Problem 46 - A Complete Resource Book in Chemistry for JEE Main

Question

Two stable ions of first transition series which have the largest number of unpaired electrons and have the highest magnetic moment are (a) \(\mathrm{Ni}^{2+}\) and \(\mathrm{Co}^{2+}\) (b) \(\mathrm{Cr}^{3+}\) and \(\mathrm{Fe}^{2+}\) (c) \(\mathrm{Fe}^{3+}\) and \(\mathrm{Mn}^{2+}\) (d) \(\mathrm{Ti}^{4+}\) and \(\mathrm{Cr}^{3+}\)

Step-by-Step Solution

Answer

The ions with the largest number of unpaired electrons and highest magnetic moment are (c) \(\mathrm{Fe}^{3+}\) and \(\mathrm{Mn}^{2+}\).

Step 1: Understand Electron Configuration

Consider the electron configuration of transition metal ions. We need to determine the number of unpaired electrons and the magnetic moment associated with them. Remember that for magnetic moment calculations, more unpaired electrons lead to a higher moment.

Step 2: Identify Electron Configuration for Each Ion

Write down the electron configurations for each ion. For example, \(\mathrm{Ni}^{2+}\) has an electron configuration of \(\mathrm{[Ar] 3d^8}\), \(\mathrm{Co}^{2+}\) is \(\mathrm{[Ar] 3d^7}\), \(\mathrm{Cr}^{3+}\) is \(\mathrm{[Ar] 3d^3}\), \(\mathrm{Fe}^{2+}\) is \(\mathrm{[Ar] 3d^6}\), \(\mathrm{Fe}^{3+}\) is \(\mathrm{[Ar] 3d^5}\), \(\mathrm{Mn}^{2+}\) is \(\mathrm{[Ar] 3d^5}\), \(\mathrm{Ti}^{4+}\) is \(\mathrm{[Ar] 3d^0}\).

Step 3: Count Unpaired Electrons

Identify the number of unpaired electrons in each ion. \(\mathrm{Ni}^{2+}\) has 2 unpaired, \(\mathrm{Co}^{2+}\) has 3 unpaired, \(\mathrm{Cr}^{3+}\) has 3 unpaired, \(\mathrm{Fe}^{2+}\) has 4 unpaired, \(\mathrm{Fe}^{3+}\) has 5 unpaired, \(\mathrm{Mn}^{2+}\) has 5 unpaired (similar to Fe^{3+}), and \(\mathrm{Ti}^{4+}\) has 0 unpaired.

Step 4: Evaluate Magnetic Moments Using Number of Unpaired Electrons

Magnetic moment \(\mu\) is calculated using the formula \[\mu = \sqrt{n(n+2)}\] where \(n\) is the number of unpaired electrons. Higher the \(n\), higher is the \(\mu\). Thus, \(\mathrm{Mn}^{2+}\) and \(\mathrm{Fe}^{3+}\) both with 5 unpaired electrons have the highest magnetic moments.

Key Concepts

Electron Configuration

Electron configuration is a fundamental concept in chemistry that explains how electrons are arranged around an atom's nucleus. It provides insight into the chemical behavior and properties of an element. Transition metals, which are located in the d-block of the periodic table, have unique electron configurations due to their partially filled d-orbitals.

The general electron configuration for elements is denoted as \(1s^2, 2s^2, 2p^6, \ldots\) indicating the energy levels and orbitals the electrons occupy. For transition metal ions, however, we often see changes in electron configurations due to the loss of electrons typically from the s and then the d orbital. For example, neutral nickel (Ni) has an electron arrangement of \[\text{[Ar]} 4s^2 3d^8\], but in its \(\text{Ni}^{2+}\) ion form, the electrons are configured as \[\text{[Ar]} 3d^8\], having lost two electrons from the 4s orbital.

• Transition metals often lose electrons from their outer s orbitals first before the d orbitals.
• The number of electrons in the d-orbitals greatly influences their magnetic and chemical properties.

Unpaired Electrons

Unpaired electrons are those that do not have another electron in their orbital to pair with. In the context of transition metals, these electrons play a crucial role in determining the magnetic properties of the ions.

If an ion has unpaired electrons, it exhibits paramagnetism, a type of magnetism where substances are attracted by an external magnetic field. The substance's extent of attraction depends on the number of unpaired electrons present. For example, in transition metal ions:

• \(\text{Fe}^{3+}\) has an electron configuration of \(\text{[Ar]} 3d^5\) with 5 unpaired electrons.
• \(\text{Mn}^{2+}\) also has a \[\text{[Ar]} 3d^5\] configuration, again with 5 unpaired electrons.

Both ions exhibit paramagnetic properties due to their high number of unpaired electrons. The greater the number of unpaired electrons, the stronger the magnetic properties of the ion.

Magnetic Moment

The magnetic moment of an ion is a quantitative measure of its magnetism. It can be calculated using the formula for magnetic moment: \[ \mu = \sqrt{n(n+2)} \] where \( n \) represents the number of unpaired electrons.

The role of unpaired electrons is crucial, as their movement within their respective orbitals generates a magnetic field. More unpaired electrons typically result in a higher magnetic moment.

• As \(\text{Mn}^{2+}\) has 5 unpaired electrons, the magnetic moment calculation would be \(\mu = \sqrt{5(5+2)}= \sqrt{35}\), which is a significant magnetic moment.
• Similarly, \(\text{Fe}^{3+}\) also results in the same magnetic moment because both ions share the same number of unpaired electrons.

When comparing different ions, those with the highest number of unpaired electrons exhibit the highest magnetic moments, making \(\text{Mn}^{2+}\) and \(\text{Fe}^{3+}\) excelling in magnetic properties among transition metal ions.