Problem 112 - A Complete Resource Book in Chemistry for JEE Main

Question

In which of the following pair, the first species is more stable than second one (a) \(\mathrm{Mn}^{2+}, \mathrm{Mn}^{3+}\) (b) \(\mathrm{S} \mathrm{c}^{2+}, \mathrm{S} \mathrm{c}^{3+}\) (c) \(\mathrm{Ti}^{3+}, \mathrm{Ti}^{4+}\) (d) \(\mathrm{Fe}^{2+}, \mathrm{Fe}^{3+}\)

Step-by-Step Solution

Answer

(a) \(\text{Mn}^{2+}\) is more stable than \(\text{Mn}^{3+}\).

Step 1: Evaluate Electronic Configuration

To assess the stability of the ions, we need to evaluate the electronic configuration of each. We'll begin by listing the configurations: - ( a ): - \( \text{Mn}^{2+} \text{: } [\text{Ar}] \, 3d^5 \) - \( \text{Mn}^{3+} \text{: } [\text{Ar}] \, 3d^4 \)- ( b ): - \( \text{Sc}^{2+} \text{: } [\text{Ar}] \, 3d^1 \) - \( \text{Sc}^{3+} \text{: } [\text{Ar}] \)- ( c ): - \( \text{Ti}^{3+} \text{: } [\text{Ar}] \, 3d^1 \) - \( \text{Ti}^{4+} \text{: } [\text{Ar}] \)- ( d ): - \( \text{Fe}^{2+} \text{: } [\text{Ar}] \, 3d^6 \) - \( \text{Fe}^{3+} \text{: } [\text{Ar}] \, 3d^5 \)

Step 2: Analyze Stability Based on Configuration

Among the electronic configurations, half-filled and fully-filled d-orbitals are particularly stable. This relates to the symmetric distribution and exchange energy.- (a): \( \text{Mn}^{2+} \) (\([\text{Ar}] \, 3d^5\) is half-filled) is more stable than \( \text{Mn}^{3+} \) (\([\text{Ar}] \, 3d^4\)).- (b): \( \text{Sc}^{3+} \) (\([\text{Ar}]\), no d-electrons) is the stable empty configuration compared to \( \text{Sc}^{2+} \).- (c): \( \text{Ti}^{4+} \) (\([\text{Ar}]\), no d-electrons) is stable over \( \text{Ti}^{3+} \).- (d): \( \text{Fe}^{3+} \) (\([\text{Ar}] \, 3d^5\)) is more stable than \( \text{Fe}^{2+} \) (\([\text{Ar}] \, 3d^6\)).Half-filled and fully-filled configurations grant stability.

Step 3: Identify Most Stable First Species

The answer requires identifying where the first species in each pair is more stable. Given the analysis, \(\text{Mn}^{2+}\) is more stable due to its half-filled d^5 configuration over \(\text{Mn}^{3+}\). The other pairs don't have the first species with added stability.

Key Concepts

Electronic Configuration

Electronic configuration refers to the specific arrangement of electrons in an atom or ion across various energy levels, sublevels, and orbitals. This arrangement is crucial because it determines an element's chemical properties and behavior. Electrons fill orbitals according to the Aufbau principle, which states that electrons fill lower-energy orbitals before higher-energy ones. The stability of an ion often hinges on having completely filled or half-filled orbitals, which provide additional energetic stability through symmetrical distribution. For instance, in the exercise question,

• Mn²⁺ with the configuration \(\text{[Ar]} \, 3d^5\) is more stable than Mn³⁺ because it has a half-filled d-subshell.
• Similarly, Sc³⁺ and Ti⁴⁺ have no d-electrons, making them more stable than their counterparts with partially filled d-orbitals.

These configurations reflect the importance of electronic arrangements in determining the stability of ions.

Ion Stability

The stability of ions is closely linked to their electronic configuration and the corresponding energy states they occupy. A particularly stable ion configuration is either fully filled or half-filled. This stability arises from:

• Spherical symmetry: Fully filled valence shells tend to be more symmetric and energetically favorable.
• Exchange energy: In half-filled subshells like \(\text{3d}^5\), electrons have a maximum number of parallel spins, which minimizes repulsions and contributes to stability.

In the exercise, Mn²⁺ and Fe³⁺ exhibit stability due to these factors, having half-filled 3d subshells... Such stability principles are often juxtaposed with less stable configurations that require either more energy or lack symmetrical electron distribution.

d-Orbitals

The d-orbitals are a set of five orbitals ( ext{d extsubscript{x²-y²} ,d extsubscript{z²}, d extsubscript{xy}, d extsubscript{xz}, d extsubscript{yz}}) found in the third shell and higher periods of the periodic table. They can hold up to 10 electrons and play a pivotal role in the chemistry of transition metals.The stability conferred by d-orbitals often depends on whether they are completely filled, partially filled, or empty. Partially filled d-orbitals that are symmetrically arranged (like half-filled in \(3d^5\)) can offer additional stability due to increased exchange energy and a favorable unpacked electronic configuration. For instance, in the given exercise:

• Mn²⁺ (\(3d^5\)) is more stable than Mn³⁺ due to its half-filled stability.
• Fe³⁺ (\(3d^5\)), with its similarly advantageous configuration, is preferred over Fe²⁺ (\(3d^6\)).

Understanding d-orbitals and their filling can provide valuable insights into the chemical reactions and properties of elements, particularly transition metals.