Problem 26 - A Complete Resource Book in Chemistry for JEE Main

Question

Which one of the following ions exhibit highest magnetic moment? (a) \(\mathrm{Cu}^{2+}\) (b) \(\mathrm{Ti}^{3+}\) (c) \(\mathrm{Ni}^{2+}\) (d) \(\mathrm{Mn}^{2+}\)

Step-by-Step Solution

Answer

The ion \(\mathrm{Mn}^{2+}\) exhibits the highest magnetic moment at \(\approx 5.92 \) B.M.

Step 1: Understand Magnetic Moment Formula

The magnetic moment is given by the formula: \( \mu = \sqrt{n(n+2)} \) Bohr Magneton (B.M.), where \( n \) is the number of unpaired electrons.

Step 2: Electron Configuration for Ions

Determine the electron configuration and unpaired electrons for each ion: - \(\mathrm{Cu}^{2+}\): Losing two electrons from the 3d subshell of copper, configuration: \([\mathrm{Ar}] 3d^9\), 1 unpaired electron. - \(\mathrm{Ti}^{3+}\): Losing three electrons, configuration: \([\mathrm{Ar}] 3d^1\), 1 unpaired electron. - \(\mathrm{Ni}^{2+}\): Losing two electrons from the 4s or 3d subshell, configuration: \([\mathrm{Ar}] 3d^8\), 2 unpaired electrons. - \(\mathrm{Mn}^{2+}\): Losing two electrons from the 4s subshell of manganese, configuration: \([\mathrm{Ar}] 3d^5\), 5 unpaired electrons.

Step 3: Calculate Magnetic Moment for Each Ion

Calculate the magnetic moment using \( \mu = \sqrt{n(n+2)} \): - For \(\mathrm{Cu}^{2+}\): \( \mu = \sqrt{1(1+2)} = \sqrt{3} \approx 1.73 \) B.M. - For \(\mathrm{Ti}^{3+}\): \( \mu = \sqrt{1(1+2)} = \sqrt{3} \approx 1.73 \) B.M. - For \(\mathrm{Ni}^{2+}\): \( \mu = \sqrt{2(2+2)} = \sqrt{8} \approx 2.83 \) B.M. - For \(\mathrm{Mn}^{2+}\): \( \mu = \sqrt{5(5+2)} = \sqrt{35} \approx 5.92 \) B.M.

Step 4: Determine Maximum Magnetic Moment

Compare the magnetic moments calculated for each ion: - \(\mathrm{Cu}^{2+}\) and \(\mathrm{Ti}^{3+}\): \(\approx 1.73 \) B.M. - \(\mathrm{Ni}^{2+}\): \(\approx 2.83 \) B.M. - \(\mathrm{Mn}^{2+}\): \(\approx 5.92 \) B.M. The highest magnetic moment is exhibited by \(\mathrm{Mn}^{2+}\) with \(\approx 5.92 \) B.M.

Key Concepts

Unpaired Electrons

Unpaired electrons are electrons that are alone in an orbital. They significantly influence the magnetic properties of ions. When atoms or ions have unpaired electrons, these electrons can produce a magnetic field. This field interacts with external magnetic fields, resulting in magnetism. In chemistry and physics, the more unpaired electrons an atom or ion has, the stronger its magnetic properties. This is because each unpaired electron has a magnetic moment, contributing to the overall magnetic moment of the substance. To identify unpaired electrons:

• Look at the electron configuration, which shows how electrons are distributed in orbitals.
• Find the orbitals with unpaired electrons after accounting for filled pairs.

Knowing the number of unpaired electrons is crucial when calculating the magnetic properties of ions, as shown by the magnetic moment formula. This formula uses the number of unpaired electrons to determine the extent of magnetism in a substance.

Electron Configuration

Electron configuration describes the arrangement of electrons in an atom or ion. This arrangement determines many chemical properties, including magnetism. For transition metal ions, the electron configuration typically involves their d subshells, where many interesting properties arise. Here are some key points about electron configurations:

• The term or symbol of an element, like [Ar], represents the electron configuration of a noble gas. This shows that all electrons are paired up until that configuration.
• The numbers and letters, like 3d or 4s, show where the electrons are placed. The number indicates the energy level and the letter specifies the type of orbital.
• The superscript tells how many electrons occupy that particular subshell.

Understanding the electron configuration helps determine which electrons are lost or gained when forming ions. For example, ions like Cu²⁺ lose electrons from their outer subshells, leading to a specific set of unpaired electrons that determine magnetism.

Magnetism in Ions

Magnetism in ions arises from the presence of unpaired electrons, as magnets are essentially materials that generate a magnetic field. This magnetic property in ions is frequently assessed using the magnetic moment, which depends on the number of unpaired electrons. Magnetic behavior in materials can be categorized as:

• Paramagnetic: Substances with unpaired electrons that align with external magnetic fields.
• Diamagnetic: Substances where all electrons are paired, exhibiting a repulsion to magnetic fields.
• Ferromagnetic: Substances with strong magnetic attractions due to unpaired electrons aligning in a persistent pattern even after the external field is removed.

The strength of magnetism in an ion is measured in Bohr Magnetons (B.M.) via the magnetic moment formula: \( \mu = \sqrt{n(n+2)} \). Here, \( n \) is the number of unpaired electrons. Using this formula, we can see that ions such as Mn²⁺ with more unpaired electrons show higher magnetic moments, indicating stronger magnetism.