Problem 126 - A Complete Resource Book in Chemistry for JEE Main

Question

The atomic number of \(\mathrm{V}, \mathrm{Cr}, \mathrm{Mn}\) and \(\mathrm{Fe}\) are respectively \(23,24,25\) and 26 . which one of these may be expected to have the highest second ionization enthalpy? (a) \(\mathrm{Mn}\) (b) \(\mathrm{Fe}\) (c) \(\mathrm{Cr}\) (d) \(\mathrm{V}\)

Step-by-Step Solution

Answer

Chromium (Cr) has the highest second ionization enthalpy due to its stable half-filled 3d subshell.

Step 1: Understand the Concept of Ionization Enthalpy

Ionization enthalpy is the amount of energy required to remove an electron from an isolated gaseous atom or ion. The second ionization enthalpy refers to the energy needed to remove the second electron after the first has been removed. It is typically higher than the first ionization enthalpy because the electron is being removed from a positively charged ion, which holds the electrons more tightly.

Step 2: Analyze Electron Configurations

The electron configurations for V, Cr, Mn, and Fe are: V: [Ar] 3d\(^3\) 4s\(^2\), Cr: [Ar] 3d\(^5\) 4s\(^1\), Mn: [Ar] 3d\(^5\) 4s\(^2\), Fe: [Ar] 3d\(^6\) 4s\(^2\). Removing one electron generally affects the 4s orbital first, except for chromium.

Step 3: Evaluate the First Ionization

The first ionization will remove one electron from the outer orbital. After the first ionization: V\(^+\) becomes [Ar] 3d\(^3\) 4s\(^1\), Cr\(^+\) becomes [Ar] 3d\(^5\), Mn\(^+\) becomes [Ar] 3d\(^5\) 4s\(^1\), Fe\(^+\) becomes [Ar] 3d\(^6\) 4s\(^1\). Notice that Cr\(^+\) achieves a half-filled 3d subshell, which is particularly stable.

Step 4: Predict Second Ionization Enthalpy

The second ionization enthalpy is highest for atoms that result in stable configurations upon losing a second electron. Cr\(^+\) loses an electron from its stable half-filled 3d subshell if ionized again, meaning it will require a lot of energy to ionize again, compared to others, who achieve less stable states.

Key Concepts

Electron Configuration

The electron configuration of an element is a representation of the distribution of electrons in its atomic orbitals. Understanding electron configuration is essential to predict the chemical behavior of an element, particularly in terms of its ionization processes.
For vanadium (V), chromium (Cr), manganese (Mn), and iron (Fe), their electron configurations are slightly different due to their positions in the periodic table. These elements are transition metals, meaning they have incompletely filled d subshells.

• V: [Ar] 3d\(^{3}\) 4s\(^{2}\)
• Cr: [Ar] 3d\(^{5}\) 4s\(^{1}\)
• Mn: [Ar] 3d\(^{5}\) 4s\(^{2}\)
• Fe: [Ar] 3d\(^{6}\) 4s\(^{2}\)

Transition metals like Cr experience unusual electron configurations. Chromium has a half-filled d subshell, which provides added stability due to electron exchange energy. This stability influences their ionization energies, as electron removal can destabilize a preferred configuration.

Second Ionization Enthalpy

Second ionization enthalpy refers to the energy required to remove an electron from a positively charged ion, after the first electron has already been removed. This process requires more energy than the first ionization because it involves removing an electron from a positively charged species.
When comparing second ionization enthalpies among elements like V, Cr, Mn, and Fe, the key is their resulting electronic configuration after the first ionization.

• V\(^{+}\): [Ar] 3d\(^{3}\) 4s\(^{1}\)
• Cr\(^{+}\): [Ar] 3d\(^{5}\)
• Mn\(^{+}\): [Ar] 3d\(^{5}\) 4s\(^{1}\)
• Fe\(^{+}\): [Ar] 3d\(^{6}\) 4s\(^{1}\)

Among these ions, the Cr\(^{+}\) already has a half-filled d subshell, which is a stable and energetically favorable configuration. Removing an additional electron disrupts this stability, requiring significantly more energy and resulting in a high second ionization enthalpy. Cr, therefore, has the highest second ionization enthalpy among them.

Transition Metals Ionization Energy

Ionization energy refers to the amount of energy needed to remove an electron from an atom or ion. Transition metals often exhibit unique ionization characteristics due to their electron configurations involving partially filled d orbitals.
Transition metals like vanadium, chromium, manganese, and iron have complex electron distributions between their s and d orbitals, influencing ionization processes.

• The 4s orbital is generally the first to lose electrons during ionization.
• In chromium, the half-filled 3d subshell (\[ 3d^{5} \]) offers special stability, leading to an unusually high ionization energy for Cr\(^{+}\).
• Once the first electron is removed, subsequent removals (like the second ionization) require consideration of the new electron configuration and resulting stability.

This uniqueness in energy levels explains transitions metals' diverse chemistry and their high second ionization energy, as seen prominently in chromium, which resists losing electrons beyond the first removal due to its half-filled subshell.