Question

The complex with spin-only magnetic moment of \(\sim 4.9\) B.M. is (a) \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3+}\) (b) \(\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}\) (c) \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4}\) (d) \([\mathrm{Fe}(\mathrm{H}, \mathrm{O})]^{2^{+}}\)

Short answer

The complex is \([\mathrm{Fe}(\mathrm{H}_{2}O)]^{2+}\).

Step-by-step solution

Understand the spin-only magnetic moment formula

The spin-only magnetic moment is calculated using the formula \( \mu = \sqrt{n(n+2)} \), where \( n \) is the number of unpaired electrons. We need to find the complex with a magnetic moment around 4.9 B.M.

Calculate for \([\mathrm{Fe}(\mathrm{CN})_{6}]^{3+}\)

Iron in this complex has a +3 oxidation state (\( \text{Fe}^{3+} \), electronic configuration: \([\text{Ar}]\,3d^5\)), and CN- is a strong field ligand that pairs up all electrons. Thus, \( n = 0 \) and \( \mu = 0 \).

Calculate for \([\mathrm{Fe}(\mathrm{H_{2}O})_{6}]^{3+}\)

Iron here is also +3 (\( \text{Fe}^{3+} \)), but \( \text{H}_{2}\text{O} \) is a weak field ligand, resulting in 5 unpaired electrons (d^5 configuration). Thus, \( n = 5 \) and \( \mu \approx \sqrt{35} \approx 5.9 \) B.M.

Calculate for \([\mathrm{Fe}(\mathrm{CN})_{6}]^{4-}\)

Iron in this complex has a +2 oxidation state (\( \text{Fe}^{2+} \), electronic configuration: \([\text{Ar}]\,3d^6\)). CN- pairs up electrons due to being a strong field ligand, leaving no unpaired electrons. Thus, \( n = 0 \) and \( \mu = 0 \).

Calculate for \([\mathrm{Fe}(\mathrm{H}_{2}O)]^{2+}\)

Here, \( \text{Fe}^{2+} \) (also \([\text{Ar}]\,3d^6\)) in a weak field environment provided by \( \text{H}_{2}\text{O} \) results in 4 unpaired electrons. Thus, \( n = 4 \) and \( \mu \approx \sqrt{24} \= 4.9 \) B.M.

Identify the correct complex

The magnetic moment closest to 4.9 B.M. is for \([\text{Fe}(`\text{H}_{2}\text{O})]^{2+}\). So, option (d) is the correct answer.

Key concepts

Spin-Only Magnetic Moment

The spin-only magnetic moment is an essential concept in coordination chemistry, used to predict the magnetic behavior of a coordination complex based on its unpaired electrons. It is calculated with the formula \( \mu = \sqrt{n(n+2)} \), where \( n \) represents the number of unpaired electrons.

This formula accounts only for the spin of the electrons, ignoring any orbital contributions to the magnetic moment, which makes it particularly useful for transition metal complexes.

• A high spin-only magnetic moment implies a high number of unpaired electrons, which leads to stronger magnetic properties.
• Conversely, a low magnetic moment signals fewer unpaired electrons or none at all, indicating weak or no magnetism.

By analyzing the magnetic moment, chemists can infer the electron configuration of the metal ion and assess the strength of the ligands involved.

Unpaired Electrons

Unpaired electrons play a crucial role in determining the magnetic properties of metal complexes. They are electrons that remain singular in an atom's electron configuration without being paired with another electron in an orbital.

The presence of unpaired electrons often leads to paramagnetism, where materials become attracted to magnetic fields. The more unpaired electrons, the stronger the paramagnetic effect.

• If a complex has unpaired electrons, it suggests a high-spin scenario with weak field ligands involved, leading to a greater magnetic moment.
• Conversely, if no unpaired electrons exist, the complex is typically diamagnetic and involves strong field ligands, causing electrons to pair up.

Unpaired electrons are critical in explaining phenomena such as the observed spin-only magnetic moments in coordination compounds.

Oxidation State

Understanding the oxidation state of a metal in a complex is essential for predicting many of its properties, including its magnetic behavior. The oxidation state is the charge left on an atom when all bonds are assumed to be ionic.

For example, in \( [\text{Fe}(\text{CN})_{6}]^{3+} \), iron is in the +3 oxidation state, which affects its electron configuration and subsequently, its magnetic properties.

• Transition metals like iron can have multiple oxidation states, influenced by the atoms or groups (ligands) bonded to them.
• The oxidation state determines how the d-orbitals are filled with electrons and the potential for unpaired electrons.

Calculating the spin-only magnetic moment relies heavily on knowing the metal's oxidation state to deduce the right electron configuration.

Ligands

Ligands are molecules or ions that coordinate to a central metal atom or ion in a coordination complex, greatly influencing its electronic structure and properties. Ligands can be classified based on their field strength into strong field and weak field ligands.

Strong field ligands like CN- can pair up electrons in the d-orbitals, leading to low spin and diamagnetism, while weak field ligands like water allow more unpaired electrons and result in high spin configurations.

• The ability of a ligand to affect the electron pairing is central to understanding changes in the spin-only magnetic moment.
• A ligand's identity influences the metal's electron arrangement and its oxidation state, contributing to whether a complex is high spin or low spin.

In essence, ligands are fundamental elements in altering and defining the behavior of coordination complexes.