Problem 89 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following has the maximum number of unpaired electrons? (a) \(\mathrm{Mg}^{2+}\) (b) \(\mathrm{Ti}^{3+}\) (c) \(\mathrm{V}^{3+}\) (d) \(\mathrm{Fe}^{2+}\)

Step-by-Step Solution

Answer

\(\mathrm{Fe}^{2+}\) has the maximum number of unpaired electrons with 4.

Step 1: Determine the Electron Configuration of the Neutral Atom

Begin by determining the electron configuration of the neutral atoms. Magnesium (Mg) has an atomic number of 12, therefore the electron configuration is \([\text{Ne}]3s^2\). Titanium (Ti) is element 22, so it is \([\text{Ar}]3d^24s^2\). Vanadium (V) is element 23 which results in \([\text{Ar}]3d^34s^2\). Iron (Fe) is element 26, so the electron configuration is \([\text{Ar}]3d^64s^2\).

Step 2: Adjust for Ion Charge

Adjust the electron configuration for each ion's charge by removing electrons, starting with the outermost shell. For \(\mathrm{Mg}^{2+}\), remove 2 electrons from \(3s\), giving \([\text{Ne}]\). For \(\mathrm{Ti}^{3+}\), remove 3 electrons: 2 from \(4s\) and 1 from \(3d\), resulting in \([\text{Ar}]3d^1\). For \(\mathrm{V}^{3+}\), remove 3 electrons: 2 from \(4s\) and 1 from \(3d\), resulting in \([\text{Ar}]3d^2\). For \(\mathrm{Fe}^{2+}\), remove 2 electrons from \(4s\) resulting in \([\text{Ar}]3d^6\).

Step 3: Count Unpaired Electrons

Compare the number of unpaired electrons for each configuration. \(\mathrm{Mg}^{2+}\) has 0 unpaired electrons, as it is isoelectronic with Ne. \(\mathrm{Ti}^{3+}\) has 1 unpaired electron in \(3d^1\). \(\mathrm{V}^{3+}\) has 2 unpaired electrons in \(3d^2\) as they occupy separate orbitals. \(\mathrm{Fe}^{2+}\) has 4 unpaired electrons in \(3d^6\) arranged as \(\uparrow\downarrow \uparrow\downarrow \uparrow\uparrow\uparrow\uparrow\).

Step 4: Identify Maximum Unpaired Electrons

Identify the option with the maximum number of unpaired electrons. Based on the electron configurations, \(\mathrm{Fe}^{2+}\) has the greatest number of unpaired electrons with 4 unpaired \(3d\) electrons.

Key Concepts

Electron Configuration

Electron configuration refers to the arrangement of electrons in an atom's orbitals around the nucleus. It’s crucial for predicting chemical behavior, bonding, and properties of elements. Each element's unique configuration follows the principles of quantum mechanics, specifically the Pauli exclusion principle and Hund’s rule.

Here's how to determine electron configuration for a neutral atom:

• Find the atomic number to get the total number of electrons.
• Use the periodic table to assign electrons to energy levels, starting from lower to higher. For example, Magnesium (Mg) with atomic number 12 has a configuration of \([\text{Ne}]3s^2\).
• Fill electrons in order of increasing energy: 1s, 2s, 2p, 3s, 3p, 4s... and so on.
• Apply Hund's rule to maximize unpaired electrons in orbitals where possible.

Understanding configurations helps predict magnetic properties and reactivity.

Ionic Charge Effects

When atoms form ions, their electron configuration changes, impacting chemical and physical properties. An ion results from gaining or losing electrons to achieve a stable electron configuration, similar to noble gases.

Here’s how ionic charges affect configurations:

• For cations (positively charged), remove electrons starting from the outermost shell. For instance, Fe becomes \([\text{Ar}]3d^6\) when it forms Fe²⁺ via losing two electrons from the \(4s\) level.
• Anions (negatively charged) gain electrons, adding them to the next available orbital.

This process is key to understanding reactivity and the formation of ionic compounds, like salts.
Knowing how ions form and stabilize is foundational for interpreting chemical interactions and enabling predictions in complex reactions.

Transition Metals

Transition metals are elements in the d-block of the periodic table, characterized by their ability to form variable oxidation states and colored compounds. These metals, spanning groups 3 to 12, have incomplete d-subshells allowing a mix of unique properties.

Key characteristics of transition metals include:

• High melting and boiling points.
• Diverse oxidation states due to d-orbital electron flexibility, e.g., Iron (Fe) can exist as Fe²⁺ and Fe³⁺.
• Complex ion formation, resulting in colorful solutions due to d-d electronic transitions.

Importantly, the behavior and chemistry of transition metals rely on their variable electron arrangements, making them central in catalysis and industrial applications.

Periodic Table Trends

The periodic table is structured to highlight trends in element properties, illustrating how atomic structure relates to chemistry.

Key trends include:

• Atomic size: reduces across a period as nuclear charge increases, pulling electrons closer.
• Ionization energy: the energy needed to remove an electron, increases across a period and decreases down a group.
• Electronegativity: tendency of an atom to attract electrons in a bond. It increases across a period and decreases down a group.
• Reactivity: varies greatly. Metals become more reactive down a group, whereas non-metals become less reactive.

Understanding these trends helps predict element behavior and interactions, such as why Fe²⁺ has more unpaired electrons and exhibits specific magnetic properties. Recognizing these patterns is fundamental for mastering chemistry.