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 correct answer is (c) \(\mathrm{Fe}^{3+}\) and \(\mathrm{Mn}^{2+}\).

Step 1: Identify the Electronic Configuration of the Ions

Firstly, determine the electronic configuration of each ion in their ground states. This helps in understanding the number of electrons and how they are configured in the d-orbitals.- Ni (28): 3d\(^{8}\) 4s\(^{2}\); Ni\(^{2+}\): 3d\(^{8}\)- Co (27): 3d\(^{7}\) 4s\(^{2}\); Co\(^{2+}\): 3d\(^{7}\)- Cr (24): 3d\(^{5}\) 4s\(^{1}\); Cr\(^{3+}\): 3d\(^{3}\)- Fe (26): 3d\(^{6}\) 4s\(^{2}\); Fe\(^{2+}\): 3d\(^{6}\), Fe\(^{3+}\): 3d\(^{5}\)- Mn (25): 3d\(^{5}\) 4s\(^{2}\); Mn\(^{2+}\): 3d\(^{5}\)- Ti (22): 3d\(^{2}\) 4s\(^{2}\); Ti\(^{4+}\): 3d\(^{0}\)

Step 2: Count the Number of Unpaired Electrons

From the electronic configurations, count the number of unpaired electrons in the d-orbitals, as this contributes to the magnetic moment.- Ni\(^{2+}\): 2 unpaired electrons- Co\(^{2+}\): 3 unpaired electrons- Cr\(^{3+}\): 3 unpaired electrons- Fe\(^{2+}\): 4 unpaired electrons- Fe\(^{3+}\): 5 unpaired electrons- Mn\(^{2+}\): 5 unpaired electrons- Ti\(^{4+}\): 0 unpaired electrons

Step 3: Determine the Magnetic Moment

Use the formula for magnetic moment: \[\mu = \sqrt{n(n+2)} \text{ BM}\]where \(n\) is the number of unpaired electrons. Calculate for ions with the most unpaired electrons:- Fe\(^{3+}\): \( n = 5 \), \( \mu = \sqrt{5(5+2)} = \sqrt{35} \approx 5.92 \text{ BM} \)- Mn\(^{2+}\): \( n = 5 \), \( \mu = \sqrt{5(5+2)} = \sqrt{35} \approx 5.92 \text{ BM} \)Both have a magnetic moment of approximately 5.92 BM, which is high.

Step 4: Select the Correct Option

Given the calculations, the ions with the largest number of unpaired electrons and the highest magnetic moment are Fe\(^{3+}\) and Mn\(^{2+}\). Therefore, the correct answer is the pair with these ions.

Key Concepts

Electronic Configuration

Understanding electronic configuration is key to grasping the behavior of transition metals like iron and manganese. Each element has its own unique configuration, which represents the arrangement of electrons around the nucleus. For transition metals, this usually involves their infamous d-orbitals, known for holding the outermost electrons that contribute significantly to chemical properties.
For example, iron, with the atomic number 26, has a ground state electron configuration of 3d\(^{6}\) 4s\(^{2}\). When it forms the Fe\(^{3+}\) ion, it loses a total of three electrons, typically from the 4s and one from the 3d orbital, leaving us with the electron configuration of 3d\(^{5}\).
Similarly, manganese, which has an atomic number of 25, usually has the configuration 3d\(^{5}\) 4s\(^{2}\). When forming Mn\(^{2+}\), it loses two electrons, both likely from the 4s orbital, resulting in a 3d\(^{5}\) configuration. By examining these configurations, we can predict properties like magnetism and binding tendencies.

Unpaired Electrons

Unpaired electrons are the unsung heroes in determining the magnetic properties of transition metals. In electronic terms, they are simply electrons in orbitals that do not have a partner with opposite spin.
The importance of unpaired electrons cannot be overstated. They give rise to magnetism in materials. For example, in the Fe\(^{3+}\) ion, with a 3d\(^{5}\) configuration, there are five unpaired electrons. This leaves us with ample magnetic interactions.
Similarly, Mn\(^{2+}\), with the configuration of 3d\(^{5}\), also presents five unpaired electrons. Both ions become especially magnetic due to these unpaired electrons, resulting in higher magnetic moment readings. You can remember that the more unpaired electrons an ion has, the stronger its magnetic capabilities.

Magnetic Moment

Magnetic moment is a measure of the magnetic strength and orientation of a magnetic source. For transition metal ions, this is mostly due to unpaired electrons.

• The magnetic moment in transition metal ions can be calculated using the formula: \[\mu = \sqrt{n(n+2)} \text{ BM}\]where \(n\) is the number of unpaired electrons. BM stands for Bohr Magneton, a unit that expresses the magnetic moment.
• For Fe\(^{3+}\), with five unpaired electrons, the magnetic moment calculates to approximately 5.92 BM.
• This is the same for Mn\(^{2+}\), which also has five unpaired electrons and thus a similar magnetic moment.

Thus, knowing the number of unpaired electrons aids in determining not just the theoretical properties but also practical observations in experiments.