Problem 30 - A Complete Resource Book in Chemistry for JEE Main

Question

Which one of the following pairs of ions have the same electronic configuration? (a) \(\mathrm{Sr}^{3+}, \mathrm{Cr}^{3+}\) (b) \(\mathrm{Fe}^{3+}, \mathrm{Mn}^{2+}\) (c) \(\mathrm{Fe}^{3+}, \mathrm{Co}^{3+}\) (d) \(\mathrm{Cr}^{3+}, \mathrm{Fe}^{3+}\)

Step-by-Step Solution

Answer

The ions Fe^{3+} and Mn^{2+} have the same electron configuration.

Step 1: Identify Electron Configurations of Neutral Atoms

First, identify the electron configurations for the neutral atoms. For Mn: 25 electrons, configuration: [Ar] 3d^5 4s^2. For Fe: 26 electrons, configuration: [Ar] 3d^6 4s^2. For Cr: 24 electrons, configuration: [Ar] 3d^5 4s^1. For Sr: 38 electrons, configuration: [Kr] 5s^2. For Co: 27 electrons, configuration: [Ar] 3d^7 4s^2.

Step 2: Determine Electron Configurations of Ions

Subtract the necessary number of electrons to determine each ion's configuration. Sr^{3+}: remove 3 electrons, ending with [Kr] 5s^1. Cr^{3+}: remove 3 electrons, resulting in [Ar] 3d^3. Fe^{3+}: remove 3 electrons, resulting in [Ar] 3d^5. Mn^{2+}: remove 2 electrons, resulting in [Ar] 3d^5. Co^{3+}: remove 3 electrons, resulting in [Ar] 3d^6.

Step 3: Compare Ion Configurations

Compare the electron configurations for each pair of ions. Sr^{3+} and Cr^{3+} are different: [Kr] 5s^1 vs. [Ar] 3d^3. Fe^{3+} and Mn^{2+} are the same: [Ar] 3d^5 for both. Fe^{3+} and Co^{3+} are different: [Ar] 3d^5 vs. [Ar] 3d^6. Cr^{3+} and Fe^{3+} are different: [Ar] 3d^3 vs. [Ar] 3d^5.

Key Concepts

Electron Configuration of Ions

Understanding the electron configuration of ions involves knowing how these atoms lose or gain electrons to form charged particles, called ions. When atoms become ions, they typically lose or gain electrons in such a way that they achieve a more stable electronic configuration. Often, this means having a similar electron distribution as the nearest noble gas.

To determine the electron configuration of an ion, we start with the configuration of the neutral atom and then remove or add the necessary electrons based on the ion's charge.

• For cations: Electrons are removed first from the outermost energy level. For transition metals like Fe, this means starting with the 4s level before the 3d.
• For anions: Electrons are added to fill the next available subshell until the desired charge is achieved.

Let's take an example: If you have Fe forming \(Fe^{3+}\), you remove three electrons, leading to a configuration of \[\text{[Ar]} 3d^5\]. This concept helps in predicting the chemical behavior and properties of elements in their ionic form.

Electron Configuration of Elements

Electron configuration of elements refers to the arrangement of electrons around the nucleus of an atom in its neutral state. Each element has a unique configuration that defines its chemical properties and how it interacts with other elements. The arrangement into various orbitals, designated as s, p, d, and f, follows the Aufbau principle, Hund's Rule, and Pauli-Exclusion Principle.

The general approach for writing an electron configuration is to fill the lowest energy levels first and move upward, following this order:

• s-orbital: can hold a maximum of 2 electrons
• p-orbital: can hold a maximum of 6 electrons
• d-orbital: can hold a maximum of 10 electrons
• f-orbital: can hold a maximum of 14 electrons

For example, the electron configuration of Iron (Fe), which has 26 electrons, is written as \[\text{[Ar]} 3d^6 4s^2\]. This format shows the subshells being filled and gives a clear picture of where the electrons are located. Such configurations are crucial for determining how atoms bond and their reactivity.

Comparing Electron Configurations

Comparing electron configurations is essential in chemistry to understand the similarities and differences in chemical behavior among elements and ions. By doing this, one can predict reactivity patterns, understand bonding mechanisms, and determine why certain elements or ions have specific properties.

When comparing electron configurations of ions, start by writing down their configurations and checking from innermost to outermost electrons. Consider these steps:

• First, compare the main energy levels (principal quantum number) to see if the ions have electrons in the same shells.
• Next, examine the sub-levels (s, p, d, f) filled by the electrons.
• Finally, observe the number and arrangement of electrons in each subshell, particularly focusing on the highest energy level electrons, as these affect ion characteristics most.

For instance, Fe^{3+} with an electron configuration of \[\text{[Ar]} 3d^5\] and Mn^{2+} also having \[\text{[Ar]} 3d^5\] show they are isoelectronic, meaning they have the same electron configuration. This similarity often implies similar chemical properties, such as comparable reactivity. By understanding these configurations, you unlock insights into the elemental behavior and potential compound formation.