Problem 14 - A Complete Resource Book in Chemistry for JEE Main

Question

Among the following series of transition metal ions, the one where all metal ions have \(3 \mathrm{~d}^{2}\) electronic configuration is (a) \(\mathrm{Ti}^{+}, \mathrm{V}^{4+}, \mathrm{Cr}^{6+}, \mathrm{Mn}^{7+}\) (b) \(\mathrm{Ti}^{2+}, \mathrm{V}^{3+}, \mathrm{Cr}^{4+}, \mathrm{Mn}^{5+}\) (c) \(\mathrm{Ti}^{3+}, \mathrm{V}^{2+}, \mathrm{Cr}^{3+}, \mathrm{Mn}^{4+}\) (d) \(\mathrm{Ti}^{4+}, \mathrm{V}^{3+}, \mathrm{Cr}^{2+}, \mathrm{Mn}^{3+}\)

Step-by-Step Solution

Answer

Option (b) has all ions with \(3d^2\).

Step 1: Determine the Electronic Configuration of Ti

Titanium (Ti) has an atomic number of 22. In the neutral state, its electronic configuration is \([ ext{Ar} ] ext{3d}^2 ext{4s}^2\). For the ion \(\text{Ti}^{3+}\), we remove three electrons. The electrons are removed first from \(4s\) and then from \(3d\), resulting in the configuration \([ ext{Ar} ] ext{3d}^1\).

Step 2: Evaluate the Configuration of V

Vanadium (V) has an atomic number of 23. Its electronic configuration in the neutral state is \([ ext{Ar} ] ext{3d}^3 ext{4s}^2\). For \(\text{V}^{2+}\), removing two electrons results in \([ ext{Ar} ] ext{3d}^3\).

Step 3: Analyze the Configuration of Cr

Chromium (Cr) has an atomic number of 24, with a usual electron configuration in the neutral state as \([ ext{Ar} ] ext{3d}^5 ext{4s}^1\). For \(\text{Cr}^{3+}\), we remove three electrons to get \([ ext{Ar} ] ext{3d}^3\).

Step 4: Check the Configuration of Mn

Manganese (Mn) has an atomic number of 25, and in its neutral state, its configuration is \([ ext{Ar} ] ext{3d}^5 ext{4s}^2\). For the ion \(\text{Mn}^{4+}\), we remove four electrons, giving \([ ext{Ar} ] ext{3d}^3\).

Step 5: Conclusion: Select the Correct Option

The transition metal ions \(\text{V}^{2+}\), \(\text{Cr}^{3+}\), and \(\text{Mn}^{4+}\) from the option (c) all yield a \(\text{3d}^3\) configuration. Ti \(\text{3+}\) results in \(\text{3d}^1\) though, hence option (c) is incorrect. An error in step is possible; reexamine.

Step 6: Reevaluation: Correct Analysis of Configuration, Step 5

Reassess, focus on ensuring the three ions \(\text{V}^{4+}\), \(\text{Cr}^{6+}\), \(\text{Mn}^{7+}\) yield \(\text{3d}^2\). In option (a), each true removal equals \(\text{3d}^2\), confirming its correctness. Each is properly evaluated for the removal.

Key Concepts

Electronic Configuration

Electronic configuration is an arrangement that demonstrates how electrons are distributed in an atom or ion. In transition metals, this distribution can reveal a lot about the metal's chemical behavior and properties. Transition metals, found in the central block of the periodic table, have their outer electrons in the d subshell. The concept of electronic configuration allows us to predict the behavior of transition metal ions.

• The electrons are filled into orbitals following several rules - primarily the Aufbau principle, Pauli exclusion principle, and Hund's rule.
• The Aufbau principle indicates that electrons fill orbitals starting with the lowest energy first.
• In transition metals, after filling the 3d orbitals, the 4s orbital is filled next. This means that in their most stable state, electrons in transition metals occupy the 4s orbital before occupying the 3d orbital.

This concept is crucial when these elements form ions because ions result from the gain or loss of electrons, typically influencing their reactivity and the types of compounds they can form.

Transition Metals

Transition metals are elements that have partially filled d subshells. They are known for their complex behavior often due to their variable oxidation states and ability to form complex ions. These metals include elements like Iron (Fe), Gold (Au), Nickel (Ni), and a plethora of others spanning across groups 3 to 12 in the periodic table.

• One key characteristic of transition metals is their ability to form various oxidation states. This means they can lose different numbers of electrons and form positively charged ions called cations. For example, Iron can exist as Fe²⁺ or Fe³⁺ ions.
• Transition metals often serve vital roles in biological systems — for instance, Iron is crucial for oxygen transport in the bloodstream via hemoglobin.
• They exhibit unique properties such as catalytic abilities and colored compounds. These properties are directly linked to their electronic configurations.

In the series of transition metal ions evaluated, understanding the electronic configuration helps determine the oxidation states and predict properties such as color and magnetism. They play a significant role in industrial applications like catalysis and the manufacturing of materials.

Ionization

Ionization refers to the process by which an atom or molecule gains a positive or negative charge by gaining or losing electrons to form ions. In transition metals, the ionization process typically involves the removal of electrons from the outermost 4s subshell first, followed by the 3d subshell.

• When a transition metal ionizes, it loses electrons starting with the s orbital before the d orbitals, as the 4s electrons, despite being filled earlier, are higher in energy when compared to 3d electrons.
• The loss of electrons typically happens progressively, forming a sequence of ions with different charges; this also plays a role in the ability to form complex ions in coordination chemistry.
• The ionization energy required to remove an electron is influenced by the nuclear charge, electron shielding, and the distance of the electron from the nucleus. Transition metals usually have higher ionization energies compared to alkaline metals because their electrons are more tightly bound to the nucleus.

In the exercise, analyzing the series of transition metal ions involves evaluating ionization to predict the resultant electronic configurations accurately. Ensuring correct ionization states is key to deducing the corresponding electronic structures for transition metals, which ultimately aids in resolving exercises involving such elements.