaired electrons.

High spin complexes are often associated with weak field ligands. These ligands are unable to generate a strong enough field to cause significant electron pairing within the metal's d-orbitals. For instance, in the \([\text{Fe}(\text{NCS})_6]^{3-}\) complex, the presence of five unpaired electrons over distinct orbitals indicates a state where the splitting is small. Consequently, this leads to a situation where electrons remain unpaired, bestowing higher magnetic properties to the complex.

Key characteristics of high spin complexes include:

• Numerous unpaired electrons, contributing to magnetic properties
• Weak field ligands causing less crystal field splitting
• Commonly found in ions with a high positive charge and a low ligand field strength

low spin complexes

Low spin complexes are marked by their distinct electron arrangement due to the influence of crystal field theory. In these complexes, the transition metal's d-electrons prefer to pair up in the lower energy t\(_{2g}\) orbits rather than occupying higher energy levels unpaired. This is a direct result of significant crystal field splitting caused by a strong field ligand.

Consider the \([\text{Fe}(\text{CN})_6]^{3-}\) complex, where the presence of a single unpaired electron indicates a low spin configuration. Here, the ligand CN\(^-\), known to be a strong field ligand, causes a significant splitting of the metal's d-orbitals. This allows electrons to preferentially pair up in the lower energy t\(_{2g}\) orbitals before occupying the higher e\(_g\) orbitals.

Characteristics of low spin complexes include:

• Strong field ligands resulting in large \(\Delta_0\), which causes pairing of electrons
• Reduced number of unpaired electrons, minimizing magnetic properties
• Often observed in systems with high ligand field strength and lower oxidation states

spectrochemical series

The spectrochemical series is a fundamental concept in ligand field theory that ranks ligands based on their ability to split the d-orbitals of the central metal atom in a coordination complex. This ability is crucial in determining whether a complex will be high spin or low spin.

In this ranking, stronger field ligands, such as CN\(^-\), cause larger energy differences between the split d-orbitals. For the complex \([\text{Fe}(\text{CN})_6]^{3-}\), this large splitting creates a low spin complex due to electron pairing in the lower-energy orbitals. On the other hand, weaker field ligands, like NCS\(^-\), result in smaller splitting, leading to high spin complexes as seen in \([\text{Fe}(\text{NCS})_6]^{3-}\).

The spectrochemical series is organized as follows, from weaker to stronger ligands:

• I\(^-\)
• Br\(^-\)
• SCN\(^-\)
• Cl\(^-\)
• F\(^-\)
• OH\(^-\)
• H\(_2\)O
• NH\(_3\)
• en (ethylenediamine)
• CN\(^-\)
• CO

Understanding this series can help predict the nature of the electron configuration in complexes, thus determining their magnetic and optical properties.