Question

Match list I with list II and select the correct answer using the codes given below the lists: List I List II (Metal ions) \(\quad\) (Magnetic moment) 1\. \(\mathrm{Cr}^{3+}\) (i) \(\sqrt{35}\) 2\. \(\mathrm{Fe}^{2+}\) (ii) \(\sqrt{30}\) 3\. \(\mathrm{Ni}^{2+}\) (iii) \(\sqrt{24}\) 4\. \(\mathrm{Mn}^{2+}\) (iv) \(\sqrt{15}\) (v) \(\sqrt{8}\) The correct matching is: \(\begin{array}{llllll}1 & 2 & 3 & 4\end{array}\) (a) (i) (iii) (v) (iv) (b) (ii) (iii) (v) (i) (c) (iv) (iii) (v) (i) (d) (iv) (v) (iii) (i)

Short answer

The correct answer is (d): 1-(iv), 2-(iii), 3-(v), 4-(i).

Step-by-step solution

Determine the Electron Configuration

To match metal ions with their respective magnetic moments, start by identifying the electron configurations. For Cr\(^{3+}\), remove 3 electrons from Cr (24 electrons originally) to get [Ar] 3d\(^3\). For Fe\(^{2+}\), remove 2 electrons from Fe (26 electrons) to have [Ar] 3d\(^6\). For Ni\(^{2+}\), remove 2 electrons from Ni (28 electrons) resulting in [Ar] 3d\(^8\). For Mn\(^{2+}\), remove 2 electrons from Mn (25 electrons) to get [Ar] 3d\(^5\).

Calculate Number of Unpaired Electrons

Count the unpaired electrons in each ion. Cr\(^{3+}\) with 3d\(^3\) has 3 unpaired electrons, Fe\(^{2+}\) with 3d\(^6\) has 4 unpaired electrons, Ni\(^{2+}\) with 3d\(^8\) has 2 unpaired electrons, and Mn\(^{2+}\) with 3d\(^5\) has 5 unpaired electrons.

Calculate Magnetic Moments

Magnetic moment \(\mu\) is given by \(\mu = \sqrt{n(n+2)}\), where \(n\) is the number of unpaired electrons. For Cr\(^{3+}\), \(\mu = \sqrt{3(3+2)} = \sqrt{15}\). For Fe\(^{2+}\), \(\mu = \sqrt{4(4+2)} = \sqrt{24}\). For Ni\(^{2+}\), \(\mu = \sqrt{2(2+2)} = \sqrt{8}\). For Mn\(^{2+}\), \(\mu = \sqrt{5(5+2)} = \sqrt{35}\).

Match with List II

The calculations give the following matches: Cr\(^{3+}\) with \(\sqrt{15}\), Fe\(^{2+}\) with \(\sqrt{24}\), Ni\(^{2+}\) with \(\sqrt{8}\), and Mn\(^{2+}\) with \(\sqrt{35}\). Corresponding to the options: Cr\(^{3+}\) - (iv), Fe\(^{2+}\) - (iii), Ni\(^{2+}\) - (v), Mn\(^{2+}\) - (i).

Identify the Correct Option

Now, check which option in the question matches the order 1: (iv), 2: (iii), 3: (v), 4: (i). The correct answer matches option (d): (iv), (v), (iii), (i).

Key concepts

Electron Configuration

Electron configuration is the arrangement of electrons within an atom or ion. This configuration follows a specific sequence based on increasing energy levels, starting from the lowest possible level. For ions, the configuration is adjusted by adding or removing electrons to reflect their charge.
When determining the electron configuration of transition metal ions, it is crucial to understand that electrons are typically removed from the outermost s-orbital before the d-orbital.
This can sometimes lead to surprising configurations for different ions:

• For ext{Cr}^{3+}, you start with chromium's atomic number, 24, leading to the ground state configuration [Ar] 4s^1 3d^5. To form Cr^{3+}, three electrons are removed, resulting in [Ar] 3d^3.
• Similarly, for ext{Fe}^{2+}, the atomic number is 26, so the initial configuration is [Ar] 4s^2 3d^6, which becomes [Ar] 3d^6 when two electrons are removed.
• Nickel, with an atomic number of 28, originally has the configuration [Ar] 4s^2 3d^8. For ext{Ni}^{2+}, subtract two electrons to get [Ar] 3d^8.
• Manganese, starting with 25 electrons, is [Ar] 4s^2 3d^5, and ext{Mn}^{2+} is [Ar] 3d^5, after removing two electrons.

Understanding these configurations is foundational for predicting magnetic properties.

Unpaired Electrons

Unpaired electrons are the electrons that are alone in an atomic or molecular orbital and do not have an electron partner. These electrons play a critical role in determining the magnetic properties of an ion or atom. In transition metal ions, the number of unpaired electrons can be found by examining their electron configuration.
Let's see how this applies to our ions:

• ext{Cr}^{3+} has an electron configuration of [Ar] 3d^3, which means it has 3 unpaired electrons.
• ext{Fe}^{2+} has the configuration [Ar] 3d^6, resulting in 4 unpaired electrons.
• ext{Ni}^{2+} is configured as [Ar] 3d^8, and has 2 unpaired electrons.
• ext{Mn}^{2+} has an electron configuration of [Ar] 3d^5, leaving it with 5 unpaired electrons.

The number of these unpaired electrons is used to determine the magnetic moment of the ion, with more unpaired electrons typically leading to a stronger magnetic moment.

Metal Ions

Metal ions are atoms that have lost or gained electrons, resulting in a positive or negative charge, respectively. Transition metals often form positive ions by losing electrons from their outermost orbitals. This loss of electrons often leads to the formation of specific configurations that dictate their chemical behavior and properties.
Metal ions in the transition series are interesting due to their incomplete d-orbitals, which significantly influence their magnetic behavior and coloration in solutions. The charge on these ions, such as ext{Cr}^{3+}, ext{Fe}^{2+}, ext{Ni}^{2+}, and ext{Mn}^{2+}, dictates their respective electron configurations, giving each a unique set of characteristics.
The specific electron loss peculiar to each ion, due to energy level considerations, affects their reactivity and types of complexes they form. They often show a variety of oxidation states as a result of losing different numbers of electrons.

Transition Metals

Transition metals are a group of elements situated in the d-block of the periodic table. They are characterized by their ability to form double and triple bonds, exhibit a wide range of oxidation states, and undergo reactions that involve the d-orbitals where the d electrons are pertinent.
This broad range of properties makes them essential in various industrial applications, from catalysis to the production of alloys. A significant characteristic of transition metals is their response to external magnetic fields, which is closely linked to their electron configurations.
Many transition metals, including the ones in this exercise, possess unpaired d-electrons, rendering them paramagnetic. This means they can be magnetically attracted but do not retain permanent magnetism.
In our context:

• ext{Cr}^{3+}, ext{Fe}^{2+}, ext{Ni}^{2+}, and ext{Mn}^{2+} are all classified under transition metals, showing varied magnetic responses based on their specific electron arrangements.

These properties highlight their versatile nature and importance in both natural and synthetic processes.