Problem 117 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following are diamagnetic? (a) \(\left[\mathrm{Ni}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) (b) \(\left[\mathrm{Zn}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}\) (c) \(\left[\mathrm{Ni}(\mathrm{CN})_{4}\right]^{2-}\) (d) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}\)

Step-by-Step Solution

Answer

Complexes (b), (c), and (d) are diamagnetic.

Step 1: Define Diamagnetism

Diamagnetism is a property of materials where they repel a magnetic field. This property is often observed in materials with all electrons paired, resulting in no net magnetic moment. To determine if a complex is diamagnetic, we need to check the electron configuration for unpaired electrons.

Step 2: Analyze (a) \( \left[\mathrm{Ni}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+} \)

Nickel in \( \left[\mathrm{Ni}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+} \) is in the +2 oxidation state, giving it an electron configuration of \([\mathrm{Ar}] 3d^8\). With water being a weak field ligand, Ni remains high spin, resulting in 2 unpaired electrons, making this complex paramagnetic.

Step 3: Analyze (b) \( \left[\mathrm{Zn}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+} \)

Zinc in \( \left[\mathrm{Zn}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+} \) is in the +2 oxidation state, with an electron configuration of \([\mathrm{Ar}] 3d^{10}\). All electrons are paired, indicating this complex is diamagnetic.

Step 4: Analyze (c) \( \left[\mathrm{Ni}( ext{CN})_{4}\right]^{2-} \)

Nickel in \( \left[\mathrm{Ni}( ext{CN})_{4}\right]^{2-} \) is in the +2 oxidation state, giving \([\mathrm{Ar}] 3d^8\). Cyanide is a strong field ligand, causing low spin configuration. This results in paired electrons, making this complex diamagnetic.

Step 5: Analyze (d) \( \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+} \)

Cobalt in \( \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+} \) is in the +3 oxidation state, with an electron configuration of \([\mathrm{Ar}] 3d^6\). Ammonia, a medium field ligand, typically forms a low spin complex for \( \mathrm{Co}^{3+} \). Here, all 6 d-electrons are paired, making the complex diamagnetic.

Key Concepts

Understanding Electron Configuration

Electron configuration is key to understanding diamagnetism and paramagnetism. It describes how electrons are arranged in an atom's orbitals. Electrons fill these orbitals according to specific rules: the Aufbau principle, Hund's rule, and the Pauli exclusion principle.

When electrons occupy orbitals, they fill the lower energy orbitals first. For example, for nickel in the complex \([ Ni(H_{2}O)_{6}]^{2+}\), in the +2 oxidation state, the electron configuration is \([\mathrm{Ar] 3d^{8}}\). This means there are eight electrons in the \(3d\) orbital.

In the case of zinc in \([\mathrm{Zn}(\mathrm{NH}_{3})_{4}]^{2+}\), all \(10\) electrons fill the \(3d\) orbital. When all electrons are paired, the configuration suggests a diamagnetic material. If there are unpaired electrons, the material is likely paramagnetic.

Determining Oxidation States

Oxidation states denote the charge of an atom after accounting for its bonds. It's crucial for understanding the electron configuration in complex ions. The oxidation state can affect whether electrons are paired or unpaired, influencing magnetic properties.

For example, in the nickel complex \([ Ni(CN)_{4}]^{2-}\), nickel is in the +2 oxidation state. This impacts its electron configuration, influencing whether it's paramagnetic or diamagnetic. Calculating oxidation states involves using the known charges of ligands and equating the total charge. For instance, in \([\mathrm{Co}(\mathrm{NH}_{3})_{6}]^{3+}\), the oxidation state of cobalt is +3. This increase results in different electron pairing and impacts the complex's magnetic behavior.

Exploring Paramagnetism

Paramagnetism is found in materials with one or more unpaired electrons, which align with magnetic fields and increase the field inside the material. Unlike diamagnetic materials, which repel magnetic fields due to all electrons being paired.

In the solution to the exercise, the complex \([ Ni(H_{2}O)_{6}]^{2+}\), showed paramagnetic behavior. This is because the electron configuration \([\mathrm{Ar} 3d^{8}]\) had unpaired electrons. Paramagnetic substances are attracted to external magnetic fields due to these unpaired electrons. This is a direct result of how the electrons fill the orbitals based on the established configuration rules.

Introduction to Ligand Field Theory

Ligand field theory helps explain how different ligands impact the electronic structure and magnetic properties of transition metal complexes. Ligands can be weak or strong field, causing high or low spin states respectively. The spin state influences whether electrons are paired or unpaired in the d-shell.

For example, cyanide (CN) in the nickel complex \([ Ni(CN)_{4}]^{2-}\) acts as a strong field ligand. This causes a low spin state, where the electrons pair up, leading to diamagnetic behavior. In contrast, water (H2O) is a weak field ligand, which doesn't cause pairing, leading to a high spin state observed as paramagnetism. The ligand type changes how electrons distribute among the d-orbitals, affecting the complex's magnetic properties.

By recognizing ligand field strength, you can predict if a complex is likely to be diamagnetic or paramagnetic.