Problem 144 - A Complete Resource Book in Chemistry for JEE Main

Question

The atomic numbers 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) \(\mathrm{V}\) (b) \(\mathrm{Cr}\) (c) \(\mathrm{Mn}\) (d) \(\mathrm{FE}\)

Step-by-Step Solution

Answer

(d) Fe has the highest second ionization enthalpy.

Step 1: Understand Ionization Enthalpy

Ionization enthalpy is the energy required to remove an electron from an atom. The second ionization enthalpy refers to the energy required to remove the second electron from a positively charged ion.

Step 2: Evaluate Electron Configurations

List the electron configurations of the given elements: - \(\mathrm{V} (23)\): [Ar] 3d\(^{3}\) 4s\(^{2}\)- \(\mathrm{Cr} (24)\): [Ar] 3d\(^{5}\) 4s\(^{1}\)- \(\mathrm{Mn} (25)\): [Ar] 3d\(^{5}\) 4s\(^{2}\)- \(\mathrm{Fe} (26)\): [Ar] 3d\(^{6}\) 4s\(^{2}\)

Step 3: Analyze Second Ionization Enthalpy Trends

The second ionization enthalpy is higher for elements which achieve a half-filled or fully filled d-subshell upon removal of the second electron. A stable electron configuration makes the ion more stable, requiring more energy to remove an additional electron.

Step 4: Removal of Second Electron

When removing the second electron:- \(\mathrm{V}^+\) goes from 3d\(^{3}\) to 3d\(^{2}\)- \(\mathrm{Cr}^+\) goes from 3d\(^{5}\) to 3d\(^{4}\)- \(\mathrm{Mn}^+\) goes from 3d\(^{5}\) to 3d\(^{4}\)- \(\mathrm{Fe}^+\) goes from 3d\(^{6}\) to 3d\(^{5}\)Only \(\mathrm{Fe}^+\) will achieve a half-filled 3d orbital, a more stable configuration, when removing the second electron.

Step 5: Determine the Element with Highest Second Ionization Enthalpy

Since removing the second electron from \(\mathrm{Fe}^+\) results in a half-filled, stable 3d\(^{5}\) configuration, \(\mathrm{Fe}\) is expected to have the highest second ionization enthalpy among \(\mathrm{V}, \mathrm{Cr}, \mathrm{Mn},\) and \(\mathrm{Fe}\).

Key Concepts

Electron Configuration

Understanding electron configuration is crucial in predicting the chemical behavior of elements. Each element's electron configuration describes the distribution of electrons in an atom's orbitals. For instance, the elements vanadium (V), chromium (Cr), manganese (Mn), and iron (Fe) possess electron configurations as follows:

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

These configurations reflect the number of electrons in the 3d and 4s orbitals, where electrons fill the lower energy 4s orbital first, followed by the 3d orbital. This sequence can help in predicting which elements will achieve stable configurations after losing electrons.

Transition Metals

Transition metals are elements found in the d-block of the periodic table and are known for their complex electron configurations. They are characterized by having an incomplete d-subshell in one or more oxidation states. This allows transition metals to form various oxidation states and contributes to their unique properties such as colored compounds and magnetic behavior.
The transition metals considered in this context, V through Fe, display diverse properties based on their electron configurations. Their ability to lose electrons and form positive ions is essential in understanding their chemistry. The transition metals are quite versatile, which is evident in their variable oxidation states that are pivotal in many biological processes and industrial applications. Moreover, the stability of their d-orbital plays a significant role in defining their ionization enthalpies—specifically the second ionization enthalpy, reflecting the energy needed to remove the second electron from the cation. This knowledge aids chemists in explaining reactivity and bonding.

Stability of d-subshells

The stability of d-subshells is an important concept in understanding the ionization enthalpies of transition metals. Full-filled and half-filled d-subshells are considered more stable due to electron repulsion and exchange energy effects.

• When the 3d subshell reaches a half-filled state, as seen in the configuration 3d\(^{5}\), it benefits from a stable configuration.
• This stability arises because it minimizes electron-electron repulsions, while exchange energy—the energy favoring parallel spin electrons—contributes an additional stability factor.

Upon ionization, if removing an electron leads to one of these stable configurations (half-filled or fully filled d-subshell), the atom achieves a lower energy, more stable state. For instance, removing the second electron from Fe\(^{+}\) leaves a half-filled 3d\(^{5}\) configuration, greatly increasing the ion's stability. This rearrangement explains why iron has the highest second ionization enthalpy among V, Cr, Mn, and Fe, as achieving this configuration requires more energy.