Question

In both \(\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) and \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}\) ions, the iron is present as \(\mathrm{Fe}(\mathrm{II}) ;\) however, \(\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) is paramagnetic, whereas \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}\) is diamagnetic. Explain this difference.

Short answer

The difference in magnetic behavior of the two complexes is due to the nature of the ligands attached to the metal center. In \(\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\), water is a weak field ligand, leading to unpaired electrons and therefore a paramagnetic complex. In contrast, in \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}\), the cyanide is a strong field ligand that causes pairing of electrons, resulting in a diamagnetic complex.

Step-by-step solution

- Understanding Complex Ions and Ligands

The first step is understanding the nature of the two complex ions. A complex ion has a metal center surrounded by ligands. Here, \(\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) has water (\(\mathrm{H}_{2} \mathrm{O}\)) as ligands, while \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}\) has cyanide (\(\mathrm{CN}^{-}\)) as ligands. Despite both having the same metal center (\(\mathrm{Fe}^{2+}\)), the ligand difference suggests they may interact with the iron differently, affecting its electron configuration and thus its magnetic properties.

- Understanding Magnetism in Coordination Complexes

Paramagnetism arises from the presence of unpaired electrons, while diamagnetism is a property of substances with no unpaired electrons. In other words, if a metal ion in a complex ion has any unpaired electrons, it will be paramagnetic; if all electrons are paired, it will be diamagnetic. The difference in ligands and their electron-pairing behavior will determine the type of magnetism.

- Analyzing the Electron Configurations

In the octahedral field as seen in both complexes, the energy levels split into two sets - the lower energy level called t2g and the higher energy level called eg. Now let's look at each complex individually.

- Understanding the \(\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) Complex

For the \(\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) complex, the \(\mathrm{Fe}^{2+}\) ion has the electron configuration 3d6, because the ligand is a weak field ligand, it doesn't cause pairing of the electrons. Therefore, four of the six electrons fill the t2g level and the remaining two electrons partially fill the eg level. The presence of these unpaired electrons results in the complex being paramagnetic.

- Understanding the \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}\) Complex

In the \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}\) complex, the \(\mathrm{Fe}^{2+}\) ion also has the electron configuration 3d6, but since cyanide (\(\mathrm{CN}^{-}\)) is a strong field ligand, it forces the electrons to pair up. In this case, all six electrons fill the lower energy t2g level and the higher energy eg level remains vacant, indicating no unpaired electrons. This makes the complex ion diamagnetic.

Key concepts

Magnetism in Complexes

Magnetism in complexes is a fascinating subject in coordination chemistry. It depends largely on the presence or absence of unpaired electrons in a metal ion. When electrons are not paired, they tend to align with an applied magnetic field, making the complex paramagnetic. This is typical when the complex contains ligands that are weak field and don't cause electron pairing. On the other hand, if all the electrons are paired due to strong interactions with ligands, the complex becomes diamagnetic, as it resists any external magnetic field.

For example, in \([\mathrm{Fe}(\mathrm{H}_2\mathrm{O})_6]^{2+}\), the water molecules act as weak field ligands. This results in unpaired electrons because the ligand doesn't provide enough energy to pair the electrons in iron(II). Therefore, the complex shows paramagnetism. Conversely, in \([\mathrm{Fe}(\mathrm{CN})_6]^{4-}\), cyanide is a strong field ligand that causes electron pairing, leaving no unpaired electrons, which makes it diamagnetic.

Understanding magnetic behavior in such complexes is vital because it affects their reactivity and properties. It is an example of how different ligands can change the overall characteristics of metal ions in coordination chemistry.

Electron Configuration

Understanding electron configuration is crucial when studying coordination complexes. It can explain how electrons are distributed in an atom or molecule, especially around a metal center. In the case of iron (Fe), which is often involved in coordination chemistry, knowing its electron configuration helps predict its magnetic properties.

The configurations of iron within complexes like \([\mathrm{Fe}(\mathrm{H}_2\mathrm{O})_6]^{2+}\) and \([\mathrm{Fe}(\mathrm{CN})_6]^{4-}\) are key. Iron(II) in both cases has the 3d6 electron configuration. However, how these electrons are arranged in the presence of different ligands influences the magnetic characteristics. With weak field ligands like water, the electrons remain unpaired, as seen in \([\mathrm{Fe}(\mathrm{H}_2\mathrm{O})_6]^{2+}\).

Contrastingly, a strong field ligand like cyanide induces pairing by splitting the d-orbital energy levels more significantly. Thus in \([\mathrm{Fe}(\mathrm{CN})_6]^{4-}\), all electrons are paired, providing a clear example of how electron configuration influences whether the complexes are paramagnetic or diamagnetic.

Ligand Field Theory

Ligand Field Theory (LFT) is essential for understanding coordination complexes' behavior, especially in terms of magnetic properties. It explains how ligands affect the distribution of d-electrons in transition metal complexes. By applying LFT, we analyze how the barriers to electron pairing vary with different ligands.

For instance, in an octahedral complex, ligands surrounding the metal ion cause d-orbitals to split into two different energy levels: lower energy \(t_{2g}\) and higher energy \(e_g\) levels. The nature of the ligands determines how much these levels split, affecting whether electrons pair or remain unpaired.

With weak field ligands like water in \([\mathrm{Fe}(\mathrm{H}_2\mathrm{O})_6]^{2+}\), the energy splitting is lesser. Consequently, electrons don't feel enough force to pair up, leading to a paramagnetic complex. On the other hand, strong field ligands such as cyanide used in \([\mathrm{Fe}(\mathrm{CN})_6]^{4-}\) cause significant splitting, making electrons pair in the lower energy level \(t_{2g}\). Hence, no unpaired electrons are present, indicating a diamagnetic complex.

Incorporating LFT in coordination chemistry allows us to predict and explain the electronic and magnetic properties of transition metal complexes.