Statement I: Fe³⁺ is more stable than Fe²⁺

Statement II: Fe³⁺ ion has more number of unpaired electrons than Fe²⁺

Statement I and Statement II are true and statement II is not correct explanation of statement I

The correct answer is option 2. Statement I and Statement II are true and statement II is not correct explanation of statement I.

Let  us delve into the statements and their explanations regarding the stability of \(Fe^{3+}\) and \(Fe^{2+}\) ions.

Statement I: \(Fe^{3+}\) has a half-filled 3d orbital, which is a more stable configuration than a partially filled 3d orbital.

\(Fe^{3+}\) ion (iron in the +3 oxidation state) has the electron configuration [Ar] \(3d^5\). In the context of electron configurations and stability:

Half-filled and fully filled configurations: Atoms and ions with half-filled or fully filled electron configurations tend to be more stable due to exchange energy and stability principles in atomic and molecular orbitals. The stability arises from the symmetry and lower energy associated with these configurations.

\(3d^5\) configuration: \(Fe^{3+}\) has a \(3d^5\) configuration, which is considered relatively stable because it is a half-filled configuration. Half-filled configurations, like \(3d^5\), have lower energy compared to configurations with fewer or more electrons in the d subshell.

Statement II: \(Fe^{3+}\) ion has more number of unpaired electrons than \(Fe^{2+}\)

The number of unpaired electrons does not directly determine the stability of an atom or ion. In fact, \(Fe^{2+}\) has a lower energy than \(Fe^{3+}\), even though \(Fe^{3+}\) has more unpaired electrons.

Unpaired electrons and stability: While unpaired electrons contribute to magnetic properties and can affect reactivity, they do not solely determine the stability of an atom or ion. Stability is influenced by various factors, including the overall energy of the ion, electron configuration, and ionic radius.

\(Fe^{2+}\) vs. \(Fe^{3+}\) energy comparison: \(Fe^{2+}\) (iron in the +2 oxidation state) has the electron configuration \([Ar] 3d^6\). Despite having fewer unpaired electrons (4 unpaired electrons) compared to \(Fe^{3+}\) (5 unpaired electrons), \(Fe^{2+}\) has a lower energy state. This lower energy state can be attributed to several factors, such as the electronic configuration and the overall stability achieved through the \(+2\) oxidation state for iron.

Ionic Radius and Stability:

\(Fe^{3+}\) vs. \(Fe^{2+}\) ionic radius: Another critical aspect influencing stability is the ionic radius. \(Fe^{3+}\) has a smaller ionic radius compared to \(Fe^{2+}\). This is because \(Fe^{3+}\) has lost one electron, resulting in a stronger electrostatic attraction between the remaining electrons and the nucleus. The smaller ionic radius of \(Fe^{3+}\) makes it less susceptible to attack by other atoms or molecules, contributing to its stability in certain chemical environments.

Conclusion: Both statements I and II are true based on the explanations provided:

Statement I: \(Fe^{3+}\) has a half-filled 3d orbital, which is indeed a more stable configuration.

Statement II:Fe³⁺ ion has more number of unpaired electrons than Fe²⁺.

However, Statement II does not directly explain Statement I. The correct explanation for the stability of \(Fe^{3+}\) lies more in its half-filled 3d orbital configuration and smaller ionic radius rather than the number of unpaired electrons alone.

This comprehensive explanation highlights the factors influencing the stability of \(Fe^{3+}\) and \(Fe^{2+}|) ions, emphasizing electron configuration, energy states, and ionic radii as key determinants.