Problem 63 - A Complete Resource Book in Chemistry for JEE Main

Question

Among the following complex ions, the one with the highest paramagnetism is (a) \(\left[\mathrm{FeF}_{6}\right]^{2+}\) (b) \(\left[\mathrm{Cu}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) (c) \(\left[\mathrm{Zn}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) (d) \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}\)

Step-by-Step Solution

Answer

The most paramagnetic ion is \(\left[\mathrm{FeF}_{6}\right]^{2+}\) with 4 unpaired electrons.

Step 1: Identify the Metal Ion

First, determine the central metal ions in each of the complex ions. For (a) it's Fe in \([\mathrm{FeF}_{6}]^{2+}\), for (b) it's Cu in \([\mathrm{Cu}(\mathrm{H}_{2}\mathrm{O})_{6}]^{2+}\), for (c) it's Zn in \([\mathrm{Zn}(\mathrm{H}_{2}\mathrm{O})_{6}]^{2+}\), and for (d) it's Cr in \([\mathrm{Cr}(\mathrm{NH}_{3})_{6}]^{3+}\).

Step 2: Determine Oxidation States

Assign oxidation states to determine the electron configurations. For (a) Fe in \([\mathrm{FeF}_{6}]^{2+}\) is +4, for (b) Cu in \([\mathrm{Cu}(\mathrm{H}_{2}\mathrm{O})_{6}]^{2+}\) is +2, for (c) Zn in \([\mathrm{Zn}(\mathrm{H}_{2}\mathrm{O})_{6}]^{2+}\) is +2, and for (d) Cr in \([\mathrm{Cr}(\mathrm{NH}_{3})_{6}]^{3+}\) is +3.

Step 3: Determine Electron Configuration

Find the electron configuration for each oxidation state: - (a) Fe in +4 state: \([\mathrm{Ar}] 3d^4\)- (b) Cu in +2 state: \([\mathrm{Ar}] 3d^9\)- (c) Zn in +2 state: \([\mathrm{Ar}] 3d^{10}\)- (d) Cr in +3 state: \([\mathrm{Ar}] 3d^3\)

Step 4: Determine Number of Unpaired Electrons

Count the unpaired electrons in each configuration to assess paramagnetism:- (a) Fe\(^{4+}\) in \([\mathrm{Ar}] 3d^4\): 4 unpaired electrons- (b) Cu\(^{2+}\) in \([\mathrm{Ar}] 3d^9\): 1 unpaired electron- (c) Zn\(^{2+}\) in \([\mathrm{Ar}] 3d^{10}\): 0 unpaired electrons- (d) Cr\(^{3+}\) in \([\mathrm{Ar}] 3d^3\): 3 unpaired electrons

Step 5: Identify the Highest Paramagnetism

The paramagnetism of a complex ion is based on the number of unpaired electrons. Here, \([\mathrm{FeF}_{6}]^{2+}\) has 4 unpaired electrons, which is the highest among the given options.

Key Concepts

Electron Configuration

Electron configuration is a fundamental concept in chemistry that describes the arrangement of electrons in an atom or ion. Electrons are arranged in shells and subshells, and the order of filling these is governed by the Aufbau principle, Hund's rule, and the Pauli exclusion principle.

- **Aufbau Principle:** Electrons fill the lowest energy orbitals first. - **Hund's Rule:** Every orbital in a subshell gets filled with one electron before any orbital is doubly filled. - **Pauli Exclusion Principle:** No two electrons in an atom can have the same four quantum numbers.

For complex ions, knowing the electron configuration helps predict their chemical properties, such as reactivity and magnetic properties. The metal ions in the complexes undergo changes in electron configuration depending on their oxidation state.

Oxidation States

Oxidation state is a concept that represents the number of electrons lost or gained by an atom in a compound. It plays a crucial role in understanding the electron configuration of ions and how they interact in chemical reactions.

To determine the oxidation state of a metal in a complex, consider the charges of the ligands and the overall charge of the ion:

• Fe in \([\mathrm{FeF}_{6}]^{2+}\) has an oxidation state of \(+4\).
• Cu in \([\mathrm{Cu}(\mathrm{H}_{2}\mathrm{O})_{6}]^{2+}\) has an oxidation state of \(+2\).
• Zn in \([\mathrm{Zn}(\mathrm{H}_{2}\mathrm{O})_{6}]^{2+}\) has an oxidation state of \(+2\).
• Cr in \([\mathrm{Cr}(\mathrm{NH}_{3})_{6}]^{3+}\) has an oxidation state of \(+3\).

Understanding the oxidation state is essential for writing the correct electron configuration of the metal ion in a complex.

Unpaired Electrons

Unpaired electrons are the electrons in an atom or ion that remain alone in their orbitals. These unpaired electrons are crucial in determining the magnetic properties of a substance. A paramagnetic material has one or more unpaired electrons and is attracted to a magnetic field.

To figure out the number of unpaired electrons, examine the electron configuration:

• Fe\(^{4+}\) in \([\mathrm{Ar}] 3d^4\): 4 unpaired electrons.
• Cu\(^{2+}\) in \([\mathrm{Ar}] 3d^9\): 1 unpaired electron.
• Zn\(^{2+}\) in \([\mathrm{Ar}] 3d^{10}\): 0 unpaired electrons.
• Cr\(^{3+}\) in \([\mathrm{Ar}] 3d^3\): 3 unpaired electrons.

More unpaired electrons generally increase the paramagnetism of the ion, which is why Fe\(^{4+}\) is the most paramagnetic in this example.

Complex Ions

Complex ions consist of a central metal ion surrounded by molecules or ions known as ligands. The formation of these complexes is an essential aspect of coordination chemistry. The nature of the ion-ligand interaction—often involving coordinate covalent bonds—affects the properties of the complex, including its magnetic, optical, and chemical behavior.

- **Ligands:** They can be neutral molecules like water (HO) or charged species such as fluoride ions (F⁻).- **Coordination Number:** This is the number of ligand atoms that are directly bonded to the central metal ion, ranging typically from 2 to 9.- **Chelation:** Some ligands can bind at multiple points, forming stable chelate complexes.

In complex ions like \([\mathrm{FeF}_{6}]^{2+}\), the choice and number of ligands, as well as the oxidation state of the metal, significantly influence the structure and hence the magnetic properties, making some ions more paramagnetic than others.